# The SAMI - Fornax Dwarfs Survey IV. Star Formation Histories of Dwarf and
Early-Type Galaxies: Insights from Full Spectral Fitting

Romero-Gómez, J.,1,2 J. A. L. Aguerri1,2, Reynier F. Peletier3, Steffen
Mieske4, Glenn van de Ven5 and Jesús Falcón-Barroso1,2,
1Instituto de Astrofísica de Canarias, Calle Vía Láctea S/N, E-38205, La
Laguna, Tenerife, Spain
2Universidad de La Laguna Avda. Astrofísico Fco. Sánchez, E-38205 La Laguna,
Tenerife, Spain
3Kapteyn Institute, University of Groningen, Landleven 12, 9747, AD,
Groningen, The Netherlands
4European Southern Observatory, Alonso de Cordova 3107, 7630355 Vitacura,
Santiago,Chile
5Department of Astrophysics, University Vienna, Türkenschanzstrasse 17, A-1180
Wien, Austria
E-mail<EMAIL_ADDRESS>(IAC)

(Accepted 2023 December 6. Received 2023 November 27; in original form 2023
June 5)

###### Abstract

We present a study on the star formation histories (SFHs) of galaxies covering
the range $10^{4}$ < M⋆/M⊙ < $10^{12}$, leveraging full spectral fitting
algorithms. Our sample consists of 31 dwarf galaxies from the SAMI-Fornax
Survey with stellar masses between $10^{7}$-$10^{9.5}M_{\odot}$, early-type
galaxies from the ATLAS3D project with stellar masses between
$10^{10}$-$10^{12}M_{\odot}$, and dwarf galaxies that are satellites of
Andromeda and the Milky Way, with $10^{4}$ < M⋆/M⊙ < $10^{8}$. We find that
galaxies from $10^{7}$-$10^{8}M_{\odot}$ exhibit the smallest star formation
rates (SFRs), while the SFR increase as we move down or up in mass. In this
sense, we find that some $10^{5}M_{\odot}$ galaxies have cumulative SFHs that
are comparable to those of $10^{12}M_{\odot}$ galaxies. Our study shows that
the evolution of giant galaxies is primarily governed by their internal
properties, with timescales that do not depend on their environmental
location. In contrast, dwarf galaxies below $10^{8}M_{\odot}$ can be
significantly affected in dense environments, such as the inner regions of a
cluster, that severely quench the galaxies before the assembly of their 50%
present-day mass. We find that, only dwarfs with stellar masses between
$10^{7}$-$10^{9}M_{\odot}$ actively form stars nowadays, while less massive
galaxies seem to remain unaffected by the environment due to the expulsion of
most of their gas at an early stage in their evolution. Our study highlights
and corroborates a critical threshold around $10^{8}-10^{9}M_{\odot}$ in
galaxy evolution from previous studies, separating more massive galaxies
minimally impacted by the environment from those less massive galaxies
quenched by it.

###### keywords:

galaxies: dwarf - galaxies: evolution - Galaxies: star formation - Galaxies:
fundamental parameters

††pubyear: 2023††pagerange: The SAMI - Fornax Dwarfs Survey IV. Star Formation
Histories of Dwarf and Early-Type Galaxies: Insights from Full Spectral
Fitting–C

##  1 Introduction

One of the fascinating objects that have captivated astronomers for centuries
are galaxies. They come in a variety of shapes and sizes, and their properties
can vary significantly from one galaxy to another. One of the key questions in
astrophysics is how galaxies form and evolve over time. By understanding the
star formation histories, one understands how galaxies form. Stars are the
building blocks of galaxies, and their formation and evolution are intimately
connected to the properties of their host galaxies. By studying the star
formation histories of galaxies, we can gain insights into the physical
processes that shape their evolution, such as cosmic reionization (Ricotti et
al., 2002; Salvadori et al., 2014; Katz et al., 2020), feedback from
supernovae (Salvadori et al., 2008; Stinson et al., 2009; Sawala et al., 2010)
and environmental processes (Gunn & Gott, 1972; Larson et al., 1980), among
others. On top of that, the shape of a SFH can be also used to study the
growth of the halo at low halo masses (Fitts et al., 2017; Scholz-Díaz et al.,
2023), or even the nature of Dark Matter, since different dark matter content
predict different accretion rates (Governato et al., 2015; Bozek et al.,
2019), which is then reflected in the SFH.

Ideally, to obtain the SFH of a galaxy in great detail we should study all of
its stars individually. Photometry can be used to analyze the light emitted by
stars, and place them in a colour-magnitude diagram (CMD) to get ages and
masses (Dolphin et al., 2005; Albers et al., 2019). If deep enough, one can
derive a SFH from the CMD as the amount of mass formed at different times.
With the current technology, such stellar CMDs can only be constructed for
galaxies within the Local Group (Mateo, 1998; Tolstoy et al., 2009; Weisz et
al., 2011; Monachesi et al., 2012). For galaxies beyond the Local Group, one
needs to analyse the integrated stellar light with spectroscopy. By analyzing
the integrated light emitted by stars in a galaxy we can get the luminosity
weighted mean value of its stellar population properties. To obtain SFHs, that
by definition go beyond mean present-day properties, we have to compare galaxy
spectra with different single stellar population models (SSP) (Prugniel et
al., 2007; Vazdekis et al., 2010; Verro et al., 2022), and then use spectral
fitting algorithms (Cappellari & Emsellem, 2004; Cid Fernandes et al., 2005).
With this technique, it is possible to constrain the weights that different
populations have in the galaxy spectra, and with the corresponding ages a SFH
can be constructed (Fahrion et al., 2021; Bidaran et al., 2022; Scholz-Díaz et
al., 2023). The disadvantage of spectroscopy is that high signal-to-noise
(S/N) spectra are needed, which depends on the mass and distance to the
galaxy. Massive galaxies have been studied for decades, and the general
consensus is that galaxies with stellar masses greater than $10^{10}$ M⊙
formed most of their stars very fast during the early epochs of the Universe
(Heavens et al., 2004; Panter et al., 2007; Carnall et al., 2019).

Dwarf galaxies, on the other hand, are small, low-mass galaxies that are much
less luminous than their larger counterparts. That is the reason why, despite
being the most common type of galaxy in clusters and groups (Binggeli et al.,
1990; Ferguson & Binggeli, 1994), our understanding is more limited. First
detailed studies of dwarf galaxies started with the Local Group (Shapley,
1938; Wilson, 1955; Cannon et al., 1977), and were then extended to nearby
galaxy clusters (e.g., Ferguson & Sandage, 1988; Binggeli et al., 1985; Smith
et al., 2009; Sybilska et al., 2017; Bidaran et al., 2020). When looking at
the stellar population ages there are star forming and quiescent dwarfs. The
stellar populations of the star forming galaxies have barely been studied
outside the Local Group (e.g. Koleva et al., 2014), because the stellar
continuum is weak. In this paper, we will focus on the ’classical’ low surface
brightness dwarfs, the quiescent dwarfs, which include dwarf ellipticals
(dEs)(Binggeli et al., 1988) and dwarf spheroidals. These dwarfs are usually
intermediate-old objects, $\sim$9 Gyr (Koleva et al., 2009; Sybilska et al.,
2017), although some of them can also be young star-forming dwarfs (Michielsen
et al., 2008; Ryś et al., 2015). The age of a stellar population is an
integrated (or averaged) star formation history: the older a galaxy is, the
faster after the Big Bang it should have formed most of their present-day
mass. Although some studies of the SFHs of dwarfs in clusters recently start
appearing in the literature (Fahrion et al., 2021; Bidaran et al., 2022), our
knowledge comes mostly from the Local Group , where detailed SFHs can be
obtained.

The analysis of the observed SFHs made by Weisz et al. (2011) reveals that,
independently of their morphological types, dwarfs with a M⋆ $\sim$$10^{7}$ M⊙
usually formed half of their current stellar mass $\sim$10 Gyr ago. Less
massive dwarfs are expected to continue the ’downsizing’ (Cowie et al., 1996;
Thomas et al., 2005; Fontanot et al., 2009; McDermid et al., 2015). This means
that massive galaxies form fast, and as we go down in mass we expect them to
form their stars more gradually. However, most of the examples we can find in
the Local Group disagree. Weisz et al. (2014a) presented photometric SFHs of
dwarfs, and argued that most less massive galaxies formed at earlier times,
while higher mass galaxies formed later. This agrees with other studies that,
using simulations, have also tried to disentangle the formation of dwarfs. For
faint dEs, studies have shown that the quenching time, the time it takes the
galaxy to form and consume the available gas, is shorter at low stellar masses
($\sim$$10^{6}$M⊙ ) than at intermediate-mass ($\sim$$10^{8}$-$10^{9}$M⊙ ) dEs
(Wheeler et al., 2014; Fillingham et al., 2015; Wetzel et al., 2015). There
are many processes that can be responsible for the quenching.

