GRAVITATIONAL MICROLENSING AND DARK MATTER IN THE GALACTIC HALO PHILIPPE JETZER Paul Scherrer Institute, Laboratory for Astrophysics, CH-5232 Villigen PSI, and Institute of Theoretical Physics, University of Zu¨rich, Winterthurerstrasse 190, CH-8057 Zu¨rich, Switzerland 9 9 Abstract. Wepresentthebasics of microlensing and givean overview of theresults obtained so far. Wealso 9 describe a scenario in which dark clusters of MACHOs (Massive Astrophysical Compact Halo Objects) and 1 cold molecular clouds (mainly of H ) naturally form in the halo at galactocentric distances larger than 10-20 2 n kpc. Moreover, we discuss various experimental tests of this picture in particular a γ-ray emission from the a cloudsduetothescatteringofhigh-energycosmic-rayprotons. Ourestimatefortheγ-rayfluxturnsouttobe J in remarkably good agreement with the recent discovery by Dixon et al. [1] of a possible γ-ray emission from 8 thehalo using EGRET data. 2 v INTRODUCTION 8 5 A central problem in astrophysics concerns the nature of the dark matter in galactic halos, whose presence is 0 1 implied by the flat rotation curves in spiral galaxies. As first proposed by Paczyn´ski [2], gravitational microlensing 0 can provide a decisive answer to that question, and since 1993 this dream has started to become a reality with 9 the detection of several microlensing events towards the Large Magellanic Cloud. Today, although the evidence for 9 MassiveAstrophysicalCompactHaloObjects(MACHOs)isfirm,theimplicationsofthisdiscoverycruciallydepend / h onthe assumedgalacticmodel. Moreover,atleasttwo ofthe eventsfound towardsthe LargeMagellanicCloudsare p due to lenses located in the Clouds themselves. Therefore, it might well be that also the other events or at least a - fractionof them are due to MACHOs in the Clouds. This issue might be solvedwhen more events will be available. o It has become customary to take the standard spherical halo model as a baseline for comparison. Within this r st model, the mass moment method yields an average MACHO mass of [3] 0.27 M⊙. Unfortunately, because of the a presently available limited statistics different data-analysis procedures lead to results which are only marginally : consistent. For instance, the average MACHO mass reported by the MACHO team based on its first two years v i of data is [4] 0.5+−00..32 M⊙. Apart from the low-statistics problem – which will automatically disappear from future X largerdata samples – we feelthat the realquestionis whether the standardsphericalhalo modelcorrectlydescribes r our galaxy. Although the answer was believed to lie in the affirmative for some years, nowadays various arguments a stronglyfavouranonstandardgalactichalo. Indeed,besidestheobservationalevidencethatspiralgalaxiesgenerally haveflattenedhalos,recentdeterminationsofboththediskscalelength,andthemagnitudeandslopeoftherotation atthesolarpositionindicatethatourgalaxyisbestdescribedbythemaximaldiskmodel. Thisconclusionisfurther strengthened by the microlensing results towards the galactic centre, which imply that the bulge is more massive thanpreviouslythought. Correspondingly,the haloplaysalessdominantrolethanwithin the standardhalomodel, thereby reducing the halo microlensing rate as well as the average MACHO mass. A similar result occurs within the King-Michie halo models [5], which take into account the finite escape velocity and the anisotropies in velocity space(typicallyarisingduringthephaseofhaloformation). Moreover,practicallythesameconclusionsalsoholdfor flattened galactic models with a substantialdegree of halo rotation. So, the expected averageMACHO mass should be smaller than within the standard halo model. Still, the problem remains to explain the formation of MACHOs, as well as the nature of the remaining dark matter in galactic halos. We have proposed a scenario [6–8] in which dark clusters of MACHOs and cold molecular clouds – mainly of H2 – naturally form in the halo at galactocentric distances larger than 10 20 kpc (somewhat similar ideas have also − been put forward by Carr and Ashman [9,10], Pfenniger, Combes and Martinet [11], Gerhard and Silk [12] and by Fabian and Nulsen [13]). Here, we discuss the dark matter problem in the halo of our Galaxy in connection with microlensing searches and we briefly review the main features of our scenario, along with its observational implications in particular with a γ-ray flux produced in the scattering of high-energy cosmic-ray protons on H2. Our estimate for the halo γ-ray flux turns out to be in remarkably good agreement with the recent discovery by Dixon et al. [1] of a possible γ-ray emission from the halo using EGRET data. The content is as follows: first, we review the evidence for dark matter in the halo of our Galaxy. As next we presentthebaryoniccandidatesfordarkmatterandwediscussthebasicsofmicrolensing(opticaldepth,microlensing rates, etc.). We then give an overview of the results of microlensing searches achieved so far and we briefly present a scenario in which part of the dark matter is in the form of cold molecular clouds (mainly of H2). MASS OF THE MILKY WAY The best evidence for dark matter in galaxies comes from the rotation curves of spirals. Measurements of the rotationvelocityv ofstarsuptothevisibleedgeofthespiralgalaxiesandofHI gasinthediskbeyondtheoptical rot