On the microlensing optical depth of the Galactic bar

Hongsheng Zhao*, Shude Mao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


The microlensing probability (optical depth τ) towards the Galactic Centre carries information about the mass distribution of the Galatic bulge/bar, and so it can be used to constrain the very uncertain shape parameters of the bar. We find τ depends on the bar mass, radial profile, angle, axis scalelengths and boxyness by a few simple analytical formulae, which show: (1) τ is largest if the angle α and the axial ratio y0/x0 conspire so that y0/x0 = tan α. (2) At a fixed field on the minor axis but away from the centre, boxy bars with a flat density profile tend to give a larger optical depth than ellipsoidal bars with a steep profile. (3) Main-sequence sources should have a significantly lower (20-50 per cent lower) optical depth than red clump giants if main-sequence stars are not observed as deep as the bright clump giants. An application to four models constrained by the COBE maps shows most models produce optical depth 2σ lower than MACHO and OGLE observed values even with both a massive bar, 2.8 × 1010 M, and a full disc. The high τ argues for a massive ( > 2 × 1010 Ṁ) boxy bar with y0/x0 ≈ tan α and α < 20° and with a flat radial profile up to corotation.

Original languageEnglish
Pages (from-to)1197-1213
Number of pages17
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
Publication statusPublished - 1 Jan 1996


  • Dark matter
  • Galaxy: centre
  • Gravitational lensing


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