An alternative hypothesis to account for the LMC microlensing events

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An alternative hypothesis to account for the LMC
microlensing events
Jordi Miralda-EscudéThe Ohio State
UniversityIEEC/ICREA
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Microlensing of stars
Einstein radius
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Microlensing lightcurves

• Lensing makes two images of the source, usually
  unresolved, with a total magnification.
• Fully specified shape, achromatic
• Measure timescale, a function of lens mass,
  distances and transverse velocity.

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Microlensing surveys

• Look at many stars for a long time, and see if
  any one is microlensed. Measure microlensing rate
  and event timescales.
• MACHO observed LMC, bulge. EROS observed LMC,
  others observed M31

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Microlensing optical depth

• Optical depth is the fraction of sky covered by
  the Einstein radii of all the lenses, or the
  probability of any source star to be microlensed
  at any given time.
• If the dark matter halo of the Milky Way were
  made of compact objects, the optical depth to LMC
  stars would be

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Results from MACHO on LMC

• 13 to 17 events detected (depending on selection
  criteria) result in optical depth

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Result interpreted as compact objects accounting
for fraction f of halo
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Puzzles from the LMC microlensing results

• It suggests some fraction ( 10) of the halo
  dark matter may be in the form of compact
  objects. They have typical stellar masses, but
  they must be dark
• White dwarfs? No (constraints from metal
  production, cosmic background radiation)
• So, perhaps this is just an error that will go
  away

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Alternative hypothesisinteracting, massive dark
matter particle

• Dark matter particles are captured by stars, and
  settle in the center to a thermal distribution.
• If sufficient dark matter accumulates, it
  collapses into a self-gravitating object in the
  star center.
• If the dark matter mass is greater than its
  Chandrasekhar mass, it collapses to a black hole.
• The black hole can then eat the whole star.
• The halo might contain black holes from stars
  formed long ago which captured too much dark
  matter.

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Limits on dark matter interaction(Starkman et
al. 1990) strong interaction is not totally
ruled out.
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Dark matter capture rate(for optically thick
star)
The accumulated mass after time t is
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Condition for dark matter collapse

• Dark matter settles in a region of width

• It becomes self-gravitating once the central dark
  matter density is equal to the baryon density.
  For a non-degenerate star, this happens when

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Dark matter Chandrasekhar mass

• Number of particles in a Chandrasekhar mass

• Chandrasekhar mass

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Example if md107 GeV

• The Sun would have accumulated 10-10fc MS of dark
  matter today, and would collapse if fcgt0.03
• Neutron stars could not exist if fcgt10-3 (owing
  to dark matter captured by progenitor, which
  collapses to a black hole once the neutron star
  is made).
• But at redshift zgt10, typical stars were in halos
  with dark matter densities 103 times larger than
  in the solar neighborhood, and velocity
  dispersions 10 times lower, and could have
  collapsed to black holes after 108 years for f
  10-4

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The "crazy" scenario

• At high redshift, many low-mass stars were formed
  in dense, low-velocity dispersion dark matter
  halos. Most of them captured enough dark matter
  to collapse to black holes.
• Below some critical redshift, most stars
  survived. At present, white dwarfs and neutron
  stars can also survive.
• Low-mass halos merged into Milky Way and LMC halo
  and were tidally disrupted, and today the black
  holes with masses 0.1 to 1 MS can produce some of
  the microlensing events.

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How can we test the model

• The excess in the LMC microlensing optical depth
  relative to that expected from known stars should
  be confirmed.
• The lenses should be in the halo.
• If a black hole with mass less than that of the
  Sun is found, no other mechanism is known of
  forming it.
• No neutron stars, many X-ray binaries at high
  redshift?
• Dark matter particle can be detected.

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Conclusions

• If the dark matter contains massive particles
  that interact strongly with baryons, they might
  have caused stars at high redshift to collapse to
  black holes, while present stars might be spared
  the same fate because of the lower densities and
  velocity dispersions in dark matter halos. The
  black holes formed at high redshift might account
  for some LMC microlensing events.
• The model is so crazy that we had better hope
  that this excess optical depth to the LMC goes
  away