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Can Neutron Stars Constrain
Dark matter?
Chris Kouvaris
Universit Libre de Bruxelles
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Mass 2010, CP3-Origins
The Missing Mass ProblemZwicky 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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Mass 2010, CP3-Origins
Rotation CurvesVera Rubin 70s: Rotatoion
curves of Andromeda are notfalling as Newtons law
predicts!
Velocity should drop as rv /1
However v roughly constant rM2
/1 r
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Mass 2010, CP3-Origins
MOND???
Tully-Fisher
Milgrom
Mond explains well theTully-Fisher relation and
the rotation curves
but fails in clusters ofgalaxies
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Mass 2010, CP3-Origins
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'sindividual galaxies are seen in the optical image data, but their total mass adds up to far less than the mass of thecluster's two clouds of hot x-ray emitting gas shown in red. Representing even more mass than the optical galaxies and x-ray gas combined, the blue hues show the distribution of dark matter in the cluster. Otherwise invisible to telescopicviews, the dark matter was mapped by observations of gravitational lensing of background galaxies. In a text bookexample of a shock front, the bullet-shaped cloud of gas at the right was distorted during the titanic collision between twogalaxy clusters that created the larger bullet cluster itself. But the dark matter present has not interacted with the clustergas except by gravity. The clear separation of dark matter and gas clouds is considered direct evidence that dark matterexists.
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Mass 2010, CP3-Origins
What Dark Matter is Not
Baryons obviously!!!! MaCHO (Massive Compact Halo Objects): Ruled out
NeutrinoseV
mh i i
94
2
Light neutrinos: are problematic in small scale structurem>500 eV (Tremaine-Gunn) otherwise neutrinos violate Pauli
blocking in dwarf galaxies. But for m>500 eV gives too muchdark matter
Heavy Neutrinos: m> 2 GeV (Lee-Weinberg)
excluded by direct dark matter search experiments unlessthe mass is huge
ChaMP (Charged Massive Particles)SIMP (Strongly Interacting Massive Particles)Ruled out by searches of Hydrogen anomalous isotope in water*
by microlensing observations
m
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Mass 2010, CP3-Origins
Direct Dark Matter Candidates
Supersymmetric (neutralino, gravitino etc)Hidden SectorsTechnicolor CandidatesKaluza KleinAxions and many other
Candidates can have:Spin independent cross section
Spin Dependent cross sectionInelastic Scattering
Self-Interacting cross section
Thermal annihilation cross section
Non-thermal annihilation cross section
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Mass 2010, CP3-Origins
Direct Dark Matter Search Experiments I
Joachim Kopp, Thomas Schwetz, Jure Zupan: arXiv 0912.4264
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Mass 2010, CP3-Origins
Direct Dark Matter Search Experiments II
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Mass 2010, CP3-Origins
Can Stars impose constraints on Dark Matter?
Neutrino production from WIMP annihilationIceCube & 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 cancause gravitational collapse (Goldman, Nussinov 89, CKTinyakov 10)
WIMP annihilation and cooling of starsWIMP annihilation as a heating mechanismfor neutron stars (CK 07, CK, P. Tinyakov, Lavallaz, Fairbairn 10)
for white dwarfs (Bertone, Fairbairn 07, McCullough 10)
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Mass 2010, CP3-Origins
Why look at compact stars?
Example: Sun
WIMP mean free pathinside the sun
,1
n
23
3108
)3/4(
nsolar
solar
mR
Mn
3/cmparticles
Even if currentlimit of CDMS
,10241
cm
,1017cm 610
solarR
Only one out of a million WIMPs scatters!
The number of accumulated WIMPs is even smallerbecause not all the scattered WIMPs get trapped.
Condition: The energy loss in the collision
should be larger than the asymptotic kineticenergy of the WIMP far out of the star.
Advantage: The sun is close!!!
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Mass 2010, CP3-Origins
White Dwarfs
When the Fermi pressure of the
electrons acts against gravitationalcollapse
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Mass 2010, CP3-Origins
Same Exercise for a White Dwarf
30
3107.1
)3/4(
nWD
WD
mR
Mn
,solarWD MM kmRWD 55003
/cmparticles
If we want onecollisions per WIMPpassing the crosssection
23910 cmcritical
However still abovethe CDMS limit!!!
