RADIO COMPACT STRUCTURE IN OQ208

The Astrophysical Journal,621:L13–L16,2005March1᭧2005.The American Astronomical Society.All rights reserved.Printed in U.S.A.RADIO COMPACT STRUCTURE IN OQ208Guiying Xie,1,2D.R.Jiang,1and Z.-Q.Shen1Received2004October10;accepted2005January18;published2005January27ABSTRACTIn light of the newly detected proper motions in two lobes of the gigahertz-peaked spectrum source OQ208, we introduced the Doppler effect into thefit to the observed spectral turnovers.It shows that two models containing the same beaming parameters but having quite different absorption mechanisms canfit two lobes equally well.In one model,only FFA(free-free absorption)is needed.In the other model,both the SSA(synchrotron self-absorption)in two lobes and an extra FFA toward the southwest lobe are required.Our analysis cannot unam-biguously distinguish between two models.Although the FFA process is invoked in both models,the geometry of the absorbing gas could be quite different.However,the beaming effects in both models are eventually the same,with an intrinsically symmetrical advance speed of≈0.33c for the two-sided lobes and an inclination angle of≈33Њfor the radio jet emission to the observer’s line of sight.Subject headings:galaxies:active—galaxies:individual(OQ208)—radio continuum:galaxies1.INTRODUCTIONThe radio source OQ208(1404ϩ286),at,isz p0.0768 one of the closest GPS(gigahertz-peaked spectrum)sources with a spectral peak at6GHz(de Vries et al.1997).Its host galaxy Mrk668is classified as a Seyfert1galaxy(de Grijp et al.1992)or a broad-line radio galaxy(Marziani et al.1993), which shows broad optical recombination lines.Thefirst published VLBI image of OQ208showed a struc-ture extended in the north-south direction(Charlot1990). Zhang et al.(1994)found it to extend6mas at a position angle of∼Ϫ145Њ.The source is widely used as the VLBI calibrator because of its stableflux density and compact ter VLBI observations(Kameno et al.2000;Fey et al.1996; Stanghellini et al.1997)revealed a double structure separated by∼7mas in northeast–southwest(NE-SW)direction.Ex-tremely stableflux densities and steep spectra above the peak frequency indicate that these two components are microlobes or hot spots.The15GHz VLBI observations discovered a weak core located between the two minilobes and confirmed that OQ208is a compact symmetric object(CSO;Kellermann et al.1998;Stanghellini et al.2001).Kameno et al.(2000)published the high-resolution VLBI Space Observatory Programme image of OQ208at1.66GHz and found that the two lobes are highly asymmetric with aflux density ratio about60:1,larger than those at higher frequencies. The apparent spectra of the two components are peaked at a few gigahertz.To explain the low-frequency cutoff seen in the spectra of two lobes,Kameno et al.(2000)fitted the spectra of the two components of OQ208with the SSA(synchrotron self-absorp-tion)and FFA(free-free absorption)models,respectively.Their results showed that the FFA model is likely to occur toward the SW component,while either the SSA or FFA model is possible for the NE component.But the intrinsicflux densities of the two components are quite different(theflux density ratio is10and 48for FFA and SSA,respectively)in their two models.They also discussed the Doppler effect.If the bright NE component is Doppler-boosted,it should have a blueshifted spectrum.Con-1Shanghai Astronomical Observatory,Chinese Academy of Sciences,80Nan-dan Road,Shanghai200030,China;gyxie@,djiang@, zshen@.2Graduate School of the Chinese Academy of Sciences,Beijing100039, China.sidering that the observed peak frequency of the NE component is lower than that of the SW component,and the extreme stability of the totalflux density at1.4GHz(Stanghellini et al.1997), they ruled out the beaming model.They explained the spectra of the two components in OQ208as an asymmetric FFA with an intrinsically asymmetricflux density.In the unified scheme,the jet and counterjet should be es-sentially the same.Observationally,we have seen nearly sym-metric structure at large scale for many lobe-dominated active galactic nuclei.If the emission of hot spots is caused by the interaction between the jet and the ambient medium and if the distribution of the circumnuclear medium in OQ208is very asymmetric,the intrinsicflux density of the two components may be very different,but we have not seen any observational evidence of this kind of distribution.So we prefer a beaming model to explain the asymmetricflux density of the two com-ponents in OQ208.The discussion by Kameno et al.