neutrino cooling of neutron stars
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General information on NS “Standard” scenario. “Minimal” cooling. Neutrino reaction rates in normal
nuclear matter in superfluid nuclear matter “Nuclear medium cooling” scenario. Medium effects on reaction rates in
normal nuclear matter in superfluid nuclear matter conclusions
Plan
Pulsar in Crab cancellation is remnant SN 1052 observed in 1968
Neutron stars are forming in supernova II explosions (M~Msol, R~10 km, initial T~30-50 MeV)
«Простираю свою персону ниц: я наблюдал в созвездии Твен-Куан явление звезды-гостьи.» Янг-Вэй-Тэ
Double neutron star binaries
1,4414(2) M☉,
1,3867(2) M☉
majority of measured NS masses are focused near the value 1.4 Msol
Pulsar J1614-2230
J. Antoniadis et al., Science (2013)
Measured Shapiro delay with high precision
Time signal is getting delayed when passing near massive object.
Highest well-known masses of NS
there are heavier, but far less precisely measured candidates)
Lowest well-known mass of NS 1.18 ±0.02 Мsol
Pulsar J0348-04232
P.Demorest et al., Nature 467 (2010)
M = (2.01± 0.04 ) Msol
New data: masses are essentially different
Klähn et al. PRC 74, 035802 (2006)
If M>2.4 Msol ( ) were observed, all these EoS would be invalid!Central densities in various NS are different! Studying various NS we may test density dependences of EoS and NN interaction
NS mass-central density diagram for different EoS
Stiffest EoS do not satisfy the HIC constraint. Only EoS near the upper boundary of the box satisfy both the HIC and NS mass constraints yielding Mmax>1.93 Msol
Danielewicz, Lacey, Lynch (2002)
- Boltzmann kinetic equation
fitted to directed & elliptic flow
HEAVY ION COLLISIONS MEET NEUTRON STARS (common constraints)
a RMF-based (KVOR, Mmax ~2 Msol )
quasiparticle model with scaled hadron masses and couplings
Khvorostukhin,Toneev,D.V. Nucl. Phys. (2007,2008)
Aim: to construct a phenomenological EoS and apply it to calculations of neutron stars and hydro. calculations of HIC reactions
following constraints from chiral symmetry restoration, SU(3) multiplet particle species are included
Kolomeitsev,D.V.Nucl.Phys. (2005); T.Klahn, et al. Phys.Rev. (2006)
rotation frequency
for non-accreting systems, period increases with time
power-law spin-down braking index
for magnetic dipole spin-down n=3
period
“spin-down age"
2) pulsar speed and position w.r. to the geometric center of the associated SNR
1) age of the associated SNR 3) historical events
Crab : 1054 ADCassiopeia A: 1680 ADTycho’s SN: 1572 AD
Explosion of SN1987A
Registration of 20 neutrinos Eν~ 10-40 МэВ
If Supernova will be exploded in our Galaxy (frequency 1/(30-100 yr)),
Superkamiokande will register ~103 neutrinos!
certainly, if not too close to our Sun !!!
White-body radiation problem (at low T<T ~1-few MeV):
direct reactions: Similar to di-lepton radiation problem in HIC
Cooling of neutron stars
After passing a minute, during 105 years a neutron star cools down by neutrino emission, than by photon emission from the surface
opac
Tsurf (t) is related to Tin (t); problem to compute Tin (t)
(except first minutes after NS formation during which NS cools down up to few MeV)
bring information straight from the dense interior
For T> min., T<Topac~ MeV neutron star is transparent for neutrino
cV - specific heat density, εv – neutrino emissivity,Ф, λ – metric coefficients
each fermion leg on a Fermi surface ~ T
neutrino phase space neutrino energy
emissivity
for t>300-500 yr
CV – specific heat,L-luminosity
~60 MeV
intermediate cooling
rapid cooling
How to describe all groups within one cooling scenario?
slow cooling
3 groups+Cas A:
Neutron star cooling data
>103 in emissivity
CaS A
Cooling: crust is light and interior is massive
most important are reactions in dense interior
(where baryon density
one-nucleon reactions:
two-nucleon reactions:
direct Urca (DU)
modified Urca (MU)
nucleon bremsstrahlung (NB)(less important)
Casino da Urca in Brazil-waist of money; pilferer, thief in Odessa
URCA “Un-Recordable Coolant Agent” (by Gamov)
n0 is the nuclear saturation density)
Phase-space separation
G.Gamov
the weak interaction constant
lepton current
nucleon current
Note 1/2 in neutral channel, since Z boson is neutral and W is charged!
