The End of the MACHO Era: Limits on Halo Dark Matter from Stellar Halo Wide Binaries

TL;DR

This study tests whether Massive Compact Halo Objects (MACHOs) can account for Galactic dark matter by exploiting halo wide binaries as sensitive perturber probes. Using impulse-approximation Monte Carlo simulations and a scattering-matrix framework, the authors compare predicted perturbation signatures to the Chanamé & Gould (2003) halo-binary sample via a likelihood analysis. They find that MACHOs with masses above $43\,M_\odot$ are excluded at 95% confidence for the standard local halo density, effectively closing the traditional MACHO mass window and strengthening constraints beyond microlensing limits. The approach demonstrates that wide halo binaries provide a robust, complementary constraint on dark-matter substructure and reinforces the case against a MACHO-dominated halo across a broad mass range in favor of non-baryonic dark matter.

Abstract

We simulate the evolution of halo wide binaries in the presence of MAssive Compact Halo Objects (MACHOs) and compare our results to the sample of wide binaries of Chaname & Gould (2003). The observed distribution is well fit by a single power law for angular separation, 3.5" < theta < 900", whereas the simulated distributions show a break in the power law whose location depends on the MACHO mass and density. This allows us to place upper limits on MACHO density as a function of their assumed mass. At the 95% confidence level, we exclude MACHOs with mass M > 43Msun at the standard local halo density rho_H. This all but removes the last permitted window for a full MACHO halo for masses M > 10^{-7.5}Msun.

Figures (7)

• Figure 1: Halo binary distribution function from the catalog of cg. Samples of wide binary systems are complete up to 900$^{\prime\prime}$ while the lower limit in angular separation is not precisely established. The circles represent actual counts in six equal logarithmic bins over $3.\!\!\hbox{$^{\prime\prime}$}5\leq\Delta <900\hbox{$^{\prime\prime}$}$. The triangles show three $1\hbox{$^{\prime\prime}$}$ bins for $\Delta <3.\!\!\hbox{$^{\prime\prime}$}5$ and are rescaled to account for the smaller bin sizes relative to the circles. Various lines represent fits for subsamples with different lower limits in angular separation. Error bars represent one standard deviation $=n^{-1/2}/\ln10$.
• Figure 2: Binary distributions as a function of semi-major axis. 100,000 binaries are generated following an arbitrarily chosen flat ($$=1) distribution represented as a thick solid line. The halo density is set to be $_H$. The squares, triangles and circles represent binary distributions for three different masses of perturber, after $T=10$ Gyrs evolution. The fitting curves for each model are shown as dashed lines.
• Figure 3: Evolution of binary distributions with the initial power law, $=1.567$ obtained in § \ref{['wb']}, represented as a thick solid line. 50,000 binaries are evolved in the presence of perturbers of mass 1000${\rm \ M_\odot}$ The circles show the binary distributions as functions of semi-major axis while the triangles show the distributions of projected physical separations of the binary components onto the sky plane. The solid lines represent fitting curves for semi-major axis, and the dashed lines for projected physical separation. Two vertical arrows indicate transitions, $a_t$, from the unperturbed to the perturbed regimes.
• Figure 4: Transition separations $a_t$ for different halo densities as a function of perturber mass. Transition separations are obtained for each model by calculating the intersection of $f(x)$ and $g(x)$ in eq. (\ref{['fit']}).
• Figure 5: The best-fit final binary distributions for various perturber masses, assuming that the initial distribution is a power-law. The halo density is set to be $_{\rm H}$. The observed halo binary distribution (Fig. \ref{['data']}) is shown for comparison. A model with 1000 $M_\odot$ perturber deviates significantly from the observations while a model with 10 $M_\odot$ is quite consistent with them.