(2000) about the beaming model is incomplete.If FFA toward both NE and SW components were the same,the Doppler-boosted NE component would have a blueshifted spectrum relative to that of the SW component.However,if there is a difference in the FFA of the two components,the observed spectrum will be modified.The peak frequency of the spectrum of the SW component with more FFA will move to the higher frequency.The proposed beaming model is further supported by the de-tection of a proper motion(Kellermann et al.2004).In this Letter we present an improved model of OQ208that can explain the observed radio properties.Throughout this Letter we use the following cosmological parameters:km sϪ1MpcϪ1,,andH p70Q p0.3Q p0m L .The spectra index is defined by the relation.a0.7S∝nn2.MODELS AND RESULTSIn our analysis,the same data published by Kameno et al.(2000)are used.They are theflux densities of both the NE and SW lobe components measured atfive frequencies,1.66,2.32,4.99,8.55,and15.3GHz.Recently,Kellermann et al.(2004)obtained the proper-motion measurements of four components in the radio compact structure of OQ208based on10epoch VLBI observations at15GHz.The apparent transversal veloc-ities of the two components B and C in the NE lobe areand(with c being the speed of light),(0.2ע0.1)c(0.3ע0.2)crespectively,and the other two components D and E in the SWL13L14XIE,JIANG,&SHEN Vol.621TABLE1Spectral Fit for Two ModelsModelS(Jy)v(deg)b S tfNtfts2x/dof FFAϩbeaming...... 6.52ע0.4532.5ע2.00.33ע0.0113.21ע0.57.77ע0.10…8.30/6SSAϩbeaming......0.208ע0.00333.8ע2.20.33ע0.0111.3ע0.3…28.2ע2.08.89/6Fig.1.—Spectra of the NE and SW components at1.66,2.32,4.99,8.55,and15.3GHz.The solid and dashed lines indicate thefitted spectra for theFFAϩbeaming and SSAϩbeaming models,respectively.The redshift correc-tion is applied to thefitting lines.Data are from Kameno et al.(2000).lobe have the apparent transversal velocities and(0.0ע0.1)c,respectively.Because the emission in the SW lobe(0.1ע0.1)cis relatively weak,and thus may have large uncertainties in themeasured proper motions,we decided to use the averaged propermotion of the two components in the NE lobe to incorporateinto the following spectralfit as a constraint on the two beamingparameters v(the angle between jet axis and the line of sight)and b(the jet velocity in units of c)using the following equation:,where the measured proper mo-b p(b sin v)/(1Ϫb cos v)apption is the averaged value of the two componentsb p0.25app(components B and C in Table2of Kellermann et al.2004)in the NE lobe of OQ208.To explain the low-frequency cutoff seen in the spectra ofthe two lobes and the big difference in the observedflux den-sities of the two components in OQ208,two possible modelsof quite different absorption mechanisms are considered.Therelativistic beaming effect is always taken into account in thefitting of the two models.In both models,the intrinsic radio spectra and the radiofluxdensities of the two lobes are assumed to be the same,and thespectral index of for the optically thin synchrotrona pϪ1.2radiation is assumed.But there are different FFA opacities inthe ambient plasma due to a slant jet axis against the line ofsight.For the same reason,the NE and SW lobes have differentDoppler factors,andd p1/[g(1Ϫb cos v)]d p1/[g(1ϩNE SW,respectively,where g(p)is the bulk21/2b cos v)][1/(1Ϫb)]Lorentz factor of the jet.2.1.FFAϩBeaming ModelFirst,only the FFA effect is considered.Assuming that theintrinsic emission of the lobes is optically thin,we obtain theobservedflux density at the observing frequency n(in units ofgigahertz)asan(1ϩz)3Ϫ2.1S p(1ϩz)d S exp{Ϫt[n(1ϩz)]},(1)n0f[]dwhere is the intrinsicflux density at1GHz in the