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Volume 431, Number 2, February IV 2005
Page(s) 673 - 677
Section Stellar structure and evolution
DOI http://dx.doi.org/10.1051/0004-6361:20041790

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)

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 $\sigma (\equiv$ $(P_0/E_0) \equiv $ the ratio of central pressure to central energy-density), the compactness ratio $u (\equiv $ (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, $u_{\rm h}$, of the homogeneous density sphere (that is, $u \leq u_{\rm h}$). The core of this model is given by the stiffest equation of state (EOS), ${\rm d}P/{\rm d}E = 1$ (in geometrized units) and the envelope is characterized by the well-known EOS of a classical polytrope ${\rm d}\ln P/{\rm d}\ln\rho = \Gamma_1 [(4/3)\leq \Gamma_1 \leq 2] $. The models yield an upper bound on surface redshift, $z_{\rm R} \simeq 0.77$, of neutron stars corresponding to the case of $\Gamma_1 = 5/3$ envelope, whereas a model-independent upper bound on neutron star masses, $M_{\rm max} \leq 4.1~ M_\odot$, is obtained for a conservative choice of the "matching density", $E_{\rm b} = 2.7 \times
10^{14}~{\rm\,g\,cm}^{-3}$ , at the core-envelope boundary. If the observational constraint of the glitch healing parameter, $Q \geq 0.7$, of the Crab pulsar is imposed on these models, the strong lower bounds on surface redshift $z_{\rm R} \geq 0.2234$ and mass $M \simeq 1.721~M_\odot$ 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 $M {\rm (nebula)} \simeq 4.6~M_\odot$) is also imposed on these models together with the observational constraint of the "central" weighted mean value $Q \approx 0.72$, the model with the $\Gamma_1 = 5/3$ envelope itself yields the value of matching density, $E_{\rm b} = 2.7 \times
10^{14}~{\rm\,g\,cm}^{-3}$, 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 $z_{\rm R} \simeq 0.2350$ and $M \simeq 1.807~M_\odot$ 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

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