A group of astronomers

and physicists discover

the gravitational

microlensing effect

and make a major

contribtion to particle

physics.

8 SPRING 2000

by KIM GRIEST

All About MACHOITH ALL THE RECENT SCIENTIFICand technological progress it is remarkablethat we still don’t know what is the mostcommon physical substance in the Uni-verse. This mysterious “dark matter” com-

pletely dominates the gravity of all systems that have been mea-sured; it controls themotion of the Sun through the Galaxy, the motion of galaxies in clusters of galaxies, and the formation and fate of all structure in the Universe. But we don’t have a clue what this stuff is. We know that there is 10–30 times more of it than there is in ordinary stars, dust, or gas, and we even know that it is distributed in large halossurrounding all galaxies, and how fast it is moving. But as forits nature we only know that it doesn’t emit or absorb muchelectromagnetic radiation in any known waveband. So whatcould it be, and how can we go about identifying it?

This article will give a short overview of how we knowdark matter exists and what the main candidates are. Then itwill focus on one of the most popular candidates, MassiveAstrophysical Compact Halo Objects (MACHOs), which hasbeen the subject of an extensive search among astronomers.After the discovery of MACHOs in 1993, some thought thatthe dark matter puzzle had been solved, but theoreticalwork, as well as very recent experimental results, show thatwhile a portion of the dark matter may consist of MACHOs,the bulk of it must be some other, still mysterious, stuff.

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DARK MATTER is seen in many places, but the most secure evi-dence comes from the speeds of stars and hydrogen gas clouds mov-ing in spiral galaxies. These speeds, accurately measured using the

Doppler effect, are much faster than can be explained if only the gravity fromobserved stars, gas, and dust is taken into account. Especially in the outerreaches of spiral galaxies, where there are very few stars, the high speeds

imply 5–10 times more material than observed. In order to explain thehigh speeds, this “dark matter” must be distributed in large

roundish halos surrounding the stellar component of spiralgalaxies. This is true of basically every spiral galaxy

measured, including our own Milky Way.On scales larger than galaxies, even more

dark matter is required to explain thespeeds of objects. For example, in large

clusters of more than a thousand galax-ies, the speeds of those galaxies implya mass of dark matter that is 10–30times greater than that of visible stars

and gas. In these systems there are otherways to measure the depth of the gravita-

tional potential well, for example from the X-raytemperature of the free hot gas or from the gravitational lensing of back-ground galaxies. These independent methods give the same large amount ofdark matter as inferred from the high speeds of the cluster galaxies. Thus,there is no controversy about the existence of large amounts of dark matter.

WHAT TYPES OF OBJECTS could make up the enormousamount of dark matter, and how does one search for somethingthat is invisible in all known electromagnetic wavebands?

For years astronomers have known of many types of objects that could fitthe dark matter invisibility requirement: black holes, Jupiter-size balls of hy-drogen and helium, white dwarf stars, neutron stars, and so forth. But fordecades, astronomers were at a loss for how to search for such objects, none

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of which give off enough light to beseen at the typical distance of a darkmatter object. Particle physicists,however, were more enthusiasticabout the prospects of detecting theirdark matter candidates. It is quitenatural that some type of exotic,weakly interacting elementary par-ticle would be left over from the BigBang with an abundance appropriateto make up the dark matter. The twomost popular classes of candidatesare the axion and the Weakly Inter-acting Massive Particle (WIMP) class,the most popular of which is the neu-tralino from supersymmetry. Axionswould exist with the proper densityto be the dark matter if they hadmasses near 10-5 eV, while WIMPscould contribute the bulk of the darkmatter with masses in the tens tothousands of GeV range. The advan-tage of particle dark matter for de-tection is that each second billionsof them would be passing througheach square centimeter of the en-tire Galaxy, including all areas of theEarth. The predicted tiny cross sec-tion makes detection difficult, butmany experimental efforts are un-derway to detect axions or WIMPs byusing very low noise, carefully in-strumented detectors. Of course forsupersymmetric WIMPs it may alsobe possible to create directly the par-ticles in an accelerator, and then touse the measured mass and cross sec-tion to predict the contribution tothe dark matter. This search is alsounderway. So far, however, no con-clusive evidence in favor of any darkmatter particle has been found.

