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GRA VITATIONAL MICROLENSING RESEARCH PHILIPPE JETZER Paul Scherrer Institute,Laboratory for Astrophysics,CH-5232Villigen PSI,and Institute of Theoretical Physics,University of Z¨u rich,Winterthurerstras 190,CH-8057Z¨u rich,Switzerland One of the most important problems in astrophysics concerns the nature of the dark matter in galactic halos,who prence is implied mainly by the obrved flat rotation curves in spiral galaxies.In the framework of a baryonic scenario the most plausible can-didates are brown dwarfs,M-dwarfs or white dwarfs and cold molecular clouds (mainly of H 2).The former can be detected with the ongoing microlensing experiments,which are rapidly leading to important new results.The French collaboration EROS and the American-Australian collaboration MACHO have reported until August 1997the obr-vation of ∼16microlensing events by monitoring during veral years the brightness of millions of stars in the Large Magellanic Cloud and one event towards the Small Magellanic Cloud.In particular,the MACHO team found 8microlensing candidates by analysing their first 2years of obrvations.This implies that the halo dark matter frac-tion in form of MACHOs (Massive Astrophysical Compact Halo Objects)is of the order of 45-50%assuming a standard spherical halo model.More than 150microlensing events have been detected in the direction of the galactic bulge by the MACHO,OGLE and DUO teams.The
measured optical depth implies the prence of a bar in the galactic centre.Here,we give an overview of microlensing and the main results achieved so far.1Introduction One of the most important problems in astrophysics concerns the nature of the dark matter in galactic halos,who prence is implied by the obrved flat rotation curves in spiral galaxies 1,2,the X-ray diffu emission in elliptical galaxies as well as by the dynamics of galaxy clusters.Primordial nucleosynthesis entails that most of the baryonic matter in the Univer is nonluminous,and such an amount of dark matter falls suspiciously clo to that required by the rotation curves.Surely,the standard model of elementary particle forces can hardly be viewed as the ultimate theory and all the attempts in that direction invariably call for new particles.Hence,the idea of nonbaryonic dark matter naturally enters the realm of cosmolgy and may help in the understanding of the process of galaxy formation and clustering of
galaxies.
The problem of dark matter started already with the pioneering work of Oort 3in 1932and Zwicky 4in 1933and its mistery is still not solved.Actually,there are veral dark matter problems on different scales ranging from the solar neighbour-hood,galactic halos,cluster of galaxies to cosmological scales.Dark matter is also needed to understand the formation of large scale structures in the univer
.Many candidates have been propod,either baryonic or not,to explain dark matter.Here,we discuss the dark matter problem in the halo of our Galaxy in con-nection with microlensing arches.We prent the basics of microlensing and an overview of the results obtained so far,without,however,being exhaustive and this also for the references we quote.The content is as follows:first,we review the evidence for dark matter in the halo of our Galaxy.In Section 3we prent the baryonic candidates for dark matter and in Section 4we give an overview of the
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results of microlensing arches achieved so far.In Section5we discuss the basics
of microlensing(optical depth,microlensing rates,etc.)and in Section6we briefly prent a scenario in which part of the dark matter is in the form of cold molecular
clouds(mainly of H2).
2Mass of the Milky Way
The best evidence for dark matter in galaxies comes from the rotation curves of spirals.Measurements of the rotation velocity v rot of stars up to the visible edge
日耳曼语
of the spiral galaxies and of HI gas in the disk beyond the optical radius(by
measuring the Doppler shift in the21-cm line)imply that v rot≈constant out to very large distances,rather than to show a Keplerian falloff.The obrvations
atopistarted around19705,thanks to the improved nsitivity in both optical and21-cm bands.By now there are obrvations for over thousand spiral galaxies with reliable rotation curves out to large radii6.In almost all of them the rotation curve isflat or slowly rising out to the last measured point.Very few galaxies show falling rotation curves and tho that do either fall less rapidly than Keplerian have nearby companions that may perturb the velocityfield or have large spheroids that may increa the rotation velocity near the centre.