When dwarf galaxies fall into a cluster environment, their star formation is
believed to be suppressed through different mechanisms (Gunn & Gott, 1972;
Larson et al., 1980; Lisker, 2009), and their gas is removed by the Intra
Cluster Medium, which could result in a jellyfish appearance (Poggianti et
al., 2016). In the field, i.e., outside clusters or groups, however, Geha et
al. (2012) found that there are no quenched dwarfs with $10^{8}$ < M⋆ <
$10^{9}$ M⊙ beyond distances of 1 Mpc from a massive host, suggesting that
very few dwarf galaxies over $10^{9}$ M⊙ have been quenched in these regions.
In addition, Geha et al. (2012) noticed that the fraction of quenched dwarfs
increased with smaller distances to the host. These environmental quenching
effects have been also detected in other environments like galaxy clusters
(Wang et al., 2022). Further observations made by Fillingham et al. (2016) are
consistent with these results. Studying HI surface density profiles, they
found that in the local Universe, stripping was more effective for galaxies
with M⋆ < $10^{8}$M⊙ , which suggests a barrier where the quenching in SFHs
goes from slow to fast. Gallart et al. (2015) also classified the SFHs of
Local Group dwarfs as fast or slow, arguing that this was related to the
position and/or the possible interaction of dwarfs with the Milky Way or M31.
These ideas are back up by simulation studies. Using the dwarfs satellites of
Milky Way-like galaxies from the AURIGA simulation (Grand et al., 2017),
Simpson et al. (2018) found that dwarfs closer to the host suffered more
quenching due to ram pressure stripping (Gunn & Gott, 1972). The effect was
more intense at lower masses, around $\sim$$10^{6}$M⊙ all dwarfs that are
satellites or have been satellites in the past are quenched. This effect is
less important the more massive the galaxy is, meaning, that the fraction of
quenched galaxies decreased with increasing stellar mass. These group effects
are also important in cluster like environments. Using the EAGLE simulations,
Pallero et al. (2019) found that around 60% of galaxies suffer a strong drop
in their star formation rates outside the virial radius of the cluster,
indicating that they were pre-processed. This means that the quenching process
started before the galaxies started to fall, and then the decline got stronger
from infall onward reaching the quench state inside the cluster. It exists, as
well, a small fraction of galaxies that are quench even before arriving at the
cluster.

Along with the environmental processes, there are other external effect
capable of quenching galaxies. Weisz et al. (2014b) found in their sample only
two dwarfs that were quenched quickly after the Big Bang, therefore compatible
with being quenched by reionization. This was supported by the observations
made by Brown et al. (2014b), who proposed that reionization is the most
likely cause for quenching the faintest galaxies (M⋆ $\sim$$10^{4}$ M⊙ ).
Other works based on Local Group objects have shown that reionization alone is
not enough to quench dwarfs within a stellar mass range of $10^{6}$-$10^{7}$M⊙
(Monelli et al., 2010; Hidalgo et al., 2011, 2013). But in terms of the
process responsible for the quenching, it is clear that not only external
processes are responsible for the evolution of the stellar populations,
internal processes can play a role too (Thomas et al., 2010). According to
simulations, supernova feedback can completely quench low mass galaxies
($10^{5}$-$10^{7}$M⊙ ) in time scales similar to reionization (Sawala et al.,
2010). Agreeing with this, observations have also shown that supernovae
feedback can quench low mass galaxies, M⋆ $\sim$$10^{4}$M⊙ , in a short time
scale (Bromm & Yoshida, 2011; Gallart et al., 2021). In addition, Benítez-
Llambay et al. (2015) studied a combination of reionization and supernova
feedback to explain the variety of SFHs in nearby dwarfs and conclude that the
relative importance of each effect depends on the mass of the object.

Ultimately, the strong suppression of star formation after reionization has
been proposed as one possible explanation for the discrepancy in the missing
satellites problem (Simon & Geha, 2007). The issue is that there is a mismatch
between the number of observed dwarfs versus the number of simulated dark halo
substructures (Klypin et al., 1999; Bullock & Boylan-Kolchin, 2017). While the
simulated distribution of dark matter halos of comparable mass seems to match
the number of observed Milky Way-sized galaxies, the number of observed dwarfs
is much lower than the number of dark halos in their mass regime. Possible
solutions to the problem include the destruction of fainter halos through
reionization (Quinn et al., 1996; Alvarez et al., 2009; Brown et al., 2014a)
or feedback from stellar processes (Dekel & Woo, 2003; Governato et al.,
2007), but the observational tests of those proposals have not been
conclusive. In addition, the effects of these processes on the galaxy’s
stellar mass function are expected to differ in different environments such as
the field and clusters. In the end, all of these processes could leave an
imprint in the formation of dwarfs. Thus, studying their SFHs could help to
solve many puzzles in understanding the evolution of dwarf galaxies.

This will be paper IV of this series of papers based on the analysis of an
integral field unit (IFU) survey of dwarfs galaxies in the Fornax cluster. We
study the SFH of galaxies in a broad total stellar mass range from $10^{4}$ to
$10^{12}$M⊙ , by adding to the SAMI-Fornax sample maassive galaxies from the
ATLAS3D survey and less massive galaxies from the Local Group . The paper it
is organized as follows: Section 2 summarizes the target selection,
spectroscopic observations and results of previous papers of this series. In
section 3 we explain the methodology used to analyse the data and to obtain
the star formations histories that we present in section 4. Then we discuss
the implication of our results in section 5, and finally, in section 6 we
summarize our findings.

Figure 1: Histograms of the distributions of different properties for our
sample of dwarf galaxies in the Fornax cluster. From left to right, the panels
show the stellar mass, projected cluster distance, age, metallicity and
[$\alpha$/Fe]. The stellar mass is from Paper II, and the rest of the
properties are computed in Paper III.

The properties of the Fornax cluster used in this work are stated in the
previous paragraphs. And throughout this paper, we use magnitudes in the AB
system and we adopt a $\Lambda$CMD cosmology with $\Omega_{m}=0.3$,
$\Omega_{\Lambda}=0.7$ and $H_{0}$ = 70 km s-1 Mpc-1.

##  2 IFU spectroscopy of Fornax dwarf galaxies

In this work, we use IFU observations of dwarfs in Fornax. Below we give a
brief description of the selection process and spectroscopic observations. For
more details on the selection of the sample, observations and data reduction
we refer to the first two papers of this series Scott et al. (2020)
(hereinafter: Paper I, ) and Eftekhari et al. (2022) (hereinafter: Paper II,
).

###  2.1 Fornax dwarf sample and spectroscopic observations

####  2.1.1 The Fornax cluster

Fornax is a nearby cluster of galaxies located in the southern hemisphere,
$\alpha$ (J2000) $=3^{h}38^{m}30^{s}$; $\delta$ (J2000) = -35∘27’18", and it
is the second closest galaxy cluster at a distance of 20 Mpc (Blakeslee et
al., 2009). It has a mean recessional velocity of 1454 km·s-1 and velocity
dispersion of 286 km·s-1 (Maddox et al., 2019). The Fornax cluster has been
the subject of numerous studies over the past few decades, which have provided
valuable information about its properties. It is smaller and less massive than
other nearby galaxy clusters, with a mass of $7\times 10^{13}M_{\odot}$ and a
0.7 Mpc virial radius (Drinkwater et al., 2001). This makes it the densest
object in the Fornax-Eridanus filament (Nasonova et al., 2011). Fornax has a
sub-group of a similar mass, Fornax A (Ekers et al., 1983; Maddox et al.,
2019), which is expected to fall into the main Fornax Cluster (Drinkwater et
al., 2001). Photometrically the cluster has been examined in the Fornax
Cluster Catalogue (FCC) (Ferguson, 1989), The Next Generation Fornax Survey
(NGFS; Eigenthaler et al., 2018) and the Fornax Deep Survey (FDS) catalogue
(Venhola et al., 2018). This last catalog in Venhola et al. (2018) is more
complete and deeper than the others, and the newest catalog, Venhola et al.
(2022), also contains many very low surface brightness dwarfs down to a level
of 27 mag arcsec-2. This study has detected about 1000 galaxies in Fornax and
Fornax A. Since, after Virgo, Fornax is the closest galaxy cluster, it is a
perfect candidate to obtain the spectra of low surface brightness galaxies,
like dwarfs. It represents an important laboratory for studying the formation
and evolution of galaxies.

####  2.1.2 Spectroscopic sample and observations

The objects selected for the spectroscopic observations were observed at the
Sydney-Australian Astronomical Observatory (AAO), using the 3.9 m Anglo-
Australian Telescope (AAT) and the Multi-Object Integral-Field Spectrograph
called SAMI (Croom et al., 2012). Using fibres, SAMI has 13 IFUs, each 15" in
diameter, with a field of view of 1º. The observations were made in 10
pointings, with a total exposure time per field of 7 hours and a dither
pattern to ensure that the S/N was distributed uniformly on each IFU. The
objects were observed in a total of 3 runs, the first in 2015 with objects
selected from the FCC, and the next runs were in 2016 and 2018, using the FDS
to select the objects. Apart from dEs other secondary targets were observed,
like giant galaxies, UCDs or background galaxies.

The full spectroscopic sample consisted of 118 galaxies. This sample contains
56 secondary targets like UCDs, giant early-type and late-type cluster
members, and background galaxies. The primary targets, 62, are classified as
early-type, dE or dS0, 38 were bright enough be able to determine their
internal kinematics (Paper II). Some dwarf galaxies in this set showed
prominent emission lines in their spectra. These galaxies are mainly late-type
dwarf irregulars and BCDs, as classified by Venhola et al. (2019), but there
is also one quiescent dwarf that has ionized gas. These galaxies with ionised
gas will not be part of the main analysis in this paper, thus, our final
sample of dwarfs is composed of 31 dEs. The sample objects are located inside
the virial radius of the Fornax cluster, and one is associated with the Fornax
A group. The distribution of some basic properties like the stellar mass or
the projected distance can be seen in Figure 1.

###  2.2 Results from the previous papers in this series

In this paper, we analyse the star formation histories of the SAMI-Fornax
dwarf galaxy sample. In the following we briefly summarise the previous
analyses made with this sample in Paper I, Paper II and Romero-Gómez et al.
(2023) (hereinafter: Paper III, ).

