FREDRIK SANDIN
IFPA, Département AGO, Université de Liège
Talk given at the second workshop of CompStar, Coimbra, Feb 2009
Effects of mirror dark matter on neutron stars
F.S. & P. Ciarcelluti [arXiv:0809.2942]
Fredrik Sandin Efects of mirror dark matter on neutron stars
Motivation
Dark matter apparently is thedominating form of matter in galaxies
How does it affect neutron stars – dowe need to be concerned?
Fredrik Sandin Efects of mirror dark matter on neutron stars
Main potential effects of dark matter
Accretion → heating / collapse
Lower critical mass for core collapse
Non-uniqueness of equilibrium sequence
Fredrik Sandin Efects of mirror dark matter on neutron stars
Outline
Introduction
Mirror-matter hypothesis
Mass-radius relation
Critical mass
Heating
Fredrik Sandin Efects of mirror dark matter on neutron stars
Dark matter – a few reminders
Motivated by rotation of galaxies, lensingand cosmological concordance (CMB, large-scalestructure, BBN, .)
CDM: 4% atoms 22% dark matter 74% dark energy
Cannot be explained with standard-model particles
Popular hypothesis: WIMPs, e.g., supersymmetry→ neutralinos with m ~ 100 GeV … TeV
For each boson there is a corresponding fermion, and vice versa
Symmetry is broken, s-particles must be massive
DM should accumulate in stellar objects (?)
Fredrik Sandin Efects of mirror dark matter on neutron stars
Effects of WIMPs on NS
Bertone & Fairbairn PRD 77, 043515 (2008)
See also Gould, Draine, Romani & Nussinov PLB 238, 337 (1990) Goldman & Nussinov, PRD 40, 3221 (1989)
Captured WIMPs should not collapse NS
Fredrik Sandin Efects of mirror dark matter on neutron stars
Effects of WIMPs on NS
Kouvaris PRD 77, 023006 (2008)c
Heating from annihilation of WIMPs Steady state surface temperature ~104 K or less
Mass of WIMP-core too low to affect structure of NS WIMPs either self-annihilate at sufficient rate
or collapses the star (Mmax
~ Mplanet
)
Fredrik Sandin Efects of mirror dark matter on neutron stars
What about other dark-matter candidates?
WIMP-picture of dark matter could be oversimplified For a recent review see Perivolaropoulos, “Six Puzzles
for LCDM Cosmology” [arXiv: 0811.4684]
Stable fermionic dark-matter particles predictedby some “hidden-sector” theories
Such particles could affect NS significantly
Fredrik Sandin Efects of mirror dark matter on neutron stars
Mirror-matter hypothesis Consequence of parity-symmetry restoration
Lee & Yang (1956); Foot, Lew & Volkas, PLB 272 (1991)History & refs: Okun, Phys. Usp. 50 (2007); hep-ph/0606202
G → GO⊗G
M → two sectors: ordinary (O) and mirror (M)
Space-time is common to both sectors
Lagrangians identical in the two sectors
Mirror and ordinary particles interact by gravity
Feasible dark-matter candidate, studied in some detail
Cosmology requires different T and B in the two sectors
Helium dominated → different structure, evolution and stellar propert.
Some effects on neutron stars discussed in literatureKhlopov et al., Sov. Astron. 35, 21 (1991)
Fredrik Sandin Efects of mirror dark matter on neutron stars
Hydrostatic equilibrium – a reminder
Ideal fluid in static isotropic spacetime
Einstein equation simplifies to
Tolman–Oppenheimer–Volkoff equation
Fredrik Sandin Efects of mirror dark matter on neutron stars
Hydrostatic equilibrium
Ideal fluid in static isotropic spacetime
Einstein equation simplifies to
“Inertia”
Gravity, common to both sectors
Separation of hydrostatic equation
Fredrik Sandin Efects of mirror dark matter on neutron stars
Mass-radius relation
Minimal parity-symmetric extension of SM
ℒM
= ℒO
→ Identical
EoS in the two sectors
DD2F EoS by S. Typelused here
Structure affected byfew % mirror baryons
Fredrik Sandin Efects of mirror dark matter on neutron stars
Radii of typical NS and maximum mass
Accretion from mirror interstellar medium too slow to affect structure
Mirror baryons mustoriginate from the progenitor star or a binary companion
Fredrik Sandin Efects of mirror dark matter on neutron stars
Critical mass for core collapse
Chandrasekhar mass is lowered Result for equal electron
fractions in the two sectors
For 50% mirror matterwe confirm estimate by
Kolb, Seckel & Turner,Nature 314, 415 (1985)
Effect on lightcurve?
Fredrik Sandin Efects of mirror dark matter on neutron stars
Accretion of mirror matter: energy budget
1.4 Msun
, DO ~ 26 km
1% mirror baryons
DM ~ 10 km
1 mirror baryon falls from “infinity”
“long time”
Q ~ ?
Equilibriumconfiguration
NO
Equilibriumconfiguration
NO, N
M+1
NM
Fredrik Sandin Efects of mirror dark matter on neutron stars
Accretion of mirror matter: energy budget
m=m0g00~940 eRM MeV~650MeV
m
Mirror baryon has kinetic energy 940 - 650 ~290 MeVon impact, which is emitted in the mirror sector
The mass-energy difference between initial and final configurations is
Gravitational binding energy in ordinary sectorpractically unchanged → no significant heating
The ordinary sector can be heated by weak interactions between the sectors (-' etc). If this heating is of order MeV, which seems optimistic, accretion from the mirror interstellar medium gives a steady-state surface temperature of at most 105 K
m0
1.4 Msun
, DO ~ 26 km
1% mirror baryons
DM ~ 10 km
∂M∂N M
~ 650MeVN O
Fredrik Sandin Efects of mirror dark matter on neutron stars
Concluding remarks
Nature of dark matter is unknownExciting time! DAMA, XENON10, CDMS II, CRESST, Pamela, …
Mirror matter is a feasible dark-matter candidatethat could have significant effects on neutron stars
M-R relation & Chandrasekhar mass depend on Ndm
/ NO
Heating by dark-matter accretion seems irrelevant
Future work Effect of dark-matter core on SN lightcurve?
Dynamical effects of dark-matter core?
Fredrik Sandin Efects of mirror dark matter on neutron stars
Accretion of mirror matter: energy budget
m
m0
1.4 Msun
, DO ~ 26 km
1% mirror baryons
DM ~ 10 km
Caution!
E=M c2=4c2∫0
Rdr r2 [O r M r ]
∂ EO∂N M
~−290MeV ,∂EM∂N M
~940MeV
E= EOEM“ “
N O N O
Fredrik Sandin Efects of mirror dark matter on neutron stars
Cooling calculation
Simple homogenous cooling model
Steady-state surfacetemperature < 105 K
1.4 Msun
star with 1% mirror baryons
Shapiro & Teukolsky:
Estimate of maximum accretion rate for an NS in a dense mirror molecular cloud~106 kg/s
From Kouvaris PRD 77, 023006 (2008)