~v (Fermi velocity) corrections are important
For
bare vertices !
emissivity:
Counting powers of T:
each external nucleon and electron line ~T
neutrino phase space neutrino energy
•one-nucleon phase-space volume (» 1027-1028 factor)
•T6 dependence
•threshold behavior (n>ncDU , nc
DU depends on EoS)
•very moderate density dependence
self-energy with free non-equilibrium Green’s functions
Cut of the diagram means removing of dE integration due to -function
D.V., Senatorov Yad.Fiz.(1987)
pion Urca (PU) processes:For
All “exotic” one-nucleon processes start only when the density exceeds some critical density
Pion Urca processes
PU is also one-nucleon process (if the model permits pion condensation)
Friman & Maxwell AJ (1979)
(3)(1)
(4)(2)
k
Additionally one should take into account exchange reactions (identical nucleons)
FOPE model of NN interaction (no medium effects)
FOPE model continues to be used by different groups, e.g. by Page et. All, Yakovlev et al.
Emissivity:
s=2 is symmetry factor. Reactions with the electron in an initial state yield extra factor 2.
Finally
Coherence: only axial-vector term contributes (!)
due to exchange reactions
+ -
+
-
+ -
+
-
+ -
+ -
-+
+ -
+ -
-
+
thick pion line (here up to 2nd order):
-+
+ -
+ -
+ -
++ ++ ----
one-nucleon process with pion
two-nucleon process
DU process schould be „exotics“ (if DU starts it is dificult to stop it)
EoS should produce a large DU threshold in NS matter !
[Kolomeitsev, D.V. (2005), Klahn et al. (2006)]
DU constraint:
MDU>1.35-1.5 Msol
since in reality masses of NS are not close to each other
Otherwise why many masses have M~1.3-1.5 Msol ?
Klähn et al. PRC 74, 035802 (2006)
should be modified
Information about density dependence of the symmetry energy
3 n0
DU -- information about nuclear EoS
L>80 MeV are excluded by the DU constraint
superfluid matter
normal matter with free vertices and Green’s functions
Diagrams with normal and anomalous Green func.
Naivegeneralization:
+ +- -
are forbidden
are allowed
new “quasi”-one-nucleon-like processes (one-nucleon phase space volume) become permitted
[Flowers, Ruderman, Sutherland, AJ 205 (1976), D.V.& Senatorov, Sov. J. Nucl. Phys. 45 (1987) ]
+ -
In superfluid (T<Tc<0.1-1 MeV) all two-nucleon processes are suppressed by factor exp(-2/T)
paired nucleonun-paired nucleon
D.V., Senatorov (1987)
nn is neutron gap and nn=exp(-nn/T)
[Page, Geppert, Weber , NPA 777, 497 (2006)]
pair breaking and formation (PBF)processes are important for cooling!
strongly depending on Δ(n)
Schaab et al. (1996)
D.V.& Senatorov, (1987)
Minimal cooling paradigm D.Page et al., D.G. Yakovlev et al. Reactions in presence of pairing
MU:
PBF:
(at least)
and for Δ> 0.1 MeV
• Minimal cooling paradigm does not allow to explain all available data
(problems or with slow coolers or with Cas A, + with rapid coolers).
attempts to fit cooling data by fitting Δ (n) dependencies and using different Ts-Tin
for different NS
Minimal cooling +exoticsD.Page et al., D.G. Yakovlev et al.
• Minimal cooling +exotics cannot appropriately explain all available modern data (either precision Cas A data or all others, with deficiency of the DU mentioned above).
The only diagram in FOPE model which contributes to the MU and NB is
For consistency one needs to calculate corrections of the second-order in f NN in other
values. Otherwise -- problems with unitarity.
Pion polarization operator in dispersion relation at order f NN2 :
Pion condensation already at n>0.3 n0
Free one-pion exchange
measure of pion softening
But there is no pion condensation in atomic nuclei
One should replace FOPE by the full NN interaction, essential part of which is due to MOPE with vertices corrected by NN correlations.
NN-1 part of the pion polarization operator is
Another inconsistency of standard scenario: it uses FOPE but adds PU processes for n > nc
PU> n0: Pion condensation arises only due to pion softening!
