The Galaxy UV Luminosity Function Before the Epoch of Reionization

We present a model for the evolution of the galaxy ultraviolet (UV) luminosity function (LF) across cosmic time where star formation is linked to the assembly of dark matter halos under the assumption of a mass dependent, but redshift independent, efficiency. We introduce a new self-consistent treatment of the halo star formation history, which allows us to make predictions at $z>10$ (lookback time $\lesssim500$ Myr), when growth is rapid. With a calibration at a single redshift to set the stellar-to-halo mass ratio, and no further degrees of freedom, our model captures the evolution of the UV LF over all available observations ($0\lesssim z\lesssim10$). The significant drop in luminosity density of currently detectable galaxies beyond $z\sim8$ is explained by a shift of star formation toward less massive, fainter galaxies. Assuming that star formation proceeds down to atomic cooling halos, we derive a reionization optical depth $\tau = 0.056^{+0.007}_{-0.010}$, fully consistent with the latest Planck measurement, implying that the universe is fully reionized at $z=7.84^{+0.65}_{-0.98}$. In addition, our model naturally produces smoothly rising star formation histories for galaxies with $L\lesssim L_*$ in agreement with observations and hydrodynamical simulations. Before the epoch of reionization at $z>10$ we predict the LF to remain well-described by a Schechter function, but with an increasingly steep faint-end slope ($\alpha\sim-3.5$ at $z\sim16$). Finally, we construct forecasts for surveys with \JWST~and \WFIRST and predict that galaxies out to $z\sim14$ will be observed. Galaxies at $z>15$ will likely be accessible to JWST and WFIRST only through the assistance of strong lensing magnification.Comment: Accepted for publication in ApJ. 11 pages, 13 figures. Corrected mislabelled redshifts in Figure

Effects of self-consistent rest-ultraviolet colours in semi-empirical galaxy formation models

Connecting the observed rest-ultraviolet (UV) luminosities of high-$z$ galaxies to their intrinsic luminosities (and thus star formation rates) requires correcting for the presence of dust. We bypass a common dust-correction approach that uses empirical relationships between infrared (IR) emission and UV colours, and instead augment a semi-empirical model for galaxy formation with a simple -- but self-consistent -- dust model and use it to jointly fit high-$z$ rest-UV luminosity functions (LFs) and colour-magnitude relations ($M_{\mathrm{UV}}$-$\beta$). In doing so, we find that UV colours evolve with redshift (at fixed UV magnitude), as suggested by observations, even in cases without underlying evolution in dust production, destruction, absorption, or geometry. The observed evolution in our model arises due to the reduction in the mean stellar age and rise in specific star formation rates with increasing $z$. The UV extinction, $A_{\mathrm{UV}}$, evolves similarly with redshift, though we find a systematically shallower relation between $A_{\mathrm{UV}}$ and $M_{\mathrm{UV}}$ than that predicted by IRX-$\beta$ relationships derived from $z \sim 3$ galaxy samples. Finally, assuming that high $1600 \r{A}$ transmission ($\gtrsim 0.6$) is a reliable LAE indicator, modest scatter in the effective dust surface density of galaxies can explain the evolution both in $M_{\mathrm{UV}}$-$\beta$ and LAE fractions. These predictions are readily testable by deep surveys with the James Webb Space Telescope.Comment: 14+4 pages, 11+5 figures, accepted for publication in MNRA

Beacons into the Cosmic Dark Ages: Boosted transmission of Lyα\alpha from UV bright galaxies at z≳7z \gtrsim 7

Recent detections of Lyman alpha (Ly$\alpha$) emission from $z>7.5$ galaxies were somewhat unexpected given a dearth of previous non-detections in this era when the intergalactic medium (IGM) is still highly neutral. But these detections were from UV bright galaxies, which preferentially live in overdensities which reionize early, and have significantly Doppler-shifted Ly$\alpha$ line profiles emerging from their interstellar media (ISM), making them less affected by the global IGM state. Using a combination of reionization simulations and empirical ISM models we show, as a result of these two effects, UV bright galaxies in overdensities have $>2\times$ higher transmission through the $z\sim7$ IGM than typical field galaxies, and this boosted transmission is enhanced as the neutral fraction increases. The boosted transmission is not sufficient to explain the observed high Ly$\alpha$ fraction of $M_\mathrm{UV} \lesssim -22$ galaxies (Stark et al. 2017), suggesting Ly$\alpha$ emitted by these galaxies must be stronger than expected due to enhanced production and/or selection effects. Despite the bias of UV bright galaxies to reside in overdensities we show Ly$\alpha$ observations of such galaxies can accurately measure the global neutral hydrogen fraction, particularly when Ly$\alpha$ from UV faint galaxies is extinguished, making them ideal candidates for spectroscopic follow-up into the cosmic Dark Ages.Comment: 6 pages, 5 figures. Accepted for publication in ApJ

