An alternative hypothesis to account for the LMC microlensing events

Jordi Miralda-EscudéThe Ohio State University

IEEC/ICREA

Microlensing of stars

s

lslE D

DD

c

GM2

2 4

Einstein radius:

2

4

bc

GM

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

7105 LMC

Results from MACHO on LMC

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

74.03.0 10)1.1(

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)

222 /1 dmescdmcapdmdm vvRvfM

The accumulated mass after time t is:

yr105v

km/s250

3.010

9dmcm

GeV

10

3 t

R

R

M

MfMM

SS

cdmSdm

Condition for dark matter collapse

• Dark matter settles in a region of width

dc

cd mG

kTh

8

3

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

2/3

d

pcoredm m

mMM

Dark matter Chandrasekhar mass

• Number of particles in a Chandrasekhar mass:

3/12

Ncm

h

c

GNm

d

d 3

d

Pl

m

mN

• Chandrasekhar mass: 2

,

d

pSddCh m

mMNmM

Example: if md=107 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…