The end of the MACHO era- revisited: new limits on MACHO masses from halo wide binaries

TL;DR

The study addresses whether MACHOs can constitute a significant portion of the Galactic halo by using halo wide binaries as dynamical sensors. It develops a Monte Carlo, impulse-approximation model to simulate binary disruption by perturbers of mass $M$ over $10~{\rm Gyr}$, comparing predicted semiaxis distributions to observations and refining fits with both dispersion $\sigma$ and KS tests. By applying the model to an expanded catalog of 211 candidate halo binaries (including 150 with computed orbits) and accounting for disk passages and non-uniform halo density, the authors derive upper limits on $M$ that range from $112~M_\sun$ down to $<3~M_\sun$, depending on the sample and assumptions. These results, consistent with microlensing constraints, strongly argue against a MACHO-dominated dark halo and highlight the value of halo binaries with well-determined orbits for constraining dark matter candidates.

Abstract

In order to determine an upper bound for the mass of the massive compact halo objets (MACHOs) we use the halo binaries contained in a recent catalog (Allen \& Monroy-Rodríguez 2013). To dynamically model their interactions with massive perturbers a Monte Carlo simulation is conducted, using an impulsive approximation method and assuming a galactic halo constituted by massive particles of a characteristic mass. The results of such simulations are compared with several subsamples of our improved catalog of candidate halo wide binaries. In accordance with Quinn et al. (2009) we also find our results to be very sensitive to the widest binaries. However, our larger sample, together with the fact that we can obtain galactic orbits for 150 of our systems, allows a more reliable estimate of the maximum MACHO mass than that obtained previously. If we employ the entire sample of 211 candidate halo stars we obtain an upper limit of $112 M_\sun$. However, using the 150 binaries in our catalog with computed galactic orbits we are able to refine our fitting criteria. Thus, for the 100 most halo-like binaries we obtain a maximum MACHO mass of $21-68 M_\sun$. Furthermore, we can estimate the dynamical effects of the galactic disk using binary samples that spend progressively shorter times within the disk. By extrapolating the limits obtained for our most reliable -albeit smallest- sample we find that as the time spent within the disk tends to zero the upper bound of the MACHO mass tends to less than $5 M_\sun$. The non-uniform density of the halo has also been taken into account, but the limit obtained, less than $5 M_\sun$, does not differ much from the previous one. Together with microlensing studies that provide lower limits on the MACHO mass, our results essentially exclude the existence of such objects in the galactic halo.

Figures (9)

• Figure 1: Evolved distribution of semiaxes for various perurber masses. The model was applied to the Quinn et al. binaries. Dots correspond to perturber masses of $1000~M_\sun$, triangles to $100~M_\sun$, small squares to $10~M_\sun$. Each symbol represents 500 modelled binaries. The graph shows results very similar to those of Yoo et al. and Quinn et al. Perturber masses of $1000~M_\sun$ appear to be too large, while masses below $10~M_\sun$ seem too small to reproduce the observed distribution (large dots). The bars in the observed distribution correspond to sampling errors
• Figure 2: Exclusion contour plot. The thick grey lines denote the limits from microlensing experiments and galactic disk stability. The thin dashed line is the result of Yoo et al. for 90 binaries. The thick dashed line is our result for the same sample, using a their method. Both results agree reasonably well. The thin full line is the result of Quinn et al. for the 90 original Yoo et al. binaries. The thick full line is our result for the same sample, using a fit to $2\sigma$. Here again, the results agree well. Finally, the thick dotted line refers to the result of Quinn for 89 binaries, omitting one spurious pair. The concordance of previous results with our method applied to the same samples of binaries appears satisfactory, especially in the region of large halo densities and small perturber masses, which is the interesting region. Previous work dealt with projected angular separations. We deal with semiaxes, and therefore the results cannot be expected to be identical.
• Figure 3: The evolved distribution of semiaxes for different perturber masses, compared with three samples of binaries from our catalog. The straight horizontal line shows the initial distribution. The large dots with error bars denote the observed data. The dashed lines show the two power-line fits to the observed samples, namely an Oepik law fit to the unevolved region and a steeper power law for the evolved region (see text). Filled squares correspond to perturber masses of $10~M_\sun$, triangles to $100~M_\sun$ and dots to $1000~M_\sun$. Depending on the sample considered, perturber masses of several hundreds $M_\sun$, about $10~M_\sun$ and less than $10~M_\sun$ appear to fit respectively the 100, 50 and 25 most halo-like binaries.
• Figure 4: Fits of the evolved model distribution to different samples of binaries. The squares show the best fit, which defines $\sigma_0$ (see text), and corresponds to perturber masses of 16, 7 and $2~M_\sun$ for the 100, 50 and 25 most halo-like stars, respectively. The triangles correspond to fits to $2\sigma_0$, which we still consider acceptable, and give more conservative estimates for the perturber mass: 21, 11 and $3~M_\sun$ for the 100, 50 and 25 most halo-like stars, respectively. The right-hand panels display the results of applying the Kolmogorov-Smirnov test to these fits. The large dots correspond to the squares ($\sigma_0$) and show that the fit is excellent ($Q=1$) for the entire range of semiaxes. The small dots correspond to the triangles ($2\sigma_0$) and show that the fit is still acceptable for all but the largest semiaxes.
• Figure 5: Cumulative distributions of observed semiaxes for three samples of binaries from our catalogue, displayed by diamonds. The KS test was applied to both a single Oepik-like fit (exponent 1) and to a two-power law fit, with an Oepik like distribution for the unevolved region and a steeper power-law for he evolved region. The $Q$ indicator for the single power-law fit, plotted on the right hand axis, shows an excellent fit for the unevolved region but drops after a certain value of the semiaxes (dashed lines). The two power-law fits are able to represent well the entire region, as shown by the empty squares and the $Q$ indicator (full line).