This is an improvement!!!
Since for the sun235
10 cmcritical
Could Coherent Scattering help???
,5.0 solarWD MM kmRWD 10000If239
107 cmcritical
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Mass 2010, CP3-Origins
Coherent Scattering WIMP-Nucleus
Dirac (non-Majorana) type of candidates can interactcoherently with the whole nucleus
This effect is taken into account in earth based experiments,where WIMPs are passing through with velocities 220 km/sputting tight constraints on these candidates.
However loss of coherence occurs when
Helm factor
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Mass 2010, CP3-Origins
Studies so far were assuming coherence in the scatteringbetween WIMP-nucleus in the White Dwarfs.
but this not true (CK, Tinyakov 10) because the potentialenergy is much larger than the asymptotic kinetic energy ofthe WIMP. WIMPs are almost relativistic while entering theWhit Dwarf.
0E
R
GM
The de Broglie wavelength is much shorter than the size ofthe nuclei and the form factor kills the enhancement of thecross section due to the coherence.
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Mass 2010, CP3-Origins
Neutron Stars
even more compact objects! Fermi pressure of neutronsand/or quark matter??? balances gravity.
For a typical neutron star ,4.1 solarNS MM kmR 10
246105 cmcritical
CK 07 Way below the CDMS
limit!!!
WIMPs are relativistic while entering the NS, and therefore also herecoherence is lost, but this is not important since for cross sections largerthan 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 incapturing WIMPs!
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Mass 2010, CP3-Origins
furthermore
since
the two cross sections become almost identical for a NS andtherefore the same constraints apply
Inelastic Dark Matter
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Mass 2010, CP3-Origins
and
Self-Interacting Dark Matter
Strong WIMP-WIMP cross section
For a Neutron star as long as the WIMP-nucleon cross section isabove the critical value, self-interactions make no difference in
the accretion and capture of the the WIMPs
Bound on the cross sectionGeVcm
m
2
2410
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Capture of WIMPs in Neutron Stars
CK 07
For a
typical
NS
Thermalization
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Mass 2010, CP3-Origins
Thermalization is so fast that allows extremely
small annihilation cross sections
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Mass 2010, CP3-Origins
Neutron Stars as Giant Detectors!
CDMS NSDensity 5 g/cm^3 10^14g/cm^31% Light production 100% Light ProductionLocal dark matter density0.3 GeV/cm^3 up to 10^10!? GeV/cm^3
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Mass 2010, CP3-Origins
Annihilation of WIMPs inside the Neutron Stars
EnergyRelease
We must compare it with the otherheating/cooling mechanisms
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Mass 2010, CP3-Origins
Basics of Neutron Star Cooling
Urca Process
Direct Urca eepn
enep
Energy release through
escaping neutrinos
However for nuclear matter triangleinequalities are not satisfied
Modified Urcapresence ofbystander
eepnnn
ennnep
For quark matter itholds!
Emissivity: 6T
Emissivity:8
T
Photon Emission Emissivity: 4T
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Mass 2010, CP3-Origins
more cooling mechanisms
Nucleon Pair Bremsstrahlung nnnn
pnpn
Neutrino Pair Bremsstrahlung ),(),( ZAeZAe
Pionic Reactions
Superfluidity
Color Superconductivity
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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 Tuc1620-26 in M4 both have temperatures roughly
610 K
Observed temperatures smaller than the ones predicted, excludesthe dark matter candidate.
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Mass 2010, CP3-Origins
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 KJ0108-1431 temperature 9 x 10^4 K
Both of them are old only problem their distance from the earth is 130-140 pcThe 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??
A supermassive star cancollapse to a neutron star viaa Supernova II explosion
The pre-existence of the starincreases the local dark matterdensity in the vicinity of thenewly born neutron star
The effect in principle can be large!
Total number of accumulatedparticles
Same order of magnitude as for a neutron star!Compactness and small WIMP mean free path iscounterbalanced 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 becarried away from the shock wave, however the WIMPs aresucked 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 thermalradius 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 annihilationcross 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 issmaller than 37 /10 cmGeV
The time needed for collapse exceeds the age of the universe!
C
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Conclusions
Neutron Stars are the only objects that have efficient accretionof 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 neutronstars 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!
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