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We need to calculate P/Pdot?

A pulsar may switch between theses two states.

For a rotation powered pulsar, it can pulse and, the pulsed Lx can be much larger than the luminosity given by its rotation?

If Lx is very small, smaller than the luminosity given by its rotation, how to tell it is rotation-powered or accretion-powered? There are not necessarily X-ray pulsations

You can see I am asking a very tricky scenario.

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  • $\begingroup$ Are you accepting drawings from university papers? $\endgroup$
    – Featherball
    Commented Dec 17, 2015 at 17:15
  • $\begingroup$ @Daniel which kind of drawings? $\endgroup$
    – questionhang
    Commented Dec 18, 2015 at 15:10
  • $\begingroup$ Diagrams and maths $\endgroup$
    – Featherball
    Commented Dec 18, 2015 at 20:00

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The spin behaviour of the two types of pulsar would usually be quite different. The $\dot{P}$ for a rotationally powered pulsar is always positive, and higher order time derivatives of $P$ are quite small. This is because the rotational kinetic energy is powering the pulsar emission and the neutron star continually spins down as it loses rotational energy.

Accretion powered pulsars can have very variable spin down or spin up characteristics, because they are powered by mass transfer and accretion in binary systems, and are influenced by a variety of factors affecting the accretion flow and how it couples to the pulsar magnetic field. The rates of spin down can be much higher than can be plausibly be accounted for by magnetic spin down as in a rotationally powered pulsar. Spin up cannot be accounted for in a rotationally powered model and neither can sign reversals or dramatic variability in $\dot{P}$.

Additionally, an accretion-powered pulsar would necessarily need to be in a short period binary system - therefore there would be a very obvious periodic modulation in the pulse period caused by the doppler shift as it travels in ts orbit.

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  • $\begingroup$ if Lx is very low, the question is tricky. $\endgroup$
    – questionhang
    Commented Dec 18, 2015 at 15:08
  • $\begingroup$ @questionhang Explain? If you think it is a pulsar then it means you can measure the pulse period. My answer exclusively focuses on this. I am not clear what you think the X-ray luminosity has to do with it. $\endgroup$
    – ProfRob
    Commented Dec 18, 2015 at 15:37
  • $\begingroup$ pulsar magnetic field. 'The rates of spin down', you mean in X-ray band, right? $\endgroup$
    – questionhang
    Commented Dec 18, 2015 at 16:25
  • $\begingroup$ @questionhang You tell me - it's your pulsar. A pulsar pulses on the rotation period, it doesn't matter what waveband the pulses are measured in. $\endgroup$
    – ProfRob
    Commented Dec 18, 2015 at 16:43
  • $\begingroup$ If a pulsar pulses in X-ray band, and its Lx is very small, how to tell it is accretion-powered or rotation-powered? $\endgroup$
    – questionhang
    Commented Dec 19, 2015 at 3:15

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