Microlensing Searches of Dark Matter

Third Latin American Symposium on High Energy Physics

PROCEEDINGS

Microlensing searches of dark matter

Esteban Roulet Depto. de F´ısica, Universidad Nacional de La Plata CC67, 1900, Argentina. E-mail: [email protected]

Abstract: The evolution of the observational results of microlensing towards the LMC and some of the suggested interpretations to account for them are discussed. It is emphasized that the results at present are indicative of a lensing population of white dwarfs, possibly in the spheroid (not dark halo) of the Galaxy, together with the more standard backgrounds of stellar populations in the Magellanic Clouds and in the Galaxy. This is also hinted by dynamical estimates of the spheroid mass and by recent direct searches of old white dwarfs.

1. Introduction: as stellar remnants (white dwarfs, neutron stars, black holes), brown dwarfs (stars with mass m< To understand the nature of the dark matter is 0.1M , which never become hot enough to start one of the pressing unsolved mysteries in cosmol- sustained nuclear fusion reactions) or even plan- ogy and particle physics nowadays. The dark ets. Also cold gas clouds have been suggested as matter problem is the fact that the matter in dark baryonic constituents of the galactic halos. luminous forms (stars and gas) is inferred to ac- The main constraints on the amount of baryons count only for Ωlum ' 0.007, i.e. for less than one percent of the critical density. On the other in the universe come from the theory of primor- ' . hand, dynamical estimates based on the gravita- dial nucleosynthesis, which requires Ωb 0 01– . / H / 2 tional influence of the mass on test bodies (gas 0 05 ( 0 70 km/s/Mpc) , with the lower (higher) orbiting galaxies, galaxies moving inside clusters) values corresponding to the high (low) primor- imply that there is at least ten times more ‘dark’ dial deuterium abundance determinations from mass than luminous one on galactic scales, and QSO absorption lines [1]. Hence, we see that for H ' even more (Ω ∼ 0.3) on cluster scales. The issue a Hubble constant 0 50–70 km/s/Mpc nu- on even larger scales is still unsettled, existing at cleosynthesis indicates that dark baryons should present indications in favor of some dark energy exist and that their total amount is probably in- sufficient to account for dark galactic halos (Ω ' (cosmological constant) accounting for ΩΛ ' 0.7, . i.e. filling the gap up to the inflation preferred 0 1). Clearly to account for the observations on value Ω = 1 corresponding to a flat universe. cluster scales non-baryonic dark matter is also The possible constituents of the dark matter required, and it would then be natural to expect naturally split into baryonic and non-baryonic to have some amount of it also at galactic scales. candidates. The last ones would be some kind of Although dark compact objects are, by defi- weakly interacting particle permeating the uni- nition, very hard to be seen directly, they may re- verse, such as supersymmetric neutralinos, ax- veal themselves through the gravitational lensing ions or massive neutrinos, while the first ones effect they produce on background stars. Indeed would be made of just ordinary protons and neu- in 1986 Paczynski [2] showed that by monitor- trons hidden in some non-luminous forms. The ing a few million stars in the Large Magellanic simplest examples to achieve this would be to Cloud (LMC) during a few years would allow to have them in MACHOs (the acronym for mas- determine whether the dark halo of the Galaxy sive astrophysical compact halo objects), such consists of MACHOs with masses in the range Third Latin American Symposium on High Energy Physics Esteban Roulet

