# On the Dust properties of the UV galaxies in the redshift range $z\sim
0.6-1.2$

M. Sharma1,2, M. J. Page1, M. Symeonidis1, I. Ferreras3,4,5
1Mullard Space Science Laboratory, University College London, Holmbury St
Mary, Dorking, Surrey, RH5 6NT, UK
2Isaac Newton Group of Telescopes, C. Álvarez Abreu, 70, E38700 Santa Cruz de
La Palma, La Palma, Spain
3Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, E38205, La
Laguna, Tenerife, Spain
4Departamento de Astrofísica, Universidad de La Laguna, E38206, La Laguna,
Tenerife, Spain
5Department of Physics and Astronomy, University College London, Gower Street,
London WC1E 6BT, UK E-mail<EMAIL_ADDRESS>(MS)

(Accepted XXX; Received YYY; in original form ZZZ)

###### Abstract

Far-infrared observations from the Herschel Space Observatory are used to
estimate the infrared (IR) properties of ultraviolet-selected galaxies. We
stack the PACS (100, 160 $\mu\mathrm{m}$) and SPIRE (250, 350 and
500$\mu\mathrm{m}$) maps of the Chandra deep field south (CDFS) on a source
list of galaxies selected in the rest-frame ultraviolet (UV) in a redshift
range of $0.6-1.2$. This source list is created using observations from the
XMM-OM telescope survey in the CDFS using the UVW1 (2910 Å) filter. The
stacked data are binned according to the UV luminosity function of these
sources, and the average photometry of the UV-selected galaxies is estimated.
By fitting modified black bodies and IR model templates to the stacked
photometry, average dust temperatures and total IR luminosity are determined.
The luminosity-weighted average temperatures do not show significant evolution
between the redshifts 0.7 and 1.0. Infrared excess, unobscured, and obscured
star formation rate (SFR) values are obtained from the UV and IR luminosities.
We see a trend wherein the dust attenuation increases as the UV luminosity
decreases. It remains constant as a function of IR luminosities at fixed
redshift across the luminosity range of our sources. In comparison to local
luminous infrared galaxies with similar SFRs, the higher redshift star-forming
galaxies in the sample show a lesser degree of dust attenuation. Finally, the
inferred dust attenuation is used to correct the unobscured SFR density in the
redshift range 0.6-1.2. The dust-corrected SFR density is consistent with
measurements from IR-selected samples at similar redshifts.

###### keywords:

galaxies: star formation — galaxies: luminosity function — infrared: galaxies
— ultraviolet: galaxies

††pubyear: 2022††pagerange: On the Dust properties of the UV galaxies in the
redshift range $z\sim 0.6-1.2$–16

##  1 Introduction

Star formation is controlled by various fundamental processes and is one of
the key global mechanisms for galaxy evolution. It has shaped the galaxies as
we observe them today. In other words, it plays a crucial role in the
evolutionary history of galaxies, and constraining the star formation rate
(SFR) is important for understanding this evolution.

The ultraviolet (UV) continuum in the spectral energy distribution (SED) of
star-forming galaxies is produced by young massive stars, and it is widely
used as one of the most important indicators of the SFR (Kennicutt & Evans,
2012). It has been employed by studies constraining the luminosity density in
the nearby Universe (e.g. Wyder et al., 2005; Budavári et al., 2005) as well
as at low (e.g. Sullivan et al., 2000), intermediate (e.g. Oesch et al., 2010;
Page et al., 2021; Sharma et al., 2022) and high redshifts (Parsa et al.,
2016; Bouwens et al., 2015; Donnan et al., 2023). The UV continuum can also be
produced by AGN, which makes it important to consider their identification in
a sample of star-forming galaxies under consideration.

Rest frame UV radiation is particularly susceptible to being obscured by dust
in star-forming regions of a galaxy. The UV flux is scattered and/or absorbed
by dust particles, which then reemit this energy as thermal black-body
radiation in the far-infrared (FIR) wavelength range. In the local universe,
for near-UV (NUV) selected sources Buat et al. (2005) and Burgarella et al.
(2006) found the typical dust attenuation in the far-UV (FUV) to be 1.1 and
1.4 mags, respectively. The effect becomes more severe with an increase in
redshift and a larger fraction of UV radiation is absorbed by dust at higher
redshifts compared to the local universe. According to a study by Takeuchi et
al. (2005), the portion of the far-UV SFR that is obscured by dust increases
from 56 per cent in the nearby universe to 84 per cent at an average redshift
of 1. Therefore, correcting UV luminosities for dust attenuation is essential
before it can be used to estimate the SFR.

One of the suggested methods to solve this issue of dust attenuation involves
utilizing the empirical correlation between UV dust attenuation
($A_{\mathrm{FUV}}$) and the slope ($\beta$) of the UV continuum described by
a power law ($f_{\lambda}\propto\lambda^{\beta}$; Calzetti et al., 1994, 2000;
Meurer et al., 1999; Overzier et al., 2010). To quantify the UV attenuation,
this approach involves the ratio of the FIR to the UV luminosity, also known
as the infrared (IR) excess or $\mathrm{IRX}$. Many studies that rely solely
on UV data have utilised this relationship as a standard practise in order to
correct their estimates of SFR or luminosity density (LD) for the effects of
dust attenuation (e.g. Schiminovich et al., 2005; Bouwens et al., 2009;
Finkelstein et al., 2012; Bouwens et al., 2015, 2020).

The central concept underlying this approach is that all galaxies possess the
same intrinsic spectral slope ($\beta$), which can only be altered by the
presence of dust obscuration. While this assumption may seem to hold in the
nearby universe (Meurer et al., 1999), the spectral slope can also be
influenced by a variety of other factors, including the redshift, the initial
mass function (IMF), the metallicity, and other quantities, in addition to
dust obscuration (Wilkins et al., 2012a, b; Tress et al., 2018). In addition,
the UV continuum slope is generally bluer than the assumed inherent value in
the Meurer relation (Wilkins et al., 2013). As a result of these various
factors, this relation, which was initially calibrated for starburst galaxies
(Meurer et al., 1999), may be subject to modification when applied to normal
galaxies, depending on various global factors such as age (e.g. Reddy et al.,
2012; Narayanan et al., 2018), stellar mass (Reddy et al., 2010, 2018;
Fudamoto et al., 2020), luminosity, and SFR of the galaxy (e.g. Casey et al.,
2014). Furthermore, this relationship has been found to be influenced by local
properties such as the geometry of the dust-emitting region (e.g. Witt &
Gordon, 2000; Narayanan et al., 2018), and it has been discovered that the
specific shape of this relationship can depend on the extinction law (e.g.
Narayanan et al., 2018) and the source selection criteria (Buat et al., 2005).

The other more direct and reliable way to measure dust attenuation is through
$\mathrm{IRX}$, which is calculated as the ratio of the luminosity in the IR
region to the luminosity in the ultraviolet region of the SEDs of the galaxy
(Meurer et al., 1999). This method works because dust absorbs UV light and re-
emits it as thermal radiation in the IR bands. By measuring the IR emission,
it is possible to determine how much UV light has been absorbed by dust. This
information can be used to correct UV/optical observations for dust
attenuation, and the FIR flux can also be used as a proxy for the amount of
obscured star formation in a galaxy. (Buat, 1992; Xu & Buat, 1995; Meurer et
al., 1995; Heckman et al., 1998; Gordon et al., 2000). Additionally, the use
of both UV and IR observations provides a way to trace both attenuated and
unattenuated star formation in a galaxy as a composite measure of star
formation (Calzetti et al., 2007).

The $\mathrm{IRX}$ ratio is based on the relative brightness of ultraviolet
(UV) radiation that has not been absorbed by dust in a system compared to the
FIR radiation that has been absorbed and reemitted by dust. The basic premise
behind the $\mathrm{IRX}$ ratio is that there should be a balance between the
UV/optical light absorbed by dust and the FIR radiation emitted (Buat & Xu,
1996; Buat et al., 1999). However, this balance may not always be
straightforward in practise and may be influenced by the age of the dust
heating system. Although this method has the advantage of being independent of
other IR properties and star-dust geometry (Gordon et al., 2000; Witt &
Gordon, 2000; Cortese et al., 2008), it is not as widely used as the previous
method based on the Meurer relation due to the ease of accessing data to
calculate the UV spectral slope and the lack of deep FIR data at high
redshifts. However, if deep FIR data is available, the $\mathrm{IRX}$ method
can be a powerful tool for studying dust attenuation in different types of
systems (Buat et al., 1999) and may provide more robust results than the other
method that relies on more uncertain assumptions.

The method of using the $\mathrm{IRX}$ ratio to estimate dust attenuation in
galaxies has been widely studied in the literature. A study using this method,
conducted by Buat et al. (2005), analysed a sample of galaxies selected by the
Galaxy Evolution Explorer (GALEX) in the near-ultraviolet (NUV) band and
Infrared Astronomy Satellite (IRAS) data at 60 $\mu\mathrm{m}$, and found that
the mean dust attenuation in the FUV was 1.6 magnitudes in the nearby
universe. Other studies have extended this to higher redshifts, finding that
the $\mathrm{IRX}$ ratio as a function of bolometric luminosity
($L_{\mathrm{IR}}+L_{\mathrm{UV}}$) of the galaxies evolves to redshift 1 for
Lyman break galaxies (Burgarella et al., 2007) and redshift 2 for BM/BX
galaxies (Reddy et al., 2006). However, Buat et al. (2009) did not see a clear
evolution in the $\mathrm{IRX}$ ratio at fixed bolometric luminosity up to a
redshift of 1 in their homogeneously selected sample of galaxies from GALEX,
and suggested that it might be more useful to look at the $\mathrm{IRX}$ ratio
as a function of UV luminosity rather than bolometric luminosity.

One challenge in studying the dust attenuation in galaxies at high redshifts
is the availability of FIR data, as current IR telescopes have limited
sensitivity and resolution, making these observations scarce and restricted to
the most massive galaxies. Stacking analysis, in which multiple data with a
lower signal-to-noise ratio are combined to increase the overall signal-to-
noise ratio (Dole et al., 2006; Marsden et al., 2009; Béthermin et al., 2010;
Kurczynski & Gawiser, 2010; Roseboom et al., 2012; Viero et al., 2013), has
been used in some studies to estimate the UV attenuation due to dust at higher
redshifts.