sourceSrest frame,is the FFA coefficient at1GHz in the galaxytfframe,z is the redshift,and d is the Doppler factor and is equalto and for the NE and SW lobes,respectively.d dNE SWThe observational data of the NE lobe and the SW lobe canbe combined,since the intrinsicflux densities of the twoSlobes,the viewing angle v,and the jet velocity b are the same.There are10data points measured atfive frequencies:1.66,2.32,4.99,8.55and15.3GHz.There seem to befive parametersinvolved in thefitting,i.e.,,v,b,,and.Here,is theN S NS t t t0f f fFFA opacity toward the NE lobe,and is the FFA opacityStftoward the SW lobe.However,with the above equation of,two spectra of both the NE andb p(b sin v)/(1Ϫb cos v)appSW lobes can be jointlyfitted by four independent parameters:,v(b),,and.Thefitting results are shown in Table1N SS t t0f fand Figure1.2.2.SSAϩBeaming ModelSecond,we consider that there exists an intrinsic SSA effectand that the two lobes have the same SSA opacity of the syn-chrotron emission in the source rest frame.Obviously,the SSAmodel by itself is inadequate,since the beaming effect wouldresult in a higher peak frequency in the NE lobe than that inthe SW lobe,which is just opposite to the observed spectra(Kameno et al.2000).To shift the peak frequency of the SWlobe to a higher frequency,an asymmetrical FFA distributionwith more absorption toward the SW lobe is needed.For thesimplest case,only an extra FFA in the SW lobe emission isintroduced in combination with the intrinsic SSA in the twolobes.In this model the observedflux density at the observingfrequency n(in units of gigahertz)for the NE lobe is2.5n(1ϩz)3S p(1ϩz)d Sn NE0[]dNEaϪ2.5n(1ϩz)#1ϪexpϪt,(2)s[]{}()dNEwhile for the SW lobe2.5n(1ϩz)3Ϫ2.1S p(1ϩz)d S exp{Ϫt[n(1ϩz)]}n SW0f[]dSWaϪ2.5n(1ϩz)#1ϪexpϪt,(3)s[]{}()dSWwhere is the intrinsic SSA coefficient at1GHz in the sourcetsNo.1,2005RADIO COMPACT STRUCTURE IN OQ 208L15rest frame and the definitions of the other parameters are the same as those in equation (1).In this case,the number of fitting parameters is also four,i.e.,,v (b ),,and .The fitted S S t t 0s f parameters and the spectra are given in Table 1and Figure 1,respectively.For the error estimation,we know that the best-fit modelshould have reduced x 2’s,,equal to unity with22x p x /dof n min a deviation of ,where dof is the degree of freedom.1/2(2/dof)However,in many cases,the value for at is larger than 22x x n min 1.0(Bietenholz et al.1996).So,we scale up the 68.3%con-fidence region of parameter space,as an increase of from 2x to with instead of 1.0.By 22222x x ϩ᭝x ᭝x p x /dof min minmin projecting this confidence contour onto the axis of the param-eter of interest,we can finally obtain the 1standard error for that single parameter.3.DISCUSSIONparison between Two ModelsStatistically,both models fit the observed spectral data equally well and thus are indistinguishable.In general,SSA and FFA are two main competing mechanisms that explain the spectral turnovers seen in the GPS radio sources.The anticorrelation between the peak frequency and the overall linear size of the source (Fanti et al.1990;O’Dea &Baum 1997;Snellen et al.2000)indicates that the SSA process is related to the observed peak frequency.However,it has been pointed out that the FFA process,through the ionized gas surrounding the radio source,can also explain the relationship between turnover frequency and size (Bicknell et al.1997).Furthermore,the measured steeper-than-2.5low-frequency spectral index is inconsistent with the SSA model alone.The optical observations (de Vries et al.2000)also support the existence of a very dense ionized medium sur-rounding the GPS sources.In the case of OQ 208,a simple SSA-only model is clearly ruled out,but a modified SSA model with partial FFA toward the receding SW lobe is still a likely process responsible for the spectral turnovers in two lobes.So,at present,it is difficult to decide which model is better.Because the ex-pected low-frequency measurements can be significantly differ-ent,future high-resolution observations at lower frequencies will be crucial in distinguishing between the two models.3.2.The Beaming Effect of Two ModelsThe fitted beaming parameters in both models are nearly the same no matter which absorption mechanism is invoked.The advance speed of the lobes is about 0.33c ,and the inclination angle of the radio jet is around 33Њ.Stanghellini et al.