We discuss whether the astrophysical objects responsible for the recently
reported microlensing events of sources in the Large Magellanic Cloud can be
identified as the brown dwarf components of the spheroid of our galaxy, rather
than the constituents of a dark baryonic halo.Comment: 10 pages, Postscript file (3 figures included). Talk given by E.R. in
  the 6^th Workshop on Neutrino Telescopes, Venice, February 199

Giudice, G. F.

Mollerach, S.

Roulet, E.

English

arXiv

Abstract: We discuss whether the astrophysical objects responsible for the recently reported microlensing events of sources in the Large Magellanic Cloud can be identified as the brown dwarf components of the spheroid of our galaxy, rather than the constituents of a dark baryonic halo.We discuss whether the astrophysical objects responsible for the recently reported microlensing events of sources in the Large Magellanic Cloud can be identified as the brown dwarf components of the spheroid of our galaxy, rather than the constituents of a dark baryonic halo

Giudice, G.F.

CERN Document Server

CERN-TH.7257/94IS THE HALO RESPONSIBLE FORTHE MICROLENSING EVENTS?1E. ROULET, S. MOLLERACH and G. F. GIUDICETheory Division, CERNGeneva, CH-1211, SwitzerlandABSTRACTWe discuss whether the astrophysical objects responsible for the recentlyreported microlensing events of sources in the Large Magellanic Cloud canbe identied as the brown dwarf components of the spheroid of our galaxy,rather than the constituents of a dark baryonic halo.CERN-TH.7257/94May 19941Talk given by E. R. at the 6thWorkshop on Neutrino Telescopes, Venice, february19941The microlensing events in the Large Magellanic Cloud (LMC) recentlyreported by the EROS [1] and MACHO [2] collaborations indicate the pres-ence of compact dark objects passing very close to the line of sight to the mon-itored stars [3{5]. These objects have been interpreted as the constituentsof the dark halo of the Galaxy. We have recently proposed an alternativeinterpretation [6] in which the dark lensing objects are, instead, the mainconstituents of the galactic spheroid. This interpretation is suggested bymodels of the Galaxy based on dynamical observations [7{9], which predicta spheroid component much heavier than accounted for by direct measure-ments of star counts at high latitudes and of high-velocity stars [10], namelyMS(lum) = 1{3109M, whileMS(dyn) = 5{71010M. The dierence be-tween the luminous and the dynamical determinations of the spheroid masscan be understood if most of the mass in the spheroid is non-luminous, inthe form of very faint stars or brown dwarfs, that are then ideal candidatesfor lensing objects. This is supported by the measured shape of the massfunction of spheroid eld stars, which behaves, below m ' 0:4Mand downto the smaller masses observed (0:14M), as dN=dm / m 4:5[11], suggestingthat most of the spheroid mass is in stars lighter than the hydrogen burninglimit mHB' 0:085Mand hence dark. In our proposed scenario, the pre-dicted event rate for sources in the LMC results lower than in the halo one,but it is still signicant and consistent with the observations (that in factseem to be in decit with respect to the predictions of the halo model). Yetanother possibility has been pointed out by Gould [12], who suggested thatthe lensing objects could be in the thick disk of the Galaxy.Spiral galaxies, as our own, have at least three main components: theexponential disk, containing most of the observed stars (that are young andmetal-rich) and gas clouds; the halo, which should account for the atness ofthe rotation curves and provides most of the mass of the galaxies, but con-tains essentially no luminous matter; and the spheroid component, a roughlyspherical distribution of old (metal-poor) stars, which mass density in ourgalaxy decreases as r 3:5. As mentioned before, the spheroid mass of theGalaxy inferred from dynamical observations is comparable to the total massof the disk, and is an order of magnitude larger than the mass contained in theobserved spheroid stars, indicating a `missing mass' problem in the spheroid.One could also mention that the relative importance of the disk and spheroidluminosities is one of the main characteristics to identify the Hubble type ofa spiral galaxy, with Sc having very small spheroids while Sa have large ones2(and ellipticals being `only spheroid' galaxies).We use for the dierent components the following simplied mass densi-ties, which are good approximations to those obtained using ts to dynamicalobservations:H= H0r20+ a2r2+ a2; (1)for the halo, andS= S0 pr0+pbpr +pb!7; (2)for the spheroid, where r0= 8:5 kpc is the distance from the sun to thegalactic centre, a = 3 kpc, b = 0:17 kpc and the local densities are H0=0:01M=pc3and S0= 0:0015M=pc3(for reference, the local density of diskstars is approximately 0:1M=pc3).The light curve of a microlensing event is an achromatic and symmetricamplication of the source star light given byA(u) =u2+ 2upu2+ 4; (3)where u is the distance of the lens to the line of sight in units of the Einsteinradius REu2(t) = dRE!2+ vr?