−7 2 10 –10 M , covering essentially all the range of closest approach. Hence, the amplification will of suggested candidates. Soon after, with the ad- vary with time in a very specific form and it is vent of CCDs this program became feasible and sizeable (A>1.34) as long as the lens distance several groups started the searches at the begin- to the line of sight is not larger than RE. Hence, ning of the nineties. one can estimate the optical depth, i.e. the prob- ability that a given star is magnified significantly 2. Microlensing expectations: for a given lens distribution with density n`,as the number of lenses within a distance RE from The gravitational deflection of light by massive the l.o.s.. If the lenses are assumed to have a bodies is one of the predictions of general relativ- common mass m, one has n` = ρ`/m, and hence ity which is now tested to better than the percent Z D 4π os level. This phenomenon leads to several beautiful τ D R2 ρ . = m d o` E ` effects such as the multiple imaging of QSOs by 0 intervening galaxies, giant arcs around clusters In the case of a halo consisting fully of MACHOs, or weak lensing distortions of faint background the lens density will be just the halo density, galaxies, which have the potential of giving cru- which from the observed rotation curve of the cial information for cosmology (measurement of Galaxy should be H0 from the time delays between different QSO 2 2 H r0 + a images, estimates of cluster masses, etc.). When ρH ' ρ0 , r2 + a2 the deflector is a compact star like object, a MA- CHO, two images of the background sources are with r0 =8.5 kpc the distance to the galactic produced, one on each side of the deflector. In center, the core radius a is of a few kpc and the H −2 3 the particular case of perfect lens-source align- local halo density is ρ0 ' 10 M /pc . This ment, the image is a ring with angular size (Ein- would lead to a predicted optical depth for LMC H −7 stein’s angle) stars of τ ' 4 × 10 . s The timescale of the events, defined as T ≡ ⊥ m − x RE/v (and determined from a fit to the light θ ' (1 ) 10kpc, E mas A u M Do` curve with the theoretical expressionp for ( )) has an average value hT i'65d m/M given where taking Dos as the distance from the ob- the typical velocity dispersion expected for halo server to the source, Do` ≡ xDos is the distance objects (σ ' 155 km/s). One can show that for to the lens. Hence, for lenses at a few kpc dis- 100% efficient searches the number of expected p tance with masses in the range of interest for events is N =(2/π)(τ/hTi)×Exposure ' 20 events M /m(Expos the MACHO searches this angle is much smaller Actually, the efficiencies are ≤ 30% and are time than the typical telescope resolution (∼ 40 mas dependent, so that a detailed prediction requires for HST!) and hence cannot be resolved. How- to convolute the differential rates with the effi- ever, the important effect is that the brightness ciencies (and also with the mass distribution of of the source is magnified due to a lensing effect the lenses). (for reviews see refs. [3, 4]) by a total amount

u2 +2 3. First microlensing results and their A = √ u u2 +4 interpretation

2 2 2 where u = ξ /RE,withRE =θEDo` being the By 1992 the observational searches towards the radius of the Einstein ring in the lens plane and LMC by the french EROS and australo-american ξ is the distance between the lens and the line of MACHO collaborations had started and already sight to the source. Due to the lens relative mo- after one year the ﬁrst candidate events had showed tion orthogonally to the l.o.s. with velocity v⊥, up. It soon became apparent however that the 2 2 ⊥2 2 one has ξ = b + v (t − t0) ,withbthe impact number of events observed were a factor ∼ 5be- parameter of the lens trajectory and t0 the time low the expectations from a halo made of objects

2 Third Latin American Symposium on High Energy Physics Esteban Roulet lighter than a few solar masses. The estimate of also as high velocity stars nearby (the observed the optical depth to the LMC from the first 3 velocity dispersion is σ ' 120 km/s). It was +7 −8 MACHO events [5] was indeed τ =8.8−5 × 10 formed in the first Gyrs of the Galaxy lifetime, and the one from the first two EROS events [6] has a probably slightly flattened spherical shape +11 −8 −α was similar, τ =8.2−5 ×10 . The typical event (c/a ' 0.7–1)with density profile r ,withα' durations of a few weeks were also indicative of 2.5–3.5 [10]. The predicted optical depth for this lens masses in the ballpark of 0.1 M , i.e. in population, adopting c/a =1andα=3.5, is S −8 S −4 3 the limit between brown dwarfs and very light τ ' 0.3 × 10 (ρ0 /10 M /pc ). This value main sequence stars. Furthermore, the non ob- would increase by 50% for α =2.5 and decrease servation of short duration events (T less than by ∼ 25% for c/a =0.7. The spheroid density S −5 3 a few days) by the EROS CCD program and inferred from star counts, ρ0 ' 5 × 10 M /pc by MACHO set stringent bounds on light lenses leads then to a tiny optical depth. However, −7 −3 (10 Milky Way has a dark halo, the rota- ally below 10−8. tion curve of the LMC suggests that this galaxy The Galaxy is also known to have a thicker also has a dark halo around it. The optical depth disc of stars, with h ' 1 kpc, probably origi- associated to it amounts to ∼ 8 × 10−8 [15, 16]. nating from a past merger of a satellite which Hence, if all the dark matter were in MACHOs somehow heated the disc stars. The column den- the total optical depth would be 20% higher than sity associated to the observed thick disc stars is the prediction from the Milky Way halo alone, TD 2 typically taken as Σ ∼ 4M /pc , and hence and this clearly worsens the discrepancies with the expected optical depth is tiny (∼ 0.5×10−8). the observations. It has to be stressed that no However, in ref. [8] it was noticed that the maxi- stellar population has been observed with the ex- mum allowed column density consistent with dy- pected LMC halo distribution. The predictions TD 2 namical observations, Σmax ' 50M /pc , would for the observed distributions of LMC stars (disc lead to τ ' 5 × 10−8(h/kpc), and hence for the and bar) are more delicate. It was actually sug- scale height adopted there (1.4 kpc) it would al- gested that the optical depth towards the central ready be close to the observed value. bar could be ∼ 5 × 10−8 [17], and hence of the Another known stellar galactic population is order of the observed τ. However, outside the the spheroid (or ‘stellar halo’), observed through bar, where several of the observed events actu- the old metal poor stars at high latitudes and ally are, τ falls significantly, and the most recent

