Photoionization and the formation of
dwarf galaxies
Thomas Quinn ,
Neal Katz , and George Efstathiou
Abstract:
It has been argued that a UV photoionizing background radiation
field
suppresses the formation of dwarf galaxies, and may even inhibit the formation
of larger galaxies. In order to test this,
we present gas-dynamical simulations of the
formation of small objects in a CDM universe with and without a
photoionizing background. The objects are selected from a
collisionless simulation at a redshift of 2.4, and rerun at higher
resolution including the effects of gas dynamics and using a hierarchical grid
of particles. Five objects, each with a circular speed of 
are simulated. The presence of the photoionizing background
has a moderate effect on the amount of gas that collapses in these
objects, reducing the amount of cold collapsed gas by 40 to 90
.
Analysis of the smaller objects found in the higher resolution simulation
indicates that the photoionizing background significantly affects the
formation of objects with a virialized halo mass less than 
and circular speeds less than 
. Although formation of
the larger objects is only moderately affected, the
ionization balance is greatly changed
by the presence of the background radiation field. Typical lines of
sight through the objects have 4 orders of magnitude less neutral
hydrogen column density when the photoionizing background is included.
cosmology:diffuse radiation --- galaxies: formation
Hierarchical clustering models have been moderately successful in
determining the upper end of the mass distribution of galaxies (White & Rees
1978).
However, most models would predict a vast number of ``mini-halos''
( i.e. galaxies with circular speeds 
), and some
mechanism is needed to prevent most of the baryonic material in the
Universe from collapsing into such objects.
Supernova driven winds (Dekel & Silk 1986) may provide
a mechanism to suppress the formation of dwarf galaxies. Another
suppression mechanism that may be effective for dwarf galaxies
involves the presence of a photoionizing UV background
radiation field that provides a source of heating and
reduces the cooling of the baryonic
material (Rees 1986, Efstathiou 1992).
Evidence for such a field is given by the lack of a Gunn-Peterson
effect even at a
redshift of 4 (Webb et al. 1992), and the proximity effect in the
Ly
forest (Lu et al. 1991). The estimated values of the
background radiation field range from 
to 
at the Lyman edge. The lower
limit may be too low owing to obscuration by dust (Fall & Pei, 1993)
Efstathiou (1992) has calculated the cooling curve of a primordial gas
with no metals
in the presence of a background radiation field and has made simple
models of the collapse of gas clouds. The photoionizing background has
two effects. First, it raises the equilibrium temperature of the gas
to about 
. This raises the gas pressure and
suppresses the collapse of gas into halos
with circular speeds less than 
. Secondly, the
photoionizing background can suppress the cooling rate by reducing the
neutral hydrogen and helium fraction, thus making the cooling
times sufficiently long such that even larger objects might not
collapse over the age of the Universe. Furthermore, the increased
cooling time may make it easier for supernovæ to drive gas out of
these objects. The simple models suggest
that there can be significant increases in the cooling time since the
neutral hydrogen and singly ionized helium that dominate cooling at
low temperatures is eliminated. However, quantifying
this effect on the formation of low mass galaxies requires
numerical simulations.
In order for the gas to be unstable against collapse in a dark matter
halo, the circular
speed of the halo must satisfy (Rees 1986)
where 
, T, and 
are respectively, the sound speed,
the temperature, and the mean molecular weight of the gas, and 
is the
proton mass. In a spherical collapse model (Gunn and Gott, 1972)
using the mass within an enclosed density contour of 170 times the
background density,
this corresponds to a halo
mass
is the Hubble constant in units of 
. For a neutral gas of primordial
abundance at 
this implies a circular speed of 
and a mass of 
at 
, while for a fully
ionized gas at 
, the circular speed is 
and
the mass is 
.
If the increase in the
cooling time caused by photoionization has a significant effect, then
the formation of objects even larger than this will also be
suppressed.
In the simulations that follow, we attempt to test the accuracy of
these estimates regarding the sizes of objects whose formation are
suppressed by the presence of
a background radiation field. We first describe our series of
simulations and the results, and then discuss the implications of
these results.
To simulate the collapse of individual clouds in their
cosmological context, we use the multi-step approach described in Katz
et al. (1994). First, we evolve a
low resolution dissipationless simulation of a box 
on a side (
) in a b = 2 CDM universe with
particles (
) to a redshift of 2.4 using
the PPPM N-body technique (Efstathiou et al. 1985).
We use this simulation to select objects of the desired mass using a
friends of friends algorithm with a linking length of 0.11 times the
mean interparticle separation, corresponding to an overdensity of 178.