Some examples of studies that have used stacking analysis to estimate UV
attenuation due to dust at higher redshifts include those by Xu et al. (2007),
who extended $\mathrm{IRX}$-based dust attenuation estimates to redshift 0.6
using data from the GALEX survey and the Spitzer Space Telescope at 24
$\mu\mathrm{m}$, and Heinis et al. (2013), who used data from the Canada-
France-Hawaii Telescope (CFHT) $u^{*}$-band imaging in the Cosmic Evolution
Survey (COSMOS) field to estimate $\mathrm{IRX}$ at redshift $\sim 1.5$. They
found mean $\mathrm{IRX}$ to be 6.6 and 6.9 respectively. These measurements
were taken to redshifts around 2 by Reddy et al. (2012), who used UV-selected
galaxies from the Low-Resolution Imaging Spectrograph (LRIS) on the Keck
telescope (Steidel et al., 2004; Reddy et al., 2006) and obtained an
$\mathrm{IRX}$ value of 7.1, indicating that only 20 per cent of the star
formation is not dust obscured.

Other works have also studied the $\mathrm{IRX}$ ratio at higher redshifts
with stacking methods on different data sets. Álvarez-Márquez et al. (2016)
calculated the $\mathrm{IRX}$ ratio at redshift $\sim 3$ using $u^{*}$,
$V_{\mathrm{J}}$ and $i^{+}$ band imaging and Herschel Space Observatory
(hereafter Herschel) maps in the COSMOS field and estimated an average value
of 7.9. Using Lyman break galaxy candidates at average redshifts 3.8 from the
NOAO Deep Wide-Field Survey of the Boötes field, Lee et al. (2012) found
$\mathrm{IRX}$ values of 3 to 4, implying that 30 to 40 per cent of the star
formation occurs without any dust attenuation. More recently, Reddy et al.
(2018) used the Hubble Space Telescope (HST) data from the 3D-HST survey
(Skelton et al., 2014) and the Hubble Deep UV (HDUV) Legacy Survey (Oesch et
al., 2018), along with Spitzer MIPS 24 $\mu\mathrm{m}$ and Herschel PACS 100
and 160 $\mu\mathrm{m}$ data, to calculate an average $\mathrm{IRX}$ value of
2.94 for redshifts between 1.5 and 2.5 in the Great Observatories Origins Deep
Survey (GOODS) fields.

For redshifts up to 1, similar studies have been performed using only GALEX
data for UV selection, which can be subjected to issues related to source
confusion due to its poor spatial resolution. More studies are needed to
revisit this redshift range with better data and determine whether the trend
observed in previous studies holds at these intermediate redshifts.

In this study, we used the UV-selected sample (Sharma et al., 2022) of
galaxies from the Chandra Deep Field South (CDFS) survey of the XMM-Newton
Optical Monitor (XMM-OM, Optical Monitor; Mason et al., 2001) onboard the XMM-
Newton observatory. The UVW1 filter ($\lambda_{\mathrm{eff}}=2910$ Å) of the
XMM-OM telescope provides rest-frame 1500 Å imaging in the redshift range of
our interest (0.6-1.2), over a field of view of 17 $\times$ 17 sq. arcminutes.
These galaxies are stacked on the FIR maps at 100, 160, 250, 350 and 500
$\mu\mathrm{m}$ from Herschel to obtain the average FIR flux of the galaxies
in bins of the UV luminosity function created for these galaxies by Sharma et
al. (2022). Using the integrated IR luminosity we calculate the $\mathrm{IRX}$
ratio and then use it to calculate the dust attenuation of the FUV radiation,
which in turn is used to correct the SFR density (SFRD) calculated using the
UV measurements of Sharma et al. (2022).

This paper is structured as follows. The data used in this work are explained
in section 2. We describe our methods in section 3. In particular the
deblending process for the SPIRE maps in section 3.1, stacking the FIR maps
and extraction of the average photometry from the stacks in section 3.2,
fitting the IR model templates to the average IR flux densities and the
estimation of dust properties like total IR luminosity and dust temperature in
section 3.3 We discuss the methods to obtain the star formation rates (un-
obscured and obscured using the UV and FIR tracers) and the average dust
attenuation of the UV light in sections 3.4 and 3.5. We summarise our results
in section 4 and discuss their implications in section 5. Finally, we conclude
this paper in section 6. Throughout the paper, we adopt a flat cosmology with
$\Omega_{\Lambda}=0.7$, $\Omega_{M}=0.3$ and Hubble’s constant $H_{0}=70$ km
s-1 Mpc-1. The distances (and volumes) are calculated in comoving coordinates
in Mpc (and Mpc3). We use the AB system of magnitudes (Oke & Gunn, 1983). The
FIR luminosities are integrated over $8-1000\mu m$, and the FUV luminosities
are defined as $\lambda L_{\lambda}$, where $\lambda=1500$ Å.

##  2 Data

Figure 1: The UV source positions overlaid on the 250 $\mu\mathrm{m}$ SPIRE
map. Figure 2: Rest frame UV ($M_{1500}$) absolute magnitudes and redshift
distribution of the UVW1 sources stacked in this study. Blue and red colours
represent the sources in the redshift bin centered at 0.7 and 1.0
respectively. The faint magnitude end of the distribution is truncated because
of the apparent magnitude limit of our flux-limited survey in the CDFS. The
apparent magnitude limit is UVW1$=24.5$ mag. Table 1: We tabulate here the
properties of the Herschel SPIRE and PACS data used in this study. The
$1\sigma$ noise for the SPIRE maps is the total noise including both the
instrumental and confusion components.

Central $\lambda$ | Pixel Scale | FWHM |  $3\sigma$ depth
---|---|---|---
($\mu$m) | (arcsec) | (arcsec) | (mJy)
100 | 1.2 | 7.2 | 4.50a
160 | 2.4 | 12 | 8.50a
250 | 6.0 | 18.15 | 6.72b
350 | 8.33 | 25.15 | 5.58b
500 | 12.0 | 36.30 | 8.04b

$a$From Gruppioni et al. (2013)

$b$From Viero et al. (2013)

Figure 3: We depict the deblending process here as described in section 3 with
an example of the 250 $\mu\mathrm{m}$ map from Hershel SPIRE. The left panel
shows the original map. In the middle panel we show our model for the 250
$\mu\mathrm{m}$ map, and the  right hand panel shows the residual map created
by subtracting the model from the original map. The colour bar represents the
pixel values of the flux density calibrated in units of Jy/beam.

For this study, we have employed the data products obtained from the XMM-OM
and Herschel telescopes, specifically focusing on the Chandra Deep Field South
(CDFS). This particular field, which is centred at RA 3h 32m 28.0s DEC
$-27^{\circ}48^{\prime}30"$ (J2000.0) (Rosati et al., 2002) in the southern
sky, has been the primary target of observation for the Chandra X-ray
Observatory (Luo et al., 2008). Over the course of the last two decades, this
field has been the subject of extensive observation through a variety of
multi-wavelength surveys, and as such, a plethora of ancillary information has
been accumulated.

###  2.1 UV selected galaxies in the CDFS

The UVW1 filter, characterised by an effective wavelength of 2910 Å, of the
XMM-OM can be used to generate samples that comprise star-forming galaxies in
the redshift range of 0.6 to 1.2. This has been demonstrated in studies
conducted in the 13 Hr field (Page et al., 2021), as well as in the CDFS
(Sharma et al., 2022) and COSMOS (Sharma et al., 2023, submitted) fields. In
the aforementioned study Sharma et al. (2022), we made use of the UV imaging
capabilities of the XMM-OM. The CDFS was observed over the course of a decade,
from 2001 to 2010 using the UVW1 filter. The data from this extensive
observing campaign enabled us to create a deep ultraviolet image of the CDFS,
which covers an area of approximately 400 sq. arcminutes. This image was
subsequently used to create a source list of galaxies by extracting photometry
in the rest frame 1500 Å, spanning a redshift range of $0.6-1.2$. The UVW1
filter can also select stars and AGNs due to their UV emissions. Quasars in
particular, where the UV radiation from the accretion disc around the
supermassive black hole outshines the stars in the host galaxy, could
contaminate our samples. Such AGN as well as the stars have been removed using
their X-ray emission. By leveraging supplementary data from other catalogues
within the CDFS, a UV catalogue that comprised 1079 galaxies, with a signal-
to-noise of $>3$, was compiled. The sample produced through this process is
used in this investigation to study the average IR properties of these star-
forming galaxies.

###  2.2 FIR observations of the CDFS

The data used in this analysis are sourced from Herschel (Pilbratt et al.,
2010), specifically utilising data taken by the Spectral and Photometric
Imaging Receiver (SPIRE; Griffin et al., 2010) and the Photodetector Array
Camera and Spectrometer (PACS; Poglitsch et al., 2010) instruments.

####  2.2.1 Herschel SPIRE

The SPIRE data were obtained at 250 $\mu\mathrm{m}$, 350 $\mu\mathrm{m}$, and
500 $\mu\mathrm{m}$ as part of the Herschel Multi-tiered Extragalactic Survey
(HerMES; Oliver et al., 2012). The maps used in this analysis were taken from
HeDam111https://hedam.lam.fr/HerMES/index/dr4 and were observed to a $3\sigma$
depth of 6.72, 5.58, and 8.04 mJy, respectively, without taking into account
confusion noise (Viero et al., 2013). The confusion noise for these SPIRE
maps, as calculated by Nguyen et al. (2010), is determined to be 5.8, 6.3, and
6.8 mJy at $1\sigma$ level for the 250 $\mu\mathrm{m}$, 350 $\mu\mathrm{m}$,
and 500 $\mu\mathrm{m}$ filters, respectively. Therefore, these maps, because
of their larger beam size, are limited by confusion noise. In Fig. 1, we
present a plot of our UV source list, which is overlaid on top of the 250
$\mu\mathrm{m}$ map that was obtained from the SPIRE instrument.

####  2.2.2 Herschel PACS

The PACS data were obtained as part of the PACS Evolutionary Probe survey
(PEP222https://www.mpe.mpg.de/ir/Research/PEP/DR1; Lutz et al., 2011), at
wavelengths of 100 $\mu\mathrm{m}$ and 160 $\mu\mathrm{m}$. The particular
area of the sky that is the focus of our analysis, characterised by UVW1
sources, is observed as part of the Extended Chandra Deep Field South leg of
the PEP survey. The overall field has been observed to a $3\sigma$ depths of
4.5 and 8.5 mJy (Gruppioni et al., 2013). It is worth noting that a portion of
the field covered by our sources, specifically the GOODS-S region, is observed
to deeper fluxes (1.2 and 2.4 mJy at the $3\sigma$ level). However, for the
purpose of maintaining uniformity in terms of depth for all sources, these
deeper data have not been included in the present analysis. In contrast to the
SPIRE maps, which are limited by confusion noise, the PACS maps, due to their
small beam size, are limited by instrumental noise.

