Detecting a neutron star quake with LIGO

[repoman]

Or other GW detector in the future.

What is the feasibility of this?

Also, would we be able to tell the direction of the spin pole from the signal? A NS quake by one not pointed at us and not visible normally still send out x-rays in all direction, I think.

How far away can a NS quake be for LIGO to detect it - assuming it has the right frequency range?

I could spent some time googling this, but I think this is a fun question to ask as a spitball.

 

[rjh01]

I doubt if it would be detectable. Two colliding neutron stars have to pretty close to Earth to be detected and earthquakes would generate a lot weaker gravity waves.

 

[lpetrich]

Likely too weak, unless the neutron star was very close. To see why, use the mass-quadrupole formula for lowest-order gravitational-wave emission. It's much like the electric-dipole formula for electromagnetic-wave emission.

Electric dipole: D = q*x
Charge: q, position: x

P ~ (D'')^2
(power: energy-emission rate)
(second time derivative)

Mass quadrupole: Q = m*((x*x) - (1/3)*x^2*I)
Mass: m, position: x
(x*x) is the dyadic or outer product

P ~ (Q''')^2
(power: energy-emission rate)
(third time derivative)

I'd have to look up the coefficients, but they are simple numerical values and units constants.

For a neutron-star quake, Q ~ Q(max) * (Dx/x) for oscillation (Dx) and size x.

This gives P ~ P(collision) * (Dx/x)^2

So it will be very hard to see a neutron-star quake unless it was a relatively close one and big one.

How hard can be estimated from an observed effect of NS quakes: pulsar glitches. These are changes in rotation rate by 10^(-6), and that means (Dx/x) ~ 10^(-6). So

P/P(collision) ~ 10^(-12)

Meaning that one can detect a pulsar glitch by G-waves if it is 10^6 times closer than a detectable neutron-star merger. One such merger has been detected:  GW170817. It was about 40 megaparsecs away (130 Mlyr), and scaling with glitch size yields 40 parsecs.

NASA - Geriatric Pulsar Still Kicking

The pulsar, PSR J0108-1431 (J0108 for short) is about 200 million years old. Among isolated pulsars -- ones that have not been spun-up in a binary system -- it is over 10 times older than the previous record holder with an X-ray detection. At a distance of 770 light years, it is one of the nearest pulsars known.

That's 240 parsecs - 6 times farther away.