Probing MACHOs Toward the Galactic Bulge(8)

If the massive compact halo object (MACHO) fraction of the Galactic dark halo is f ~ 20% as suggested by some microlensing experiments, then about 1.2% of lensing events toward the Galactic bulge are due to MACHOs. For the 40% of these that lie nearby (D_l

Afteraccountingforobservedstarsandextrapolatingdowntobrowndwarfsanduptotheprogenitorsofremnants,Gouldetal.(1998)estimate6.4×10 5M⊙pc 3.However,bothDahnetal.(1995)andGould(2003) ndsubstantiallymorelow-luminosity(MV>8)starsthandidGouldetal.(1998)intheirmorelocalsample(seeFig.2fromGould2004b),soIhaveadjustedtheirestimateupward.Thepower-lawslopeismeasuredbyseveraltechniques(Gouldetal.1998andreferencestherein).

Figure1showstheopticaldepthperunitdistanceduetospheroidstarsandtoputativeMACHOsundertheassumptionthatf=20%.ItshowsthatevenwithaMACHOfractionof20%,thehalodominatesthespheroidfromR=R0toR=4kpc,whichlatterisaboutthelimittowhichthelocalspheroiddensitypro lecanbereliablyextrapolated.However,thisdominationisnotoverwhelming:atR=4kpcitisonlyafactorof5andevenatR=7kpc(wherethehaloopticaldepthhasfallenbyafactor5)thehaloonlydominatesbyafactor

10.Thismeansthat2or3halolenseswouldhavetobeidenti edtoconstituteareliable“MACHOdetection”.Otherwise,therewouldbeasigni cantpossibilitythatspheroidlenseswereresponsible.

SinceonemustrestrictattentiontoDl<4kpc,thetotalavailablehaloopticaldepthisreducedbyafactor0.4relativetothe1.3×10 7calculatedbyGriestetal.(1991).Ifwefurtherassumef=20%,theavailablehaloopticaldepthisfurtherreducedto10 8,about0.5%oftheobservedopticaldepthofτ～2×10 6(Afonsoetal.2003b;Popowski2005;Sumietal.2005).Hence,assumingforthemomentthattheeventratesareinproportiontotheopticaldepths,roughly200measurementswouldberequiredtoidentifyasinglehalolens.Thus,iftheSIMmissionwereextendedfrom5to10years(asiscurrentlyenvisioned)thenonemightexpectto ndabout2halolenses.Asnotedabovethisisjustatthemarginofaviabledetection.

4.PracticalConsiderations

4.1.EventTimescales

TheEinsteintimescalesofthesehaloeventsaregivenby,

tE=15day M

0.25 1/2 v⊥

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