Recent Developments in Gravitational Microlensing

a r X i v :0803.4324v1[astro-ph]3Mar28The Variable Universe:A Celebration of Bohdan Paczy´n ski ASP Conference Series,Vol.000,2008K.Stanek,ed.Recent Developments in Gravitational Microlensing Andrew Gould Ohio State University Abstract.Twenty-one years after Bohdan’s seminal paper launched the field of gravitational microlensing,it has radically diversified from a method narrowly focused on finding dark matter to a very general astronomical tool.Microlensing has now detected 12planets,including several that are inaccessible by other search methods.It has resolved the surfaces of distant stars,served as a magnifying glass to take spectra of extremely faint objects,and revealed a number of surprising phenomena.I take a sweeping look at this remarkable technique,giving equal weight to its successes and to the tensions that are continuing to propel it forward.1.Introduction While the idea of microlensing goes back to the famous Einstein (1936)paper in Science ,and is worked out in even greater detail in Einstein’s notebooks from 1912(Renn et al.1997),Bohdan Paczy´n ski (1986)was the first to recognize that with the arrival of modern CCDs and the high-speed computing required to analyze them,microlensing’s time had come.The focus of Bohdan’s original paper on this subject was dark matter,and it prompted two major surveys toward the Large Magellanic Cloud (LMC),which are reviewed by Charles Alcock in this volume.But Bohdan was always looking to push microlensing in new directions,most notably in his two seminal papers that launched microlensing studies of Galactic structure (Paczy´n ski 1991)and microlensing planet searches (Mao &Paczy´n ski 1991).Over the past 15years,microlensing has developed as an important tool in both these areas,and a thirdarea as well:stellar atmospheres.Parallel to this broad invasion of several areas of astrophysics,microlens-ing activists pushed the field in a number of narrow,rather arcane,directions,exploring weird higher-order effects such as those due to finite source size,or-bital parallax,terrestrial parallax,xallarap,lens rotation,as well as degenerate solutions,and microlensed variables.One of the most exciting and unexpected developments in microlensing has been that these weird effects,originally of in-terest only to microlensing nerds,have started to interpenetrate with the more mainstream investigations outlined in the previous paragraph.This is because they provide additional information that is of interest to a more general astro-nomical audience and make microlensing applications more powerful.In this contribution,I review some of these developments,pointing to these interconnections whenever possible.12Andrew GouldO L D L D LSS IθS αθI −θSS L O r E~r E θE α= −−−−−4GM r E c2Figure 1.Left:Point-lens microlensing.Mass (M)deflects light from source (S)by Einstein bending angle α=4GM/(c 2D L θI )to observer (O).Right:Relation of higher-order observables,the angular (θE )and projected (˜r E )Einstein radii,to physical characteristics of the lensing system.Adapted from Gould (2000).2.Microlensing BasicsIt is a mark of the simplicity of point-lens microlensing that the basic results,including the main higher-order effects,can be encapsulated in two simple dia-grams (Fig.1)and a few simple equations.Equating (from Fig.1a)u 2+4)/2,where u ≡θS /θE and u ±≡θI ±/θE are scaled to θE .Because surface brightness is conserved,the magnification A is given by the ratio of the combined area of the images to the area of the source:A ±= u ±du ,A =A ++A −=u 2+2u 2+4.(1)The two higher-order observables shown in Figure 1b,the angular (θE )and projected (˜r E )Einstein radii,can be measured if the event can be compared to standard rulers on the sky and observer planes,respectively.See §5.These are then easily related to the mass M and the source-lens relative parallax πrel =AU(D −1L −D −1S ).First,α/˜r E =θE /r E ,so θE ˜r E =αr E =4GM/c 2.Next,by the exterior angle theorem,θE =˜r E /D L −˜r E /D S =(˜r E /AU)πrel .In summary,M =θE κMπrel ,πE = κM ,(2)Gravitational Microlensing3 whereκ≡4GM/(c2AU)∼8.14mas M−1⊙andπE≡AU/˜r E.3.Microlensing Planet SearchesMao&Paczy´n ski(1991)showed that if a lens had a companion,it would distort the primary lens’s magnificationfield,inducing an“astigmatism”or“caustic structure”near the peak.These caustics are closed contours of formally infinite magnification(see,e.g.,Fig.2a,below):the magnification diverges according to a square-root singularity as the source approaches the caustic from the inside. The bigger the companion,the bigger the caustic,and so the greater the chance that the source would pass close enough