# Size, shade or shape? The contribution of galaxies of different types to the
star-formation history of the Universe from SDSS-IV MaNGA

Thomas Peterken,1 Alfonso Aragón-Salamanca,1 Michael Merrifield,1 Vladimir
Avila-Reese,2 Nicholas F. Boardman,3 Helena Domínguez Sánchez,4 Dmitry
Bizyaev,5 Niv Drory,6 Kaike Pan,5 Joel R. Brownstein7
1School of Physics and Astronomy, University of Nottingham, University Park,
Nottingham NG7 2RD, UK
2Instituto de Astronomía, Universidad Nacional Autónoma de México, A.P.
70–264, 04510 CDMX, México
3Department of Physics and Astronomy, University of Utah, Salt Lake City, UT
84112, USA
4Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Magrans,
E-08193 Barcelona, Spain
5New Mexico State University, Apache Point Observatory, P.O. Box 59, Sunspot,
NM 88349
6McDonald Observatory, The University of Texas at Austin, 1 University
Station, Austin, TX 78712, USA
7Department of Physics and Astronomy, University of Utah, 115 S. 1400 E., Salt
Lake City, UT 84112, USA E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Draft copy: )

###### Abstract

By fitting stellar populations to SDSS-IV MaNGA survey observations of $\sim
7000$ suitably-weighted individual galaxies, we reconstruct the star-formation
history of the Universe, which we find to be in reasonable agreement with
previous studies. Dividing the galaxies by their present-day stellar mass, we
demonstrate the downsizing phenomenon, whereby the more massive galaxies
hosted the most star-formation at earlier times. Further dividing the galaxy
sample by colour and morphology, we find that a galaxy’s present-day colour
tell us more about its historical contribution to the cosmic star formation
history than its current morphology. We show that downsizing effects are
greatest among galaxies currently in the blue cloud, but that the level of
downsizing in galaxies of different morphologies depends quite sensitively on
the morphological classification used, due largely to the difficulty in
classifying the smaller low-mass galaxies from their ground-based images.
Nevertheless, we find agreement that among galaxies with stellar masses
$M_{\star}>6\times 10^{9}\,M_{\odot}$, downsizing is most significant in
spirals. However, there are complicating factors. For example, for more
massive galaxies, we find that colour and morphology are predictors of the
past star formation over a longer timescale than in less massive systems.
Presumably this effect is reflecting the longer period of evolution required
to alter these larger galaxies’ physical properties, but shows that
conclusions based on any single property don’t tell the full story.

###### keywords:

galaxies: evolution

††pubyear: 2020††pagerange: Size, shade or shape? The contribution of galaxies
of different types to the star-formation history of the Universe from SDSS-IV
MaNGA–Size, shade or shape? The contribution of galaxies of different types to
the star-formation history of the Universe from SDSS-IV MaNGA

##  1 Introduction

The question of when and where the stars residing in today’s galaxies formed
is essential to understanding the present-day Universe. Since early works by
Madau et al. (1996), Connolly et al. (1997) and others, many studies have
measured the average instantaneous star-formation rate in galaxy populations
observed at different redshift snapshots to build a picture of the overall
cosmic star-formation history; see Madau & Dickinson 2014 for a comprehensive
review. These approaches have built up a picture of a two-phase star-formation
history of the Universe, with the mean star-formation rate per unit of
comoving volume rising rapidly during the first $1-2\,\textrm{Gyr}$ (i.e.
$z>4$) after the Big Bang, and declining in more recent times. The exact
lookback time at which the peak of cosmic star-formation occurred is
uncertain, but most sources agree that it is broadly in the range of $z=1-3$,
corresponding to approximately $8-11\,\textrm{Gyr}$ before the present day;
see analyses by Hopkins & Beacom (2006), Behroozi et al. (2013), and Madau &
Dickinson (2014), and references therein.

Within this picture, studies of galaxy populations at different redshifts have
demonstrated the link between the star-formation history of the Universe and
the evolution of its constituent galaxies. For example, many show that the
star-formation rate of galaxies with high stellar mass peaked and declined at
preferentially earlier times than low-mass galaxies (Cowie et al., 1996;
Fontanot et al., 2009; Peng et al., 2010; Muzzin et al., 2013), an effect
normally referred to as “downsizing”. Others have proven that a link between a
galaxy’s morphology and its contribution to the cosmic star-formation history
exists over a range of redshifts (Wuyts et al., 2011; Bell et al., 2012;
Cheung et al., 2012; Mortlock et al., 2013; Moresco et al., 2013), although
determining detailed morphologies at high redshift is of course difficult.

It has long been known that in the present-day Universe, spirals are generally
bluer in colour (e.g. Holmberg 1958) due to their higher rate of star
formation (e.g. Roberts 1963; Kennicutt 1983), and are less massive (Blanton &
Moustakas, 2009) than earlier-type galaxies, suggesting an evolutionary
sequence of galaxies transitioning from late to early types as they grow and
subsequently cease their star-formation. However, the exact mechanisms by
which galaxies are able to alter their shape and colour are still not fully
understood. One avenue to studying the typical evolution processes which have
occurred in galaxies could be to determine whether a present-day galaxy’s
colour111“Colour” here refers to a broadband measure of the spectral energy
distribution in the optical region or its morphology is the strongest
indicator to its past. It would then be possible to understand which property
transition — morphology or colour; “shape” or “shade” — is more fundamental,
and whether the associated timescales vary according to galaxy properties such
as stellar mass.

Unfortunately, by their nature, studies of galaxy populations at different
redshifts are limited to studying the average statistical behaviour of a
galaxy population’s star-formation at different snapshots in the Universe’s
history, and are therefore unable to trace how individual galaxies have
evolved. In order to understand the link between a galaxy’s present-day
properties and its past contribution to the cosmic star-formation history, an
alternative approach is therefore required.

Using large samples of galaxies from spectroscopic surveys, Panter et al.
(2003); Panter et al. (2007) and Heavens et al. (2004) showed that by
measuring galaxies’ individual star-formation histories using spectral fitting
techniques, the star-formation history of the Universe can be reconstructed.
Despite significant progress in more recent years, obtaining accurate non-
parametric star-formation histories of galaxies in this manner is still
subject to significant uncertainties, particularly those due to difficulties
in creating reliable stellar population templates using stellar evolution
models which are still poorly understood (Charlot et al., 1996; Maraston,
1998, 2005; Yi, 2003; Lee et al., 2007; Ge et al., 2019), and also due to
assumptions about the behaviour of the stellar initial mass function
(Maraston, 1998; van Dokkum et al., 2008; Pforr et al., 2012; Cid Fernandes et
al., 2014) and the treatment of stellar elemental abundances. See Conroy et
al. (2009, 2010), and Conroy & Gunn (2010) for a set of detailed reviews and
discussion on this important subject.

However, notwithstanding these difficulties, many studies have shown that non-
parametric stellar population fitting methods produce generally reliable
results (see e.g. Cid Fernandes et al. 2005; Panter et al. 2007; Sánchez et
al. 2016; Li et al. 2017; de Amorim et al. 2017; Ge et al. 2018; Cid Fernandes
2018; see also Appendix A of Peterken et al. 2020 for tests specific for the
spectral fitting methods used here), and these stellar population “fossil
record” methods have therefore been successfully applied to modern integral-
field spectroscopic galaxy surveys to uncover the history of low-redshift
galaxies and their physical components (see e.g. Cid Fernandes et al. 2013;
Pérez et al. 2013; Ibarra-Medel et al. 2016; González Delgado et al. 2016,
2017; Peterken et al. 2019; Peterken et al. 2020; García-Benito et al. 2019;
Fraser-McKelvie et al. 2019). Others have used spectral fitting analyses to
show that a galaxy’s observed colour (e.g. Ibarra-Medel et al. 2016; or
equivalently star-formation rate, e.g. Sánchez et al. 2019) and morphology
(e.g. García-Benito et al. 2017; López Fernández et al. 2018; Lacerna et al.
2020; Bellstedt et al. 2020) are directly linked to the historical evolution
of its star formation rate. In a cosmological context, López Fernández et al.
(2018) and Sánchez et al. (2019) have demonstrated the power of using fossil
record techniques to reconstruct how galaxies’ physical properties have
evolved over cosmic time, showing good agreement with redshift snapshot
studies, and thereby justifying this approach as a complementary analysis
technique to study the connection between the Universe’s evolution with its
present-day galaxies.