(t  to)RE!2; (4)with d the impact parameter, vr?the lens velocity relative to the microlensingtube (see below) in the direction orthogonal to the line of sight, andRE 2sGM(L   x)xc2L; (5)with L the distance to the source and x that to the lens of mass M . Themaximum amplication is reached at the time to, when u takes its mini-mum value umin= d=RE. The light curve can then be tted by the threeparameters to, Amax= A(umin) and the event duration T  RE=vr?.The probability that a star is being microlensed at a given time is theso-called optical depth  =ZL0dxddx; (6)3Table 1: The optical depth ( ), the average distance to the lenses (hxi), theevent rate ( ), and the average event duration (hT i), for microlensing eventsin the LMC. The lensing object mass m0:05is in units of 0:05M. We havetaken uT= 1 and  / u2T;  / uT.Model  hxi   hT i[kpc] [eventsyr 106stars] [days]Halo 5:8  10 716 9:2=pm0:0515pm0:05Spheroid 4:6  10 811 0:7=pm0:0516pm0:05withddx=4Gu2Tx(L  x)(x)c2L: (7)A special property of  is that it is independent of the mass function of thelensing objects dN=dm. The rst column of Table 1 shows the value of  forthe halo and spheroid models.In Fig. 1, we plot the function (L= )d=dx that measures the contributionof the lenses to  in terms of their distance to us. Deninghxi 1ZL0dxxddx; (8)that is the average distance at which microlensing takes place, we obtainhxi = 11 kpc and 16 kpc for the spheroid and halo models, respectively (asshown in Table 1). This shows that although the spheroid density decreasesvery steeply when moving out of the galactic centre, hxi is still relativelylarge for the spheroid, partly because the LMC line of sight is at nearly 80from the galactic centre; hence it is only for points along the line of sight atx > 10 kpc that the galactocentric distance starts to increase signicantly(we show ticks corresponding to galactocentric distances r = 10; 20; 30 and40 kpc in Fig. 1).4Fig. 1: Contribution to  vs. the distance to the lensing objects x for the LMC.More important than  is the microlensing rate  . Assuming an isotropicand isothermal Maxwellian velocity distribution for the lenses, with one-dimensional dispersion , the dierential rate is given byd dT=Z10dmZL0dxdN(x)dm8uT2z4e (z2+2)I0(2z); (9)where z  RE=(p2T ) and   j(x=L)~vs?+(1 x=L)~v?j=(p2), with ~vs?and ~v?the component of the source and the sun velocity in the directionorthogonal to the line of sight. If the total gravitational potential of theGalaxy leads to a constant rotation velocity vc, an isothermal componentwith  / r nshould have a velocity dispersion  = vc=pn; hence, for thespheroid we get S' 120 km/s, in agreement with the observations, and forthe halo H' 155 km/s. The total event rate,   R10dT (d =dT ), is shownin column 3 of Table 1, assuming that all the lenses have the same mass M ,i.e. dN(x)=dm = ((x)=M)(M  m). There is a simple relation giving the5Table 2: The optical depth ( ), the event rate ( ), and the average eventduration (hT i), for microlensing events in Baade's window. The results fordisk DM and faint disk stars are taken from Ref. [15].Model  hxi   hT i[kpc] [eventsyr 106stars] [days]Halo 2:6 10 75:3 10=pm0:056pm0:05Spheroid 5:1 10 77:1 25=pm0:055pm0:05Faint stars (2:9  9:6)  10 74:5 2:2{7:5 30average event duration hT i = (2=)= , whose values are shown in the lastcolumn of Table 1. Note that the EROS/MACHO events, with durations T =17; 9; 14; 27 and 30 days suggest lens masses in the brown dwarf range of m 10 2{10 1Mfor both models. At the time of this writing, both the EROSand MACHO experiments have accumulated a statistics of approximately107stars yr and have seen two and three events respectively. We then seefrom Table 1 that, unless the (still unavailable) observational eciencies werebelow 10%, the spheroid predictions are quite consistent with observationswhile the halo ones seem to be somewhat in excess.A third microlensing experiment, the OGLE collaboration [13], as wellas the MACHO team, have been looking for microlensing events on starsin the galactic bulge. Here the contribution of the spheroid dark objectsis expected to be particularly important, due to the rise in the spheroiddensity towards the galactic centre. However, a strong background for theseobservations is due to the faint stars in the disk itself [14{15], which canbe computed from the knowledge of the disk stellar mass function [16] andtaking into account the star rotation. It is also important in this case to takeinto account the large velocity dispersion of source stars Bulge' 105 km/s.This is performed by integrating Eq. (9) over the source velocities using aMaxwellian distribution. We show in Table 2 the same quantities as in Table1, but for observations in Baade's window (BW), for the spheroid, the haloand for disk stars.6Figure 2 shows (L= )d=dx for observations in the