Transcript Lecture 17: Black Holes

An alternative hypothesis to
account for the LMC
microlensing events
Jordi Miralda-Escudé
The Ohio State University
IEEC/ICREA
Microlensing of stars
4GM

2
bc
Einstein radius:
E
2
4GM Dl Dls
 2
c
Ds
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.
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
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
 LMC  5  10
7
Results from MACHO on LMC
• 13 to 17 events detected (depending on
selection criteria) result in optical depth
  (1.1
0.4
 0.3
) 10
7
Result interpreted as compact objects
accounting for fraction f of halo
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…
Alternative hypothesis:
interacting, 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.
Limits on dark matter interaction
(Starkman et al. 1990): strong interaction is
not totally ruled out.
Dark matter capture rate
(for optically thick star)

2
2
2

M dm   dm f capvdmR 1  vesc / vdm

The accumulated
mass after time t is:
 dm f c 250km/s M  R
t
M dm  10 M S
9
GeV
0.3 cm
v dm M S RS 5 10 yr
10
3
Condition for dark matter collapse
• Dark matter settles in a region of width
3kTc
hd 
8G c md
• It becomes self-gravitating once the central dark
matter density is equal to the baryon density. For
a non-degenerate star, this happens when:
M dm
 mp 

 M core 
 md 
3/ 2
Dark matter Chandrasekhar mass
• Number of particles in a Chandrasekhar mass:
GNmd
h
1/ 3

N
2
c
md c
• Chandrasekhar
mass:
M Ch ,d
 mPl 

N  
 md 
3
 mp 

 Nmd  M S 
 md 
2
Example: if md
7
=10
GeV…
• The Sun would have accumulated 10-10fc MS of dark
matter today, and would collapse if fc>0.03
• Neutron stars could not exist if fc>10-3 (owing to
dark matter captured by progenitor, which collapses
to a black hole once the neutron star is made).
• But at redshift z>10, 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
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.
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.
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…