In Paper I, the SAMI-Fornax Survey is described in terms of target selection,
observation design and data reduction, and the specific angular momentum of
the sample galaxies is analysed. For that purpouse, on the final spectra of
the galaxies a kinematic analysis is done using the Voronoi binning techniques
(Cappellari & Copin, 2003), ensuring a minimum signal-to-noise ratio (S/N).
Spatially resolved maps of the line-of-sight velocity (V) and velocity
dispersion ($\sigma$) are constructed using full-spectral-fitting techniques
(FSF). From these properties, the specific angular momentum ($\lambda_{R}$) of
the galaxies is derived. We find that dwarf galaxies exhibit significantly
lower $\lambda_{R}$ values than more massive counterparts around
$10^{10}M_{\odot}$, while only slightly higher than those seen in massive
ellipticals that have almost no rotation. To explain those results, two
scenarios are proposed: first, quiescent dwarfs with stellar masses below
$10^{9}M_{\odot}$ could originate from low-mass spirals (M⋆
$\sim$$10^{10}M_{\odot}$) that lose about 90% of their mass during their
cluster infall. Alternatively, quiescent dwarfs might originate from star-
forming dwarfs that fell into the cluster and were subsequently quenched by
the environment. In this case, dwarf irregulars demonstrate kinematics similar
to dwarf spheroidals, as ram pressure stripping has negligible impact on the
stars. These unexpected results requires further studies to comprehend and
verify their implications.

In Paper II the scaling relations on the fundamental plane (FP) and stellar
mass fundamental plane are studied. The results pointed to an increase in the
mass-to-light ratio of galaxies for lower masses since dwarfs with masses
between $10^{7}$ and $10^{8.5}$ $M_{\odot}$ deviate slightly from the FP
defined by all galaxies. Another result, based on the dynamical-to-stellar
mass ratio, is that low-mass galaxies have more dark matter than brighter
dwarfs and giants. In particular, dwarfs in Fornax have dark matter content
comparable to the Local Group dwarfs of similar masses.

In Paper III, studying the galaxies as a whole and using again FSF, integrated
stellar population parameters like age, metallicity and [$\alpha$/Fe] are
obtained. The distribution of these and other properties of our Fornax dwarfs
can be seen in Figure 1. To compare with more massive galaxies the spectra of
the giant galaxies from the ATLAS3D project are also analysed with the same
methodology. The results showed that the typical [$\alpha$/Fe]-stellar mass
linear relation derived for massive galaxies (Worthey et al., 1992; McDermid
et al., 2015) does not fit the dwarfs. Instead, a second-order polynomial is
needed to fit the whole sample, displaying a U-shape relation. In terms of the
environment, age and metallicity are independent for both dwarf and giants,
but for dwarf galaxies, we found a linear relation between [$\alpha$/Fe] and
projected distance to the cluster, with more $\alpha$-enhanced galaxies at the
center (Smith et al., 2009). Using the properties of Milky Way satellites, we
were able to confirm that a relation between [$\alpha$/Fe] and the distance to
the Milky Way also exists for low-mass dwarfs living in the Local Group.
Additionally, we noticed that the [$\alpha$/Fe]-stellar mass U-shape derived
from the Fornax dwarfs and ATLAS3D giants, can easily be extended to the low-
mass galaxies of the Local Group. These results suggests that the
[$\alpha$/Fe] values of galaxies are driven by a combination of internal and
external properties. Massive galaxies are barely affected by the environment,
with $\alpha$-enhancement decreasing with stellar mass down to $\sim
10^{9}M_{\odot}$, where we find solar-like values. For galaxies with stellar
masses between $10^{7}$ to $10^{9}M_{\odot}$ the environment starts to quench
galaxies as they approach a cluster or group. For even less massive galaxies,
given the linear relation with projected distance, the environment seems to
quickly quench galaxies, giving us high [$\alpha$/Fe] values.

Figure 2: Figure with the scheme followed during regularizaton. _Top blue
dashed panel, step 1_ : $\chi^{2}$ of pPXF fitting as a function of the
regularization, with each point coloured with the latter parameter. The green
horizontal line represents the desired $\Delta\chi^{2}$, which depends only on
the number of fitted pixels, and the vertical red line is the maximum tested
regularization that does not surpass the desire $\Delta\chi^{2}$. _Central
blue panel, step 2_ : mini panels, from A to D show the SFHs for different
regularizations, marking with a dotted line those that are excluded in this
step. The red dashed line represents the SFH without regularization, and the
grey band in A, B, C and D indicates how much we allowed the SFHs to be
smoothed. This band has been computed as the maximun peak of the SFH at R = 0,
minus 1/number-of-age-models. The mini panel E show the cumulative SFHs for
all the allowed regularizaiton according to step 1, the un-regularized
cumulative SFH. The two horizontal black dotted lines in this mini panel show
the formation of the 50% and 90%. _Bottom dotted blue panel, step 3_ : ages
and metallicities of each regularization that overlaps with the grey band in
panels A to D of step 2, with a legend indicating the distance to the the
stellar populations of the un-regularized fit, marked with a red cross. At
this final step, if two points have the same distance, we choose the higher
regularization. In the example presented in this figure we choose a
regularization of 0.08.

##  3 Recovering star formation histories

To recover the star formation histories we first treated the spectra in
exactly the same way as we did in Paper III to study the stellar population
properties. The specific details are given in that paper, and here we provide
a summary.

First, we convolved all spectra to a resolution of 2.5 Å in FWHM, which is the
resolution of the spectra in the MILES stellar library (Sánchez-Blázquez et
al., 2006; Vazdekis et al., 2010; Falcón-Barroso et al., 2011). These models
have been used to study stellar population properties as well as the SFHs,
using FSF. With the penalized Pixel-Fitting Code (pPXF, Cappellari & Emsellem
2004 and Cappellari 2017), we fitted the kinematics of each galaxy spectrum
employing the ELODIE stellar library (Prugniel et al., 2007) and additive
Legendre polynomials. To obtain the stellar populations and SFHs, we first
have to fit the kinematics, for that we used ELODIE models because with its
resolution of 0.55 Å in FWHM pPXF is capable of reaching the velocity
dispersion typical of dwarf galaxies, $\sim$10 km/s (Toloba et al., 2012).
Once the recessional velocity and velocity dispersion have been fixed, the
stellar population properties are obtained by applying multiplicative
polynomials during the fitting process. For this latter part, we decided to
work with the Vazdekis/MILES models because they have a wider scope of stellar
parameters that are updated frequently, even though their resolution is worst
than that of SAMI.

###  3.1 Star formation histories

After the process of obtaining the stellar population parameters with pPXF a
series of weights are returned, each one corresponding to the relative
contribution of the specific stellar template to the final best fit. To
optimise the time performance of the fitting, we limited the ages of the
models from MILES to 0.04, 0.5, 1, 3, 5, 7, 9, 11, 13, and 14 Gyr. These
models also span a wide range in metallicities and a possible [$\alpha$/Fe] of
0.0 and 0.4 dex (see Romero-Gómez et al., 2023, for more details). We tested
this grid selection to ensure that the resulting stellar properties were not
significantly affected by this choice. We constructed the star formation
history of each galaxy, by summing up the weights returned by pPXF over all
metallicities and [$\alpha$/Fe] at a given template age, which can be seen as
the fraction of the galaxy that formed at that specific time. For our result,
the pPXF fit was light-weighted, hence, we can draw the SFH of a galaxy as the
light fraction formed at different epochs.

The main problem is that the distribution of the weights from pPXF is usually
discrete, meaning that it only selects a few populations from a library that
contains hundreds, even if a high resolution grid is used. Consequently, the
SFH will always look like a spiky function instead of a smooth distribution.
For some galaxies, the SFH could really consist only of different bursts at
different epochs, which in turn will look like two or three peaks. But for
some others, the SFH could be a more continuous star-forming process and pPXF
will still select only a discrete number of populations. Thus, the SFH will
look as if it consists only on a few bursts disperse over time, when the
correct SFH would be a continuous function. We mitigate this problem using a
technique called regularization (Press et al., 1992). In brief, this technique
allows to identify the smoothest solution among the set of degenerate
solutions that fit the data equally well (see also Cappellari, 2012).
Mathematically, the smoothing of the regularization process forces two
neighbouring templates to have zero derivatives, which in practice makes one
population share its weight with the neighbours.

The level of regularization, R, during the pPXF fit is controlled by its own
keyword inside the code. The SFH can be smoothed as much as needed, although
finding the correct regularization is a complicated process. First of all, as
said before, a given SFH may not be smooth. Star formation is a stochastic
process that with enough time resolution can be full of small bursts induced
by different events. For that reason, while finding the correct amount of
smoothness that matches the input spectra, one has to be aware of where the
significant physics is: the essential information resides in the general shape
of the recovered SFHs, and not in small features that can appear. This is
mainly due to the degeneracy problem of the fit, since the recovered solution
is not unique. Among the mathematically compatible and smooth solutions of the
regularization, the weight difference between neighbours templates becomes
smaller as the regularization increases, so, a flat SFH could be obtained if
the regularization is set too high.

A detailed description of the approach to address this maximum regularization
searching is described in Cappellari (2017). In summary, the standard
procedure is as follows: first, perform an un-regularized fit adjusting the
input noise (1$\sigma$ uncertainty in the galaxy spectrum) until the
$\chi^{2}$ of the fit is $\sim$1, and then, raising the input regularization,
while doing several tests until the difference between $\chi^{2}$ of the un-
regularized and the current fit has increased by
$\Delta\chi^{2}\sim\sqrt{2N}$, where $N$ is the number of fitted pixels. In
the top panel of Figure 2, which represent the step 1, it can be seen how
$\Delta\chi^{2}$ changes with the regularization parameter. For each galaxy in
our sample we tested different regularization values, and chose as possible
regularizations those below the $\Delta\chi^{2}\sim\sqrt{2N}$ level, which can
be seen as an horizontal line in the top panel of Fig. 2. With this recipe,
the smoothest SFH possible is recovered using the maximum regularization among
the allowed values.