There are also measurements of the rotation velocity for our Galaxy.However, the obrvations turn out to be rather difficult,and the rotation curve has been measured only up to a distance of about20kpc.Without any doubt our own galaxy has a typicalflat rotation curve.A fact this,which implies that it is possible to arch directly for dark matter characteristic of spiral galaxies in our own Milky Way.
In oder to infer the total mass one can also study the proper motion of the
Magellanic Clouds and of other satellites of our Galaxy.Recent studies7,8,9do not yet allow an accurate determination of v rot(LMC)/v0(v0=210±10km/s being the local rotational velocity).Lin et al.8analyzed the proper motion obrvations and concluded that within100kpc the Galactic halo has a mass∼5.5±1×1011M⊙and a substantial fraction∼50%of this mass is distributed beyond the prent distance of the Magellanic Clouds of about50kpc.Beyond100kpc the mass may continue to increa to∼1012M⊙within its tidal radius of about300kpc.This value for the total mass of the Galaxy is in agreement with the results of Zaritsky et al.7,who found a total mass in the range9.3to12.5×1011M⊙,the former value by assuming radial satellite orbits whereas the latter by assuming isotropic satellite orbits.
The results of Lin et al.8suggest 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(withflat rotation curve up to the LMC and spherical shape),implying thus the same reduction for the number of expected microlensing events.Kochanek9analyd the global mass distribution of the Galaxy adopting a Jaffe model,who parameters are determined using the obrvations on the proper motion of the satellites of the Galaxy,the Local Group timing constraint a
nd the ellipticity of the M31orbit.With the obrvations Kochanek9concludes that the mass inside50kpc is5.4±1.3×1011M⊙.This value becomes,however,slightly smaller when using only the satellite obrvations and the disk rotation constraint,
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in this ca the median mass interior to50kpc is in the interval3.3to6.1(4.2to 6.8)without(with)Leo I satellite in units of1011M⊙.The lower bound without Leo I is65%of the mass expected assuming aflat rotation curve up to the LMC. 3Baryonic dark matter candidates
Before discussing the baryonic dark matter we would like to mention that another class of candidates which is riously taken into consideration is the so-called cold dark matter,which consists for instance of axions or supersymmetric particles like neutralinos10.Here,we will not discuss cold dark matter in detail.However, recent studies em 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 curves11,12,13.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.n2
From the Big Bang nucleosynthesis model14,15and from the obrved abun-dances of primordial el
ements one infers:0.010≤h20ΩB≤0.016or with h0≃0.4−1 one gets0.01≤ΩB≤0.10(whereΩB=ρB/ρcrit,andρcrit=3H20/8πG).Since for the amount of luminous baryons onefindsΩlum≪ΩB,it follows that an important fraction of the baryons are dark.In fact 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 other-wi there would be a large X-rayflux,for which there are stringent upper limits16. The abundance of neutral hydrogen gas is inferred from the21-cm measurements, which show that its contribution is small.Another possibility is that the hydro-gen gas is in molecular form clumped into cold clouds,as we will briefly discuss in Section6.Baryons could otherwi have been procesd in stellar remnants(for a detailed discussion e17).If their mass is below∼0.08M⊙they are too light to ignite hydrogen burning reactions.The possible origin of such brown dwarfs or Jupiter like bodies(called also MACHOs),by fragmentation or by some other mech-anism,is at prent 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 stars18.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 hydrogenoid sphere be insufficient to halve its mass in a billion years le
ads to the following lower limit on their mass18:M>10−7M⊙(T S/30K)3/2(1g cm−3/ρ)1/2 (T S being their surface temperature andρtheir average density,which we expect to be of the order∼1g cm−3).whom
Otherwi,MACHOs might be either M-dwarfs or el white dwarfs.As a matter of fact,a deeper analysis shows that the M-dwarf option looks problematic. The null result of veral arches 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 quence M-dwarfs.Optical imaging of high-latitudefields taken with the Wide Field Camera of the Hubble Space Telescope indicates that less than∼6% of the halo can be in this form19.Obrve,however,that the results are derived
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under the assumption of a smooth spatial distribution of M-dwarfs,and become considerably less vere in the ca of a clumpy distribution20,21.
