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Can Neutron Stars Constrain
Dark matter?
Chris Kouvaris
Université Libre de Bruxelles
The “Missing Mass Problem”
Zwicky 1933: Virial Theorem
applied on Coma cluster
Zwicky took 5*1015 cm2s-2 as the value for the time and mass averaged squared velocity and 2
million light-years for the radius of the cluster. The total cluster mass is then about 7*1013 solar
masses. Since the cluster contains about 1000 galaxies, this yields an average galactic mass of
7*1010 solar masses. However, the average galactic luminosity in the Coma cluster is found to be
only 8.5*107 solar luminosities. Thus, the average mass to light ratio, in solar units, of the galaxies
in the Coma cluster is approximately 800.
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Rotation Curves
Vera Rubin 70’s: Rotatoion
curves of Andromeda are not
falling as Newton‟s law
predicts!
Velocity should drop as
v  1/ r
However v roughly constant
M r
  1/ r 2
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MOND???
Mond explains well the
Tully-Fisher relation and
the rotation curves
Milgrom
Tully-Fisher
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… but fails in clusters of
galaxies
Fluctuations of the Microwave Background Radiation
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Bullet Cluster
The galaxy cluster 1E 0657-56, known as the "bullet cluster“. A mere 3.4 billion light-years away, the bullet cluster's
individual galaxies are seen in the optical image data, but their total mass adds up to far less than the mass of the
cluster's two clouds of hot x-ray emitting gas shown in red. Representing even more mass than the optical galaxies and xray gas combined, the blue hues show the distribution of dark matter in the cluster. Otherwise invisible to telescopic
views, the dark matter was mapped by observations of gravitational lensing of background galaxies. In a text book
example of a shock front, the bullet-shaped cloud of gas at the right was distorted during the titanic collision between two
galaxy clusters that created the larger bullet cluster itself. But the dark matter present has not interacted with the cluster
gas except by gravity. The clear separation of dark matter and gas clouds is considered direct evidence that dark matter
exists.
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What Dark Matter is Not
• Baryons obviously!!!!
• MaCHO (Massive Compact Halo Objects): Ruled out
by microlensing observations
• Neutrinos
 h 2 
 m
i
94eV
i
m<2 eV
Light neutrinos: are problematic in small scale structure
m>500 eV (Tremaine-Gunn) otherwise neutrinos violate Pauli
blocking in dwarf galaxies. But for m>500 eV gives too much
dark matter
Heavy Neutrinos: m> 2 GeV (Lee-Weinberg)
excluded by direct dark matter search experiments unless
the mass is huge
• ChaMP (Charged Massive Particles)
•SIMP (Strongly Interacting Massive Particles)
Ruled out by searches of Hydrogen anomalous isotope in water*
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Direct Dark Matter Candidates
•Supersymmetric (neutralino, gravitino etc)
•Hidden Sectors
•Technicolor Candidates
•Kaluza Klein
•Axions
•… and many other
Candidates can have:
Spin independent cross section
Spin Dependent cross section
Inelastic Scattering
Self-Interacting cross section
Thermal annihilation cross section
Non-thermal annihilation cross section
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Direct Dark Matter Search Experiments I
Joachim Kopp, Thomas Schwetz, Jure Zupan: arXiv 0912.4264
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Direct Dark Matter Search Experiments II
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Can Stars impose constraints on Dark Matter?
Neutrino production from WIMP annihilation
IceCube & Super-Kamiokande can impose
constraints on the WIMP-nucleon cross section
WIMP accumulation and formation of Black Holes
In neutron stars at rich dark matter regions, WIMPs can
cause gravitational collapse (Goldman, Nussinov ’89, CK
Tinyakov ‘10)
WIMP annihilation and cooling of stars
WIMP annihilation as a heating mechanism
•for neutron stars (CK ‘07, CK, P. Tinyakov, Lavallaz, Fairbairn ’10)
•for white dwarfs (Bertone, Fairbairn ‘07, McCullough ‘10)
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Why look at compact stars?
Example: Sun
M solar
3
1
WIMP mean free path
23
particles
/
cm
n


8

10

,
3
inside the sun
(4 / 3)Rsolar
mn
n
Even if current   1041cm 2 ,
limit of CDMS
  1017 cm,
Rsolar

 10 6
Only one out of a million WIMPs scatters!
The number of accumulated WIMPs is even smaller
because not all the scattered WIMPs get trapped.
Condition: The energy loss in the collision
should be larger than the asymptotic kinetic
energy of the WIMP far out of the star.
Advantage: The sun is close!!!
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White Dwarfs
When the Fermi pressure of the
electrons acts against gravitational
collapse
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Same Exercise for a White Dwarf
M WD  M solar,
RWD  5500km
If we want one
collisions per WIMP
passing the cross
section
Since for the sun
n
M WD
30

1
.
7

10
particles / cm3
3
(4 / 3)RWD mn
   critical  1039 cm 2
 critical  1035 cm 2
If M WD  0.5M solar, RWD  10000km
This is an improvement!!!
However still above
the CDMS limit!!!
   critical  7 1039 cm 2
Could Coherent Scattering help???
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Coherent Scattering WIMP-Nucleus
Dirac (non-Majorana) type of candidates can interact
coherently with the whole nucleus

