Download Constraints on Bosonic Dark Matter  From Observations of Old Neutron From Observations of Old Neutron  Stars

Constraints on Bosonic Dark Matter From Observations of Old Neutron
From Observations of Old Neutron Stars
Jason Kumar
w/ Joe Bramante, Keita Fukushima
/
k h
1301.0036 (PRD 87, 055012)
University of Hawaii
dark matter capture
dark matter capture
•
basic idea
– take any dense concentration of baryonic matter (star, etc)
– dark matter scatters off baryons
– loses kinetic energy to recoil
– can fall below escape velocity
– gravitationally captured, and settles in the core
•
main application is neutrino‐
based searches
– capture rate balanced by annihilation
•
but what if dark matter can’t annihilate?
ihil t ?
Dawn Williams
neutron star bounds
neutron star bounds
if dark matter cannot annihilate/decay, it just keeps accumulating in the core
• eventually will cross the Chandrasekhar bound and trigger black hole collapse, which can eat the star (Michigan group; Kouvaris, Tinyakov)
• most likely for dense stars in regions of high dark matter density
• neutron stars in globular clusters
• benchmarks
•
– neutron star B = 7.8 ⨯ 1038 GeV / cm3 , R = 10.6 km , tns = 10 Gyr , T = 105 K
– globular cluster  X = 0.3 ‐ 103 GeV / cm3
•
•
•
observations of old neutron stars can thus bound the scattering cross‐
observations
of old neutron stars can thus bound the scattering cross
section for dark matter with no annihilation/decay tightest for bosonic dark matter (no Fermi pressure to obstruct collapse)
usually phrased as a bound on asymmetric dark matter
ll h
d
b
d
ti d k
tt
annihilation
•
actually, asymmetric dark matter can annihilate
– to forbid annihilation, need something extra...
– asymmetric  requires DM charged under unbroken continuous symmetry
– stable  requires DM lightest particle charged under some symmetry
• need not be continuous  could be Z2, which permits self‐annihilation
– need not be the same symmetry • in this case asymmetric dark matter could annihilate
– a Standard Model example ... if B & L were Z2 , then pp e+e+ possible
•
we can think about it in the following way...
– there’s an unbroken continuous symmetry which keeps dark matter complex
– there’s an approximately unbroken symmetry which keeps dark matter stable
– stabilizing symmetry is approximately continuous
• if weakly broken to Z2, dark matter can annihilate
• if weakly broken entirely, dark matter can also decay
self interaction
self‐interaction
•
dark matter can also have self‐interactions
•
•
•
we’ll focus on the case of bosonic dark matter
 = dark matter
= dark matter
(/4!) |*|2 interaction term
– generally not forbidden or constrained by any symmetry of the dark matter theory (consistent with stabilizing and complexifying symmetries)
theory (consistent with stabilizing and complexifying
•
expect  to naturally be O(1)
•
moreover, if dark matter interacts with baryons, then self‐interactions will if d k
i
i hb
h
lf i
i
ill
be generated at one‐loop order (Bell, Melatos, Petraki)
effect
•
annihilation and decay deplete the dark matter in the neutron star
– relax bounds on dark matter‐neutron scattering
– can also heat the star
• assume this effect is small
•
dark matter self‐interactions alter the Chandrasekhar limit
– more dark matter required before a black hole is formed
– for small , actually tightens bounds
• black hole is bigger, and grows
– for large , bounds are loosened
• black hole may never form
•
goal is to understand the effect of annihilation, decay and self‐interaction on bounds on bosonic dark matter from neutron stars
– see also Bell, Melatos, Petraki – 1301.6811
slide from Hai‐Bo Yu
basic analysis
basic analysis
•
dark matter accumulated by the neutron star
– accumulated by capture, depleted by annihilation and decay
•
dark matter forms a black hole
– can only form a black hole if dark matter thermalizes within tns
– dark matter must self‐gravitate and cross Chandrasekhar bound
– bosonic dark matter can form a Bose‐Einstein condensate (BEC) which is more (
)
dense, and self‐gravitates earlier
•
black hole evolution
– black hole will accrete baryonic and dark matter, and emit Hawking radiation
– a black hole formed from a BEC will accrete dark matter efficiently
– self‐interactions lead to bigger black holes, which can grow (if they can form)
gg
,
g
(
y
)
dark matter capture
dark matter capture
•
•
borrow heavily from McDermott, Yu, Zurek; Kouvaris, Tinyakov
CX = rate at which dark matter scatters to a speed < vesc.
– if dark matter scatters, kinematics determines likelihood of capture
•
•
for nX ≳sat., probability of dark matter scatter goes to 1
if recoil energy is small, neutron needs to be near Fermi surface
– else can’t reach unoccupied state
– Pauli‐blocking
– relevant for mX < 1 GeV
Psca
p   nnX dl
scatt.  1  exp


