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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. Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins MOND??? Mond explains well the Tully-Fisher relation and the rotation curves Milgrom Tully-Fisher Mass 2010, CP3-Origins … but fails in clusters of galaxies Fluctuations of the Microwave Background Radiation Mass 2010, CP3-Origins 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. Mass 2010, CP3-Origins 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* Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins Direct Dark Matter Search Experiments I Joachim Kopp, Thomas Schwetz, Jure Zupan: arXiv 0912.4264 Mass 2010, CP3-Origins Direct Dark Matter Search Experiments II Mass 2010, CP3-Origins 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) Mass 2010, CP3-Origins 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 1041cm 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!!! Mass 2010, CP3-Origins White Dwarfs When the Fermi pressure of the electrons acts against gravitational collapse Mass 2010, CP3-Origins 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 1039 cm 2 critical 1035 cm 2 If M WD 0.5M solar, RWD 10000km This is an improvement!!! However still above the CDMS limit!!! critical 7 1039 cm 2 Could Coherent Scattering help??? Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins 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. Mass 2010, CP3-Origins 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 1046 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! Mass 2010, CP3-Origins … furthermore Inelastic Dark Matter since the two cross sections become almost identical for a NS and therefore the same constraints apply Mass 2010, CP3-Origins … 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 Mass 2010, CP3-Origins Capture of WIMPs in Neutron Stars CK „07 For a typical NS Thermalization Mass 2010, CP3-Origins Thermalization is so fast that allows extremely small annihilation cross sections Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins Annihilation of WIMPs inside the Neutron Stars Energy Release We must compare it with the other heating/cooling mechanisms Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins T8 …more cooling mechanisms •Nucleon Pair Bremsstrahlung n n n n n p n p •Neutrino Pair Bremsstrahlung •Pionic Reactions •Superfluidity •Color Superconductivity Mass 2010, CP3-Origins e ( A, Z ) e ( A, Z ) Cooling Equation Mass 2010, CP3-Origins Cooling Curves CK „07 Mass 2010, CP3-Origins Galactic Center CK , Tinyakov „10 Mass 2010, CP3-Origins 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. 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 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) Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins 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 Mass 2010, CP3-Origins 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% Mass 2010, CP3-Origins 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! Mass 2010, CP3-Origins 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