to the lens to be affected.But their main point was:even a planet could in principle be detected.Of course,just as the planet perturbs the magnification pattern of its host, the host also perturbs the planetfield.Since the host is much bigger than the planet,this perturbation is also much bigger,so a random source is much more likely to pass over the resulting“planetary caustic”than the“central caustic”highlighted by Mao&Paczy´n ski(1991).This fact led Gould&Loeb(1992)to focus on planetary caustics the next year when we advocated a search+followup strategy forfinding planets.Microlensing events are extremely rare(optical depthτ∼10−6),so huge areas must be surveyed each night,which limits the number of observations of eachfield.But since the planetary perturbations are extremely short t p∼(M planet/M Jupiter)1/2day,the events that are found must be intensively monitored by other,“followup”telescopes scattered around the globe,in order to trace out the planetary signature.Although hardly noticed at the time,this subtle difference in emphasis be-tween these two papers grew into a major divergence,which has since dominated all issues connected with microlensing planet searches.3.1.1st Microlensing Planet–Pure-Survey JupiterIn1995,Penny Sackett formed the PLANET collaboration(Albrow et al.1998) to carry out this survey+followup strategy,but it was not until2003that thefirst planet was discovered,OGLE-2003-BLG-235/MOA-2003-BLG-53Lb,and this was by the survey teams themselves,not the followup groups(Bond et al.2004). Why?The event had a7-day planetary deviation,so the nightly survey data were basically adequate to characterize it,which would not have been the case had it lasted just1day(or less),as expected.The perturbation was long because the planet was sitting right next to the Einstein ring,and so induced a big caustic.Such alignments are rare,but the survey groups are well poised tofind them because they monitor of order600events per year.The followup groups, by contrast,monitor only the few dozen“most promising”events.The survey-group discovery of thefirst microlensing planet was thefirst piece of evidence that the survey+followup strategy originally advocated by Gould&Loeb(1992) would require radical rethinking if it were to be successful.3.2.High-Magnification EventsIn the meantime,Jaroszy´n ski&Paczy´n ski(2002)found a planet-candidate based on a single deviant point,which consequently could not be confirmed.This4Andrew Gouldprompted Andrzej Udalski(see these proceedings)to develop the OGLE“Early Early Warning System(EEWS)”,which would alert the OGLE observer when an already-identified event was behaving“unusually”,thereby enabling OGLE both to alert the community and to carry out“auto-followup”observations itself.This system actually went offon OGLE-2004-BLG-343,a spectacular magnification A=3000event,but unfortunately the alarm was ignored by the observer.However,Dong et al.(2006)showed that if this event had been prop-erly monitored,it would have had excellent sensitivity to Earth-mass planets, and even some sensitivity to Mars-mass planets.That is,the“central caus-tic”(i.e.high-magnification)events originally highlighted by Mao&Paczy´n ski (1991)were actually much better targets than the larger-caustic events singled out by Gould&Loeb(1992).Even though the caustics(and so the number of caustic-crossing events)are smaller,the events in which this happens can be identified in advance,enabling intensive followup right in the period of greatest sensitivity.Actually,this same point had previously been made by several the-orists(Griest&Safizadeh1998;Rattenbury et al.2002),but as often happens, it was the practical demonstration that had the biggest impact.Another,completely unrelated development,pushed the Microlensing Fol-low Up Network(µFUN)in the direction of high-mag events.Jennie McCormick, a New Zealand amateur,sent me an email one day saying“I have data on your event,what do you want me to do with it?”Of course,it seemed preposterous that a12′′telescope in one of the wettest places in world could make a material contribution,but I started sending her our microlensing alerts.She contacted Grant Christie,another NZ amateur,who ultimately made contact with almost a dozen other amateurs around the southern hemisphere.As these amateurs had to work during the day,we had to limit requests to only the most sensi-tive events,generally high-mag events.Eventually,we realized that even at our professional-class telescopes,we were wasting our time following non-high-mag events.By2005,our conversion was complete.3.3.2nd Microlensing Planet–High-Mag JupiterThefirst fruit of this new strategy came early the next