This effect is taken into account in earth based experiments,
where WIMPs are passing through with velocities 220 km/s
putting tight constraints on these candidates.
However loss of coherence occurs when
Helm factor
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Studies so far were assuming coherence in the scattering
between WIMP-nucleus in the White Dwarfs….
…but this not true (CK, Tinyakov „10) because the potential
energy is much larger than the asymptotic kinetic energy of
the WIMP. WIMPs are almost relativistic while entering the
Whit Dwarf.
GM
 E0
R
The de Broglie wavelength is much shorter than the size of
the nuclei and the form factor kills the enhancement of the
cross section due to the coherence.
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Neutron Stars
even more compact objects! Fermi pressure of neutrons
and/or quark matter??? balances gravity.
For a typical neutron star
M NS  1.4M solar, R  10km
   critical  5 1046 cm 2
CK „07
Way below the CDMS
limit!!!
WIMPs are relativistic while entering the NS, and therefore also here
coherence is lost, but this is not important since for cross sections larger
than the critical one, every WIMP passing the NS will scatter at least once
on average.
Neutron Stars seem to be the objects with the best efficiency in
capturing WIMPs!
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… furthermore
Inelastic Dark Matter
since
the two cross sections become almost identical for a NS and
therefore the same constraints apply
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… and
Self-Interacting Dark Matter
Strong WIMP-WIMP cross section
Bound on the cross section

m
 10
 24
cm 2
GeV
For a Neutron star as long as the WIMP-nucleon cross section is
above the critical value, self-interactions make no difference in
the accretion and capture of the the WIMPs
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Capture of WIMPs in Neutron Stars
CK „07
For a
typical
NS
Thermalization
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Thermalization is so fast that allows extremely
small annihilation cross sections
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Neutron Stars as Giant Detectors!
CDMS
Density 5 g/cm^3
1% Light production
Local dark matter density
0.3 GeV/cm^3
NS
10^14g/cm^3
100% Light Production
up to 10^10!? GeV/cm^3
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Annihilation of WIMPs inside the Neutron Stars
Energy
Release
We must compare it with the other
heating/cooling mechanisms
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Basics of Neutron Star Cooling
Urca Process
n  p  e  e
p  e  n  e
Direct Urca
However for nuclear matter triangle
inequalities are not satisfied
Emissivity:
Energy release through
escaping neutrinos
For quark matter it
holds!
T6
Modified Urca
presence of
bystander
Photon Emission
n  n  n  p  e  e
Emissivity:
p  e  n  n  n  e
Emissivity:
T4
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T8
…more cooling mechanisms
•Nucleon Pair Bremsstrahlung
n  n  n  n   
n  p  n  p   
•Neutrino Pair Bremsstrahlung
•Pionic Reactions
•Superfluidity
•Color Superconductivity
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e  ( A, Z )  e  ( A, Z )  
Cooling Equation
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Cooling Curves
CK „07
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Galactic Center
CK , Tinyakov „10
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Globular Clusters
NFW for M4
Baryonic contraction might reduce the temperature up to 30%
Examples: X7 in 47 Tuc
1620-26 in M4 both have temperatures roughly
106
K
Observed temperatures smaller than the ones predicted, excludes
the dark matter candidate.
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Isolated Neutron Stars
…maybe the best candidates for the constraints
•No accretion from bystander white dwarf or other star
•Probably better knowledge of the local dark matter candidate
Examples: J0437-4715 temperature 10^5 K
J0108-1431 temperature 9 x 10^4 K
Both of them are old
… only problem their distance from the earth is 130-140 pc
•The local dark matter density should be small (or maybe not)
•Other heating mechanisms can take place
Reisenegger ‟94 (chemical energy converted to thermal),
Alford, CK, Kundu, Rajagopal ‟04 (color superconducting matter)
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Can A Progenitor change the picture??
The pre-existence of the star
increases the local dark matter
density in the vicinity of the
newly born neutron star
A supermassive star can
collapse to a neutron star via
a Supernova II explosion
The effect in principle can be large!
Total number of accumulated
particles
Same order of magnitude as for a neutron star!
Compactness and small WIMP mean free path is
counterbalanced by huge mass and radius
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After the explosion…
The mean free path of the WIMPs is too large for them to be
carried away from the shock wave, however the WIMPs are
“sucked” inside the neutron star very fast (exponentially)
Neutron star kicks up to several thousands of km/s do not alter the picture.
WIMPs remain gravitationally bound to the neutron star within the thermal
radius of the last stage of the star (silicon).
…still the annihilation cannot compete with the Urca process
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however…
Non-thermally produced WIMPs can have extremely small annihilation
cross section (supersummetry etc.)
In that case:
It can change the temperature estimate by 50%
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Black Hole formation
Neutron Stars close to the galactic center might accrete to many WIMPs,
and gravitational collapse might occur
For fermionic WIMPs there is a Chandrasekhar limit by setting
Fermi momentum
For gravitational collapse, it takes
If the dark matter density is
smaller than
107 GeV / cm3
The time needed for collapse exceeds the age of the universe!
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Conclusions
•Neutron Stars are the only objects that have efficient accretion
of WIMPs for WIMP-nucleon cross section below the current
experimental limits.
•The constraints apply to thermally and non-thermally produced
WIMPs with extremely small annihilation cross section.
•Although observing neutron stars at the galactic center is an
extremely difficult task, globular clusters or isolated neutron
stars can impose constraints.
•We set lower bounds on the surface temperature of a NS. If a
NS is observed with a temperature lower than what we predict,
a huge class of candidates is ruled out!
Mass 2010, CP3-Origins