With its consistent radial coverage of a large sample of galaxies with varying
physical properties, the integral-field spectroscopic MaNGA survey (Bundy et
al., 2015) (part of the fourth generation of the Sloan Digital Sky Survey;
SDSS-IV; Blanton et al. 2017) offers an ideal tool to investigate the link
between today’s galaxies and the Universe’s past. In Peterken et al. (2021),
we explored how the stellar population fossil record can reveal the cosmic
evolution of the star-formation “main sequence” and the mass function of
galaxies. Here, we use the same measured star-formation histories of a large
sample of galaxies to derive the star-formation history of the Universe, and
make use of morphological information from both citizen science and machine
learning classifications to explore the connection between present-day stellar
mass, colour, and morphology to a galaxy’s star-formation rate evolution over
the age of the Universe.

This paper is structured as follows. In Section 2, we outline the relevant
details of the SDSS-IV MaNGA survey. We outline how the samples were selected
and describe the division of these samples into morphological and colour sub-
samples in Section 3. We then briefly summarise the spectral fitting methods
we employ to measure galaxy star-formation histories in Section 4. Section 5
contains the derivation of the cosmic star-formation history and its
contribution from galaxies of different present-day stellar masses (5.1),
colour (5.2), and morphological classifications (5.3). Finally, we interpret
how these results fit into a context of downsizing and discuss the relative
importance of morphology and broadband colour in Section 6.

Throughout this paper, we assume a flat $\Lambda$CDM cosmology with
$H_{0}=68\,\textrm{km}\,\textrm{s}^{-1}\,\textrm{Mpc}^{-1}$ and $\Omega_{\rm
m}=0.308$, consistent with Planck Collaboration et al. (2016).

##  2 MaNGA

As part of the SDSS-IV, Mapping Nearby Galaxies at Apache Point Observatory
(MaNGA; Bundy et al. 2015) is an integral-field spectroscopic galaxy survey.
As of the time of writing, on-site operations have been completed, and by the
end of 2020 the fully-reduced observations will be available for over 10,000
low-redshift ($0.01<z<0.15$, median $z\sim 0.3$) galaxies with a spatial
resolution of 2.5 arcseconds (Yan et al., 2016b). Observations make use of
specially-designed integral field units of five sizes ranging from 12 to 32
arcsecond diameters with 19 to 127 fibres (Drory et al., 2015), which are
mounted onto plates on the 2.5-metre Sloan telescope at Apache Point
Observatory in New Mexico (Gunn et al., 2006). The fibres are fed into the
BOSS spectrographs (Smee et al., 2013) and the spectra are calibrated to
better than 5% accuracy (Yan et al., 2016a) covering a wavelength range of
$3600-10300\,\textrm{\AA}$ with a resolution of $R\approx 2000$. Observations
are designed to reach a minimum signal-to-noise ratio of
$5\,\textrm{\AA}^{-1}$ at $1.5\,R_{\rm e}$ (Law et al., 2015), where $R_{\rm
e}$ is the effective radius of each observed galaxy measured by the NASA-Sloan
Atlas (NSA; Blanton et al. 2011).

The calibrated spectra are reduced and combined into three-dimensional
datacubes by a custom data reduction pipeline (DRP; Law et al. 2016; Law et
al. in preparation), and a data analysis pipeline (DAP; Westfall et al. 2019;
Cherinka et al. 2019) provides data analysis products such as spectral index
maps, stellar and gas kinematics, and emission line fluxes (Belfiore et al.,
2019).

##  3 Sample selection

MaNGA targets galaxies with a flat distribution in log(stellar mass) over the
range of $10^{9}M_{\odot}<M_{\star}<10^{11.5}M_{\odot}$, and the full
targeting catalogue assigns galaxies to designated samples. The Primary sample
galaxies are observed to a radius of $1.5\,R_{\rm e}$, while the Secondary
sample contains observations to $2.5\,R_{\rm e}$. The Primary sample is
supplemented by a colour-enhanced sample to form the Primary+ sample, which
over-samples unusual regions of the stellar mass–colour plane such as high-
mass blue galaxies, low-mass red galaxies, and the “green valley” (Law et al.,
2015).

From the latest internal MaNGA data release (MaNGA Product Launch 9; MPL-9),
we selected all galaxies belonging to any of the Primary, Primary+, or
Secondary samples. In doing so, we required the MaNGA DRP to have assigned no
warning flags at all to any galaxy (i.e. drp3qual=0 for all galaxies). We also
require the DAP to have successfully modelled an emission spectrum cube for
each galaxy. These criteria produce a full sample of 6861 galaxies, of which
3255 belong to the Primary sample, 4342 to the Primary+ sample, and 2519 to
the larger-coverage Secondary sample.

###  3.1 Sample weightings

As a result of MaNGA’s sampling, none of the survey’s galaxy samples are
intrinsically volume-limited. However, since the sampling strategies are well-
defined, each galaxy can be assigned an appropriate weighting such that any
analysis can be performed on an effectively volume-limited sample (Wake et
al., 2017). An implementation of these weightings is described in detail by
Wake et al. (2017), but here — as in Peterken et al. (2021) — we use
weightings generated using the method implemented by Sánchez et al. (2019);
see also Rodriguez-Puebla et al. (2020) and Calette et al. (in preparation)
for further details. This choice of which set of weightings to use was due to
the Sánchez et al. (2019) weightings being more robust at lower stellar masses
and more detailed in its treatment of galaxy colour. However, since the
sample-weighting calculations are similar, we find that the results shown here
are unchanged when the Wake et al. (2017) sample weightings are used instead.
The adopted galaxy weights are reliable for galaxies with stellar mass
$M_{\star}>10^{9}\,M_{\odot}$, making this the limit above which each of the
properly-weighted samples are effectively volume-limited.

###  3.2 Comparison to single-fibre spectra

Figure 1: The weighted distributions of galaxy radii. Each galaxy is sampled
to $1.2\,R_{\rm e}$ (and $2.3\,R_{\rm e}$ for Secondary-sample galaxies),
resulting in a distribution of on-sky apertures. All samples probe to larger
angular apparent radii than SDSS single-fibre spectra (marked as a vertical
dashed line) would.

The weighted distributions of angular radii for each of the samples is shown
in Figure 1. For each of the samples, the majority of galaxies’ $1.2\,R_{\rm
e}$ radius threshold (as used in this work; see Section 4) is larger than the
$3\,\textrm{arcsec}$ radius probed by single-fibre SDSS spectra, highlighting
the extra information available with integral-field spectroscopic
observations. As well as including more of the total star-formation in the
Universe, the spectra we use here are measuring consistent radii in all
galaxies regardless of their observed redshift.

##  4 Spectral fitting

In Peterken et al. (2021), we describe how we implemented full-spectrum
fitting techniques to each Primary+ galaxy. We use an identical method here
but also including galaxies in the Secondary sample. To summarise; we removed
emission lines from each spaxel using the DAP’s emission-line spectrum, and
combined all spaxels’ spectra within $1.2\,R_{\rm e}$ of each galaxy after
removing line-of-sight velocities. We then fit a single spectrum of the
stellar component for each galaxy using Starlight, with a combination of 54
single stellar population (SSP) spectra from the E-MILES (Vazdekis et al.,
2016) and Asa’d et al. (2017) libraries as templates. We also assume a
Calzetti et al. (2000) dust extinction model and fit within the range
$3541.4\leq\lambda\leq 8950.4\,\textrm{\AA}$. Typical combined signal-to-noise
ratios for each galaxy within the fitting range are at least $\sim 500$.
Further description of the fitting method can be found in Peterken et al.
(2021), and we also refer the reader to Peterken et al. (2020) for a full
assessment of its reliability.

As well as fitting the spectrum of each galaxy sampled to $1.2\,R_{\rm e}$, we
also repeat the above fitting method using all spaxels of all Secondary
galaxies sampled to $2.3\,R_{\rm e}$. We therefore obtained 9380 individual
fits; one of each Primary+ galaxy, and two for each Secondary galaxy (sampled
to each radius limit). The two aperture limits were chosen to balance the
inclusion of as much of the MaNGA field of view as possible, while avoiding
overlap with the hexagonal IFU edges which might contaminate and bias results
(see e.g. Ibarra-Medel et al. 2016).

