On The Non Thermal Emission and Acceleration of Electrons in Coma and Other Clusters of Gal
Linear sigma model at finite temperature
2 is the order of this transition, is it first–order with latent heat, or second–order, or maybe a crossover between the A. The potential at one–loop 27 phases? Lattice calculations suggest that when we consider two massless quarks, the transition is second order B. One loop mass correction 27 and the same suggest other approaches based on effective models. If we consider three massless flavours of quarks, C. The Keldysh contour 28 the transition is probably first–order [3, 6]. The aim of this work is to study the chiral phase transition. D. The pion self–energy graphs 28 1. The pion self–energy graph with one thermal pion28 Chiral symmetry breaking is a necessary ingredient for low energy hadron physics, since unbroken chiral symmetry results in massless baryons, without parity doubled 2. The pion
什么是 NDT
什么是 NDT ?NDT 是无损检测的英文(Non-destructive testing)缩写。
NDT 是指对材料或工件实施一种不损害或不影响其未来使用性能或用途的检测手段。
通过使用 NDT,能发现材料或工件内部和表面所存在的缺欠,能测量工件的几何特征和尺寸,能测定材料或工件的内部组成、结构、物理性能和状态等。
NDT 能应用于产品设计、材料选择、加工制造、成品检验、在役检查(维修保养)等多方面,在质量控制与降低成本之间能起最优化作用。
NDT 还有助于保证产品的安全运行和(或)有效使用。
NDT 包含了许多种已可有效应用的方法,最常用的 NDT 方法是:射线照相检测、超声检测、涡流检测、磁粉检测、渗透检测、目视检测、泄漏检测、声发射检测、射线透视检测等。
由于各种 NDT 方法,都各有其适用范围和局限性,因此新的 NDT 方法一直在不断地被开发和应用。
通常,只要符合 NDT 的基本定义,任何一种物理的、化学的或其他可能的技术手段,都可能被开发成一种 NDT 方法。
在我国,无损检测一词最早被称之为探伤或无损探伤,其不同的方法也同样被称之为探伤,如射线探伤、超声波探伤、磁粉探伤、渗透探伤等等。
这一称法或写法广为流传,并一直沿用至今,其使用率并不亚于无损检测一词。
在国外,无损检测一词相对应的英文词,除了该词的前半部分——即 non-destructive 的写法大多相同外,其后半部分的写法就各异了。
如日本习惯写作 inspection,欧洲不少国家过去曾写作 flaw detection、现在则统一使用 testing,美国除了也使用 testing 外,似乎更喜欢写作 examination 和 evaluation。
这些词与前半部分结合后,形成的缩略语则分别是 NDI、NDT 和 NDE,翻译成中文就出现了无损探伤、无损检查(非破坏检查)、无损检验、无损检测、无损评价等不同术语形式和写法。
实际上,这些不同的英文及其相应的中文术语,它们具有的意义相同,都是同义词。
The Non-Thermal Sunyaev-Zel'dovich Effect in Clusters of Galaxies
a r X i v :a s t r o -p h /0211649v 1 29 N o v 2002Astronomy &Astrophysics manuscript no.sznt˙babFebruary 2,2008(DOI:will be inserted by hand later)The Non-Thermal Sunyaev–Zel’dovich Effect in Clusters ofGalaxiesS.Colafrancesco 1,P.Marchegiani 2and E.Palladino 21INAF -Osservatorio Astronomico di Roma via Frascati 33,I-00040Monteporzio,Italy.Email:cola@coma.mporzio.astro.it 2Dipartimento di Fisica,Universit`a di Roma “La Sapienza”,Piazzale A.Moro 2,I-000Roma,Italy Received 21May 2002/Accepted 13August 2002Abstract.In this paper we provide an general derivation of the non-thermal Sunyaev-Zel’dovich (SZ)effect in galaxy clusters which is exact in the Thomson limit to any approximation order in the optical depth τ.The general approach we use allows also to obtain an exact derivation of the thermal SZ effect in a self-consistent framework.Such a general derivation is obtained using the full relativistic formalism and overcoming the limitations of the Kompaneets and of the single scattering approximations.We compare our exact results with those obtained at different approximation orders in τand we give estimates of the precision fit.We verified that the third order approximation yields a quite good description of the spectral distortion induced by the Comptonization of CMB photons in the cluster atmosphere.In our general derivation,we show that the spectral shape of the thermal and non-thermal SZ effect depends not only from the frequency but also from the cluster parameters,like the electron pressure and the optical depth and from the energy spectrum of the electron population.We also show that the spatial distribution of the thermal and non-thermal SZ effect in clusters depends on a combination of the cluster parameters and on the spectral features of the effect.To have a consistent description of the SZ effect in clusters containing non-thermal phenomena,we also evaluate in a consistent way -for the first time -the total SZ effect produced by a combination of thermal and non-thermal electron population residing in the same environment,like is the case in radio-halo clusters.In this context we show that the location of the zero of the total SZ effect increases non-linearly with increasing values of the pressure ratio between the non-thermal and thermal electron populations,and its determination provides a unique way to determine the pressure of the relativistic particles residing in the cluster atmosphere.We discuss,in details,both the spectral and the spatial features of the total (thermal plus non-thermal)SZ effect and we provide specific predictions for a well studied radio-halo cluster like A2163.Our general derivation allows also to discuss the overall SZ effect produced by a combination of different thermal populations residing in the cluster atmosphere.Such a general derivation of the SZ effect allows to consider also the CMB Comptonization induced by several electron populations.In this context,wediscuss how the combined observations of the thermal and non-thermal SZ effect and of the other non-thermalemission features occurring in clusters (radio-halo,hard X-ray and EUV excesses)provide relevant constraints onthe spectrum of the relativistic electron population and,in turn,on the presence and on the origin of non-thermalphenomena in galaxy clusters.We finally discuss how SZ experiments with high sensitivity and wide spectralcoverage,beyond the coming PLANCK satellite,can definitely probe the presence of a non-thermal SZ effect ingalaxy clusters and disentangle this source of bias from the cosmologically relevant thermal SZ effect.Key words.Cosmology:theory –Galaxies:clusters:general –Intergalactic medium –Radiation mechanism:thermal –Radiation mechanism:non-thermal –Cosmic microwave background1.IntroductionCompton scattering of the Cosmic Microwave Background (CMB)radiation by hot Intra Cluster (hereafter IC)elec-trons –the Sunyaev Zel’dovich effect (Zel’dovich and Sunyaev 1969,Sunyaev &Zel’dovich 1972,1980)–is an im-portant process whose spectral imprint on the CMB can be used as a powerful astrophysical and cosmological probe (see Birkinshaw 1999for a review).Such a scattering produces a systematic shift of the CMB photons from the Rayleigh-Jeans (RJ)to the Wien side of the spectrum.2Sergio Colafrancesco et al.:Non-Thermal SZ effect in clustersAn approximate description of the scattering of an isotropic Planckian radiationfield by a non-relativistic Maxwellian electron population can be obtained by means of the solution of the Kompaneets(1957)equation(see, e.g.,Sunyaev&Zel’dovich1980).The resulting change in the spectral intensity,∆I th,due to the scattering of CMB photons by a thermal electron distribution can be written as(k B T0)3∆I th=2x e x+1(e x−1)2m e c2 dℓn e k B T e,(3) where n e and T e are the electron density and temperature of the IC gas,respectively,σT is the Thomson cross section,valid in the limit T e≫T0,k B is the Boltzmann constant and m e c2is the rest mass energy of the electron.The Comptonization parameter is proportional to the integral along the line of sightℓof the kinetic pressure,P th=n e k B T e, of the IC gas.Thus,the previous Eq.(3)can be written asσTy th=Sergio Colafrancesco et al.:Non-Thermal SZ effect in clusters3 Nonetheless,in addition to the thermal IC gas,many galaxy clusters contain a population of relativistic electrons which produce a diffuse radio emission(radio halos and/or relics)via synchrotron radiation in a magnetized ICM(see,e.g.,Feretti2000for a recent observational review).The electrons which are responsible for the radio halo emission must have energies E e∼>a few GeV to radiate at frequenciesν∼>30MHz in order to reproduce the main properties of the observed radio halos(see,e.g.,Blasi&Colafrancesco1999;Colafrancesco&Mele2001,and references therein).A few nearby clusters also show the presence of an EUV/soft X-ray excess(Lieu et al.1999,Kaastra et al.1999, 2002;Bowyer2000)and of an hard X-ray excess(Fusco-Femiano et al.1999-2000;Rephaeli et al.1999;Kaastra et al.1999;Henriksen1999)over the thermal bremsstrahlung radiation.These emission excesses over the thermal X-ray emission may be produced either by Inverse Compton Scattering(hereafter ICS)of CMB photons offan additional population of relativistic electrons or by a combination of thermal(reproducing the EUV excess,Lieu et al.2000) and suprathermal(reproducing the hard X-ray excess by non-thermal bremsstrahlung,Blasi et al.2000,Dogiel2000, Sarazin&Kempner2000)populations of distinct origins.However,since the inefficient non-thermal bremsstrahlung mechanism would require a large energy input and thus imply an excessive heating of the IC gas-which is not observed -a more complex electron population is required tofit both the radio halo and the EUV/hard X-ray spectra of galaxy clusters(Petrosian2001).The high-energy part(E∼>1GeV)of such spectrum contains non-thermal electrons and produce synchrotron radio emission which canfit the observed radio-halo features:this is the best studied region of the non-thermal spectrum in galaxy clusters.Indeed,in many of the clusters in which the SZ effect has been detected there is also evidence for radio halo sources(see Colafrancesco2002).So it is of interest to assess whether the detected SZ effect is,in fact,mainly produced by the thermal electron population or there is a relevant contribution from other non-thermal electron populations.We will show specifically in this paper that each one of the electron populations which reside in the cluster atmosphere produces a distinct SZ effect with peculiar spectral and spatial features.The description of the non-thermal SZ effect produced by a single electron population with a non-thermal spectrum has been attempted by various authors(McKinnon et al.1991;Birkinshaw1999;Ensslin&Kaiser2000;Blasi et al. 2000).Several limits to the non-thermal SZ effect are available in the literature(see,e.g.,Birkinshaw1999for a review) from observations of galaxy clusters which contain powerful radio halo sources(such as A2163)or radio galaxies(such as A426),but only a few detailed analysis of the results(in terms of putting limits to the non-thermal SZ effect)have been possible so far.Only a single devoted search for the SZ effect expected from a relativistic population of electrons in the lobes of bright radio galaxies has been attempted to date(McKinnon et al.1991).No signals were seen and a detailed spectralfit of the data to separate residual synchrotron and SZ effect signals was not done,so that the limits on the SZ effect do not strongly constrain the electron populations in the radio lobes.Also the problem of detecting the non-thermal SZ effect in radio-halo clusters is likely to be severe because of the associated synchrotron radio emission. In fact,at low radio frequencies,such a synchrotron emission could easily dominate over the small negative signal produced by the SZ effect.At higher frequencies there is in principle more chance to detect the non-thermal SZ effect, but even here there are likely to be difficulties in separating the SZ effect from theflat-spectrum component of the synchrotron emission(Birkinshaw1999).From the theoretical point of view,preliminary calculations(Birkinshaw1999,Ensslin&Kaiser2000,Blasi etal.2000)of the non-thermal SZ effect have been carried out in the diffusion approximation(τ≪1),in the limit of single scattering and for a single non-thermal population of electrons.Specifically,Ensslin&Kaiser(2000)and Blasi et al.