Although it is usual to use as the final SFH that of the maximum
regularization (McDermid et al., 2015; Fahrion et al., 2021), we notice that
for some of our dwarfs the smoothest SFH solution, though it is mathematically
compatible with the data, was close to a straight line and the weights of the
main populations contributing had melted away. In the central panel D of Fig.
2 we show how the two main populations contributing to the un-regularized fit
of a galaxy are replaced by an almost constant star formation rate at the
maximum regularization allowed. In addition, the stellar population parameters
of this featureless SFH were slightly different from the un-regularized
results (Paper III). For this reason, we devise a second step to the
regularization procedure to ensure that the SFH is not smooth down to a
straight line and at the same time the stellar population parameters are as
close as possible to the un-regularized results. So after having found the
maximum allowed regularizatfion for one galaxy, we look for the maximum weight
of the un-regularized fit, which defines us a top value for the SFH. While we
increase the regularization, this top weight will lose its relative importance
with the other populations. We decided that this top level will only be
allowed to smooth down 1/number-of-age-models, thus, creating a band like the
one represented in the central panels A, B, C or D of Fig. 2. We tested this
smoothed number and choose it to be inversely proportional to the number of
models because the more models you use, the more smooth the SFH is at R = 0.
Thus, the more age models the less you need to smooth. For example in the
central panel D of Fig. 2 it can be seen that, when the regularization is
high, the SFH has been smoothed to much, the maximum allowed in that case is
R=7, and the two populations from the un-regularized SFH are not
distinguishable. For this reason, we select only regularization values whose
SFH maximum are inside the grey band, like those in the central panels A or B,
to ensure that they have not been smoothed down too much. We want to remark
that this process is just to define how smooth we want the SFHs to look,
because any of the regularization values below the maximum level are
mathematically compatible. As an example, in the central-bottom panel E of
Fig. 2, we show the various possibilities for the times at which 50% and 90%
of the current mass were formed and they are all similar for the allowed
regularization values. The differences are of the same magnitude as the
typical age error for these galaxies. Finally, as a fine tunning, with the
selection of regularization values with a SFH overlapping with the grey band
we look at the distance to the un-regularized fit in the age-metallicity
plane, and chose the point for which the distance is minimal (see bottom panel
of Fig. 2). The [$\alpha$/Fe] parameter was not considered, since MILES only
provides two possible values, 0.0 and 0.4 dex. This means that the
regularization divides the weights 50/50 and the $\alpha$-enhancement was
always close to or equal to 0.2 dex in all cases. Usually, the minimum
distance is expected to be related to the lowest non-zero value of
regularization, however, this was not the case for most galaxies since this is
a highly non-linear process. Finally, once the regularization has been chosen,
we fix this parameter and using the residuals of the fit we randomly perturb
the best fit from pPXF using Monte-Carlo (MC) simulations and computing the
uncertainties of the weights.

###  3.2 Computing cumulative formation times

Based on the age grid where a given SFH is distributed, as illustrated in
Figure 2, the cumulative sum of the weights would reveal the time at which
different mass fractions were formed. For example, the time at which 20% of
the mass was formed, t20. Our age grid consists of models with ages between
0.04 and 14 Gyr, so in order to have a more continuous function we
interpolated the cumulative SFHs, to extract them with a finer age grid, of
ages from 0 to 14 Gyr equally spaced by steps of 0.1 Gyr. We obtained the
aforementioned t20 from the finer grid. Since the process could introduce
noise and affect the calculations, we made use of the weights errors of each
SFH to run MC simulations. Finally, the formation times and their
uncertainties are computed as the mean and standard deviation values of the
distribution, respectively.

##  4 Results

This section presents the resulting SFHs computed with pPXF and the MILES
library. As stated before, we limit this analysis to dwarf galaxies without
emission lines, which leaves us with a sample of 31 dEs covering a stellar
masses between $10^{7}$ and $10^{9}$ M⊙ .

Figure 3: Star formation histories of dEs in our SAMI-Fornax sample. The
galaxies are ordered according to their stellar mass from left to right and
from top to bottom. Only galaxies with S/N higher than 15 are included here.
For each galaxy, we show two panels, one with the light fraction and the other
with the cumulative fraction, both as a function of the lookback time (Gyr).
In each panel, the mean SFH from the MC simulations is shown with a blue line,
and the errors are the light-blue shadow. For comparison of the smoothing
process, the red dashed line represent the unregularized SFH. We also included
the name of each galaxy, the mean light-weighted age obtained from the SFH,
and the corresponding stellar mass. The curves with the cumulative fraction
incorporate two vertical dashed black lines indicating the formation time of
the 50% and 90% of the present-day stellar mass.

###  4.1 Star formation histories of dwarf galaxies

In Fig. 3 we present the SFHs of SAMI-Fornax dEs. We also included vertical
lines indicating two characteristic formation times, t50 and t90. These are
useful and interesting parameters that indicate the time when the 50% and 90%
of the mass was formed. It is usually considered that $t_{50}$ is related to
the formation time of the galaxy halo (Tojeiro et al., 2017), while $t_{90}$
is considered as a proxy of the quenching time of the galaxy, when the star
formation has entirely ceased (see Ferré-Mateu et al., 2018a).

In our sample of dEs, 80% of them formed half of their present-day mass more
than 8 Gyr ago, with a mean $t_{50}$ of 11 $\pm$ 3 Gyr. But only a few of them
built this percentage of mass in less than 2 Gyr since the Big Bang. On the
other hand, we notice that only three of our dwarfs are compatible with being
already quenched 12 Gyr ago, and by 4 Gyr ago only half of our SAMI-Fornax
sample put a stop to their star-forming activity. The mean $t_{90}$ of our
sample is 5 $\pm$ 3 Gyr. These numbers are not surprising, since the SFH is
just the time distribution of the different populations that conforms a
galaxy, and our sample is composed mostly of intermediate-old ages (see Paper
III). For most of our galaxies, the star-forming process took several Gyr to
increase from 50% to 90% of their current stellar mass, as can be seen in Fig.
3. Note that this process only lasted for about $\sim$3 Gyr for 10% of our
sample. This is an indication of how fast these galaxies were formed.

###  4.2 Comparison with the star formation histories of massive galaxies

As in our previous work, we have also re-analysed the data from the ATLAS3D
Project (Cappellari et al., 2011a), to be able to compare our results with a
sample of massive galaxies. In Paper III we reported the ages, metallicities
and $\alpha$-enhancement of these galaxies. Here we present the complementary
SFHs, using the exact same methodology explained in section 3. The ATLAS3D
sample is composed of early-type galaxies (ETGs), with a stellar mass between
$10^{10}$ and $10^{12}M_{\odot}$. Some of these galaxies belong to the Virgo
cluster, and some of them are in the field.

As we did for our SAMI-Fornax dwarfs, for every object in the ATLAS3D sample
we have derived the SFH and the corresponding formation times. To test our
results we have also compared the SFHs and the time at which 50% of the mass
was formed with the results published in McDermid et al. (2015)(hereafter:
McD15, ) (see appendix A for more details). In McD15, they notice some issues
during the spectral analysis of some galaxies for not having enough S/N,
emission lines or some other problems. We have excluded the galaxies that
display these effects as well.

Figure 4: SFHs (left column) and cumulative fraction (right column) of SAMI-
Fornax and ATLAS3D samples color coded as function of different galaxy
properties. We grouped the galaxies into four equally spaced bins, for the
different properties displayed in the colour bars. For each bin, the SFH is
the mean of the SFHs of the galaxies inside the bin, and the error is the
standard deviation. These bins are colour-coded according to the property in
the colour bars with the mean value of galaxies inside that stellar-mass bin.
From the top row to the bottom, the properties displayed are logarithmic
stellar mass, age, metallicity and [$\alpha$/Fe]. We separate with distinct
colour maps the SFHs from bins containing dEs and ETG. With blue to green
colours we represent the dwarfs in our SAMI-Fornax sample, and from yellow to
red the giant galaxies from ATLAS3D.

With the combination of the SAMI-Fornax and ATLAS3D samples, we have the SFHs
of a total of 260 galaxies with stellar masses between $10^{7}$-$10^{12}$M⊙ .
To be able to compare that many galaxies, we grouped them into bins depending
on different properties: stellar mass, age, metallicity and [$\alpha$/Fe] . We
used four equally spaced bins for the dwarfs and another four for the giants.
The final cumulative SFHs can also be seen in Fig. 4 as a function of
different internal properties of the galaxy.

As expected, the shape of the SFHs is tightly related to the stellar mass, as
shown in the top panel of Fig. 4. More massive galaxies formed at earlier
epochs, while less massive galaxies formed slower and took a longer period of
time. This trend is visible for both giant and dwarf galaxies, although it is
less pronounced for the latter. The most massive galaxies of the ATLAS3D
sample formed built up to 90% of their present-day mass within about 2 Gyrs
after the Big Bang, while the less massive dwarfs have been forming stars
until recently. For intermediate masses, 109 < M⋆ < 1010 M⊙, we notice that
the cumulative SFHs of both the lowest mass galaxies from the ATLAS3D sample
and the more massive dwarfs from the SAMI-Fornax follow a similar path and it
would be difficult to distinguish them only with the information of the
cumulative SFH. This is expected since we are always looking at early-types
galaxies, although the classification of these objects in ATLAS3D Cappellari
et al. (2011a) and SAMI-Fornax Venhola et al. (2018, 2019) is different,
probably due to the fact that each group uses a different definition for
classifying a galaxy as dwarf. But since, independently of the morphology, we
see that the star-formation rate is faster, the more massive the galaxy is.
This star-formation rate that goes from massive galaxies to intermediate-mass
giants, gradually connects to massive dwarfs and then continues to the less
massive dwarfs.

