Moments of inertia for neutron and strange stars: Limits derived for the Crab pulsar
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'' I =~ a(x) M R^{2}, where x=(M/M_{sun}) (km/R), 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 a_{NS}(x)=x/(0.1+2x) for x<=0.1 (valid for M>0.2 M_{sun}) and a_{NS}(x)={2/ 9}(1+5x) for x>0.1. For strange stars a_{SS}(x)={2/ 5}(1+x) (not valid for strange stars with crust and M<0.1 M_{sun}). We obtain also an approximate expression for the maximum moment of inertia I_{max},45 =~ (0.37 + 7.12* x_{max}) (M_{max}/M_{sun})(R_{M_max}/ {10 km})^{2}, where I_{45} = I/10^{45} g* cm^{2}, valid for both neutron stars and strange stars. Applying our formulae to the evaluated values of I_{Crab}, we derive constraints on the mass and radius of the pulsar. { A very conservative evaluation of the expanding nebula mass, M_{neb}=2 M_{sun}, yields M_{Crab}>1.2 M_{sun} and R_{Crab}= 1014 km. Setting the most recent evaluation (``central value'') M_{neb}=4.6 M_{sun} rules out most of the existing equations of state, leaving only the stiffest ones: M_{Crab}>1.9 M_{sun}, R_{Crab}= 1415 km.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 December 2002
 DOI:
 10.1051/00046361:20021241
 arXiv:
 arXiv:astroph/0209151
 Bibcode:
 2002A&A...396..917B
 Keywords:

 dense matter;
 equation of state;
 stars: neutron;
 Astrophysics
 EPrint:
 5 pages, 2 figures included  accepted for publication in A&