Simulating the First Dwarf Galaxies and Globular Clusters

A Common Origin for Globular Clusters and Ultra-faint Dwarfs in Simulations of the First Galaxies

Massimo Ricotti, Owen H. Parry and Nickolay Y. Gnedin

This paper presents the results of simulations of four cosmological boxes, each 1 Mpc/h a side, using the Adaptive Refinement Tree (ART) technique. The adaptive refinement scheme creates finer spatial and temporal resolutions in regions of high density, where the physics is more interesting. In the highest-resolution run, the authors resolve individual star particles as small at 40, at sub-parsec sizes. The numerical simulation ends at z ~ 9, sufficient to make predictions about what the James Webb Space Telescope would see. Afterwards, an analytical prescription extrapolates what the galaxies found at z=9 would look like today, and comparisons are made to dwarf galaxies and globular clusters in the Local Group.

The physics implementation here is very neatly explained and physically motivated. Stars form whenever a gas cell meets certain criteria of metallicity, number density and molecular hydrogen fraction. There are two sets of prescriptions, corresponding to metallicity requirements for Pop III and Pop II stars. Unless the gas cell is of the minimum mass, i.e. 40, it is converted into a stellar particle, which is understood as a population of stars following the Chabrier IMF. Feedback occurs in the form of supernova (SNe) explosions 3 Myr after star formation has occurred in a given cell – this timescale corresponds to the main sequence lifetime of an 8 star. This releases ergs of thermal energy into the neighbouring cells, on time scales that range from 0 (for Pop III hypernovae) to 35 Myr (for Pop II supernovae). The feedback also serves to enrich the gas with metals.

Finally, substructure is identified at every time step using the friend-of-friends (FoF) algorithm and refined using SubFind. The high-res simulation produced galaxies as small as 2.8, comparable to ultra-faint dwarfs today! Btw, I was elated that someone finally explained linking length, which is key to FoF! Particles are considered linked if their separation is less than

 (linking length)*(mean separation between particles in the box)

The group catalogues are then used to construct merger trees.

At z = 9, they find that many galaxies have gas disks, but stars still form spheroids –

This makes sense if a spheroidal gas cloud was cool enough for star formation before dissipative processes turned it into a disk.

What do the orbits of the stars look like? Defining circularity as the angular momentum of a star particle in the direction of the mean angular momentum of the galaxy, divided by that of a particle of that mass moving on a circular orbit. The star particles in the simulated galaxies are consistent with non-rotating spheroids, i.e. symmetric distributions of circularity peaking at zero. In some galaxies, the mean circularity is positive, indicating that at least some stars are undergoing some rotation. No difference between metal rich and metal poor stars, divided at [Fe/H] = -1.5.

How big are the galaxies? Half-light radius computed at 100 different viewing angles, error bars represent range between 10th and 90th percentile of measured values for each. Unlike observations in Local Group, where scales with luminosity/stellar mass, in the simulation there is a large spread in at fixed stellar mass. That said, a lot can happen between z = 9 and the present day. If tidal stripping, for example, occurs at a rate inversely proportional to the density of the dwarf galaxy, more extended low-mass galaxies at high z would be smaller by z=0. Patience – this comes a couple sections later!

Of the ten most compact objects, 5 are DM dominated and 5 baryon-dominated. In fig 6, this is seen as a wide range in pseudo mass-to-light ratios at a fixed dynamical mass. There is, nevertheless, an apparently bimodal distribution – one where mass/light hovers around 10, and another around 10,000.

The money plot: 

The three panels correspond to three different values adopted for star formation efficiency, ranging from 1-100%. To quote the authors, “luminosity of dwarfs increases by about a factor of two whenis increased by a factor of 100”; i.e. the qualitative results are depend very weakly on the assumed (which is excellent, since this quantity is still poorly constrained by observations)! The grayscale is the log of the stellar mass to dark matter mass.

Takeaway: the simulation self-consistently forms several objects with half-light radii ranging from 1-150 pc and stellar-to-dark matter ratios ranging from 1:1,000 to 10,000:1! The latter systems live in the top left corner of each plot, and are consistent with the mass-to-light ratios observed in globular clusters today. The more dark-matter dominated systems, on the other hand, would be the progenitors of dwarf galaxies.

[The plots in this paper are so damn nice. Like, they really know the physics point they’re trying to get across.]

Finally, the paper analytically calculates what these high-redshift compact objects would look like in the Local Universe, and compare it to observations. 

Overall, it seems to me that the dwarf galaxies in the simulation don’t fit observations nearly as well as the globular clusters do – the simulation+analytic evolution produce dwarfs that are more compact, have smaller velocity dispersions, and with a smaller range of masses than observed. That said, the 13 billion years between the end of the simulation and the present day are very complex to model, and the fact that the predictions are so close to the observations is pretty impressive!

Ultimately the conclusion is that globular clusters and dwarf galaxies form through the same processes in the very early universe. How do you form very compact, baryon-dominated systems at high redshifts, though? I might have to re-read the paper to get this one.