(1997)mentioned that the optical image of the galaxy has an axial ratio of 0.7,which corresponds to an inclination of 45Њwith respect to the plane of the sky.Given the large uncertainty of the value in the optical image,the 33Њviewing angle derived from the radio emission is in reasonable agreement with the optical result.This means that the radio axis is likely to be in alignment with the optical axis in OQ 208.This further supports the beaming model.If the advance speed b of the lobes is a constant,the radio activity age t in the compact region of OQ 208will be given by ,where mas is the angular sep-t p v D /2b c sin v v p 7T A T aration of the two lobes and Mpc is the angular D p 300A diameter distance of the source.It is about 92years.If this is confirmed,OQ 208would be the youngest CSO known so far (Polatidis &Conway 2003;Taylor et al.2000).3.3.About the FFA AbsorberThe introduction of the Doppler effect can naturally account for the large ratio in the observed flux density of the two components but will result in a differential Doppler shift of the SSA spectral components;thus,the asymmetric FFA is inev-itable in order to explain that the beamed peak frequency of the approaching NE lobe is lower than that of the receding SW lobe in OQ 208.However,the absorber responsible for the FFA process might be different in the two models,reflecting the difference in the distribution of the ionized gas.In the FFA-only model,both the the NE and SW lobes undergo the free-free absorption,although the amount is different.This means that the absorber may have a more or less spherically symmetric distribution,for example,the clouds in the narrow-line region,with the different FFA opacities in the two lobes mainly the result of the difference in the path length along the line of D L sight.Here is given by .This gives D L D L p v D /tan v T A pc with in OQ 208.D L ∼15.9v p 33ЊBut in our SSA model,only an extra FFA toward the SW lobe is needed,and the emission from the NE lobe is free of any FFA process.As such,the absorbing plasma could be distributed in a disk or torus perpendicular to the jet,which just obscured the receding SW lobe emission.The difference in the FFA opacity between the NE and SW lobes can be used to estimate the electron density of the FFA plasma in a few parsecs from the SW lobe.We assume that the plasma distributes homogeneously along the absorption path,the difference in the FFA opacity is given by (Kamenoet al.2000),where and are the Ϫ3/22Dt p 0.46T n D L T n f e e e e electron temperature (K)and the electron density (cm Ϫ3)of the ambient plasma,respectively.The electron density of the FFA absorber is for the first model 343/4Ϫ3n p 0.86#10(T /10)cm e e and for the second model.343/4Ϫ3n p 1.24#10(T /10)cm e e 3.4.About the Assumption That the Two Lobes AreIntrinsically Identical In fact,the lobe pointed toward us is seen to be quite older than that pointed away from us.At an inclination angle of 33Њwith a projected distance between the two lobes of ≈10pc (Kameno et al.2000),the age difference is about 50years.The electronic cooling age of SSA at the source rest frame can be estimated by (Rybicki &Lightman 1979)118.7#10t p .(4)sy 3/21/23/2B n sin am Applying and GHz for the SSA ϩbeaming B ∼10mG n ≈2.49m model (see §4.1),we have yr.For the FFA ϩbeaming t Ӎ550sy model,we assumed that the synchrotron emission is still op-tically thin at 1GHz,so the corresponding magnetic field B and turnover frequency are much smaller than the ones de-n m rived from the SSA model.The resultant cooling time for the FFA model would be much longer than 550yr.Thus,we con-clude that the assumption is reasonable that the two lobes with an age difference of ≈50yr are intrinsically identical.4.SOME PHYSICAL PARAMETERS ESTIMATED FROMSSA ϩBEAMING MODELThe following discussion is based on the assumption that the SSA ϩbeaming