Pergamon Prog. Part. NucL Phys., Vol. 32, pp. 105-106, 1994

Copyright © 1994 Elsevier Scimo~ Ltd Printed in Great Britain. All rights reserved

0146-6410/94 $24.00

0146-6410(93)E0009-F

Neutrinos and the Evolution of Newly Born Neutron Stars

WOLFGANG KEIL

Max-Planck-lnstitut fllr Astrophysik, Kad.Schwarzschild-Str. 1, D-85748 Garching, Germany

Abstract

The role of neutrinos in the evolution of a newly born neutron star is discussed. Special attention is given to the influence of an uncertain description of neutrino cross sections at high densities on a calculated neutrino signal.

Keywords

Neutrinos- star: collapsed - star: neutron

1. The role of neutrinos in the evolution of a neutron star

Neutron stars are believed to be formed in a Type II supernova (Hillebrandt 1993). Only 1% of the total gravitational energy released in such a supernova is used for the kinetic energy of the debris and for the observable light. 99% emerge as neutrinos from the newly born neutron star. The bulk of these neutrinos is radiated during the cooling phase of the neutron star, which lasts a few seconds.

In a neutron star electron neutrinos are produced by the inverse/5-decay, whereas the other neutrino species are mainly produced by thermal pair processes. Right after its formation, the neutron star is hot and lepton-rich. But it can not be cooled by photons efficiently, because the matter is so dense that it is opaque to photons. Since neutrinos couple to the matter only by the weak interaction, their cross sections are approximately 10 -19 times smaller than the cross sections of the photons. Therefore neutrinos can leave the neutron star, and they carry energy and electron-lepton flavor out of the star. The neutron star becomes cooler and more compact, and its lepton fraction decreases. Nontheless the free mean path of the neutrinos, A,, = (a,,n) -1 (a,, = neutrino cross section, n - number density of target particles), is only in the range between 10 cm and 10 m, whereas typical radii of neutron stars, R., are of the order of 10 - 20 km. So neutrinos diffuse out of the star, and the cooling timescale (,,, A~ / (R . c ) ) is of the order of seconds.

The major contributors to the neutrino cross sections are the following scattering and absorption processes:

v + n -~ v + n v e + n "~ p + e - v + p ~ v + p O , + p --+ n + e + v + A --+ v + A

The cross sections for these reactions would be well-known, if nucleons were isolated. But at the high densities in a protoneutron star nucleons are not free at all, and in large regions of the star nucleons

105

106 W. Keil

u

• . i . . . . i . . . . i . . . .

. f . / S / S " = . . . . t m . . . . . ~ . . . . . . ~,~.~.

[ q m . . . . " " . . . . . . . . . . . . . . . . . . . . . . . . . .

• • f . . . . i . . . . t . . . .

0 . 5 1 1 . 5

~ J ~m

Figure 1: Dependency of the neutrino signal on the variation of the neutrino cross sections (Keil 1993)

are degenerate. Pauli blocking, Fermi liquid and Plasmon effects reduce the effective cross sections. The problem is, that the theoretical treatment of these effects is not satisfactory to date, and this density regime is not accessible to laboratory experiments. So neutrino cross sections in neutron stars are known to no better than a factor of 2 (Burrows & Lattimer 1986).

2. C o n s e q u e n c e s o f o u r incomplete knowledge of neutrino c ross s ec t i ons

This uncertainty in neutrino cross sections will affect the results of protoneutron star simulations. In such simulations the evolution of a young neutron star and its neutrino signal observable on earth are calculated.

To examine the effect of uncertain neutrino cross sections quantitatively, we calculated several neutron star evolutions and modified the original cross section, a0, by a constant factor A:

~0=tr0 x A , 0 .3< A < 2 . 0 .

Figure 1 shows the results of our calculation. ~'9o is the time after which 90% of the total gravitational energy has left the star. Therefore ~'90 is a typical cooling time of the neutron star. As expected, the cooling time increases with increasing cross sections, because the neutrinos diffuse slowlier. Also the duration of the detectable neutrino signals, tK11, 1~tB, for the Kamiokande II and the IMB detector increases slightly with increasing ~r0, until it reaches a saturation value. The number of detectable neutrinos, NKII, IMB, decreases with increasing cross sections to a minimum value. The behaviour of tK11, ZMB and NKIZ, ZMB can be explained by the reduction of the mean energy of neutrinos, E~, emerging from the star. E~ becomes smaller with greater values of 00, and the detection probability drops with E~ as the capture cross section of ~, in the water Cerenkov detectors.

We can conclude, that neutrinos play a very important role in the cooling of protoneutron stars. But the uncertainties of their cross section cause a significant variation of the resulting neutrino signal.

R e f e r e n c e s

Burrows A., Lattimer J. (1986), Astrophys. J. 307, 178. Hillebrandt W. (1993), this volume Keil W. (1993), Diplomarbeit, Techn. Univers. Mfinchen