A detailed description of my work

The dark matter haloes of galaxies

... WORK IN PROGRESS ...

Galaxies are embedded in massive dark matter haloes. This view is supported by a broad range of observations, and is in good agreement with simulations. It is thought that galaxies form in the gravitational potentials of these haloes, and the dark matter and baryons are therefore coupled. Baryonic processes severly complicates an analytical description of this connection, which is why people usually fit scaling relations like the Tully-Fisher relation to gain insight in the physical processes that determine the coupling of the dark matter to the baryons. Improvement on these constraints is necessary for a better understanding of the physics of galaxy formation, and one excellent technique that can be used for this purpose is weak gravitational lensing.

Weak gravitational lensing has become a commonly used tool in the studies of the dark matter haloes of galaxies and galaxy clusters, and for constraining the values of the parameters of cosmological models. In weak lensing one measures the distortion of the faint background galaxies (sources) that is caused by the bending of light rays by foreground mass structures (lenses). The main advantage of lensing is that it probes all (baryonic and dark) matter along the line of sight, indepent on its physical state. It is therefore very well suited for measuring the mass of galaxy dark matter haloes.

The relation between baryons and dark matter in galaxies have been studied before, both using simulations and observations. In one of her 2006 papers, Rachel Mandelbaum uses the SDSS survey to study the relation between stellar mass and the total halo mass, and the relation between luminosity and halo mass, of galaxies as function of environment and galaxy type (link). Using the halo model to model the measured shear signal, she puts constraints on both the central halo mass and the satellite fraction - the fraction of galaxies that is actually a satellite of a larger halo. Given that the SDSS is the largest lensing survey currently available, one cannot improve the lensing constraints at low redshift. However, with its limiting magnitude of ~22 in the r-band, the SDSS is not very deep, and the lensing efficiency drops rapidly when the lens redshift approaches the peak of the source redshift distribution: this happens for a redshift of 0.3-0.4. Significant improvement is possible at higher redshifts when we combine the SDSS with a deeper survey.

Figure 1: the galaxy-galaxy lensing signal of 1.6 &sdot 106 stacked lenses in the RCS2 survey. Galaxies with 19.5 < mr' < 21.5 are defined as lenses, and objects with 22 < mr' < 24 are sources. The clustering of galaxies causes an excess signal at lens-source separations >~ 1 arcminute.

The RCS2 survey is ~2 magnitudes deeper than the SDSS survey and has better seeing. Roughly 350 sqd of the surveys overlap, and we use the spectroscopic redshift and stellar mass from the SDSS for our lenses. The lensing analyis is conducted on the RCS2 survey, which enables us to tighten the constraints on the most massive early type galaxies, which are typically found near the limiting magnitude of the SDSS. That the RCS2 survey is very well suited for lensing can be observed in Figure 1. It shows the galaxy-galaxy lensing signal of the full survey. The dashed line shows a SIS fit, the dotted line a NFW fit. Both fits underpredict the lensing signal at scales larger than approximately 1 arcminute. This comes from the fact that galaxies live in clustered environments; when we measure the shear around galaxies, we start to pick up the shear of neighbouring galaxies as well. To accurately model the lensing signal around galaxies, we have implemented the halo model.

For about 20 000 galaxies we obtained the spectroscopic redshift, stellar mass and luminosity. We splitted this lens sample up in early and late types based on their brightness profile. We defined seven stellar mass bins, and measured the shear signal around the stacked lenses in each bin. We fitted the halo model to the measurements, and fitted for the halo mass and satellite fraction. Figure 2 shows the shear measurements and the different components of the fitted halo model for two stellar mass bins.

Figure 2: the lensing signal and halo model fit of the 10 < log(M*) <10.5 (top panel) and 11.75 < log(M*) <12 bin (bottom panel). The one halo satellite term is prominently visible for the lower stellar mass bin, implying that a large fraction of these galaxies is a satellite. The high mass bin is very well fit by a NFW profile.

Our halo model is coded up following the approach of Mandelbaum et al. (2005) (link), and consists therefore of five terms. A galaxy is either a central galaxy residing in the central dark matter halo, or it is a satellite galaxy residing in a subhalo which itself resides in a central halo. If it is a central galaxy, then there are two terms that dominate the shear signal: the shear coming from the central halo (a NFW), and the shear coming from neighbouring haloes (the central 2-halo term). If it is a satellite galaxy, there are three terms contributing to the shear: the shear from the subhalo (a stripped NFW), from the central halo (the 1-halo satellite term), and from neighbouring haloes (the 2-halo satellite term).

Figure 2 serves to demonstrate that different terms dominate the lensing signal for the low and high stellar mass bins. For the low stellar mass bin (top panel), there is not much shear coming from the central dark matter halo, hence the haloes hosting these galaxies are not massive. The 1-halo satellite term is very prominent, which indicates that a significant fraction of our galaxies are actually satellites of larger systems. The high stellar mass bin (bottom panel) is very well fitted by the central NFW term. This indicates that most of these galaxies are residing in the central dark matter halo, and only few are satellite galaxies. The 2-halo terms start to become important at >~ three Mpc, and are not well constrained by the measurements.

Figure 3: the stellar mass versus the halo mass for early type galaxies (red) and late type galaxies (blue). The halo mass is independent of galaxy type below a stellar mass of log(M*) <11, and becomes more massive for early types galaxies at higher stellar masses.

We compare the stellar mass to the central halo mass for the early and late type galaxies in our sample in Figure 3. Galaxies with higher stellar mass live in more massive haloes. The halo mass is independent of galaxy type below a stellar mass of log(M_*) <11, and becomes more massive for early types galaxies at higher stellar masses.There are several complicating factors that hinder a direct interpretation of the results shown in Figure 3. I discuss these factors in detail in my paper, which we expect to submit very soon, and I would like to refer the interested reader to read this paper.

The satellite fraction is fitted as well for each of the stellar mass bins, and is shown for as function of galaxy type in Figure 4. We can see that the satellite fraction is decreases for the early type galaxies with increasing stellar mass, while it is roughly constant for the late type galaxies. Furthermore, what catches the eye is that the error bars are very large for the high stellar mass bin.

Figure 4: the stellar mass versus the satellite fraction for early type galaxies (red) and late type galaxies (blue). The fraction decreases as function of stellar mass from 40% to 0% for early type galaxies, and is constant with a value of about 10% for late type galaxies.

The reason for this is explained in my paper.