For the astronomical candidatesMACHOs, the situation changed in1986 when Bodhan Paczynski sug-gested a method of detecting any

compact object that might make upthe dark matter in our Galaxy. Start-ing in 1989, this idea gave rise to sev-eral experiments, culminating in1993 with their discovery!

GRAVITATIONAL micro-lensing is the method capa-ble of detecting the presence

of dark objects in the Galaxy at greatdistance. This idea, studied even byAlbert Einstein, says that if a darkobject moves directly in front of adistant source star, the source starwill appear to be magnified by thedark object acting as a gravitation-al lens (see the illustration on theleft). If the alignment is perfect, thesource would in fact appear as a ring,called the Einstein ring, with radiusRE = [4GmLx(1-x)/c2]1/2, where G isNewton’s constant, m is the mass ofthe lens, L is the distance to thesource star, and x is the distance tothe lens divided by the distance tothe source. In the much more likelycase of imperfect alignment, for ex-ample, missing perfect alignment byan impact parameter b, there will betwo images of the source instead ofa ring. For distances and masses typ-ical of microlensing experiments,these images will be too close to-gether to be resolved, but the lightfrom them will add, giving a totalmagnification of the source star by afactor A = (u2+2)u-1(u2+4)-1/2, whereu = b/RE.

Thus the idea is to monitor manystars in a nearby galaxy, such as theLarge Magellanic Cloud (cover im-age), and see if any of them becomemagnified as a dark matter MACHOpasses in front. If the halo of theMilky Way consists of MACHOS (andnot WIMPs or axions), then there

Light from the star can reach the observer bytwo different paths, making a double image.The paths are enormously exaggerated above,and usually the atmosphere blurs the twoimages into one, but in any case more light thannormal is seen coming from the star.

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should be trillions of MACHOs mov-ing at speeds near 300 km/secthrough the halo. As the Earth,source star, and MACHO move intoand out of alignment, the source starappears to brighten, then goes backto its normal brightness, in a time-symmetric and very specific uniqueway. One can calculate the proba-bility of a MACHO passing in front ofa star and also the typical durationof the magnification event. One findsthat for a full MACHO halo, aboutone star in two million will be mag-nified and that the duration of theevent (A > 1.34) will be t̂ ~– 130 (m/MO. )1/2

days, where m/MO. is the mass of theMACHO in units of solar masses.Thus if one monitored millions ofstars over a period of several years,one could in principle detect MACHOdark matter. If one did not see anymicrolensing events, one could alsorule them out as dark matter candi-dates. Since one can monitor stars ontimes scales of minutes to years, thistype of experiment has sensitivity toany compact dark matter objects inthe 10-7 MO. to 10 MO. range.

IN 1989 two experiments startedwith the purpose of monitoringmillions of stars for microlensing

to detect dark matter. The EROS col-laboration, consisting mostly ofFrench astrophysicists and particlephysicists, used a telescope in SouthAmerica, while the MACHO collab-oration of American and Australianscientists used a telescope in Aus-tralia. I will focus on the MACHO col-laboration, since I am a member ofit. In addition, OGLE, a Polish col-laboration, began monitoring starsfor microlensing in the Galacticbulge for non-dark matter purposes.