3 Third Latin American Symposium on High Energy Physics Esteban Roulet estimates for the expected average depth [18] are going alerted microlensing events (GMAN, MOA, τ ' 2.4×10−8, although with some spread among PLANET, MPS). This allowed for instance to different models. measure in great detail an event in the Small Summarizing, the expectations from known Magellanic Cloud caused by a binary lens [22]. stellar populations amount to τ ' 3–4×10−8, When the lens is a binary, the signatures are while from the Milky Way and LMC halos one quite different from the single lens case. For would expect τ ' 5 × 10−7. The observed value large impact parameters there are now three im- ∼ 8 × 10−8 was clearly larger than the first one, ages of the source, one on the exterior side of but only a small fraction of the second. Since the each of the lenses and the third one in between main purpose of the microlensing searches was the lenses. An extra pair of images can appear to establish whether the halo consisted of MA- however for small impact parameters when the CHOs, the results are most commonly presented source crosses the so called caustic, and then two in terms of the fraction f of the Milky Way halo images disappear again when the source leaves in the form of compact objects, which for the ob- the region delimited by the caustic. At these served τ would correspond to f ' 20%. The re- caustic crossings the magnification formally di- maining fraction could be just in cold gas clouds verges. This means that one has an extremely or in non-baryonic dark matter. An alternative powerful magnifying glass to look at the source. explanation was to have instead a heavy spheroid Actually, effects associated to the finite size of or thick disc made mainly of MACHOs or a very the source become observable and in particular large LMC self-lensing contribution, and instead they limit the maximum amplification to a fi- a completely non-baryonic halo. nite value. If one knows the radius of the source, one can also infer the relative lens-source proper 4. The second period (1996-2000) motion µ, and since this quantity is expected to differ significantly for lenses in the Magellanic In 1996, the results of the analysis of the first two Clouds (µ ∼ 1 km/s/kpc) or in the galactic pop- years of MACHO data were announced [19]. A ulations (µ ≥ 10 km/s/kpc), it was possible to total of 8 candidate events were observed and the establish that the binary lens belonged to the average event duration turned out to be longer. SMC and not to the halo. Also one of the MA- +1.4 −7 The conclusion was that now τ =2.9−0.9 × 10 CHO LMC events was a binary and its proper and also that the typical lens masses increased motion again suggested that it belonged to the to m ' 0.5M . The picture which emerged then LMC. This shows that indeed the contribution was that 50% of the halo should be in objects of the lenses in the Magellanic Clouds is signifi- with the characteristic mass of a white dwarf. cant, and actually in the SMC it is expected to This scenario was quite unexpected, and was shown be relatively larger than in the LMC due to the to be also potentially in trouble with the chemical elongated shape of the SMC along the l.o.s.. enrichment of the galaxy due to all the metal pollution which would result from the white dwarf 5. Recent developments progenitors [20, 21]. There were also attempts to explain the observed rates as due to some The most recent microlensing results appeared a tidal debris of the LMC or even due to a previ- few months ago and again changed the overall ously undetected satellite galaxy along the l.o.s. picture. The analysis of 5.7 yrs of MACHO data to the LMC [23], but it is not clear whether [9] in 30 fields (out of a total of 82) found 13–17 these ideas are actually supported by observa- events (depending on the criteria used), leading +0.4 tions [24, 25, 26, 27]. to a significantly reduced depth τ =1.1−0.3 × In the period after 1996 significant improve- 10−7 (for the 13 event sample). Another relevant ments on the observational programs took place: observation was that no particular increase in τ the EROS and OGLE collaborations started to towards the center of the Cloud was observed, use better cameras in new telescopes and net- contrary to the expectations from a rate domi- works of telescopes were organized to follow on- nated by LMC stars. Also the EROS group pre-

