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*Astron. Astrophys. 330, 1005-1016 (1998)*
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## Rapid differential rotation of protoneutron stars
and constraints on radio pulsars periods
**
J-O. Goussard **^{ 2},
P. Haensel ^{ 1, 2} and
J.L. Zdunik ^{ 1}
^{1} N. Copernicus Astronomical Center, Polish Academy of
Sciences, Bartycka 18, PL-00-716 Warszawa, Poland
^{2} Département d'Astrophysique Relativiste et de
Cosmologie, UPR 176 du CNRS, Observatoire de Paris, Section de
Meudon,
F-92195 Meudon Cedex, France
(e-mail: goussard@obspm.fr, haensel@camk.edu.pl, jlz@camk.edu.pl)
*Received 11 April 1997 / Accepted 7 October 1997*
**Abstract**
Models of differentially rotating protoneutron stars are
calculated, using realistic equations of state of dense hot matter.
Various conditions within the stellar interior, corresponding to
different stages of protoneutron star evolution, are considered.
Numerical calculations are performed within the approximation of
stationary equilibrium, using general relativistic equations of
stationary motion of differentially rotating, axially symmetric stars
and using a numerical code based on spectral methods. Families of
differentially rotating models of a given baryon mass are calculated,
using a two-parameter formula describing the angular velocity profile
within a rotating protoneutron star. Apart from the usual "mass
shedding limit", we introduce an additional "minimal mass limit" for
differentially rotating protoneutron stars resulting from a type II
supernovae. Maximum angular momentum, which can be accommodated by a
protoneutron star within these limits is calculated, for various
thermal conditions in stellar interior, for a baryon mass of
. In the case of a thermally homogeneous
(isentropic or isothermal) neutrino-opaque interior this maximum
angular momentum turns out to be somewhat higher than that of a cold
neutron star of the same baryon mass, rotating uniformly at the mass
shedding angular velocity. However, if the protoneutron star has a
thermal structure characteristic of initial state, with a low entropy
(unshocked) core, and a high entropy (shocked) outer half of baryon
mass, the maximum angular momentum is significantly lower. This leads
to a minimum period of uniform rotation of cold neutron stars of
baryon mass , formed directly (i.e. without a
subsequent significant accretion of mass) from protoneutron stars with
shocked envelope, of about 1.7 ms and strengthens the hypothesis
that millisecond pulsars are accretion accelerated neutron stars.
**Key words:** dense
matter
stars: neutron
stars: pulsars:
general
stars: rotation
*Send offprint requests to:* J-O. Goussard
© European Southern Observatory (ESO) 1998
Online publication: January 27, 1998
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