radius (by measuring the Doppler shift in the 21-cm line) imply that v constant out to very large distances, rot ≈ rather than to show a Keplerian falloff. These observations started around 1970 [14], thanks to the improved sensitivity in both optical and 21-cm bands. By now there are observations for over thousand spiral galaxies with reliable rotation curves out to large radii. In almost all of them the rotation curve is flat or slowly rising out to the last measured point. Very few galaxies show falling rotation curves and those that do either fall less rapidly than Keplerianhavenearbycompanionsthatmayperturbthe velocityfieldorhavelargespheroidsthatmayincreasethe rotation velocity near the centre. There are also measurements of the rotation velocity for our Galaxy. However, these observations turn out to be ratherdifficult,andtherotationcurvehasbeenmeasuredonlyuptoadistanceofabout20kpc. Withoutanydoubt our own galaxy has a typical flat rotation curve. A fact this, which implies that it is possible to search directly for dark matter characteristic of spiral galaxies in our own Milky Way. InodertoinferthetotalmassonecanalsostudythepropermotionoftheMagellanicCloudsandofothersatellites of our Galaxy. Recent studies [15–17] do not yet allow an accurate determination of vrot(LMC)/v0 (v0 =210 10 ± km/s being the local rotational velocity). Lin et al. [16] analyzed the proper motion observations and concluded that within 100 kpc the Galactic halo has a mass 5.5 1 1011M⊙ and a substantial fraction 50% of this ∼ ± × ∼ mass is distributed beyond the present distance of the Magellanic Clouds of about 50 kpc. Beyond 100 kpc the mass may continue to increase to 1012M⊙ within its tidal radius of about 300 kpc. This value for the total mass ∼ of the Galaxy is in agreement with the results of Zaritsky et al. [15], who found a total mass in the range 9.3 to 12.5 1011M⊙,the formervaluebyassumingradialsatelliteorbitswhereasthe latterbyassumingisotropicsatellite × orbits. The results of Lin et al. [16] suggest that the mass of the halo dark matter up to the Large Magellanic Cloud (LMC) is roughly half of the value one gets for the standard halo model (with flat rotation curve up to the LMC and spherical shape), implying thus the same reduction for the number of expected microlensing events. Kochanek [17] analysed the global mass distribution of the Galaxy adopting a Jaffe model, whose parameters are determined using the observations on the proper motion of the satellites of the Galaxy, the Local Group timing constraint and the ellipticity of the M31 orbit. With these observations Kochanek [17] concludes that the mass inside 50 kpc is 5.4 1.3 1011M⊙. This value becomes, however, slightly smaller when using only the satellite observations and ± × the disk rotation constraint, in this case the median mass interior to 50 kpc is in the interval 3.3 to 6.1 (4.2 to 6.8) without (with) Leo I satellite in units of 1011M⊙. The lower bound without Leo I is 65% of the mass expected assuming a flat rotation curve up to the LMC. BARYONIC DARK MATTER CANDIDATES Before discussing the baryonic dark matter we would like to mention that another class of candidates which is seriously taken into consideration is the so-called cold dark matter, which consists for instance of axions or supersymmetric particles like neutralinos [18]. Here, we will not discuss colddark matter in detail. However,recent studies seem to point out that there is a discrepancy between the calculated (through N-body simulations) rotation curve for dwarf galaxies assuming an halo of cold dark matter and the measured curves [19–21]. If this fact is confirmed, this would exclude cold dark matter as a major constituent of the halo of dwarf galaxies and possibly also of spiral galaxies. From the Big Bang nucleosynthesis model [22,23] and from the observed abundances of primordial elements one infers: 0.010 h20ΩB 0.016 or with h0 0.4 1 one gets 0.01 ΩB 0.10 (where ΩB = ρB/ρcrit, and ρ = 3H2/8≤πG). Sinc≤e for the amount of l≃umino−us baryons one find≤s Ω ≤ Ω , it follows that an important crit 0 lum B ≪ fraction of the baryons are dark. Indeed, the dark baryons may well make up the entire dark halo matter. The halo dark matter cannot be in the form of hot ionized hydrogen gas otherwise there would be a large X-ray flux, for which there are stringent upper limits [24]. The abundance of neutral hydrogen gas is inferred from the 21-cm measurements, which show that its contribution is small. Another possibility is that the hydrogen gas is in molecular form clumped into cold clouds, as we will discuss later on. Baryons could otherwise have been processed in stellar remnants (for a detailed discussion see [25]). If their mass is below 0.08 M⊙ they are too light to ignite ∼ hydrogenburning reactions. The possible originof suchbrowndwarfs orJupiter like bodies (called alsoMACHOs), by fragmentation or by some other mechanism, is at present not well understood. It has also been pointed out that the mass distribution of the MACHOs, normalized to the dark halo mass density, could be a smooth continuation of the known initial mass function of ordinary stars [26]. The ambient radiation, or their own body heat, would make sufficiently small objects of H and He evaporate rapidly. The condition that the rate of