# Stacked Average Far-Infrared Spectrum of Dusty Star-Forming Galaxies from the Herschel/SPIRE Fourier Transform Spectrometer

## TL;DR

This study compiles and analyzes stacked far-infrared spectra of 197 dusty star-forming galaxies across a broad redshift range, revealing insights into their interstellar medium properties and molecular gas conditions using Herschel data.

## Contribution

It provides the first comprehensive average spectral line analysis of DSFGs over a wide redshift span, utilizing Herschel/SPIRE FTS data to model PDR conditions and molecular gas properties.

## Key findings

- High-redshift DSFGs have intense radiation fields and dense gas similar to low-redshift counterparts.
- Line ratios indicate a significant evolution in interstellar medium conditions with redshift.
- PDR models suggest molecular gas exposed to radiation fields over 1000 times stronger than the Milky Way.

## Abstract

We present stacked average far-infrared spectra of a sample of 197 dusty, star-forming galaxies (DSFGs) at $0.005 < z < 4$ using close to 90% of the SPIRE Fourier Transform Spectrometer (FTS) extragalactic data archive from the Herschel Space Observatory based on 3.5 years of science operations. These spectra explore an observed-frame $\rm 447\,GHz-1568\,GHz$ ($\rm 191\,\mu m-671\,\mu m$) frequency (wavelength) range allowing us to observe the main atomic and molecular lines emitted by gas in the interstellar medium. The sample is sub-divided into five redshift bins at $0.005 < z < 0.05$, $0.05 < z < 0.2$, $0.2 < z < 0.5$, $0.8 < z <2$, and $2 < z < 4$. To study the dependence of observed spectral lines on total infrared luminosity, the sources in a subset of the redshift bins are stacked in luminosity bins. These stacked spectra are used to determine the average properties of the interstellar medium and dense molecular gas properties of DSFGs, in particular, the fine-structure line ([CII] 158 $\mu$m and [OI] 63 $\mu$m) luminosity ratios, and the line to far-IR luminosity ratios are used to model the gas density and radiation field strength in the photodissociation regions (PDRs). For the low-redshift sample, we additionally present the average spectral line energy distributions (SLED) of CO and $\rm{H_2O}$ rotational transitions and also consider PDR conditions based on a combination of [CI] 370 $\mu$m and 609 $\mu$m and $\rm CO (7-6)$ lines. For the high-z ($0.8 < z < 4$) sample PDR models suggest a molecular gas distribution in the presence of a radiation field that is at least a factor of 10$^3$ larger than the Milky-Way and with a neutral gas density of roughly 10$^3$ to 10$^5$ cm$^{-3}$. The corresponding PDR models for the low-z sample suggest a UV radiation field and gas density comparable to those at high-z.