A scenario with white dwarfs as a major constituent of the galactic halo dark matter has been explored22.However,it requires a rather ad hoc initial mass function sharply peaked around2-6M⊙.Future Hubble deepfield exposures could eitherfind the white dwarfs or put constraints on their fraction in the halo 23.Also a substantial component of neutron stars and black holes with mass high
er
more more more>listeningtomusicthan∼1M⊙is excluded,for otherwi they would lead to an overproduction of heavy elements relative to the obrved abundances.
4Prent status of microlensing rearch
It has been pointed out by Paczy´n ski24that microlensing allows the detection of MACHOs located in the galactic halo in the mass range1810−7<M/M⊙<1,as well as MACHOs in the disk or bulge of our Galaxy25,26.Since thisfirst proposal microlensing arches have turned very quickly into reality and in about a decade they have become an important tool for astrophysical investigations.Microlensing is very promising for the arch of planets around other stars in our Galaxy and generates also very large databas for variable stars,afield which has already benefitted a lot.Becau of to the increa of obrvations,due also to the fact that new experiments are becoming operative,the situation is changing rapidly and,therefore,the prent results should be considered as preliminary.Within few years the amount of data will be such that veral problems will be solved or at least allow to achieve substantial progress.The following prentation is also not exhaustive with respect to all what has been found so far.
4.1Towards the LMC and the SMC
有所裨益In September1993the French collaboration EROS27announced the discovery of 2microlensing candidates and the American–Australian collaboration MACHO of one candidate28by monitoring stars in the LMC.
In the meantime the MACHO team reported the obrvation of altogether8 events(one is a binary lensing event)analysing theirfirst two years of data by monitoring about8.5million of stars in the LMC29.The inferred optical depth is
τ=2.1+1.1
−0.7×10−7when considering6events a(e Table3)(orτ=2.9+1.4−0.9×10−7 when considering all the8detected events).Correspondingly,this implies that about45%(50%respectively)of the halo dark matter is in form of MACHOs and
theyfind an average mass0.5+0.3
−0.2M⊙assuming a standard spherical halo model.It
may well be that there is also a contribution of events due to MACHOs located in the LMC itlf or in a thich disk of our galaxy,the corresponding optical depth is estimated to be only29τ=5.4×10−8.Other events have been detected towards the LMC by the MACHO group,which have been put on their list of alert events. In particular2events are reported in1996and already4events in1997.The full analysis of the1996and1997asons is still not published.
EROS has also arched for very-low mass MACHOs by looking for microlensing events with time scales ranging from30minutes to7days30.The lack of candidates in this range places significant constraints on any model for the halo that relies on objects in the range5×10−8<M/M⊙<2×10−2.Indeed,such objects may make up at most20%of the halo dark matter(in the range between5×10−7< M/M⊙<2×10−3at most10%).Similar conclusions have also been reached by the MACHO group29.Recently,the MACHO team reported31thefirst discovery of a microlensing event towards the Small Mgellanic Cloud(SMC).The full analysis of the four years data on the SMC is still underway,so that more candidates may be found in the near future.A rough estimate of the optical depth leads to about the same value as found towards the LMC.
The EROS group has completed hisfirst campaign bad on photographic plates and CCD,the latter one for the short duration events.Since the middle of1996 the EROS group has put into operation a
new1meter telescope,located in La Silla (Chile),and which is fully dedicated to microlensing arches using CCD cameras. The improved experiment is called EROS II.