In the second panel of Fig. 4 we can see how older galaxies are more massive
than younger galaxies. This is in agreement with other works of the literature
where usually a relation between age and stellar mass is found (Sybilska et
al., 2017; Romero-Gómez et al., 2023). In the third panel of Fig. 4 we show
the relation of the SFHs with metallicity. The metallicity-stellar-mass
relation is a well know relation for galaxies (Kirby et al., 2013). Since the
cumulative SFHs are related to stellar mass, it is expected they are related
to the metallicity too. We can see that the ATLAS3D galaxies follow this
trend, while for dwarfs the trend is somewhat less clear. For both of these
last two properties, we see again that giants and dwarfs with similar ages or
metallicities have indistinguishable evolutionary paths.

In the fourth row of Fig. 4 we can see the SFHs according to their
$\alpha$-enhancement . Since we used the MILES models, our range in
[$\alpha$/Fe] is limited, only from 0.0 to 0.4 dex. Both dwarfs and giants
cover the same values and there is no segregation between the different
morphological types in terms of [$\alpha$/Fe] range. However, for the ATLAS3D
galaxies we see clearly a relation between the cumulative SFHs and the
$\alpha$-enhancement values. Giants with higher enhancements formed faster a
long time ago, and those with lower [$\alpha$/Fe] have been building up more
slowly, until a few Gyr ago (Paper III). This is associated with the fact that
there is a [$\alpha$/Fe] -stellar-mass linear relation for giant galaxies, but
this is not the case for the dwarfs. We see the cumulative SFH of low
[$\alpha$/Fe] below the curve of high [$\alpha$/Fe] , but we also see another
low [$\alpha$/Fe] curve following a similar path to those of higher
$\alpha$-enhancement . This is because for the mass regime of the dwarfs, the
[$\alpha$/Fe] values are not only a function of the stellar mass, but also of
the environment (Paper III). In general, as it will be discuss later in
section 5.4, the [$\alpha$-Fe] values could be used as an interpretation of
the timescales of star formation in a galaxy.

For the mass regime of the dwarfs, the formation timescales can be affected by
the environment (Smith et al., 2009). In Fig. 5 we show the cumulative SFHs in
relation to the galaxy projected distance to the center of the cluster. Based
on the mass range of the giant sample, some of them could also be affected by
the environment, but if we bin them by distance, the ATLAS3D galaxies inside
the virial radius of Virgo do not show any meaningful signs of the SFHs being
strongly affected by their present-day environment. Only when we move farther
away than the virial radius, we see that giant galaxies have slower cumulative
SFHs. On the other hand, the dwarfs in Fornax, all of them inside or close to
the virial radius of the cluster, show a clear dependence on the present-day
environment distance. The relation represents how the environmental quenching
of the star formation, for those galaxies closer to the center of the cluster,
start to be effective a few Gyrs after the Big Bang.

Figure 5: Cumulative SFHs of SAMI-Fornax and ATLAS3D samples colour coded as a
function of their distance to the cluster. We grouped the galaxies according
to their r/R200 into 4 bins. For the giants, we only use here those that fill
our definition of cluster members, and the Virgo membership definition from
Cappellari et al. (2011a). The colour codes are the same as in Fig. 4.

###  4.3 Formation times

We now analyze the formation times of the galaxies, defined as the parameters
t50 and t90, i.e., the times that 50 and 90% of the stars were formed,
respectively. In order to have a sample of galaxies covering also the lower
end of the mass spectrum, we need to include the t50 and t90 values of the
galaxies in the Local Group. For less massive galaxies is a challenge to get
an accurate spectroscopic observation, given their low surface brightness, and
when they are close enough to be easily observed, like in our Local Group , it
is impossible to get one spectrum that covers the whole galaxy. For that
reason we have relied on the photometric SFHs from Weisz et al.
(2014a)(hereafter: W14, ). Their sample is composed of 40 Local Group dwarfs,
satellites from both the Milky Way and Andromeda. They obtained the SFHs by
analyzing the colour-magnitude diagram (CMD) and using single stellar
populations to assemble an artificial CMD to fit the observed populations (see
W14, for more details). Since their methodology is different from ours the
numbers and timescales of their SFHs will not be directly comparable to ours,
but they should show similar results. For that reason, what we are interested
in, is the overall shape of the cumulative SFHs and the relation with the
different galaxy properties.

In Fig. 6 we show the cumulative SFHs coloured by the stellar-mass of each
galaxy, the curves are directly taken from W14. Here we have selected only the
dSph from their sample, avoiding the dIrr and dTrans to have a similar filter
selection to our dwarfs from Fornax. In Fig. 4, where we consider galaxies in
the mass range $10^{7}$-$10^{12}$ M⊙ , we identified the trend that for less
massive galaxies (in the Fornax cluster) the star-formation rates were
smaller. However, when considering the Local Group dwarf galaxies that cover
the stellar mass range from $10^{4}$-$10^{8}$ M⊙ , we see an opposite trend.
Those Local Group galaxies that have a stellar-mass in the same range as our
dwarf galaxies from the SAMI-Fornax sample, follow a similar evolutionary
path. The less massive galaxies, with masses below $10^{7}$ M⊙ , have SFH
curves more analogous to those of giant galaxies. To quantify this effect, we
now consider the formation times t50 and t90.

Figure 6: Cumulative SFHs as a function of the lookback time (Gyr) directly as
given by W14 (see appendix B). For each galaxy, we used the corresponding
colour code of the stellar-mass also published in W14. We applied a colour map
where the less massive galaxies are purple, and then the colour gradually goes
cyan for the most massive galaxies. The galaxies represented here are all dSph
from the Local Group, including both Milky Way and Andromeda satellites. This
sample is included to consider dwarfs down to a stellar mass o $10^{4}$ M⊙ .
Figure 7: Derived formation times of the galaxies as a function of their
stellar-mass. The panels show, from top to bottom, t50 and t90, respectively.
The giants from the ATLAS3D sample that we defined as cluster galaxies are the
filled black dots, and the empty black dots are the field ETGs. The red
circles are the dEs from our SAMI-Fornax sample, and the triangles are the dEs
located in the Fornax A sub-group. These red symbols are filled if the galaxy
has S/N > 15, otherwise is empty. The orange diamonds are the Local Group
galaxies from W14. In both panels we added a dashed grey line representing the
mean formation time for different mass bins, and a shadow with the mean error.
We used bins of 1 log(M/M⊙ ) to cover the whole range of stellar masses.

For a first comparison of the formation times, we used the SFHs from W14 to
compute the t50 and t90 times. For that, as in our galaxies, we interpolated
the cumulative curves with a function that was then used to extract the SFHs
with a finer grid. The formation times are obtained as the closest value from
the grid to the desired mass fraction. With the errors provided by W14, we
repeat the process running MC simulations. Finally, we obtained the formation
times as the mean value and the standard deviation of the distributions are
used as errors. To test these estimations, in the appendix B we show how the
SFHs of W14 looked after this interpolation process. Also in a following paper
they used the SFHs to compute the t70 (Weisz et al., 2014b), and a comparison
shows that we obtained the same formation times (see Fig. 16).

In Fig. 7 we present the t50 and t90 as a function of the stellar-mass, for
all the samples. We divided the ATLAS3D sample into cluster and non-cluster
according to the density parameter from Cappellari et al. (2011b). We defined
galaxies with a local mean surface density higher than log($\Sigma_{10}$) >
0.6 Mpc-2 as cluster members. We see that most of the Local Group galaxies
took less time than our Fornax dwarfs to reach 90% of their mass, but they
also took more time than massive galaxies, which is confirmed by the
statistics of each sample. For the t90, the quartiles (25%, 75%) of the Local
Group and SAMI-Fornax dwarfs are (5, 8) and (1, 5) Gyr, respectively, while
for the giants go all the way up to (7, 11) Gyr. The times for the less
massive dwarfs in the Local Group are therefore in between the ATLAS3D and
SAMI-Fornax samples. To make this more visible, in Fig. 7 we also show with a
dashed line the mean formation time for different mass bins of 1 log(M/M⊙ ).
The combined sample, covering stellar masses from $10^{4}$ to $10^{12}$ M⊙ ,
defines a U-shape, with the minimum around log(M/M⊙ )=8. Only in galaxies
between 107 to 1010 M⊙ there are objects that have been forming mass until
recently. For the formation time of 50% of the galaxy mass, we see the same
effects, although somewhat diluted. The Local Group objects have times closer
to our dwarfs in Fornax, with mean values between 10-11 Gyr, while most of the
massive galaxies had already formed 50% of their mass 13 Gyr ago.

##  5 Discussion

In this work, we have analyzed the spectroscopic SFHs of a sample of dwarf
galaxies. We have compared them to more massive galaxies from the ATLAS3D
project, and other low-mass dwarfs from the Local Group. The results point out
two key factors shaping the SFHs, the stellar mass and the projected distance
to the cluster center. These two quantities are representative of internal and
external processes, respectively. In the following we consider now how these
two aspects affect other properties of the galaxy.

For the next figures we want to highlight that the individual values of the
represented properties were obtained with different methodologies, which could
introduce systematic effects into the comparison. With this word of caution in
mind, we want to study the general behaviour of different galaxy properties
and their relation with internal and external properties, with these figures
about the projected distance-stellar mass plane.