The MACHO collaboration usedthe 1.3 meter telescope at MountStromlo Observatory for eight years,1992–1999. We took over 80,000 ob-servations, recording more than 6 ter-abytes of raw image data, and madeover 300 billion individual photo-metric measurements (of the bright-ness of a star). These measurementswere arranged by date into more than40 million stellar “light curves,”which were then each searched forsigns of variability and gravitationalmicrolensing. Most of the starsshowed no sign of variability, butabout 1 percent did vary, almost al-ways in a way known to astronomersfrom their extensive studies of vari-able stars. These variable stars con-stitute background, but luckily thebrightness variation due to micro-lensing is unique in its light curveshape. Thus it is possible to pick outthe one-in-a-million light curve thatcontains a gravitational microlens-ing event. In 1993, the first such eventwas announced (see above illustra-tion), and in 1997 a complete analy-sis of six events was finished. Morerecently, the MACHO collaborationhas finished analysis of five-and-a-

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Blue

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Abl

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0200 300 400

Days from January 2, 1992

500

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A microlensing event discovered by theMACHO collaboration in 1993. Brightnessof the star is plotted against time in twodifferent band passes.

The 1.3 meter “Great Melbourne” tele-scope at Mt. Stromlo, Australia, used bythe MACHO collaboration.

12 SPRING 2000

may in fact be “blends” of severalstars that happen to be near eachother on the sky. As the quality ofthe atmosphere changes, the amountof blending will vary with time, giv-ing unequal quality brightness mea-surements. Thus, it is a major taskto understand how many micro-lensing events one would expect tosee, even if the Milky Way halo con-sisted entirely of MACHOs. A majoreffort involving creation of artificialimages under different conditionsand Monte Carlo of the effects of allthe above errors was undertaken, andthe efficiency of the experiment cal-culated. This efficiency ranges fromaround 10 percent for events that last10 days, to 50 percent for events ofduration 200 days, to below 5 percentfor events of duration 1000 days.Using this efficiency curve, one cando a proper comparison of the num-ber of microlensing events expectedand the number of microlensingevents observed.

The result of this comparison isthe likelihood plot shown in the il-lustration on the left. One sees thatif the 14–17 microlensing events ob-served in the recent data set are alldue to lensing of MACHOs, they rep-resent about 20 percent of the darkmatter in the Milky Way halo. In-cluding Poisson uncertainties, the 95percent confidence level for halo frac-tion is between 8 percent and 50 per-cent for a typical halo model. Themass of the MACHOs can also be es-timated and is found to be between0.15 MO. and 0.9 MO. . Note that all theobserved Large Magellanic Cloud mi-crolensing events have durationslonger than 20 days and that the non-observation of short duration eventsallows objects in the range 10-2 MO. to

half years of data containing 14–17microlensing events, and has giventhe best analysis to date. The EROScollaboration has also recently an-nounced limits on the amount ofMACHO dark matter.

TURNING the observed mi-crolensing events into thefraction of dark matter that

consists of MACHOs is not an easytask. First one must worry about con-tamination from variable stars andbackground supernova. For example,early analyses counted supernovasas potential microlensing. However,by checking the light curve shape,and by searching for the backgroundgalaxies associated with supernovas,this background can be removed, andit is expected that there is very littlesupernova contamination in themost recent microlensing samples.There are also types of variable stars(nicknamed “bumpers”) that havea constant brightness for a long time,then brighten for a short time in atime-symmetric way, quite similarto microlensing. These, howeverseem to occur only in stars of a spe-cific brightness and color (as expectedfor a new type of variable star) andtherefore can be eliminated as back-ground. Microlensing is expected tooccur randomly on stars of everytype, color, and brightness.

Next, it is not an easy task to cal-ibrate the experiment. There arerainy days, telescope glitches, badseeing, full moons, and so forthwhich mean that the experiment isnot equally sensitive to all the micro-lensing that occurs. In addition, thesampling of each star is not constant,and light curves that are assumedto consist of the light from one star,

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Mo)

Results of recent microlensing analysis.Likelihood contours for the dark matterhalo fraction f and the MACHO mass m.Contours are at confidence levels of 99percent, 90 percent, and 68 percent. Themost likely value is marked with a +, ahalo made up of 20 percent MACHOs,with masses of 0.4 MO. .