4.2Towards the galactic centre
Towards the galactic bulge the Polish-American team OGLE32announced hisfirst event also in September1993.Since then OGLE found in their data from the1992-1995obrving asons altogether18microlensing events(one being a binary lens). Bad on theirfirst9events the OGLE team estimated the optical depth towards the bulge as33τ=(3.3±1.2)×10−6.This has to be compared with the theoretical calculations which lead to a value25,26τ≃(1−1.5)×10−6,which does,however, not take into account the contribution of lens in the bulge itlf,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 bigger34and might easily be compatible with the measured value.This implies the prence of a bar in the galactic centre.In the meantime the OGLE group got a new dedicated1.3meter telescope located at the Las Campanas Obrvatory.The OGLE-2collaboration has started the obrvations in1996and is monitoring the bulge,the LMC and the SMC as well.
The French DUO35team found12microlensing events(one of which being a binary event)by monitori
ng the galactic bulge during the1994ason with the ESO 1meter Schmidt telescope.The photographic plates were taken in two different colors to test achromaticity.The MACHO36collaboration found by now more than∼150microlensing events towards the galactic bulge,most of which are listed among the alert events,which are constantly updated b.They found also3events by monitoring the spiral arms in the region of Gamma Scutum.During theirfirst ason they found45events towards the bulge.The MACHO team detected also in a long duration event the parallax effect due to the motion of the Earth around the Sun37.The MACHOfirst year data leads to an estimated optical depth of τ≃2.43+0.54
−0.45×10−6,which is roughly in agreement with the OGLE result,and
which also implies the prence of a bar in the galactic centre.The 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.
4.3Towards the Andromeda galaxy
Microlensing arches have also been conducted towards M31.In this ca,however,
one has to u the so-called“pixel-lensing”method,since the source stars are in gen-eral no longer resolvable.Two groups have performed arches:the French AGAPE 38using the2meter telescope at Pic du Midi and the American VATT/COLUMBIA
39,which ud the1.8meter VATT-telescope located on Mt.Graham and the4 meter KNPO telescope.Both teams showed that the pixel-lensing method works, however,the small amount of obrvations done so far does not allow to drawfirm conclusions.The VATT/COLUMBIA team found six candidates which are con-sistent with microlending,however,additional obrvations are needed to confirm this.Pixel-lensing could also lead to the discovery of microlensing events towards the M87galaxy,in which ca the best would be to u the Hubble Space Telescope 40.It might also be interesting to look towards dwarf galaxies of the local group.
4.4Further developments
A new collaboration between New Zealand and Japan,called MOA,started in june 1996to perform obrvations using the0.6meter telescope of the Mt.John Obr-vatory41.The targets are the LMC and the galactic bulge.They will in particular arch for short timescale(∼1hour)events,and would then be particularly nsitive to objects with a mass tipical for brown dwarfs.
network
It has to mentioned that there are also collaborations between different obr-vatories(for instance PLANET42and GMAN43)with the aim to perform accurate photometry on alert microlensing events.The GMAN collaboration was able to accurately get photometric data on a1995event towards the galactic bulge.The light curve shows clearly a deviation due to the extension of the source star44.A major goal of the PLANET and GMAN collaborations is tofind planets in binary microlensing events45,46,47.Moreover,microlensing arches are also very powerful ways to get large databa for the study and discovery of many variable stars.
At prent the only information available from a microlensing event is the time scale,which depends on three parameters:distance,transver velocity and mass of the MACHO.A possible way to get more information is to obrve an event from different locations,with typically an Astronomical Unit in paration.This could be achieved by putting a parallax satellite into solar orbit48,49.
The above list of prently active collaborations and main results shows clearly that thisfield is just at the beginning and that many interesting results will come in the near future.
5Basics of microlensing
In the following we prent the main features of microlensing,in particular its probability and rate of e
vents(for reviews e also50,51,whereas for double lens e
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