###  5.1 From giants to dwarfs

Figure 9 shows a 2D color map interpolation of the SFHs that represents a
complete picture of how the SFHs evolve with stellar-mass. Since we used the
same finer age grid to derive the formation times for all the samples
described in this paper, we can put all the cumulative SFHs together creating
a uniformly distributed 2D array. Here we ordered the galaxies as a function
of stellar mass, having in total a stellar mass range from 104 to 1012 M⊙. To
create a continuous 2D image of SFHs as a function of the stellar-mass, we
used the Scipy.KDTree algorithm (Maneewongvatana & Mount, 1999) to look up the
nearest neighbours of every point with which we created the smooth map in Fig.
9.

In our previous results, we have seen how the SFH smoothly varies as we move
from giants to dwarfs. This could indicate that independently of the
morphology the star-forming rate is primarly related to internal properties,
i.e. the stellar-mass. This is clearly shown in Fig. 8, where we used
different bins of stellar mass to group the galaxies and plot the mean SFH. We
mixed here all the samples, meaning that in the same bin there could be a mix
of ATLAS3D and SAMI-Fornax galaxies, or cluster and Local Group dwarfs. As
expected from Fig. 7, the cumulative SFHs become more extended as we go down
in mass, however, we again see how galaxies with total stellar mass <
$10^{6}$M⊙ formed faster than those galaxies with total stellar masses between
107 to 1010 M⊙.

For higher mass galaxies our map agrees with the results of Thomas et al.
(2005) and McD15. On average these galaxies formed at least 50% of their mass
in just a few Gyr after the Big Bang, the more massive were quenched faster.
Meanwhile, less massive objects are built more and more gradually. This effect
is called ’downsizing’ (Cowie et al., 1996; Fontanot et al., 2009), and it
relates the galaxy mass with some key properties like the star-forming rate or
the stellar population properties. However, this relation does not seem to
persist at even lower masses since we detect a change in this trend around
107-108 M⊙. In their study of the Local Group dwarfs, Weisz et al. (2014a)
already pointed out this reversed trend, but they did not consider it to be
evidence against the galaxy downsizing. They argue that this ’upsizing’ is
caused by the environment since most of the less massive galaxies from their
sample are inside the virial radius of the Milky Way or Andromeda. This makes
them vulnerable to environmental processes, caused by the circumgalactic
medium in the halo, that can play a similar role as ram-pressure stripping
(Putman et al., 2021; Akins et al., 2021). One has to note the fact that at
the low mass end, other factors such as reionization as well as internal
quenching can also play a role.

Analyzing Fig. 7 and 9, we realize that this behaviour is comparable to the
[$\alpha$/Fe]-stellar mass relation we proposed in Paper III, which looks like
a U-shape. With this in mind, we fitted a U-shape to the formation times of
galaxies from Fig. 7 and overplotted them onto the colormap, conforming once
again this U-shape, which agrees well with the colormap of Fig. 9.

Figure 8: Cumulative SFHs of galaxies for of different stellar masses. We
grouped the galaxies according to their stellar mass, and plot the mean SFH of
each bin. In blue we show the mean SFH for those galaxies with M⋆ < 106 M⊙,
green for galaxies with 106 < M⋆ < 108 M⊙, yellow for 108 < M⋆ < 1010 and red
for the massive galaxies 1010 < M⋆ < 1012. The bins are also stated in the
legend of the figure. Figure 9: Color map of the cumulative SFHs as a function
of the galaxy mass. The vertical axis represents the lookback time in Gyr, and
the colours are the cumulative fraction of stellar-mass formed at different
times and at different stellar-masses. The dashed black lines represent a
second-degree fit to the formation times, as shown in Fig. 7, as a function of
the stellar-mass.

The change in the trend, giving rise to the U-shape, could be considered a
mere bias, caused by the more massive dwarfs being located outside the virial
radius of their host. However, in our previous study, we argue, analogously to
Weisz et al. (2014a), that ’upsizing’ part of the U-shape is in fact due to
the environment and is indeed a sign that the environmental processes are more
and more effective the less massive a galaxy is.

Figure 10: Color map of the different formation times of the galaxies as a
function of their position in the projected distance-stellar mass plane. The
panels represent the time it took to form a certain percentage of the current
day mass. From left to right we show t20, t50, t70, t90. The scatter points
are smoothed using the LOESS technique, and then with Scipy.KDTree the
background maps are extrapolated.

###  5.2 Relation between the environment and the formation of galaxies

To further study this interplay between the internal and external properties,
we plot the different formation times computed from the SFHs in a
cluster/group center projected distance-stellar mass plane. We argued that the
’upsizing’ part of the U-shape [$\alpha$/Fe]-stellar mass relation is due to
environmental processes mainly because we found a linear relation between
[$\alpha$/Fe] and the projected distance for the dwarf galaxies. This relation
is present independently if they are cluster or group galaxies (Paper III).
Another reason to explain the ’upsizing’ with environment is that quiescent
dwarfs are mostly not found far away from their massive companions.

Figure 11: Color map of the different properties of the galaxies as a function
of their position in the projected distance-stellar mass plane. The panels
show from left to right the logarithmic velocity dispersion, metallicity, and
age. The scatter points are smoothed using the LOESS technique, and then with
Scipy.KDTree the background maps are extrapolated. The almost vertical lines
that are defined by the maps, tell us that these quantities are independent of
the environment and that they are mainly driven by internal properties like
the stellar mass.

To explore this possible connection between stellar mass, environment and the
formation time of galaxies, we show in Fig. 10 the projected distances of the
galaxies as a function of their stellar mass, and as a 3rd dimension we
coloured them according to different properties. While on Fig. 9 we
interpolated a continuous set of arrays to create the maps, now we want to
create the map from a not uniformly distributed scatter of points, so in order
to create the 2D maps of the properties we first smooth the points using the
LOESS technique (Cleveland & Devlin, 1988). This algorithm estimates a
regression fit for each point using nearby points to create a smooth curve.
The technique is used when working with noisy data or scatter plots in order
to smooth the results, with the intention of revealing underlying trends or
patterns. Once the distribution of points has been smoothed, we used again the
Scipy.KDTree to produce a continuous 2D map.

In Fig. 10 we show the distribution of the galaxies in the projected distance
- stellar mass plane, with each galaxy coloured according to their formation
times t20, t50, t70 and t90. As a background, Fig. 10 also shows the
extrapolated 2D map of the different formation times of the galaxies in the
Local Group , SAMI-Fornax and ATLAS3D samples. We see that for galaxies more
massive than 1010M⊙ the environment does not seem to have any significant
effect on the evolution of the galaxy at any point in time, which is
represented by the vertical iso-contours. It has to be kept in mind that these
results only apply to the present-day environment, and some of these
relatively massive galaxies ($\sim$1010M⊙) could have been preprocessed in
smaller structures that were later accreted into the final cluster. In
general, this means that the galaxy downsizing holds for this mass regime.

In general, at the moment that the galaxies have formed 20% of their current
mass, the environment has not done anything notable yet and all galaxies
reached this point $\sim$13 Gyr ago. This could indicate that at the beginning
of the formation of the galaxy, the galaxies were mostly isolated and were not
affected by the environment yet. Later in time, when the galaxies have reached
50% of their mass, even though the scale is small, we detect a more
significant trend as a function of the environment for galaxies up to 108M⊙.
At this point, the galaxies in the inner regions have already started to
experience some environmental quenching, and the maps begin to exhibit a
U-shape. The parabolic shape becomes even more obvious for the t70 and t90
maps in Fig. 10. Here, the times of massive galaxies are always independent of
the environment, and for less massive galaxies only those with a stellar mass
around 108M⊙ have kept forming stars until recently. For even less massive
dwarfs like the ones in our Local Group , there is almost no environmental
effect at this point, because the gas has already been blown away
independently of its stellar mass.

We want to remark here that our sample is not homogeneously distributed, and
there are several areas in Fig. 10 that do not contain many galaxies. As a
result, the extrapolation for those under mapped regions could bias our
interpretations. However, judging from the behaviour of the SAMI-Fornax
dwarfs, we expect that less massive dwarfs in less dense environments, like a
group, are quenched as fast as indicated by Fig. 10.

###  5.3 Environment independent properties

We have discussed how the SFHs relate to both internal and external
properties, but not all properties depend on both factors. Figure 11 shows the
location of each galaxy in the projected cluster distance - stellar mass
plane, colored by: velocity dispersion, metallicity, and age.

Figure 12: Color map of the different properties of the galaxies as a function
of their position in the projected distance-stellar mass plane. The panels
show from left to right the [$\alpha$/Fe] , $\Delta$t50 and $\Delta$t90. The
scatter points are smoothed using the LOESS technique, and then with
Scipy.KDTree the background maps are extrapolated. For all the panels we can
see traces of the U-shape that dictates the evolution time scales.

Our analysis reveals that there appears to be no correlation between the age,
metallicity, or velocity dispersion of a galaxy and its location within a
cluster or group of galaxies. These properties are primarily dependent on the
internal properties of the galaxy, like its stellar mass, as represented by
the vertical iso-contours shown in Fig. 11.

The velocity dispersion is determined by the dynamical mass, and part of that
is the stellar mass. The relation has been extensively studied for early-type
galaxies (Auger et al., 2010), at different redshifts (Cannarozzo et al.,
2020), and even with analogous quantities such as luminosity (Faber & Jackson,
1976; Eftekhari et al., 2022).