evaporation of such a hydrogenoidspherebe insufficient tohalveits massina billionyearsleadsto the followinglowerlimit ontheir mass [26]: M > 10−7M⊙(TS/30 K)3/2(1 g cm−3/ρ)1/2 (TS being their surface temperature and ρ their average density, which we expect to be of the order 1 g cm−3). ∼ Otherwise, MACHOs might be M-dwarfs or white dwarfs. As a matter of fact, a deeper analysis shows that the M-dwarf option looks problematic. The null result of several searches for low-mass stars both in the disk and in the halo of our Galaxy suggests that the halo cannot be mostly in the form of hydrogen burning main sequence M-dwarfs. Opticalimaging of high-latitude fields takenwith the Wide Field Camera ofthe Hubble Space Telescope indicates that less than 6% of the halo can be in this form [27]. However, these results are derived under the ∼ assumptionofasmoothspatialdistributionofM-dwarfs,andbecomeconsiderablylesssevereinthecaseofaclumpy distribution [28]. A scenario with white dwarfs as a major constituent of the galactic halo dark matter has been explored [29]. However,itrequiresaratheradhocinitialmassfunctionsharplypeakedaround2-6M⊙. FutureHubbledeepfield exposures could either find the white dwarfs or put constraints on their fraction in the halo [30]. Also a substantial component of neutron stars and black holes with mass higher than 1 M⊙ is excluded, for otherwise they would ∼ lead to an overproductionof heavy elements relative to the observed abundances. BASICS OF MICROLENSING In the following we present the main features of microlensing, in particular its probability and rate of events (for reviewsseealso[31–33],whereasfordoublelensesseeforinstanceref.[34]). Animportantissueisthedetermination from the observations of the mass of the MACHOs that acted as gravitational lenses as well as the fraction of halo darkmattertheymakeup. Themostappropriatewaytocomputetheaveragemassandotherimportantinformation is to use the method of mass moments developed by De Ru´jula et al. [35]. Microlensing probability When a MACHO of mass M is sufficiently close to the line of sight between us and a more distant star, the light from the source suffers a gravitational deflection. The deflection angle is usually so small that we do not see two images but rather a magnification of the original star brightness. This magnification, at its maximum, is given by u2+2 A = . (1) max u(u2+4)1/2 Here u=d/R (d is the distance of the MACHO from the line of sight) and the Einstein radius R is defined as E E 4GMD R2 = x(1 x) (2) E c2 − with x=s/D, and where D and s are the distance between the source, respectively the MACHO and the observer. An important quantity is the optical depth τ to gravitationalmicrolensing defined as opt 1 4πG τ = dx ρ(x)D2x(1 x) (3) opt Z0 c2 − with ρ(x) the mass density of microlensing matter at distance s=xD from us along the line of sight. The quantity τ is the probabilitythata sourceis foundwithin aradiusR ofsomeMACHO andthus hasa magnificationthat opt E is larger than A=1.34 (d R ). E ≤ We calculate τ for a galactic mass distribution of the form opt ρ(~r)= ρ0(a2+RG2C) , (4) a2+~r2 ~r being the distance from the Earth. Here, a is the core radius, ρ0 the local dark mass density in the solar | | systemandR the distancebetween the observerandthe Galactic centre. Standardvalues forthe parametersare GC ρ0 = 0.3 GeV/cm3 = 7.9 10−3M⊙/pc3, a = 5.6 kpc and RGC = 8.5 kpc. With these values we get, for a spherical halo, τ 5 10−7 for the LMC and τ 7 10−7 for the SMC [36]. opt opt ≃ × ≃ × The magnification of the brightness of a star by a MACHO is a time-dependent effect. For a source that can be considered as pointlike (this is the case if the projected star radius at the MACHO distance is much less than R ) E the light curve as a function of time is obtained by inserting (d2+v2t2)1/2 u(t)= T (5) R E into eq.(1), where v is the transverse velocity of the MACHO, which can be inferred from the measured rotation T curve (v 200 km/s). The achromaticity, symmetry and uniqueness of the signal are distinctive features that T ≈ allow to discriminate a microlensing event from background events such as variable stars. The behaviour of the magnification with time, A(t), determines two observables namely, the magnificationat the peak A(0) - denoted by A - and the width of the signal T (defined as being T =R /v ). max E T Microlensing rate towards the LMC ThemicrolensingratedependsonthemassandvelocitydistributionofMACHOs. Themassdensityatadistance s=xD from the observer is given by eq.(4). The isothermal spherical halo model does not determine the MACHO number density as a function of mass. A simplifying assumption is to let the mass distribution be independent of the position in the galactic halo, i.e., we assume the following factorized form for the number density per unit mass dn/dM, dn dM = dn0 a2+RG2C dµ= dn0H(x)dµ , (6) dM dµ a2+R2 +D2x2 2DR xcosα dµ GC − GC with µ = M/M⊙ (α is the angle of the line of sight with the direction of the galactic centre, which is 820 for the LMC), n0 not depending on x and is subject to the normalization dµddnµ0M = ρ0. Nothing a priori is known on the distribution dn0/dM. R A different situation arises for the velocity distribution in the isothermal spherical halo model, its projection in the plane perpendicular to the line of sight leads