(2000)considered the SZ effect produced,under the previous approximations,by a supra-thermal tail of the Maxwellian electron distribution claimed to exist in the Coma cluster and concluded that the SZ effect,even though of small amplitude,could be measurable in the sub-mm region by the next coming PLANCK experiment. However,Petrosian(2001)showed that the suprathermal electron distribution faces with several crucial problems, the main being the large heating that such electrons would induce through Coulomb collisions in the ICM.The large energy input of the suprathermal distribution in the ICM of Coma would heat the IC gas up to unreasonably high temperatures,k B T e∼1016K,which are not observed.In addition,Colafrancesco(2002)noticed that dust obscuration does not allow any detection of the SZ signal from Coma at frequencies∼>600GHz.Matters are significantly more complicated if the full relativistic formalism is used.However,this is necessary,sincemany galaxy clusters show extended radio halos and the electrons which produce the diffuse synchrotron radio emission are certainly highly relativistic so that the use of the Kompaneets approximation is invalid.Moreover,the presence of thermal and non-thermal electrons in the same location of the ICM renders the single scattering approximation and the single population approach unreasonable,so that the treatment of multiple scattering among different electronic populations coexisting in the same cluster atmosphere is necessary to describe correctly the overall SZ effect.Here we derive the spectral and spatial features of the SZ effect using an exact derivation of the spectral distortion induced by a combination of a thermal and a non-thermal population of electrons which are present at the same time in the tely,we also consider the case of the combination of several non-thermal and thermal populations. The plan of the paper is the following:in Sect.2we will provide a general derivation of the SZ effect in an exact formalism within the framework of our approach,i.e.,considering the fully relativistic approach outlined in Birkinshaw4Sergio Colafrancesco et al.:Non-Thermal SZ effect in clusters(1999)and the effect induced by multiple scattering.We work here in the Thomson limit hν≪m e c2.Within such framework,we derive the exact SZ effect for a single electron population both in the thermal and non-thermal cases. In Sect.3we derive the SZ effect produced by a single population of non-thermal electrons providing both exact and approximate(up to any order inτ)expressions for the non-thermal SZ effect.In Sect.4we derive the total SZ effect produced by a combination of two populations:a distribution of thermal electrons-like that responsible for the X-ray emission of galaxy clusters-and a non-thermal electron distribution-like the one responsible for the radio halo emission which is present in many galaxy clusters.Our general approach allows to derive the expression for the SZ effect produced by the combination of any electronic population.So,in Sect.5we consider also the SZ effect generated by the combination of two different thermal populations.In Sect.6we discuss the spatial features associated to the presence of a non-thermal SZ effect superposed to the thermal SZ effect.In Sect.7we derive limits on the presence and amplitude of the non-thermal SZ effect discussing specifically the cases of a few clusters in which there is evidence for the presence of non-thermal,high-energy electrons.We show how the possible detection of a non-thermal SZ effect can set relevant constraints on the relative electron population.We summarize our results and discuss our conclusions in thefinal Sect.8.We use H0=50km s−1Mpc−1andΩ0=1throughout the paper unless otherwise specified. 2.The SZ effect for galaxy clusters:a generalized approachIn this section we derive a generalized expression for the SZ effect which is valid in the Thomson limit for a generic electron population in the relativistic limit and includes also the effects of multiple scattering.First we consider an expansion in series for the distorted spectrum I(x)in terms of the optical depth,τ,of the electron population.Then, we consider an exact derivation of the spectral distortion using the Fourier Transform method already outlined in Birkinshaw(1999).An electron with momentum p=βγ,withβ=v/c andγ=E e/m e c2increases the frequencyνof a scatteredCMB photon on average by the factor t≡ν′/ν=43,whereν′andνare the photon frequencies after and beforethe scattering,respectively.Thus,in the Compton scattering against relativistic electrons(γ≫1)a CMB photon is effectively removed from the CMB spectrum and is found at much higher frequencies.We work here in the Thomson limit,(in the electron’s rest frameγhν≪m e c2),which is valid for the interesting range of frequencies at which SZ observations are feasible.The redistribution function of the CMB photons scattered once by the IC electrons writes in the relativistic limit as, P1(s)= ∞0dpf e(p)P s(s;p),(5)where f e(p)is the electron momentum distribution and P s(s;p)is the redistribution function for a mono-energetic electron distribution,with s≡ln(t).An analytical expression for the redistribution function of CMB photons which suffer a single scattering,P s(s;p),has been given by Ensslin&Kaiser(2000).The expression for such a redistribution function has been also given analytically by Fargion et al.(1997)and by Sazonov&Sunyaev(2000).Once the function P1(s)is known,it is possible to evaluate the probability that a frequency change s is produced by a number n of repeated,multiple scattering.This is given by the repeated convolutionP n(s)= +∞−∞ds1...ds n−1P1(s1)...P1(s n−1)P1(s−s1−...−s n−1)≡P1(s)⊗...⊗P1(s)n times(6)(see Birkinshaw1999),where the symbol⊗indicates each convolution product.As a result,the location of the maximum of the function P n(s)moves towards higher values of s for higher values of n and the distribution P n(s) widens a-symmetrically towards high values of s giving thus higher probabilities to have large frequency shifts.The resulting total redistribution function P(s)can be written as the sum of all the functions P n(s),each one weighted by the probability that a CMB photon can suffer n scatterings,which is assumed to be Poissonian with expected valueτ:P(s)=+∞n=0e−ττn2τ2P2(s)+...=e−τ δ(s)+τP1(s)+1Sergio Colafrancesco et al.:Non-Thermal SZ effect in clusters5 whereI0(x)=2(k B T0)3e x−1(9)is the incident CMB spectrum in terms of the a-dimensional frequency x.In the following we will derive the expression for the distorted spectrum usingfirst an expansion in series ofτand then the exact formulas obtained with the Fourier Transform(FT)method.2.1.High orderτ-expansionIn the calculation of the SZ effect in galaxy clusters it is usual to use the expression of P(s)which is derived in the single scattering approximation and in the diffusion limit,τ≪1.In these limits,the distorted spectrum writes,in our formalism,as:I(x)=J0(x)+τ J1(x)−J0(x) ,(10) whereJ0(x)= +∞−∞I0(xe−s)P0(s)ds= +∞−∞I0(xe−s)δ(s)ds=I0(x),(11) J1(x)= +∞−∞I0(xe−s)P1(s)ds.(12)To evaluate the SZ distorted spectrum I(x)up to higher order inτ,we make use of the general expression of the series expansion of the function P(s)P(s)=+∞n=0a n(s)τn,(13)which can be written,using Eq.(7),asP(s)=+∞k=0(−τ)k k′!P k′(s).(14)The general n-th order term is obtained by selecting the terms in the double summation which contain the optical depthτup to the n-th power.These terms are obtained for k′=n−k,and provide the following expression for the series expansion coefficients:a n(s)=nk=0(−1)k n!n k=0 n k (−1)k P n−k(s).(15)Inserting the coefficients a n(s)given in Eq.(15)in Eq.(13)and this last one in Eq.(8),the resulting spectral distortion due to the SZ effect can be written as:I(x)=+∞n=0b n(x)τn,(16)where the coefficients b n(x)are given by b n(x)=16Sergio Colafrancesco et al.:Non-Thermal SZ effect in clusters2.2.Exact derivation of the SZ effectTheredistribution function P (s )can also be obtained in an exact form considering all the terms of the series expansion in Eq.(14).In fact,since the Fourier transform (hereafter FT)of a convolution product of two functions is equal to the product of the Fourier transforms of the two functions,the FT of P (s )writes as˜P(k )=e −τ 1+τ˜P 1(k )+12π +∞−∞˜P (k )e iks dk (21)which is obtained as the anti Fourier transform of ˜P(k )given in Eq.(19).To compare the exact calculations of the SZ spectral distortion with those obtained in the non-relativistic limit [see eqs.(1-2)as for the thermal case],it is useful to write the distorted spectrum in the form∆I (x )=2(k B T 0)3I 0 1e x −1=∆i (x )2(k B T 0)3.The Comptonization parameter y is defined,in our general approach,in terms of the pressureP of the considered electron population:y =σT 1+p 2)with η=m e c 2/k B T e ,one writes the pressure asP th =n e k B T e(25)and it is easy from Eq.(24)to re-obtain the Compton parameter in Eq.(3)asy th =σTm e c 2(26)(we consider here,for simplicity,an isothermal cluster).The relativistically correct expression of the function ˜g (x )for a thermal population of electrons writes,at first order in τ,as:˜g (x )=∆iτk B T ek B T e [j 1−j 0],(27)where j i ≡J i(hc )2k B T e (j 1−j 0)+16τ2(j 3−3j 2+3j 1−j 0) .(28)Notice that while the expression derived for ˜g (x )at first order approximation in τis independent of τ,the expression for ˜g (x )at higher order approximation in τdepends directly on τ.This is even more the case for the exact expressionSergio Colafrancesco et al.:Non-Thermal SZ effect in clusters 7of ˜g (x )given in the following.In fact,using the exact form of the function P (s )given in Eq.(22),it is possible to write the exact form of the function ˜g (x )as:˜g (x )=m e c 2τ +∞−∞i 0(xe −s )P (s )ds −i 0(x ) .(29)The expression of ˜g (x )approximated at first order in τas given byEq.(27)is the one to compare directly with the expression of g (x )obtained from the Kompaneets (1957)equation,since both are evaluated under the assumption of single scattering suffered by a CMB photon against the IC electrons.Fig.1shows how the function ˜g (x )tends to g (x )for lower and lower IC gas temperatures T e .This confirms that the distorted spectrum obtained from the Kompaneets equation is the non-relativistic limit of the exact spectrum.Notice that the function ˜g (x )given in Eq.(29)is the spectral shape of the SZ effect obtained in the exact calculation while the function g (x )refers to the 1st order approximated case of a single,thermal,non-relativistic population of electrons.Fig.1.The function g (x )(solid line)is compared with the function ˜g (x )for thermal electron populations with k B T e =10(dot-dashed),5(dashes),3(long dashes)and 1(dotted)keV,respectively.It is worth to notice that while in the non-relativistic case it is possible to separate the spectral dependence of the effect [which is contained in the function g (x )]from the dependence on the cluster parameters [which are contained in Compton parameter y th ,see eqs.(1-3)],this is no longer valid in the relativistic case in which the function J 1depends itself also on the cluster parameters.Specifically,for a thermal electron distribution,J 1depends non-linearly from the electron temperature T e through the function P 1(s ).This means that,even at first order in τ,the spectral shape ˜g (x )of the SZ effect depends on the cluster parameters,and mainly from the electron pressure P th .To evaluate the errors done by using the non-relativistic expression g (x )instead of the relativistic,correct function ˜g (x )given in Eq.(29)we calculate the fractional error ε=|[g (x )−˜g (x )]/˜g (x )|for thermal populations with k B T e =10,5,3,2and 1keV and for three representative frequencies (see Table 1).The fractional errors in Table 1tend to decrease systematically at each frequency with decreasing temperature.Note,however,that the error found in the high frequency region,x =15,is much higher than the errors found at lower frequencies and produces uncertainty levels of ∼>50%for T e ∼>5keV.This indicates that the high frequency region of the SZ effect is more affected by the relativistic corrections and by multiple scattering effects.In Table 2we show the fractional error εdone when considering the exact calculation of the thermal SZ effect and those at first,second and third order approximations in τfor two values of the optical depth,τ=10−2and τ=10−3,as reported in the Table caption.Even for the highest cluster temperatures here considered,k B T e ∼20keV,the difference between the exact and approximated calculations is ∼<0.25%at the minimum of the SZ effect (x ∼2.3)and is ∼<2.23%in the high-frequency tail (x ∼15),the two frequency ranges where the largest deviations are expected and could be measurable,in principle.For high-temperature clusters,the third-order approximated calculations of the SZ effect ensures a precision ∼<2%at any interesting frequency.8Sergio Colafrancesco et al.:Non-Thermal SZ effect in clustersk B T e=5keV k B T e=2keVx=2.33.681.5714.814.331.40x=1545.9923.87F irst order T hird orderτ=10−2x=2.30.220.120.27x=151.71k B T e=20keV0.240.23x=6.50.230.230.18τ=10−2x=2.30.020.70.02x=150.21k B T e=10keV0.010.01x=6.50.020.310.25Table2.The fractional errorεdone considering thefirst,second and third order approximation inτcompared with the exact calculation of the thermal SZ effect is reported for three interesting values of the frequency x.The assumed values of k B T e and τare shown in thefirst column of the Table.The values ofεare given in units of10−2.Using the general,exact relativistic approach discussed in this section,we evaluate the frequency location of the zero of the thermal SZ effect,x0,for different cluster temperatures in the range2−20keV.The frequency location of x0depends on the IC gas temperature(or more generally on the IC gas pressure)and in Fig.2we compare the temperature dependence of x0evaluated atfirst order inτ(which actually does not depend onτ)with that evaluated in the exact approach for valuesτ=10−3andτ=10−2.The location of the null of the SZ effect increases by ∼4.4%for k B T e up to∼20keV.Assuming a quadraticfit x0≈a+bθe+cθ2e,whereθe=k B T e/m e c2,we calculate the coefficients a,b and c whichfit the temperature dependence of x0.These are given in Table3.In particular thebExactτ=0.0014.60593.8262−5.4895F irst order4.4304Sergio Colafrancesco et al.:Non-Thermal SZ effect in clusters9Fig.2.The location of x0for a thermal electron population is shown as a function of k B T e.The exact calculation forτ=10−2 (solid line)and forτ=10−3(dashed line)are shown together with the approximated calculation tofirst order inτ(dotted line).while forτ=0.001one getsx0=3.830+4.453θe−3.128θ2e.