4 Third Latin American Symposium on High Energy Physics Esteban Roulet sented the reanalysis of their old data together mass function of spheroid stars would have to be with two new years of EROS II data [28], find- peaked at a few solar masses to account for the ing a total of only 4 events, a result inconsistent large number of white dwarf progenitors, and the with the ’96 MACHO result. This shifted the gas released during the ejection of their envelopes situation somehow back to the initial stage in would have ended up in the disc and bulge, but which the observed rates are a factor ∼ 5below producing certainly less metal pollution than the the halo predictions but ∼ 3–4 above the expec- halo white dwarf models due to the much smaller tations from known populations. The inferred total spheroid mass. The future searches of white masses m ' 0.5M continue to suggest however dwarfs should also be able to distinguish between that the objects could be old white dwarfs. thick disc and spheroid/halo populations due to Another important related result has been their significantly different proper motions. the recent activity related to the direct search Regarding the future of microlensing obser- of old white dwarfs. Hansen [29] realized that vations, the MACHO experiment has finished tak- the spectra of old white dwarfs having molecu- ing data, while EROS II and OGLE II are still lar hydrogen atmospheres (i.e. probably half of running. A significant increase in the number of the total) would look much bluer and brighter events is then expected when all the data avail- than previously believed due to the strong ab- able gets analysed. Furthermore, a new anal- sorption at wavelength larger than 1 µm by their ysis technique (Difference Image Analysis), de- atmospheres. This prediction was actually con- vised for the study of lensing in crowded fields firmed by the direct measurement of the spec- such as the Andromeda galaxy, has been suc- trum of a cool (T ' 3800 ◦K) nearby white cessfully applied to several bulge fields by the dwarf [30]. With this new scenario the search MACHO group [34], doubling the number of ob- for old white dwarfs becomes feasible, and in- served events with respect to previous analyses, deed analyses of two Hubble Deep Fields taken and also by EROS to their first CCD data [35]. two years apart were done searching for objects The use of this technique for all the LMC data with large proper motions [31]. The candidate should then also help to get more decent statis- objects they found, with colours consistent with tics and hence to discriminate among the popu- being old ‘halo’ white dwarfs, led them to infer lation(s) responsible for the microlensing events. that their density could be comparable to the lo- Clearly the possibility that the dark halo is com- −2 3 cal halo density (∼ 10 M /pc ). However, re- pletely made of non-baryonic dark matter still cently two new searches in larger nearby volumes remains open, and hence the search for its even (not so deep but wider) have found results in- more elusive constituents is crucial to finally un- consistent with such large white dwarf densities. ravel the dark matter mystery. Flynn et al. [32] found no candidates while ex- pecting a few tens based on ref. [31], while Ibata Acknowledgments et al. found two nearby white dwarfs [33], infer- ∼ × −4M / 3 ringadensityof 7 10 pc for these This work was supported by CONICET, AN- hydrogen atmosphere white dwarfs. A remark- PCyT and Fundación Antorchas, Argentina. able thing is that this value is just in the required range to account for the missing mass of References the heavy spheroid models, whose proper motions would be only ∼ 20% smaller than those [1] K. Olive, G. Steigman and T. P. Walker, astro- assumed for ‘dark halo’ objects and hence con- ph/9905320. sistent with those found. To analyse the pos- [2] B. Paczynski, ApJ 304 (1986) 1. sibility that these old white dwarfs are geneti- [3] E. Roulet and S. Mollerach, Phys. Rep. 279 cally related to the old population II spheroid (1997) 68. stars, and not to an independent halo population with no observed counterpart, seems then partic- [4] B. Paczynski, ARAA 34 (1996) 419. ularly relevant. If this were the case, the initial [5] C. Alcock et al., ApJ 461 (1996) 84.

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