BW. We see that inthis case the main contribution to the spheroid rates comes from the inner 1{2 kpc around the galactic centre. The values of   reported in Table 2 indicatethat the expected rates from the spheroid are larger than those from the haloand that the main characteristic of these events is their short duration, of justa few days for brown dwarf masses. Of course, to relate the `theoretical' rateswith the actual observations, a knowledge of the experimental eciencies isrequired. These are however not yet available, but since at present typicallyone image per eld is taken each night, not all nights are good for observation,and the selection criteria for the events require typically ve points in thelight curve above the amplication threshold, the eciency becomes verypoor for events of durations shorter than a week, where most of the spheroid(and halo) events are expected.Fig. 2: Contribution to  vs. the distance to the lensing objects x for the Bulge.Figure 3 shows the theoretical rates for events with duration T > T0asa function of T0, i.e.  (T > T0) =R1T0dT (d =dT ). We can see that they are7very sensitive to the minimumdetectable duration T0. Hence, it seems crucialfor bulge observations to reach good sensitivity to events of a few days byincreasing the number of exposures to the same eld during the same night.Another attractive strategy would be to combine observations of the OGLEand MACHO experiments of the same stars, since if this were possible thedierent terrestrial longitudes of the two observatories (Chile and Australia,respectively) would provide a more complete time coverage of events of shortduration. It should be noted that the events observed up to now by OGLE,with durations of 11, 12, 14, 26 and 45 days, and those of MACHO, withdurations of 10, 21, 24 and 25 days, are probably due mainly to faint diskstars.Finally, as discussed in Ref. [6], there are other signatures that couldallow to distinguish among halo and spheroid lenses, such as the angulardependence of the bulge rates (using measurements in elds other than theBW) or the angular dependence of the rates in the Andromeda galaxy, ifthose observations become feasible.Fig. 3: Rate  (T > T0) vs. T0for bulge observations.8The explanation of the microlensing events as due to a spheroid darkpopulation is particularly attractive in the light of its implications for cos-mology and structure formation. A recent determination of the `primordial'deuterium abundance [17], combined with the nucleosynthesis predictions,suggests that the baryonic content of the Universe is just of the order of theamount of luminous matter. This does not leave much room for large quan-tities of dark baryons, as would be required if galactic haloes were baryonic,but is perfectly consistent with `mostly dark' baryonic spheroids. If non-baryonic dark matter also exists, as seems necessary to make compatible thedeterminations of  at large scales with the nucleosynthesis predictions, therewould be no reason for it not to fall in the potential wells of the galaxies andto be around us. The haloes would then be the natural place for it to reside.The presence of non-baryonic dark matter (of the so-called `cold' type) in thegalaxies is also desirable in the light of our present understanding of structureformation in the Universe, in which baryons fall in the potential wells createdby the cold dark matter density perturbations. Due to the dissipative natureof baryons, we expect them to become more concentrated towards the centreof the galaxy than the non-dissipative dark matter after the gravitationalcollapse, and this would explain the dierent spatial distribution of the twocomponents.References[1] E. Aubourg et al., Nature 365 (1993) 623.[2] C. Alcock et al., Nature 365 (1993) 621.[3] B. Paczynski, Astrophys. J. 304 (1986) 1.[4] K. Griest, Astrophys. J. 366 (1991) 412.[5] A. de Rujula, P. Jetzer, and E. Masso, Mon. Not. R. Astr. Soc. 250(1991) 348.[6] G. F. Giudice, S. Mollerach and E. Roulet, CERN preprint CERN-TH.7127/93, Phys. Rev. D in press.[7] J. A. R. Caldwell and J. P. Ostriker, Astrophys. J. 251 (1981) 61.9[8] J. P. Ostriker and J. A. R. Caldwell, in Dynamics and Structure of theMilky Way (1982), ed. W. L. H. Shuter, Reidel, Dordrecht.[9] K. Rohlfs and J. Kreitschmann, Astron. Astrophys. 201 (1988) 51.[10] J. N. Bahcall, M. Schmidt, and R. M. Soneira, Astrophys. J. 265 (1983)730.[11] H. B. Richer and G. G. Fahlman, Nature 358 (1992) 383.[12] A. Gould, Ap. J. 421 (1994) L71. A. Gould, J. Miralda-Escude and J.N. Bahcall, Princeton preprint IASSNS-AST-93-63, 1993.[13] A. Udalski et al., Acta Astronomica 42[14] B. Paczynski, Astrophys. J. 371 (1991) L63.[15] K. Griest et al., Astrophys. J. 372 (1991) L79.[16] J. M. Scalo, Fund. of Cosmic Physics 11 (1986) 1.[17] A. Songaila et al., Nature 368 (1994) 599.10

Is the halo responsible for the microlensing events?

Abstract

Similar works

Full text

Available Versions

CERN Document Server