PRIMORDIAL GAS COLLAPSING WITH H2 COOLING
1
TAKAHIRO OOSATO
AND TATSUO YOSHIDA
Ibaraki University, Mito 310-8512, Japan
1
Junior Research Associate, RIKEN, Wako 351-0198, Japan
1.
Introduction
We have investigated that stability and hydrodynamics of a primordial
cloud embedded in a external pressure. Whitworth (1981) and Tohline et
al. (1987) discussed the role of cooling in the formation of clouds, assuming
the spherical symmetry and polytropic equation of state. They pointed out
that mildly nonlinear disturbances in cooling medium can collapse the cloud
which has initially the sub-Jeans mass. We have performed hydrodynamical
simulations, taking account into H2 cooling and chemical evolution, and
examined whether the cloud which has the sub-Jeans mass can collapse in
the primordial gas by mild uctuation.
2.
Models and Numerical Simulations
We assume that each spherical cloud is initially in hydrostatic equilibrium
and isothermal. We solve the basic hydrodynamic equations numerically
by using Lagrangian Godunov method. We also take account of chemical
reactions of ve species H; H2 ; H+ ; H0 , and e0 , and determine the fraction
of H2 in order to calculate the cooling rate of H2 . The full set of reactions
and rates is listed in Palla et al. (1983). As disturbance, we imposed an
initial velocity prole onto each cloud of a form v(r) = v (r=r ), where r
denotes the cloud radius and the sux b the boundary, respectively. We
determine the minimum of velocity required for the collapse of a cloud by
numerical simulations. The results are shown in Table 1.
b
3.
b
Discussion
We have conrmed that the cloud with the sub-Jeans mass can collapse in
primordial gas. Furthermore, we have found that the minimum of Mach
54
T. OOSATO AND T. YOSHIDA
TABLE 1. Initial conditions and velocities required for the collapse of a cloud.
model
A1
A2
A3
B1
B2
cloud mass
(M )
number density
at the center (cm 3 )
102
10
0
103
10
102
100
104
103
10
100
Jeans mass
the minimum of Mach number
(M )
required for the collapse of a cloud
2 103
8 1 2 103
8 1 2 103
2 6 2 103
2 6 2 103
8:1
:
13.1
8.4
:
6.3
:
10.6
:
6.4
MM
M
Figure 1.
The thermal evolution of clouds in model A1 on the density-temperature
plane. A dashed curve represents the case of collapse (
b = 13:14, where
b is Mach
number at rb ), and a dot curve the case of no collapse (
b = 12:97), respectively.
number required for the collapse of a cloud is larger than that of the
Tohline's model, because in our simulation we consider the energy equation with H2 cooling. In the early stage, when the dynamical time is shorter
than the cooling time, the temperature increases with adiabatic compression as the cloud collapses. After the temperature reaches maximum, the
cooling becomes eective, and the eective adiabatic index is less than one,
as shown in Figure 1. For the Mach number higher than the minimum, the
cloud can collapse. On the other hand, for the Mach number lower than
the minimum, the cloud nally attains equilibrium.
References
Whitworth, A. (1981) Global gravitational stability for one-dimensional polytropes.,
M.N.R.A.S., 195, pp. 967{977
Tohline, J.E., Bodenheimer, P.H. and Christodoulou, D.M. (1987) The crucial role of
cooling in the making of molecular clouds and stars., ApJ, 322, pp. 787{794
Palla, F., Salpeter, E.E. and Stahler, S.W. (1983) Primordial star formation: the role of
molecular hydrogen., ApJ, 271, pp. 632{641