year when OGLE-2005-BLG-071started approaching high magnification.Both OGLE andµFUN Chile intensively observed the event as it approached its peak until observations were cut offby dawn.Shortly thereafter,however,Jennie and Grant began observing on their12′′and14′′scopes(see Fig.2a).Over four nights,OGLE andµFUN telescopes traced out a triple-peak event:two big peaksflanking a small peak in the middle,implying that the source passed by a caustic with three cusps: strong,weak,strong(see lower inset to Fig.2a).It can be proved mathematically that such a geometry can only be produced by a planet.Jennie’s comment:“It just shows that you can be a mother,you can work full time,and you can still go out there andfind planets.”3.4.3rd Microlensing Planet–Survey+Followup Super-EarthThe PLANET collaboration has dedicated access to41m-class telescopes for May–August.This caused them to miss OGLE-2005-BLG-071,which peaked in April,but enables them to follow many more events during the4-month“high season”,i.e.,not just the rich but rare high-mag events,but the run-of-the-millGravitational Microlensing 53440346034803500HJD - 2450000Figure 2.Left:Jupiter-mass planet in high-mag event OGLE-2005-BLG-071.Two major peaks and small peak in middle (upper inset)imply source passes by two major cusps and a weak cusp in between (lower inset).This caustic geometry can only be produced by planetary companions,in this case with mass ratio q =7×10−3.From Udalski et al.(2005).Right:Neptune-mass planet in high-mag event OGLE-2005-BLG-169.Upper panel shows “basically normal”event,but residuals to point-lens fit reveal 2%deviations.Detailed modeling is required to uncover the caustic structure (inset)due to planet with q =8×10−5,i.e.almost 100times smaller than OGLE-2005-BLG-071.From Gould et al.(2006).events originally advocated by Avi and me.One of these,OGLE-2005-BLG-390showed a second bump well after peak.The rounded shape of this bump implies that its full duration,2t p ∼0.6days is dominated by the size of the source rather than the caustic.This is expected because the source was very bright and red,hence very big.Under these conditions,it is straightforward to show that the planet/star mass ratio is approximately,q =(A p /2)(t p /t E )2,where A p is the amplitude of the second bump and t E =10days is the Einstein timescale.That is,one can simply read offthe lightcurve,without any analysis,q =9×10−5.In fact,detailed analysis (Beaulieu et al.2006)yields q =8×10−5,corresponding to5.5Earth masses at the estimated M ∼0.2M ⊙mass of the host.This is also the first event for which both survey and followup were absolutely required.Both of the previous planets had perturbations lasting several days,which allowed them to be basically characterized from survey data alone,even though the followup data did substantially improve the characterization in the case of OGLE-2005-BLG-071Lb.3.5.4th Microlensing Planet –High-Mag NeptuneJust a week after OGLE-2005-BLG-071subsided,another event was approaching peak,OGLE-2005-BLG-169.In this case,OGLE did not observe the event at all for 6days before peak,the first 4because of weather and the last 2because the telescope was dedicated to Chilean observations.Based on “general suspicion”that it might become high-mag,µFUN obtained some observations,but the night before peak,the case was still not convincing:µFUN (i.e.,AG)failed to pursue6Andrew Gouldthe event aggressively,but did ask Andrzej(who was at the OGLE telescope, service observing for the Chileans)to sneak in an observation of this event.An email came back at3a.m.:the event was extremely high-mag and there were no observations being taken!I was asleep,but heard the“ping”of my email and went upstairs to have a look.I was quite dazed but eventually realized that the event could be observed over peak from MDM,despite its northern location.I called up the observer who happened to be an OSU grad student, Deokkeun An.I implored him to take time out of his own observing to obtain 9images of this event over the next3hours.Recognizing that my request was much too timid,Deokkeun actually took over1000observations,which traced out a2%deviation from a magnification A=800event(see Fig.2b).As in a number of other microlensing events,the initiative of the observer proved crucial! Exhaustive analysis eventually demonstrated that this was a“cold Neptune”with q=8×10−5.3.6.5th+6th Microlensing Planets–Jupiter/Saturn SystemOn28March2006,the OGLE EEWS noted a tiny0.1mag deviation in the previously unremarkable lightcurve of OGLE-2006-BLG-109,but Andrzej was confident enough to issue a public announcement:“Because short-lived,low amplitude anomalies can be a signature of a