We have applied two pair counting methods and found that the Patton et al. (2000) method delivers a pair fraction higher than the technique of Le F`evre et al. (2000) because the former includes fainter companions. To reconcile these two different results with a single mass assembly history, we estimate the stellar mass accretion rate associated with merging galaxies. Because it is not known which companions are physically associated with their host, the stellar mass of companions can only be determined in a statistical sense. We first fit our VIK′ photometry of host galaxies
Figure 5.3 Stellar mass accretion rate per galaxy in three redshift bins. Filled symbols are the results from the Patton et al. weighted analysis. Open symbols are the results of the Le F`evre et al. (2000) technique. The first redshift bin is again the least significant since it contains the fewest host galaxies.
(with redshifts) to template SEDs spanning a range of ages, star formation histories and metallicities, assuming a Salpeter IMF (with the range 0.1−100M⊙, Bruzual &
Charlot 2000, private communication). We then scale to the Ks-band luminosity to estimate the stellar mass (see Brinchmann et al. 2000). We assume the companions follow the same distribution of M∗/LK′ vs. LK′ as the hosts and use this distribution to estimate the stellar mass of companion galaxies. Finally, though the merging timescale depends on the details of the interaction, we follow previous studies (e.g., Patton et al. 2000) and assume an average value of 0.5 Gyr for galaxies separated by rp <20 kpc.
With these assumptions, we demonstrate that the two very different pair statistics are consistent with a similar merger history in terms of the accreted stellar mass. In Figure 5.3, open symbols are the mass accretion rate from the Le F`evre et al. (2000) method, and solid symbols are that from the Patton et al. method. The large error bars include both statistics and 50% uncertainties inM∗/LK′. Both methods illustrate
a rise in the stellar mass accretion rate at the highest redshifts, with the Patton et al. method giving a value of 2×109±0.2 M⊙ galaxy−1 Gyr−1 at z ∼ 1. This mass corresponds to ≈4% of the average stellar mass of host galaxies at these redshifts.
The result may be compared with an estimate made by Conselice et al. (2003) of 6.4×108±0.1 M⊙ galaxy−1 Gyr−1 at 0.8< z < 1.4 using morphological indicators to distinguish merger remnants.
We contrast our assembly rate from pre-existing stellar systems with theintegrated stellar mass density (Dickinson et al. 2003), which reflects the growth of galaxies from newly-formed stars. While not necessarily completely independent (for example if merging triggers new star formation), the relative magnitudes of the two phenomena are interesting to consider. Using the luminosity functions of Kashikawa et al (2003) to determine the comoving number density of host galaxies, we integrate the mass accretion rate to estimate the stellar mass assimilated by galaxies in the host K-band luminosity range, finding ∆ρm∗ ≈ 3×108±0.2 M⊙ Mpc−3. For a Salpeter IMF, we deduce that 30% of the local stellar mass in luminous galaxies was assimilated via merging of pre-existing stars since z ∼ 1, comparable to the build-up deduced by Dickinson et al. (2003) from ongoing star formation.
Acknowledgments
We thank Dr. Chris Simpson and Dr. Kentaro Aoki for their help during our observations at the Subaru Telescope. RSE and MF acknowledge the generosity of the Japanese Society for the Promotion of Science.
Chapter 6
The Relationship Between the Stellar and Total Masses of Disk Galaxies 1
Using a combination of Keck spectroscopy and near-infrared imaging, we investigate the K-band and stellar mass Tully-Fisher relation for 101 disk galaxies at 0.2< z <1.2, with the goal of placing the first observational constraints on the assembly history of halo and stellar mass. Our main result is a lack of evolution in either the K-band or stellar mass Tully-Fisher relation from z = 0−1.2. Furthermore, although our sample is not statistically complete, we consider it suitable for an initial investigation of how the fraction of total mass that has condensed into stars is distributed with both redshift and total halo mass. We calculate stellar masses from optical and near- infrared photometry and total masses from maximum rotational velocities and disk scale lengths, utilizing a range of model relationships derived analytically and from simulations. We find that the stellar/total mass distribution and stellar-mass Tully- Fisher relation for z >0.7 disks is similar to that at lower redshift, suggesting that baryonic mass is accreted by disks along with dark matter at z < 1 and that disk galaxy formation atz <1 is hierarchical in nature. We briefly discuss the evolutionary trends expected in conventional structure formation models and the implications of extending such a study to much larger samples.