These objects are then simulated again with hydrodynamics using a
hierarchical grid of particles that provides high resolution in the
object while capturing the tides of the cosmological context. The
effective resolution of these simulations is 
with the high
resolution region starting as a sphere of radius 500 comoving kpc
containing 8700 collisionless particles and 8700 gas particles. A
further 4000 more massive particles are used to represent the evolution of
the fluctuations in the rest of the 
cube. On this hierarchical grid we impose the same fluctuations as
the low resolution simulation, and we add fluctuations to continue the
CDM spectrum to smaller scales. In accordance with big bang
nucleosynthesis (Walker et al. 1991), we
choose 
, giving a dark matter particle mass of
and a gas particle mass of 
. We use a gravitational softening length of 0.5 comoving
kpc for the high resolution particles, and the heavier particles have
correspondingly larger softenings.
We evolve the simulations using a comoving, periodic version of
TREESPH (Hernquist & Katz 1989; Katz, Weinberg, & Hernquist 1995) with
and 
years for the largest
timestep. Owing to the multiple timestep nature of TREESPH some particles
are integrated with timesteps 16 times smaller than the largest timestep.
We start the simulations at a redshift of 20, and include both
radiative and Compton cooling of the gas.
To study the effects of a
photoionizing background, we simulate each object twice: once with an
initial gas temperature of 
and no photoionizing background,
and once with an initial temperature of 
and a uniform photoionizing
flux of the form 
, where 
is the Lyman limit, 
is 1, and 
evolves as
as in Efstathiou (1992). This radiation field is much stronger than any
estimates of the observed radiation field. We choose such a strong background
field to quantify the maximum possible effect. The high initial
temperature is also likely to be higher than expected if the
intergalactic medium is photoionized, although temperatures of 
K can be achieved if the intergalactic medium is photoionized impulsively
(Miralda-Escudé and Rees, 1994).
The treatment of the photoionization is
fully described in Katz, Weinberg & Hernquist (1995), and
is similar to the approach of Vedel et al. (1994).
We simulate five separate objects using this technique. We choose
objects that are the smallest mass we could reasonably resolve
in the low resolution simulation, or about 200 particles. This
corresponds to a mass of 
or a circular
speed of 
at 
. The gas in such an object will
be stable against collapse only at very high temperatures; ( 
) however, at the level of background radiation
chosen for these simulations the gas can have equilibrium temperatures
of this order and cooling times longer than the Hubble time at
moderate (
--100) over densities. (See
Efstathiou, 1992, Figure 2).
Figure 1:
Comparison of the enclosed mass, circular
speed, enclosed baryonic mass, and gas temperature
as a function of radius for a halo at 
with and without a
photoionizing background. The solid lines are for the simulation
without the photoionizing background, and the dotted lines are with
the photoionizing background.
At 
we compare the radial profiles of the chosen objects
evolved with and without the photoionizing background. A typical
comparison is shown in Figure 1, where we show the enclosed mass, the
circular speed, the enclosed gas mass, and the gas temperature as a
function of radius for one of our objects. The effect of
the photoionizing background on the mass structure of this
object is moderate. The total mass differs very little, and the gas mass is
lowered by 40%. However, the gas temperature outside
the cold core is raised from 
in the no
ionization case to nearly 
with the ionizing
background.
Also note that for the run without photoionization 47% of the gas
within the virial radius is in a diffuse hot component, while the run
with photoionization has 53% of its gas in a hot component.
Figure 2:
Distribution in the mass of cold collapsed gas
for objects at 
. The solid lines are for the
simulation without the photoionizing background, and the dotted lines
are with the photoionizing background.
It appears that the UV background field has a moderate effect on the
collapse of gas into halos of the size that we chose to simulate in
the low resolution simulation. The amount of cold gas in three of the
objects was reduced by about 40% and in the other two by 50% and
90%. However, our high
resolution simulations also
include some halos that were too small to be well resolved in the low
resolution simulation. Comparing these halos, we may be able to
determine the mass at which the photoionizing background
suppresses gas collapse. To find these
halos, we use an algorithm similar to DENMAX (Bertschinger & Gelb,
1991; Stadel et al. 1995, in preparation) to identify bound groups of
particles associated with density maxima. For each object we then
determine how much of its mass is in cold (
) gas.
In Figure 2 we compare the distribution in the cold gas mass of the
objects found in all the high resolution runs with and without the
photoionizing background. The presence of the
background field has a moderate effect on the distribution of
collapsed gas mass down to a total gas mass of 
,
but below this mass,
the effect is quite marked. There are 50 objects with a cold gas mass
between 
(50 particles) and 
(1000 particles) in the
simulations without the background field, while there are only 3
objects in this mass range in the simulations with the background
field. Suppression of formation occurs below a total halo mass of 
(a cold gas mass of 
),
or a circular speed of 
. Another possibility that can't be
completely ruled out is that we are reaching the resolution limit of our
simulations (see Weinberg et al. 1995).