(31) The remaining differences with our coefficients given in Table3are due to the different T e andτranges used for the quadraticfit.3.The SZ effect generated from a non-thermal electron populationUsing the same general analytical approach derived in Sect.2above we derive here the exact spectral features of the SZ effect produced by a single non-thermal population of electrons.Such an exact derivation has been not done so far. For such a population we consider here two different phenomenological spectra:i)a single power-law energy spectrum, n rel=n0E−α,like that which is able tofit the radio-halo spectra of many clusters,and ii)a double power-law spectrum which is able tofit both the radio halo spectrum and the EUV and hard X-ray excess spectra observed in some nearby clusters(see Petrosian2001).Our formalism is,nonetheless,so general that it can be applied to any electron distribution so far considered tofit both the observed radio-halo spectra and those of the EUV/Hard X-ray excesses(see,e.g.,Sarazin1999,Blasi&Colafrancesco1999,Colafrancesco&Mele2001,Petrosian2001).The single power-law electron population is described by the momentum spectrumf e,rel(p;p1,p2,α)=A(p1,p2,α)p−α;p1≤p≤p2(32) where the normalization term A(p1,p2,α)is given by:(α−1)A(p1,p2,α)=10Sergio Colafrancesco et al.:Non-Thermal SZ effect in clustersthe IC gas produced by Coulomb collisions of the relativistic electrons becomes larger than the bremsstrahlung cooling rate of the IC gas (see,e.g.,Petrosian 2001).This would produce unreasonably and unacceptably large heating of the IC gas.For this reason,we consider also a double power-law electron spectrum which has a flatter slope below a critical value p cr :f e,rel (p ;p 1,p 2,p cr ,α1,α2)=K (p 1,p 2,p cr ,α1,α2) p −α1p 1<p <p cr p −α1+α2crp −α2p cr <p <p 2(34)with a normalization factor given by:K (p 1,p 2,p cr ,α1,α2)= p 1−α11−p 1−α1crα2−1 −1.(35)If p cr ∼400,the electron distribution of Eq.(34)withα1∼0.5at p ∼<p cr can be extended down to very low energies without violating any constraint set by the IC gas heating.Hence,we assume here the following parameter values:α1=0.5,α2=2.5,p cr =400e p 2→∞.We again consider p 1as a free parameter.A crucial quantity in the calculation of the non-thermal SZ effect is given by the number density of relativistic electrons,n e,rel .The quantity n e,rel in galaxy clusters can be estimated from the radio halo spectrum intensity,but this estimate depends on the assumed value of the IC magnetic field and on the model for the evolution of the radio-halo spectrum (see,e.g.Sarazin 1999for time-dependent models and Blasi &Colafrancesco 1999,Colafrancesco &Mele 2001for stationary models).For the sake of illustration,the radio halo flux J νfor a power-law spectrum is,in fact,given by J ν∝n e,relB αr −1ν−αr ,where αr is the radio halo spectral slope.Because of the large intrinsic uncertainties existing in the density of the relativistic electrons which produce the cluster non-thermal phenomena,a value n e,rel =10−6cm −3for p 1=100has been assumed here.Our results on the amplitude of the non-thermal SZ effect can be easily rescaled to different values of n e,rel :in fact,decreasing (increasing)n e,rel will produce smaller (larger)amplitudes of the SZ effect,as can be seen from eqs.(22,24,28,29).The density n e,rel increases for decreasing values of p 1.In fact,multiplying the electron distribution in Eq.(32)by the quantity n e,rel (p 1)one obtainsN e (p ;p 1)≡n e,rel (p 1)A (p 1)p −α(36)where the function A (p 1)is given by Eq.(33).Thus,the electron density scales asn e,rel (p 1)=n e,rel (˜p 1)A (˜p 1)3pv (p )m e c =n e m e c 2(α−1)1+p 2 α−22 p 1p 2(38)(see,e.g.,Ensslin &Kaiser 2000),where B x is the incomplete Beta functionB x (a,b )= x0t a −1(1−t )b −1dt(39)(see,e.g.,Abramowitz &Stegun 1965).The optical depth of the non-thermal electron population is given byτrel (p 1)=2·10−6A (˜p 1)10−6cm −3ℓK (p 1).(41)。
Hubble Fellow
An RXTE study of M87and the core of the Virgo clusterChristopher S.Reynolds,Sebastian Heinz and Andrew C.Fabian ReceivedABSTRACTWe present hard X-ray observations of the nearby radio galaxy M87and the core of the Virgo cluster using the Rossi X-ray Timing Explorer.These are thefirst hard X-ray observations of M87not affected by contamination from the nearby Seyfert2galaxy NGC4388.Thermal emission from Virgo’s intracluster medium is clearly detected and has a spectrum that is well described by athermal plasma with approximately25%cosmic abundances.No non-thermal(power-law)emission from M87is detected in the hard X-ray band,withfluctuations in the Cosmic X-ray Background being the limiting bining with ROSAT data,we infer that the X-ray spectrum of the M87core and jet must be steep(and),and we discuss the implications of this result.In particular,these results are consistent with M87being a mis-aligned BL-Lac object.1.IntroductionThe nearest giant elliptical galaxy,M87(NGC4486),holds a central place in the study of low-luminosity radio galaxies and extragalactic radio jets.This galaxy,situated at the center of the Virgo cluster of galaxies,is associated with the Faranoff-Riley class I radio source Virgo-A and displays the most prominent extragalactic radio jet in the northern sky.It was thefirst extragalactic jet to be discovered(Curtis1918)and has since been subjected to intense observational study at all available wavelengths(see Biretta1993for a review).The close proximity of this source, about16Mpc(e.g.,Tonry1991),makes it a crucial laboratory for testing our understanding of both extragalactic jets and the central engine structure of radio-loud AGN.In the soft X-ray band,imaging with the high-resolution imagers(HRIs)on both the Einstein and ROSAT satellites have resolved emission from the core of M87and knots A,B and D of its optical jet(Schreier,Gorenstein &Feigelson1982;Biretta,Stern&Harris1991;hereafter BSH91).The mechanisms underlying any of these emission components is unknown.Suggestions for the jet emission mechanism include synchrotron emission from ultra-relativistic()electrons in the jet plasma,inverse Compton scattering of infra-red/optical photons by a population of electrons in the jet plasma,and thermal bremsstrahlung from shock heated gas surrounding the jet.The observed core emissions could represent the inner jet with one of the above mechanisms producing the X-rays.On the other hand,emission from an accretion disk corona(as in the Seyfert case)or a hot accretion disk (such as an Advection Dominated Accretion Flow;Reynolds et al.1996)might also be important for understanding the core emissions.For years there was a mystery surrounding the hard X-ray emission from M87and the Virgo cluster.Whereas the centroid of the low-energy emission lies on M87,Davison(1978)used Ariel-V data to show that the higher-energy emissions possessed a different centroid(displaced to the north-west by).This puzzle was resolved by the coded-mask imaging from Spacelab-2which found that the high-energy emissions(or greater)of the Virgo cluster are dominated by the Seyfert2galaxy NGC4388(Hanson et al.1990).NGC4388is displaced fromM87by just over a degree to the north-west.An unambiguous measurement of the hard X-rayflux,spectrum and variability properties of M87has proven difficult due to the presence of this confusing source.Takano&Koyama (1991)analyzed Ginga scanning data and determined a photon index of and a10–20keVflux of,corresponding to a2–10keVflux of(assuming a simple extrapolation of the10–20keV powerlaw to lower energies).Hanson et al.(1990)report upper limits that are5times weaker.Takano&Koyama(1991)take this as evidence for variability.With the exception of the EXOSAT ME which suffered from severe background subtraction issues at highenergies,the Rossi X-ray Timing Explorer(RXTE)is thefirst hard X-ray observatory with a sufficiently smallfield of view to avoid contamination by NGC4388.In this letter we report four RXTE observations of M87.The AGN/jet is not detected above the thermal emission of the Virgo cluster,and upper limits on itsflux are given.We include the effect of unknownfluctuations in the Cosmic X-ray Background(CXB)when deriving our limits on the non-thermal emission and these,indeed,turn out to be the limiting factor for these data.Astrophysical implications of this non-detection are discussed in Section4.2.Observations and basic data reductionWe observed M87with RXTE four times.The dates(and good on-source exposure times)were30-Dec-1997to 2-Jan-1998(42600s),9-Jan-1998to12-Jan-1998(43500s),19-Jan-1998to22-Jan-1998(35500s),and30-Jan-1998 to3-Feb-1998(44900s).The motivation of the project was to search for the hard X-rays from M87and its jet,and study their spectrum and variability.RXTE is a hard X-ray observatory possessing two pointed instruments,the Proportional Counter Array(PCA) and the High Energy X-ray Timing Experiment(HEXTE),as well as an all-sky monitor(ASM).In this work,we use data from the PCA and HEXTE.The PCA consists offive nearly identical co-aligned Xenon proportional counter units(PCUs)with a total effective area of about6500cm and is sensitive in the energy range from2keV to keV(Jahoda et al.1996). Data taken in S TANDARD-2mode were extracted into spectra and lightcurves using F TOOLS V4.1supplemented with the RXTE patch(A.Smale,private communication).For spectralfitting,response matrices were generated using the FTOOLS routine PCARMF V3.3(corrected for the1998-Aug-29bug in which PCARMF failed to account for temporal variations of the response matrix).To take into account the remaining uncertainties of the matrix we added1%systematic errors to our data.This value was determined from the deviations from a pure power-law in afit to the Crab Nebula and pulsar spectrum.Background subtraction was performed using the latest background models(released in June1998as part of the RXTE patch to FTOOLS V4.1).To increase signal-to-noise,only data from the top layer of the PCUs are considered here.We limit our consideration to the energy range4–15keV—the lower bound is determined by the lower limit of the well calibrated energies,whereas the upper bound is the energy at which the data become background dominated.The HEXTE consists of two clusters of four NaI/CsI-phoswich scintillation counters,sensitive from15to 250keV(Rothschild et al.1998).Background subtraction is done by source-background rocking of the two clusters. No signal from M87was detected in HEXTE for either the individual observations or the co-added data of all of ourdatasets.However,the limits set by these non-detections are uninteresting compared with the PCA limits that we shall address below,and hence we shall not discuss HEXTE data any further.The total background subtracted PCA count rate was for all5PCUs,with no evidence for variability either between the four observations or within individual observations.In the absence of any temporal structure,we focus on the spectral aspects.We have extracted4PCA spectra,one for each individual observation, and rebinned to at least20photons per energy bin.This is a requirement for the analysis of the following section to be appropriate.Spectralfitting was then performed using the XSPEC V10.0package.3.Spectral resultsIn this section,the4–15,keV spectra resulting from the four observations are analyzed individually in order to assess spectral variability.Since we fail to detect spectral variability,we alsofit the combined spectrum jointly.We expect each spectrum to be dominated by thermal plasma emission from the ICM of the Virgo cluster.Non-thermal emission from the AGN or jet,if present,would be revealed as a hard tail above and beyond the thermal emission.For these data,unknownfluctuations in the CXB are the limiting factor in our ability to study the non-thermal emission from M87.The spectralfitting presented in section3.1(and in Table1)incorporates this uncertainty by including suchfluctuations as an extra model component.In detail,we include a power-law component with photon index which is allowed to vary in normalization(measured at1keV)between(i.e.,the1-fluctuations of the CXB estimated by scaling the Ginga results of Butcher et al.