Dwarf Galaxies


“Dwarf galaxies” is a general term for galaxies that are faint. Their mass in stars is at least two orders of magnitude below the stellar mass of a galaxy like the Milky Way.

As any other kind of galaxy, dwarfs can be found in the field (isolated dwarfs) as well as orbiting around a more massive companion (satellite dwarf). The closest dwarfs from Earth are precisely the satellites of the Milky Way. Astronomers have so far discovered dozens of them with luminosities as low as L~1e3 Lsun. Among the most massive dwarfs nearby, we find a pair: the Magellanic Clouds. Named “Small” and “Large” they are visible by the naked eye on dark nights from the Southern Hemisphere.

Fig. 1) Relation between the halo mass (M200) and the mass in stars (Mgal) in the central galaxy.  This relation is expected by counting the predicted abundance of halos and the observed abundance of galaxies. Green dots are the results obtained from the semi-analytical model of Guo et al. (2011).

(Source: Ferrero et al. 2012)

Why are Dwarf Galaxies exciting?

Dwarfs are interesting objects for many reasons. First of all, they dominate --by number-- the total galaxy population. Dwarfs are also our closest neighbors, allowing us to collect data of the highest quality available about  galaxies besides our own. Their structure, chemical composition and kinematics pose important challenges to our theoretical understanding of galaxy formation. You will find out more below...

The cold dark matter model makes clear predictions about the abundance of collapsed objects at any given time. We can compare the number of halos expected, with the number of galaxies observed and, by assuming they should match, obtain a link between the galaxy stellar mass and the halo mass (see Fig. 1). Such a technique is called “abundance matching” and has provided very useful guidelines to our galaxy formation models.

The efficiency with which halos are able to condense gas at their centers and form stars is called “galaxy efficiency”. Abundance matching models suggest that this galaxy efficiency should depend  strongly on halo mass: for objects like the Milky Way (M200 ~1e12 Msun) about 20% of the available baryons are turned to stars. This number drops quickly to ~5% for halos an order of magnitude smaller, and plumbers to even less than 1% for dwarf galaxies inhabiting halos with mass M200 < 1e10 Msun (see Fig.1).

However, observations become increasingly difficult as we focus on fainter and fainter objects.  The galaxy luminosity function is only reliably measured for dwarfs with stellar masses log(M*)~8.5 and above, not fainter. This means that, if we are interested on dimmer dwarfs, we have to make an extrapolation of the halo mass-galaxy mass relation observed towards faint dwarfs.

Can we observationally constraint this extrapolation somehow?

The dark matter halos of Dwarfs

Using satellites to constraint the halos of Dwarf Galaxies

(Sales et al. 2012b)

For this project, we used the Sloan Digital Sky Survey to study primary galaxies and their satellites. The novel point of our work was to include primaries in a very wide range of stellar masses: from central BCGs to isolated dwarf galaxies. Nobody compare such a thing before, they all concentrated on primaries like our Galaxy and above. In order to have a good handle on the theoretical expectations, we performed the exactly same analysis done over the observed galaxies also on a simulated mock catalog, constructed from the semi-analytical model of Guo et al. (2011).

The key idea is as follows. We know that CDM predicts a substructure mass function (i.e. the abundance of subhalos of a given mass) that is independent of host halo mass once normalized to the virial mass of the host. If you construct the satellite luminosity function you expect such self-similarity to be broken, just because the relation between dark matter mass and stellar mass or light is not a 1 to 1 correspondence. However, abundance matching would predict that, for galaxies less massive than M*~1e8 Msun the M*-M200 relation should turn a power-law. If that is true, the self-similarity of the dark matter should also be reflected on the satellite stellar mass function for systems where the primary and the satellites fall below M*~1e8 Msun

(You can find more details reading our paper, Sales et al. 2012b)

We therefore selected primary galaxies in a wide range  of masses from SDSS and looked out for their satellites. We defined them as the excess of companions within the estimated virial radius for each central. We then studied the satellite stellar mass functions of primaries binned according to their stellar mass.

The results came out exactly as expected: the abundance of satellites of a given magnitude difference scale with primary stellar mass; with more massive primaries having more satellites. However, for all the bins containing faint primaries, typically below log(M*)=1e10, the abundance of satellites overlaps (see Fig. 2). This is precisely the effect we were looking for, i.e. the recovery of a self-similarity below a certain primary stellar mass. This provides strong support for a power-law behavior of the M*-M200 relation that agrees well with simple extrapolations of current abundance matching models. Moreover, a similar analysis performed in the mock catalog retrieve the same result, making our conclusions more robust.

