Observations from Australasia using the Gravitational Microlensing Technique

Philip Yock
, PASA, 17 (1), 35.

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Dark Matter

The study of dark matter, and in particular brown dwarfs, was the first application of the gravitational microlensing technqiue to be proposed, and it motivated the early observations by the pioneering groups in the field, viz. MACHO, EROS and OGLE. The technique is particularly suited to the study of brown dwarfs or similar dark objects because it does not rely on optical detection. Paczynski (1986) showed that, if the Galactic halo is composed of brown dwarfs, then approximately one star in a million in the Magellanic Clouds would be lensed at any one time by a brown dwarf for a duration

$\sim140\sqrt{M/M_{\odot}}$ days. Here M denotes the mass of the brown dwarf, which is

$<0.08M_{\odot}$. Hence the expected duration for these lensing events is $\sim$40 days or less. The MACHO group has now monitored several million stars in the Magellanic Clouds for several years. Amongst their database of LMC stars to 1997, no events were found with duration less than 20 days. A similar result was obtained by the EROS group working from Chile. These results were combined to yield a 95% confidence upper limit $\sim10\%$ on the halo-mass-fraction of low-mass brown dwarfs with masses in the range

$(10^{-7}-10^{-2})M{_\odot}$ (Alcock et al. 1998). This result eliminates low-mass brown dwarfs, planets that have been ejected from planetary systems, and any other compact non-luminous objects in the stated mass range as a significant component of halo dark matter for standard models of the halo.

Figure 1: Upper limits to mass fractions of halo objects of various masses determined by Alcock et al. (1998a) - thin line, by Afonso et al. (1999a) - thick line, by Gilmore & Unavane (1998) - thin dashed line, and by Abe et al. (1999b) - thick dashed line. The possible detection is by Alcock et al. (1997a). The limits by Gilmore & Unavane, and by Abe et al., were obtained by surface photometry of external galaxies. They apply to main-sequence stars only.
\begin{figure} \begin{center} \psfig{file=fig1B.eps,height=7cm} \end{center} \end{figure}

The MACHO and EROS groups extended their searches to include events of longer duration corresponding to brown dwarfs and other non-luminous objects with masses in the range

$(0.01-1)M{_\odot}$. The EROS group did not detect any events caused by halo objects in this mass range in the direction of the SMC (Afonso et al. 1999a). The MACHO group has, however, recorded several events in this mass range in their database towards the LMC, corresponding to a halo fraction of $\sim50\%$ of objects with mass

$\sim0.5M{_\odot}$ (Alcock et al. 1997a). The result, which is marginally consistent with the above result of the EROS group, was generally unexpected. It has proven difficult to interpret. The above results are shown collectively in Figure 1. This figure also includes data from Gilmore and Unavane (1998) and the MOA group (Abe et al. 1999) that were obtained by surface photometry of external galaxies. The surface photometry data apply to main-sequence stars, i.e. to red dwarfs. Similarly restrictive limits on the abundance of red dwarfs in the Galactic halo have been obtained from studies of the Hubble deep field (Graff & Freese 1996, Flynn, Gould & Bahcall 1996). It is clear that the objects being detected by the MACHO group cannot be red dwarfs. Two types of interpretations of the data have been proposed. The first assumes a halo comprised mainly of old white dwarfs (Alcock et al. 1997a) or of primordial black holes (Nakamura 1998). The white dwarf hypothesis requires the initial mass function to be strongly peaked at

$\sim2M{_\odot}$, to enable the white dwarfs to cool sufficiently to escape detection in other surveys (Chabrier et al. 1996), and it leaves unexplained the metal enrichment that would be expected to accompany them (Gibson and Mould 1997). The primordial black hole hypothesis requires their mass function to be peaked at

$\sim0.5M{_\odot}$, surprisingly close to the mass of a normal star. Both these interpretations may be tested in the future by independent observations. Direct observations of white dwarfs should be possible if they are a major component of the halo (Chabrier 1999), and gravitational mergers of primordial black holes may be detectable if primordial black holes are a major component (Nakamura 1998).

Figure 2: Light curve of gravitational microlensing event MACHO-1995-BLG-30. The additional schematic relates the scale of the lens's Einstein radius to the angular size of the source star, and indicates transit of the lens across the source face. The Einstein radius RE is the impact parameter of the light at the lens plane assuming the lens to be perfectly aligned with the source.
\begin{figure} \begin{center} \psfig{file=fig2.ps,height=8cm} \end{center} \end{figure}

The second type of interpretation that has been proposed for the MACHO events has potential implications for galactic structure. Sahu (1994) proposed that foreground stars in the LMC may lens background stars in the LMC, a process known as 'self lensing'. Initially, the expected event rate for self-lensing was expected to be too low to account for the observations (Gould 1995a). However, examples of self-lensing were subsequently detected (see section 5.2 below), and these lend weight to Sahu's hypothesis. Modified models of the LMC have been proposed that may accommodate a high self-lensing rate (Aubourg et al. 1999; Salati et al. 1999; Weinberg 1999), and methods have been proposed to test such models (Zhao 1999a, 1999b, 1999c; Graff et al. 1999). In a related proposal, Evans et al. (1998) proposed significant flaring and/or warping of the disk of the Milky Way to account for the MACHO events, a possibility that may also be tested by direct observation. In summary, the microlensing experiments have shown conclusively that halo dark matter is not composed mainly of brown dwarfs. Not all the data that have been obtained to date have been explained yet. Possibilities have been proposed, including old white dwarfs, primordial black holes, or modifications to current models of galactic structure. These may all be tested through independent observations. Also, further applications of the microlensing technique may yet reveal that brown dwarfs provide a substantial fraction of the mass of the Galactic Bulge.

Figure 3: Peak structure of microlensing event MACHO-1995-BLG-30, showing the best standard microlensing fit to the data (dashed curve), and an extended source microlensing fit incorporating source limb-darkening (solid curve).
\begin{figure} \begin{center} \psfig{file=fig3.ps,height=9cm} \end{center} \end{figure}


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