Is PSR B1757-24 a binary pulsar?

Binary pulsars with very small radial velocity corresponds to weak orbital effect at time scale of orbital period, and thus be treated as singular ones. However such pulsars may show their binary nature at long time scale by affecting pulsar frequency derivatives. Subtracting the magnetic dipole radiation predicted frequency derivatives from the measured ones, the intensity of long term orbital effect can be estimated and thus the orbital period can be predicted, i.e., 2.0day for PSR B1757-24. Therefore, binary pulsars can also be found by analysis of pulse frequency derivatives in “singular” pulsars. Moreover, difficulties concerning frequency derivatives, such as braking index, age and timing noise of pulsars can be explained naturally by the new model. Subject headings: : pulsars individual (PSR B1757-24) 1. Orbital effect at long time scale The time for the pulsed light to travel across the projection of the orbit into observer’s line of sight from the instantaneous position of the pulsar is z c = r sin i c sin(ω + f) . (1) where c is speed of light. r is the distance between the focus and the pulsar, f is the true anomaly, ω is the angular distance of periastron from the node, i is orbital inclination, as shown in Fig 1. The second of the phenomena due to orbital motion is the change of pulse frequency, ∆ν, ∆ν ν = v · np c = K[cos(ω + f) + e cosω] . (2) where K ≡ 2πap sin i/[cPb(1 − e )] is the semiamplitude, e, Pb, ap are eccentricity, orbital period, and pulsar semi-major axis respectively. The effect of Eq.(2) is more difficult to measure. Because the typical orbital speed in binary pulsars are v ≈ 300km s, the change in frequency ∆ν ≈ 0.001ν, so that the effect of Eq.(2) on pulse arrival times can be determined only in favorable situations (Hilditch 2001). The amplitude of Eq.(1) and the semi-amplitude of Eq.(2) are dependent of the mass function, F (M) = (M2 sin i) /M, where M2 is the mass of the companion and M is the total mass, M = M1 + M2. When the mass function of a binary pulsar is so small (M2 or sin i small), that its variation in one orbital period cannot be detected, the binary pulsar may be treated as an singular pulsar. Can a binary pulsar (which is appeared as singular one) show its identity when the short periodic orbital effect is unmeasurable? The answer is yes, the long term orbital effect of a ”singular” pulsar may affect the pulse frequency and frequency derivatives, and therefore show its binary nature. If Eq.(1) and Eq.(2) are averaged over one orbital period, then the time delay of Eq.(1) vanish but the Doppler shift of Eq.(2) is still there, ∆ν ν =< v · np c >= Ke cosω . (3) The period of Eq.(3) is 2π/ω̇, which determined by the advance of periastron, ω̇. The period of the averaged Doppler shift of Eq.(3) is much larger than that of normal Doppler shift of Eq.(2), i.e., when the period of Eq.(2) is Pb = 1hr, the period of Eq.(3), 2π/ω̇, is approximately years. Differentiating (denoted by ) Eq.(3) gives, ν̇L = −ν < v · np c > . (4) Eq.(4) means that at long time scale a “singular”