planetary companion to the lensing star(cf.OGLE-2005-BLG-390)follow-up observations of OGLE-2006-BLG-109 are strongly encouraged!!!”This triggered observations from MDM only a few hours later,which ultimately were important,but the event quickly returned to normal.A few days later,however,it was clearly becoming high-mag,and so drew many observations.Grant Christie caught what seemed like a caustic exit at magnification roughly A=500,8days after thefirst deviation,which definitely raised the excitement level.Within hours,Scott Gaudi had a tentative model.He drew a6-sided(or6-cusp)caustic due to a Saturn-mass-ratio planet. Thefirst small bump occurred when the source passed by a cusp.Somehow the source had entered the caustic without being noticed and had just exited.Scott’s trajectory would take the source by another cusp3days later,so he predicted another bump at that time.However,reports soon came in from the Wise observatory that the event was rising again,and hours later OGLE observations showed that it was again falling.This new bump,just12hours after Grant’s “caustic exit”,seemed to contradict Scott’s3-day prediction.Nevertheless,after 3days,Scott’s predicted bump did occur:the Israel/Chile bump had been due to another planet,this one of Jupiter mass-ratio.It took quite a while to fully decipher this event.The Saturn mass planet was very close to the Einstein ring.In such cases,the size of the caustic scales as|b−1|−1,where b is the planet-star separation in units of the Einstein ring. If b∼1,then very small changes in b can lead to large changes in the caustic. Thus,the tiny planetary motion during the8-day interval from thefirst cusp approach to the caustic exit can lead to big changes in the caustic.On the plus side,this means that if all these features can be properly modeled,one can measure some of the planet-orbit parameters,something no one thought would be possible when microlensing planet searches were initiated.On the minus side,analysis of the lightcurve requires very smart algorithms applied to a supercomputer.Dave Bennett took the lead in this analysis,eventuallyGravitational Microlensing7Figure 3.First Jupiter/Saturn analog.This spectacular lightcurve of OGLE-2006-BLG-109has5distinct lightcurve features,which together re-veal two planets.Features1,2,3,and5come from the black portion of the caustic(inset A)due to a Saturn mass-ratio planet very close to the Ein-stein ring.Feature4,a sharp“bump”seen from Israel and Chile,cannot be explained by this planet,but it occurs very near the center of the lens ge-ometry,just where perturbations would be expected from other planets thatare not near the Einstein ring(inset B).This proves to have a Jupiter mass ratio.Because the Saturn is near the Einstein ring,its very small motion leads to dramatic changes in the caustic between the time of Feature1(gray caustic)and the time of Feature3(black caustic).Twelve observatories con-tributed data,notably OGLE(who announced Feature1in real time)and New Zealand amateurs Grant Christie and Jennie McCormick,who caughtthe peak at Feature3.From Gaudi et al.(2008a).8Andrew Gouldlog(Temp/Kelvin)l o g (M /M J ) 3.53 2.52 1.5−2−101RV Transits µlensingB −V M V.511.51050Figure 4.Left:Planet mass vs.equilibrium temperature of planets de-tected by the Doppler (red circles ),transit (blue squares ),and microlensing (green stars )techniques,as of June 2007.Microlensing detects planets in the cold,outer regions of their solar systems,where planet formation is ex-pected to be most robust.Right:CMD of the host stars of microlensing planets.Microlensing detects planets without serious selection bias due to host properties.It demonstrates that planet frequency in the outer regions is not strongly dependent on stellar type.deriving more comprehensive parameters for this system than any other.It is a true Jupiter/Saturn analog,with similar mass ratios and separation ratios as the solar-system gas giants.The equilibrium temperatures of these planets are also similar to Jupiter/Saturn,but a bit cooler (Gaudi et al.2008a).It appears that in 2007,microlensers have discovered about 6more planets,but I have neither the space nor the permission to write about these in detail.3.7.What Have We Learned About Planets?Given that microlensing has discovered only a handful of planets,compared to 250+by other techniques,the scientific payoffhas been remarkably high.The difference between community expectations (which were rather dim)and what has actually been achieved is due to two factors.First,microlensing detections have yielded far more information about the individual star-planet systems than had been thought possible.Originally,it was believed