The simulations presented here suffer from many limitations, but these
limitations arise from compromises made to attain as high a resolution
as possible using a moderate number of particles. First, they were run
to a fairly high redshift with a somewhat low amplitude of
fluctuations. This gives the advantages of needing a smaller high
resolution region, a smaller number of timesteps, and not going as
far into the non-linear regime. Second, the dissipationless run from
which we chose our objects is by no means a fair sample of the
Universe, although this is ameliorated by the low amplitude
fluctuations and high redshift. Thirdly, the high resolution region
is just large enough to contain the material that fell into the
central object. In fact, as many as 10 lower resolution particles
with 8 times the mass of the high resolution particles fell within the virial
radius of the
central object at the end of the run. As well as their effect on the
dynamics, the presence of these heavier particles indicates that more
gas would have fallen into the object than we have accounted for,
since only the high resolution region contains gas particles.
Despite these drawbacks, these simulations are unique in their
combination of a mass resolution of 
with the
representation of the cosmological context in a 
cube.
These simulations help to quantify some numbers in the analytic arguments
of Efstathiou (1992). The equilibrium temperatures and particularly
the cooling times are both density dependent. In the haloes of the
objects the density is low enough that the photoionization has a
significant effect. However, a significant amount of gas collapses to
a high enough density that the suppression of the cooling rate by
photoionization becomes ineffective.
This conclusion is in good agreement with the one dimensional
hydrodynamic simulations of Thoul and Weinberg (1995). They
find that a
photoionizing background reduces the amount of cold collapsed gas for
objects and completely suppresses the formation of objects
with circular speeds less than 
.
The conclusions are also consistent with those of Weinberg, Hernquist, & Katz
(1995) who conclude that a photoionizing background field does not affect
the formation of objects with circular speeds 
.
Figure 3: Neutral Hydrogen map of a 
cube centered on an object simulated without a photoionizing
background. The contours show the logarithm of the neutral hydrogen
column density in atoms per square centimeter. They are spaced by
factors of 10 from 
to 
.
Figure 4: Neutral Hydrogen map of the same object as
figure 3a, but simulated with a photoionizing background. The
contours have the same values as in figure 3a.
Our results show that photoionization alone is not sufficient to
suppress the formation of dwarf galaxies in order to bring the
predictions of hierarchical clustering models into agreement with
observations. The hierarchical models tend to overproduce galaxies
with luminosities less than 
or circular speeds
less than 
. (White & Frenk, 1991) However, even with the
generous amount of photoionizing flux in our simulations, we are not
able to completely suppress the formation of objects with circular
speeds of 
. Furthermore, most of the limitations of our
simulations (lack of metal cooling, limited resolution, and missing
infalling gas) make it harder to form objects. These results differ
from those of Cen & Ostriker (1992) who find a good match to the
observed galaxy luminosity function with a reasonable mass to light
ratio. We believe that this discrepancy is due to different
resolutions. Cen and Ostriker's highest resolution simulation has a
resolution (two grid cells) of 
, a factor of 60 larger
than our resolution. A lower resolution simulation is not able to
resolve the small dense knots that cool quickly. The lower
resolution simulations of Cen and Ostriker support this hypothesis, since
their next lowest resolution simulation with 
resolution has 10
times fewer collapsed objects with 
in baryons.
Although the UV background field only moderately affects the formation
of 
objects,
it completely changes their ionization structure, and therefore has
significant implications for their absorption line characteristics. Figure
3a shows a map of the neutral hydrogen column density in atoms per
square centimeter in a 
cube around an object simulated with
no photoionizing
background. Figure 3b shows the same object, but simulated with a
photoionizing background. Note that over much of the area the neutral
hydrogen column density is reduced from 
to 
. The size of
the region with greater than 
is
comparable to the size of collapsed objects in the simulation of Cen
et al. (1994); however, this object has a high density knot not seen in
the Cen et al. simulation, probably owing to their poorer spatial
resolution. Since the simulations and the maps assume that the gas is
optically thin to the UV radiation field, the column densities in Figure 3b
are underestimated when the column densities are greater than about
(Katz, Weinberg, Hernquist &
Miralda-Escudé, 1995).
In a future paper, we will use the absorption
cross-sections determined from simulations like these to
calculate number densities of objects from the absorbers seen in
quasar spectra.
N. Katz and T. Quinn wish to acknowledge support from a NASA HPCC/ESS
grant NAG 5-2213.
N. Katz also received support from NASA Astrophysics Theory grant NAGW-2523.
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dwarf galaxies
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- ...Quinn
- Department of Astronomy, University of Washington, Seattle,
WA 98195
- ...Katz
- Department of Astronomy, University of Washington, Seattle, WA 98195
- ...Efstathiou
- Department of Physics, University of Oxford,
Oxford, OX1 3RH