Triaxiality of the Milky Way dark matter halo and the microlensing optical depth towards the Large Magellanic Cloud
Abstract
The microlensing optical depth towards the Large Magellanic Cloud (LMC), τLMC, bounds the compact-object fraction of the Galactic dark matter halo, but is almost always evaluated for a spherical halo. We compute it for triaxial haloes and show that the shape dependence is carried entirely by the projection of the line of sight onto the halo principal axes: for a scale-free halo ρ∝ R−α at fixed local density it factorises exactly as τ/τsph=S⊙α⟨ S−α⟩w, with S(Ω) the ellipsoidal shape function. The LMC lies only 0fdg78 from perpendicular to the Sun-Galactic Centre line, making it a near-optimal probe of in-plane elongation and a poor probe of vertical flattening. For the halo shapes favoured by \textit{Gaia} we find τLMC/τsph=0.95--$1.15$ at fixed local density, $1.57$ for the Law-Majewski logarithmic potential, and $0.67−−1.54$ when the major-axis azimuth is left free. For the Einasto halo required by the declining \textit{Gaia} DR3 rotation curve, truncation near 25kpc is offset by the larger local density it implies and τ falls by only $7−−15$ per cent; but the median lens distance moves inwards from $13.4$ to 8.5kpc, where the logarithmic slope is steep and rising, amplifying the shape sensitivity: the \textit{Gaia} RR~Lyrae enhancement grows from $15$ to $23$ per cent and the orientation-free range widens to $0.62−−1.62$. The systematic on the inferred MACHO or primordial-black-hole fraction is two-sided, of order ±15 per cent for the measured shapes and a factor $2.6$ under full orientation freedom, exceeding the statistical errors of the EROS-2 and OGLE bounds.
Related
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BibTeX
@misc{garciabellido2026triaxiality,
title = {{Triaxiality of the Milky Way dark matter halo and the microlensing optical depth towards the Large Magellanic Cloud}},
author = {J. García-Bellido and M. R. S. Hawkins},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08988},
eprint = {2609.08988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08988},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triaxiality of the Milky Way dark matter halo and the microlensing optical depth towards the Large Magellanic Cloud
AU - J. García-Bellido
AU - M. R. S. Hawkins
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08988
UR - https://arxiv.org/abs/2609.08988
AB - The microlensing optical depth towards the Large Magellanic Cloud (LMC), τ_LMC, bounds the compact-object fraction of the Galactic dark matter halo, but is almost always evaluated for a spherical halo. We compute it for triaxial haloes and show that the shape dependence is carried entirely by the projection of the line of sight onto the halo principal axes: for a scale-free halo ρ∝ R^−α at fixed local density it factorises exactly as τ/τ_sph=S_⊙^α⟨ S^−α⟩_w, with S(Ω) the ellipsoidal shape function. The LMC lies only 0fdg78 from perpendicular to the Sun-Galactic Centre line, making it a near-optimal probe of in-plane elongation and a poor probe of vertical flattening. For the halo shapes favoured by \textit{Gaia} we find τ_LMC/τ_sph=0.95--$1.15$ at fixed local density, $1.57$ for the Law-Majewski logarithmic potential, and $0.67−−1.54$ when the major-axis azimuth is left free. For the Einasto halo required by the declining \textit{Gaia} DR3 rotation curve, truncation near 25kpc is offset by the larger local density it implies and τ falls by only $7−−15$ per cent; but the median lens distance moves inwards from $13.4$ to 8.5kpc, where the logarithmic slope is steep and rising, amplifying the shape sensitivity: the \textit{Gaia} RR~Lyrae enhancement grows from $15$ to $23$ per cent and the orientation-free range widens to $0.62−−1.62$. The systematic on the inferred MACHO or primordial-black-hole fraction is two-sided, of order ±15 per cent for the measured shapes and a factor $2.6$ under full orientation freedom, exceeding the statistical errors of the EROS-2 and OGLE bounds.
ER -