##  3 Methods

###  3.1 Deblending SPIRE maps

When there are a large number of sources situated in close proximity to each
other, it can be challenging to accurately distinguish and identify them as
individual entities. This situation can arise when the sources are so close to
each other that they appear to blend together and appear as a single source.
This can have a significant impact on source identification and compromise the
accuracy of the identified source positions, which in turn affects the cross-
matching with other catalogues. When two or more sources are blended together,
the measurements of flux density can be overestimated, which can skew the
calculations of derived estimates such as dust temperatures and total IR
luminosities. In addition, when sources appear separated but are still close
together, the emission from the wings of one source may be incorrectly
attributed to another nearby source. The SPIRE instrument, in particular, is
affected by this blending due to its coarse beam, and, as a result, its FIR
maps need to be corrected before they can be used to calculate flux densities.
Furthermore, the clustering of sources in the IR sky can have a significant
impact on the stacking measurements performed on such sources, as it has the
potential to contribute at the wings of the stacked signals and thus boost the
overall flux (Dole et al., 2006; Béthermin et al., 2010; Kurczynski & Gawiser,
2010; Béthermin et al., 2012; Heinis et al., 2013; Álvarez-Márquez et al.,
2016). In particular, Béthermin et al. (2012) carried out an estimation of
clustering contribution for a sample selected at 24 $\mu\mathrm{m}$, and found
that stacked flux measurements are boosted by approximately 8, 10, and 19 per
cent at 250, 350 and 500 $\mu\mathrm{m}$, respectively.

To address these issues, we employ a technique known as deblending to correct
the SPIRE maps. The basic concept behind this process is relatively
straightforward. We model the SPIRE maps using the positions of sources in the
24 $\mu\mathrm{m}$ and radio catalogues, under the assumption that the
majority of sources detected in the SPIRE (250, 350 and 500 $\mu\mathrm{m}$)
bands should have a corresponding detection in these bands. To this end, a
comprehensive prior catalogue is created utilizing the 24 $\mu\mathrm{m}$
catalogue of the CDFS as part of the Far-Infrared Deep Extra-galactic Legacy
(FIDEL) Survey. For the area of the CDFS that overlaps with GOODS-South, we
use a more detailed and deep catalogue from Magnelli et al. (2011) in place of
the sources from the CDFS. However, it is important to note that some of the
SPIRE sources may not have been detected in the 24 $\mu\mathrm{m}$ band, thus,
to make the prior catalogue as complete as possible, radio catalogues from
Miller et al. (2013) and Franzen et al. (2015) are also employed. For the 250
and 350 $\mu\mathrm{m}$ bands, we use sources that are brighter than 30
$\mu$Jy and have a signal-to-noise ratio of at least $3$ and $5$ respectively,
from the FIDEL and GOODS-S catalogues. To prevent over-deblending of the 500
$\mu\mathrm{m}$ maps, it is necessary to use a source list with a relatively
low number density of sources. To accomplish this, we create a separate prior
source list specifically for the 500 $\mu\mathrm{m}$ maps by applying more
stringent constraints to the 24 $\mu\mathrm{m}$ FIDEL and GOODS-S 24 $\mu$m
catalogues. For the 500 $\mu\mathrm{m}$ prior list, we use sources with fluxes
> 40 $\mu$Jy at $5\sigma$ for both FIDEL and GOODS-S catalogues.

The deblending process is performed in two steps, with the first step using
the prior catalogue to produce an initial set of models for the SPIRE maps.
However, it is likely that some sources may still be missed due to the
incompleteness of the prior catalogues. So, in order to improve our models, we
undertake a second run of the process, this time utilising a modified prior
catalogue. Any sources missing from the initial catalogue are identified
through source detection on residual maps produced in the first step. This is
accomplished using SExtractor (Bertin & Arnouts, 1996) with a detection
threshold of 3, 3.5 and $4\sigma$, respectively, for the 250, 350 and 500
$\mu\mathrm{m}$ maps. These newly detected sources are then added to the
original catalogue, and the entire modelling process is re-run. The resulting
models, along with the original and residual maps from the second run, are
illustrated in Fig. 3 (for the 250 $\mu\mathrm{m}$ band). The equivalent
figures for 350 and 500 $\mu\mathrm{m}$ are shown in Appendix A. Similar
methods have been used in several previous studies, such as those conducted by
Swinbank et al. (2014), Thomson et al. (2017) and Liu et al. (2018).

The sources in the final prior catalogue that are also present in the UV
source list are added back to the residual maps to preserve their FIR
contribution because, as explained in the next section, the stacking and
average photometry are performed on the residual maps.

Figure 4: The PACS and SPIRE stacks used in this work for redshift range
0.6-0.8 (on the left) and 0.8-1.2 (on the right). The first two columns
represent the PACS 100 and 160 $\mu$m band and the last three columns
represent respectively the SPIRE 250, 350 and 500 $\mu$m wavelength bands. The
top stack of each column is labelled with the Herschel waveband (from 100 to
500 $\mu$m) they represent. Each row represents a UV luminosity bin in
descending order of UV luminosity from top to bottom. These UV luminosities of
the UV LF bins are labelled in the first (left most) stack of each row in
units of $\times 10^{10}\,\mathrm{L_{\odot}}$. Table 3 lists the UV
luminosity, and IR luminosity of each UV luminosity bin along with the number
of sources stacked to produce these stacks. The size of the stacks in
arcseconds is labelled on the bottom edge of each stack in the bottom row.
Every stack has a total width of roughly 5 times the FWHM. Due to the
different pixel scales of the maps each map has a different size in
arcseconds.

###  3.2 Stacking FIR maps

Astronomical imaging at long wavelengths, such as FIR and sub-millimeter, is
often hindered by high levels of noise. Additionally, the point spread
function (PSF) is large at these wavelengths, which means that individual
sources appear to spread out and blend together. This makes it difficult to
resolve individual sources and determine the fluxes of each source. One way to
overcome this is to use stacking analysis, a technique that utilises the
improved positional accuracy of short-wavelength catalogues from the same
region of the sky as the long-wavelength imaging. These catalogues can be used
to identify the positions of sources that are likely to be present in the
long-wavelength images. Using this positional information, one can extract
fluxes at the prior source positions from the long-wavelength maps. By
averaging the fluxes of many sources together, the stacking process results in
an improved signal-to-noise (S/N) ratio by a factor of $1/\sqrt{N}$, where $N$
is the number of sources averaged and assuming that the individual sources
have the same S/N. This improvement in the S/N ratio makes it possible to
extract information about faint sources that would otherwise be hidden in the
noise, and impossible to detect.

Figure 5: Here we show the radial profiles of various components in the
Herschel SPIRE photometry described by equation 1, by using examples of the
250 and 350 $\mu\mathrm{m}$ stacks at redshift 0.6-0.8 in the first and fourth
luminosity bins (rows) and the third and fourth column of the left panel of
Fig. 4). The original stack is shown in black colour with error bars. The
stack is corrected for stacking bias and this correction is represented by
blue and brown colours respectively. The radial profile of the model fitted to
the stacking bias-corrected stack is shown by the solid red line. We show the
components of this model: the extracted flux, clustering contribution and
constant background by yellow, green and purple colours respectively. The
dotted red colour represents the residual between the bias-corrected stack and
its model.

In our case, we used the prior positions of the UV-selected galaxies from the
UVW1 source list from Sharma et al. (2022). We stack our UVW1 sources on the
(stacking) bias-corrected PACS maps. However, for SPIRE maps, we use the
residual maps coming out of the deblending process, which are corrected for
issues related to confusion noise and clustering. The stacking of residual
maps should give results consistent with the stacking of the actual maps, as
demonstrated by Reddy et al. (2012), with the advantage of a lower noise level
or uncertainty than the stacking of the actual maps.

####  3.2.1 Stacking Process

We take small square sections (“stamps") from the SPIRE and PACS maps at the
predefined location of each UV-selected source. The dimensions of these square
stamps, which are centred on the prior position of each UV-selected source,
are $S$ $\times$ $S$, where $S$ is approximately 5 times the full width at
half-maximum (FWHM) of the corresponding Herschel map. Once the stamps have
been extracted, we then proceed to sort them into UV luminosity bins based on
the UV luminosity function from Sharma et al. (2022). To ensure that our
statistics are robust and reliable, we eliminate bins that contain less than
25 sources. As a result of this process, we are left with a collection of data
cubes, each cube corresponding to a specific bin in the UV LF. Subsequently,
we collapse these data cubes by averaging the pixel values of all the stacked
stamps contained within each bin. This process yields a stacked average image
for every bin.

During this stacking procedure, a rotation of $\pi/2$ clockwise with respect
to the preceding stamp is applied to each stamp, to cancel out any potential
wing-like structures of bright sources located in proximity of the stacked
signal. We repeat this process for the SPIRE (250, 350 and 500
$\mu\mathrm{m}$) and for PACS (100 and 160 $\mu\mathrm{m}$) maps, resulting in
stacked images for each FIR waveband in each UV luminosity bin. Fig. 4 shows
these stacked images for each FIR waveband in the redshift ranges $0.6-0.8$
and $0.8-1.2$, sorted according to their UV luminosities. A clear signal can
be seen at the centres of most stacks.

####  3.2.2 Stacking bias

The stacking procedure, by its very nature, is prone to a certain degree of
bias, particularly toward those sources that are relatively brighter and
situated in regions of the sky that are less densely populated with other
objects. This means that galaxies that are either too faint to be detected or
that are situated in close proximity to a particularly bright source may be
missed during the detection process, resulting in their exclusion from the
stacked source list. As a result, the average background in the local vicinity
is likely to be underestimated during the photometry of the stacks, which in
turn can cause an overestimation of the flux density. This issue is closely
related to the problem of catalogue completeness and is particularly
pronounced for the faintest UV luminosity bins. In order to rectify this
issue, we can make use of the completeness simulation (as described in section
3 of Sharma et al., 2022) that was implemented during the creation of the UVW1
source list that is to be stacked. By stacking the sources that were recovered
through our completeness simulations on the FIR maps, we can create correction
maps. These correction maps can then be subtracted from the stacks to account
for the local background that is lost due to the stacking bias.

Table 2: The flux densities we obtain for the Herschel PACS and SPIRE bands
after making the clustering correction in section as explained in section 3.2.
We ignore UV luminosity bins with $<$ 25 sources. The top half of the table
corresponds to the redshift bin 0.6-0.8, and the bottom half represents the
bin 0.8-1.2.