[1997]to account for the instrumental responses,effective areas andfields of view).3.1.The thermal plasma and limits on a power-lawInitially,these spectra werefitted with a single temperature thermal plasma model(Mewe,Gronenschild,&van den Oord1985;Kaastra1992)modified by Galactic absorption()and redshifted appropriately for the Virgo/M87system().The resultingfits are acceptable(for25degrees of freedom)and are shown in Table1.As can be seen from Table1,all spectra are adequately described by a plasma with an abundance of.Extrapolating thefits in the2–4keV range,the total inferred2–10keVflux is ,although there may well be a cooler cluster component contributing to the cluster X-ray emission below4keV(e.g.Lea et al.1982;Matsumoto et al.1996).The corresponding2–10keV luminosity is .The results of the thermal plasmafit to all four datasets simultaneously(i.e.,the combinedfit)are shown in Fig1.A‘line-like’feature can be seen at.This feature is seen in all PCU detectors individually and in each observing period.An additional narrow Gaussian line with energy,slightly less than the cold ironfluorescent line energy of iron,and equivalent width describes this feature well and produces a large improvement in the goodness offit().There are several reasons for suspecting that this line is not real.Firstly,one must be immediately suspicious since this is a weak line-feature embedded in the wings of a much stronger line(i.e.,the ionized emission line from the thermal cluster gas).Secondly,such a line is not seen in ASCA data of the Virgo cluster(an examination of archival ASCA data gives an upper limit of on the equivalent width of a line at these energies).Thirdly,there is no astrophysical precedent for observing such a line from a cluster dominated system.While we cannotfirmly reject the hypothesis that this line is real,we suspect that it is due to a small mismodelling of the ionized emission lines.Furthermore,the presence of this line in the spectrum does not affect the bestfit values or uncertainties of the other spectral parameters.Thus,we shall not discuss this feature any further,and shall not include it in the spectralfitting described below.In order to assess the presence of hard non-thermal emission from the AGN or jet,a power-law component was added to the thermal plasma model.In no case did the addition of the power-law component lead to any significant improvement in the goodness offit.Table1quotes the90per cent limits on the normalization of the power law(at )assuming a photon index of(close to the canonical value for Type-1AGN).3.2.Detailed limits on non-thermal emissionGiven the lack of any spectral variability,we choose to refine our limits on the non-thermal emission using the combined spectrum(i.e.,summing the spectra from our individual observations).Here,we compute confidence contours on the-plane using a more rigorous treatment of the effect of CXBfluctuations on our spectral fitting.Since we know the probability distribution of the CXBfluctuations(Butcher et al.1997),we can integrate over possiblefluctuations and obtain‘averaged’confidence contours.We define a likelihood function given a particular CXBfluctuation,Fig.1.—The bestfitting two-component thermalfit to the combined PCA data.NH+MEKA+BACK(keV)()(@1keV)/dof28.6/2527.4/2527.4/2527.2/25120/109Table1:Spectralfits to RXTE-PCA data in4–15keV range.and are the normalizations of the power-law component and the thermal component,respectively,at1keV.The power-law is assumed to have a photon index of in thesefits.All errors are quoted at the90per cent confidence level for one interesting parameter().1.0 1.2 1.4 1.6 1.82.02.2 2.4Photon Index 0.00000.00100.00200.00300.0040P o w e r -l a w n o r m a l i z a t i o n ROSAT core flux ROSAT knot-A flux ROSAT core+jet Fig.2.—Confidence contours on the -plane.Parameter space to the top left of the plane is inconsistent with these data.From the top to the bottom,the contours mark the 95%,90%and 68%(two contours)confidence levels for two interesting parameters.Also shown (as thick lines)are the lines in parameter space that are consistent with the Jan-1998ROSAT data of Harris,Biretta &Junor (1998),assuming that a single power-law form exists from the ROSAT -band to the RXTE band (modified by Galactic absorption of).integrate the likelihood function over this parameter,(2)Operationally,we compute the surfaces over the -plane with given values ofusing the XSPEC package (as would be done if we were to compute regular confidence contours).Given thesesurfaces,we approximate eqn (2)by a simple sum weighted according to the Gaussian probability function.From ,we can produce confidence contours on the -plane in which the CXB fluctuations have been averaged over.Figure 2shows the resulting 68%,90%,and 95%contours.The resulting upper limit on the hard X-ray power-law from M87assuming is(3)corresponding to an isotropic luminosity of(4)using a distance of 16Mpc.These limits are quoted at the 90per cent confidence level.4.DiscussionOur upper limit on the hard X-ray power-law component of M87are the most stringent to date.They are superior to the upper limits derived from Spacelab-2data[;Hanson et al.1990] and ASCA data[;Reynolds et al.1996].Note that Matsumoto et al.(1996)claim a detection of the M87power-law with using the same ASCA data as Reynolds et al.(1996).However,the complex structure of the thermal ICM,which possesses temperature and abundance gradients as well as a possible multiphase structure,makes the thermal ICM spectrum difficult to model and so renders such conclusions about superposed non-thermal emission open to suspicion.Our limits are also inconsistent with the value of derived from Ginga scanning data(Tanako&Koyama1991).While this may be evidence for variability,it is also possible that scattered flux from NGC4388coupled with the complex thermal ICM influences the subtle analysis of Tanako&Koyama (1991).In summary,we would argue that there has never been an irrefutable detection of a hard X-ray power-law from M87.However,both the Einstein and ROSAT HRIs have imaged variable soft X-ray point sources coincident with the core of M87and knot-A(Schreier,Gorenstein&Feigelson1982;BSH91;Harris,Biretta&Junor1998;hereafter HBJ98).The last ROSAT measurement shown by HBJ98was taken on5-Jan-1998and hence lies within these RXTE observations.Assuming a single(absorbed)power-law form extending from the ROSAT band into the RXTE band, the1998ROSATfluxes can be converted into loci on the-plane,as shown in Fig.2.It can be seen that the ROSAT sources must possess a fairly steep high-energy spectrum(and for the core and jet respectively)in order to avoid detection by RXTE.If the core and jet components have the same hard X-ray spectrum, then the spectral slope must exceed in order for the combined hard X-rays from these two sources to remain undetected.If there is significant intrinsic absorption in this system,even steeper intrinsic spectra are required.It is informative to compare these limits with the photon indices found in various classes of AGN.In a recent ASCA study,Reeves et al.(1997)found that radio-loud quasars possess ASCA band photon indices of(see also studies by Lawson et al.1992,and Williams et al.1992).Our data rule out the possibility that the ROSAT source seen in the core of M87possesses such aflat X-ray spectrum when extrapolated to the RXTE band.However, Tsvetanov et al.(1998)have recently suggested that M87is a misaligned example of a BL-Lac object.These AGN typically possess steep ASCA-band X-ray spectra with for the low-energy peaked BL-Lacs(LBL)and for the high-energy peaked BL-Lacs(HBL;e.g.Kubo et al.1998).The lack of an observed break in the optical-UV spectrum of the jet(Tsvetanov et al.1998),and the steep X-ray spectral index,would suggest that itbelong to the HBL catagory.Thus,our data are entirely consistent with the suggestion that M87is a misaligned HBL.5.ConclusionsWe have presented four RXTE observations of M87spread over the month of Jan-1998and totaling approximately 167ksec of on-source exposure time.Thermal plasma emission from the Virgo cluster ICM is clearly detected in the PCA with a temperature of.The metal abundance of the plasma is inferred to be, although this must be treated as an average abundance given the known abundance gradients in this system (Matsumoto et al.1996).There was no detection in the HEXTE.Once the thermal ICM emission has been modeled,there is no detection of any hard X-ray non-thermal (power-law)emission in the PCA spectrum.Our upper limit on theflux of a power-law component is.Fluctuations in the CXB are the limiting factor in our ability to set upper limits on the non-thermal emission.If the core and jet sources detected by ROSAT possess a power-law spectrum into the RXTE band,the photon indices of this sources must be and respectively.This is entirely consistent with the hypothesis that M87is a misaligned HBL.AcknowledgmentsWe thank Julia Lee,Michael Nowak,Beverly Smith,and J¨o rn Wilms for useful discussions.We also thank Andrew Hamilton for sharing his statistical expertise,and Craig Sarazin for pointing out an error in a previous draft of this manuscript.CSR thanks support from NASA under LTSA grant NAG5-6337.CSR also thanks support from Hubble Fellowship grant HF-01113.01-98A awarded bythe Space Telescope Institute,which is operated by the Association of Universities for Research in Astronomy,Inc.,for NASA under contract NAS5-26555.ACF thanks the Royal Society for support.ReferencesBiretta J.A.,1993,in Astrophysical Jets,p.263,eds.Burgarella D.,Livio M.,O‘Dea C.P.,Cambridge University Press,Cambridge Biretta J.A.,Stern C.P.,Harris D.E.,1991,AJ,101,1632(BSH91)Butcher J.A.et al.,1997,MNRAS,291,437Curtis H.D.,1918,Pub.Lick Obs.,13,31–11–Davison P.J.N.,1978,MNRAS,183,39Ford H.C.et al.1995,ApJ,1994,435,L27Jahoda K.,Swank J.H.,Giles A.B.,Stark M.J.,Strohmayer T.,Zhang W.,Morgan E.H.,1996,in EUV,X-ray,and Gamma-Ray Instrumentation for Astronomy VII,ed.O.H.Siegmund,(Bellingham,WA:SPIE),59Hanson C.G.,Skinner G.K.,Eyles C.J.,Willmore A.P.,1990,MNRAS,242,262Harris D.E.,Biretta J.A.,Junor W.,1998,The M87Ringberg Workshop,eds H.J.Roser&K.Meisenheimer,Spinger (astrop-ph/9804201;HBJ98)Kaastra J.S.,1992,An X-Ray Spectral Code for Optically Thin Plasmas(Internal SRON-Leiden Report,updated version2.0) Kubo H.,Takahashi T.,Madejski G.,Tashiro M.,Makino F.,Inoue S.,Takahara F.,1998,ApJ,504,693Lawson A.J.,Turner M.J.L.,Williams O.R.,Stewart G.C.,Saxton R.D.,1992,MNRAS,259,743Lea S.M.,Mushotzky R.F.,Holt S.S.,1982,ApJ,262,24Matsumoto H.,Koyama K.,Awaki H.,Tomida H.,Tsuru T.,Mushotzky R.F.,Hatsukade I.,1996,PASJ,48,201Mewe R.,Gronenschild E.H.B.M.,van den Oord G.H.J.,1985,A&AS,62,197Reeves J.N.,Turner M.J.L.,Ohasi T.,Kii T.,1997,MNRAS,292,468Reynolds C.S.,Di Matteo T.,Fabian A.C.,Hwang U.,Canizares C.R.,1996,MNRAS,283,L111Rothschild R.E.et al.,1998,ApJ,496,538Schreier E.J.,Gorenstein P.,Feigelson E.D.,1982,ApJ,261,42Takano S.,Koyama K.,1991,PASJ,43,1Tonry J.L.,1991,ApJ,373,L1Tsvetanov Z.I.et al.,1998,ApJ,493,L83Williams O.R.et al.,1992,ApJ,389,157。
通常的化合物结晶是通过降温实现,但这篇钙钛矿的结晶是通过升温实现的,而且速度超快,还是单晶-2015-NC
of Physical Sciences and Engineering, Solar and Photovoltaics Engineering Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia. 2 Department of Chemistry, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. 3 Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK. 4 Materials Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia. 5 Imaging and Characterization Lab, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to O.M.B. (email: osman.bakr@.sa).
