Galaxy Clustering in the NEWFIRM Medium Band Survey: The Relationship Between Stellar Mass and Dark Matter Halo Mass at 1 < z < 2

We present an analysis of the clustering of galaxies as a function of their stellar mass at 1 < z < 2 using data from the NEWFIRM Medium Band Survey (NMBS). The precise photometric redshifts and stellar masses that the NMBS produces allow us to define a series of stellar mass limited samples of galaxies more massive than 7 × 10⁹ M _sun, 1 × 10¹⁰ M _sun, and 3 × 10¹⁰ M _sun in three redshift intervals centered on z = 1.1, 1.5, and 1.9, respectively. In each redshift interval, we show that there exists a strong dependence of clustering strength on the stellar mass limit of the sample, with more massive galaxies showing a higher clustering amplitude on all scales. We further interpret our clustering measurements in the ΛCDM cosmological context using the halo model of galaxy clustering. We show that the typical halo mass of both central and satellite galaxies increases with stellar mass, whereas the satellite fraction decreases with stellar mass, qualitatively the same as is seen at z < 1. We see little evidence of any redshift dependence in the relationship between stellar mass and halo mass over our narrow redshift range. However, when we compare our measurements with similar ones at z ~= 0, we see clear evidence for a change in this relation. If we assume a universal baryon fraction, the ratio of stellar mass to halo mass reveals the fraction of baryons that have been converted to stars. We see that the peak in this star formation efficiency for central galaxies shifts to higher halo masses at higher redshift, moving from sime7 × 10¹¹ h ^-1 M _sun at z ~= 0 to sime3 × 10¹² h ^-1 M _sun at z ~= 1.5, revealing evidence of "halo downsizing." Finally, we show that for highly biased galaxy populations at z>1 there may be a discrepancy between the space density and clustering predicted by the halo model and the measured clustering and space density. This could imply that there is a problem with one or more ingredient of the halo model at these redshifts, for instance, the halo bias relation may not yet be precisely calibrated at high halo masses or galaxies may not be distributed within halos following a Navarro-Frenk-White profile.