The metallicity-stellar mass relation is usually explained by self enrichment
in the potential wells of the galaxies (Dekel & Silk, 1986): the more massive
a galaxy is the more metals from the stellar and supernova winds it can
retain, which are then reprocessed in subsequent star formation events.
Although it is also related with the star formation rate (Mannucci et al.,
2010). The relation is maintained for all the masses (Kirby et al., 2013) and
morphological types (Calura et al., 2009). Although some studies such as
Ellison et al. (2009) and Thomas et al. (2005) have found some that galaxies
in high-density environments could be slightly more metal-rich (by about 0.05
dex), they conclude that these differences are related to local density
changes (Paper III).

Like the SFHs, age is related to the galaxy mass. Previous studies have
already stated that dwarfs are on average younger than giants (Sybilska et
al., 2017; Romero-Gómez et al., 2023). As for the environment, Mateo (2008)
study the Local Group and found that most dSph have intermediate-old ages and
are close to the host. To the contrary, young galaxies like dTrans and dIrr
can be found mostly beyond the virial radius. Given that we do not analyze
star-forming galaxies here, we can only agree on the ages of dSph being
independent of the distance to the host.

###  5.4 Formation time scales

Our results show that less massive dwarfs are dominated by environmental
processes, resulting in the SFHs of these types of galaxies being peaked and
similar to those of giants galaxies. The similarities have been already
pointed out in the past. Leitner (2012) compared photometry-based SFHs of
nearby star forming galaxies, the lowest average stellar mass was 107.6M⊙,
with spectra-based SFHs of massive galaxies from the SDSS, which reached a
stellar mass up to 1011.3M⊙. Studying the star formation rate-stellar mass
relation, they noticed that the least massive galaxies have SFHs that
resembled those of the highest mass galaxies. This was inconsistent with the
downsizing trend obtained from the SDSS sample, and they discussed that this
could be due to technical problems derived from systematic errors in the
models rather than a change in the physical reasons. We also acknowledge that
systematic effects could be introduced by the different methodologies used to
obtain the SFHs. However, this change in the stellar mass relations that we
present as a U-shape, has been detected not only in the SFHs, but also in the
[$\alpha$-Fe] values and even in simulations. Akins et al. (2021) studied
simulations of dwarfs satellites in Milky Way-like halos and found that for
most galaxies with masses between 106 and 108M⊙ the environment produced a
fast quenching. This agrees well with Fig. 10, where we see that Local Group
galaxies are quenched in a few Gyr while more massive dwarfs keep forming
stars.

To shed more light on this issue, we use again the projected distance-stellar
mass plane. The SFHs, as already noticed by Leitner (2012), could be affected
by some systematics derived from the models. For that reason, we now look at
parameters that represent how fast the star formation happened, independently
of when it starts. The first of these parameters is the [$\alpha$/Fe], which
we already studied in Paper III. The $\alpha$-elements, like Mg or C among
others, are produced in Supernovae type II, while Fe is mostly produced in
Supernovae type Ia. The firsts are the final stage of the evolution of stars
that have lived very short lives, while the latter comes from progenitors with
a very long lifespan. Thus, the [$\alpha$-Fe] values could be used as a proxy
of the timescales of star formation in a galaxy (Peletier, 1989; Worthey et
al., 1992). We can obtain the other timescale parameters from the formation
times we derived from the cumulative SFHs (Ferré-Mateu et al., 2018b). Using
14 Gyr as an approximation for the time of the Big Bang (Planck Collaboration
et al., 2014), we can define $\Delta$t50 = 14 - t50. This scale is
representative of how long it took for the galaxy to build up 50% of its mass,
or similarly the mass of the halo (Tojeiro et al., 2017). Then we can also
define $\Delta$t90 = t50 \- t90. With these three parameters, we cover how
fast the overall star formation was, [$\alpha$/Fe], and then how fast the
galaxy was in forming the first half of its mass, $\Delta$t50, and then the
second half, $\Delta$t90.

In Figure 12 we present again the location of the galaxies in the projected
cluster distance -stellar mass plane coloured this time by their
$\alpha$-enhancement , $\Delta$t50 and $\Delta$t90. In all three panels, we
can see the U-shape effect, meaning that a given property linearly relates to
stellar mass until 107-108M⊙, and then the slope of that relation starts to be
the opposite. The result is that, as we have discussed before, the lowest
massive dwarfs have $\Delta$t90 closer to that of the giants than those of
intermediate-mass dwarfs. Despite the similarity, this does not mean that the
physical processes responsible for the evolution of dwarfs and giants are the
same (Haines et al., 2007).

Looking at the $\Delta$t50 and $\Delta$t90 of giant galaxies in the central
and right panels of Fig. 12, these galaxies were all quenched 2-3 Gyr after
the Big Bang, which means that probably most of them were already quenched
before falling to their cluster. In any case, we see that they self-regulate
their own evolution, as shown by the vertical iso-contours of Fig. 12. Dwarf
galaxies, on the other hand, are expected to be quenched by the environment
(Barmentloo & Cautun, 2023). In the central panel of Fig. 12 we see how the
first half of the SFH is completed faster by those dwarfs that are close to
their host. For the second half of the SFH only galaxies with stellar masses
between 107 and 109M⊙ have kept forming stars until recently. This mass range
keeps appearing as a turning point in galaxy downsizing, which could be
interpreted as an indication that only certain processes occur above/below
this threshold. Sawala et al. (2010) studied the effects of Supernovae type II
and Ia, as well as the effect of UV background radiation on a sample of
simulated dwarf galaxies. They found that galaxies with total mass below
$\sim$108M⊙ could be quenched by the combination of these two processes. The
majority of the dwarfs studied here do not have t90 compatible with being
quenched at the end of the re-ionization epoch (z$\sim$6 or 12.5 Gyr (Gallart,
2013)), which point out to the environment being most likely responsible for
the quenching. However, some studies have found that the least massive dwarfs
could also be quenched only because of supernovae feedback (Gallart et al.,
2021).

Looking at the whole picture of our results, we see that they provide strong
evidence supporting the idea that the evolution of dwarf galaxies, with
$10^{4}$ < M⋆ < $10^{8}$ M⊙ , is dictated by their stellar mass and their
local environment (Thomas et al., 2010). The TNG50-simulations of dwarfs in
the mass regime of our SAMI-Fornax studied by Joshi et al. (2021) agree well
with our assumptions. They concluded that the SFHs were strongly dependent on
the stellar mass, with the less massive being assembled earlier, and the t90
relations flattening for stellar masses between 109 and 1010M⊙. They also
found that the environment was a secondary dependence, that could be
negligible in the case of central galaxies or those with M⋆ > 1010M⊙.
Gathering all the information it seems that for the less massive dwarfs, M⋆ <
107M⊙, the environment is responsible for blowing most of their gas away. The
little amount of gas remaining is then consumed in a fast burst of star
formation, which produces enough supernovae feedback to completely quench the
galaxy. As a result of this process, the [$\alpha$/Fe] of these galaxies
remains high. More massive dwarfs, between 108 and 109M⊙, endure the
environmental process and are able to keep enough gas to keep forming stars
until recently. Even more massive galaxies, the giants, as have been
extensively studied in the literature, are barely affected by various
environments.

As pointed out before, in future works it would be interesting to see if the
star-forming dwarfs deviate from the previous relations and if they follow the
continuity of galaxy downsizing at lower masses (Koleva et al., 2011). In
Romero-Gómez et al. (2023) we highlight a small sample of dwarfs from the
SAMI-Fornax survey, and a few from the Local Group, that followed a relation
more similar to the one proposed by the downsizing. Probably one of the main
reasons behind this behaviour is that these young systems are mostly outside
the virial radius of the host or are infalling at present, which indicates
that there has not been enough time for them to be quenched by the
environment.

##  6 Summary and Conclusions

We present the analysis of the star formation histories of 31 dwarfs
elliptical galaxies in the Fornax cluster, obtained with full spectral fitting
algorithms. For comparison, using the same methodology, we obtained the SFHs
from the 260 ETGs galaxies of the ATLAS3D project. At the low mass end, we
include a sample of photometric SFHs of dwarf galaxies from the Local Group .
After a careful inspection of the data we draw the following conclusions:

  * •

The shape of the SFHs is strongly related to the stellar mass of the galaxy.
Massive galaxies formed fast, in a few Gyr after the Big Bang, while the star-
formation rate for less massive galaxies is smaller. This galaxy downsizing
continues until dwarfs of M⋆ $\sim$107-108M⊙. Dwarf galaxies with smaller
stellar masses, on the other hand, quenched earlier.

  * •

We find that the environment does not influence the evolution of massive
galaxies much. For bright dwarfs, there is a combination between internal and
external effects, while for faint dwarfs with stellar mass lower than $10^{6}$
M⊙ the evolution is mostly determined by the environment.

  * •

We considered the location of galaxies in a plane of projected distance vs.
stellar mass to inspect the dependence of formation time scales on external
and internal factors. Galaxies more massive than 1010M⊙ are completely
independent of the environment and evolve according to their own internal
properties. For less massive galaxies we find that the time scales are
distributed following a U-shape. This means that down to $\sim$108M⊙ dwarfs
follow the downsizing scheme that comes from the giants, while for less
massive galaxies we find an ’upsizing’, giving them an SFH shape similar to
that of the giants.

  * •

Other parameters like the velocity dispersion or the metallicity appear to be
independent of the environment, and their values are only related to internal
properties. The age seems also to be affected only by the stellar mass,
although not linearly because given the U-shape of the time scales the less
massive dwarfs from the Local Group are older than those of our SAMI-Fornax
sample.