NRL_FORMULARY_11
3
Euler-Mascheroni constant1 γ = 0.57722 Gamma Function Γ(x + 1) = xΓ(x): Γ(1/6) Γ(1/5) Γ(1/4) Γ(1/3) Γ(2/5) Γ(1/2) = = = = = = 5.5663 4.5908 3.6256 2.6789 2.2182 √ 1.7725 = π Γ(3/5) Γ(2/3) Γ(3/4) Γ(4/5) Γ(5/6) Γ(1) = = = = = = 1.4892 1.3541 1.2254 1.1642 1.1288 1.0
C
dl · A dl × A f dg = − gdf
C
(35)
S
(d S × ∇) × A = d S · (∇f × ∇g ) =
C
(36)
S
C
DIFFERENTIAL OPERATORS IN CURVILINEAR COORDINATES5 Cylindrical Coordinates Divergence ∇·A= Gradient (∇f )r = Curl (∇ × A)r = ∂Aφ 1 ∂Az − r ∂φ ∂z ∂Ar ∂Az − ∂z ∂r 1 ∂ 1 ∂Ar (rAφ ) − r ∂r r ∂φ ∂f ; ∂r (∇f )φ = 1 ∂f ; r ∂φ (∇f )z = ∂f ∂z 1 ∂Aφ ∂Az 1 ∂ (rAr ) + + r ∂r r ∂φ ∂z
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温度反演经典文章
(This is a sample cover image for this issue.The actual cover is not yet available at this time.)This article appeared in a journal published by Elsevier.The attached copy is furnished to the author for internal non-commercial research and education use,including for instruction at the authors institutionand sharing with colleagues.Other uses,including reproduction and distribution,or selling or licensing copies,or posting to personal,institutional or third partywebsites are prohibited.In most cases authors are permitted to post their version of thearticle(e.g.in Word or Tex form)to their personal website orinstitutional repository.Authors requiring further informationregarding Elsevier’s archiving and manuscript policies areencouraged to visit:/copyrightReviewSatellite-derived land surface temperature:Current status and perspectivesZhao-Liang Li a ,b ,⁎,Bo-Hui Tang a ,Hua Wu a ,Huazhong Ren c ,Guangjian Yan c ,Zhengming Wan d ,Isabel F.Trigo e ,f ,JoséA.Sobrino gaState Key Laboratory of Resources and Environmental Information System,Institute of Geographic Sciences and Natural Resources Research,Beijing 100101,China bLSIIT,UdS,CNRS,Boulevard Sebastien Brant,BP10413,67412Illkirch,France cState Key Laboratory of Remote Sensing Sciences,School of Geography,Beijing Normal University,Beijing 100875,China dERI,University of California,Santa Barbara,CA 93106,USA eInstituto Português do Mar e da Atmosfera,Lisbon,Portugal fInstituto Dom Luiz,University of Lisbon,Portugal gImage Processing Laboratory,University of Valencia,Valencia 46071,Spaina b s t r a c ta r t i c l e i n f o Article history:Received 24May 2012Received in revised form 19October 2012Accepted 11December 2012Available online xxxx Keywords:Land surface temperature Land surface emissivity RetrievalThermal infraredLand surface temperature (LST)is one of the key parameters in the physics of land surface processes from local through global scales.The importance of LST is being increasingly recognized and there is a strong interest in de-veloping methodologies to measure LST from space.However,retrieving LST is still a challenging task since the LST retrieval problem is ill-posed.This paper reviews the current status of selected remote sensing algorithms for estimating LST from thermal infrared (TIR)data.A brief theoretical background of the subject is presented along with a survey of the algorithms employed for obtaining LST from space-based TIR measurements.The discussion focuses on TIR data acquired from polar-orbiting satellites because of their widespread use,global applicability and higher spatial resolution compared to geostationary satellites.The theoretical framework and methodolo-gies used to derive the LST from the data are reviewed followed by the methodologies for validating satellite-derived LST.Directions for future research to improve the accuracy of satellite-derived LST are then suggested.©2012Elsevier Inc.All rights reserved.Contents 1.Introduction ...............................................................152.Basic theoretical background .......................................................152.1.Radiative transfer equation .....................................................162.2.Dif ficulties and problems in the retrieval of LST from space measurements ..............................173.Estimation of LST from space .......................................................183.1.LST retrieval with known LSEs ...................................................183.1.1.Single-channel method ..................................................183.1.2.Multi-channel method ..................................................193.1.3.Multi-angle method ....................................................213.2.LST retrieval with unknown LSEs ..................................................223.2.1.Stepwise retrieval methods ................................................223.2.2.Simultaneous LST and LSE retrieval methods with known atmospheric information ......................233.2.3.Simultaneous retrieval of LST,LSEs,and atmospheric pro files ..........parison and analysis of different methods ............................................264.Validation of satellite derived LST .....................................................294.1.Temperature-based method (T-based)...............................................294.2.Radiance-based method (R-based).................................................294.3.Cross validation method ................................ (30)Remote Sensing of Environment 131(2013)14–37⁎Corresponding author at:LSIIT,UdS,CNRS,Boulevard Sebastien Brant,BP10413,67412Illkirch,France.Tel.:+33368854516.E-mail address:lizl@ (Z.-L.Li).0034-4257/$–see front matter ©2012Elsevier Inc.All rights reserved./10.1016/j.rse.2012.12.008Contents lists available at SciVerse ScienceDirectRemote Sensing of Environmentj o u r n a l h om e p a g e :ww w.e l s e v i e r.c o m /l o c a t e /r s e5.Future development and perspectives (30)5.1.Methodology to simultaneously derive LST,LSE,and atmospheric profiles(atmospheric quantities)from hyperspectral TIR data (30)5.2.Methodology to simultaneously derive LST and LSE from the new generation of geostationary satellites with multispectral andmulti-temporal data (31)5.3.Refinement of LST retrieval algorithms with the consideration of aerosol and cirrus effects (31)5.4.Retrieval of component temperatures in heterogeneous pixels (31)5.5.Methodology for retrieving LST from passive microwave data and for combining LSTs retrieved from TIR and passive microwave data..315.6.Methodology for angular normalization of LST (32)5.7.Methodology for temporal(time)normalization of LST (32)5.8.Concerns on the newly developed Hyperspectral Infrared Imager (32)5.9.Physical meaning of satellite-derived LST and its applications (33)5.10.Validation of satellite-derived LST (33)Acknowledgments (33)References (33)1.IntroductionAs the direct driving force in the exchange of long-wave radiation and turbulent heatfluxes at the surface–atmosphere interface,land sur-face temperature(LST)is one of the most important parameters in the physical processes of surface energy and water balance at local through global scales(Anderson et al.,2008;Brunsell&Gillies,2003;Karnieli et al.,2010;Kustas&Anderson,2009;Zhang et al.,2008).Knowledge of the LST provides information on the temporal and spatial variations of the surface equilibrium state and is of fundamental importance in many applications(Kerr et al.,2000).As such,the LST is widely used in a variety offields including evapotranspiration,climate change,hy-drological cycle,vegetation monitoring,urban climate and environ-mental studies,among others(Arnfield,2003;Bastiaanssen et al., 1998;Hansen et al.,2010;Kalma et al.,2008;Kogan,2001;Su,2002; Voogt&Oke,2003;Weng,2009;Weng et al.,2004)and has been recog-nized as one of the high-priority parameters of the International Geosphere and Biosphere Program(IGBP)(Townshend et al.,1994). Due to the strong heterogeneity of land surface characteristics such as vegetation,topography,and soil(Liu et al.,2006;Neteler,2010),LST changes rapidly in space as well as in time(Prata et al.,1995;Vauclin et al.,1982)and an adequate characterization of LST distribution and its temporal evolution,therefore,requires measurements with detailed spatial and temporal sampling.Given the complexity of surface temper-ature over land,ground measurements cannot practically provide values over wide areas.With the development of remote sensing from space,satellite data offer the only possibility for measuring LST over the entire globe with sufficiently high temporal resolution and with complete spatially averaged rather than point values.Satellite-based thermal infrared(TIR)data is directly linked to the LST through the radiative transfer equation.The retrieval of the LST from remotely sensed TIR data has attracted much attention,and its his-tory dates back to the1970s(McMillin,1975).To better understand the Earth system at the regional scale and to get the evapotranspiration with an accuracy better than10%,LST must be retrieved at an accuracy of1K or better(Kustas&Norman,1996;Moran&Jackson,1991;Wan& Dozier,1996).However,direct estimation of LST from the radiation emitted in the TIR spectral region is difficult to perform with that accuracy,since the radiances measured by the radiometers onboard sat-ellites depend not only on surface parameters(temperature and emis-sivity)but also on atmospheric effects(Li&Becker,1993;Ottlé& Stoll,1993;Prata et al.,1995).Therefore,besides radiometric calibration and cloud screening,the determination of LSTs from space-based TIR measurements requires both emissivity and atmospheric corrections (Li&Becker,1993;Vidal,1991).Many studies have been carried out, and different approaches have been proposed to derive LSTs from satel-lite TIR data,using a variety of methods to deal with the emissivity and atmospheric effects(Becker&Li,1990b;Gillespie et al.,1998; Hook et al.,1992;Jiménez-Muñoz&Sobrino,2003;Kealy&Hook,1993;Kerr et al.,1992;Pozo Vazquez et al.,1997;Price,1983,1984; Qin et al.,2001;Susskind et al.,1984;Tonooka,2001;Wan&Dozier, 1996;Wan&Li,1997).Consequently,there have been quite a large number of publications on LST retrieval algorithms and methods.It is important to present an overview of the state of the art in LST retrieval algorithms and to direct future research into improving the accuracy of satellite-derived LST.Although there have been earlier reviews on LST retrieval from space,presented by Prata et al.(1995)and Dash et al. (2002),since then there have been several new developments in LST re-trieval algorithms and this review is intended to supplement those re-views with latest approaches.The objective of this paper is to review the progress in estimation of LST from TIR data primarily taken using sensors onboard polar-orbit satellites which have been acquiring data since the mid-eighties and to suggest directions for future research on the subject.Section2provides the theoretical basis for retrieving the LST from satellite TIR data and briefly discusses some major difficulties in LST retrieval from space measurements,including:(i)the coupling of the LST,the land surface emissivity(LSE)and the atmosphere;(ii)the physical meaning of satellite-derived LST;and(iii)validation problems related to satellite-derived LST.Section3presents an overview of a variety of methods and algorithms for estimating the LST.For each method or algorithm,the main theoretical basis and assumptions in-volved in the development of the model will be outlined,and the method's advantages,drawbacks and potential will be highlighted. Section4reviews methods of validating satellite-derived LST.Finally, Section5suggests future developments and provides perspectives on retrieving LST from remotely sensed data.2.Basic theoretical backgroundAll objects with temperatures greater than absolute zero emit radia-tion,and the amount of radiation from a black body in thermal equilib-rium at wavelengthλand temperature T is described by Planck's law: BλTðÞ¼C1λ5exp C2λT−1h i;ð1Þwhere Bλ(T)is the spectral radiance(W m−2μm−1sr−1)of a black body at temperature T(K)and wavelengthλ(μm);C1and C2are physical constants(C1=1.191×108Wμm4sr−1m−2,C2=1.439×104μm·K). Because most natural objects are non-black bodies,the emissivityε, which is defined as the ratio between the radiance of an object and that of a black body at the same temperature,must be taken into account. The spectral radiance of a non-black body is given by the spectral emis-sivity multiplied by Planck's law as shown in Eq.(1).Obviously,if the atmosphere exerts no influence on the measured radiance,LST(i.e.T) can be retrieved by making temperature as the subject of Eq.(1)once the emitted radiance and emissivity are known.The wavelengthλmax15Z.