The z ∼ 6 Luminosity Function Fainter than −15 mag from the Hubble Frontier Fields: The Impact of Magnification Uncertainties

Abstract

We use the largest sample of z 6 galaxies to date from the first four Hubble Frontier Fields clusters to set constraints on the shape of the z 6 luminosity functions (LFs) to fainter than M 14 AB UV, = -mag. We quantify, for the first time, the impact of magnification uncertainties on LF results and thus provide more realistic constraints than other recent work. Our simulations reveal that, for the highly magnified sources, the systematic uncertainties can become extremely large fainter than −14 mag, reaching several orders of magnitude at 95% confidence at approximately−12 mag. Our new forward-modeling formalism incorporates the impact of magnification uncertainties into the LF results by exploiting the availability of many independent magnification models for the same cluster. One public magnification model is used to construct a mock high-redshift galaxy sample that is then analyzed using the other magnification models to construct an LF. Large systematic errors occur at high magnifications ( 30  m ) because of differences between the models. The volume densities we derive for faint (−17 mag) sources are ∼3-4× lower than one recent report and give a faint-end slope 1.92 0.04 a = - , which is 3.0-3.5σ shallower (including or not including the size uncertainties, respectively). We introduce a new curvature parameter δ to model the faint end of the LF and demonstrate that the observations permit (at 68% confidence) a turn-over at z 6 in the range of −15.3 to −14.2 mag, depending on the assumed lensing model. The present consideration of magnification errors and new size determinations raise doubts about previous reports regarding the form of the LF at 14 mag >-. We discuss the implications of our turn-over constraints in the context of recent theoretical predictions.

Warm Dark Matter and Cosmic Reionization

“…This result, we emphasize again, is a theoretical assumption, not a known fact. Several recent large computational projects achieved similar level of precision in matching observational constraints to the CROC projects, and they all predict the turnover to occur at widely varying luminosities (Bouwens et al 2017). Hence, the location and the shape of the turnover cannot be considered as a reliable theoretical prediction and will have to be constrained by future observations.…”

Stellar Mass Function of Active and Quiescent Galaxies via the Continuity Equation

“…Solid lines refer to the rendition from UV plus far-IR/sub-mm/radio data; dotted lines (only plotted at z ≈ 0 and 1) refer to the rendition from UV data (dust corrected according to standard prescriptions based on the UV slope). UV data (open symbols) are from van der Burg et al (2010;diamonds), Bouwens et al (2016Bouwens et al ( , 2017pentagons), inverse triangles), Cucciati et al (2012;triangles), Wyder et al (2005;spirals), Oesch et al (2010;crosses), Alavi et al (2016;asterisks); far-IR/sub-mm data from Gruppioni et al (2015;hexagons), Magnelli et al (2013;circles), Gruppioni et al (2013;squares), Lapi et al (2011;stars), and Cooray et al (2014;pacmans); radio data from Novak et al (2017;clovers). extinction law, but note that switching to a Small Magellanic Cloud (SMC) extinction law affects mildly the SFR function at the faint end (see also Sect.…”

“…The redshift evolution of each parameter has been measured via an educated fit to the observed data in unitary redshift bins by Mancuso et al (2016a,b). As extensively discussed by the latter authors, the SFR function is mainly determined by (dust-corrected) UV data for SFṘ M ⋆ 30 M ⊙ yr −1 since in this range dust emission is mainly due to the diffuse (cirrus) dust component and standard UV dust-corrections based on the UV slope are reliable (see Meurer et al 1999;Calzetti 2000;Bouwens et al 2015Bouwens et al , 2016Bouwens et al , 2017); here we use the Meurer/Calzetti Figure 1. The SFR functions at redshifts z = 0 (green), 1 (red), 3 (orange) and 6 (blue) determined according to the procedure by Mancuso et al (2016a,b) and Lapi et al (2017).…”

“…Such achievement has become feasible only recently thanks to wide-area far-IR/sub-mm surveys conducted by Herschel, ASTE/AzTEC, APEX/LABOCA, JCMT/SCUBA2, and ALMA-SPT (e.g., Gruppioni et al 2013Gruppioni et al , 2015Lapi et al 2011;Weiss et al 2013;Strandet et al 2016;Koprowski et al 2014Koprowski et al , 2016, in many instances eased by gravitational lensing from foreground objects (e.g., Negrello et al 2014Negrello et al , 2017Nayyeri et al 2016). In fact, galaxies endowed with star formation ratesṀ ⋆ a few tens M ⊙ yr −1 at redshift z 2 were largely missed by rest-frame optical/UV surveys because of heavy dust obscuration, difficult to correct for with standard techniques based only on UV spectral data (e.g., Bouwens et al 2016Bouwens et al , 2017Mancuso et al 2016a;Pope et al 2017;Ikarashi et al 2017;Simpson et al 2017). High-resolution, follow-up observations of these galaxies in the far-IR/sub-mm/radio band via ground-based interferometers, such as SMA, VLA, PdBI, and recently ALMA, have revealed star formation to occur in a few collapsing clumps distributed over spatial scales smaller than a few kpcs (see Simpson et al 2015;Ikarashi et al 2015;Straatman et al 2015;Spilker et al 2016;Barro et al 2016;Tadaki et al 2017).…”

HST Imaging of the Brightest z ∼ 8–9 Galaxies from UltraVISTA: The Extreme Bright End of the UV Luminosity Function

“…The higher S/N of the HST observations in these fields greatly reduces the chances of uncertain redshifts identification of their redshifts. Nonetheless, issues in the assessment of the nature of candidate LBGs arise at the faint end of the UV LF (see e.g., Bouwens et al 2017).…”