Defection Detection: Measuring and Understanding the Predictive Accuracy of Customer Churn Models

The authors express their gratitude to Sanyin Siang (Managing Director, Teradata Center for Customer Relationship Management at the Fuqua School of Business, Duke University); research assistants Sarwat Husain, Michael Kurima, and Emilio del Rio; and an anonymous wireless telephone carrier that provided the data for this study. The authors also thank participants in the Tuck School of Business, Dart-mouth College, Marketing Workshop, for comments and the two anony-mous JMR reviewers for their constructive suggestions. Finally, the authors express their appreciation to former editor Dick Wittink (posthumously) for his invaluable insights and guidance. This article provides a descriptive analysis of how methodological factors contribute to the accuracy of customer churn predictive models. The study is based on a tournament in which both academics and practitioners downloaded data from a publicly available Web site, estimated a model, and made predictions on two validation databases. The results suggest several important findings. First, methods do matter. The differences observed in predictive accuracy across submissions could change the profitability of a churn management campaign by hundreds of thousands of dollars. Second, models have staying power. They suffer very little decrease in performance if they are used to predict churn for a database compiled three months after the calibration data. Third, researchers use a variety of modeling "approaches," characterized by variables such as estimation technique, variable selection procedure, number of variables included, and time allocated to steps in the model-building process. The authors find important differences in performance among these approaches and discuss implications for both researchers and practitioners

The Evolution of the Lyman-Alpha Luminosity Function During Reionization

The time frame in which hydrogen reionization occurred is highly uncertain, but can be constrained by observations of Lyman-alpha (Ly$\alpha$) emission from distant sources. Neutral hydrogen in the intergalactic medium (IGM) attenuates Ly$\alpha$~photons emitted by galaxies. As reionization progressed the IGM opacity decreased, increasing Ly$\alpha$~visibility. The galaxy Ly$\alpha$~luminosity function (LF) is thus a useful tool to constrain the timeline of reionization. In this work, we model the Ly$\alpha$~LF as a function of redshift, $z=5-10$, and average IGM neutral hydrogen fraction, \overline{x}_\textsc{hi}. We combine the Ly$\alpha$~luminosity probability distribution obtained from inhomogeneous reionization simulations with a model for the UV LF to model the Ly$\alpha$~LF. As the neutral fraction increases, the average number density of Ly$\alpha$~emitting galaxies decreases, and are less luminous, though for \overline{x}_\textsc{hi} \lesssim 0.4 there is only a small decrease of the Ly$\alpha$~LF. We use our model to infer the IGM neutral fraction at $z=6.6, 7.0, 7.3$ from observed Ly$\alpha$~LFs. We conclude that there is a significant increase in the neutral fraction with increasing redshift: \overline{x}_\textsc{hi}(z=6.6)=0.08^{+ 0.08}_{- 0.05}, \, \overline{x}_\textsc{hi}(z=7.0)=0.28 \pm 0.05 and \overline{x}_\textsc{hi}(z=7.3)=0.83^{+ 0.06}_{- 0.07}. We predict trends in the Ly$\alpha$~luminosity density and Schechter parameters as a function of redshift and the neutral fraction. We find that the Ly$\alpha$~luminosity density decreases as the universe becomes more neutral. Furthermore, as the neutral fraction increases, the faint-end slope of the Ly$\alpha$~LF steepens, and the characteristic Ly$\alpha$~luminosity shifts to lower values, concluding that the evolving shape of the Ly$\alpha$~LF -- not just its integral -- is an important tool to study reionization.Comment: 20 pages, 10 figures, submitted to Ap