A newly timed binary pulsar has orbital period

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Astrophysics & Cosmology · Stellar death and compact objects

Stars from the Inside, Ch Neutron stars and pulsars: the densest matter, the maximum mass and the spinning magnet

Problem

A newly timed binary pulsar has orbital period Pb=10.0 hP_b = 10.0\,\mathrm{h}, eccentricity e=0.20e = 0.20, and measured relativistic periastron advance ω˙=2.00∘ yr−1\dot\omega = 2.00^\circ\,\mathrm{yr^{-1}}. Timing also gives the pulsar's projected orbital semi-major axis x1≡a1sin⁡i/c=1.45 sx_1 \equiv a_1\sin i/c = 1.45\,\mathrm{s}. Assume the orbit is viewed edge-on, i=90∘i = 90^\circ. ((a)) Use ω˙=3(2π/Pb)5/3(GMtot/c3)2/3/(1−e2)\dot\omega = 3(2\pi/P_b)^{5/3}(GM_{\rm tot}/c^3)^{2/3}/(1-e^2) to find the total mass Mtot=Mp+McM_{\rm tot} = M_p + M_c. ((b)) The mass function of the pulsar's orbit is f(Mc)=4π2G(x1c)3Pb2=(Mcsin⁡i)3(Mp+Mc)2.f(M_c) = \frac{4\pi^2}{G}\frac{(x_1c)^3}{P_b^2} = \frac{(M_c\sin i)^3}{(M_p+M_c)^2}. Using MtotM_{\rm tot} from part (a) and sin⁡i=1\sin i = 1, find McM_c and MpM_p. ((c)) Compare the pulsar mass from part (b) with the heaviest measured neutron stars, about 2.02.0 to 2.1 M⊙2.1\,M_\odot, and with the causal bound near 3 M⊙3\,M_\odot. Then explain how a true inclination below 90∘90^\circ would change McM_c and MpM_p.

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