Hello! I just watched the video of Prof. Soichiro Morisaki. I was wondering about the axis labels in the graph he showed about the black hole mergers at the very beginning of the talk. In the y-axis, it said rh+/M, does r represent a distance scale? it is the distance between the compact objects? How do we transform it to a simple strain h+ with the values are of the order of 10⁻22? And about the x-axis, it said t(M), does it mean that the unit of time is in terms of M? And finally, M would mean the total mass of the binary system, right? Thank you very much!
1 Like
Another question related to the first lecture of today is about the number of parameters for a BNS. Just checking, they would be: m1, m2, spin1, spin2, lambda1, lambda2, chirp mass, q, Dec, AR, D_L, t_c, Phi_JN, polarization angle, phi_c. They count as 15 parameters so far, but in the lecture he said there should be 15 + 1 parameter for each NS, so that is 17 parameters. Then, which parameters am I missing in a BNS?
Hello! After watching the video of Prof. Viola Sordini, I got interested in the values she mentioned about the mass of observed black holes. The least value a BH can have is 3M_sun, that value was calculated by solving the TOV equations, right? My question is, which EoS model was used in order to get to that theoretical value? And if that is so, why the 2.6M_sun compact object of the GW190814 can’t be classified simply just as a NS? Thank you!
2 Likes
@Lucy, you’re overcounting some parameters while undercounting others! A binary merger only has two independent mass parameters, this could be m1, m2 or chirp_mass, q or any combination from these two sets. What I mean by this is that given m1 and m2, you can tell what is the chirp mass and q for a binary system. so 2 mass parameters! Spin for each NS is a vector so you have 6 unknowns for spins of two NS. Then rest are as you mentioned above: lambda1, lambda2, RA, DEC, D_L, t_c, inclination (also known as theta_jn for non-precessing systems), polarization and phi_c — 9 parameters. So total number of parameters: 2 + 6 + 9 = 17!
That’s a good question! So the first point: there is no theoretical lower limit on the mass of a black hole it’s just that we haven’t seen any with mass smaller then 5 solar mass! TOV equation predict the maximum mass of a NS but it requires an understanding of the equation of state (i.e. how pressure or density varies with the radius of NS). Now we don’t know which EoS is the correct one, there is an uncertainty on the maximum of NS as well. Observationally (mostly pulsar observations), we haven’t seen any NS with mass > 2.35 solar mass, so we don’t really know whether 2.6 solar mass object in GW190814 is really a NS! It could be a BH also! I hope I haven’t confused you further!
Hi @Lucy, yes the r represents a distance. Specifically it is the distance at which we extract the gravitational wave information from the numerical relativity simulation. This is typically a few hundred kilometers from the source and the multiplication is necessary to make the strain independent from the specific distance chosen for the extraction. It is already a strain, what you can do is rescaling the distance, for example multiplying by 10 Mpc (megaparsec) converted in solar masses to obtain the strain as it would be seen by LIGO if the source is 10 Mpc away from us. The M usually stands for the total mass of the BHs in solar masses indeed. In NR we usually output all the data in solar masses and assume c=G=1.
Thank you @mattia_emma! Then r is the distance to the source in the NR simulation. How about the horizontal axis? It is time measured in terms of M? or is it t/M?
Hi! I made a mistake in my question! When I was talking about that 3M_sun value, I was thinking in the NS problem actually. That is why I mentioned the TOV equations and the EoS hehehe. Anyway, then the uncertainty comes from the fact that we do not know which EoS is the correct one and we don’t have observations in that mass gap either. Nice! Thank you so much @singhmukesh!
…thinking about it further… that lack of observations in the mass gap doesn’t have to do with the sensitivity in frequency and distance of the detectors?
@Lucy the time is measured in terms of solar masses/total mass of the binary in solar masses, you can convert this to seconds multiplying by the mass of the binaries in kg and then by the appropriate power of G/c
1 Like
Certainly, there is a selection effect that GW detectors will less likely see lighter mass black holes, if they exists, than the heavier ones as former will be less louder! But it will also depend on the intrinsic merger rate of these lighter mass black holes. If it’s highly suppressed, then they will less likely be detected. The rate of the BH mergers in this mass gap is largely unknown and rather unexplored since we don’t know of any stellar processes that can lead to the formation of BHs in this mass range. However, I might be limited by my knowledge. 
1 Like