to the following distribution in the transverse velocity v T f(v )= 2 v e−vT2/vH2 (7) T v2 T H (v 210 km/s is the observed velocity dispersion in the halo). H ≈ Inordertofindthe rateatwhichasinglestarismicrolensedwithmagnificationA A ,weconsiderMACHOs min ≥ withmassesbetweenµandµ+δµ,locatedatadistancefromtheobserverbetweenxandx+δxandwithtransverse velocity between v and v +δv . The collision time can be calculated using the well-known fact that the inverse T T T of the collision time is the product of the MACHO number density, the microlensing cross-sectionand the velocity. The rate dΓ, taken also as a differential with respect to the variable u, at which a single star is microlensed in the interval dµdudv dx is given by [35,37] T dΓ=2v f(v )Dr [µx(1 x)]1/2H(x)dn0dµdudv dx, (8) T T E T − dµ with r2 = 4GM⊙D (3.2 109km)2. (9) E c2 ∼ × One has to integrate the differential number of microlensing events, dN =N t dΓ, over an appropriate range ev ⋆ obs for µ, x, u and v , in order to obtain the total number of microlensing events which can be compared with an T experiment monitoring N stars during an observation time t and which is able to detect a magnification such ⋆ obs thatA A . Thelimitsoftheuintegrationaredeterminedbytheexperimentalthresholdinmagnitudeshift, max TH ≥ ∆m : we have 0 u u . TH TH ≤ ≤ The range of integration for µ is where the mass distribution dn0/dµ is not vanishing and that for x is 0 x ≤ ≤ D /D where D is the extent of the galactic halo along the line of sight (in the case of the LMC, the star is inside h h thegalactichaloandthusD /D=1.) Thegalacticvelocitydistributioniscutattheescapevelocityv 640km/s h e ≈ and therefore v ranges over 0 v v . In order to simplify the integration we integrate v over all the positive T T e T ≤ ≤ axis, due to the exponential factor in f(v ) the so committed error is negligible. T However, the integration range of dµdudv dx does not span all the interval we have just described. Indeed, each T experiment has time thresholds T and T and only detects events with: T T T , and thus the min max min max ≤ ≤ integration range has to be such that T lies in this interval. The total number of micro-lensing events is then given by N = dN ǫ(T) , (10) ev ev Z where the integration is over the full range of dµdudv dx. ǫ(T) is determined experimentally [4,55]. T is related T in a complicated way to the integration variables, because of this, no direct analytical integration in eq.(10) can be performed. To evaluate eq.(10) we define an efficiency function ǫ0(µ) dN⋆ (µ¯) ǫ(T) ǫ0(µ) ev , (11) ≡ R dN⋆ (µ¯) ev R which measures the fraction of the total number of microlensing events that meet the condition on T at a fixed MACHO mass M =µ¯M⊙. We now can write the total number of events in eq.(10) as Nev = dNev ǫ0(µ) . (12) Z Due to the fact that ǫ0 is a function of µ alone, the integration in dµdudvTdx factorizes into four integrals with independent integration limits. The averagelensing duration can be defined as follows 1 <T >= dΓ T(x,µ,v ) , (13) T Γ Z where T(x,µ,v )=R (x,µ)/v . One easily finds that <T > satisfies the following relation T E T 2τ opt <T >= u . (14) TH πΓ In order to quantify the expected number of events it is convenient to take as an example a delta function distribution for the mass. The rate of microlensing events with A A (or u u ), is then min max ≥ ≤ Γ(A )=u Γ˜ =u Dr √π v ρ0 1 1dx[x(1 x)]1/2H(x) . (15) min max max E H M⊙√µ¯ Z0 − Inserting the numerical values for the LMC (D=50 kpc and α=820) we get Γ˜ =4 10−13 vH ρ0 1 s−1. (16) × (cid:18)210 km/s(cid:19)(cid:18)0.3 GeV/cm3(cid:19) M/M⊙ p For an experiment monitoring N stars during an observation time t the total number of events with a magni- ⋆ obs fication A A is: N (A ) = N t Γ(A ). In Table 1 we show some values of N for the LMC, taking min ev min ⋆ obs min ev t =1 yea≥r, N =106 stars and A =1.34 (or ∆m =0.32). obs ⋆ min min TABLE1. MACHO mass in M⊙ Mean RE in km Mean microlensing time Nev 10−1 0.3×109 1 month 4.5 10−2 108 9 days 15 10−4 107 1 day 165 10−6 106 2 hours 1662 Mass moment method A more systematic way to extract information on the masses is to use the method of mass moments [35,38,39]. The mass moments <µm > are defined as <µm >= dµ ǫ (µ) dn0µm . (17) n Z dµ <µm >is relatedto <τn >= τn, withτ (v /r )T,as constructedfromthe observationsandwhichcan events ≡ H E also be computed as follows P <τn >= dN ǫ (µ) τn =Vu γ(m)<µm > , (18) ev n TH Z with m (n+1)/2. For targets in the LMC γ(m)=Γ(2 m)H(m) and ≡ − b N t V 2N t D r v =2.4 103 pc3 ⋆ obs , (19) ≡ ⋆ obs E H × 106 star years − ∞ v 1−n T Γ(2 m) f(v )dv , (20) T T − ≡Z0 (cid:18)vH(cid:19) 1 H(m) (x(1 x))mH(x)dx . (21) ≡Z0 − b The efficiency ǫ (µ) is determined as follows [35] n dN⋆ (µ¯) ǫ(T) τn ǫ (µ) ev , (22) n ≡ R dN⋆ (µ¯) τn ev R where dN⋆ (µ¯) is defined as dN in eq.