Fig. 2) Satellite mass functions for primary galaxies binned according to their stellar mass (color lines). Each curve represents, for a central primary of a given mass, the average number of satellites with a given magnitude difference w.r.t. the host. Vertical error bars indicate the scatter. We find good agreement between results of a simulated mock catalog (left) with those obtained for the observed galaxy sample from SDSS (right). This provides support to a power-law M*-M200 relation below log(M*) ~ 1e10 Msun, in agreement with extrapolation of abundance matching models.

(Source: Sales et al. 2012b)

You can also use the kinematics of gas and stars to constrain the halos of dwarfs.

Baryons move according to the underlying  potential which, in a dwarf galaxy, is dominated by the dark matter. This means that, by studying the way gas and stars move, you can grasp some details on the halo they inhabit.

Using rotation curves to constrain the halos of Dwarfs Galaxies

(Ferrero et al. 2012b)

If the stellar mass - halo mass relation is correct, for all dwarfs with measured stellar mass we know the halo they live in. Now, is the predicted halo consistent with the kinematics of their gas?

Ismael Ferrero, a PhD student at IATE in Córdoba, explored this issue using arxiv data of rotation curves of dwarfs.

The method is quite simple: with the stellar mass of a given dwarf, estimate the mass and structure of their dark matter halos (from a relation alike Fig. 1 plus theoretical arguments for the halo profile). We can then check whether the circular velocity profile predicted by such halo agrees well with the measured rotation curve of the dwarf (they should, as gas is almost a massless tracer particle in the much more dominant dark matter potential). Looking at Fig. 1, we expect that all dwarfs with stellar masses larger than M*~1e6 Msun live in halos with virial mass M200 =1e10 Msun and larger. 

What we find?

We find that in some cases the dwarf’s rotation curve agrees well with their expected halos, but in several others  the gas rotates much too slowly to live in the predicted halos. In other words: a large fraction of our dwarfs seems to have the mass of their halos overestimated by at least an order of magnitude. 

Some examples are shown in Fig. 3. The theoretical prediction is indicated by the red shaded region (which assumes a Navarro-Frenk-White (or NFW) profile with concentrations consistent with state-of-the-art numerical simulations. The observed rotation curve is shown in solid red line with errorbars. For the galaxy on the left panel, UGC 7559, the NFW circular velocity profile and its gas rotation curve overlap reasonably well. But the same is not true for the dwarf on the right, SDIG. This tiny fella should be living in a M200~1e10 Msun halo, but its kinematics is consistent with a halo of only M200=1e9 Msun, as shown by the good agreement between red curve and dashed black line in Fig. 3.

In total, we find that about a half of the dwarfs with masses between 1e6<M*<1e7 are inconsistent with the restriction of M200>1e10 Msun. Does this signal a fundamental problem for LCDM? Maybe... 
For a detailed discussion see the full version of the paper. http://arxiv.org/abs/1111.6609shapeimage_3_link_0

Fig. 3) Comparison between theoretical circular velocity profiles (shaded red) and measured rotation curves (solid red line with errorbars) for two dwarf galaxies. The kinematics of UGC 7559 (left) agrees well with theoretical expectations. On the other hand, SDIG (right) has too low rotation on its gaseous component and prefers a halo about 10 times smaller than predicted from Fig.1.

(Source: Ferrero et al. 2012)

The halos of Dwarf Galaxies and their unseen companions

(Helmi et al. 2012)

An interesting consequence of all the above discussion is that, if dwarf galaxies indeed populate massive dark matter halos, they should also contain lots of embedded “substructures”. This substructure --namely subhalos-- will orbit the dwarf in the same fashion than small satellites orbit around the Milky Way; but with the caveat that the subhalos of the dwarf are way less massive and therefore will no host any visible galaxy inside. 

This population of “dark satellites” is thus very difficult to pinpoint observationally (as they host no stars or gas). We explored the observational signatures of substructure in dwarfs in collaboration with Amina Helmi (Kapteyn Institute, Netherlands). We use a combination of collisionless simulations + semi-analytical modeling of dwarf galaxies from the Aquarius Simulation

We found that “dark satellites” can leave a clear imprint in isolated dwarfs with low gas fractions. For such cases, the continuous bombardment of substructure close to the disk induces heating of the stellar component, puffing up the luminous central dwarf (see Fig. 4).

Our model predict that dwarfs with low gas fractions should be thick and dynamically hot, in agreement with observations.

You can see a cool movie of the interaction between a disky-dwarf and an invisible companion here.   

Or read more about all this in the original paper, Helmi et al. 2012

Fig. 4) Edge-on projections of the stellar disk of two dwarf galaxies before (left) and after (right) an encounter with a dark satellite. This unseen companions induce a dramatic change on the appearance of these disky dwarfs, now looking significantly thicker and dynamically hot than before the interaction.

(Source: Helmi et al. 2012)