From the Protogalactic Gas Mass to Fragments capable of making Stars
Last time we saw how and when the earliest protogalaxies are formed and also realised that only the protogalaxies which can cool significantly are capable of forming stars. Now the questions arise – how the gas in these protogalaxies evolve? How many stars of what mass scale can be formed from one such protogalaxy? And to know that basically we need to determine if all the mass will sink to the center and form just one clump of overdense region or their will be fragmentation possible. Now, the most probable outcome is to have most of the mass getting concentrated on the center to form one big blob but there are scenarios when this mass can get fragmented.
The simplest and most easily guessed cause of fragmentation is gravity. Gravitational fragmentation is effective when –
1. The fragments formed are gravitationally bound.
2. Before the protogalaxy as a whole collapses, the overdense regions within manages to collapse under their self-gravity.
The protogalactic gas will continue to fragment to smaller and smaller scales till pressure force becomes effective enough to prevent further fragmentation. The smallest fragments formed hence will have a mass of the scale of Jeans Mass (as at this mass termed hereafter as Mj, the pressure balances gravity). Now, as the protogalaxy evolves, it’s temperature and density, and thus it’s Mj will change. The minimum value of Mj (let’s call it Mm) i.e. the minimum mass of the star that will be formed eventually is reached when the fragment first becomes optically thick – thus the term opacity-limited fragmentation.
Finding this Minimum Mass
There are theoretical treatments to find Mm – two most important of these being that of Lynden-Bell’s and of Rees’s who have presented with theoretical expressions to calculate Mm. But recently it has been shown that a better procedure to find Mm is actually to follow it’s actual thermal evolution.
Many attempts have been made to model the thermal evolution of a collapsing protogalaxy in order to estimate Mm:
1. Yoneyama (1972) constructed evolutionary track for the gas and calculated evolution of Mj till wither gas becomes optically thick or hot enough to dissociate molecular hydrogen. He estimated Mm to be around 60 solar mass for smaller protogalaxies and a bit larger value for larger protogalaxies.
2. Hutchins (1976) studied thermal evolution of spherical and spheroidal protogalaxies using very simple chemical models and by terminating it when molecular hydrogen dissociates, calculated Mm to be around 200 solar mass.
3. Silk (1977) and Carlberg (1981) took a step further and included Lyman-alpha cooling in the scenario which significantly lowered the calculated value of Mm to be around 0.3-0.5 solar masses.
4. Palla, Sarpeter, Stahler (1983) also showed that at higher densities, the formation and cooling rate of H2 increases and hence Mm may go as small as 0.1 solar mass.
Conclusion : Well, get the thermal evolution model right – otherwise the calculated Mm value will have a vast range from 0.1 till 200 solar mass. Makes no sense!
But.. Is this how ‘actually’ fragmentation occurs?
Now, why will someone think that Hierarchical Fragmentation system is incorrect?
Well, mainly because of their oversimplified assumptions, As we saw earlier, this whole treatment of fragmentation due to gravity is based mainly on two gross assumptions which are a bit too oversimplified :
1. The first one is the fact that we are assuming the balance between pressure and gravity to be the only determinant of if the fragment is gravitationally bound, which implies that we expect all fragments with mass higher than Jean’s mass to be gravitationally bound.
2. We here approximate gas flow on scales larger than Jean’s scale to be pure gravitational free-fall which implies that the gas fragments down to Jean’s scale very rapidly.
Many theorists argued against these assumptions and the whole scenario as a whole. Four most important of them being :
1. Layzer (1963) showed that as protogalaxy fragments, angular momentum will be imparted to the individual fragments form the neighbors. As the fragments contract, they will spin faster and after a limit they will be centrifugally supported.
2. Later Larson (1984) explained how in isothermal evolution even if teh first generation of fragments are centrfugally-supported but unstable, their successive generations will stabilize.
3. Tohlin (1980) argued that it is not correct to assume that fragmentation occur very rapidly till it reaches thee Jeans Mass as Mj may vary much faster than the gas can respond to. He predicted that Mm should be larger than what the models (talked about in last section) suggest.
4. And the most problematic thing with Hierarchical Fragmentation is the fact that the gas is assumed to be uniform – initially and even during collapse. Now, that is a bit too oversimplified. Of course as the collapse evolves, there will be a tendancy of the gas to concentrate more in the center.
The main thing to remember is that – fragmentation in real protogalaxies will be much less effective than what hierarchical fragmentation assumes.
What else can cause Fragmentation?
If gravity does not stay so effective all the way, it is time we consider other physical processes resulting into fragmentation. Well, two other effective causes will be :
1. Thermal Instability –
If a region of gas has a small perturbations in terms of density or temperature, the temperature evolution there may be significantly different from that in the unperturbed gas. If that happens, a pressure gradient will be formed and thus the thermal instability could drive dynamical flow. But in primordial gas, if we keep chemical composition of gas to be fixed than it should always be thermally stable. But studies have shown that in very hot gas (~10,00,000K) when cooling via HeII increase sharply with a decrease in temperature, gas in ~3000K where equilibrium abundance of H2 becomes a strong function of temperature and at very high densities chemo-thermal instabilities become possible.
To speak a bit against it – it is unlikely that Thermal Instability will effect the protogalaxies much. We just saw that it is only in very restricted temperature range that such instability can be hoped for. Moreover thermal instabilities grow on cooling timescale and hence we need t(cool)<<t(dyn), but typically the thermally unstable protogalaxies are seen to have t(cool)~t(dyn).
2. Supersonic Turbulence –
Another way to create dense structures in gas is by compressing it by shocks, specially if the shock is supersonic and turbulent. Of course in the Galactic context it makes real sense to consider it but in the protogalactic level work is still going on in terms of simulations and analysis. None of the attempts till now has received world-wide acceptance.
Trying to summarize
From protogalaxies to protostars, it is a very tricky path. The hierarchial fragmentation which takes fragmentation to be highly efficient was widely accepted till it was shown that there are various effects which combine to inhibit fragmentations. There have been many simulations worldwide and loads of theoretical treatments to enrich our knowledge on how galaxies evolve while walking down this path of fragmentations. To just have an overview –
Specially for gas with high ratio of thermal to gravitational energy, fragmentation is inefficient. During these collapses, large thermal pressure creates a density distribution which has a strong peak – thus the gas at the center collapse to protostellar density much before the bulk of the gas gets to fragment. So the most probable outcome is a single central protostar. But iff the collapse of this high density gas can be felayed sufficiently, fragmentation becomes possible. This delay can be caused by rotation to a certain degree but outward transfer of angular momentum reduces it’s efficiency to cretae fragments. Thermal instabilities and supersonic turbulence can also boost fragmenation but they are not expected to be highly effective in primordial gas. Finally, well, a lot of work is needed to be done to have a better, clearer and widely accepted view of this path of a protogalaxy’s evolution to from protostellar densities.
For Details : For the detailed explanation with equations and to have a brief overview of the numerical simulations performed in this area, please refer to the amazingly written Review Paper on Structure Formation by Simon Glover. 🙂