(10) with the MACHO mass distribution concentrated at a fixed mass µ¯: ev ev dn0/dµ = n0 δ(µ µ¯)/µ. ǫ(T) is the experimental detection efficiency. For a more detailed discussion on the − efficiency see ref. [40]. A mass moment < µm > is thus related to < τn > as given from the measured values of T in a microlensing experiment by <τn > <µm >= . (23) Vu γ(m) TH The mean local density of MACHOs (number per cubic parsec) is < µ0 >. The average local mass density in MACHOs is <µ1 > solar masses per cubic parsec. The mean mass, which we get from the six events detected by the MACHO team during their first two years, is [3] <µ1 > <µ0 > =0.27 M⊙ . (24) When taking for the duration T the values correctedfor “blending”,we get as averagemass 0.34 M⊙. If we include also the two EROS events we get a value of 0.26 M⊙ for the mean mass (without taking into account blending effects). The resulting mass depends onthe parametersusedto describe the standardhalomodel. In orderto check this dependence we variedthe parametersofthe standardhalomodelwithin their allowedrangeandfound thatthe average mass changes at most by 30%, which shows that the result is rather robust. Although the value for the ± average mass we find with the mass moment method is marginally consistent with the result of the MACHO team, it definitely favours a lower average MACHO mass. One can also consider other models with more general luminous and dark matter distributions, e.g. ones with a flattened halo or with anisotropy in velocity space [5], in which case the resulting value for the average mass would decrease significantly. Anotherimportantquantitytobe determinedisthe fractionf ofthe localdarkmassdensity(the latteronegiven by ρ0) detected in the form of MACHOs, which is given by f M⊙/ρ0 126 pc3 < µ1 >. Using the values given ≡ ∼ by the MACHO collaboration for their two years data [4] we find f 0.54, again by assuming a standard spherical ∼ halo model. Once several moments < µm > are known one can get information on the mass distribution dn0/dµ. Since at present only few events towards the LMC are at disposal the different moments (especially the higher ones) can be determined only approximately. Nevertheless, the results obtained so far are already of interest and it is clear that in a few years, due also to the new experiments under way (such as EROS II, OGLE II and MOA in addition to MACHO), it will be possible to draw more firm conclusions. PRESENT STATUS OF MICROLENSING RESEARCH IthasbeenpointedoutbyPaczyn´ski[2]thatmicrolensingallowsthedetectionofMACHOslocatedinthegalactic halo in the mass range [26] 10−7 < M/M⊙ < 1, as well as MACHOs in the disk or bulge of our Galaxy [41,42]. Since this firstproposalmicrolensingsearcheshaveturnedveryquickly into realityandinabouta decadethey have become an important tool for astrophysical investigations. Microlensing is also very promising for the search of planets around other stars in our Galaxy and generates large databases for variable stars, a field which has already benefitted a lot. Because of the increase of observations,since severalnew experiments are becoming operative, the situation is changing rapidly and, therefore, the present results should be considered as preliminary. Towards the LMC and the SMC InSeptember 1993the FrenchcollaborationEROS[43]announcedthe discoveryof2 microlensingcandidates and the American–Australian collaboration MACHO of one candidate [44] by monitoring stars in the LMC. Inthe meantimethe MACHOteamreportedthe observationofaltogether8events(one isabinarylensing event) analysing their first two years of data by monitoring about 8.5 million of stars in the LMC [4]. The inferred optical depth is τ = 2.1+1.1 10−7 when considering 6 events 1 (or τ = 2.9+1.4 10−7 when considering all the 8 opt −0.7 × opt −0.9 × detectedevents). Correspondingly,thisimpliesthatabout45%(50%respectively)ofthehalodarkmatterisinform of MACHOs and they find an average mass 0.5+−00..32M⊙ assuming a standard spherical halo model. It may well be thatthereisalsoacontributionofeventsduetoMACHOslocatedinthe LMCitselforinathickdiskofourgalaxy, in which case the above results will change quite substantially. In particular for the binary event there is evidence thatthe lens is locatedin the LMC.It hasbeen estimatedthatthe opticaldepth forlensing due to MACHOs inthe LMC or in a thick disk is about τ =5.4 10−8 [4]. However, this value is model dependent so that at present it opt × is not clear which fraction of the events are due to self-lensing in the LMC (and similarly for the SMC). Other events have been detected towards the LMC by the MACHO group, which have been put on their list of alert events. The full analysis of the 1996 - 1998 seasons is still not published. EROS has also searched for very-low mass MACHOs by looking for microlensing events with time scales ranging from 30 minutes to 7 days [45]. The lack of candidates in this range places significant constraints on any model for the halo that relies on objects in the range 5 10−8 < M/M⊙ < 2 10−2. Indeed, such objects may make up at most 20% of the halo dark matter (in the ran×ge between 5 10−7×< M/M⊙ < 2 10−3 at most 10%). Similar × × conclusions have also been reached by the MACHO group [4]. Recently,theMACHOteamreported[46]thefirstdiscoveryofamicrolensingeventtowardstheSmallMagellanic Cloud(SMC).Thefullanalysisofthe fouryearsdataonthe SMCisstillunderway,sothatmorecandidatesmaybe found in the near future. A rough estimate of the opticaldepth leads to about the same value as found towardsthe LMC. The same eventhas also been observedby the EROS[47] and the Polish-AmericanOGLE collaboration[48]. A second event has been discovered in 1998 and found to be due to a binary lens. This event has been followed by the different collaborations,so thatthe combined data leadto a quite