A&A 396, 917-921 (2002)

DOI: 10.1051/0004-6361:20021241

## Moments of inertia for neutron and strange stars: Limits derived for the Crab pulsar

**M. Bejger and P. Haensel**

N. Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland

e-mail: haensel@camk.edu.pl

(Received 28 March 2002 / Accepted 1 October 2002)

** Abstract **

Recent estimates of the properties of the Crab nebula are used to
derive constraints on the moment of inertia, mass and radius of the
pulsar. To this purpose, we employ an approximate formula combining
these three parameters.
Our "empirical formula"
, where
,
is based on numerical results obtained for thirty theoretical
equations of state of dense matter.
The functions
*a*(*x*) for neutron stars
and strange stars are qualitatively different. For neutron stars
for
(valid
for
)
and
for
*x*>0.1.
For strange
stars
(not valid for strange stars
with crust and
).
We obtain also an approximate expression for the maximum moment of
inertia
,
where
, valid for
both neutron stars and strange stars.
Applying our formulae to the evaluated values of
,
we derive constraints on the mass and radius of the pulsar.
A very conservative evaluation of the expanding nebula mass,
, yields
and
10-14
. Setting the most recent evaluation
("central value")
rules out most of the existing equations
of state, leaving only the stiffest ones:
,
14-15
.

**Key words:**dense matter

**--**equation of state

**--**stars: neutron

Offprint request: M. Bejger, bejger@camk.edu.pl

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*ESO 2002*