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Neutrino Processes in Neutron Stars. Evgeni E. Kolomeitsev (Matej Bel University, Banska Bystrica, Slovakia). What can we learn from neutron stars about processes in dense matter?. Data: star temperatures and ages Interpretation: star cooling

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slide1

Neutrino Processes in Neutron Stars

Evgeni E. Kolomeitsev

(Matej Bel University, Banska Bystrica, Slovakia)

slide2

What can we learn from neutron stars about processes in dense matter?

Data: star temperatures and ages

Interpretation: star cooling

Theory: ns cooling in a nutshell

luminosity of basic reactions

Problems: one scenario for all data points

How to calculate nuclear reactions in dense medium?

Green’s function method

Fermi liquid approach

quasiparticles and effective charges

Fermi liquid approach for superfluid medium

anomalous Green’s functions

conservation laws and Ward Identity

slide5

density increase

~10 km

..a little beacon

Nuclei and electrons

Neutron-rich nuclei and electrons

Nuclei, electrons and neutrons

neutrons, protons,

electrons, muons

Exotics:

hyperons,

meson-condensates,

quark matter

fastly rotating magnetized body

slide6

mass, size, dynamics of SN explosion

integral quantity

equation of state of dense matter

phase transitions

changed in degrees of freedom

We want to learn about properties of microscopic excitations in dense matter

How to study response function of the NS?

How to look inside the NS?

slide7

At temperatures smaller than the opacity temperature (Topac~1-few MeV)

mean free path of neutrinos and antineutrinos is larger than the neutron star radius

white body radiation problem

After >105 yr –black body radiation of photons

At temperatures T>Topac

neutrino transport problem

important for supernova

slide8

internal T

M=1.4 Msol

R=10 km

external T

Text depends on

envelop composition

[Yakovlev et al., A&A 417, 169]

debris of supernova explosion;accreted “nuclear trash”

slide9

1) age of the associated SNR

3) historical events

Crab : 1054 AD

Cassiopeia A: 1680 AD

Tycho’s SN: 1572 AD

2) pulsar speed and position w.r. to the

geometric center of the associated SNR

rotation frequency

period

for non-accreting systems, period increases with time

power-law spin-down

braking index

for magnetic dipole spin-down n=3

“spin-down age"

slide10

Given:

  • EoS
  • Cooling scenario[neutrino production]

Mass of NS

Cooling curve

slide11

3 groups:

slow cooling

intermediate cooling

rapid cooling

How to describe all groups within one cooling scenario?

slide12

emissivity

neutron star is transparent for neutrino

CV – heat capacity, L - luminosity

each leg on a Fermi surface /T

neutrino phase space ´ neutrino energy

slide13

where n0 is the nuclear saturation density)

(The baryon density is

Cooling: role of crust and interior?

most important are reactions in the interior

direct URCA (DU)

~T6

one-nucleon reactions:

modified URCA (MU)

two-nucleon reactions:

~T8

nucleon bremsstrahlung (NB)

URCA=Gamow’s acronym for “Un-Recordable Coolant Agent”

slide14

black body radiation

star is too hot;

crust is not formed

external temperature

heat transport

thru envelop

“memory” loss

crust is formed

1 yr ' 3 ¢107s

slide15

DU:

neutrino cooling

MU:

Tn

DATA

photon cooling

volume neutrino radiation

slide16

effective weak coupling constant

nucleon current

Low-energy weak interaction of nucleons

Cabibbo angle

lepton current

slide17

Weinberg’s Lagrangian:

lepton current

nucleon current

Note 1/2 in neutral channel,

since Z boson is neutral and W is charged!

slide19

emissivity:

matrix element

traces over lepton (l) and nucleon (n) spins

slide20

phase space integration

simplifications for

on Fermi surfaces

angle integration

triangle inequality

critical condition

slide21

energy integration

since the integration over energy goes from -¥ to +¥ and

under integral we can replace

slide23

energy-momentum conservation

requires

processes on neutral currents are forbidden!

slide24

energy-momentum conservation is easily fulfilled

assume e reaches m

Bose condensate of pions

k=(m ,0)

neutrons in both initial and final states

slide25

condensate amplitude

Migdal’s pion condensate k=(,kc): <m, kc» pF,ep-wave condensate

Kaon condensate processes yield a smaller contribution

All “exotic” processes start only when the density exceeds some critical density

slide28

Friman & Maxwell AJ (1979)

(1)

(3)

k

(2)

(4)

Additionally one should take into account exchange reactions (identical nucleons)

slide29

Emissivity:

s=2 is symmetry factor. Reactions with the electron in an initial state yield extra factor 2.

Finally

due to exchange reactions

Coherence:only axial-vector term contributes (!)

whereas for PU processes both vector and axial-vector terms contribute

slide30

[Blaschke, Grigorian, Voskresensky A&A 424 (2004) 979]

But masses of NS

are not close to each others

slide34

attraction

repulsion

Hebeler, Schwenk, and Friman,

PLB 648 (2007) 176

slide36

[Kaminker, Yakovlev, Gnedin,

A&A 383 (2002) 1076]

1ns for neutrons

1p for protons

HSF

slide37

for HDD EoS from

[Blaschke, Grigorian, Voskresnesky PRC 88, 065805(2013)]

For the s-wave paring

slide38

Ground state

Excited state

unpaired

fermions

paired

fermions

pair

breaking

“exciton”

D

pairing gap

excitation spectrum

emission spectrum

slide39

In superfluid (T<Tc<0.1-1 MeV) all two-nucleon processes are suppressed by factor exp(-2/T)

new “quasi”-one-nucleon-like processes (one-nucleon phase space volume) become permitted

[Flowers, Ruderman, Sutherland, AJ 205 (1976), Voskresensky& Senatorov, Sov. J. Nucl. Phys. 45 (1987) ]

un-paired nucleon

paired nucleon

[ Voskresensky, Senatorov, Sov. J. Nucl. Phys. 45 (1987); Senatorov, Voskresensky, Phys. Lett. B184 (1987); Voskresensky astro-ph/0101514 ]

nn is neutron gap

not

as in Flowers et al. (1976)

Naively one expect the emissivity of p p to be suppressed by extra cV2~0.006 factor.

slide40

pair breaking and formation (PBF)

processes are important!

[Page, Geppert, Weber , NPA 777, 497 (2006)]

slide41

standard

exotic

slide42

How to calculate nuclear reactions in dense medium?

Green’s function method

Fermi liquid approach

quasiparticles and effective charges