accuratelightcurve,from whichit is possible 1) In fact, thetwo disregarded eventsare a binary lensing and one which is rated as marginal. to get an upper limit for the value of the proper motion of the lens [49,50]. The result indicate that the lens system is most probably located in the SMC itself, in which case the lens may be an ordinary binary star. It is remarkable that both the binary events detected so far are due to lenses in the Clouds themselves, making it plausible that this is the case for the other lenses as well. Since the middle of 1996 the EROS group has put into operation a new 1 meter telescope, located in La Silla (Chile), and which is fully dedicated to microlensing searches using CCD cameras. The improved experiment is called EROS II. Towards the galactic centre TowardsthegalacticbulgethePolish-AmericanteamOGLE[51]announcedhisfirsteventalsoinSeptember1993. Since then OGLE foundin their datafromthe 1992- 1995observingseasonsaltogether18microlensingevents(one being a binary lens). Based on their first 9 events the OGLE team estimated the optical depth towards the bulge as [52] τ = (3.3 1.2) 10−6. This has to be compared with the theoretical calculations which lead to a value opt [41,42] τ (1 ±1.5) ×10−6, which does, however, not take into account the contribution of lenses in the bulge opt ≃ − × itself, which might well explain the discrepancy. In fact, when taking into account also the effect of microlensing by galactic bulge stars the optical depth gets bigger [53] and might easily be compatible with the measured value. This implies the presence of a bar in the galactic centre. In the meantime the OGLE groupgota new dedicated 1.3 meter telescope located at the Las Campanas Observatory. The OGLE-2collaborationhas started the observations in 1996 and is monitoring the bulge, the LMC and the SMC as well. The French DUO [54] team found 12 microlensing events (one of which being a binary event) by monitoring the galactic bulge during the 1994 season with the ESO 1 meter Schmidt telescope. The photographic plates were taken in two different colors to test achromaticity. The MACHO [55] collaboration found by now more than 150 ∼ microlensingeventstowardsthegalacticbulge,mostofwhicharelistedamongthealertevents,whichareconstantly updated 2. They found also 3 events by monitoring the spiral arms in the region of Gamma Scutum. During their first season they found 45 events towards the bulge. The MACHO team detected also in a long duration event the parallaxeffectduetothemotionoftheEartharoundtheSun[56]. TheMACHOfirstyeardataleadstoanestimated opticaldepthofτ 2.43+0.54 10−6,whichisroughlyinagreementwiththeOGLEresult,andwhichalsoimplies opt ≃ −0.45× the presence of a bar in the galactic centre. These results are very important in order to study the structure of our Galaxy. In this respect the measurement towards the spiral arms will give important new information. Some globular clusters lie in the galactic disk about half-way between us and the galactic bulge. If globular clusters contain MACHOs, the latter can also act as lenses for more distant stars located in the bulge. Recently, we have analysed the microlensing events towards the galactic bulge, which lie close to three globular clusters and found evidence that some microlensing events are indeed due to MACHOs located in the globular clusters [57]. If this finding is confirmed, once more data will be available, it would imply that also globular clusters contain an important amount of dark matter in form of MACHOs, which probably would be brown dwarfs or white dwarfs. Towards the Andromeda galaxy Microlensing searches have also been conducted towards M31, which is an interesting target [58–60]. In this case, however, one has to use the so-called “pixel-lensing” method, since the source stars are in general no longer resolvable. Two groups have performed searches: the French AGAPE [61] using the 2 meter telescope at Pic du MidiandtheAmericanVATT/COLUMBIA[62],whichusedthe 1.8meterVATT-telescopelocatedonMt. Graham and the 4 meter KNPO telescope. Both teams showed that the pixel-lensing method works, however, the small amount of observations done so far does not allow to draw firm conclusions. The VATT/COLUMBIA team found six candidates which are consistent with microlending, however,additional observations are needed to confirm this. Pixel-lensing could also lead to the discoveryof microlensing events towards the M87 galaxy, in which case the best would be to use the Hubble Space Telescope [63]. It might also be interesting to look towards dwarf galaxies of the local group. 