-L.Li et al./Remote Sensing of Environment131(2013)14–37of the peak monochromatic radiance at a given temperature (T)is given by Wien's displacement law:T λmax ¼2897:9K μm :ð2ÞAccording to this equation,the wavelength λmax at which maxi-mum emission occurs varies roughly from 11.6μm to 8.8μm if the LST ranges from 250K to 330K with the average temperature of the Earth being approximately 288K.The wavelength region be-tween 8and 13μm coincides within a clear window in the atmo-sphere which is most transparent to TIR radiation.In cases where the temperature of the surface exceeds 330K,the wavelength peak moves to shorter and shorter wavelengths,for example for a wild fire (about 800K),the maximum emission is around 3.6μm in the mid-infrared (MIR)region (3–5μm)which also coincides with a clear window in the atmosphere.2.1.Radiative transfer equationAn infrared sensor onboard a satellite viewing the Earth's surface measures the radiation from the Earth and its atmosphere along the line of ing the radiative transfer equation (RTE)and assum-ing a cloud-free atmosphere under local thermodynamic equilibrium,as illustrated in Fig.1,the channel infrared radiance I i received by a sensor at the top of the atmosphere (TOA)can be written as I i θ;φðÞ¼R i θ;φðÞτi θ;φðÞ|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}Surf ace outgoing radiation term attenuated by the atmosphereþR at i ↑θ;φðÞ|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}Atmospheric emission termþR sl i ↑θ;φðÞ|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}Atmospheric scattering term;ð3Þwith R i being the channel radiance observed in channel i at ground level given byR i θ;φðÞ¼εi θ;φðÞB i T s ðÞ|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}Surf ace emission termþ1−εi θ;φðÞ½ R at i ↓|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Surf ace ref lected downwelling atmospheric emissiontermþ1−εi θ;φðÞ½ R sl i ↓|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}Surf ace ref lected downwelling atmospheric scattering termþρb i θ;φ;θs ;φs ðÞE i cos θs ðÞτi θs ;φs ðÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Surf ace ref lected downwelling solar beam term;ð4Þin which θand φrepresent the zenithal and azimuthal viewing angles.For simplicity,the zenithal and azimuthal viewing angles are ignored in the following expressions.τi is the effective transmittance of the atmosphere in channel i .R i τi is the radiance observed at ground level attenuated by the atmosphere (path ①in Fig.1).R ati ↑is the upward at-mospheric thermal radiance (path ②in Fig.1).R sli ↑is the upward solar diffusion radiance resulting from atmospheric scattering of the solar ra-diance (path ③in Fig.1).εi and T s are the effective surface emissivity and surface temperature in channel i .εi B i (T s )represents the radiance emitted directly by surface (path ④in Fig.1).R ati ↓is the downward atmospheric thermal radiance.R sli ↓is the downward solar diffusion ra-diance.(1-εi )R ati ↓and (1-εi )R sli ↓represent the downward atmospheric thermal radiance and solar diffusion radiance re flected by the surface (paths ⑤and ⑥in Fig.1).ρbi is the bi-directional re flectivity of the sur-face,E i is the solar irradiance at the TOA,θs and φs are the solar zenithal and azimuthal angles.ρbi E i cos(θs )τi (θs ,φs )is the direct solar radiance re flected by the surface (path ⑦in Fig.1).Because the contribution of solar radiation at the TOA is negligible in the 8–14μm window during both day and night and in the 3–5μm window at night,theFig.1.Illustration of radiative transfer equation in infrared regions (see the text for the de finitions of symbols).Here,I i is the radiance measured by channel i at the top of atmo-sphere.Path ①represents the radiance observed at ground level attenuated by the atmosphere.Paths ②and ③represent the upward atmospheric thermal radiance and the up-ward solar diffusion radiance,respectively.Path ④represents the radiance emitted directly by the surface.Paths ⑤and ⑥represent the downward atmospheric thermal radianceand solar diffusion radiance re flected by the surface,respectively.Path ⑦represents the direct solar radiance re flected by the surface.16Z.-L.Li et al./Remote Sensing of Environment 131(2013)14–37solar-related items (paths ③,⑥and ⑦in Fig.1)in Eqs.(3)and (4)can be neglected without loss of accuracy.For convenience and mathematical shorthand,the radiances I i and R i measured at the TOA and at ground level are generally expressed in terms of the brightness temperatures where the emissivity is fixed at 1.0.The TOA and ground level brightness temperatures T i and T gi are de fined respectively by B i T i ðÞ¼I iand B i T gi¼R ið5ÞIt is worth noting that all variables/parameters in Eqs.(3)–(5),ex-cept for the angles (θ,φ,θs and φs ),are channel-effective values.Most satellite sensors measure the outgoing radiation with a finite spectral-bandwidth,and the channel-effective quantities of interest are therefore a weighted average expressed by:X i ¼∫λ2λ1g i λðÞX λd λ∫λ2λ1g iλðÞd λ;ð6Þwhere g i (λ)is the spectral response function in channel i ;λ1and λ2are the lower and upper boundaries of the wavelength in channel i ;and X stands for B (T ),I ,R ,R at ↑,R sl ↑,R at ↓,R sl ↓,E ,ε,τ,or ρb .Eqs.(3)and (4)are actually approximations to the theoretical RTE in which monochromatic quantities are replaced with channel-effective values,but these approximations or simpli fications require several important preconditions:•The integral of a product is assumed to be equal to the product of the integrals.This assumption is true only if the variables are con-stant within the integration limits,which is rarely the case.Fortu-nately,the bandwidth of the channel is generally narrow,and the various spectral quantities X λinvolved in Eq.(6)should not feature rapid variations.Therefore,the use of the weighted averages de-fined by Eq.(6)in Eqs.(3)and (4)is a good approximation to the RTE with monochromatic quantities.•Either the surface is assumed to be Lambertian or the downward at-mospheric and solar diffuse radiation are assumed to be isotropic in the calculation of the downward radiations re flected by the surface (paths ⑤and ⑥in Fig.1).In practice,these conditions are never ful filled.However,because the surface-re flected downward atmo-spheric thermal radiation term is much smaller than the surface thermal emission,and the surface-re flected diffuse solar radiation term is much smaller than the surface-re flected direct solar term,this simpli fication of Eqs.(3)and (4)is reasonable and does not in-troduce signi ficant errors.2.2.Dif ficulties and problems in the retrieval of LST from space measurementsAs seen from Eqs.(3)and (4),estimating the LST from the radi-ance measured at the TOA requires corrections for both atmospheric and emissivity effects.Applying these corrections is not a simple task,and some key dif ficulties and problems involved in the retrieval of the LST must be overcome and resolved.These key dif ficulties and problems are the following:(1)The retrieval of the LST from space is mathematicallyunderdetermined and unsolvable (Hook et al.,1992;Kealy &Hook,1993).The RTE described in Eqs.(3)and (4)shows that,if the radiance is measured in N channels,there will always be N +1unknowns,corresponding to N emissivities in each channel and an unknown LST for N equations,even if quantities other than the emissivities and LST are known a priori.Such an ill-posed problem makes the solution of the RTE sets underdetermined at ground level even if the atmospheric quantities involved in Eqs.(3)and (4)are accurately estimated.To make LSTdeterministic,one or more of the LSEs must be known,or the LST and LSEs have to be simultaneously solved with the aid of some assumptions or constraints on the LSEs (Dash et al.,2002;Gillespie et al.,1996;Hook et al.,1992;Kealy &Hook,1993).(2)Measurements in the TIR region are highly correlated,implying that instrumental noise and errors in the atmospheric corrections exert strong in fluences on the accuracy of the LST retrieval.This correlation represents a problem even if the LST is made solvable either by reducing the number of unknowns or by increasing the number of equations through reasonable assumptions or con-straints on the LSEs (Gillespie et al.,1996;Li et al.,2013).These highly correlated measurements make LST retrieval unsta-ble and have hampered the methodological development of LST retrieval.(3)It is dif ficult to decouple the LST,the LSEs,and the downward at-mospheric radiance in the measured radiances.As seen from Eq.(4),the downward atmospheric radiance and the surface emitted radiance are coupled together through LSEs.The non-unity LSE of a natural surface reduces the surface-emitted radiance while increasing the re flection of the down-ward atmospheric radiance back to the atmosphere,which com-pensates partly for the reduction in the surface-emitted radiance.This process can reduce or increase the total surface-leaving radi-ance depending on the atmospheric and surface conditions.This coupling of the re flected downwelling and surface-emitted radi-ation can be used to retrieve LST with the online/of fline method but requires high spatial resolution data.However in passively observed multispectral TIR data,it is impossible to separate,on a physical basis,the contributions of the LST from the contribu-tions of the LSEs and the atmosphere in the observed radiance.For this reason,determining LST from space requires not only the atmospheric corrections but also the knowledge of the LSEs and vice versa.(4)The atmospheric corrections are dif ficult to implement.The pres-ence of the atmosphere between the surface and the sensors af-fects the radiances measured by a radiometer at the TOA.These radiances result primarily from emission/re flection at the surface modulated by the effects of the attenuation,and emission of the atmosphere.The atmospheric corrections thus consist of correcting the radiance measured by the sensors for the effects of atmospheric attenuation,emission and emission-re flection.Correcting for the atmospheric effects requires accurate knowl-edge of the vertical pro files of atmospheric water vapor and tem-perature both of which are highly variable (Perry &Moran,1994).(5)During the daytime,the re flected solar radiation is dif ficult to re-move in the MIR measurements.As mentioned earlier,the highly correlated TIR measurements make LST retrieval unstable even if the solution of the RTE sets becomes deterministic through some assumptions and constraints on the LSEs.In the MIR since the di-rect solar irradiation re flected by the surface is on the same order of magnitude as the radiance directly emitted by the surface,if the surface albedo is about 0.1,the introduction of the MIR chan-nels in LST retrieval signi ficantly reduces the correlation of the RTE sets and greatly improves the accuracy of the estimated LST (Li et al.,2013).Additionally,MIR channels are less sensitiv-ity to the water vapor in the atmosphere compared with TIR channels,and the LST retrieval from the MIR is only half as sensi-tive to errors in emissivity as that from the TIR (Mushkin et al.,2005).Therefore,LST retrieval with the MIR instead of the TIR sounds more appropriate.However,solar effects are dif ficult to eliminate in the MIR during the daytime because the separation of solar irradiation from the total energy measured in the MIR re-quires not only the accurate atmospheric information but also the knowledge of the bidirectional re flectivity of the surface.This information is typically unknown and affected by several factors (Adams et al.,1989;Mushkin et al.,2005),resulting in17Z.-L.Li et al./Remote Sensing of Environment 131(2013)14–37large uncertainties that can lead to an even larger error on the LST retrieved from MIR measurements.Therefore,while the in-troduction of the MIR channels may benefit the retrieval of the LST in certain cases,it can also introduce even larger uncer-tainties in others.(6)How to physically interpret the results of the LST measurementremains a crucial question.As noted by Prata et al.(1995),the def-inition of the surface temperature may depend strongly on the type of application and the method of measurement.Because the surface temperature T s in Eq.(4)is defined using the radiance emitted by a surface,this temperature is called the radiometric temperature(or the skin temperature)that corresponds to the ra-diation emitted from depths less than the penetration depth of a given wavelength(Becker&Li,1995;Norman&Becker,1995).The penetration depth is usually within a few millimeters in the TIR region(Wan,1999).This radiometric temperature physically differs from other definition of temperatures,such as the thermo-dynamic temperature defined for a medium in thermal equilibri-um and measured by a thermometer.For homogeneous and isothermal surfaces,the radiometric and thermodynamic temper-atures are reported to be equivalent.As the thermodynamic tem-perature is actually hard to measure in reality,even for water,the radiometric temperature is often the only practical measure for the homogeneous and isothermal surface.However,most surfaces are not in equilibrium and for heterogeneous and non-isothermal surfaces,these two temperatures are different.Considering that the spatial resolution of the current onboard sys-tems varies approximately from10−2to10km2,there may be several surface types with different temperatures and emissivities within one pixel,which complicates the physical understanding of the LST values retrieved from space and the relation of the ra-diometric temperature at large scales to other temperatures used in different applications.To date,no consensus has been reached on the definition of the LST for heterogeneous and non-isothermal surfaces,but the definition by Becker and Li (1995),which depends on the distributions of the LST and the LSE within a pixel,is measurable from space and is thus recommended for LST retrieval from space.