white body radiation problemGeneral consideration: Knoll, D.V. Ann. Phys. 249 (1996)
Only for low T<<εF, quasiparticle approximation is valid
(each G - + yields T2, allows to cut diagrams over G -+ )For soft radiation: quasiclassics (all graphs in first line are of the same order):LPM effect
Direct reactions from piece of matter (v in NS, e+e-, γ, K+ in HIC)
expansion in full non-equilibrium G - +
pion with residual (irreducible in NN-1 and N-1) s-wave N interaction and scattering``
Part of the interaction involving isobar is analogously constructed:
explicit nucleon-nucleon hole and Delta-nucleon hole degrees of freedom
small
Fermi liquid approach
full pion propagator:enhancement of the amplitude
dressed vertex:suppression
Poles yield zero-sound modes in scalar and spin channels
Low energy excitations in nuclear Fermi liquid (Landau-Migdal approach)
based on a separation of long and short scalesRe-summed NN interaction
Landau-Migdal parameters of short-range interaction are extracted from atomic nuclei
known phenomena in Fermi liquid
Similar to Debye screening in plasma
provided short-scale interaction can be reduced to the local one
see Migdal et al., Phys.Rep. (1990)
A.B. Migdal ZhETF (1971)
free π
the smaller collision energy, the larger is in-medium effect
: ω <0 for n>n2
cr
similar for π0 in neutron matter
Kolomeitsev,D.V. (1996)
[Migdal,Markin,Mishustin, JETP (1974)]
variational calculations [Akmal, Pandharipande, Ravenhall, PRC58 (1998)]:
pion condensate:
neutral pion condensate:
Charged pion spectra in neutron matter and pion condensation
pion gap for n<ncPU
no pion condensate
reconstruction of pion spectrum on top of the pion condensate
|*|~ amplitude of the condensate
1st-order phase transition
Г –vertex suppression factor
Pion softening with increase of the density
possibility of no π-cond.
From the cooling fit nc >2.5 n0
The weak coupling vertex is renormalized in medium:
[D.V., Senatorov, Sov. J. Nucl. Phys. 45 (1987)]
wavy line corresponds to weak current
For the -decay:
For processes on the neutral currents
with the correlation functions
Very strong density dependence
emissivity: larger smaller
Very important in our scenario!
Straight generalization of MU
The Ward identity is fulfilled and the current is conservedsuperfluid matter
normal matter free vertices and Green’s functions
free vertices and non-interacting quasi-particles with a gapped spectrum
Gap appears due to a non-trivial self-energy
Vertex must be modified accordingly. Otherwise the current is not conserved
Diagrams with normal and anomalous Green func.
Problem!
Naivegeneralization:
-+
+ +- -
Main contribution is due to the axial current.
Suppression is of the order ~0.1
moderate suppression strong suppression Leinson,Perez (2006),Kolomeitsev,D.V. (2008) Kolomeitsev,D.V. (2008)
with free vertices
D.V., Senatorov JETP 1986 all the data known to that time were explained by MMU process assuming different
masses (here different average densities) of NS
upper limits on surface temperatures
that time most of researches believed thatall NS have the very same masses ~1.4 Msol
Nuclear medium cooling scenario[D.Blaschke, H. Grigorian, D.V., AA 424 (2004)]
1S0 Gaps model I, heat conductivity from Baiko et al. 2001(left) , varied (right). If we suppress Baiko result by k~0.3 we are able to describe CaS A data 2010.
All data are explained by different masses of objects
DU
Model I for pairing
Thermal conductivitywith taking into account of medium effects
lepton termwith inclusion of Landau damping
nn- term with inclusion of pion softening
Blaschke, Grigorian, D.V. 2013
yields suppression of Baiko result
NS Mass-central density for EoS that we use
We incorporated excluded volume effect: resulting HDD EoS is very close to KVOR, APR EoS for n<4 n0 (thus we satisfy the HIC-flow constraint) but EoS stiffens
for n>4n0 increasing Mmax.
Blaschke, Grigorian, D.V. 2013
Cas A data (observations 2000-2010) show very sharp temperature drop
minimal cooling (Page et al. 2011, Yakovlev et al.2011) requires 3Р2 pairing Tc~0.05MeV (but some
other data are not explained within the same scenario).
Nuclear medium cooling (Blaschke, Grigorian, Weber, D.V. 2012, Blaschke, Grigorian,D.V. 2013)
Region of r-mode instability Coriolis driving force
Kolomeitsev,D.V. preliminary
Stable owing toshear viscosity
bulk visc.
Unstable region
Max. rotatingyoung pulsar
Within nucl.medium cooling we are able toexplain low frequencies of young pulsars
Theoretically medium effects and pion dressing are necessary, otherwise calculations become inconsistent.
Cooling data motivate strong density (neutron star mass) dependence of neutrino emissivities. (Supported by new measurements of different neutron star masses in supernova remnants.) Within our nuclear medium cooling scenario we explain precision Cas A data (for that we used tiny 3P2 pairing gaps).
Models of EoS with a strong density dependence of the symmetry energy (low DU threshold) have problems with description of NS cooling. DU constraint: MDU
crit >1.3-1.5 Msol .
Our new EoS is compatible with NS mass measurements and flow constraint.
Statement of some works that fit of Cas A allows to measure the value of 3P2 pairing gap (Tc ~0.5 MeV) seems as misleading.
Within nuclear medium cooling scenario we may explain absence of rapidly rotating young pulsars
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