EROS and MACHO Combined Limits on Planetary-Mass Dark Matter in the Galactic Halo

Abstract

The EROS and MACHO collaborations have each published upper limits on the amount of planetary mass dark matter in the Galactic Halo obtained from gravitational microlensing searches. In this paper the two limits are combined to give a much stronger constraint on the abundance of low mass MACHOs. Specifically, objects with masses 10 −7 M ⊙ < ∼ m < ∼ 10 −3 M ⊙ make up less than 25% of the halo dark matter for most models considered, and less than 10% of a standard spherical halo is made of MACHOs in the 3.5 × 10 −7 M ⊙ < m < 4.5 × 10 −5 M ⊙ mass range.

Galactic searches for dark matter

“…Though microlensing events were indeed detected by these experiments, it is generally concluded that they do not have significant enough abundance to dominate the mass of the Galactic halo. As no conclusive signature for MACHOs was found, these experiments combined to place strong upper limits on the number of MACHOs in the Galaxy in the mass regime of approximately 10 −7 − 30 M (Alcock et al, 1998;Tisserand et al, 2007;Wyrzykowski et al, 2011).…”

Gravipulsons

“…In turn, as it follows from (24), the stability of the general solution X n ðÞ is determined by the behavior of the functions X þ n ðÞ and X À n ðÞ. It is clear that all solutions X n ðÞ satisfying the initial conditions (33) and (34) are unstable in the resonance case n > 0. Indeed, any perturbation of the initial values X n ð0Þ, X n ð0Þ, determined by (33) and (34), leads to the appearance of terms $ expð n Þ on the right-hand side of (24), thus making the corresponding function X n ðÞ, and hence the solution (9), exponentially growing in time.…”

“…On the other hand, in the nonresonance case n ¼ i n , the functions X þ n ðÞ, X À n ðÞ as well as X n ðÞ in (24) are bounded, and a small perturbation of the initial conditions (33) and (34) results in the appearance of only small oscillating terms in X n ðÞ. So we can expect that the solution (9) is stable if all modes X n ðÞ are nonresonant.…”

“…Thus, under the conditions (30), (33), and (34) the solution (16) is T periodic with respect to . This means the solution (9) is also periodic [with the period ð1 þ ßÞ À1 T with respect to t].…”

Constraints on the induced gravitational wave background from primordial black holes

“…From the analysis of MACHO [57] and EROS [58] microlensing surveys, fðM BH Þ < 0:1 for 10 À6 M < M BH < M and fðM BH Þ < 0:04 for 10 À3 M < M BH < 0:1M . There are some additional constraints on fðM BH Þ for other mass ranges, reviewed, e.g., in [34], but they are generally rather weak (fðM BH Þ % 1) and we do not use them here.…”