In summary, only galaxies with stellar masses between 108 and 109M⊙ can resist
the quenching induced by different environmental processes, retaining enough
gas to keep forming stars until recently. Giants are barely affected by the
environment, and the least massive galaxies can lose their gas as soon as they
arrive at a high-density environment. This behaviour agrees well with
simulations, suggesting that 108M⊙ represents a threshold in galaxy evolution.
For future investigations, it would be interesting to see if this U-shape
relation can be confirmed in other galaxy clusters, groups and other types of
galaxies, as well as for other important properties. These findings could have
significant implications for our understanding of the complex relation of SFHs
with galaxy properties and pave the way for future investigations in this
exciting field.

## Data availability

The reduced data underlying this article will be made available through the
CDS. The raw data is publicly available in the AAT data archive.

## Acknowledgements

JRG and JALA are supported by the Spanish Ministry of Education, Culture and
Sports under grant AYA2017-83204-P and by the Spanish Ministerio de Ciencia e
Innovación y Universidades by the grant PID2020-119342GB-I00.

For the analysis we have used Python http://www.python.org; Matplotlib
(Hunter, 2007), a suite of open source python modules that provide a framework
for creating scientific plots; and Astropy, a community-developed core Python
package for Astronomy (Astropy Collaboration et al., 2013).

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##  Appendix A Star formation histories of ATLAS3D galaxies

To expand the sample of this work, we combined our dwarf sample with the giant
galaxies of ATLAS3D (Cappellari et al., 2011a). As explained in Romero-Gómez
et al. (2023), we collapsed all spatially resolved spectra into one single
spectrum per galaxy, and using the same methodology as for the dwarfs we
obtained the stellar populations parameters and SFH.

In Fig. 13 we show a comparison between the SFHs we derived, and those from
McDermid et al. (2015). For the sake of comparison, we combined the SFHs in
the same stellar mass bins McDermid et al. (2015) used. As a grid for the
diagram they used the models from Schiavon (2007), and for this reason, their
values are not directly comparable to ours with different methodologies and
template models. Despite the differences, we can see that the SFHs are fairly
similar. Adiotionally, in Fig. 14 we also show a comparison of the t50 form
our work, and that of McDermid et al. (2015). There we see some differences
between both values, but these are expected given the different models and
methodologies used, as explain in Paper III.

(a)  (b)

Figure 13: In the top panel, (a), we show the SFH of the ATLAS3D galaxies
derived in our study, while in the bottom panel are the SFH of the ATLAS3D
galaxies derived by McDermid et al. (2015). For a better comparison of both
results we binned the galaxies using the same mass bin as in McD15. The color
of each bin is stated in the legend of the figures. In both cases is clear
that the more massive galaxies formed faster in a few Gyr after the Big Bang.
Figure 14: Comparison of our t50 with those published in McD15 for the ATLAS3D
galaxies. Each galaxy is colour coded with the S/N, and the red X are those
points of bad quality according to McD15. The 1:1 relation is represented by
the black dashed line on each panel.

##  Appendix B Star formation histories of Local Group galaxies

In order to have the SFHs from the Local Group in the same age grid as our
SAMI-Fornax and ATLAS3D results, we interpolated the SFHs from W14. We used
their errors and Monte Carlo simulations to compute the errors of the
interpolation, as explain in Section 4.3. In Fig. 15 we show a comparison of
the SFH from W14 for the Ursa Minor galaxy, and our interpolation. To test
this, in Fig. 16 we also compare the t70 published by Weisz et al. (2014b)
with the times computed from our interpolation method. In general there is a
well agreement between both values.

Figure 15: Example of the interpolation on the SFH of the Ursa Minor galaxy
from W14. The SFH and erros from W14 are the dashed black line and grey
shadow, respectively. The interpolated SFH and error we used in this work is
represented by the red dash line and shadow, respectively. Figure 16:
Comparison of our t70 with those published in W14 for the Local Group
galaxies. Each galaxy is colour coded with its stellar mass, and the 1:1
relation is represented by the black dashed line on each panel.

##  Appendix C Star formation histories of the SAMI-Fornax dwarfs

In this appendix we present tables with the information relative to the SFHs
of the SAMI-Fornax dwarfs. Table C has for each galaxy the weight,
corresponding to the formed light fraction, at different lookback times. Table
C has the formation times used in this paper.

Table 1: Table with the star formation histories of the SAMI-Fornax dwarfs.
The first column shows the galaxy name, while the rest of the columns are the
different lookback times in Gyr. Then for each galaxy the rows has the name
and the light fraction formed at the corresponding lookback time.

FCC name | 0.04 | 0.5 | 1.0 | 3.0 | 5.0 | 7.0 | 9.0 | 11.0 | 13.0 | 14.0
---|---|---|---|---|---|---|---|---|---|---
FCC100 | 0.047 | 0.013 | 0.066 | 0.136 | 0.08 | 0.138 | 0.163 | 0.125 | 0.106 | 0.126
FCC106 | 0.004 | 0.0 | 0.047 | 0.066 | 0.084 | 0.1 | 0.228 | 0.298 | 0.15 | 0.023
FCC134 | 0.263 | 0.04 | 0.298 | 0.123 | 0.066 | 0.069 | 0.058 | 0.024 | 0.017 | 0.044
FCC135 | 0.057 | 0.0 | 0.001 | 0.189 | 0.061 | 0.036 | 0.14 | 0.27 | 0.187 | 0.06
FCC136 | 0.009 | 0.001 | 0.003 | 0.07 | 0.086 | 0.086 | 0.166 | 0.255 | 0.229 | 0.095
FCC143 | 0.019 | 0.002 | 0.0 | 0.001 | 0.003 | 0.007 | 0.054 | 0.247 | 0.414 | 0.252
FCC164 | 0.048 | 0.0 | 0.013 | 0.306 | 0.041 | 0.05 | 0.087 | 0.15 | 0.221 | 0.084
FCC178 | 0.03 | 0.022 | 0.036 | 0.069 | 0.119 | 0.166 | 0.186 | 0.17 | 0.125 | 0.077
FCC181 | 0.106 | 0.013 | 0.03 | 0.021 | 0.024 | 0.007 | 0.049 | 0.042 | 0.196 | 0.511
FCC182 | 0.004 | 0.0 | 0.001 | 0.011 | 0.033 | 0.094 | 0.223 | 0.312 | 0.237 | 0.085
FCC188 | 0.027 | 0.0 | 0.02 | 0.111 | 0.065 | 0.081 | 0.143 | 0.216 | 0.223 | 0.115
FCC195 | 0.073 | 0.005 | 0.008 | 0.025 | 0.037 | 0.091 | 0.192 | 0.248 | 0.2 | 0.121
FCC202 | 0.009 | 0.008 | 0.043 | 0.108 | 0.168 | 0.197 | 0.188 | 0.148 | 0.092 | 0.041
FCC203 | 0.071 | 0.0 | 0.008 | 0.435 | 0.064 | 0.031 | 0.062 | 0.135 | 0.151 | 0.042
FCC211 | 0.039 | 0.014 | 0.024 | 0.062 | 0.112 | 0.156 | 0.179 | 0.175 | 0.144 | 0.095
FCC222 | 0.005 | 0.001 | 0.01 | 0.033 | 0.076 | 0.152 | 0.255 | 0.234 | 0.115 | 0.119
FCC223 | 0.044 | 0.0 | 0.001 | 0.016 | 0.035 | 0.077 | 0.221 | 0.335 | 0.14 | 0.13
FCC245 | 0.028 | 0.032 | 0.064 | 0.109 | 0.147 | 0.166 | 0.161 | 0.136 | 0.098 | 0.059
FCC250 | 0.298 | 0.008 | 0.029 | 0.06 | 0.082 | 0.143 | 0.109 | 0.101 | 0.104 | 0.066
FCC252 | 0.024 | 0.001 | 0.002 | 0.003 | 0.006 | 0.01 | 0.036 | 0.166 | 0.453 | 0.297
FCC253 | 0.088 | 0.008 | 0.069 | 0.17 | 0.157 | 0.209 | 0.123 | 0.058 | 0.063 | 0.055
FCC264 | 0.023 | 0.0 | 0.006 | 0.009 | 0.019 | 0.067 | 0.182 | 0.307 | 0.225 | 0.161
FCC266 | 0.017 | 0.001 | 0.01 | 0.007 | 0.016 | 0.085 | 0.283 | 0.361 | 0.163 | 0.057
FCC274 | 0.038 | 0.022 | 0.031 | 0.017 | 0.023 | 0.047 | 0.088 | 0.097 | 0.186 | 0.451
FCC298 | 0.018 | 0.0 | 0.007 | 0.019 | 0.016 | 0.054 | 0.202 | 0.174 | 0.32 | 0.19
FCC300 | 0.031 | 0.009 | 0.034 | 0.024 | 0.048 | 0.086 | 0.177 | 0.257 | 0.162 | 0.172
FCC301 | 0.013 | 0.003 | 0.132 | 0.095 | 0.078 | 0.119 | 0.171 | 0.178 | 0.117 | 0.093
FCC277 | 0.023 | 0.037 | 0.084 | 0.141 | 0.178 | 0.181 | 0.153 | 0.109 | 0.064 | 0.03
FCCB442 | 0.181 | 0.316 | 0.296 | 0.12 | 0.027 | 0.014 | 0.01 | 0.008 | 0.009 | 0.018
FCCB904 | 0.047 | 0.002 | 0.016 | 0.03 | 0.036 | 0.069 | 0.176 | 0.172 | 0.172 | 0.28

Table 2: Table with the formation times of the SAMI-Fornax dwarfs. The columns
are: galaxy name, t20, t50, t70, t90 and the name of the corresponding data
file on CDS. The data in CDS are the reduce data cubes. All the times are in
lookback time Gyr.