2) Current information on the MACHO Collaboration’s Alert events is maintained at the WWW site http://darkstar.astro.washington.edu. Further developments A new collaborationbetween New Zealand and Japan, called MOA, started in june 1996 to perform observations using the 0.6 meter telescope of the Mt. John Observatory [64]. The targets are the LMC and the galactic bulge. Theywillinparticularsearchforshorttimescale( 1hour)events,andwillthenbeparticularlysensitivetoobjects ∼ with a mass typical for brown dwarfs. It has to mentioned that there are also collaborations between different observatories (for instance PLANET [65] and GMAN [66]) with the aim to perform accurate photometry on alert microlensing events. The GMAN collaboration was able to accurately get photometric data on a 1995 event towards the galactic bulge. The light curve shows clearly a deviation due to the extension of the source star [67]. A major goal of the PLANET and GMAN collaborations is to find planets in binary microlensing events [68–70]. Moreover, microlensing searches are also very powerful ways to get large database for the study and discovery of many variable stars. At present the only information available from a microlensing event is the time scale, which depends on three parameters: distance, transverse velocity and mass of the MACHO. A possible way to get more information is to observeaneventfromdifferentlocations,withtypicallyanAstronomicalUnitinseparation. This couldbe achieved by putting a parallax satellite into solar orbit [71,72]. The above list of presently active collaborations and main results shows clearly that this field is just at the beginning and that many interesting results will come in the near future. FORMATION OF DARK CLUSTERS We turn now to the discussion of a scenario for the formation of dark clusters of MACHOs and cold molecular clouds. Our scenario [6–8] encompasses the one originally proposed by Fall and Rees [73] to explain the origin of globular clusters and can be summarized as follows. After its initial collapse, the proto galaxy (PG) is expected to be shock heated to its virial temperature 106 K. Because of thermal instability, density enhancements rapidly ∼ grow as the gas cools. Actually, overdense regions cool more rapidly than average, and so proto globular cluster (PGC) clouds form in pressure equilibrium with hot diffuse gas. When the PGC cloud temperature reaches 104 K,hydrogenrecombinationoccurs: atthis stage,their massandsize are 105(R/kpc)1/2M ⊙ and 10(R/kp∼c)1/2 pc, respectively (R is the galactocentricdistance). Below 104 K, the main∼coolants areH2 molecule∼s andany heavy elementproducedinafirstchaoticgalacticphase. ThesubsequentevolutionofthePGCcloudswillbeverydifferent in the inner and outer part of the Galaxy, depending on the decreasing ultraviolet (UV) flux as the galactocentric distance R increases. As is well known, in the centralregionof the Galaxy an Active Galactic Nucleus (AGN) and a firstpopulation of massive stars are expected to form, which act as strong sources of UV radiation that dissociates the H2 molecules. It is notdifficult to estimate that H2 depletionshouldhappen for galactocentricdistances smallerthan 10 20kpc. − As a consequence, cooling is heavily suppressed in the inner halo, and so the PGC clouds here remain for a long time at temperature 104 K, resulting in the imprinting of a characteristic mass 106M⊙. Eventually, the UV flux will decrease,the∼reby permitting the formationof H2. As a result, the cloudtem∼perature drops below 104 K ∼ and the subsequent evolution leads to star formation and ultimately to globular clusters. Our main point is that in the outer halo – namely for galactocentric distances larger than 10 20 kpc – no − substantial H2 depletion should take place (owing to the distance suppression of the UV flux). Therefore,the PGC clouds cool and contract. When their number density exceeds 108 cm−3, further H2 is produced via three-body ∼ reactions (H +H +H H2 +H and H +H +H2 2H2), which makes in turn the cooling efficiency increase → → dramatically. This fact has three distinct implications: (i) no imprinting of a characteristic PGC cloud mass shows up, (ii) the Jeans mass can drop to values considerably smaller than 1 M⊙, and (iii) the cooling time is much ∼ shorterthanthefree-falltime. Insuchasituationasubsequentfragmentationoccursintosmallerandsmallerclouds thatremainopticallythinto their ownradiation. The processstops whenthe clouds becomeopticallythick totheir ownlineemission–this happenswhenthe Jeansmassisaslowas 10−2 M⊙. Inthis manner,darkclustersshould form, which contain brown dwarfs in the mass range 10−2 10−1∼M⊙. − Before proceeding further, two observations are in order. First, it seems quite natural to suppose that – much in thesamewayasitoccursforordinarystars–alsointhiscasethe fragmentationprocessthatgivesrisetoindividual browndwarfsshouldproduceasubstantialfractionofbinarybrowndwarfs. Itisimportanttokeepinmindthatthe mass fractionofprimordialbinariescan be as large as50%. Hence, we see thatMACHOs consistofboth individual and binary brown dwarfs in the present scenario [74,75]. Second, we do not expect the fragmentation process to be able to convert the whole gas in a PGC cloud into brown dwarfs. For instance, standard stellar formation mechanismsleadtoanupper limitofatmost40%forthe conversionefficiency. Thus,asubstantialfractionf˜ofthe primordial gas – which is mostly H2 – should be left over. Because brown dwarfs do not give rise to stellar winds, this gasshouldremainconfinedwithin a darkcluster. So, alsocoldH2 self-gravitatingclouds shouldpresumablybe clumped into dark clusters, along with some residualdiffuse gas (the amount of diffuse gas inside a dark cluster has to be low, for otherwise it would have been observed in optical and radio bands). Unfortunately, the total lack of any observational information about dark clusters would make any effort to understand their structure and dynamics practically impossible, were it not for some remarkable