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10-7MO. to be ruled out as the darkmatter. This is a very powerful result.

Microlensing aficionados usuallyquote results using the “opticaldepth” to microlensing. This is theprobability than a given star is un-dergoing microlensing at any giventime. A full MACHO halo predicts anoptical depth towards the Large Mag-ellanic Cloud of about 5´10-7. Theresult of the above analysis gives ameasured optical depth of 1.2+0.4

-0.3´10-7,quite consistent with the likelihoodanalysis.

The EROS collaboration has alsorecently reported the results of theiranalysis. They report two micro-lensing events and interpret their re-sults as a limit on the amount ofMACHO dark matter. They rule outa 50 percent MACHO halo at the 95percent confidence level for MACHOsof masses under 0.4 MO. .

IT SEEMS that while a portionof the dark matter may consist ofMACHOs, the bulk of it cannot.

Thus, the need to search for parti-cle dark matter becomes more im-portant than ever. Even before themicrolensing results one had goodtheoretical reasons, based on BigBang nucleosynthesis, to expect alarge amount of non-baryonic darkmatter. With the microlensing re-sults, it becomes clear that even thedark matter in the halo of the MilkyWay must consist mostly of somequite exotic material, such as a newtype of elementary particle.

We also note that the measure-ment that 20 percent of the MilkyWay dark matter consists of MACHOsrequires several caveats. For exam-ple, it has been suggested that theLarge Magellanic Cloud itself con-

tains a large extended population offaint stars. Such objects have notbeen detected, but also have not beenruled out. If they exist, the micro-lensing observed by the experimentsmay be due to “Large MagellanicCloud self-lensing” rather thanMACHOs moving in the dark halo ofthe Milky Way. Thus, in fact, theMACHO contribution to the MilkyWay dark matter may be zero! How-ever, this question has not beensettled, and at this point a 20 per-cent MACHO halo is a reasonablehypothesis.

How will this question be settled?A main problem in current micro-lensing experiments is that they areincapable of determining the distanceof the lens object. If Large MagellanicCloud self-lensing is responsible forthe observed microlensing events,then the lenses should all be at about50 kpc, the distance of the Large Mag-ellanic Cloud. If halo MACHOs areresponsible, the typical lens distanceshould be around 10 kpc. Thus evena few determinations of lens dis-tances would solve the problem. For-tunately there are several ways thatnew microlensing experiments coulddetermine these distances. For ex-ample, the Space Interferometry Mis-sion is capable of measuring the par-allax of the lens and obtaining thelens distance. Other satellite orground-based monitoring efforts maybe able to determine parallaxes forcertain classes of microlensingevents. In addition, a certain fractionof microlensing events are “exotic”in that the light curve shape is mod-ified by effects such as a binary lens,or the finite size of the source star.In such cases, it is sometimes pos-sible to determine the lens distance.

One such binary event was seen to-wards the Small Magellanic Cloud(SMC), and the lens was determinednot to be a member of the dark halo,but to be a SMC star lensing anotherSMC star. The Small MagellanicCloud is known to be quite extendedalong the line-of-sight, so it was notsurprising that the one measuredevent was SMC self-lensing. However,even one such event towards theLarge Magellanic Cloud, which is notknown to be extended, would bemost valuable in settling the ques-tion of where the Large MagellanicCloud lenses are located.

OF ALL THE SEARCHESfor dark matter, the micro-lensing experiments have

been the most powerful. They havedetected what may be a significantportion of the dark matter, but per-haps as important, they have elimi-nated the main baryonic dark mattercandidate as the primary constituentof the dark matter. Since all the mainremaining candidates are exotic par-ticles, it could be said that the micro-lensing experiments have given usone of the most important particlephysics results in recent years! Thereare still puzzles to be solved con-cerning the nature of the discoveredmicrolensing events, but severalpaths towards the solution of thesepuzzles are being pursued. We expectthe answers in the near future.