A&A 431, 673-677 (2005)

DOI: 10.1051/0004-6361:20041790

*Research Note*

## An upper bound on the energy of a gravitationally redshifted electron-positron annihilation line from the Crab pulsar

**P. S. Negi**

Department of Physics, Kumaun University, Nainital - 263 002, India

e-mail: negi@upso.ernet.in

(Received 4 August 2004 / Accepted 5 November 2004)

** Abstract **

We present a causally consistent and pulsationally stable two component neutron star model on the basis of
the criterion that for each assigned value of
the ratio of
central pressure to central energy-density),
the compactness ratio
(*M*/*R*), where
*M* is the total mass and
*R* is the radius of the
configuration) of the
static configuration does not exceed the compactness ratio,
, of the homogeneous density sphere
(that is,
). The core of this model is given by the stiffest equation of
state (EOS),
(in geometrized units) and the envelope is characterized by the well-known EOS
of a classical polytrope
. The models yield an upper bound on surface redshift,
, of neutron
stars corresponding to the case of
envelope, whereas a model-independent upper bound on neutron star masses,
, is obtained for a conservative choice of the "matching density",
, at the core-envelope boundary. If the observational constraint of the glitch healing parameter,
, of
the Crab pulsar is imposed on these models, the strong lower bounds on surface redshift
and mass
are obtained for the Crab pulsar. However, if the other observational constraint of the
recently evaluated value of the moment of inertia for
the Crab pulsar (based upon the newly estimated "central value" of the Crab nebula mass
) is also imposed on these models together with the observational constraint of the
"central" weighted mean value
, the model with the
envelope itself yields the value of
matching density,
, adopted in this study and in this sense does not
represent a fiduciary quantity. For these constraints, the minimum surface redshift and mass of the Crab pulsar
are slightly increased to the values
and
respectively. The confirmation of these results requires evidence of the observation of the
gravitationally redshifted electron-positron annihilation line in the energy range of about 0.414-0.418 MeV
from the Crab pulsar, which is
in agreement with the energy of the gamma-ray line at about 0.40 MeV, observed in the mid 1970s.

**Key words:**dense matter

**--**equation of state

**--**stars: neutron

**--**pulsars: individual: Crab

SIMBAD Objects

**©**

*ESO 2005*