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Thread: Detecting a neutron star quake with LIGO

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    Contributor repoman's Avatar
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    Detecting a neutron star quake with LIGO

    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.

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    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.

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    Administrator lpetrich's Avatar
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    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.

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