We then obtain a $0.2\,\textrm{dex}$ time-smoothed star-formation history of
each of the fits using the SSP weights assigned by Starlight using the method
described in Peterken et al. (2021). In smoothing, the Starlight-derived star-
formation history (in units of $M_{\odot}\,\textrm{yr}^{-1}$) is first
resampled at 250 lookback times which are evenly spaced in log(time) over the
range of stellar populations used in fitting, and then convolved in the
log(time) axis with a Gaussian function of width $0.2\,\textrm{dex}$.

###  4.1 Comparison of measured star-formation rates

Figure 2: The present-day star-formation rates measured using both H$\alpha$
emission SFRHα are consistent with Starlight-derived total star-formation rate
over the last $100\,\textrm{Myr}$ $\textrm{SFR}_{{\rm SSP},\,(t\leq 100\,{\rm
Myr})}$ (top). The NSA $u-i$ broad-band colours are also closely linked to the
present-day specific star formation rate (bottom). Coloured contours indicate
lines of 20%, 40%, 60%, and 80% of the peak density for each of the unweighted
samples.

To establish the trustworthiness of the spectral fitting methods, we compare
the measured outputs with known results obtained through established analyses.
We find that the total stellar mass measurements for each galaxy agree well
with those determined photometrically by the NASA-Sloan Atlas (see Peterken et
al. 2020).

We are also able to compare the present-day star-formation rates of each
galaxy measured using the Starlight-derived star-formation histories with
those calculated entirely independently from H$\alpha$ fluxes. For each
galaxy, we corrected the DAP’s map of Gaussian-modelled H$\alpha$ emission
line flux using the Balmer decrement, assuming an intrinsic value of $f_{\rm
H\alpha}/f_{\rm H\beta}=2.87$ (corresponding to electron temperature $T_{\rm
e}=10^{4}$ K and density $n_{\rm e}=10^{2}$ cm-3 under Osterbrock & Ferland
(2006) “Case B” recombination) and a Calzetti et al. (2000) reddening curve
with $R_{V}=3.1$. Note that in the stellar population modelling in Section 4,
we assume $R_{V}=4.05$, but the lower value is used when considering the
emission lines; see Catalán-Torrecilla et al. (2015) and Greener et al. (2020)
for an explanation on the difference between dust corrections applied to
stellar and gas spectra. These calculations and corrections are detailed fully
by Greener et al. (2020).

We then summed the flux from all spaxels within $1.2\,R_{\rm e}$ (and
$2.3\,R_{\rm e}$ for the Secondary sample) which have an emission-line signal-
to-noise ratio of at least 10 and calculated the star-formation rate
$\textrm{SFR}_{\rm H\alpha}$ using the relation described by Kennicutt (1998).
For consistency with the SSP templates used in fitting with Starlight, we
assume a Chabrier (2003) IMF for this calculation.

We also calculate a present-day star-formation rate from Starlight
$\textrm{SFR}_{{\rm SSP},\,(t\leq 100\,{\rm Myr})}$ by extracting from the
smoothed star-formation histories the total mass added to each galaxy over the
last $100\,\textrm{Myr}$. By plotting the offset between $\textrm{SFR}_{\rm
H\alpha}$ and $\textrm{SFR}_{{\rm SSP},\,(t\leq 100\,{\rm Myr})}$ as a
function of $\textrm{SFR}_{{\rm SSP},\,(t\leq 100\,{\rm Myr})}$, we show in
Figure 2 that these two measurements of the ongoing star-formation rate are
broadly comparable despite the H$\alpha$ emission having been removed from the
spectra prior to fitting. The offset from the line of equality is to be
expected given that the two measurements are using completely different
approaches and calibrations, contain differing systematics, and are sensitive
to different timescales of star-formation. For the Primary+ sample, we find
that the relationship between the two measurements can be described by

$\log\left(\frac{\textrm{SFR}_{\rm H\alpha}}{\textrm{SFR}_{{\rm SSP},\,(t\leq
100\,{\rm Myr}}}\right)=-0.5\log\left(\textrm{SFR}_{{\rm SSP},\,(t\leq
100\,{\rm Myr})}\right)-0.1$ (1)

with a root mean square deviation of $\sim 0.7\,\textrm{dex}$ from this best-
fit line. Comparable relationships are found for the other samples. The
relatively small offset does not affect any conclusions, reassuring that the
stellar population fits are reliable.

We obtain Starlight-derived specific star-formation rates $\textrm{sSFR}_{{\rm
SSP},\,(t\leq 100\,{\rm Myr})}$ by calculating the ratio of
$\textrm{SFR}_{{\rm SSP},\,(t\leq 100\,{\rm Myr})}$ to the total Starlight-
measured stellar mass contained within each present day galaxy. We also show
in Figure 2 that such specific star-formation rates are closely correlated
with a galaxy’s $u-i$ NSA broadband colour, with a best-fit relation in the
Primary+ sample described by

$u-i=-0.3\log\left(\textrm{SFR}_{{\rm SSP},\,(t\leq 100\,{\rm
Myr})}\right)-1.7$ (2)

which has a root mean square devation of $\sim 0.4\,\textrm{mag}$. As before,
comparable relationships also exist for the other galaxy samples. This link is
unsurprising, as the redder $i$ band is most sensitive to the low-mass stars
which comprise the bulk of a galaxy’s total stellar mass, while the $u$ band
is more sensitive to bluer stars and is therefore indicative of recent star-
formation, making $u-i$ a suitable proxy for specific star-formation rate.

##  5 The star-formation history of the Universe

Having obtained individual star-formation histories for each galaxy, the
cosmic star-formation history can be constructed. To do so, the individual
star-formation histories measured for each galaxy must be carefully weighted
and combined. In combining galaxy star-formation histories, we account for the
lookback time due to the observed reshift of each galaxy. Each star-formation
history’s age sampling is shifted onto a lookback-time sampling by adding the
galaxy’s redshift’s lookback time. The galaxy star-formation histories are
then combined and interpolated onto a common sampling of lookback times.

Figure 3: Fractional cumulative completeness in sample-weighted stellar mass
as a function of lookback time, due to galaxies’ observed redshifts. The
Secondary sample contains galaxies at higher redshifts than the Primary and
Primary+ samples. The lookback times corresponding to a 90% mass completeness
for each sample are given in the legend, and are illustrated by vertical
dotted lines. We do not sample star-formation histories at lookback times
below these limits.

Since the Primary(+) and Secondary samples are selected from different
redshift distributions (Wake et al., 2017) — as shown in Figure 3 — any
derived star-formation history of the Universe will only be able to probe down
to a specific limit in lookback times, depending on which sample is used.
Since the distribution of galaxy redshifts within any sample is dependent on
the galaxy mass, we only measure cosmic star-formation histories at lookback
times greater than that for which each sample has at least 90% completeness in
sample-weighted mass. The specific adopted limits are shown in the legend in
Figure 3.

Figure 4: The star-formation history of the Universe determined using the
different galaxy samples (solid coloured lines). The agreement between the
Primary and Primary+ samples is too close to be able to properly distinguish
between them. Also shown is the Madau & Dickinson (2014) best-fit parametric
function to the cosmic star-formation history derived from galaxy redshift
studies (black dotted line). For consistency, this comparison study has been
smoothed according to our treatment of each individual galaxy’s star-formation
history.

The cosmic star-formation histories measured from each sample is shown for
each sample in Figure 4. We show that the calculated star-formation history of
the Universe measured within 1.2 $R_{\rm e}$ of each galaxy agrees well at all
lookback times regardless of the MaNGA sample used, and that all samples show
a peak cosmic star-formation history at a lookback time of $10^{9.80\pm
0.01}\,\textrm{years}$ (corresponding to $z\approx 0.67\pm 0.02$).

Figure 4 also shows the best-fit function derived by Madau & Dickinson (2014)
of the cosmic star-formation history measured through galaxy redshift studies.
To ensure a like-for-like comparison, we calculated the mass weights which
would be assigned to each SSP template age used in our fitting method based on
Equation 15 of Madau & Dickinson (2014), by integrating the curve within a box
centred in log-space on each SSP’s nominal age, to obtain a raw star-formation
history as might ideally be measured using the stellar population fitting
methods described in Section 4. We then smoothed the modelled SSP weights
using the procedure described in Section 4 and in Peterken et al. (2021). This
smoothing procedure results in the smoothed profile showing a broader peak in
the cosmic star-formation history which occurs at a lower redshift (at $z\sim
1$ rather than $z\sim 2$) compared to the unsmoothed Madau & Dickinson (2014)
best-fit function (not shown).

