Evolution of the galaxy stellar mass functions and UV luminosity functions at $z=6-9$ in the Hubble Frontier Fields

Abstract: We present new measurements of the evolution of the galaxy stellar mass functions (GSMF) and UV luminosity functions (UV LF) for galaxies from $z=6-9$ within the Frontier Field cluster MACSJ0416.1-2403 and its parallel field. To obtain these results, we derive the stellar masses of our sample by fitting synthetic stellar population models to their observed spectral energy distribution with the inclusion of nebular emission lines. This is the deepest and farthest in distance mass function measured to date and probes down to a level of M${*} = 10^{6.8}M{\odot}$. The main result of this study is that the low-mass end of our GSMF to these limits and redshifts appears to become steeper from $-1.98_{-0.07}^{+0.07}$ at $z=6$ to $-2.38_{-0.88}^{+0.72}$ at $z=9$, steeper than previously observed mass functions at slightly lower redshifts, and we find no evidence of turnover in the mass range probed. We furthermore demonstrate that the UV LF for these system also appears to show a steepening at the highest redshifts, without any evidence of turnover in the luminosity range probed. Our $M_{\mathrm{UV}}-M_{}$ relation exhibit shallower slopes than previously observed and are in accordance with a constant mass-to-light ratio. Integrating our GSMF, we find that the stellar mass density increases by a factor of $\sim15_{-6}^{+21}$ from $z=9$ to $z=6$. We estimate the dust-corrected star formation rates (SFRs) to calculate the specific star formation rates ($\mathrm{sSFR}=\mathrm{SFR/M_{}}$) of our sample, and find that for a fixed stellar mass of $5\times10^{9}M_{\odot}$, sSFR $\propto(1+z)^{2.01\pm0.16}$. Finally, from our new measurements, we estimate the UV luminosity density ($\rho_{\textrm{UV}}$) and find that our results support a smooth decline of $\rho_{\textrm{UV}}$ towards high redshifts.

Evolution of Galaxy Stellar Mass Functions and UV Luminosity Functions at $z=6-9$

The study conducted by Bhatawdekar et al. investigates the evolution of galaxy stellar mass functions (GSMF) and ultraviolet (UV) luminosity functions over a redshift range of $z = 6-9$ using the Hubble Frontier Fields. The research aims to provide new measurements on these functions, offering insights into the properties and development of early galaxies. Given the limitations until the launch of the James Webb Space Telescope (JWST), these problems are best addressed through the gravitational lensing technique provided by massive clusters in conjunction with deep imaging from the Hubble Space Telescope (HST).

Methodology

To derive stellar masses for the sample, synthetic stellar population models that include nebular emission lines were fitted to the observed spectral energy distribution. This study utilizes the massive cluster MACSJ0416.1-2403 as a gravitational lens to magnify the light from distant galaxies, thereby enabling deeper observations.

The researchers implemented a novel "Divide and Conquer" approach to overcome the challenge of bright foreground galaxies. By iteratively fitting and subtracting these foreground galaxies, they enhanced the detection capability of the faint background galaxies.

Key Findings

1. Galaxy Stellar Mass Function (GSMF):
   • The low-mass end of the GSMF shows a steepening trend across the studied redshifts, steepening from $-1.98_{-0.07}^{+0.07}$ at $z=6$ to $-2.38_{-0.88}^{+0.72}$ at $z=9$.
   • This steepening is more pronounced than observed in previous studies at lower redshifts.
   • The stellar mass density was found to increase by a factor of approximately $15_{-6}^{+21}$ from $z=9$ to $z=6$.
2. UV Luminosity Function (LF):
   • The UV LF also demonstrated a steepening at higher redshifts without a turnover within the probed luminosity.
   • The distributions of the faint-end slopes suggest a consistent trend with lower redshift observations, with the slope increasing from $-2.03_{-0.10}^{+0.12}$ at $z=6$ to $-2.20_{-0.47}^{+0.51}$ at $z=9$.
3. $M_{\mathrm{UV}}-M_{*}$ Relation:
   • The study presented shallower slopes in the relation between stellar mass and UV magnitude than previously observed, consistent with a constant mass-to-light ratio.
   • Normalization evolved weakly from $z\sim6$ to $z\sim9$.
4. Star Formation Rates:
   • Dust-corrected star formation rates indicated that sSFR $\propto (1+z)^{2.01\pm0.16}$.
   • UV luminosity density ($\rho_{\textrm{UV}$ was shown to support a smooth decline towards higher redshifts.

Implications and Future Directions

The study expands understanding of early galaxy formation and hints at significant star formation activity before $z=9$. The analysis demonstrates the capability of gravitational lensing to study faint and distant galaxies and suggests that the advent of JWST will allow investigations into galaxy evolution at even higher redshifts with greater clarity and depth.

Future research utilizing the complete Hubble Frontier Fields dataset could enhance the signal-to-noise ratio further, thereby refining the observed trends and yielding more precise constraints on galaxy formation models. Until the JWST is operational, such studies exemplify the critical importance of meticulous foreground subtraction and the strategic application of gravitational lensing for early Universe exploration.