# | ${}^{a}L_{\mathrm{FUV}}$ | $S_{100\,\mu\mathrm{m}}$ | $S_{160\,\mu\mathrm{m}}$ | $S_{250\,\mu\mathrm{m}}$ | $S_{350\,\mu\mathrm{m}}$ | $S_{500\,\mu\mathrm{m}}$
---|---|---|---|---|---|---
sources | ($\times 10^{10}\,\mathrm{L_{\odot}}$) | (mJy) | (mJy) | (mJy) | (mJy) | (mJy)
53 | $1.98\pm 0.40$ | $1.96\pm 0.55$ | $4.22\pm 0.98$ | $3.08\pm 0.58$ | $1.86\pm 0.49$ | $1.05\pm 0.31$
111 | $1.33\pm 0.27$ | $1.44\pm 0.32$ | $2.19\pm 0.62$ | $1.86\pm 0.33$ | $1.27\pm 0.26$ | $1.04\pm 0.28$
135 | $0.89\pm 0.17$ | $0.94\pm 0.18$ | $0.95\pm 0.57$ | $1.41\pm 0.33$ | $0.84\pm 0.27$ | $0.34\pm 0.12$
159 | $0.59\pm 0.12$ | $0.72\pm 0.17$ | $1.80\pm 0.44$ | $1.46\pm 0.23$ | $1.30\pm 0.22$ | $0.70\pm 0.17$
66 | $0.40\pm 0.08$ | $0.61\pm 0.20$ | $0.73\pm 0.67$ | $1.23\pm 0.47$ | $1.15\pm 0.39$ | $0.61\pm 0.19$
25 | $4.44\pm 0.90$ | $0.75\pm 0.33$ | $<2.16$ | $1.94\pm 0.57$ | $1.57\pm 0.43$ | $0.41\pm 0.36$
85 | $2.97\pm 0.60$ | $1.04\pm 0.24$ | $1.81\pm 0.63$ | $1.96\pm 0.36$ | $1.61\pm 0.28$ | $0.64\pm 0.23$
115 | $1.98\pm 0.40$ | $0.96\pm 0.25$ | $2.54\pm 0.68$ | $1.57\pm 0.29$ | $1.78\pm 0.29$ | $0.89\pm 0.23$
165 | $1.33\pm 0.27$ | $0.64\pm 0.18$ | $0.98\pm 0.42$ | $1.49\pm 0.22$ | $0.94\pm 0.21$ | $0.73\pm 0.17$
111 | $0.89\pm 0.17$ | $0.33\pm 0.19$ | $<0.86$ | $0.93\pm 0.22$ | $0.51\pm 0.27$ | $0.32\pm 0.23$
25 | $0.59\pm 0.12$ | $0.44\pm 0.33$ | $1.23\pm 0.81$ | $0.96\pm 0.33$ | $0.37\pm 0.24$ | …

$a$The bin centers of the UV LF of Sharma et al. (2022).

####  3.2.3 Stacked Photometry

The process of creating the maps using the Herschel-PACS and Herschel-SPIRE
instrumentation is carried out through the use of various pipelines and
techniques, which are independently developed and implemented by separate
teams. As a result of these distinct methods, the maps produced by these
instruments exhibit variations in their units and calibrations. So, in order
to extract accurate flux densities from the PACS and SPIRE stacks, different
approaches are employed.

The aperture photometry technique is particularly well-suited for the
Herschel-PACS maps, as they are provided in Jy/pixel units. This technique
involves measuring fluxes by using a circular aperture of a certain size to
enclose the source of interest and integrate its pixel values. For the 100
$\mu\mathrm{m}$ maps, we use an aperture radius of 7.2 arcseconds, while for
the 160 $\mu\mathrm{m}$ maps, we use a radius of 12 arcseconds. This happens
because the size of the PSF varies between the different bands and the
aperture size needs to be adjusted accordingly. However, it is important to
note that these extracted fluxes are not necessarily the true fluxes of the
sources. To correct this, we apply corrections for the fraction of the PSF
that falls outside the aperture and for any losses resulting from high-pass
filtering of the data. These corrections are determined using empirical
results from the PEP Data Release 1 (DR1)
notes333https://www.mpe.mpg.de/resources/PEP/DR1_tarballs/readme_PEP_global.pdf.

Figure 6: IR SED fits for the redshift bins $0.6-0.8$. Each panel represents
the UV luminosity bins from brightest to the faintest (from a to e). The UV
luminosity of each UV LF bin is labelled at the bottom-left of each panel. The
black hollow circles show the FIR flux densities from Herschel PACS at 100 and
160 $\mu\mathrm{m}$ and Herschel SPIRE at 250, 350 and 500 $\mu\mathrm{m}$.
The red curve represents the best fit Boquien & Salim (2021) template to the
FIR data. The shaded region represents the range of templates within the
$|\chi^{2}-\chi^{2}_{\mathrm{min}}|\leq 1$. The grey curve is the best fit
modified black body curve. The estimates for the dust temperature and the
integrated IR luminosity are labelled at the top-left of each panel. Note that
the IR luminosity on the x-axis is in $\nu L\nu$. Figure 7: IR SED fits for
the redshift bins $0.8-1.2$. Each panel represents a luminosity bin, going
from the brightest to the faintest UV luminosity (a-f for $z=0.8-1.2$), also
labelled at the bottom-left of each panel. The colour coding is the same as in
Fig. 6. The dust temperature and the integrated IR luminosity are labelled at
the top left of each panel.

The SPIRE maps are expressed in units of Jy/beam, making PSF fitting an
effective method for determining the photometry of these stacks. This involves
determining the flux densities of the SPIRE stacks which are equal to the peak
of the PSF models fitted to the central pixels of the stacks. However, it is
important to note that the SPIRE stacks can be susceptible to clustering
effects, which can result in confusion and overestimation of the stacked
photometry. To mitigate this, we use a deblending approach (in section 3) that
enables us to overcome the confusion limit and minimize the clustering
contribution from sources present in the prior catalogue. However, while
stacking on deblended residual images reduces the flux contribution of bright
off-centre sources in the prior catalogue, this method does not take into
account the clustering of objects that are not part of the prior catalogue or
are too faint to be detected in our residual maps. Such sources might be
clustered in the IR imaging along with our UV-selected galaxies. This inherent
clustering of sources can still result in an overestimation of the stacked
photometry. To solve this problem, a method prescribed by Béthermin et al.
(2010) is used. The method involves fitting the final stack as a linear sum of
the PSF and its convolution with the angular correlation function. This is
expressed mathematically as follows:

$\mathcal{S}(\theta,\phi)+\mathcal{B}\,=\,\alpha\times\mathcal{P(\theta,\phi)}\,+\,\beta\times\
\left[\mathcal{P}(\theta,\phi)\,\ast\,\mathit{w}(\theta,\phi)\right].$ (1)

Here, $\mathcal{S}(\theta,\phi)$ represents the stacked stamp,
$\mathcal{P(\theta,\phi)}$ represents the PSF, and $\mathit{w}(\theta,\phi)$
represents the angular correlation function of the galaxies under
consideration. The fixed background level is represented by $\mathcal{B}$. The
best-fit values for $\alpha$, $\beta$ and $\mathcal{B}$ are found for each FIR
band and UV luminosity bin, and the value of $\alpha$ is considered to be the
final flux value for each SPIRE stack. This method provides a more
comprehensive approach to account for the inherent clustering of sources and
ensures more accurate photometry results.

In Fig. 5 an example of this process is shown for 250 and 350 $\mu\mathrm{m}$
maps, in the first and fourth luminosity bins in the redshift range $0.6-0.8$.
For this particular example, we find that clustering contributions are 18.8
and 27.3 per cent of the actual flux in the first and fourth luminosity bins
for the 250 $\mu\mathrm{m}$ map. Corresponding values for the 350 map are 22.6
and 15.0 per cent. The average value of this fraction, for the 250, 350 and
500 $\mu\mathrm{m}$ maps were found to be 16, 18 and 22 per cent respectively
in the redshift bin $0.6-0.8$ and 14, 6 and 41 per cent respectively in the
redshift bin $0.8-1.2$.

####  3.2.4 Errors

We use standard bootstrap to calculate the statistical errors on stacked flux
densities in each bin. In each bin, N stamps are selected at random with
replacement and stacked. The flux densities are calculated from these error
stacks in the same fashion as the original stacks (i.e. aperture photometry
for PACS and PSF photometry for SPIRE). Using 1000 bootstraps, we calculate
the 68 per cent confidence intervals around the measured values. In Table 2 we
show the resulting average fluxes extracted from the stacks at all FIR bands
considered in this study.

###  3.3 IR SED fits

Now that we have obtained the stacked photometry for our galaxy sample, the
next task is to extract the average IR properties from the stacked flux
densities. We fit two different types of model to the SEDs, one for
determining the IR luminosity and the other for the dust temperatures.

To estimate the total IR luminosity, we fit FIR model templates to our
dataset. Specifically, we utilised the two-parameter dust templates from
Boquien & Salim (2021). These templates are parameterised in the total IR
luminosity and specific star-formation rate, and they are built upon
physically motivated dust models by Draine & Li (2007). These templates are
well suited to star-forming galaxies in the luminosity range of our sample.
The resulting fits are shown in Figs. 6 and 7. We measure the integrated IR
luminosity by integrating the rest-frame flux density from 8 to 1000 $\mu$m
range, determining the fluxes, and subsequently employing the luminosity
distance to calculate the IR luminosity

$L_{\mathrm{8-1000\mu\mathrm{m}}}=\,4\,\pi\,d^{2}_{\mathrm{L}}\left(z\right)\,\int_{\nu_{1}}^{\nu_{2}}\,S_{\nu}\,\mathrm{d}\nu$
(2)

where $\nu_{1}$ and $\nu_{2}$ are the rest-frame frequencies corresponding to
$8-1000\,\mu$m limit and $d_{\mathrm{L}}$ is the luminosity distance.

We determine the dust temperatures by fitting the isothermal grey bodies. Most
of the FIR originates from large grains that radiate as isothermal grey bodies
at temperatures $10-50$ K and are in equilibrium with the ambient interstellar
radiation field. An isothermal black-body model can be adjusted to account for
variable source emissivities and opacities, resulting in a grey-body or
modified black-body model. It takes the form,

$S(\nu)\propto\,\nu^{\alpha}\,B_{\nu}(T_{\mathrm{d}})=\,\frac{\nu^{\alpha+3}}{\mathrm{exp}\displaystyle\left(\frac{h\nu}{k_{B}T_{\mathrm{d}}}\right)-1}$
(3)

for the approximation of optically thin media. Here $\alpha$ is the source
emissivity and $T_{\mathrm{d}}$ is the characteristic dust temperature. The
typical values of $\alpha$ fall within the range of 1.5 to 2 (Blain et al.,
2003; Chapin et al., 2011; Casey et al., 2011; Viero et al., 2012) and for
this work we use $\alpha=1.5$ following Blain et al. (2003); Casey et al.
(2011). We fit these grey bodies to our stacked SEDs, with the amplitude and
the dust temperature as the free parameters.