We find that the smoothed Madau & Dickinson (2014) star-formation history is
in general agreement with the results obtained through the completely
independent approach performed here — with particularly strong agreement at
lookback times less than $\sim 6\,\textrm{Gyr}$ ($z\sim 0.63$) — lending
further evidence that such a fossil record analysis is trustworthy. We suggest
that the broader peak obtained here is due to having co-added multiple star-
formation histories which have each been smoothed to $0.2\,\textrm{dex}$
rather than simply smoothing a single function by $0.2\,\textrm{dex}$ in the
comparison measurement. We argue that this effect could also partly explain
the difference in lookback times to the peak in cosmic star formation,
although the observed difference is small given the entirely independent
approaches of the two methods. Our results also show good quantitative
agreement with the cosmic star-formation histories obtained through fossil-
record analyses performed by both López Fernández et al. (2018) and Sánchez et
al. (2019), and also with the earlier best-fit parametric models to
observational redshift studies determined by Behroozi et al. (2013) and
Hopkins & Beacom (2006).

If the measured lookback time corresponding to the peak of cosmic star-
formation was dictated primarily by artefacts of the SSP templates or of the
fitting method, we would expect to find that the peak in each galaxy’s
individual star-formation history might be biased towards a certain stellar
population age. In such a case, the derived cosmic star-formation history
measured in each sample would therefore display its peak at different lookback
times once galaxies’ observed redshifts are accounted for, since each MaNGA
sample targets galaxies from different redshift distributions. The close match
between star-formation histories shown in Figure 4 therefore shows that the
signal being measured is intrinsic to the data rather than being the product
of artefacts. Indeed, we find that the agreement between the star-formation
histories measured using each MaNGA sample is only seen when the galaxy
redshifts are taken into account, and that the above close agreement is
smaller than the difference in median lookback times for each sample’s galaxy
populations.

We find that increasing the aperture from $1.2\,R_{\rm e}$ to $2.3\,R_{\rm e}$
using the Secondary sample results in a cosmic star-formation history which is
greater at all lookback times than Madau & Dickinson (2014)’s best fit to
cosmological results. This excess could either be due to overly-conservative
aperture corrections or to surface brightness limits causing cosmological
studies to have underestimated the total star-formation rates at different
redshifts.

Figure 5: The fractional excess in measured cosmic star formation at all
lookback times from the Secondary sample when the aperture is increased from
$1.2\,R_{\rm e}$ to $2.3\,R_{\rm e}$. At more recent times, the fractional
increase is larger, indicative of inside-out growth occurring in most
galaxies.

Having derived the cosmic star-formation history using the Secondary-sample
galaxies with radius limits of $1.2\,R_{\rm e}$ and $2.3\,R_{\rm e}$
separately, we are able to quantify what extra fraction of star-formation is
included by increasing the FOV diameter by a factor of $\sim 1.9$. Comparison
between the two Secondary-derived cosmic star-formation histories of Figure 4
shows that the effect of the increased FOV results in a 35–40% enhancement in
the measured star-formation histories at lookback times $\gtrapprox
5\,\textrm{Gyr}$, increasing to a 55% enhancement by $\sim 1.5\,\textrm{Gyr}$,
as illustrated in Figure 5. This increase over time is indicative of inside-
out growth resulting in a greater star formation contribution by the galaxy
outskirts at more recent times, as we explored for spiral galaxies in Peterken
et al. (2020); see also Pérez et al. (2013); Ibarra-Medel et al. (2016);
García-Benito et al. (2017); Goddard et al. (2017). It is interesting to note
that even at recent times, the ratio in star-formation rate between larger to
the smaller aperture of $\sim 1.5$ is smaller than the corresponding ratio of
sky coverage area ($\sim 3.7$), showing that star-formation density is still
greatest at galactic centres on average despite the effect of inside-out
growth.

###  5.1 Size222We are not using “size” here in its usual meaning of a
galaxy’s physical or apparent radius or diameter; rather, we mean its stellar
mass. Still, such a simple substitution is suitable to sufficiently sustain a
satisfactory sibilance with subsequent subheadings.: effects of present-day
stellar mass

Figure 6: The star-formation history of the Universe stratified by its
contributions from galaxies in different present-day stellar mass bins, in
absolute star-formation rates (top) and by the fractional contribution from
each mass bin (bottom). Shown is for the Primary+ sample (red line), but all
other samples are similar. Higher-mass galaxies have become less dominant in
the more recent Universe and vice-versa.

Having obtained the cosmic star-formation history, we now begin to explore the
connection between a galaxy’s present-day physical properties with its
historical contribution to the Universe’s star-formation. We split the galaxy
sample into five discrete bins of present-day photometrically-measured stellar
mass $M_{\star\,{\rm NSA}}$ such that each bin contains an equal (unweighted)
number of Primary+-sample galaxies. The thresholds of these bins and the star-
formation history of the Universe split into contributions of these mass bins
are shown in Figure 6. We have shown the stellar-mass breakdown for the
Primary+ sample within $1.2\,R_{\rm e}$, but all other samples’ are similar.
We see that the star-formation contribution from higher-mass galaxies becomes
less significant at more recent times. For example, galaxies with present-day
stellar mass $M_{\star}<10^{10.29}\,M_{\odot}$ dominated the cosmic star
formation until $\sim 2\,\textrm{Gyr}$ ago to contribute only $\sim 50\%$ in
the local Universe. We have therefore recovered the known observational
effects of downsizing.

Figure 7: The lookback time to the peak of star-formation $t_{\rm peak}$ as a
function of present-day stellar mass $M_{\star\,{\rm NSA}}$, using each of the
MaNGA samples. The solid lines indicate the sample-weighted median values, and
the shaded regions lie between the one-third and two-thirds percentiles.
Greyscale-shaded background regions indicate the mass bins used in Figure 6
and elsewhere.

A similar perspective of downsizing is gained by measuring the lookback time
at which each individual galaxy reached its maximum star-formation rate. The
volume-weighted median lookback time $t_{\rm peak}$ of peak star-formation in
galaxies as a function of their present-day stellar mass $M_{\star}$ is shown
in Figure 7. We find that the peak in star formation typically occurred at
$t_{\rm peak}=8\pm 1\,\textrm{Gyr}$ ago (corresponding to $z\approx 1.1\pm
0.3$) in the galaxies with the highest present-day stellar masses in the
samples ($M_{\star}>10^{11}\,M_{\odot}$), falling to $t_{\rm peak}\lessapprox
2\,\textrm{Gyr}$ ($z\lessapprox 0.2$) for galaxies with present-day stellar
masses of $M_{\star}<3\times 10^{9}\,M_{\odot}$. We also see some signs of
downsizing effects being strongest among low-mass galaxies where the gradient
$\Delta t_{\rm peak}/\Delta M_{\star}$ is greatest.

By measuring the lookback time by which galaxies had built the bulk of their
present-day stellar mass, Ibarra-Medel et al. (2016), García-Benito et al.
(2017), and Peterken et al. (2020) have previously found that low-mass
galaxies typically show larger variation in the characteristic formation times
than high-mass galaxies. However, we find here that the scatter in $t_{\rm
peak}$ remains approximately constant at $\sim 0.3\,\textrm{dex}$ over all
stellar masses. The two results are not incompatible: we interpret such an
apparent dichotomy as indicative of low-mass galaxies having greater variation
in the rate of decline in star-formation after their common peak time.

Figure 7 again shows strong agreement between each MaNGA sample. We therefore
present hereafter only results measured using the Primary+ sample, but results
for other samples are similar throughout.

###  5.2 Shade: effects of present-day colour

By splitting each galaxy sample by the galaxies’ locations on the stellar
mass–colour plot, we are also able to investigate the effect of present-day
colour on a galaxy’s contribution to the cosmic star-formation history.