sat.  2.1  10 45 cm2
   GeV 
CX  2.3  1045 Gyr 1  X 
 f  nX   if mX >GeV

m
 0  X 
 
CX  3.4  1045 Gyr 1  X  f  nX   if mX <GeV
 0 
f
nX
if nX  sat.
if sat.
f  1 if nX  sat.
  1 if m
if mX  106 GeV
0  103 GeV / cm3
dark matter accumulation
dark matter accumulation
•
•
dark matter depleted by annihilation or decay
dark matter lifetime ≳ tns
– decay can only change the amount of dark matter by an O(1) fraction
•
•
focus on annihilation
assume uniform dark matter density within thermalization
region
– determined by gravitational potential, virial theorem and temperature
– if dark matter doesn’t thermalize, ,
won’t collect in core, form black hole
A v N2acc.
dNacc.
 CX 
dt
Vth
Nacc. 

C  v
CX Vth
tanh  tns X A
A v
Vth




4
Vth  rth3
3
1/2
 T GeV 
∼100 cm
rth  240cm  5

 10 K mX  for mX=10 GeV
5
 mX   10 K  1
6
t th  5.4  10 yr 
f
 
G V  T 
 GeV
2
black hole formation
black hole formation
•
•
black hole collapse occurs if
energy decreases with radius
need gravitational potential dominated by self‐energy (1/r)
– for given mX, r, minimal NDM
needed for dark matter to become self‐gravitating
•
need enough dark matter for gravitational potential energy to dominate kinetic energy
– NDM > Nchand.
– depends on  and mX, not r
•
for fermion DM, larger kinetic energy from Fermi pressure
f
1
Ekin. 
r
GNm2XNDM
Eself  
 O 
r
2GNBmXr2
Ebary. 
3
1/2
2
2mpl2 
 mpl 
Nchand. 
1

2 

mX  32 m2X 
≳1036
for mX=10 GeV
effect of a Bose‐Einstein
effect of a Bose
Einstein condensate
condensate
•
if dark matter density is high enough, dark matter forms a BEC
NBEC
– wavefunction symmetrization
kills phase space of excited states
•
•
after BEC forms, most captured particles fall into BEC state
radius of BEC is roughly size of ground state wavefunction
– much smaller than rth
– small r = self‐grav. for small NDM – by the time NDM > Nchand., BEC is already self‐gravitating
•
self‐interactions don’t change r much if  ≪ 10‐18 (mX/GeV)3
 3  m T 
    X 
 2  2 
 T 
 10  5 
 10 K 
3/2
 4 rth3 


3


3
36
1/4
rBEC


3


2
8

G
m

N X B 

1/2
 GeV 
4
1 5  10 cm 
 1.5
 ∼10‐4 cm
 mX  for mX=10 GeV
N2
E  3 2
rBECmX
black hole evolution
black hole evolution
•
baryonic Bondi accretion
– accrete dark matter from the sphereical distribution around it
– vs = speed of sound
– larger black holes accrete faster
•
Hawking radiation
– smaller black holes have larger emission rate
•
dark matter accretion
– depends on if BEC forms
– like Bondi accretion if no BEC
•
initial condition is mass of black hole when it forms
dMBH  dMBH 
 dMBH 
 dMBH 








dt
dt
dt
 dt bary.