###  3.4 Star Formation Rate

The integrated IR luminosity calculated from the IR templates and the UV
luminosity can be used to calculate obscured and un-obscured SFR respectively
by using the following scaling relation (Kennicutt, 1998; Murphy et al., 2011;
Kennicutt & Evans, 2012),

$\log\left(\frac{\mathrm{SFR}_{\mathrm{FUV}}}{M_{\odot}\,\mathrm{yr}^{-1}}\right)=\,\log\left(\frac{L_{\mathrm{FUV}}/\nu_{\mathrm{FUV}}}{\mathrm{ergs}\,\mathrm{s}^{-1}\,\mathrm{Hz}^{-1}}\right)-27.85$
(4)

assuming a continuous and constant SFR with the Salpeter (1955) initial mass
function (IMF) over timescales longer than $10^{8}$ yr and a mass range from
0.1 to 100 $M_{\odot}$ and

$\log\left(\frac{\mathrm{SFR}_{\mathrm{FIR}}}{M_{\odot}\,\mathrm{yr}^{-1}}\right)=\,\log\left(\frac{L_{\mathrm{FIR}}}{\mathrm{ergs}\,\mathrm{s}^{-1}}\right)-43.41$
(5)

assuming continuous bursts from 10 to 100 Myr, adopting the Kroupa (2001) IMF.
Total SFR ($\mathrm{SFR}_{\mathrm{Tot}}$) is obtained as the sum of the
contributions from the luminosities of FIR ($\mathrm{SFR}_{\mathrm{FIR}}$) and
FUV ($\mathrm{SFR}_{\mathrm{FUV}}$). The $\mathrm{SFR}_{\mathrm{FUV}}$ value
based on the Salpeter (1955) IMF is transformed into the equivalent value
corresponding to the Kroupa (2001) IMF through a multiplication by a factor of
1.8.

Table 3: The main results of this chapter are summarised in this table. The
first three columns show the number of sources, the central luminosity of the
UV luminosity bins, and the median UV luminosity of the sources inside a
particular bin. The fourth and fifth columns show the total IR luminosity and
the dust temperatures from the IR template and MBB fits. The sixth column
shows the dust attenuation in UV magnitudes. the last two columns show the SFR
estimated from the IR luminosity and the total SFR calculated as the sum of
the IR and UV components. The top and bottom halves of the table correspond to
the redshift bins 0.6-0.8 and 0.8-1.2 respectively.

# | ${}^{a}L_{\mathrm{FUV}}$ | ${}^{b}L_{\mathrm{FUV}}$ | $L_{\mathrm{IR}}$ | $T_{\mathrm{dust}}$ | $A_{\mathrm{FUV}}$ | $\mathrm{SFR}_{\mathrm{FIR}}$ | $\mathrm{SFR}_{\mathrm{FIR+FUV}}$
---|---|---|---|---|---|---|---
sources | ($\times 10^{10}\,\mathrm{L_{\odot}}$) | ($\times 10^{10}\,\mathrm{L_{\odot}}$) | ($\times 10^{10}\,\mathrm{L_{\odot}}$) | (K) |  | $(\mathrm{M_{\odot}}\,\mathrm{yr}^{-1})$ | $(\mathrm{M_{\odot}}\,\mathrm{yr}^{-1})$
53 | $1.98\pm 0.40$ | $1.95\pm 0.24$ | $6.30\pm 0.67$ | $30.93\pm 2.70$ | $1.15\pm 0.39$ | $9.42\pm 1.00$ | $15.18\pm 2.33$
111 | $1.33\pm 0.27$ | $1.31\pm 0.15$ | $4.09\pm 0.42$ | $31.28\pm 2.20$ | $1.13\pm 0.38$ | $6.11\pm 0.64$ | $9.97\pm 1.54$
135 | $0.89\pm 0.17$ | $0.89\pm 0.10$ | $2.73\pm 0.35$ | $31.98\pm 1.79$ | $1.13\pm 0.39$ | $4.08\pm 0.52$ | $6.66\pm 1.07$
159 | $0.59\pm 0.12$ | $0.60\pm 0.07$ | $2.63\pm 0.44$ | $27.88\pm 3.68$ | $1.39\pm 0.57$ | $3.87\pm 0.66$ | $5.59\pm 0.91$
66 | $0.40\pm 0.08$ | $0.41\pm 0.04$ | $2.14\pm 0.65$ | $27.04\pm 4.13$ | $1.53\pm 0.84$ | $3.08\pm 0.97$ | $4.23\pm 1.06$
25 | $4.44\pm 0.90$ | $4.43\pm 0.58$ | $6.49\pm 1.54$ | $32.16\pm 3.39$ | $0.68\pm 0.26$ | $9.71\pm 2.30$ | $22.60\pm 5.23$
85 | $2.97\pm 0.60$ | $2.92\pm 0.31$ | $8.07\pm 1.01$ | $33.82\pm 2.00$ | $1.04\pm 0.35$ | $12.07\pm 1.50$ | $20.69\pm 3.49$
115 | $1.98\pm 0.40$ | $2.02\pm 0.21$ | $7.49\pm 1.02$ | $33.25\pm 2.11$ | $1.28\pm 0.47$ | $11.20\pm 1.52$ | $16.96\pm 2.60$
165 | $1.33\pm 0.27$ | $1.33\pm 0.16$ | $5.08\pm 0.76$ | $31.61\pm 3.22$ | $1.29\pm 0.49$ | $7.60\pm 1.13$ | $11.45\pm 1.81$
111 | $0.89\pm 0.17$ | $0.92\pm 0.10$ | $2.84\pm 0.72$ | $31.28\pm 7.09$ | $1.16\pm 0.52$ | $4.25\pm 1.07$ | $6.82\pm 1.42$
25 | $0.59\pm 0.12$ | $0.64\pm 0.05$ | $3.58\pm 1.26$ | $36.63\pm 3.52$ | $1.66\pm 0.98$ | $5.36\pm 1.88$ | $7.07\pm 1.98$

$a$The bin centers of the UV LF in Sharma et al. (2022). These values are used
as labels.

$b$Mean of the UV luminosity of the sources inside the UV LF bins. We use
these values for all the calculations in this paper.

###  3.5 Dust Attenuation

Using the IR and UV luminosities, we calculate the IRX (Meurer et al., 1999),
such that $\mathrm{\mathrm{IRX}}=L_{\mathrm{IR}}/L_{\mathrm{UV}}$. Different
relations are used in the literature (Meurer et al., 1999; Seibert et al.,
2005; Hao et al., 2011; Nordon et al., 2013) to convert the $\mathrm{IRX}$
ratio into the dust attenuation in the UV luminosity. For the sake of
comparison, we apply the relation commonly used in previous studies (e.g.
Nordon et al., 2013; Heinis et al., 2013; Álvarez-Márquez et al., 2016),

$A_{\mathrm{FUV}}=\,2.5\log\ \left(1+0.59\times\mathrm{IRX}\right).$ (6)

This can be used to correct for the UV light absorbed by the dust and
calculate the total SFR in the next section. In order to make this correction
to the unobscured SFR we use the relation from Nordon et al. (2013) given by

$\log\left(\mathrm{SFR}_{\mathrm{Tot}}\right)=\,\log\left({\mathrm{SFR}_{\mathrm{FUV}}}\right)+0.4\times
A_{\mathrm{FUV}}$ (7)

##  4 Results

Figure 8: Dust temperature as a function of total IR luminosity, redshift and
UV luminosity. Left panel: dust temperature in logarithmic IR luminosity bins.
The results from this work at redshifts bins centred at 0.7 and 1.0 are shown
in blue and red circles, respectively. For comparison, we also plot the
literature results from Magdis et al. (2012) as green diamond symbols. The
solid and hollow symbols represent the values from stacking analysis and
individual star-forming galaxies, respectively. The grey squares represent the
median temperatures of the IR-selected galaxies from Symeonidis et al. (2013).
The hollow squares represent the values for the galaxies in their local sample
($z<0.1$). The yellow triangles represent the results for the $H_{\alpha}$
selected samples from Thomson et al. (2017). Middle panel: average temperature
as a function of the redshift. The solid circles in black show the values
obtained in this work by luminosity weighing the temperatures in redshift bins
centred at 0.7 and 1.0. We show the redshift weighted mean dust temperature of
the galaxies in the local universe from Hwang et al. (2010) as a pink downward
triangle. The brown stars and purple pentagons represent the estimates from
Béthermin et al. (2015) and Schreiber et al. (2018). These values are taken
from the compilation of Bouwens et al. (2020). The grey shaded area shows the
fit from Bouwens et al. (2020). The dashed black line is the predicted trend
for the $T_{\mathrm{d}}-z$ relation from Liang et al. (2019). Right panel:
dust temperature of the grey body fits as a function of UV luminosity. The
blue and red histograms represent the distributions of the star-forming
galaxies in the UV luminosity space for redshift bins centred at 0.7 and 1.0
respectively. The y-axis on the right represents the number of sources. The
data points share the redshift colour scheme with the histograms.

We are stacking maps of FIR emission obtained from Herschel on ultraviolet
(UV) selected sources that lie in the redshift range of 0.6 to 1.2. To
determine the average stacked photometry in the FIR for these sources, we fit
the IR model templates from Boquien & Salim (2021) and integrating the results
over the wavelength range of 8 to 1000 $\mu\mathrm{m}$. The results indicate
that the typical IR luminosities of the stacked galaxies fall within the range
of $2.15\text{\times}{10}^{10}$ $\mathrm{L_{\odot}}$ to
$6.30\text{\times}{10}^{10}$ $\mathrm{L_{\odot}}$ at redshift 0.7 and
$3.58\text{\times}{10}^{10}$ $\mathrm{L_{\odot}}$ to
$6.49\text{\times}{10}^{10}$ $\mathrm{L_{\odot}}$ at redshift 1.0. On average,
our sample is composed of galaxies belonging to the normal (sub-luminous;
$L_{\mathrm{IR}}<10^{11}{\mathrm{L}_{\odot}}$) infrared galaxies.

In order to obtain the average dust temperatures, we fit isothermal grey
bodies to the average FIR photometry in each UV luminosity bin. These
temperatures are presented in the left panel of Fig. 8 as functions of IR
luminosity. Additionally, we have plotted the luminosity-weighted dust
temperatures as a function of redshift in the middle panel of Fig. 8, along
with literature values for comparison. The individual temperatures, as
calculated in the UV Luminosity Function (UV LF) bins, are shown as a function
of UV luminosity in the right panel of Fig. 8.

Using the estimated FIR luminosities, we have calculated the IRX in each UV
luminosity bin. In Fig. 9, we have plotted the average value of $\mathrm{IRX}$
as a function of redshift. $\mathrm{IRX}$ as a function of FIR and FUV
luminosities is plotted in Fig. 10 and Fig 11. The top panel of Fig 11 also
shows the UV LF from Sharma et al. (2022). This dust attenuation
($A_{\mathrm{FUV}}$) in the UV radiation is parametrised in terms of the
$\mathrm{IRX}$ ratio, as described by equation 6, and labelled as the
secondary y-axis on the right-hand side of the panels in Figs. 9 and 10. We
estimate the SFR of our galaxies in section 3.4, and present the results in
Fig. 12 comparing the estimates from the UV and IR luminosities as well as the
total SFR. Then in Fig. 13, we show $\mathrm{IRX}$ as a function of the total
SFR.