(7)Validation of LST retrieved from spaceborne measurements atthe scale of the sensor's pixels is also challenging.Validation is problematic due to the difficulty of conducting in situ LST mea-surements,and in obtaining representative LST data at the scale of a single pixel.Generally,temperatures over the land surfaces vary strongly in space and time(Prata et al.,1995),and it is not unusual for the LST to vary by more than10K over just a few centimeters of distance or by more than1K in less than a minute over certain cover types.Appropriately scaling the satellite-derived LSTs to those measured at ground level,especially at large scale is also difficult.The strong spatial heterogeneity and temporal variation of the LST limits ground-based validation to several relatively homogeneous land surfaces,such as lakes,de-serts,and densely vegetated land using direct comparisons of in situ temperature measurements with temperatures retrieved from the satellite data(e.g.Hook et al.,2005,2003,2007).A com-plementary approach is to use sites which are homogenous in terms of emissivity using the radiance based validation approach (Hulley et al.,2009).Sand dunes can be one example of this type of sites which are referred to as pseudo-invariant sites(Hulley et al.,2009).Furthermore,how to perform a representative mea-surement of the LST of a complex heterogeneous surface is alsoa critical question.Scaling methods should be developed to relatethe measurements at different scales and help validate the re-trieved LST(Liu et al.,2006;Wu&Li,2009).Besides the difficulties mentioned above in the retrieval of LST from space,the accuracy of the LST data also depends on the performance of the cloud mask used to isolate clear sky data and on the quality of the TIR data,i.e.,the stability of the spectral response function g i(λ),the SNR and the accuracy of the radiometric calibration.3.Estimation of LST from spaceOver the past several decades,LST estimation from satellite TIR mea-surements has significantly improved.Many algorithms have been pro-posed to treat the characteristics of various sensors onboard different satellites and utilizing different assumptions and approximations for the RTE and LSEs.These algorithms can be roughly grouped into three categories:single-channel methods,multi-channel methods,and multi-angle methods,provided that the LSEs are known a priori.If the LSEs are not known,then the algorithms can be categorized into three types:stepwise retrieval method,simultaneous retrieval of LSEs and LST with known atmospheric information,and simultaneous retrieval with unknown atmospheric information.3.1.LST retrieval with known LSEs3.1.1.Single-channel methodThe single TIR channel method,also called the model emissivity method(Hook et al.,1992),uses the radiance measured by the satellite sensor in a single channel,chosen within an atmospheric window,and corrects the radiance for residual atmospheric attenuation and emission using atmospheric transmittance/radiance code that requires input data on the atmospheric profiles.LST is then retrieved from the radiance measured in this channel by inverting the RTE given in Eqs.(3)and(4), provided that the LSE is well known or estimated in advance(Chédin et al.,1985;Hook et al.,1992;Li et al.,2004a;Mushkin et al.,2005;Ottlé& Vidal-Madjar,1992;Price,1983;Susskind et al.,1984).Accurate deter-mination of the LST using this method requires high-quality atmospher-ic transmittance/radiance code to estimate the atmospheric quantities involved in Eqs.(3)and(4),good knowledge of the channel LSE,an ac-curate atmospheric profile,and a correct consideration of the topo-graphic effects(Sobrino et al.,2004b).Generally,the accuracy of atmospheric transmittance/radiance code is primarily limited by the radiative transfer model(RTM)used in the code and by the uncertainties in atmospheric molecular absorption co-efficients and aerosol absorption/scattering coefficients(Wan,1999). The most popular atmospheric RTMs,such as the series of MODTRAN (Berk et al.,2003)and4A/OP(Chaumat et al.,2009),have been widely used to perform atmospheric corrections and/or to simulate satellite TIR data.A few studies have shown that the accuracy of the different RTMs ranges from0.5%to2%within known atmospheric windows,such as 3.4–4.1μm and8–13μm,leading to uncertainties in the retrieved LST of0.4K to1.5K(Wan,1999).It is worth noting that the incomplete characterizations of atmospheric profiles used in compensation for at-mospheric absorption and path radiance constitute a serious problem even if the RTM itself is completely error-free(Gillespie et al.,2011). Studies have also demonstrated that an error of1%in the LSE can give rise to an error in the LST ranging from0.3K for a hot and humid atmo-sphere to0.7K for a cold and dry atmosphere(Dash et al.,2002).As the single channel is usually chosen around10μm where the LSE for most land surfaces can be known within a few percent,the uncertainty in LSE may lead to an error of1K to2K in LST if the single-channel meth-od is used.However,if the LSE is known at a wavelength within the TIR atmospheric window,then any error will be solely due to incorrect re-moval of the atmospheric contribution.Atmospheric profiles are gener-ally obtained either from ground-based atmospheric radiosoundings, from satellite vertical sounders or from meteorological forecasting models.Due to the high spatial and temporal variability of the atmo-spheric water vapor,the use of ground-based radiosoundings far from the area of interest and/or far from the time of satellite overpass may re-sult in large errors in the LST(Cooper&Asrar,1989).On top of these, radiosoundings reported measurement errors are of the order of0.5K18Z.-L.Li et al./Remote Sensing of Environment131(2013)14–37。
The properties of carbon nanotubes
The properties of carbon nanotubesCarbon nanotubes (CNTs) have emerged as one of the most promising materials in the world of nanotechnology. Since their discovery in the early 1990s, they have been the subject of intense research due to their extraordinary physical and mechanical properties. CNTs are cylindrical structures made of carbon atoms, which are arranged in a honeycomb lattice. They can be single-walled or multi-walled, depending on the number of layers of carbon atoms.CNTs have many unique properties, including high tensile strength, thermal conductivity, and electrical conductivity. These properties make them suitable for a wide range of applications, from electronics to energy storage. In this article, we will explore the properties of CNTs in more detail.Tensile StrengthOne of the most remarkable properties of CNTs is their incredible tensile strength. In fact, CNTs are the strongest materials known to man. They are up to 100 times stronger than steel, yet only a fraction of the weight. This makes them ideal for use in materials that require high strength and low weight. For example, CNTs could be used to make stronger and lighter aircraft engines and components.Thermal ConductivityCNTs also have a high thermal conductivity, which makes them excellent heat conductors. This means that CNTs can quickly transfer heat from one point to another. This makes them ideal for use in heat sinks, which are used to dissipate heat from electronic devices. Additionally, CNTs can be used to improve the efficiency of energy storage devices, such as batteries and supercapacitors.Electrical ConductivityCNTs are also excellent electrical conductors, which makes them ideal for use in electronics. They have a very high current carrying capacity, which means they can carrya large amount of electricity without overheating. Additionally, they have a low resistance, which means that electrical signals can travel through them quickly and efficiently. CNTs could be used to make faster and more efficient computer chips, as well as more durable electronic components.Chemical StabilityCNTs are also very chemically stable, meaning they are resistant to chemical reactions. This is due to the strong covalent bonds between the carbon atoms in the honeycomb lattice. This property makes CNTs ideal for use in environments with harsh chemicals, such as in the oil and gas industry. They could be used to make stronger and more durable pipes and other components that are needed in these environments.ConclusionIn conclusion, CNTs have many unique and fascinating properties that make them ideal for a wide range of applications. From their incredible tensile strength to their high thermal and electrical conductivity, CNTs are proving to be one of the most promising materials in the world of nanotechnology. As research continues, it is likely that we will discover even more amazing properties of CNTs that could revolutionize the way we live and work.。
科技英语阅读(李健版)
Unit 1 EnvironmentEarth’s Health in Sharp Decline, Massive Study Finds大规模研究发现:地球的“健康”每况愈下The report card has arrived from the largest ever scientific Earth analysis, and many of the planet’s ecosystems are simply not making the grade.有史以来对地球进行的最大规模的科学分析结果表明,地球上的许多生态系统都达不到标准。
The UN-backed Millennium Ecosystem Assessment Synthesis Report found that nearly two-thirds of Earth’s life-supporting ecosystems, including clean water, pure air, and stable climate, are being degraded by unsustainable use.由联合国主持的《千年生态系统评估综合报告》指出,由于不可持续的使用,地球上将近三分之二的用来维持生命的生态系统(包括干净的水源、纯净的空气以及稳定的气候)正遭受破坏。
Human has caused much of this damage during the past half century. Soaring demand for food, fresh water, timber, fiber and fuel have led to dramatic environmental changes, from deforestation to chemical pollution, the report says. The already grim situation may worsen dramatically during the first half of the 21st century, the report’s authors warn.以上大部分的破坏都是人类在过去的半个世纪里造成的。
南昌2024年08版小学6年级下册U卷英语第二单元自测题[含答案]
南昌2024年08版小学6年级下册英语第二单元自测题[含答案]考试时间:80分钟(总分:140)A卷考试人:_________题号一二三四五总分得分一、综合题(共计100题共100分)1. Wall served as a defense against ________ (攻击). 填空题:The Grea2. 听力题:My sister is a ______. She loves fashion design.3. 填空题:I love playing with my ______ blocks.4. 填空题:The __________ (奥斯曼帝国) lasted for centuries.5. 选择题:What is the name of the instrument used to measure temperature?A. BarometerB. ThermometerC. HygrometerD. Altimeter6. 填空题:The owl has specialized ______ (视觉) for seeing in darkness.7. 听力题:The sun is very ________ today.8. 填空题:The _____ (猫) loves to stretch and play.9. 填空题:________ (植物保护倡议) promote awareness.My friend is a big __________ of dance. (爱好者)11. 听力题:She is studying for her ___. (test)12. 听力题:The ______ teaches us about teamwork.13. 听力题:Water's unique properties are due to its _______ bonds.14. 听力题:Sedimentary rocks often contain ______ that can tell us about the environment of the past.15. 选择题:What is the capital of Ethiopia?A. Addis AbabaB. AsmaraC. NairobiD. Khartoum16. 选择题:What is the name of the famous scientist who developed the theory of evolution?A. Charles DarwinB. Albert EinsteinC. Isaac NewtonD. Galileo Galilei17. 听力题:A _______ is a small particle made up of atoms.18. 听力题:The cat is ________ on the sofa.19. 填空题:The __________ (绿叶) produce oxygen for us to breathe.20. 填空题:Understanding the life cycle of a plant includes knowing its ______.(了解植物的生命周期包括了解其繁殖方式。
乙腈不同温度下的表面蒸气压_概述及解释说明
乙腈不同温度下的表面蒸气压概述及解释说明1. 引言1.1 概述乙腈(化学式CH3CN)是一种常用的有机溶剂,广泛应用于化学实验室、工业生产和科研领域。
乙腈的表面蒸气压是其在不同温度下从液态向气态转变时产生的压强。
了解乙腈在不同温度下的表面蒸气压变化规律对于科学研究及工业应用有着重要意义。
1.2 文章结构本文将首先介绍乙腈的物性特点,包括分子结构、物理性质和化学性质等方面。
接着将对表面蒸气压的概念进行解释,并探讨影响乙腈表面蒸气压变化的因素。
最后,通过实验方法与结果分析,详细讨论不同温度下乙腈表面蒸气压的变化规律,并总结归纳实验结果。
1.3 目的本文旨在深入探讨乙腈在不同温度下的表面蒸气压变化规律,并通过实验结果分析验证相关理论模型。
通过研究乙腈的表面蒸气压,可以拓宽我们对乙腈及相关有机溶剂的认识,并为实验室操作、工业生产以及科学研究提供技术参考和应用前景展望。
2. 正文2.1 乙腈的物性介绍乙腈是一种常见的有机溶剂,化学式为CH3CN。
它具有无色、透明、有刺激性气味以及良好的溶解性等特点,在化工、制药等多个领域广泛应用。
乙腈的分子量为41.05 g/mol,密度为0.786 g/cm^3。
它的沸点为81.6°C,熔点为-45°C。
2.2 表面蒸气压的概念和影响因素表面蒸气压指在一定温度下,液体与其饱和蒸气之间达到动态平衡时所对应的气相压强。
表面蒸气压受多种因素影响,包括温度、分子间吸引力以及液体分子挥发速率等。
较高温度和较强分子间相互作用力会提高液体表面上的分子挥发速率,从而增加表面蒸气压。
2.3 不同温度下乙腈表面蒸气压的变化规律随着温度升高,乙腈的表面蒸气压将增加。
根据饱和蒸气压与温度之间的关系,一般而言,液体的饱和蒸气压随着温度的升高而增加。
对于乙腈来说也是如此。
以常规大气压下为例,乙腈在25°C时的表面蒸气压约为76.15 mmHg,在50°C时增至131.3 mmHg。
Langmuir-Efficient Fluorescence Quenching in Carbon Dots by Surface-Doped Metals - Disruption of
Department of Chemistry and Laboratory for Emerging Materials and Technology, Clemson University, Clemson, South Carolina 29634, United States ‡ Air Force Research Laboratory, Propulsion Directorate, Wright-Patterson Air Force Base, Dayton, Ohio 45433, United States § University of Dayton Research Institute, Sensors Technology Office, Dayton, Ohio 45469, United States