model is correct.L16XIE,JIANG,&SHEN Vol.6214.1.The Magnetic Field in the LobesWe use the spectrum of the lobe in the source rest frame and the redshift correction to determine the turnover frequency GHz and the corresponding peak flux density n ≈2.49ע0.02m Jy.Adopting an angular size of mas S ≈1.37ע0.04v ≈1.63m from the 2.3GHz VLBI measurement (Fey et al.1996),we can obtain the equipartition magnetic field B ∼10ע1mGfrom the relation .1/52/5Ϫ4/51/5n ∼8B S v (1ϩz )m m 4.2.Mass in the LobeWe have obtained the optical depth of the SSA in the lobes at 1GHz and the magnetic field within from the SSA ϩbeaming model.So it is possible to estimate the electron density and the mass of the lobe under some assumptions.Assuming that the number density of the relativistic electron is distributed as a power-law function of energy in the OQ 208lobes,it is given by .The optical depth of the SSA in the Ϫp n (E )dE p n E dE 0lobes is given by ,where is the absorption co-t p k L k s n lobe n efficient of the synchrotron emission.Assuming that the ge-ometry of the lobes is a uniform sphere with the radius R with the averaged absorption length of the lobe ,we can L ∼4R /3lobe derive the normalized constant .Ϫ9Ϫ3n ∼1.30#10cm 0The number density of the relativistic electron is n n pe e .The minimum energy of the emitting electron1Ϫp[n /(p Ϫ1)]E 0min is .We cannot determine whether the emitting gas is a 2g m c e ,min e plasma or an electron-position pair,and we assumed that the emitting gas is composed of the plasma.In this case,a value of g p e ,min (Falcke &Biermann 1996)may be reasonable,and thus the 100number density of the relativistic electron is .The Ϫ3n ∼3.5cm e number of electrons in one lobe can be estimated as N ∼e ,and the mass of a lobe as ,which gives 3(4/3)p R n M Ӎm N e lobe p e .If the mass of the two lobes was supplied by a M ∼0.6M lobe ,jet,the mass ejection rate in the jet would be about Ϫ21.3#10.Ϫ1M yr , 4.3.The Jet PowerThe integrated radio luminosity of the two lobes is 421.2#10ergs s Ϫ1,the kinetic power of the two lobes is about 434.0#10ergs s Ϫ1,and the internal energy of the density of the relativistic electrons and magnetic fields in the two lobes is about 4.88#ergs cm Ϫ3,which corresponds to a variation of the internalϪ410energy in the two lobes per unit time of ∼ergs s Ϫ1.So 436.9#10the jet power is larger than ergs s Ϫ1,since the power 441.1#10of the expansion of hot spots is not included.4.4.The Accretion RateFor OQ 208,the bolometric luminosity can be estimated from its optical luminosity by the equation (Kaspi et L Ӎ9l L bol l ,5100al.2000),where can be estimated from the V magnitude L l ,5100.With mag (Ve ´ron-Cetty &Ve ´ron 2000),after m m p 15.35V V the Galactic extinction correction (mag)and K -cor-A p 0.061V rection (),we obtained ergs s Ϫ1.45a p Ϫ1L Ӎ1.73#10opt bol The accretion rate is given by .Therefore,2˙˙MM p L /h c bol the accretion rate in OQ 208would be Ϫ1˙M Ӎ0.27M yr ,(assuming ).Comparing this with the above mass ejec-h p 0.1tion rate in the jet,about 4.8%of the accreting material is ejected by the jet.5.CONCLUSIONSTo explain the asymmetric flux densities of the two lobes in OQ 208,we incorporate the beaming model into the two most plausible models,FFA-only and modified SSA plus partial FFA toward the receding lobe.In the FFA ϩbeaming model,the intrinsic emission from the two lobes is the optically thin syn-chrotron emission,and it undergoes different FFA.In the SSA ϩbeaming model,the intrinsic emission from the two lobes is the synchrotron emission with self-absorption,and the emis-sion from the SW lobe further undergoes an extra FFA that could be due to the ionized gas in a disk or torus perpendicular to the jet.It is clear that our spectral fit with both models does not favor one model over another as the dominant process for the observed spectral turnover.Future high-resolution obser-vations at lower frequencies are necessary to further differ-entiate these two models.However,the fitted beaming param-eters from the two models are almost the same.The advance speed of the lobes 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