# Thesis midterm

Thesis Progress Report

Introduction
The goal of this thesis is to compare the stellar mass growth rate vs mass at various redshift of local group dwarf galaxies with distant galaxies. This work was started in the fall, but was registered with the astronomy department. As this is the first term registered in the Physics department, this progress report will cover work done since the fall.

Data
The early part of the project was spent familiarizing myself with the data that would be used, and the techniques used to gather that data.

The data used for distant galaxies was presented by Tomczak et al (Tomczak 2014). This paper contains a table of mass vs number density (number of galaxies per unit volume) for $$0.2 < z < 3$$ which we use to construct the stellar mass function (SMF) which shows the frequency of galaxies at different masses and redshifts. However, while we plotted this data and various subsets of it (only star forming or quiescent galaxies) we do not use the raw data. Instead, we use a fitting function - a paramaterised double Schechter function - from Leja et al (Leja 2015) which smooths the data and ensures the number density at each mass is monotonically increasing as $$z \rightarrow 0$$. With this done, graphs showing the mass over $$0.2 < z < 3$$ for various start masses were constructed.

The local group dwarf galaxy data was taken from Weiza et al (Weisz 2014). This paper determines the mass of a subset of the known dwarf galaxies between $$0 < z < 2.6$$. It does this by constructing a color magnitude diagram and determining, using know properties of stars, when star formation occurred. This is the star formation history (SFH). As with the distant galaxies, graphs showing the percentage of mass over time for various groups of the galaxies (grouped by galaxy shape or location) were plotted to better understand the data.

A second distant galaxy data set was introduced later in the project. This data, taken from Whitaker et al (Whitaker 2014) was used to confirm that the comparison between the two main data sets were reasonable and conformed to other data. Again, a parameterization rather than raw data was used.

Analysis
A number of corrections must be applied to these data sets before they can be compared.

The first correction is for mergers. The local group data is based on galaxies that have not undergone mergers, while some of the distant galaxies will have. This has the effect of reducing the total number of galaxies in the sample over time, reducing the overall number density. We make the merger correction to the SMF using the method shown in Gomez et al (Rodriguez-Gomez 2015). Supporting material such as plots of expected merger rates at various mass ratios and redshifts were also constructed to ensure that we were applying this correction correctly.

We also apply a correction for mass loss to both the local group and (Whitaker 2014) data. As these both determine mass by integrating the star formation rate over time, the data shows the total stellar mass formed by a certain time, rather than the total stellar mass present at that time. Much of this mass loss is caused by the death of high mass, short lifespan ($$< 100Myr$$) stars and so can be approximated as instantaneous using a multiplicative factor. The Tomczak et al (Tomczak 2014) data is the instantaneous mass and not calculated from the SFH and so this correction is not applied.

Finally, a environmental correction was applied to the local group data. We expect that galaxies in different places in the Local Group (satellites of the Milky Way, satellites of M31 (Andromeda) and galaxies attached to neither of the main galaxies) would have different growth rates. However, the Weisz et al (Weisz 2014) data contains only a subset of approximately half of all known local group galaxies and does not sample evenly from these three environments (for observational reasons). To correct for this, we weight galaxies to ensure that at each mass and redshift the different environments are correctly weighted.

A significant analysis was also performed on the errors on the local group data reported by Weisz et al (Weisz 2014). These errors were calculated using methods defined in Dolphin; (Dolphin 2012) (systematic) and (Dolphin 2013) (random) but are considered extremely conservative. A method to determine a more reasonable set of uncertainties was not found and so we adopt the literature convention established by Weisz et al (Weisz 2014a) and simply apply a 50% fractional uncertainty to all masses. This method is also considered conservative but significantly improves on the original.

Comparison
Having made the corrections discussed above, we compare the data sets. We find that the Tomczak et al (Tomczak 2014) data broadly agrees with the Whitaker et al (Whitaker 2014) data, but that both show higher growth rates than the local group data. If this continues to hold as the final corrections are applied and the work is checked, this is an interesting result as it would should galaxy strangulation; a process by which stellar mass growth rates are slowed in the presence of large gravitational fields.

Conclusion
While we have preliminarily done most of the corrections needed to compare these data sets, there is still work to do. In particular, the merger correction is not perfectly understood and may be the source of some of the discrepancy between the two distant galaxy data sets. Tests to show that the code used for analysis is performing correctly also need to be written. Finally, this work also needs to be written up and presented.

### References

1. Adam R. Tomczak, Ryan F. Quadri, Kim-Vy H. Tran, Ivo Labbé, Caroline M. S. Straatman, Casey Papovich, Karl Glazebrook, Rebecca Allen, Gabriel B. Brammer, Glenn G. Kacprzak, Lalitwadee Kawinwanichakij, Daniel D. Kelson, Patrick J. McCarthy, Nicola Mehrtens, Andrew J. Monson, S. Eric Persson, Lee R. Spitler, Vithal Tilvi, Pieter van Dokkum. GALAXY STELLAR MASS FUNCTIONS FROM ZFOURGE/CANDELS: AN EXCESS OF LOW-MASS GALAXIES SINCE z = 2 AND THE RAPID BUILDUP OF QUIESCENT GALAXIES. ApJ 783, 85 (2014). Link

2. Joel Leja, Pieter G. van Dokkum, Marijn Franx, Katherine E. Whitaker. RECONCILING THE OBSERVED STAR-FORMING SEQUENCE WITH THE OBSERVED STELLAR MASS FUNCTION. ApJ 798, 115 (2015). Link

3. Daniel R. Weisz, Andrew E. Dolphin, Evan D. Skillman, Jon Holtzman, Karoline M. Gilbert, Julianne J. Dalcanton, Benjamin F. Williams. THE STAR FORMATION HISTORIES OF LOCAL GROUP DWARF GALAXIES. I. HUBBLE SPACE TELESCOPE /WIDE FIELD PLANETARY CAMERA 2 OBSERVATIONS. ApJ 789, 147 (2014). Link

4. Katherine E. Whitaker, Marijn Franx, Joel Leja, Pieter G. van Dokkum, Alaina Henry, Rosalind E. Skelton, Mattia Fumagalli, Ivelina G. Momcheva, Gabriel B. Brammer, Ivo Labbé, Erica J. Nelson, Jane R. Rigby. CONSTRAINING THE LOW-MASS SLOPE OF THE STAR FORMATION SEQUENCE AT 0.5 < z < 2.5. ApJ 795, 104 (2014). Link

5. Vicente Rodriguez-Gomez, Shy Genel, Mark Vogelsberger, Debora Sijacki, Annalisa Pillepich, Laura V. Sales, Paul Torrey, Greg Snyder, Dylan Nelson, Volker Springel, Chung-Pei Ma, Lars Hernquist. The merger rate of galaxies in the Illustris Simulation: a comparison with observations and semi-empirical models. (2015).

6. Andrew E. Dolphin. ON THE ESTIMATION OF SYSTEMATIC UNCERTAINTIES OF STAR FORMATION HISTORIES. ApJ 751, 60 (2012). Link

7. Andrew E. Dolphin. ON THE ESTIMATION OF RANDOM UNCERTAINTIES OF STAR FORMATION HISTORIES. ApJ 775, 76 (2013). Link

8. Daniel R. Weisz, Benjamin D. Johnson, Charlie Conroy. THE VERY FAINT END OF THE UV LUMINOSITY FUNCTION OVER COSMIC TIME: CONSTRAINTS FROM THE LOCAL GROUP FOSSIL RECORD. ApJ 794, L3 (2014). Link