Small semiconductor nanoparticles and related core−shell nanostructures, generally referred to as quantum dots (QDs) due to the presence of quantum confinement effects, have attracted much attention for their excellent optical properties and a variety of potential applications.1 Among well-established QDs are those based on insoluble cadmium salts, especially the popular and now commercially available CdSe/ZnS core−shell nanoparticles with various surface coatings.1−5 However, there have also been some significant concerns on these presently dominating QDs, especially with respect to their toxicity associated with the heavy metal content.6,7 Therefore, the search for alternative QD-like optical nanomaterials that are nontoxic yet still high performance has continued.8−11 Nanoscale carbon particles have recently emerged as a unique class of optical nanomaterials targeting both biomedical and energy conversion applications.11−30 Small carbon nanoparticles upon surface functionalization by organic molecules were found to exhibit bright and colorful fluorescence emissions. These strongly fluorescent nanoparticles, dubbed “carbon dots” (Scheme 1),11 have been demonstrated for their competitive optical performance to that of well-established
西电研究生英语复习资料
西电研究生英语复习资料Unit 11.除非我们共同快速we are on a trajectory for gloal warming tobecome much more intense unless we begin a concerted rapid shift toward a low carbon economy.2.尽管Some of the dire projection may not occur, but in light of thewarning from our best scientists, it would be beyond irresponsible to take the bet.3.我们极大地破坏了大气层,By badly disrupting that envelope, weadversely affect every dimension of human well-being that is tied to the environment.4.诸如干旱、Extreme weather events, such as drought , floods, andsevere storms, become more intense and inflict greater damage to life and property.5.即使我们明天停止气体排放Even if we cut off emissions tomorrow,the concentration of greenhouse gases in the atmosphere would continue rising since these gases persist in the atmosphere for a very long time—from decades to thousands of years after they are first emitted depending on the specific type of greenhouse gas.6.如果我们忽视气候变化和依赖石油的风险,。
冷原子光谱法 英语
冷原子光谱法英语Okay, here's a piece of writing on cold atom spectroscopy in an informal, conversational, and varied English style:Hey, you know what's fascinating? Cold atom spectroscopy! It's this crazy technique where you chill atoms down to near absolute zero and study their light emissions. It's like you're looking at the universe in a whole new way.Just imagine, you've got these tiny particles, frozen in place almost, and they're still putting out this beautiful light. It's kind of like looking at a fireworks display in a snow globe. The colors and patterns are incredible.The thing about cold atoms is that they're so slow-moving, it's easier to measure their properties. You can get really precise data on things like energy levels andtransitions. It's like having a super-high-resolution microscope for the quantum world.So, why do we bother with all this? Well, it turns out that cold atom spectroscopy has tons of applications. From building better sensors to understanding the fundamental laws of nature, it's a powerful tool. It's like having a key that unlocks secrets of the universe.And the coolest part? It's just so darn cool! I mean, chilling atoms to near absolute zero? That's crazy science fiction stuff, right?。
学术英语习题及部分答案
Training and Practice for English for Academic PurposesPart I1.Discuss the following questions.What are basic principles the researchers must try to follow when they write their research papers? And would you please list some deadly sins a researcher must avoid when they want to publish a research paper? What are the main contents of a research paper?2. Translate the following Chinese introduction into English.提高起重机生产力和安全性的设备研究近些年来,就用研究人员对起重机(crane)的研究兴趣与日俱增。
起重机种类繁多,从樱桃采摘机(cherry pickers)到巨型塔式起重机(huge tower cranes) ,是建筑工地不可或缺的重要设备之一。
由于建筑用起重机工作环境多变(constantly changing working environment), 操作者(operator)责任重大(heavy reliance)。
过去几十年里,超重机技术日新月异,但是操作员与其他工种人员配合协作方面的技术发展缓慢。
起重机的发展步伐如此迅猛,我们似乎要问,在某些方面,是不是已经超出(outstrip)了人们安全使用的能力?本文旨在探讨如何通过新型设备的引进提高起重机生产力以及提出相关安全性的举措,进而为新型起重机的应用和案例提供新的思路。
In recent years, researchers have become more interested in crane research.The variety of cranes, from cherry pickers to giant tower cranes, is one of the most important equipment on construction sites.As a result of the changing working environment of the construction crane, operator is responsible for heavy reliance.Over the past few decades, the technology of overweight machines has been changing rapidly, but the operators have been slow to cooperate with other workers in collaboration.The pace of development of cranes is so rapid that we seem to be asking whether in some respects, the outstrip has exceeded the ability of people to safely use it.This paper aims to explore how to improve crane productivity and raise related security measures through the introduction of new equipment, so as to provide new ideas for the application and case of new cranes.3. You are writing a research paper entitled “The Effects of Radiation from the Sun on Life o n Earth”. In your introduction you need to review, in general terms, how the sun supports life on the earth. Prepare an Introduction section for your paper based on the information below.⏹Distance from the earth: 92,976,000 miles⏹The Sun’s energy comes from nuclear fusion of hydrogen to helium.⏹Intense radiation, including lethal ultraviolet radiation, arrives at the earth’s outer atmosphere.⏹Ozone in the stratosphere protects life on earth from excessive ultraviolet radiation.⏹The seasons of the earth’s climate results from (1) the 23.30tilt of the earth’s axis of rotation from the normal to the plane of the earth’s orbit around the Sun, (2) the large coverage area of water on the earth (about 75% of the earth’s surface), an d (3) the rotation of the earth with associated generation of jet-stream patterns.⏹Radiation passing through the earth’s atmosphere loses most short-wave radiation, butsome arriving at the surface is converted into infrared radiation which is then trapped by water vapor and other tri-atomic molecules in the troposphere and stratosphere, causing global warming.Life on earth is maintained from photosynthesis and conversion of carbon dioxide to oxygen by plants.4.Translate the following parts of sentences in Introduction into proper English.(1)过去对……的研究工作说明……The previous work on … has indicated that…(2)A在1932年做了关于……的早期研究。
散发光与热的英语作文题目
散发光与热的英语作文题目Light and Heat: The Electromagnetic Spectrum.The electromagnetic spectrum is a continuous range of frequencies of electromagnetic radiation, which includes visible light, infrared radiation, and ultraviolet radiation. Light and heat are both forms of electromagnetic radiation, but they have different properties and different effects on matter.Visible light is the only part of the electromagnetic spectrum that we can see. It has a frequency range of approximately 400 to 700 nanometers (nm). The color oflight is determined by its frequency, with shorter wavelengths appearing blue and longer wavelengths appearing red.Infrared radiation has a lower frequency than visible light, and it is therefore invisible to the human eye. It has a frequency range of approximately 700 nm to 1millimeter (mm). Infrared radiation is emitted by warm objects, and it can be used to detect heat signatures.Ultraviolet radiation has a higher frequency than visible light, and it is also invisible to the human eye.It has a frequency range of approximately 10 nm to 400 nm. Ultraviolet radiation can cause damage to skin and eyes, and it is used in tanning beds and sun lamps.Light and heat can both be used to transfer energy. Light can be used to illuminate objects, and it can also be used to heat objects. Heat can be used to warm objects, and it can also be used to power engines.The sun is the primary source of light and heat for the Earth. The sun emits visible light, infrared radiation, and ultraviolet radiation. The visible light from the sun allows us to see, and the infrared radiation from the sun warms the Earth's surface. The ultraviolet radiation from the sun is harmful to life, but it is absorbed by theEarth's atmosphere.Light and heat are essential to life on Earth. Light allows us to see, and heat keeps us warm. Without light and heat, life on Earth would not be possible.。
冥王星 Pluto
New Horizons Finds Blue Skies and Water Ice on Pluto
Last Updated: Oct. 10, 2015 Editor: Lillian Gipson
阴霾颗粒本身很可能呈灰色或红色,但它们散射蓝光的方式已经得 到新地平线号科学小组的注意。 蓝天往往是由于太阳光的散射非常小的 颗粒。在地球上,这些颗粒非常微小的氮分子。冥王星上他们似乎要更 大一些,类似烟灰的粒子 (但仍然相对较小) 科学家称之为“tholins”
Scientists believe the tholin particles form high in the atmosphere, where ultraviolet(紫外线的) sunlight breaks aplecules and allows them to react with one another to form more and more complex negatively and positively charged ions.
•
水冰并不存在于 冥王星 表面的大片区域, 因为它显 然是以其他形式被掩藏;围 绕在星球表面大多数地方更 多的为不稳定的冰。明白为 什么水恰好在这些区域,而 不是在其他地方,是我们钻 研它的一个挑战。
A curious aspect of the detection is that the areas showing the most obvious water ice spectral signatures correspond to areas that are bright red in recently released color images. At present, scientists don’t yet understand the relationship between water ice and the reddish tholin colorants on Pluto's surface.
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1Astronomy Program and Departments of Physics and Applied Physics
–2–
Subject headings: Galaxies: Clusters: General–Galaxies: Clusters: Individual–XRays–Magnetic Fields–Acceleration of Particles.
We show that continuous and in situ acceleration in the ICM of the background thermal electrons is difficult and requires unreasonably high energy input. Similarly acceleration of injected relativistic electrons, say by galaxies, seems unreasonable because it will give rise to a much flatter spectrum of electrons than required, unless a large fraction of energy input is carried away by electrons escaping the ICM, in which case one obtains EUV and HXR emissions extending well beyond the boundaries of the diffuse radio source. A continuous emission by a cooling spectrum resulting from interaction with ICM of electrons accelerated elsewhere also suffers from similar shortcomings. The most likely scenario appears to be an episodic injection-acceleration model, whereby one obtains a time dependent spectrum that for certain phases of its evolution satisfies all the requirements.
arXiv:astro-ph/0101145v2 21 Mar 2001
Байду номын сангаас
Submitted to ApJ, Jan. 2001, Revised March 2001
On The Non Thermal Emission and Acceleration of Electrons in Coma and Other Clusters of Galaxies
We show that NTB cannot be the source of the HXRs (except for a short period) and that the difficulty with that the low magnetic field in the IC model is alleviated if the effects of observational selection bias, non isotropic pitch angle distribution and spectral breaks in the energy distribution of the relativistic electrons are taken into account. From these consideration and the strength of the EUV emission, we derive a spectrum for the radiating electrons and discuss possible acceleration scenarios for its productions.
1. INTRODUCTION
The most prominent radiation from the intercluster medium (ICM) of clusters of galaxies is the thermal bremssstrahlung (TB) or free-free emission in the soft X-ray (2 to 10 keV, SXR) region which can reach a luminosity LSXR ∼ 1045 erg/s and implies gas temperatures of T ∼ 108K and emission measures of EM ∼ 1068cm−3 (density n ∼ 10−3cm−3, radius R ∼ 1 Mpc). For Coma cluster LSXR ≃ 5 × 1044, kT = 8.2 keV. There is, however, a growing evidence for a significant nonthermal activity in some clusters. The first of these to be discovered in just a few clusters, notably in the Coma cluster (for the most recent observations see Giovannini & Feretti 2000) was the diffused (so-called halo) radio emission of luminosity LR ∼ 1041 erg/s in the frequency range 30MHz < ν < 4GHz whose source must be synchrotron radiation by relativistic electrons. The range and distributions of the Lorentz factor γ of these electrons and their total energy depends on the strength, geometry and distribution of the magnetic field B. The field is measured by Faraday rotation to be a few microGauss (µG) in some clusters which would require electrons with γ > 103. The exact source of these electrons is still a matter of considerable debate. For a review see Eilek (1999), Giovannini et al. (1993), Kim et al. (1990), and references there to earlier works. More recently, radiation (most likely nonthermal in origin) have been discovered in form of excess flux at low and high ends of the thermal radiation in several clusters. The Extreme Ultraviolet Explorer (EUVE), with the passband of 69 to 245 eV, has detected excess radiation from Coma (Lieu et al. 1996a). The luminosity of this soft excess radiation in the 0.07 to 0.4 keV range is LEUV ∼ 2 × 1043 erg/s (Lieu et al. 1999). Similarly, BeppoSAX and Rossi X-ray Timing Explorer (RXTE) have detected excess hard X-ray (HXR) radiation in the 20 to 80 keV range from Coma (Fusco-Femiano et al. 1999, Rephaeli et al. 1999), A2256 (Fusco-Femiano et al.2000), and possibly A2199 (Kaastra et al. 1999). The luminosity of Coma in this range is LHXR ∼ 4 × 1043 erg/s. The EGRET instrument on board the Compton Gamma-Ray Observatory (CGRO) set an upper limit of Lγ−Ray 1043 erg/s above 100 MeV (Sreekumar et al. 1996). These observations are summarized in Table 1 and assume a Hubble constant of 60 km/(s Mpc).