# I What is the minimum mass of a neutron star?

#### PAllen

I'm looking for a paper I can cite that gives a lower credible limit for a neutron star mass, specifically to rule out an NS being below 0.5 Msun which I think should be possible. Do you have a specific source for your statement, it would be very helpful.

Thanks.
George
I don’t know of a paper that gives a strong theoretical limit for the lowest mass neutron star we should see. But observation of neutron stars a little below the Chandrasekhar limit are easy to find.

#### jedishrfu

Mentor
I think this limit is the Chandrasekhar limit as mentioned by @PAllen so you could refer to his paper on it.

#### PAllen

I think this limit is the Chandrasekhar limit as mentioned by @PAllen so you could refer to his paper on it.

No, the Chandresekhar limit sets a theoretical maximum mass for a white dwarf, not a minimum mass for neutron stars. The paper I just linked above discusses observation of neutron stars a little below the Chandresekhar limit. This phenomenon is expected from theory, but what I don't know are any results saying how much smaller a neutron star can be given plausible formation scenarios.

#### jedishrfu

Mentor
But wouldn’t a neutron star of insufficient mass revert back to an ordinary star since the gravity is insufficient to force the electrons into the nucleus? and this then would indicate that the Chandrasekhar limit defines a kind of minimum neutron star stability.

#### PeterDonis

Mentor
wouldn’t a neutron star of insufficient mass revert back to an ordinary star since the gravity is insufficient to force the electrons into the nucleus?
No, because that would require it to do a huge amount of work against its own gravity, to expand to the radius of a normal star (or even a white dwarf).

his then would indicate that the Chandrasekhar limit defines a kind of minimum neutron star stability.
AFAIK it's quite possible for a neutron star of mass significantly less than the Chandrasekhar limit to be stable on theoretical grounds, if one were somehow formed. I don't have my copy of Shapiro & Teukolsky handy, but I believe they derive a minimum stable neutron star mass on the order of about half a solar mass. (Oppenheimer and Volkoff actually did the first crude estimate of this back in 1939 and came out with a value in the same range.) The issue is how such a neutron star, with mass much less than the Chandrasekhar limit, could form in the first place, since the collapse of any star or star-like object of such mass would stop at the white dwarf stage unless it were exceptionally rapid and violent, and the only such collapse we know of is a supernova, which requires a star much more massive.

Staff Emeritus
I don't have my copy of Shapiro & Teukolsky handy
I do. They give 0.18 solar masses under Harrison-Wheeler EOS. The Oppenheimer and Volkoff EOS has no lower bound. The reason they don't spring back to white dwarfs is, as you way, that this requires work, and the energy to do that work has already left the system.

#### GeorgeDishman

I've found this paper which probably meets my needs:

Equation (3) gives a range at formation for an isolated NS as:

M_birth∼1.08–1.57M_☉

Presumably a star exceeding the Chandrasekhar limit would start to collapse but the implosion of the core could eject some surface material to leave a remnant slightly below the limit.

In binary systems, mass transfer raises the mass of the first NS formed as the companion sheds so they have a different distribution with a higher mean (see figure 2) but I don't see any way the mass could be reduced significantly after formation.

"What is the minimum mass of a neutron star?"

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