####  5.2.1 Colour classifications

Figure 8: Mass–colour plane of the Primary+-sample galaxies, with galaxies
classified according tho their colour as used in Section 5.2. Galaxy stellar
masses $M_{\star\,\textrm{NSA}}$ and $\left(u-i\right)_{\textrm{NSA}}$
broadband colours are NSA measurements. Shaded backgrounds indicate the bins
in stellar mass in Figure 6 and elsewhere.

We separate galaxies by their colours according to the following criteria:

  * •

Red sequence: $\left(u-i\right)_{\rm NSA}>0.25\log\left(M_{\star\,{\rm
NSA}}\right)-0.2$

  * •

Green valley:
$0.25\log\left(M_{\star\,{\rm NSA}}\right)-0.5\leq\left(u-i\right)_{\rm
NSA}\leq 0.25\log\left(M_{\star\,{\rm NSA}}\right)-0.2$

  * •

Blue cloud: $\left(u-i\right)_{\rm NSA}<0.25\log\left(M_{\star\,{\rm
NSA}}\right)-0.5$

where the galaxies’ stellar masses $M_{\star\,{\rm NSA}}$ (measured in
$M_{\odot}$) and $\left(u-i\right)_{\rm NSA}$ broadband colours are taken from
the NSA (Blanton et al., 2011) photometry-derived measurements.333Note that a
galaxy’s broadband colour is affected by its inclination due to increased
internal dust extinction. We do not attempt to correct for this effect, so
that our measurements resemble those of other studies of galaxy populations as
closely as possible. These thresholds and the subsequent classifications of
Primary+ galaxies are illustrated in Figure 8.

Figure 9: Comparison of galaxies with colour classifications defined in
Section 5.2 (left panels, based on $\left(u-i\right)_{\rm NSA}$ broadband
colours) and the specific star-formation rate classifications defined in
Peterken et al. (2021) (right panels) in the $\left(u-i\right)_{\rm
NSA}$–$M_{\star\,{\rm NSA}}$ plane (top panels) and $\textrm{SFR}_{\rm
SL}$–$M_{\star\,{\rm SL}}$ (bottom panels) plane at a lookback time of
$t=0.68\,\textrm{Gyr}$ for Primary+ galaxies. The classifications of blue
cloud, green valley, and red sequence are analogous to classifications of
star-forming, retiring, and retired galaxies respectively. Dashed lines in the
top panels indicate the boundaries used to separate blue cloud, green valley,
and red sequence galaxies, and those in the bottom panels indicate those used
to separate star-forming, retiring, and retired galaxies.

We showed in Section 4.1 and Equation 2 that broadband colour and specific
star-formation rate are closely correlated. To demonstrate how the above
colour classifications are linked to star-formation properties, we have also
split the galaxy sample into star-forming, retiring, and retired populations
using thresholds of $\textrm{sSFR}_{{\rm SL}\left(t=0.68\,{\rm
Gyr}\right)}=10^{-11}$ and $10^{-12}\,\textrm{yr}^{-1}$ — as used in Peterken
et al. (2021) — where $\textrm{sSFR}_{{\rm SL}\left(t=0.68\,{\rm Gyr}\right)}$
is the ratio of the average Starlight-measured instantaneous star-formation
rate to the Starlight-measured instantaneous stellar mass $M_{\star\,{\rm
SL}}$ at a lookback time of $t=0.68\,{\rm Gyr}$, which is the lowest lookback
time measurable with the Primary+ sample as defined in Figure 3. Figure 9
shows a direct comparison of galaxies’ classifications under both schemes on
the $\left(u-i\right)_{\rm NSA}$–$M_{\star\,{\rm NSA}}$ plane (using NSA-
measured colours $\left(u-i\right)_{\rm NSA}$ and stellar masses
$M_{\star\,{\rm NSA}}$) and on the $\textrm{SFR}_{\rm SL}$–$M_{\star\,{\rm
SL}}$ plane at a lookback time of $t=0.68\,\textrm{Gyr}$ (using Starlight-
derived star-formation rates SFRSL and stellar masses $M_{\star\,{\rm SL}}$).
We find that most star-forming galaxies map onto the blue cloud region, most
retiring galaxies to the green valley region, and most retired galaxies to the
red sequence region, and vice-versa, showing that the $u-i$ colour
classifications defined above are broadly analogous to classifications of star
formation444This strong link is by constuction; we chose the $u-i$ broadband
colour in Section 4.1 as a proxy for specific star-formation rate due to the
sensitivity of $u$ to recent star-formation and $i$ to the total stellar mass.
Classifications based on broadband colours at longer wavelengths (e.g. $i-z$)
will not be so closely linked to the classifications of specific star-
formation rates., and therefore linking the observed measurements to physical
galaxy properties.

Having demonstrated the commutativity of broadband colour and specific star-
formation rate, it would be feasible to investigate how either of these
properties relates to a galaxy’s history. Ibarra-Medel et al. (2016) showed
that colour and specific star-formation rate have similar effects on the star-
formation history of galaxies. However, since colour is a more readily-
measurable property of a galaxy, we will continue to investigate the role of
present-day broadband colour rather than present-day specific star-formation
rate in the analysis shown here, for more straightforward application of the
results to other studies of galaxy populations.

####  5.2.2 Present-day colour and the star-formation history of the Universe

Figure 10: The star-formation history of the Universe inferred from the
Primary+ sample, separated into its contributions from galaxies belonging to
each galaxy classification (indicated by colours) defined in Section 5.2.1.
Each colour classification is also stratified by present-day stellar mass
(darkest to lightest shades for most to least massive galaxies) within each
broadband colour classification, using the mass bins of Section 5.1. The upper
panel shows the total contribution to the star-formation history, while the
lower panel shows the fractional contributions to the total star-formation
history.

Figure 10 shows the Primary+-derived star-formation history of the Universe
showing the relative contributions from galaxies classified as currently
belonging to the blue cloud, the green valley, and the red sequence as defined
above. There is a strong correlation between a galaxy’s present-day colour and
its past contribution to the total star formation, with the blue cloud
contributing only 20% at early times and rising to more than 70% at the
present day. We recover how galaxies which are currently exhibiting very low
levels of star formation were once the dominant source of new stars.

Figure 11: The absolute (top row) and fractional (middle row) contributions to
the star-formation history of the Universe of galaxies of different present-
day colour classifications (colours) in each mass bin (columns; transparencies
equivalent to those used in Figure 10), and the relative contribution of each
colour classification to each mass bin’s star-formation history (bottom row).

However, stellar mass and colour classification are not independent galaxy
properties, as can be seen in Figure 8. Specifically, high-mass galaxies are
more likely to belong to the red sequence and vice-versa. To determine how the
effect of present-day colour varies with a galaxy’s stellar mass, we show the
relative contribution of each colour classification to each mass bin’s star-
formation history in Figure 11. We find that the blue cloud’s increase in
contribution to the star-formation history between lookback times of 10 and 1
Gyr varies from a $\sim 20$% increase in the highest-mass bin to a $\sim 40$%
increase in the lowest-mass bins:555The discrepancy between these mass-bin
values and the increase of $\sim 50$% in the blue cloud’s contribution overall
is due to the dependent nature of colour and stellar mass: lower-mass bins
with a larger fraction of blue cloud galaxies becoming more dominant at more
recent times. a galaxy’s colour is therefore more strongly correlated to its
historical contribution to the star-formation history in low-mass than in
high-mass galaxies.

We additionally see some evidence for the colour designations reflecting
shorter star-formation timescales in low-mass galaxies than in their high-mass
counterparts. The most massive blue cloud galaxies began increasing their
contribution to that mass bin’s star-formation history $\sim 6\,\textrm{Gyr}$
ago to reach its current level $\sim 2\,\textrm{Gyr}$ ago, while the lowest-
mass bin’s blue cloud only started to become more dominant $\sim
2\,\textrm{Gyr}$ ago and appears to still be increasing to the present-day.