Finally, we use these values of $A_{\mathrm{FUV}}$ to correct the SFR density
(SFRD), which is calculated from dust-attenuated UV radiation. The SFRD is
estimated from the luminosity density estimates as explained in section 3.4,
where the estimates for luminosity density calculated using rest-frame UV
radiation come from Sharma et al. (2022). In Fig. 14, we present the estimates
for the total SFRD after it has been corrected for dust attenuation, providing
a more accurate picture of the star formation activity in these galaxies.

##  5 Discussion

The aim of this paper is to study the dust properties of UV-selected galaxies
in the redshift range of 0.6-1.2. The galaxies selected through the UVW1
filter on XMM-OM are stacked on the FIR imaging from Herschel PACS and SPIRE
instruments, and the dust properties are constrained in UV luminosity bins of
the UV LF in the same redshift range. We considered only luminosity bins with
at least 25 sources in each redshift bin (at 0.7 and 1.0), in order to have
robust statistics.

###  5.1 Dust Temperature and Infrared Luminosities

We start with the dust temperature and total IR luminosities of galaxies and
explore their correlation if any. The relationship between dust temperature
and IR luminosity pertains to the physical conditions within star-forming
regions, from which the IR emission originates. In this context, higher
temperatures indicate either more compact or more luminous star-forming
regions. The equilibrium temperature essentially depends on the UV flux that
impinges on the dust grains. A correlation between dust temperature and IR
luminosity has been observed in some previous studies (e.g. Soifer et al.,
1987; Dunne et al., 2000; Dale et al., 2001; Chapman et al., 2003; Symeonidis
et al., 2009; Magnelli et al., 2014) and it is suggested to be likely a result
of the transition of galaxies into starburst phase (Magnelli et al., 2014).

In our study, we use the isothermal graybody and IR model templates to fit the
stacked Herschel PACS and SPIRE photometry, allowing us to calculate the dust
temperature and IR luminosities. Our results are directly comparable to other
studies in the literature that have adopted similar definitions of dust
temperature and used MBBs for calculations. However, if a different definition
or technique is used, it will be specifically noted. Our findings do not
suggest any significant trend in the dust temperature with the IR luminosity
for a fixed redshift (as seen in the left panel of Fig. 8).

If averaged over the UV LF bins, the average temperature increases very
slightly with redshift within the range explored in this study. However, the
difference is not very significant. If we include measurements at other
redshifts from previous studies (from redshift 0.15-1.5; Magdis et al., 2012;
Symeonidis et al., 2013; Béthermin et al., 2015; Thomson et al., 2017;
Schreiber et al., 2018), there is an apparent weak trend, which is also
confirmed by the fit from Bouwens et al. (2020). The fit is mainly driven by
values from Béthermin et al. (2015) and Schreiber et al. (2018), but as we can
see (middle panel of Fig. 8) it is also somewhat consistent with other works
considered in our study. The values seem to be in agreement with these
previous studies and the fit from Bouwens et al. (2020). In the same plot, we
show the trend found by Liang et al. (2019) for galaxies at redshifts 2 and
higher, extrapolated to redshift 0.01. This trend is offset towards lower
temperatures from the values obtained in this and previous works. We compare
our results with the values of dust temperature calculated by Hwang et al.
(2010) and Symeonidis et al. (2013) for their samples of IR galaxies. About 90
per cent of Hwang et al. (2010) galaxies have
$\mathrm{log}(L_{\mathrm{IR}}/\mathrm{L_{\odot}})\leq 11.2$, which is roughly
the upper limit of the highest IR luminosity bin. They estimated the median
dust temperature to be 28.98 K, with a 16-84th percentile range of 24.78 K to
37.13 K. These values as a function of the median redshift of the galaxies are
plotted in the middle panel of Fig. 8 along with the mean dust temperature for
the Symeonidis et al. (2013) local sample. Upon comparison, it can be seen
that the average dust temperature does not evolve significantly from redshift
1 to the present time.

Figure 9: Here we show the $\mathrm{IRX}$ ratio as a function of redshift. On
the right side of the panel, we plot the attenuation $A_{\mathrm{FUV}}$ in the
UV radiation due to dust, which is parameterised as a function of the
$\mathrm{IRX}$. The blue and red solid circles show the values obtained in
this work. The hollow circular symbols represent the literature estimates from
Xu et al. (2007), Heinis et al. (2013), Reddy et al. (2018) and Burgarella et
al. (2013) in yellow, black, green and purple colours respectively. The pink
hollow circles represent the subset of Reddy et al. (2018) sample, referred to
as “Red" galaxies. The redshift 0 data from Xu et al. (2007) and Burgarella et
al. (2013).

Despite a lot of effort, determining the precise relationship between dust
temperature and redshift is a difficult task, especially in light of recent
results, which often appear contradictory. Some studies observe that the dust
temperature increases from the local universe to high redshifts (e.g. Magdis
et al., 2012; Magnelli et al., 2014; Béthermin et al., 2015; Schreiber et al.,
2018). Conversely, others argue for a colder dust temperature at higher
redshifts (e.g. Chapman et al., 2002; Hwang et al., 2010; Symeonidis et al.,
2009, 2013; Kirkpatrick et al., 2012, 2017). There is a third group of studies
that find no compelling evidence for a redshift-dependent evolution of dust
temperature (e.g. Casey et al., 2018; Drew & Casey, 2022). These conflicting
outcomes can be partly attributed to selection bias in flux-limited samples
(Liang et al., 2019), as well as to the influence of various factors capable
of significantly affecting dust temperature. These factors include, but are
not limited to, the specific SFR (Magnelli et al., 2014), the amount and
opacity of dust, the gas metallicities etc. (Liang et al., 2019). In fact, the
correlation between dust temperature and specific SFR is suggested to be more
robust and statistically significant than that with redshift (Magnelli et al.,
2014; Schreiber et al., 2018). Our results for the UV-selected galaxies agree
with the findings of the third group of studies mentioned above. However, we
remark here that all of these studies are conducted on IR-selected galaxies
samples.

The dust temperature and UV luminosity, are plotted in the right panel of Fig.
8. From the plot, we observe a modest correlation between these two parameters
only for redshift 0.7. The Spearman correlation coefficients for these
variables are 0.60 and -0.03, at redshifts of 0.7 and 1.0; however, the
significance for any correlations are very low.

###  5.2 Dust Attenuation

The $\mathrm{IRX}$, which is a ratio of total IR to UV luminosity, is commonly
used to estimate the amount of dust attenuation of UV light. We calculated the
median dust attenuation values to be 1.15 and 1.22 magnitudes (equivalent to
IRX of 3.17 and 3.49) in the redshifts bins centered at 0.7 and 1.0
respectively. These values suggest that the dust content of our galaxies does
not change significantly over this redshift range.

Figure 10: We plot the $\mathrm{IRX}$ ratio as a function of FIR luminosity in
this figure. The symbols and colour coding is the same as in Fig. 9. We plot
the individual galaxies in the nearby universe, from the NUV selected sample
(with a median redshift of 0.013) from Iglesias-Páramo et al. (2006) as grey
hollow squares, in addition to other literature values mentioned in Fig. 9.

As depicted in Fig. 9, the average dust attenuation appears to remain constant
from the local Universe up to a redshift of 2.5 (Xu et al., 2007; Heinis et
al., 2013; Burgarella et al., 2013). We note here that Xu et al. (2007) used
24 $\mu$m data to estimate their average dust attenuation, while Burgarella et
al. (2013) used the 60 $\mu$ m LF of Takeuchi et al. (2005) for their $z=0$
estimates. Our results at redshifts of 0.7 and 1.0 are offset below other work
at similar redshifts (Xu et al., 2007; Burgarella et al., 2013), but are in
good agreement with studies in the local Universe (Burgarella et al., 2013) or
redshifts higher than those explored in our study (Burgarella et al., 2013;
Reddy et al., 2018).

We do observe a weak trend between the dust attenuation and the total IR
luminosity for our UV-selected galaxies in the redshift range $0.6-1.2$ (Fig.
10), wherein the dust attenuation decreases with IR luminosity at redshifts
0.7 and 1.0. The correlation coefficients are -0.61 and -0.43. However, these
correlations have low significance (p values of 0.28 and 0.36 at z = 0.7 and
1.0), and the range of IR luminosities of our galaxies is not wide enough to
draw any definitive conclusions.

Previous studies at redshifts ranging from 0.6 to 3 do not report any trends
with IR luminosity (Xu et al., 2007; Heinis et al., 2013; Álvarez-Márquez et
al., 2016; Reddy et al., 2018). In Fig. 10, we plot the NUV-selected galaxies
from GALEX surveys in the local Universe of Iglesias-Páramo et al. (2006), who
used the IRAS 60 $\mu$m data to estimate $L_{\mathrm{IR}}$. Their galaxies
follow a relation (grey dashed line in Fig. 10), obtained by Bell (2003) for a
local compilation which contains sources from the literature with FUV,
optical, IR (60 and 100 $\mu$m) and radio wavelengths. The local galaxies thus
show a correlation wherein galaxies with high IR luminosity are more dust
attenuated, which is expected as the increased dust attenuation results in a
larger fraction of UV radiation being absorbed by dust, consequently leading
to a higher IR luminosity. It is interesting why this behaviour stops as we go
past redshift 0.6. The majority of galaxies in the local datasets described in
Iglesias-Páramo et al. (2006) and Bell (2003) do not appear to exceed a
luminosity of $2\times 10^{11}\mathrm{L_{\odot}}$. Below this IR luminosity,
the results from the local samples of Bell (2003), Iglesias-Páramo et al.
(2006), and the high redshift values from the literature are consistent.
However, above this limit, there seems to be a noticeable discrepancy. The
discrepancy may imply that the Bell (2003) relation does not apply beyond the
luminosity range of local galaxies from which it was derived, although it is
also possible that the relationship between IRX and IR luminosity may change
with redshift. The range of IR luminosities in our sample closely resembles
that of the local datasets. However, our findings align with local results
only at IR luminosities below $5\times 10^{10}\mathrm{L_{\odot}}$. As
luminosity increases, our results begin to deviate from the Bell (2003) curve
and other high redshift measurements.

Figure 11: The $\mathrm{IRX}$ ratio as a function of UV luminosity. In the top
panel we show the values calculated in our study as blue and red solid circles
at redshifts 0.7 and 1.0. We also show the UV luminosity function of galaxies
at redshifts 0.7 (blue) and 1.0 (red) from Sharma et al. (2022) over-plotted
on the $\mathrm{IRX}$ ratio with the values marked on the y-axis in the right.
The bottom panel shows our IRX values along with the results from the
literature. The symbols and colour coding is the same as in Figs. 9 and 10.

