Determining Mass & Info of Merging Neutron Stars from LIGO Signal

[jordankonisky]

How does one determine/calculate the masses, orbital period, and separation of two merging neutron stars from the characteristics of its gravity wave LIGO signal? And how does this information allow one to calculate the distance to the galaxy that housed the merger? And how can one calculate the speed of recession of that galaxy from the characteristics of the accompanying gamma ray burst?

 

[pervect]

I'd suggest looking at the first LIGO paper, https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102.

What's measured is the frequency of the GW as a function of time. This signal is referred to as a "chirp", because it starts out with a low frequency and the frequency increases as the masses spiral together, getting closer and the orbital period reducing. There is a formula which gives a measure of the combined mass of the system , called the "chirp mass" in the paper, given the frequency and it's time derivative. They have references in the paper that talk about where the concept was derived, but I didn't dig into it that deeply.

As far as separation goes, they talk about "Keplerian effective black hole separation". I'm not sure if they give the details in the paper, but I assume they use keplers law (so it's an approximate concept, not something you'd measure with a ruler or via the SI definition of separation), the chirp mass (to estimate the total mass / reduced mass used in Kepler's law), and the orbital period /frequency. As the paper mentions, this is half the gravitatioanl wave frquency (which would be twice the period).

I'm a bit unclear on how they estimated the distance (specifically, the luminosity distance, which is the sort of distance they report). Sorry, at one time I thought I knew the anser to that, but it's escaping me.

 

[PeterDonis]

I'm a bit unclear on how they estimated the distance (specifically, the luminosity distance, which is the sort of distance they report).

The basic idea is that if you know the intrinsic luminosity of a source (i.e., how much energy it emits), then you can use the observed luminosity plus the inverse square law to come up with a distance to the source. The caveat here is that in an expanding universe, i.e., a curved spacetime, the luminosity "distance" doesn't mean quite what you might think it means--it doesn't have a simple interpretation in terms of "how far away" the object is (as it would in a static, flat spacetime). But it's still a common "distance" measure because it's easy to calculate (at least for a source with known intrinsict luminosity--for black hole mergers that is obtained from numerical simulations, which as I understand it relate the chirp mass, and possibly other characteristics of the signal, to intrinsic luminosity, somewhat similar to the way supernova light curves are used to calculate intrinsic luminosity).

how can one calculate the speed of recession of that galaxy from the characteristics of the accompanying gamma ray burst?

As I understand it, that's just the redshift of the gamma rays combined with the luminosity distance and the Hubble relation from our current best-fit model of the expansion history of the universe.

 

[Ibix]

I'm a bit unclear on how they estimated the distance (specifically, the luminosity distance, which is the sort of distance they report). Sorry, at one time I thought I knew the anser to that, but it's escaping me.

Doesn't the mass and period give you a power emission? The power received plus information about the "antenna" design and the inverse square law ought to do the rest. Or is that hopelessly naive?

Edit: never mind - Peter answered while I was typing.

 

[phyzguy]

As I understand it, that's just the redshift of the gamma rays combined with the luminosity distance and the Hubble relation from our current best-fit model of the expansion history of the universe.

I don't think one can get an accurate measure of the redshift from the gamma ray signal. There are no spectral lines to base a redshift on, and the emitted radiation energy distribution is broad. If you read this paper, they got the redshift from optical measurements of NGC4993 once it was established that this was where the event occurred.

 

[PeterDonis]

I don't think one can get an accurate measure of the redshift from the gamma ray signal. There are no spectral lines to base a redshift on, and the emitted radiation energy distribution is broad.

Ah, good point.

 

[George Jones]

An early undergrad-level overview of the analysis is given in the Physics Teacher article

https://arxiv.org/abs/1602.04666

It includes luminosity distance in "v) Distance to the source".

 

[jordankonisky]

An early undergrad-level overview of the analysis is given in the Physics Teacher article

https://arxiv.org/abs/1602.04666

It includes luminosity distance in "v) Distance to the source".

I want to thank everyone for your helpful reply to my questions. George, I especially appreciate your bringing the Physics Teacher article to my attention.