We find that galaxies currently in the green valley have contributed an
approximately constant 20% to the star-formation history in all mass bins.
Such a consistency of the green valley’s contribution between mass bins is to
be expected assuming that the timescale of star-formation transition is
independent of stellar mass. However, the constancy of the present-day green
valley’s contribution over the last $10\,\textrm{Gyr}$ indicates a complex
picture. If these galaxies are those caught in the act of a rapid “quenching”
transition from the blue cloud to the red sequence or a rapid rejuvenation
transition in the opposite direction, it would be expected that their
historical contributions to the cosmic star-formation history should be
similar to either the blue cloud’s or the red sequence’s until recent times.
The fact that this does not hold true could hint towards the possibility that
the galaxies designated as belonging to the green valley using the colour
criteria above contain a mix of quenching and rejuvenating galaxies. However,
further analysis of the individual star-formation histories of galaxies
currently in the green valley shows that this is not true in that most show
declining levels of star-formation over the last Gyr, and there is no
significant population of rejuvenating green valley galaxies. Instead, it
seems that most present-day green valley galaxies have always had low but
sustained levels of star formation, with star-formation histories which have
generally followed the star-formation history of the Universe as a whole.

While we do not speculate here as to a possible physical explanation for this
observation, it might reflect the slower retiring processes proposed by
Schawinski et al. (2014), for example. Possible drivers of such a “slow
quenching” scenario are thought to be predominantly internal processes (Martig
et al., 2009; Fang et al., 2013; Bluck et al., 2014; Smethurst et al., 2018;
Das et al., 2021). There is observational evidence to suggest that cessation
of star-formation occurs on long (several Gyr) timescales in a significant
number of galaxies, including ellipticals (see e.g. Smethurst et al. 2015,
2017; Belfiore et al. 2018; Lacerna et al. 2020), although other studies argue
otherwise (see e.g. Bremer et al. 2018).

Figure 12: The absolute (top row) and fractional (middle row) contributions to
the star-formation history of the Universe of galaxies of different stellar
masses in each colour classification, and the relative contribution of
galaxies with different stellar mass to each colour classification’s star-
formation history (bottom row).

By considering how galaxies of each colour classification in the five bins of
stellar mass used in Section 5.1 have contributed to the cosmic star-formation
history, we see in Figure 10 some signs of downsizing effects being present in
all colour classifications; low-mass galaxies of all colours become relatively
more dominant at smaller lookback times. To measure how downsizing effects
vary between colour classifications in this way, we also show the relative
contribution of galaxies in each mass bin to each colour classification’s
star-formation history in Figure 12. We find evidence for downsizing having
occurred most strongly in galaxies currently in the blue cloud, with galaxies
in the two lowest-mass bins increasing their contribution by 20% in the red
sequence and 30% in the blue cloud, with the green valley lying in between.

Figure 13: The lookback time to the peak star formation rate of galaxies
currently belonging to each of the colour classifications. Solid lines
indicate median values, and shaded regions lie between the one- and two-third
percentiles. Blue cloud galaxies peaked in star formation more recently and
show stronger downsizing effects than red sequence galaxies.

This difference in the strength of the downsizing effect seen in galaxies of
different colour classifications is illustrated further in Figure 13, where we
see that red sequence galaxies reached peak star formation at earlier times
than green valley or blue cloud galaxies at all stellar masses, but that this
effect is greatest in low-mass galaxies.

###  5.3 Shape: effects of present-day morphology

Having quantitatively measured the link between a galaxy’s present day colour
and its historical contribution to the cosmic star-formation history, we can
now independently assess the relative role of a galaxy’s present-day
morphology.

####  5.3.1 Morphological classifications

Over 91% of galaxies in all MaNGA samples have been classified by the Galaxy
Zoo “citizen science” project (Lintott et al., 2008), in which volunteers are
asked to classify galaxies’ morphological features. We make use of the
redshift-debiased vote fractions of Hart et al. (2016) from Galaxy Zoo 2
(Willett et al., 2013) to split the galaxy samples by their present-day
morphology. We classify each galaxy according to the following criteria:

  * •

Elliptical: $p_{\rm features\,or\,disk}<0.5$

  * •

S0: $p_{\rm features\,or\,disk}>0.5$ and $p_{\rm spiral}<0.5$

  * •

Spiral: $p_{\rm features\,or\,disk}>0.5$ and $p_{\rm spiral}>0.5$

where $p_{\rm[class]}>0.5$ indicates the debiased vote fraction for [class]
from Hart et al. (2016). These thresholds were chosen to minimise the number
of unclassifiable or ambiguous galaxies, and are therefore less stringent than
those recommended by Willett et al. (2013), and hence open to significant
contamination between morphological classes.

Figure 14: The distribution of galaxies in the stellar mass–colour plane (as
Figure 8), with galaxies coloured by their Galaxy Zoo (top) and Domínguez
Sánchez et al. (2018) machine learning (bottom) morphological classifications
as used in Section 5.3. Spiral galaxies occupy the blue region of this
parameter space in both schemes. There is ambiguity at low stellar masses
where the Galaxy Zoo classifications are less reliable due to difficulties in
distinguishing spiral structure in SDSS imagery and the low thresholds used
for separating morphologies. Galaxies with low stellar mass are more likely to
have spiral-morphology machine learning classifications compared to their
Galaxy Zoo classifications. Contours of 30%, 50%, and 80% of the peak
unweighted density are shown for each classification. For reference, dashed
black lines delineate the boundaries between the colour classifications used
in Section 5.2, and shaded background regions indicate the stellar mass bins
used throughout.

The stellar mass–colour distribution of the Primary+ galaxies indicating their
Galaxy Zoo morphologies is shown in the upper panel of Figure 14. Over most of
the sample’s range in stellar mass, the spirals occupy the bluer region of
parameter space, but at the low-mass ($<2\times 10^{9}\,~{}M_{\odot}$) end,
blue galaxies are likely to have been classified as earlier-type galaxies, as
we noted in Peterken et al. (2021). This unexpected trend is likely because
spiral structure in low-mass disk galaxies is harder to discern in SDSS
imagery due to resolution effects. The classifications we have implemented
from the vote fractions to minimise the number of unclassified galaxies will
therefore result in a high level of contamination between morphologies. A
lower spiral vote-fraction threshold might more reliably distinguish between
morphologies in low-mass galaxies, but only at the expense of increasing the
number of high-mass early-type disk galaxies being mis-classified as spirals.
Alternatively, using the recommended criteria of Willett et al. (2013) to
obtain clean samples of galaxies of each morphology creates a large number of
unclassified “ambiguous” galaxies, which when removed from the sample will
render the MaNGA sample weightings described in Section 3.1 inaccurate.
However, we have repeated the analysis using debiased vote fraction thresholds
of 80% instead of 50% in the criteria above and found no change to the results
at high stellar masses, but at low stellar masses the dominance of galaxies
with “ambiguous” morphologies makes any quantitative results impossible.

Alternative morphological classifications using the deep learning methods
developed by Domínguez Sánchez et al. (2018) are available for galaxies which
were part of the SDSS data release 15 (DR15; Aguado et al. 2019). This
approach uses Galaxy Zoo and Nair & Abraham (2010) classifications as training
sets to classify SDSS galaxy images. Instead of replicating vote fractions for
the presence of morphological features in each galaxy, the Domínguez Sánchez
et al. (2018) approach directly provides a prediction for each galaxy’s
morphological T-type. The resulting separation of different morphologies is
cleaner at low stellar masses in the colour–mass plane, as illustrated in the
lower panel of Figure 14. The question then arises of which classification
method should be used. Fortunately, in most cases we find that the results
presented here do not change depending on which classification we use and we
have therefore primarily presented results using the Galaxy Zoo
classifications to make use of the larger sample size. In the instances where
we find that the two classification methods provide conflicting results, we
will describe and discuss those differences.

####  5.3.2 Present-day morphology and the star-formation history of the
Universe

Figure 15: The star-formation history of the Universe inferred from the
Primary+ sample, stratified into its contributions from galaxies in different
stellar mass bins (shades; darkest to lightest for most- to least-massive
galaxies) and of different Galaxy Zoo morphologies (colours), analogous to
Figure 10. The top panel shows the star-formation history, and the bottom
panel shows the percentage contribution from each of the sample’s subdivisions
to the total cosmic star-formation history. Machine learning morphologies of
Domínguez Sánchez et al. (2018) show similar results.

The cosmic star-formation history separated into contributions from galaxies
of different present-day stellar masses and the Galaxy Zoo morphologies is
shown in Figure 15. Present-day spiral galaxies have contributed the greatest
amount (at least 40%) to the total star formation of any morphology at all
lookback times, and contribute the majority (60%) at the present day. This 20%
morphology effect on a galaxy’s past contribution to the star-formation
history of the Universe is smaller than the 40% colour increase seen in Figure
10, implying that colour is a stronger indicator of a galaxy’s full star-
formation history than morphology, as found by others (e.g. Ibarra-Medel et
al. 2016).