1Much of this chapter has been previously published as Conselice et al. (2005)
6.1 Introduction
In the currently popular hierarchical picture of structure formation, galaxies are thought to be embedded in massive dark halos. These halos grow from density fluc- tuations in the early universe and initially contain baryons in a hot gaseous phase.
This gas subsequently cools, and some fraction eventually condenses into stars. Much progress has been made in observationally delineating the global star formation his- tory and the resulting build-up of stellar mass (e.g., Madau et al. 1998; Brinchmann
& Ellis 2000; Dickinson et al. 2003; Bundy et al. 2005a). However, many of the phys- ical details, particularly the roles played by feedback and cooling essential for a full understanding of how galaxies form, remain uncertain. Models (e.g., van den Bosch 2002; Abadi et al. 2003) have great predictive power in this area but only by assum- ing presently untested prescriptions for these effects. Obtaining further insight into how such processes operate is thus an important next step not only in understanding galaxy evolution, but also in verifying the utility of popular models as well as the hierarchical concept itself. One approach towards understanding this issue is to trace how the stellar mass in galaxies forms in tandem, or otherwise, with its dark mass.
The first step in this direction began with studies of scaling relations between the measurable properties of disk galaxies, specifically the relation between luminosity and maximum rotational velocity (Tully & Fisher 1977). Studies utilizing roughly a thousand spiral galaxies have revealed a tight correlation between absolute magnitude and the maximum rotational velocity for nearby galaxies (Haynes et al. 1999). The limited data at high redshift suggests the TF relation evolves only modestly, equiva- lent to at most 0.4 - 1 magnitudes of luminosity evolution toz ∼1 (Vogt et al. 1997;
Ziegler et al. 2002; B¨ohm et al. 2004). How the Tully-Fisher relation evolves with redshift is still controversial, although it appears that fainter disks evolve the most (B¨ohm et al. 2004) and that selection effects are likely dominating the differences found between various studies. Furthermore, it has been difficult for modelers to re- produce the Tully-Fisher relation to within 30% (e.g., Cole et al. 2000), making it an important constraint on our understanding of the physics behind galaxy formation.
Unfortunately, any interpretation of the TF relation is complicated by the fact that both luminosity and virial mass might be evolving together. A more physically motivated comparison would be between stellar and virial mass. Not only does this relation break potential degeneracies in the TF technique, but it also samples more fundamental quantities. In this study we begin this task by investigating the evolu- tion in the fraction of the total mass in stars. This can be accomplished with some uncertainty by contrasting the stellar mass of a galaxy with its halo mass. We se- lected disk galaxies for this effort since these two quantities can be effectively probed observationally for such galaxies with various assumptions (e.g., van den Bosch 2002;
Baugh et al. 2005).
This study presents the first investigation of the near-IR TF relation, as well as a comparison between stellar and halo masses, for 101 disk galaxies within the redshift range 0.2 < z < 1.2 drawn mostly from the DEEP1 redshift survey (Vogt et al. 2005). Our goal is to address several questions relating to the mass assembly history of disks. As our sample is not formally complete in any sense, we cannot derive general conclusions concerning the history of all present-day disks. However, we can determine whether the disks selected from the DEEP1 survey in the sampled redshift range are still accreting matter and converting baryons into stellar disks at a significant rate. We construct the stellar mass Tully-Fisher and stellar mass/halo mass relation for our sample and find that there is little evolution in either from z ∼0−1.2. This suggests that the dark and stellar components of disk galaxies grow together during this time.
This chapter is organized as follows: §6.2 contains a description of the sample including the fields used, the different data products, and a discussion of uncertainties.
§6.3 describes how various quantities such as the halo and stellar masses are derived from the data. §6.4 presents our results and§6.5 presents our conclusions. We assume the following cosmology throughout this work: H0 = 70 km s−1 Mpc−1, ΩΛ = 0.7, and Ωm = 0.3.