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I am currently reading A Brief History of Time and Chapter 6 about black holes.

Now, here it says

He found it too large to be caused by a gravitational field: if it had been a gravitational redshift, then the object would have to be so massive and near to the Solar System that it would disturb the orbits of the planets

My question is: Why would the object have to be near to us and very massive? Why couldn't we get the same redshift from an extremely massive, but far away object, or less massive and far (so that there might be some hindrance caused by astrophysical entities apart from the emitting ones [of radio waves from 3C273] that could cause gravitational effects and redshift?)

I am unable to understand the logic of "massive and near to us".

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    $\begingroup$ Can you provide just a little more context? Is it saying that the redshift actually is just coming from the expansion of the universe? $\endgroup$
    – Justin T
    Mar 28, 2022 at 16:15
  • $\begingroup$ Yes yes After that it said: "Therefore he assumed it that it was due to the expansion of the universe" $\endgroup$
    – Aveer
    Mar 29, 2022 at 9:45
  • $\begingroup$ "In 1963, however, Marteen Schmidt, an astronomer at the Palamar Observatory in California, measured the red shift of a faint starlike object in the direction of the source of the radio waves called 3C273. And then as is in the question $\endgroup$
    – Aveer
    Mar 29, 2022 at 9:48
  • $\begingroup$ I think it’s related to the fact that if somethings dim, it’s either really far away and intrinsically bright, or really close and intrinsically dim, because if it’s in the middle it would either be bright or not seen at all because it’s too dim, and then if it is gravitational redshift, it’s gotta be intense for that kind of redshift, hence the massiveness of it. $\endgroup$
    – Justin T
    Mar 29, 2022 at 12:14

1 Answer 1

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When 3C273 was discovered then Hubble's law was well established - so if the redshift of 3C273 was non-cosmological then it would have to be (roughly) part of the local group of galaxies.

However, 3C273 is a point source, so that would put a limit on the angular extent and hence on the physical size. Let's do some rough numbers. Assume that it could be up to 5 Mpc away and is of angular size <1 arcsec (regardless of its distance). This would make it less than 20 pc in diameter.

If we assume a spherical object and that the emission is coming from a surface of radius $r$, then we can estimate a gravitational redshift from the Schwarzschild metric as $$z = \left( 1 - \frac{2GM}{c^2r}\right)^{-1/2} -1\ .$$ and so $$ M = \frac{c^2 r}{2G} \left( 1 - \frac{1}{(1+z)^2}\right)\ .$$

The redshift of 3C273 is 0.158 and if $r=10$ pc then $M\simeq 3 \times 10^{13} M_\odot$, which would be much bigger than the entire mass of the local group!

Now you could argue that it is much closer than 5 Mpc - which reduces $r$ and hence the required $M$.

However, if we put it at the edge of the Milky Way (at 100 kpc), then $r\sim 10^{16}$m and $M \sim 10^{12}M_\odot$ (similar to the entire mass of the Milky Way!) or if you put it at the edge of the Solar System (at 100 au), then $r \sim 10^8$ m and $M\sim 10^4M_\odot$ ! i.e. This would totally disrupt the Solar System.

Thus, at whatever non-cosmological distance you put it at, if the redshift was gravitational, then the mass of 3C273 would totally dominate the dynamics of the local group, the Galaxy, or the Solar System respectively.

This argument alone isn't foolproof. One could assume the object is much smaller than implied by the upper limit to its angular diameter, leading to a smaller radius and a smaller implied mass. But the density goes as $M/r^3$ and so goes up as $r^{-2}$ as we make the radius smaller. The argument used by Greenstein & Schmidt (1963) was that you required neutron-star densities to get the required gravitational redshift in a stellar-mass object and that was totally incompatible with the presence of "forbidden lines" in the spectrum, which would be quenched at high densities. In addition, the blackbody temperature of a neutron-star sized object with the flux of 3C273 would need to be $\sim 10^{11}$ K. i.e. They ruled out a high-density, small radius possibility.

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