that microlensing detections would return exactly two pieces of information about the system,the planet/star mass ratio q and the planet-star projected separation (in units of the Einstein radius θE )b .Only the first quantity was regarded as truly interesting,since the second could not be translated into a physical distance without knowing both θE and the distance to the lens D L .In practice,we have generally been able to make pretty good estimates of the host mass M (and hence the planet mass m =qM ),as well as θE and D L (and so the projected separation r ⊥=bD L θE ).I will discuss exactly how we do this in §5.2.Second,microlensing probes a region of parameter space to which other methods are at present largely insensitive,namely the cold regions out pastGravitational Microlensing9 the snow line,where(at least according standard core-accretion theory)planet formation should be most robust.See Figure4a.Microlensing is also essentially unbiased by host mass,in sharp contrast to other methods.Hence,as shown by the CMD of planet hosts(Fig.4b),microlensing detects planets of the most common potential hosts,te-type stars.The fact that there are two microlensing detections of cold Neptunes/super-Earths means that these planets are probably extremely common.Gould et al. (2006)estimated that if all stars had planets in this mass range,and in a0.4dex annulus bracketing the Einstein ring of the host,then there would have been about6detections.In fact there were2,indicating a rate of roughly1/3in this fairly narrow range of radii.Microlensing sensitivity scales roughly as planet mass.There are4Jovian-mass detections and two Neptune-mass detections,and the two classes of planets differ in mass by about1.5dex(see Fig.4a).This indicates that gas giants are of order7times less common than ice giants.Of the5planetary hosts,one has two detected planets.As discussed above, these are close analogs of the Jupiter/Saturn pair that dominate the mass in our own solar system.Before planets were discovered,it was generally believed that most solar systems would be like our own.Then with the discovery of the pulsar planets and51Peg,weird planets became more fashionable.But the fact is,only microlensing actually has sensitivity to Jupiter/Saturn analogs,so this is the only information we have on how common they are.Microlensing has detected Jovian-mass planets around3stars(OGLE-2003-BLG-235/MOA-2003-BLG-53,OGLE-2005-BLG-071,and OGLE-2006-BLG-109).In thefirst of these,there was a very low probability of detecting a second,Saturn-mass companion had it been there.In the second,there was a modest(roughly30%) chance.In the third there was an excellent chance(and it was actually detected). This suggests that for systems where there is a Jupiter,it may be highly likely that there is also a Saturn.Higher-Order Microlensing EffectsBohdan was fond of pointing out that microlensing is fundamentally such a simple phenomenon that one could predict effects fromfirst principles and then go out and observe these effects in actual events.His favorite example of this was parallax.4.Microlens ParallaxesAlcock et al.(1995)made thefirst microlensing parallax detection but parallax was actually observed in the veryfirst microlensing event observed toward the LMC,MACHO-LMC-5,although no one realized it at the time(Alcock et al. 1997).Indeed no one realized it was thefirst event at the time:hence its enumer-ation.MACHO-LMC-5was weird for other reasons:the CMD position of the apparent source star does not coincide with any LMC population.Gould et al. (1997)had already suggested that this“source”was a foreground M dwarf and that it actually was the lens.After6years,MACHO observed this and many other events with HST and resolved two stars separated by about0.1′′,a blue10Andrew Gould 2.5 l o g (F /F b a s e )0102030405001234JD − 2449000R e s i du a l s 01020304050−.4−.2.2.4E i n s t e i n r a d i i (N o r t h )Einstein radii (East)1.50−.5−1−1−.50.51Figure 5.Microlens parallaxes and degeneracies.Left:Lightcurve of MACHO-LMC-5shows clear asymmetry due to accelerated motion of Earth,falling more rapidly than its rise.Right:4possible trajectories of source-lens separation,all curved due to accelerated motion of Earth projected onto the plane of the sky (lower inset).Deviations (from straight lines)are propor-tional to ∆S (the accelerated displacement of the Earth)and πE (=AU/˜r E ,the size of the Earth’s orbit relative to the projected Einstein radius).The fact that there are two sets of trajectories with radically different directions and Einstein radii was totally unexpected,but is now understood analytically.From Gould (2004).LMC star that was clearly the