The MACHO Project LMC Microlensing Results from the First Two Years and the Nature of the Galactic Dark Halo

TL;DR

The MACHO project analyzes 2.1 years of LMC microlensing data, identifying 8 candidate events with timescales from 34 to 145 days and deriving an optical depth of $\tau_{2}^{200} = 2.9^{+1.4}_{-0.9} \times 10^{-7}$, indicating a significant excess over known stellar lenses. Through maximum-likelihood fits across halo models, the results favor a substantial halo fraction of Machos with a most probable mass around $0.4$–$0.5\,M_\odot$, implying a non-negligible total Macho mass within 50 kpc. Constraints on low-mass Machos ($m \lesssim 0.03\,M_\odot$) are strong, limiting their contribution to roughly $<20\%$ of the standard halo, while heavier lenses remain broadly compatible depending on the halo model. The findings point toward compact objects, possibly white dwarfs, as plausible halo constituents, while highlighting model dependence and blending as key systematic considerations; future real-time alerts and parallax measurements are planned to sharpen the mass and spatial distribution of the lensing population.

Abstract

The MACHO Project is a search for dark matter in the form of massive compact halo objects (Machos). Photometric monitoring of millions of stars in the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and Galactic bulge is used to search for gravitational microlensing events caused by these otherwise invisible objects. Analysis of the first 2.1 years of photometry of 8.5 million stars in the LMC reveals 8 candidate microlensing events. This is substantially more than the number expected ($\sim 1.1$) from lensing by known stellar populations. The timescales ($\that$) of the events range from 34 to 145 days. We estimate the total microlensing optical depth towards the LMC from events with $2 < \that < 200$ days to be $τ_2^{200} = 2.9 ^{+1.4}_{-0.9} \ten{-7}$ based upon our 8 event sample. This exceeds the optical depth, $τ_{\rm backgnd} = 0.5 \ten{-7}$, expected from known stars, and the difference is to be compared with the optical depth predicted for a ``standard" halo composed entirely of Machos: $τ_{halo} = 4.7\ten{-7}$. Likelihood analysis gives a fairly model independent estimate of the halo mass in Machos within 50 kpc of $2.0^{+1.2}_{-0.7} \ten{11} \msun$, about half of the ``standard halo" value. We also find a most probable Macho mass of $0.5^{+0.3}_{-0.2}\msun$, although this value is strongly model dependent. Additionally, the absence of short duration events places stringent upper limits on the contribution of low-mass Machos: objects from $10^{-4} \msun$ to $0.03 \msun$ contribute $\simlt 20\%$ of the ``standard" dark halo.

Figures (26)

• Figure 1: An R-band image of the LMC, $8.2$ degrees on a side (G. Bothun, private communication), showing the locations of the 22 MACHO fields used here.
• Figure 2: The final cuts for selection of microlensing candidates. The x-axis is $\Delta\chi^2/\chi^2_{ml}$, where $\Delta\chi^2 \equiv \chi^2_{const} - \chi^2_{ml}$ is the improvement in $\chi^2$ between a constant brightness fit and a microlensing fit. The y-axis is the fitted maximum magnification. The symbols are explained in § 3.1. The solid lines show the final cuts (10) and (11); the circles in the upper right are the 12 events (10 stars) discussed in § \ref{['sec-events']}. Events 2 and 3 from A96 are also indicated.
• Figure 3: The lightcurves for the 12 candidates (10 stars) in § \ref{['sec-events']}. For each object, the upper and lower panels show blue and red passbands. Flux is in linear units with $1\sigma$ estimated errors, normalized to the fitted unlensed brightness. For clarity, the points shown are averages in time bins roughly matched to the event timescales, as indicated on each panel. For events 1a, 6 and 8, the wavy lines indicate that different templates were used before and after day 330; thus a separate baseline normalization has been used for each portion; see § \ref{['sec-obs']} .
• Figure 4: A mosaic of 2 images centered on each candidate event; the labelled image shows the event near maximum observed brightness, and the un-labelled image shows the event at normal brightness. These are R-band CCD images, with a scale of $0.63"$/pixel. Each box is $40$ arcsec square; North is up and East is left.
• Figure 5: The full lightcurve of event 9, including data from additional observations taken after 1994 October. Many of the red data points corrupted by a CCD trap have been removed as described in the text.