insights that our unified treatment of globular and dark clusters provides us. In the first place, it looks quite natural to assume that alsodarkclustershaveadenser coresurroundedby anextendedsphericalhalo. Moreover,inthe lackofanyfurther information it seems reasonable to suppose (at least tentatively) that the dark clusters have the same averagemass density as globularclusters. Hence, we obtainrDC 0.12(MDC/M⊙)1/3 pc, where MDC and rDC denote the mass ≃ andthemedianradiusofadarkcluster,respectively. Asafurtherimplicationoftheabovescenario,westressthat– atvariancewith the caseofglobularclusters –the initialmass functionofthe darkclusters shouldbe smooth, since the monotonic decreaseof the PGC cloudtemperature fails to single outany particular mass scale. In addition, the absence of a quasi-hydrostatic equilibrium phase for the dark clusters naturally suggests MDC 106 M⊙. Finally, ≤ we suppose for definiteness that all brown dwarfs have mass 0.1 M⊙, while the molecular cloud spectrum will be taken to be 10−3 M⊙ Mm 10−1 M⊙. ≃ ≤ ≤ OBSERVATIONAL TESTS We list schematically some observational tests for the present scenario. Clustering of microlensing events – The most promising way to detect dark clusters is via correlationeffects in microlensing observations, as they are expected to exhibit a cluster-like distribution [76]. Indeed, it has been shown that a relatively small number of microlensing events would be sufficient to rule out this possibility, while to confirm it more events are needed. However, we have seen that core collapse can liberate a considerable fraction of MACHOs from the less massive clusters, and so an unclustered MACHO population is expected to coexist with dark clusters in the outer halo– detectionof unclustered MACHOs wouldtherefore notdisprovethe presentmodel. γ-rays from halo clouds – A signature for the presence of molecular clouds in the galactic halo should be a γ-rayfluxproducedinthescatteringofhigh-energycosmic-rayprotonsonH2 [6,7]. Asamatteroffact,anessential ingredient is the knowledge of the cosmic ray flux in the halo. Unfortunately, this quantity is unknown and the only available information comes from theoretical estimates. Moreover, we assume the same energy distribution of the cosmic rays as measured on Earth. The presence of magnetic fields in the halo is expected to give rise to a temporary confinement of cosmic ray protons similar to what happens in the disk. In addition, there can also be sourcesofcosmicrayprotonslocatedinthe haloitself,asforinstanceisolatedorbinarypulsarsinglobularclusters. The best chance to detect the γ-raysin question is providedby observations at high galactic latitude. We find that - regardless of the adopted value for the flatness of the halo - at high-galactic latitude Φ DM(> 1 GeV) lies in the γ range 6 8 10−7 γ cm−2 s−1 sr−1 (assuming a fraction f˜ 0.5 for the dark matter in form of cold clouds). ≃ − × ≃ However, the shape of the contour lines strongly depends on the flatness parameter [77]. A few months ago, Dixon et al. [1] have re-analyzed the EGRET data concerning the diffuse γ-ray flux with a wavelet-basedtechnique. Aftersubtractionoftheisotropicextragalacticcomponentandoftheexpectedcontribution from the Milky Way, they find a statistically significant diffuse emission from the galactic halo. At high-galactic latitude, the integrated halo flux above 1 GeV turns out to be 10−7 10−6 γ cm−2 s−1 sr−1, which is slightly ≃ − less than the diffuse extragalactic flux (Sreekumar et al. [78]). Our estimate for the halo γ-ray flux turns out to be in remarkably good agreement with the discovery by Dixon et al. [1]. The next generation of γ-ray satellites like AGILE and GLAST will be able to test our model, thanks to their better angular resolution. CBR anisotropy – An alternative way to discover the molecular clouds under consideration relies upon their emissioninthemicrowaveband[79]. Thetemperatureofthecloudshastobeclosetothatofthecosmicbackground radiation (CBR). Indeed, an upper limit of ∆T/T 10−3 can be derived by considering the anisotropy they would ∼ introduce in the CBR due to their higher temperature. Realistically, molecular clouds cannot be regarded as black body emitters because they mainly produce a setof molecularrotationaltransitionlines. If we consider clouds with cosmologicalprimordial composition, then the only molecule that contributes to the microwaveband with optically thick lines is LiH, whose lowest rotational transition occurs at ν0 = 444 GHz with broadening 10−5 (due to ∼ the turbulent velocity of molecular clouds in dark clusters). This line would be detectable using the Doppler shift effect. To this aim, it is convenient to consider M31 galaxy, for whose halo we assume the same picture as outlined above for our galaxy. Then we expect that molecular clouds should have typical rotational speeds of 50-100 km s−1. Given the fact that the clouds possess a peculiar velocity (with respect to the CBR) the emitted radiationwill be Doppler shifted, with ∆ν/ν0 10−3. However, the precise chemical composition of molecular clouds in the ∼ ± galactic halo is unknown. Even if the heavy molecule abundance is very low (as compared with the abundance in interstellar clouds), many optically thick lines corresponding to the lowest rotational transitions would show up in