We find that a galaxy’s morphology only reflects the last $2-3\,\textrm{Gyr}$
of its star-formation history on average, in that the relative contributions
to the cosmic star-formation history by galaxies of different morphologies did
not change until this lookback time. We have previously demonstrated this
result in more detail (see Peterken et al. 2021).

Figure 16: The absolute (top row) and fractional (middle row) contributions to
the star-formation history of the Universe of galaxies of different
morphologies in each bin of stellar mass (columns), and the relative
contribution of different Galaxy Zoo morphologies to each mass bin’s star-
formation history (bottom row). Analogous to Figure 11.

However, morphology and mass are correlated, as shown in Figure 14: observed
morphology effects could be simply a result of early-type galaxies having
higher stellar mass on average, and will therefore exhibit star-formation
histories with higher star-formation rates at earlier lookback times than
their late-type and less massive counterparts, as we saw in Figure 7. To
properly distinguish between downsizing and morphological effects, Figure 16
shows the same data as in Figure 15 but with each mass bin separated. We find
that regardless of the morphological composition of the mass bin, spirals have
increased their contribution to the star-formation history by $\sim 20$%
between lookback times of 10 and 1 Gyr. We therefore find the effects of
present-day morphology on the contribution to the star-formation history of
the Universe to be independent of present-day stellar mass.

However, we also see some evidence for the morphological classifications
reflecting different timescales of star-formation histories in different mass
bins in the same manner as we saw for the colour classifications in Figure 11.
Spiral galaxies with the largest present-day stellar mass began increasing in
their contribution to their mass bin’s star-formation history $\sim
4\,\textrm{Gyr}$ ago to reach the current level $\sim 2\,\textrm{Gyr}$ ago,
compared to $\sim 2\,\textrm{Gyr}$ ago for the lowest-mass spirals to start
increasing their contribution with a trend of continued increase.

Figure 17: The absolute (top row) and fractional (middle row) contributions to
the star-formation history of the Universe of galaxies with different present-
day Galaxy Zoo moprhologies, stratified by the contributions from each stellar
mass bin. The relative contribution of galaxies with different stellar mass to
each morphology’s star-formation history is also shown (bottom row). Analogous
to Figure 12.

As in Figure 10, we are also able to reorganise the area plot of Figure 15 by
morphology, to show how galaxies of different present-day stellar masses have
contributed to each morphological classification’s star-formation history to
reveal how the effects of stellar mass change among galaxies of different
morphologies, as shown in Figure 17. For the Galaxy Zoo morphologies, we find
that downsizing effects are stronger in earlier-type galaxies; galaxies in the
lowest-mass bin become more dominant among lenticular and elliptical galaxies
at smaller lookback times than the equivalent effect in spiral galaxies.

Figure 18: As Figure 17 but using the Domínguez Sánchez et al. (2018) machine
learning morphologies. The galaxies which were not included in DR15 have been
removed, and the weights of the remaining galaxies have been scaled such that
the total weighted mass in the sample remains the same. The total star-
formation history for the full Primary+ sample (black line) is shown,
resulting in the sum of all shown contributions from each morphology to not
equal exactly 100% of the total at some lookback times.

However, when using the Domínguez Sánchez et al. (2018) machine learning
morphological classifications — as shown in Figure 18 — we find the opposite;
spiral galaxies show stronger downsizing effects than lenticular or elliptical
galaxies. We also find that elliptical galaxies have contributed almost no
star formation in the last $\sim 2\,\textrm{Gyr}$. This difference highlights
how carefully morphological classifications must be used to avoid biases
associated with the difficulties inherent in identifying structures in low-
mass galaxies.

The observed differences are easily explained by uncertainty in the
classification of low-mass spiral galaxies, which appears to be more reliably
resolved by the machine learning approach. We wish to stress here that such a
discrepancy merely highlights the importance of careful consideration of what
exact morphological classifications are being used, and does not imply that
Galaxy Zoo classifications are inherently flawed. Instead, we argue that
studies using any morphological classification method should be wary of how
galaxies with potentially ambiguous morphologies are treated. This is
especially important if the classification scheme is based on a “pure” Hubble
approach, which often contains significant subjectivity (Naim et al., 1995)
and assumptions (Freeman, 1970; Hart et al., 2017, 2018; Masters et al.,
2019), and does not necessarily reflect the physical processes occurring
within galaxies (Cappellari, 2016; Wang et al., 2020). Indeed, we note again
here that the implementation of morphological classifications using Galaxy Zoo
vote fractions described in Section 5.3.1 goes contrary to the advice of
Willett et al. (2013), who detail how low-contamination samples of Galaxy Zoo
galaxies with any required morphology can be effectively obtained.

In Figure 18 (and to a lesser extent also in Figure 17), we see some apparent
“upsizing” occurring in elliptical galaxies; high-mass galaxies appear to
increase their relative contribution to the star-formation history of all
ellipticals in the last $\sim 2\,\textrm{Gyr}$. This phenomenon is likely due
to the problems that we addressed in Peterken et al. (2020) of the “UV upturn”
(see also Yi 2008; Cid Fernandes & González Delgado 2010) being most dominant
in high-mass ellipticals due to their extremely old stellar populations. That
this effect is strongest using the Domínguez Sánchez et al. (2018)
morphological classifications is therefore due to the population of possibly
misclassified low-mass galaxies in the Galaxy Zoo classifications diluting the
effect with “real” star formation; see also Fischer et al. (2019, Section 4.4)
who describe this phenomenon in more detail. However, we note that the
observed effects are extremely small; even with this spurious increase of
star-formation rate in high-mass elliptical galaxies, those galaxies still
only account for $<1\%$ of the star formation in the present-day Universe
regardless of which morphological classification method is used, so these
effects do not significantly affect the derived cosmic star-formation history.

We find the total star-formation histories of all galaxies with stellar mass
$M_{\star}>10^{10.29}\,M_{\odot}$ (i.e. in the three bins of greatest stellar
mass) to be similar for lenticular and elliptical classifications. This
similarity could imply that all massive present-day early-type galaxies have
experienced similar star-formation histories, with the difference in
morphologies due to other factors such as merger rate histories.
Alternatively, it could be evidence for visually-determined shape being an
ineffective way to separate the bimodality of fast- and slow-rotating early-
type galaxies (Emsellem et al., 2007; Cappellari et al., 2011; Cappellari,
2016; Graham et al., 2018), or a combination of both of these effects.

Figure 19: The peak in star-formation history of galaxies of each present-day
morphological classification in the Primary+ sample, as determined using
Galaxy Zoo. Solid lines indicate the weighted medians and the coloured shaded
regions enclose the area between the one- and two-thirds weighted percentiles.
Figure 20: As Figure 19, but using the Domínguez Sánchez et al. (2018) machine
learning morphological classifications of DR15 galaxies. Figure 21: The offset
$\Delta\log\left(t_{\rm peak}\right)$ in lookback time of peak star-formation
rate $t_{\rm peak}$ observed between present-day red sequence and blue cloud
galaxies (blue dashed line), and between present-day elliptical and spiral
galaxies (purple dotted line) using Galaxy Zoo classifications, as a function
of present-day galaxy stellar mass $M_{\star}$. The effect of present-day
colour is larger than that of present-day morphology at all stellar masses,
but is particularly significant in the range $7\times
10^{9}M_{\odot}\lessapprox M_{\star}\lessapprox 4\times 10^{10}M_{\odot}$.

By comparing the lookback time of peak star formation of galaxies with
different present-day morphologies in Figures 19 (for Galaxy Zoo morphologies)
and 20 (for Domínguez Sánchez et al. (2018) machine learning morphologies), we
see that spiral galaxies peaked more recently than early-type galaxies at all
present-day stellar masses regardless of the classification method. We find
that this difference is greater in galaxies with low stellar mass, and is
greatest around $M_{\star}=6\times 10^{9}\,M_{\odot}$; above this threshold we
find that both classification schemes display stronger downsizing among
spirals than in early-type galaxies, in agreement with Goddard et al. (2017).

