Guided mainly by the observational data from the local and distant universe, ‘most of the’ cosmologists and astrophysicists believe that we live in a flat universe with the baryons (the visible matter in the universe) accounting for just 5% of the total density while 25% of the density is provided by dark matter and the rest 70% by some form of a ‘dark energy’. We can not see this dark matter (yet?), it’s only through their gravitational interaction with the baryons that we are aware of the presence of this unseen-unknown matter (will write about Dark Matter soon, hopefully). Now, though strange, but the evolution of this dark matter component (if at all it exists) is studied and believed to be understood quite intensively (like the detailed understanding of how the small inhomogeneity in early universe evolves and gives rise to the temp anisotropies detected in the CMB today). But somehow we are not so confident yet about the evolution of the baryonic component.
The formation of the first gravitationally bound objects in the universe dominated by dark matter is now thought to be in a bottom-up fashion – that means the smallest objects are formed first and then by merging or accretion, larger objects are formed (which happens in a more rapid rate). The evolution of mass function of these dark matter halos as a function of redshift is most commonly described by Press-Schechter function and more accurately by the modified mass function given by Sheth and Tormen. But these functions though can tell us when the first dark matter halos of a given mass will be formed, does not give any information on how the baryonic component grows and therefore we can not talk about development of first protogalaxies with them.
The first protogalaxies
Now, looking independently just at the baryonic part of the universe – unlike the dark matter scenario, the initial baryonic structures formed can not be small as they will be acted on by pressure forces which will suppress the growth of small-scale perturbations (basically it is a play between gravity and pressure – while gravity forces the mass to collapse, the pressure tries to prevent it – and when gravity wins, structures are formed). There is a length scale called Jeans’s length where pressure balances gravity and till the perturbation scale does not exceed that, it’s growth is suppressed. The associated mass scale is called Jean’s mass and only when the halo mass exceeds it, gravity can dominate over the pressure and collapsing of the overdense region to form gravitationally bound object becomes possible. By looking quantatively with the help of theoretical predictions, simulation analysis and observational data (for more information on this part, look at the Review on First Star Formation by Glover in 2004), it can be figured out that the first protogalaxies will be formed at a redshift of z~30 and will have a mass around 10000 times the solar mass.
Cool enough to form stars?
Now the next question arises – Is every such Protogalaxy capable of forming stars? To find the answer, let us look at a gas cloud undergoing gravitational collapse. Due to the adiabatic compression, the gravitational potential energy will be transformed to kinetic energy and then to thermal energy. If this thermal energy is somehow not dissipated, the gas cloud will heat up. Moreover as it is collapsing, it’s density will increase too. Now with higher density and temp, pressure will also increase and finally will be able to win over gravity – and then this collapse will stop long before the protostellar density is reached. So, star formation is impossible untill there is some cooling mechanism to take care of the rising temperature. The normal cooling mechanisms of Primordial gas like Lyman-Alpha cooling happens only at a temperature more than 10,000K, while the first protogalaxies we are talking about have temp range of something like 100-1000K. At this temprature range the main coolant is H2 which fortunately was abundant in early universe.
Evolution Models – from the Theorist’s Table
The most common models are the Free Fall Collapse Models which assume a spherically symmetric gas cloud with uniform density having a free fall collapse and predicts –
* Initially cooling by Molecular Hydrogen is negligible
* Gas evolves in adiabatic rate
* The collapse proceeds
* Temperature, density and H2 abundance increases
* The cooling rate of H2 increases rapidly too
* So cooling timescale reduces
* Cooling time approaches collapsing time
* Collapse is no more adiabatic
* Temperature increases and reaches a peak
* As collapse proceeds, higher density is reached
* Radiative cooling becomes dominant over compressive heating
* The temperature then decreases
An Alternative model which is more closer to reality is provided by Tegmark and follows the same set of approximations. But unlike the previous models where every protogalaxy can cool once it has reached the temperature of ~1000K, this model says that the collapse will halt when either Temp(gas)>Temp(viral) or Density(gas)>Density(Dark Matter Halo). So only the protogalaxies with Virial temperature greater than 1000K will cool and proceed to form stars.
Evolution Models – as Simulations Suggest
(The readers who are not much into Simulations can directly jump to the Summary)
Well, now this is a bit tough, trying to simulate the collapse of a protogalaxy. I mean, you need to go over a dynamical range of something like 10 to the power of 10 – from the big giant Gas Clouds to the small (comparatively) tiny stars. Going over a few important trials and their rather interesting results (though I understand nothing about these codings and stuff) :
1. Simplest one – using Lagrangian Grids:
The most significant demonstration from these simulations is the need to have pressure playing a role while describing dynamical evolution of a small protogalaxy. Of the two theroetical models described before, the later agrees more with the results. But the 1-D Langrangian Simulation is over-simplified as it does not take into account rotation, turbulence etc. What we need is a 3-D scenario which can not be gracefully handled by Lagrangians as the grids gets prone to high distortion.
2. Moving to 3D – Smoothed Particle Hydrodynamics:
Here we abandon the use of a grid and move to a Lagrangian which is particle-based. Three of such SPH ventures are introduced here:
2a. HYDRA: Performed by Fuller and Couchman, this simulations results in a protogalaxy with a cosmological infall region in it’s boundary, terminated by accretion shock at the viral radius, a subsequent broad post-shock cooling zone and a cold dense under-resolved central core.
2b. TREESPH: This simulation concentrates on the evolution of a single protogalaxy. On larger scale, the results are fairly the same as HYDRA but on smaller scale as we have better resolution to look at now, it is actually possible to structure formation (which will be discussed here later in this week).
2c. GADGET: Yoshida et al. (2003) used this largest protogalactic simulation till date and found that to cool efficiently we need to have the Mass of Protogalaxy to be larger than expected till now.
3. Multigrid Simulation:
Here we take a single large top-level grid that represents the whole volume of interest and supplement it with one or more levels of subgrids where higher resolution is needed.
3a. HERCULES: This is the simplese implementation of Multigrid simulation where the placement of all grids is set in the beginning of simulation. It could resolve basic filamentary structures of the InterGalactic medium surrounding the Protogalaxy but the Protogalaxy was still under-resolved. To make the resolution better we need more subgrids but where to place them for best result is a bit confusing as in the beginning of the simulation it is tough to predict correctly where we will need more resolution.
3b. ENZO: This is a moified version of the previous and is called Adaptive Mesh Simulation where placement of subgrids need not be specified a priori. The results are almost same as the SPH simulations but the collapse can be followed till higher densities. It was shown by ENZO that spherical symmetry was a crude assumption and most of the gas fall into the protogalaxy potential well along a few overdense filaments.
Assuming that the LCDM model of universe works, the earliest protogalaxies were formed at z~30-40 with a M ~ 10^4 solar mass with very less molecular hydrogen. Hence most of them can not cool effectively enough to form stars. The star-forming protogalaxies were first formed at z~30 and were more massive (M ~ 10^5-10^6 solar mass). If some form of warm dark matter is needed along with the assumed CDM then the first protogalaxies will be larger (M ~ 10^7 solar mass) and will be formed later (z~20).
For the next phase: From Protogalaxies through Fragmentation till Formation of Protostars, read here!
For Further Details : For the detailed explanation with equations, please refer to the Review Paper here!