Star formation and black hole formation

in 1920, astronomers Herber Curtis
and Harlow Shapley famously debated
whether certain faint nebulae in the
sky were external galaxies or structures
within our own Milky Way1. This was
resolved a few years later by Edwin Hubble
who determined that the Andromeda
nebula was an external galaxy by
identifying known types of pulsating
stars therein2. Although Curtis’s view that
the Universe contained many galaxies
was vindicated, Shapley’s insistence
that our Milky Way was larger than
previously thought also turned out
to be correct, once stellar distance
measurements improved.
We have long since learned3 that the
Universe contains many billions of galaxies,
each a gravitationally bound collection of
billions of stars with a central supermassive
black hole. And, if we accept conventional
gravity theory, the total mass in galaxies
is actually dominated by a dark-matter
halo that reveals itself only through the
motion of the stars and gas on which
it pulls4. Understanding how galaxies
acquire their constituents has been a longstanding
goal. Focusing on spiral galaxies,
Larson proposes a simple paradigm5
that could prove essential for progress in
this field.
Spiral galaxies (Fig. 1) display an
extended disc of stars and gas orbiting
at speeds of the order 150–250 km s–1.
That the rotation speed remains constant
over most of a galaxy’s disc is thought
to result from the gravitational effect of
a dark-matter halo4. Towards the centre
is a dense quasispherical bulge with less
prominent rotation, as its stars move on
more randomly oriented orbits. In the
Milky Way for example, this bulge extends
out to one quarter the distance of the Sun’s
location in the Galaxy and contains about
one quarter of the Galaxy’s total 80 billion
solar masses of stars. At the bulge core is
a supermassive black hole6 of less than a
billionth of the 1017 km bulge diameter, but
with 1/5,000 of the mass. Many galaxies,
including Andromeda, have more massive
black holes7.
Observations have established two
empirical constants common to spiral
galaxies that astronomers have struggled
to explain. First, the ratio of total stellar
mass to the fourth power of the disc
rotation speed is a constant8 (the so called
Tully–Fisher relation). Second, the ratio
of their inferred central black-hole mass
to the fourth power of the mean random
stellar velocities in the bulge is a second
constant9 (the so-called MH–σ relation).
Larson argues that the two constants
may be determined by understanding the
conditions in which gravitationally bound
gas in a protogalaxy forms stars and when
it would instead form a black hole. A
proto-galaxy forms out of the expanding,
cooling Universe when a region of gas with
sufficient density stops expanding owing
to its own self-gravity. By assuming that
proto-galaxies are quasispherical and that
the gas at all radii is a fixed fraction of the
dark-matter mass, Larson uses elementary
mechanics to relate the total gas mass
inside a given radius to the fourth power of
the gas velocity, and inversely related to the
surface density at that radius as required for
the Tully–Fisher and MH–σ relations. The
proportionality has been derived before,
but Larson gives important new insight
into how the surface density determines the
proportionality constants.
Much as regions of the expanding
Universe that become proto-galaxies
must achieve a critical density, regions
within a galaxy that become stars
must be dense enough for gravity to
overcome a competing force of thermal
expansion. At the required densities for
star formation, ions interact, radiate away
heat and combine to form molecules.
Star-forming regions are cooler, denser
and predominantly molecular compared
to the progenitor gas from which they
form. Remarkably, Larson finds that the
critical density required for the gas to form
stars equals that required to explain the
Tully–Fisher relation if the gas within the
galactic radius of critical density turns into
the stellar mass entering that relation.
Larson argues that a second critical
density arises in the very inner galactic
core. Here the dusty gas is so dense and
opaque that it traps heat, which at lower
densities would escape by radiative
cooling. Where cooling is inhibited, star
formation is quenched. Larson estimates
that this occurs when the surface density
exceeds a critical value of an extraordinary
coincidence: if all the gas that is as dense
as or denser than this critical value
forms a black hole, Larson estimates
this is just what is needed to explain the
MH–σ relation.
Larson has thus potentially explained
the two hitherto unexplained Tully–Fisher
and MH–σ empirical relations by
identifying two critical surface densities
that distinguish the formation of stars
from that of a central black hole. The
paradigm also predicts a maximum stellar
surface density in galaxies, owing to the
derived critical density above which star
formation is quenched. The predictions
are in general agreement with present
observational trends.
But even if Larson has pinpointed a
‘necessary’ condition for distinguishing star
formation from black-hole formation, the
complete set of ‘necessary and sufficient’
conditions remains to be determined. A
key issue, acknowledged by Larson, is how
the gas that forms the black hole loses its
angular momentum: the orbital angular
speed of gas, which moves inward and
conserves angular momentum, would
increase inversely to the square of the
distance from the centre. A small orbital
speed at large distances would become
Keplerian, and thus prohibitive for further
inward motion, well before the gas could
form a black hole. The dominant angularmomentum
transport mechanism is
not yet known but likely involves some
combination11,12 of gravitational and
magnetohydrodynamic instabilities
or outflows.
There are other uncertainties. Larson’s
numbers assume a standard dust-to-gas
mass ratio but, as dust determines the
opacity of the gas, tighter constraints
on its properties and mass fraction in
individual sources is desired. Furthermore,
if gravitational instabilities make the
distribution of dusty gas clumpy, more
free-streaming of radiation for a given
surface density might occur, increasing
the predicted critical density above which
a black hole forms. The extent to which
very massive stars may then be allowed to
form even if low-mass-star formation is
suppressed remains to be determined. It
is also natural to wonder whether Larson’s
paradigm applies to elliptical galaxies,
which have larger surface densities.
Finally, there remains an often
disdained but lingering possibility that
our understanding of gravity on galactic
scales and beyond is incomplete, and that
the rotation curves in galaxies usually
cited as evidence for dark matter may
instead partly highlight an incomplete
understanding of Newtonian gravity at
low accelerations. Among the predictions
of the most developed alternative12 to
conventional gravity is the Tully–Fisher
relation, independent of the gas surface
density. This directly contrasts Larson’s
approach in which the surface density is
crucial and a conventional role of dark
matter is assumed.
Future study of the complex interactions
between gravity, magnetized gas dynamics
and radiation transport in the formation of
stars and black holes in galaxies continue
to benefit from computer simulations11.
Simulations are often the closest tool
astronomers have to experiments, but
simple paradigms such as the one proposed
by Larson are essential in guiding the
construction and interpretation of these
simulations, and comparison of the results
with observations. ❐
Eric G. Blackman is in the Department of Physics
and Astronomy, University of Rochester, Rochester,
New York 14627-0171, USA.
e-mail: blackman@pas.rochester.edu
References
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