source and a red foreground star,the putative lens (Alcock et al.2000).But how could one be sure that the red star was not just an unrelated foreground star?Dave Bennett went back to original lightcurve and noticed the slight asym-metry (Fig.5a),which led him to fit it for microlens parallax.In analogy to trigonometric parallax,the amplitude of the deviation from rectilinear motion of the source-lens trajectory in microlensing parallax is inversely proportional to the size of what one is trying to measure,i.e.,the projected Einstein radius ˜r E .So just as one writes π=AU /D for trig parallax,it is convenient to define the microlens parallax πE =AU /˜r E .However,in contrast to trig parallaxes,the microlens parallax simultaneously measures the direction of lens-source relative motion.So the microlens parallax is actually a vector,πE .Dave found that the direction of πE was the same as the vector linking the red and blue stars (Alcock et al.2001).So the red star was the lens,not just a chance interloper!This result had two important consequences.First,it showed that at least in this case,the lens was not part of a putative dark-matter halo (“MACHO”)population,but was an ordinary disk star.Second,it led to the first mass measurement of an isolated star,which I describe in the next section.Microlens parallax measurements are relatively rare.Poindexter et al.(2005)found only 22events (out of about 3000to that date)for which including par-allax effects decreased χ2by more than 100.Nevertheless,microlens parallaxes have proved incredibly important,as I discuss in §5.4.Gravitational Microlensing115.Microlens MassesFrom equation(2),one can determine the microlens mass(as well as the lens-source relative parallax),if one can just measureθE and˜r E(orπE).As just mentioned,there are very few events for whichπE can be measured.It alsoturns out that there are very few events for which some“angular ruler”on theplane of the sky permits measurement ofθE.The number for which the two mea-surements overlap is minuscule.Nevertheless,microlensing nerds have pursuedmicrolens mass measurements like a holy grail,ultimately with major payoffs.Thefirst microlens mass measurement was EROS-2000-BLG-5(An et al.2002),which I discuss in§5.2..5.1.First Mass Measurement of an Isolated StarThe second was MACHO-LMC-5.At one level this was trivial:since Alcock et al.(2001)had measured the lens-source separation∆θ=0.134′′after∆t=6.3yrs,they could immediately determine the lens-source relative proper motionµrel=21mas yr−1.Then from the measured Einstein timescale t E=21days,theycould inferθE=µrel t E=1.2mas.Unfortunately,when combined with their measurementπE=4.2(and eq.[2]),this gave them a mass M=0.036M⊙anddistance D L=200pc,which of course would be inconsistent with it being visiblein the HST image.Bohdan played a significant role in the resolution of this puzzle.Smith,Mao,&Paczy´n ski (2003)developed an abstract formalism for analyzing parallaxes,which(as ref-eree)I found unexpectedly powerful.They Taylor-expanded the square of thesource-lens separation to fourth order in the approximation of uniform acceler-ation by the Earth.This led them to discover a degeneracy,which changed thetrajectory from one side of the Earth to the other(see Fig.5b,upper inset).Be-cause this degeneracy basically left the magnitude ofπE unchanged,it could notexplain the“wrong”mass obtained by Alcock et al.(2001).However,by includ-ing jerk in the Taylor expansion,I discovered a second,so-called“jerk-parallax”degeneracy,which did yield a differentπE(see Fig.5b,main panel).The dis-tance implied by this solution D L∼550pc was later confirmed by Drake et al.(2004)using trig parallax,and the mass estimate M=0.097±0.016M⊙isconsistent with photometric estimates(Gould et al.2004).5.2.Multiple Paths to Microlens Mass MeasurementsThere are basically4paths to the microlens parallaxπE:Earth-orbital parallax, trigonometric parallax,Earth-satellite parallax,and terrestrial parallax.All fourhave been successfully employed.There are also basically4angular rulers for measuringθE:lens-source proper motion,finite-source effects,image resolution,and centroid displacement.Thefirst of these is measured after the event andthe last three during the event.Only thefirst two have been successfully carriedout.As mentioned,microlens mass measurements require one from column A(πE)and one from column B(θE).For MACHO-LMC-5,θE was measured by lens-source proper motion,butthis is quite unusual:its proper motion was about6times larger than typicallenses toward the bulge,there was a6-year delay for the second epoch,and HST observations were still required to separately resolve the lens and source.By。