We also find that the peak in star-formation history of lenticular and
elliptical galaxies is similar for early-type galaxies with stellar masses
$M_{\star}>\sim 10^{10}\,M_{\odot}$ using the Galaxy Zoo classifications
(Figure 19) and for stellar masses $M_{\star}>\sim 10^{9}\,M_{\odot}$ using
the Domínguez Sánchez et al. (2018) classifications (Figure 20), again
reflecting either the similar histories of these galaxies or the difficulty in
distinguishing between them through imagery alone. We see that the star-
formation peak in present-day lenticular galaxies classified by Galaxy Zoo
becomes systematically more recent for lower stellar masses, highlighting
likely contamination of mis-classified spiral galaxies using the thresholds
applied here.

However, regardless of which classification method is used, we see again that
the effect of morphology on a galaxy’s contribution to the cosmic star-
formation history is smaller than the effect of colour: the difference in peak
star-formation times between early- and late-type galaxies is smaller than the
difference between blue cloud and red sequence galaxies ($\sim 0.2$ dex and
$\sim 0.5$ dex respectively at $M_{\star}=10^{10}\,M_{\odot}$ for example).
This is illustrated at all present-day stellar masses in Figure 21.

##  6 Size versus shade versus shape: Conclusions and interpretation

Here, we have recovered evidence for downsizing, in that the fraction of star-
formation occurring in the galaxies with greatest present-day stellar mass was
largest at early times, with low-mass galaxies dominating the cosmic star-
formation at more recent times, and that the lookback time corresponding to a
galaxy’s peak star-formation rate is therefore correlated with its present-day
stellar mass. We find that this correlation exhibits the strongest gradient
among low-mass galaxies, suggesting accelerating downsizing at more recent
times. By further splitting the galaxy sample, we subsequently showed that
downsizing effects are present in galaxies of all present-day colours (which
we showed to be analogous to specific star-formation rate) and morphologies. A
galaxy’s present-day stellar mass is therefore a significant indicator of its
star-formation history regardless of its other properties.

In quantifying these effects, we found that galaxies currently in the blue
cloud exhibited stronger downsizing effects than those in the green valley or
red sequence. However, we found some differences in whether downsizing is
strongest in present-day early- or late-type galaxies depending on which
classification method was used, which we argue is due to our non-standard
implementation of Galaxy Zoo morphologies, and therefore highlights the care
that must be taken when separating galaxies by their visual morphologies.
Reassuringly, there is agreement that late-type galaxies exhibit the stronger
downsizing effects among galaxies with stellar mass $M_{\star}>6\times
10^{9}\,M_{\odot}$ and that high-mass elliptical and lenticular galaxies have
had similar star-formation histories.

Irrespective of classification scheme, we find that the effect of present-day
colour is greater than the effect of present-day morphology on a galaxy’s
star-formation history — confirming previous results (Ibarra-Medel et al.,
2016; García-Benito et al., 2019) — in that the contribution from present-day
blue cloud galaxies increased by $\sim 40\%$ over the past $10\,\textrm{Gyr}$
but that from spirals only increased by $\sim 20\%$ over the same time period
by comparison. Similarly, although we found that present-day spirals and blue
cloud galaxies exhibited the more recent peaks in star-formation at all
stellar masses, the typical difference between spiral and elliptical galaxies
($\sim 0.3\,\textrm{dex}$) is less than that between blue cloud and red
sequence galaxies ($\sim 0.6\,\textrm{dex}$). These results suggest that
galaxies of similar morphologies are more likely to have undergone more
significantly different histories compared to the equivalent variation in
histories among galaxies of similar colours.

However, we also find evidence that these straightforward results do not tell
the complete story. Specifically, we find that both present-day colour and
morphology reflect only the more recent star-formation histories among lower-
mass galaxies compared to their counterparts with high stellar mass. We
interpret this as reflective of a galaxy’s inertia to change. The physical
processes required to suppress or rejuvenate star-formation or to restructure
a galaxy must occur over longer timescales to significantly alter a massive
galaxy’s observed properties. Meanwhile, the tidal, stripping, starvation, or
inflow processes experienced by less massive galaxies are able to affect their
star-formation rates (and therefore colours) and morphologies much more
rapidly.

We have therefore demonstrated that a galaxy’s mass, colour and morphology —
size, shade and shape — all indicate its historical contribution to the cosmic
star-formation history, but to different extents and with codependencies such
that all three properties must be considered to build a full picture.

##  7 Summary

Using an established stellar population “fossil record” analysis, we obtained
star-formation histories of the inner $1.2\,R_{\rm e}$ of 6861 galaxies from
the SDSS-IV MaNGA survey, with 2519 galaxies also sampled to $2.3\,R_{\rm e}$.
By carefully weighting each galaxy to create an effectively volume-limited
sample, we inferred the star-formation history of the Universe, which was
found to be in general agreement with previous observations of galaxy
populations at different redshifts.

We showed that a galaxy’s star-formation history is linked to its present-day
mass, its colour, and its morphology, although colour is more strongly
connected than morphology regarding historical contributions to the cosmic
star-formation history. We also found evidence for downsizing effects being
significant in galaxies of all present-day colours and morphologies, in that
low-mass galaxies of all types have become more dominant in their contribution
to the cosmic star-formation rate in more recent times. These effects,
however, were found to be most significant among galaxies currently in the
blue cloud. Different morphological classification schemes gave contradictory
results on whether downsizing is strongest among galaxies designated as being
currently early or late type, but show agreement that spiral galaxies exhibit
the stronger effects among galaxies with present-day stellar mass
$M_{\star}>6\times 10^{9}\,M_{\odot}$.

We also found that the historical contribution to the cosmic star-formation
history from galaxies currently in the “green valley” does not directly follow
that of either the blue cloud or the red sequence populations, with these
galaxies’ star-formation histories being remarkably representative of that of
the Universe as a whole.

These results once again demonstrate the power of stellar population fossil
record techniques in uncovering the link between the Universe’s past with the
galaxies we see today.

##  8 Data Availability

This publication uses the team-internal MPL-9 version of the MaNGA science
data products, which are broadly similar to previous versions available
publicly through SDSS Data Releases DR13 (Albareti et al., 2017), DR14
(Abolfathi et al., 2018), and DR15 (Aguado et al., 2019). Comparable data
products containing the full MaNGA galaxy sample — including the full sample
used here — will be publicly released in 2021 as part of SDSS DR17, as will
the raw data and all previous versions of the data reduction pipeline.

## Acknowledgements

The authors thank the anonymous reviewer for their helpful suggestions and
improvements to this paper.

The authors also thank S. F. Sánchez, D. Wake, A. R. Calette and A. Rodriguez-
Puebla for their extensive help and support on the technical aspects of this
work.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS acknowledges support and resources from the
Center for High-Performance Computing at the University of Utah. The SDSS web
site is www.sdss.org.

SDSS is managed by the Astrophysical Research Consortium for the Participating
Institutions of the SDSS Collaboration including the Brazilian Participation
Group, the Carnegie Institution for Science, Carnegie Mellon University, the
Chilean Participation Group, the French Participation Group, Harvard-
Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The
Johns Hopkins University, Kavli Institute for the Physics and Mathematics of
the Universe (IPMU) / University of Tokyo, the Korean Participation Group,
Lawrence Berkeley National Laboratory, Leibniz Institut f ur Astrophysik
Potsdam (AIP), Max-Planck-Institut f ur Astronomie (MPIA Heidelberg), Max-
Planck-Institut f ur Astrophysik (MPA Garching), Max-Planck-Institut f ur
Extraterrestrische Physik (MPE), National Astronomical Observatories of China,
New Mexico State University, New York University, University of Notre Dame,
Observatório Nacional / MCTI, The Ohio State University, Pennsylvania State
University, Shanghai Astronomical Observatory, United Kingdom Participation
Group, Universidad Nacional Autónoma de México, University of Arizona,
University of Colorado Boulder, University of Oxford, University of
Portsmouth, University of Utah, University of Virginia, University of
Washington, University of Wisconsin, Vanderbilt University, and Yale
University.

This publication uses data generated via the Zooniverse.org platform,
development of which is funded by generous support, including a Global Impact
Award from Google, and by a grant from the Alfred P. Sloan Foundation.

We are grateful for access to the University of Nottingham’s Augusta high
performance computing facility.

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