HR
b
DM
4 B (GNMBH )2
 dMBH 



dt
v 3s

bary.
1
 dMBH 




15360(GNMBH )2
 dt HR
v s  0.1c
dark matter accretion
dark matter accretion
•
•
if dark matter forms a BEC, then subsequent captured dark matter falls into BEC state
BEC radius small compared to BH impact parameter (MYZ)
– b ∼ 4rBEC
•
•
•
dark matter captured is directly captured by the black hole
dark matter accretion rate = dark matter capture rate
more efficient than Bondi
accretion from a distribution in the thermal radius
(BEC)
 dMBH 
 CXmX


 dt DM
rapid growth/evaporation
rapid growth/evaporation
•
•
assume dark matter is in a BEC
as black hole grows, baryonic accretion rate grows and radiation rate falls
– quickly consumes typical mass neutron star
•
if black hole starts to shrink, radiation rate grows and baryonic accretion rate falls
– quickly evaporates away
•
don’t need to track the entire evolution just need to know if it starts to grow or shrink
tcollapse
ll
tevaporate
2
 mpl 
 mX  
5
 2.6  10 yr 
  1 
2 

GeV
32

m


X 
 GeV 
 1.3  1010 yr 

m
 X 
3
1/2
how do we get bounds?
how do we get bounds?
•
•
•
•
 does black hole form?
 does black hole grow?
dMBH
dt
bound on 
bound
on nX is is ∝ X‐1
effect of self‐interactions
– need a large black hole to form in order to grow
order to grow
– larger  leads to larger black hole
– but if  too large, black hole is so large that it never forms
g
•
Nacc.  nX ,mX ,  A v   NBHforms mX ,  
annihilations deplete dark matter
– less dark matter accumulates, and black hole may not form
y
•
•
•
0
MBH mXNBHforms
no constraint unless nX ≤ sat.
no bound if 〈av〉 > 10‐38cm3/s
even a tiny, unobservable i
b
bl
annihilation cross section can kill bounds from neutron stars!
=0
=10‐30
=10‐25
=10‐15
A v  0
results
 A v  10 50 cm3 / s
 A v  10 45 cm3 / s
 A v  10 42 cm3 / s
dark matter annihilation from BEC
dark matter annihilation from BEC
•
•
have thus far assumed that dark matter annihilation is in thermalization
region
what if dark matter annihilates in BEC?
– can deplete dark matter much more rapidly
– can heat dark matter
•
•
•
•
•
initially, rBEC / rth ∼10‐6, so BEC is much more dense
but cross section for annihilation from BEC state is not the same as 〈av〉, but cross section for annihilation from BEC state is not the same as because 〈av〉 is thermal average at temperature of the neutron star
as more dark matter falls into BEC, dark matter in BEC becomes self‐
gravitating, and size shrinks
gravitating, and size shrinks
dark matter goes from non‐relativistic to relativistic
so the effect of self‐annihilation can be even more dramatic in the BEC phase
conclusion
•
interesting bounds on bosonic dark matter arise from dark matter capture in neutron stars
in neutron stars
•
but the effect of self‐interactions and annihilation is important
•
even a small annihilation cross‐section will eliminate neutron star bounds
•
even p‐wave suppressed annihilation from a thermal relic will evade bounds!
•
if continuous stabilizing symmetry is broken to parity, must be very weakly broken
•
self‐interactions can tighten bounds, by causing the formation of large black holes, which do not evaporate away
black holes, which do not evaporate away
but large self‐interactions will prevent black hole from forming at all....
•
Mahalo!
Back‐up
Back
up slides
slides
when is dark matter in equilibrium?
when is dark matter in equilibrium?
if a BEC doesn’tt form...?
if a BEC doesn
form...?
if a BEC doesn
if
a BEC doesn’tt form, then what occurs first... self‐gravitation, or crossing the Chandrasekhar form then what occurs first self‐gravitation or crossing the Chandrasekhar
bound?
bounds, if a BEC doesn’tt form....
bounds, if a BEC doesn
form....