In Fig. 11, we present the relationship between $\mathrm{IRX}$ and UV
luminosity. We observe a trend in both redshift ranges for IRX to be smaller
at higher luminosities. The Spearman correlation coefficients are -0.6 and
-0.8 (with p-values of 0.28 and 0.04) at redshifts of 0.7 and 1.0.

In the existing literature, various studies have proposed different
behaviours. There are studies using UV selection from the local universe up to
redshift 8, which report a decreasing trend of $\mathrm{IRX}$ with increasing
$L_{\mathrm{UV}}$ (e.g. Buat et al., 2009; Bouwens et al., 2009; Kurczynski et
al., 2014). Some others report a flat $\mathrm{IRX}-L_{\mathrm{UV}}$
relationship for UV-selected galaxies with average redshifts in the range
$0.6-2$ (e.g. see Xu et al., 2007; Heinis et al., 2013) and for Lyman-break
galaxies with average redshifts from 2 to 8 (see Wilkins et al., 2011; Bouwens
et al., 2012; Álvarez-Márquez et al., 2016; Reddy et al., 2018). We remark
here that Bouwens et al. (2009, 2012), Wilkins et al. (2011), and Kurczynski
et al. (2014), used the UV spectral slope to estimate the dust attenuation,
and the results of Buat et al. (2009) were based on rather uncertain mid-IR to
total-IR calibrations.

Our average IRX values within the two redshift bins ($0.6-0.8$ and $0.8-1.2$)
are lower than those reported in previous stacking studies conducted at
different redshifts, specifically at $z=0.6$ (Xu et al., 2007), $z=1.5$
(Heinis et al., 2013) and $z=3.0$ (Álvarez-Márquez et al., 2016). Furthermore,
comparing to the results of (Xu et al., 2007), who stacked the local ($z=0$)
UV-selected sample of Iglesias-Páramo et al. (2006), we observe that their
average IRX value is also higher than what we find in both our redshift bins
(Figs. 10 and 11). A similar observation was made by Reddy et al. (2018),
using a sample that is dominated by blue ($\beta\leq-1.4$) star-forming
galaxies at redshift $\sim 2$. Our average results at redshifts 0.7 and 1.0
tend to align more closely with the values reported by Reddy et al. (2018)
than the other studies.

The discrepancies in the behaviour of the $\mathrm{IRX}-L_{\mathrm{UV}}$
relation are often attributed to the way samples are selected (Buat et al.,
2007a). UV-selected samples, in particular, tend to favour galaxies with lower
dust content, resulting in most bright UV galaxies having low IR luminosities.
Consequently, $\mathrm{IRX}$ is expected to exhibit a negative correlation
with $L_{\mathrm{UV}}$ for a UV-selected sample. For our case, the downward
trend can be explained if we assume a population of star-forming galaxies and
a distribution of extinction in those galaxies. We would expect the lowest
extinction galaxies to have the largest contribution in the brightest absolute
magnitude bins, so that the balance of absorbed sources, or the typical degree
of extinction, will change as we move from the bright end to the faint end of
the LF.

Figure 12: We plot the SFR as a function of the UV luminosity at redshifts 0.7
and 1.0 respectively in the top and bottom panels of this figure. The
histograms represent the distributions of the star-forming galaxies in the UV
luminosity space with the number of galaxies marked on the y-axis on the right
axis similar to the right panel of Fig 8. The blue and red-filled circles show
the total SFR at redshifts 0.7 and 1.0. The gray-filled triangles show the SFR
from IR luminosity and the lines show the SFR calculated using the UV
luminosity. Figure 13: We plot here the $\mathrm{IRX}$ ratio and the dust
attenuation ($A_{\mathrm{FUV}}$) as a function of the bolometric luminosity
(which is used as a proxy for the total SFR by the studies, we compare our
results to. The red and blue solid circles represent our values at redshift
$0.6-0.8$ and $0.8-1.2$. The green dashed line, grey solid line and yellow
dot-dashed line show the results from Xu et al. (2007); Buat et al. (2007b)
and Reddy et al. (2010). The yellow hollow circles represent the values of
average dust attenuation from Reddy et al. (2012). Figure 14: The SFRD of the
UV-selected star-forming galaxy sample. Our results are presented as black
solid circles. We plot the literature results as blue squares (Cucciati et
al., 2012), purple stars (Burgarella et al., 2013), green diamonds (Hagen et
al., 2015) and yellow triangles showing Moutard et al. (2020) values corrected
for dust attenuation using Le Floc’h et al. (2005). The grey circles represent
dust-corrected UV-based SFRD from the Hopkins & Beacom (2006) compilation.
From this compilation, we plot the SFRD values calculated using the Arnouts et
al. (2005) data in red circles. Trends obtained from Hopkins & Beacom (2006)
and Madau & Dickinson (2014) are shown as solid black and dashed lines,
respectively.

###  5.3 Total star formation rate

We estimate the SFR for our UV-selected sample using equations in section 3.4.
The resulting values of the total SFR, which is the sum of the UV and infrared
components of the SFR
($\mathrm{SFR}_{\mathrm{Tot}}=\mathrm{SFR}_{\mathrm{UV}}+\mathrm{SFR}_{\mathrm{IR}}$),
are shown in Fig. 12 assuming the Kroupa (2001) IMF. For comparison, we have
also plotted the SFR values that were calculated using the UV luminosity
($\mathrm{SFR}_{\mathrm{UV}}$) and the IR luminosity
($\mathrm{SFR}_{\mathrm{IR}}$) separately.

It is evident from Fig. 12 that if we relied solely on the ultraviolet (UV)
indicators, we would be underestimating the mean SFR by approximately a factor
of 3 in redshift bins centered at 0.7 and 1.0, respectively. At redshift 0.7,
the underestimate decreases as the UV luminosity increases. This is expected
behaviour, as we observe the same in the IRX vs ${L_{\mathrm{UV}}}$ plot (Fig.
11).

The difference between UV-derived and total SFR is indicative of the
substantial amount of dust present, which attenuates the UV light, thereby
obscuring the star formation. The relationship between this attenuation and
the SFR shound be worth investigating. Some previous studies using samples
selected using the UV (Buat et al., 2007b; Reddy et al., 2010, 2012), the
Lyman-break (Reddy et al., 2006) and 24 $\mu$m observation (Zheng et al.,
2007) have demonstrated a positive correlation between these two quantities
i.e. higher dust attenuation for higher SFR (or bolometric luminosity).
However, we did not find a significant correlation between these quantities in
either redshift bin in this study: in Fig. 13, apart from a single low
datapoint, IRX appears roughly constant with bolometric luminosity. We also
show results from UV-selected galaxies in the local Universe (Buat et al.,
2007b), at redshift of 0.6 (Xu et al., 2007) and at redshift of 2 (Reddy et
al., 2012). For comparison, the values for Lyman-$\alpha$ galaxies at redshift
2 (Reddy et al., 2010) are also plotted. We can see that the Buat et al.
(2007b) findings also have a flat trend in the luminosity range of our
sources, although their values have a higher normalisation. Among the redshift
bins of our study ($0.6-0.8$ and $0.8-1.2$) we did not observe any significant
change in the dust attenuation given the bolometric luminosity.

###  5.4 The star formation rate density

We calculate the contribution to the SFRD at redshift 0.7 and 1.0 from the UV
sources using our UV-selected galaxy sample. To estimate the SFRD, we use the
UV luminosity density provided by Sharma et al. (2022) at these redshifts,
which is then converted into the SFRD using equation 4, assuming the Kroupa
(2001) IMF. We take into account the impact of dust on the UV estimates and
correct them accordingly by using the dust attenuation inferred from the IRX
ratio (see equation 6 in section 3.5).

Our results are illustrated in Fig. 14 along with previous estimates based on
UV luminosity. We do not find any significant evolution of the SFRD from
redshift 1.0 to 0.7. Compared to previous works such as Arnouts et al. (2005)
and other UV luminosity-based estimates compiled in Hopkins & Beacom (2006),
we observe a good level of agreement at redshifts 0.7 and 1.0. It is worth
noting that this fit is primarily driven by a large number of data points at
redshifts smaller than 0.5, covers a wider range of redshifts, and takes into
consideration the SFRD measured from tracers other than UV. At redshift 0.7,
we notice a deviation of more than $1\sigma$ from the UV compilation of
Hopkins & Beacom (2006) and Moutard et al. (2020). However, our results are
within the error bars of the SFRD calculated using the Arnouts et al. (2005)
results.

We calculate the fraction of obscured star formation, using the obscured to
total star formation ratio, assuming the energy balance argument. These are
estimated to be 65 and 68 per cent at redshifts 0.7 and 1.0, suggesting the
dominance of dust-obscured components in the overall SFRD in these redshift
bins. These figures also imply that the dust content of our galaxies does not
change significantly over this redshift range. Contrasting these results with
those from the local Universe - roughly 75 per cent dust obscured star
formation obtained by Magnelli et al. (2013), it is evident that there is no
significant evolution in the fraction of dust-obscured star formation rate
density from redshift 0 to 0.7, and even further to redshift 1 (Le Floc’h et
al., 2005).

Table 4: The luminosity and SFR density of the UV-selected galaxies from CDFS
at redshifts 0.7 and 1.0.

${}^{a}\langle z\rangle$ | ${}^{b}\mathrm{log}\ \rho$ | ${}^{c}A_{\mathrm{FUV}}$ | ${}^{d}\mathrm{log}\ \dot{\rho}_{*}^{\mathrm{UV}}$ | ${}^{e}\mathrm{log}\ \dot{\rho}_{*}^{\mathrm{corr}}$
---|---|---|---|---
| $(\mathrm{erg}\ \mathrm{s}^{-1}\mathrm{Hz}^{-1}\mathrm{Mpc^{-3}})$ | (mag) | $(\mathrm{M_{\odot}}\ \mathrm{yr}^{-1}\mathrm{Mpc^{-3}})$
0.7 | $26.31_{-0.06}^{+0.07}$ | $1.75$ | $-1.80_{-0.06}^{+0.07}$ | $-1.34_{-0.06}^{+0.07}$
1.0 | $26.43_{-0.12}^{+0.18}$ | $1.70$ | $-1.68_{-0.12}^{+0.18}$ | $-1.19_{-0.12}^{+0.18}$

$a$The center of the redshift bin.

$b$From Sharma et al. (2022).

$c$The median value for all UV luminosity bins.

$d$un-obscured SFRD Calculated from the UV luminosity density using the
Kennicutt (1998) calibration assuming the Kroupa (2001) IMF.

