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Dark matter capture in compact stars
-stellar
on dark matterin constraints
neutron stars
with exotic phases
Motoi Tachibana
(Saga Univ.)
Oct. 20, 2014 ＠ QCS2014, KIAA, Beijin
What/Why dark matter (DM) ?
Undoubtedly
exists, but
properties
unknown
Proposed
by Zwicky
as missing
mass
(1934)
Interacting with other particles very weakly
What/Why neutron star (NS) ?
Landau’s
gigantic
nucleus
Proposed
by Baade
and
Zwicky
Good
market
selling
ultimate
environments
as a
remnant
after
supernova
explosion
(1934)
R ~ 10km
M ~ 1.4M SUN
T < 10MeV
B ~ 10
12-15
G
P ~ 2 - 3ms
Why the connection
between
DM and NS?
Possibly constraining WIMP-DM properties via NS
CDMSII, 1304.4279
1
s=
nl
l : mean -46
free path2
s NS »M5´10 cm
n»
Way(4
below
limit!
/ 3)pthe
R mCDMS
N
For a typical neutron star,
3
M » 1.4M SUN , R » 10km
Impacts of dark matter on NS
• NS mass-radius relation with dark matter EOS
• NS heating via dark matter annihilation
• NS seismology
：
• 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)
Cooling curves of Neutron Star
T
C. Kouvaris (‘10)
t
DM capture in NS
*based on paper by McDermott-Yu-Zurek (2012)
*
(1) Accretion of DM
dN c
dt
= CB ( N c ) CB : DM capture rate
(1) Thermalization of DM (energy loss)
dE
= -x nBs N c vd E s N c : DM - nucleon cross section
dt
(2) BH formation and destruction of host NS
N c mc
4p rth3 / 4
³ r B rth : thermal radius
condition of
self-gravitation
Capturable number of DMs in NS
dN c
dt
= Cc N + Ccc N c - Cc a N c
Capture rate due to DM-neutron scattering
Self-capture rate due to DM-DM scattering
DM self-annihilation rate
2
(A)
Ccc = 0(no self-capture)
Nc =
Cc N
Cc a
tanh
(
Reaches the steady state value
within time
t ~ 1/ Cc N C. c a
C c N Cc a t
)
N c¥ = Cc N ,/ Cc a
(B)
Cc a = 0(no self-annihilation)
Nc =
Cc N
Ccc
Linearly grows until
éëexp(Ccc t) -1ùû
t
-1
~ C, ccand then
exponentially grows until the geometric
limit is reached.
(C)
Ccc = Cc a = (no
0 self-capture/annihilation)
N c = Cc N t
Just linearly grows and
CcisN the growth rate.
Realized when DM carries a conserved charge,
analogous to baryon number?
Below we consider the case (C)
DM capture rate
The accretion rate (A. Gould, 1987)
C c N = 4p ò r
Rn
0
2
dCc N (r)
dV
dr
neutron-DM elastic cross section
-B 2 ù
é
dCc N (r)
6
v(r)
1- e
=
nc (r)nB (r)x 2 (v s N c )ê1ú
2
dV
p
v
B úû
êë
2
nc (r) : DM density nB (r) : baryon density
v = 220 km s : DM velocity v(r) : escape velocity
2
mc
m c mB
3
v(r)
4m
2
B =
, m=
, mr =
2
2
2 v (m -1)
mB
m c + mB
Capture efficiency factor ξ
In NS, neutrons are highly degenerated
(i) If momentum transfer δp
is less than p ,Fonly neutrons
with momentum larger than
p F-δp can participate in
pF
(ii) If not, all neutrons can join
dp
éd p
x = Min ê ,
ë pF
ù
1ú
û
Thermalization of DM
After the capture, DMs lose energy via scattering
with neutrons and eventually get thermalized
DM mass ≦ 1GeV,
æ 2.1´10-45 cm2 öæ 0.1GeV öæ 105 K ö
÷÷çç
÷÷ç
tth » 7.7´10-5 yrs çç
÷
s Nc
è
ø è mc øè T ø
DM mass ≧ 1GeV,
æ 2.1´10-45 cm 2 öæ m ö2 æ 105 K ö
c
÷÷ç
tth » 0.054yrs çç
÷
֍
s Nc
è
øè100GeV ø è T ø
Then, the DM gets self-gravitating once the total
number of DM particles is larger than a critical one
GN c mc
2
r
>
4p G r B m c
3
r Þ
2
N self mc
4p r / 4
3
th
= rB
æ 100GeV ö æ T ö3/2
41
÷÷ ç 5 ÷
@ 4.8 ´10 çç
è mc ø è 10 K ø
5/2
Þ N self
If this condition is met, for the wide range of the
DM mass, gravitational collapse takes place, i.e.,
Nself exceeds the Chandrasekhar limit.
Condition
N c < Nself
Observational constraints
N c = Cc N t < N self
For the case of the pulsar B1620-26:
t = 2.82 ´10 years, T =10 K, r c =10 GeV / cm
8
McDermott-Yu-Zurek (2012)
6
3
3
Neutron star is
Landau’s But…
gigantic nucleus!
So far people have been mainly studying
the issue from particle physics side.
However, hadrons in 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?
Possible effects
M. Ruggieri and M.T. (2013)
① Modification of capture efficiency via energy gap
(e.g.) color-flavor-locked (CFL) quark matter
x = Minéëd p / ( pF - DCFL ), 1ùû
sizable effect?
② Modification of low-energy effective theory
(e.g.) neutron superfluidity
dominant d.o.f. is a superfluid phonon.
We are still struggling…
Bertoni, Nelson and Reddy, Phys. Rev. D88 (2013)
• Asymmetric
(Ccc = Cca = 0)
• Complex scalar
• M_DM ~ 1 keV – 5 GeV
• Couples to regular matter
via heavy vector boson
• Pauli blocking
• Kinematic constraints
• Superfluidity/Superconductivity
Significantly affects thermalization time!
Summary
Stellar constraints on dark matter properties
Dark matter capture in neutron stars
--Accretion, thermalization and on-set of BH formation—
Models for DM, but not considering NS seriously
Proposal of medium effects for hadrons in NS
--modified vacuum structures and collective modes--
Study of dark matter from neutron stars!