# Pulses from a pulsar

What is/was the motivation behind attributing the pulses received from a pulsar to the rotation of an object (neutron star) and emission from the magnetic poles (of the said neutron star), given that fact that pulsars have not been resolved yet in various wavelengths?

Could the pulses have been a product of a non-rotating but radially vibrating radio emitting star?

The key is to compare the range of pulsar periods and ther behaviour with the typical dynamical timescales of stars. Pulsar periods range from just less than $$10^{-3}$$ s to $$\sim 10$$ s. And $$\dot{P}$$ is positive - the periods are getting longer for most pulsars (and all of them that aren't in binary systems).

The dynamical timescale is $$\tau \simeq (G\bar{\rho})^{-1/2}$$, where $$\bar{\rho}$$ is an average density for the object.

For a star like the Sun $$\bar{\rho} \sim 10^{3}$$ kg/m$$^3$$ and $$\tau \sim 1$$ hour.

For a white dwarf star $$\bar{\rho} \sim 10^{10}$$ kg/m$$^3$$ and $$\tau \sim 1$$ second.

For a neutron star $$\bar{\rho} \sim 10^{18}$$ kg/m$$^3$$ and $$\tau \sim 10^{-4}$$ seconds.

Whatever mechanism you choose to cause the pulsar phenomenon, it cannot happen any faster than a few times this dynamical timescale if it is something involving the whole star. This basically rules out pulsations from normal stars and white dwarfs because they could not have pulsation periods that are short enough to explain most pulsars.

Next one might consider binarity, but again, the minimum orbital period, where the components are touching, is a few times the dynamical timescale and some sort of phenomenon involving binarity is ruled out by the long dynamical timescales of normal stars and white dwarfs.

Next one considers rotation; again, simple Newtonian physics can be used to show that an object will rip itself apart if it spins any faster than the dynamical timescale, so again this rules out normal stars and white dwarfs.

So we are left demanding that whatever object causes the pulsar phenomenon is highly dense. In addition there is microstructure in the pulses which indicates the entire source is varying on timescales shorter than a ms, which means the entire emitting region must be much more compact than about 300 km (i.e. $$c\times 10^{-3}$$s).

So why a rotating neutron star? I think the argument here is that if this were some kind of oscillatory motion you might expect the period to be stable. For some kind of binary phenomenon you would expect the period to get shorter, due to the emission of gravitational waves. The rotation of a magnetised neutron star and the loss of power by magnetic dipole radiation can explain why pulsar periods get longer.

• The strong and changing polarization state of the radiation within each cycle might also be hard to explain if it were radial oscillations.
– uhoh
Mar 11, 2020 at 0:38