$e$The un-obscured SFRD corrected for the dust attenuation using
$A_{\mathrm{FUV}}$.

The results presented above may not accurately reflect the total star
formation activity in the studied redshift range because of the possibility of
missing heavily obscured systems in our UV selection. It has previously been
shown that these particular galaxies, (U)LIRGs, dominate star formation
activity in the redshift range explored in our study (Le Floc’h et al., 2005).
So, we test whether or not the contribution from bright IR galaxies (which
might not have been detected in our UV-selected catalogue) makes a significant
difference to the SRFD estimated in this study. To estimate the SFRD of these
bright IR galaxies, we used the results from Le Floc’h et al. (2005) and
Magnelli et al. (2013). The study conducted by Le Floc’h et al. (2005)
utilised a sample of 24 $\mu\mathrm{m}$ sources from Spitzer MIPS in CDFS to
determine the IR luminosity function and the total IR luminosity density at
redshift $0\leq z\leq 1$. On the other hand, Magnelli et al. (2013) used
observations of GOODS fields from Herschel PACS to obtain the IR LF and
luminosity density. Both of these studies also provide insight into the
relative contribution of Luminous Infrared Galaxies (LIRGs;
$10^{11}{\mathrm{L}\odot}<L_{\mathrm{IR}}<10^{12}{\mathrm{L}\odot}$; see
Sanders & Mirabel (1996), Ultra-Luminous Infrared Galaxies (ULIRGs;
$10^{12}{\mathrm{L}\odot}<L_{\mathrm{IR}}<10^{13}{\mathrm{L}\odot}$; Sanders &
Mirabel (1996); Genzel et al. (1998)), and the normal (sub-luminous;
$L_{\mathrm{IR}}<10^{11}{\mathrm{L}_{\odot}}$) infrared galaxies. A summary of
their findings is depicted in Fig. 15, which shows reasonable consistency up
to redshift 0.6. However, as we move towards redshift 1, the values obtained
by Le Floc’h et al. (2005) start to deviate slightly above the ones from
Magnelli et al. (2013). It is important to note here that neither of these
studies are corrected for the contribution of the AGN to the IR galaxies, and
AGN are known to have a significant effect on the IR luminosity of galaxies
from local Universe up to a redshift 2.5 (Symeonidis & Page, 2019, 2021).

Figure 15: We compare our results for the SFRD with and without dust
correction. For reference, we also plot the total SFRD calculated from the IR
galaxies from the studies by Le Floc’h et al. (2005) and Magnelli et al.
(2013) as hatched and shaded regions, respectively. These works also
considered the contributions of normal IR galaxies (sub-LIRGs), LIRGs, and
ULIRGs to the total IR luminosity density (and SFRD). Here, we show the total
SFRD from the IR galaxies as green-coloured regions. Contributions from sub-
LIRGs, LIRGs, and ULIRGs are shown as blue, yellow, and red regions. The data
points show the values obtained in this work. The blue hollow circles
represent the unobscured SFRD obtained from the UV luminosity density of
Sharma et al. (2022) without correcting for dust attenuation. The red hollow
circles are the dust-corrected values using the attenuation factor
($A_{\mathrm{FUV}}$) calculated as shown in section 3.5. The red hollow
circles represent the SFRD obtained if we add the contribution of the ULIRGs
from the studies mentioned above to the dust-corrected UV SFRD (black
circles).

We compare the values estimated in our study to the average of these two works
in Fig. 15. The blue circles show our unobscured SFRD calculated from direct
UV observations. It is noteworthy that these values are observed to fall on
the blue-shaded regions, which represent the contribution of sub-LIRGs to the
overall IR contribution. This indicates that our sample may account, to some
extent, for the contribution from these sub-LIRGs observed in the 24
$\mu\mathrm{m}$ and FIR samples of Le Floc’h et al. (2005) and Magnelli et al.
(2013), respectively. This behaviour is somewhat expected, as the IR
luminosities of the majority of our UV-selected galaxies fall within the
range, which is typically associated with the sub-LIRG population. Thus, the
sub-LIRG populations might receive some contribution to the SFRD from the UV-
bright sources. The black hollow circles in Fig. 15 show the dust-corrected
SFRD values. These values are generally consistent with the total IR SFRD
estimates of Le Floc’h et al. (2005) and Magnelli et al. (2013). We added the
average of the (U)LIRGs SFRD from these studies to our dust-corrected UV SFRD
measurements. This yields values (red circles in Fig. 15) that greatly exceed
the total IR luminosity density (and the dust-corrected UV SFRD estimates).
This is an interesting outcome, suggesting that if we consider (U)LIRGs as a
distinct population from our UV galaxies and sum their SFRD values to our
dust-corrected UV SFRD, we arrive at a value much higher than if we were to
correct the UV SFRD for dust extinction using a mean attenuation correction.
This implies that although these populations (ULIRGs and LIRGs) might not be
represented in our sample, we have not missed much extinction from our UV
selection, provided that we account for dust extinction. This holds true
despite the inherent uncertainties associated with attenuating UV galaxies.

##  6 Conclusion

In this work, we investigate the dust properties of a sample of UV-selected
galaxies from the Chandra deep field south (CDFS) in the redshift range
$0.6-1.2$. The sample under consideration comprises 1070 galaxies, with a
magnitude range of $M_{\mathrm{UV}}=[-21.15,-19.0]$, after removing the UV LF
bins containing < 25 sources. This conservative cut makes sure we have robust
enough statistics for our calculations. To assess the average FIR properties
of this UV-selected sample, we make use of the FIR maps of the CDFS, generated
by the Herschel Multi-tiered Extragalactic Survey (HerMES). The FIR maps are
created on the basis of observations from the PACS and SPIRE instruments
onboard Herschel.

We stack the UV sources from the CDFS dataset onto the FIR maps obtained from
Herschel-PACS at 100 and 160 $\mu\mathrm{m}$, as well as Herschel-SPIRE at
250, 350 and 500 $\mu\mathrm{m}$, in order to determine the average flux
densities as a function of the redshift and UV luminosity binned according to
the UV LF of these galaxies. Prior to stacking, we deblend the FIR maps to
mitigate the effects of blending and confusion of sources in the Herschel IR
maps. Using the stacked fluxes, we determined the average dust temperature and
total FIR luminosities (from 8-1000 $\mu\mathrm{m}$) for the galaxies in each
bin of the UV LF. These FIR luminosities, along with the UV luminosities, are
then employed to estimate the dust attenuation of the galaxies and to
characterise the evolution of the comoving SFR density between redshifts
$0.6-1.2$. The primary conclusions derived from our study can be summarised as
follows:

1\. The IR luminosities of our UV-selected sources are on average in the range
$2.15\text{\times}{10}^{10}$ to $6.5\text{\times}{10}^{10}$
$\mathrm{L_{\odot}}$, placing them in the sub-LIRG category. We find that the
typical luminosity-weighted dust temperatures at redshifts 0.7 and 1.0 are
$30.28\pm 1.33$ K and $33.12\pm 1.26$ K, respectively. We have not observed
any significant trends between the average dust temperatures and integrated IR
luminosities of these galaxies at a fixed redshift. Furthermore, our analysis
of the temperature (averaged over the UV LF bins) within the redshift range
explored in our study has revealed no significant variation with redshift.
When we add data from other studies conducted in the redshift range of 0.1 to
1.5, our values agree with a rather weak trend between these parameters
observed in previous studies.

2\. Our UV-selected galaxies have median dust obscuration levels of
$\mathrm{IRX}=3.17\pm 0.52$ and $3.49\pm 0.51$, which correspond to dust
attenuation of $1.15\pm 0.24$ and $1.22\pm 0.23$ magnitudes, at redshifts 0.7
and 1.0, respectively. We did not find any changes in the dust attenuation
within the redshift range covered by our study, which suggests that the dust
content in UV-selected star-forming galaxies does not evolve very much between
redshifts of 1.0 to 0.7. We do observe a pattern in the values of IRX with IR
luminosity, wherein the IRX decreases as the IR luminosity increases for a
constant redshift. However, the trend is very weak and cannot be substantiated
due to the small range of IR luminosities covered in this study. No
significant trends are detected between IRX and redshift at a constant IR
luminosity. However, in the case of local galaxies, there is a positive
correlation between IRX and IR luminosity. We speculate that this difference
may be due to selection bias. We see an increase in IRX with decreasing UV
luminosity.

3\. It is observed that the SFR calculated using UV indicators is
underestimated by a factor of 3 at redshifts of 0.7 and 1.0 compared to the
total SFR. This offset decreases as the UV luminosity increases for both
redshift bins. This indicates that the dust obscuration decreases as the UV
luminosity of the galaxies increases, within the range analysed in this study.
It has also been found that the relationship between IRX and bolometric
luminosity remains unchanged from redshift 1 to 0.7. The IRX exhibits a
roughly constant trend with increasing bolometric luminosity, which is in
agreement with the local relations for UV-selected galaxies, where these
quantities show a weak correlation within the luminosity range of our sources.
Overall, the results are consistent with the proposed picture from previous
studies that the UV-selected galaxies at higher redshifts exhibit a lesser
degree of dust attenuation at a fixed bolometric luminosity compared to those
in the local Universe. However, we did not observe any evolution of the dust
attenuation at a given bolometric luminosity from redshift 0.7 to 1 in our
sample.

4\. We did not find any significant change in the SFR density with the
redshift changing from 1.0 to 0.7. The values at both our redshifts agree
reasonably well with previous investigations. The ratio of the obscured to the
total star formation is in the 65-70 per cent range.

##  7 Acknowledgements

This research makes use of observations taken with the Herschel telescope.
Herschel is an ESA space observatory with science instruments provided by
European-led Principal Investigator consortia and with important participation
from NASA. This research has used data from the HerMES project
(http://hermes.sussex.ac.uk). HerMES is a Herschel Key Programme utilising
Guaranteed Time from the SPIRE instrument team, ESAC scientists, and a mission
scientist. The HerMES data were accessed through the Herschel Database in
Marseille (HeDaM - http://hedam.lam.fr) operated by CeSAM and hosted by the
Laboratoire d’Astrophysique de Marseille. MS thanks Unnikrishnan Sureshkumar
for the help and discussions regarding the calculation of the angular
correlation functions used in this work. MS also extends their gratitude to
Benjamin Magnelli for providing the MIPS-24$\mu$m/70$\mu$m ECDFS FIDEL data.

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##  Appendix A Deblended maps and stacks

Here we show the deblending process for 350 and 500 $\mu$m maps from Herschel
SPIRE in Fig. 16. These maps are produced as explained in section 3.

Figure 16: The deblending process as described in section 3 for the 350 and
500 $\mu\mathrm{m}$ maps from Hershel SPIRE. The arrangement of the panels is
the same as in Fig. 3.