Dark matter capture in neutron stars with exotic phases

Motoi Tachibana (Saga Univ.)

Dec. 12, 2014 ＠ Nuclear Aspects of DM Searches

Why the connection between DM and NS? Possibly constraining WIMP-DM properties via NS

CDMSII, 1304.4279 1    : mean free46 path2  n 510 cm NS M n  (4 /3) 3 Way below theR m CDMSN limit!

For a typical neutron star, M  1.4MSUN, R  10km Impacts of dark matter on NS

• NS mass-radius relation with dark matter EOS • NS heating via dark matter annihilation ：

• Dark matter capture in NS and formation of black-hole to collapse host neutron stars cf) This is not so a new idea. People have considered the DM capture by Sun and the Earth since 80’s.

cosmion W. Press and D. Spergel (1984) Application to NS : Goldman-Nussinov (1989) Cooling curves of Neutron Star T

C. Kouvaris (‘10) dT C ˙ L  L L V dt   DM

Cv : heat capacity L : luminosity

t DM capture in NS *

*Ref.) McDermott-Yu-Zurek (2012) (1) Accretion of DM

dN  C N C : DM capture rate dt B  B

(1) Thermalization of DM (energy loss)

dE n  vE  : DM  nucleon cross section dt B N N

(2) BH formation and destruction of host NS

N m self    r : thermal radius condition of 3 B th self-gravitation 4rth /3 Capturable number of DMs in NS

dN   C C N C N 2 dt N   a 

Capture rate due to DM-nucleon scattering

Self-capture rate due to DM-DM scattering

DM self-annihilation rate (no self-capture/annihilation) C  Ca  0

N  CNt

Just linearly grows and C isN the growth rate. Realized when DM carries a conserved charge, analogous to baryon number.

Below we consider this case DM capture rate

The accretion rate (A. Gould, 1987)

Rn 2 dCN (r) C  4 r dr neutron-DM elastic cross section N 0 dV 2  B2  dCN (r) 6 v(r) 1 e  n (r)nB (r) (v N )1   dV  v 2  B2 

n (r):DM density nB (r):baryon density v  220km s: DM velocity v(r):escape velocity 2 m m m B 2 3 v(r) 4   B  2 2 ,   , mr  2 v ( 1) mB m  mB Capture efficiency factor ξ

In NS, neutrons are highly degenerated

(i) If momentum transfer δp is less than p , only neutrons F with momentum larger than

p F-δp can participate in pF (ii) If not, all neutrons can join  p p    Min ,1 pF  Thermalization of DM

After the capture, DMs lose energy via scattering with neutrons and eventually get thermalized

DM mass ≦ 1GeV,  45 2   5  5 2.110 cm 0.1GeV 10 K t  7.710 yrs    th    T   N  m 

DM mass ≧ 1GeV,

2  45 2   5  2.110cm m 10 K t  0.054yrs    th    T   N  100GeV Self-gravitation of DM

Then, the DM gets self-gravitating once the total # of DM particles is larger than a critical value GN m2 4G m    B  r2 r 3

Nself m  3  B 4rth /3

If this condition is met, gravitational collapse takes place. Condition

N  Nself McDermott-Yu-Zurek (2012) However… Hadrons inside NS are in EXTREME, and exotic matter states could appear.

(e.g.) neutron superfluidity meson condensation superconductivity of quarks

What if those effects are incorporated? Brief ideas M. Ruggieri and M.T. (2013)

① Modification of capture efficiency via energy gap (e.g.) color-flavor-locked (CFL) quark matter

    Minp /pF CFL,1 sizable effect?

② Modification of low-energy effective field theory (e.g.) neutron superfluidity dominant d.o.f. is a superfluid phonon. Some work in progress

w/ T. Hatsuda DM thermalization (Ref.) Bertoni-Nelson-Reddy (2013)

Hyperon degrees of freedom?

NS mass-radius relation (Ref.) Ciarcelluti-Sandin (2011)

TOV eq. w/ dark star core Summary

Stellar constraints on dark matter properties

Dark matter capture in neutron stars --Accretion, thermalization and BH formation—

Models for DM, but not considering NS seriously

Proposal of medium effects for hadrons in NS --modified vacuum structures and collective modes--

DM study via NS is interesting! Thank you ! 感謝