From: sbs@weyl.bu.edu (Stephen Selipsky)
Newsgroups: sci.physics
Subject: Re: hubble and black hole
Date: 23 Nov 92 15:32:53 GMT
Reply-To: sbs@weyl.bu.edu
Organization: Boston University Physics Department


In article <1992Nov22.211548.23960@news2.cis.umn.edu>,
 sawdey@matterhorn.ee.umn.edu (Aaron Sawdey) writes:
|>
|>In <FRANL.92Nov21141214@draco.centerline.com> franl@centerline.com
|> (Fran Litterio) writes:
|>
|>>llew@bigwpi.WPI.EDU (Lok C. Lew Yan Voon) writes:
|>
|>>> anyway, nbc news had a short piece 2 days ago that the
|>>> space telescope had resolved the nucleus of a galaxy
|>>> to a much better resolution than b/f, i think it's
|>>> supposed to be a 100 times smaller than previously
|>>> believed. from the picture they showed, one can easily
|>>> discern the boundary plus a jet-like structure emanating
|>>> from one of the poles.
|>>> 
|>>> apparently, it's highly unlikely to be anything but a black hole.
|>
|>>I want to know why it can't be a really massive neutron star.  Don't
|>>they have accretion disks and spew jets of hot gas out from their
|>>magnetic poles?  What data is available other than the image from
|>>Hubble?
|>
|>It's too big. I think that an object with neutron-star density
|>and a mass greater than 3 or 4 solar masses (somebody: what's
|>the real figure for this?) turns into a black hole. The structures
|>imaged by Hubble have scale measured in 1000's of light-years (they're
|>45 Million light years away). I don't think a neutron star big enough
|>to create these effects could exist.
|>
   For sure.  The exact maximum mass for a compact object depends on details
of nuclear physics which we don't know-- basically, how hard can matter (e.g.
at the center of a star) push back against gravity?  If you don't want the
details below, the bottom line is Probably less than 2.7 M_solar, but NOT
PROVEN; certainly on the order of magnitude of solar masses.  See
Shapiro & Teukolsky, "Black Holes, White Dwarfs, and Neutron Stars" for an
undergrad-level treatment.
  Rhoades and Ruffini (Phys. Rev. Let. 32, 324 (1974)) developed a BOUND
on that maximum mass and Hartle (Phys. Reports 46, 201 (1978)) has a nice
review.  They said that for the densest part of the star, you should
assume the "stiffest possible" equation of state consistent with
causality (speed of sound less than speed of light), and some other
technical requirements (one-parameter eqn.of state, positive density rho,
microscopic stability dP/d.rho > 0), and assume that the outer parts of the
star (everything with a density below an arbitrary amount rho_0 \approx
nuclear density) can still be described by an equation of state using known
nuclear physics.  Then General Relativity gives a maximum neutron star mass 
(for a non-spinning star, but centrifugal support doesn't buy you much more)

  M_max < (6.8 M_solar) * (10^14 gm/cm^3 / rho_0)^(1/2) .

There's still an argument about phase vs. group velocities and causality,
and if you drop the sound-speed requirement then Hartle gets 11.4 instead
of 6.8; remember that nuclear density is 2.8 * 10^14 gm/cm^3.
   Realistic equations of state are less stiff, and give numbers around
2.0 M_solar, up to 2.7 for "pion condensation".  My thesis discussed an
extremely speculative equation of state, which potentially allowed masses
exceeding tens of solar masses, but probably not so much when you consider
various observational bounds.
   In any case, millions of solar mass objects occupying galactic centers
etc. can't possibly be anything but black holes, in anything even vaguely
resembling current theories.
                                 Back to work,   -- Stephen Selipsky
Newsgroups: sci.physics