Star Formation Histories of Dwarf Spheroidal and Dwarf Elliptical Galaxies in the Local Universe

We selected the two sub-types of early-type dwarf galaxies, dSphs and dEs, from the galaxies in the CVCG which provides detailed morphological types of 5638 galaxies located in the local universe. The galaxies listed in the CVCG are mostly taken from KIAS-VAGC (Choi, Han & Kim, 2010) which is a value-added catalogue based on the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). The CVCG supplements the original catalogue with galaxies brighter than $r=14.5$ whose redshifts were taken from literature (Choi, Han & Kim, 2010, references there in). The CVCG took about 1000 galaxies from the NASA Extragalactic Database (NED) which were not included in the KIAS-VAGC due to selection criteria adopted. Thus, the CVCG is nearly complete for galaxies brighter than $r=17.77$ for the regions surveyed by the SDSS. Ann, Seo & Ha (2015) distinguished dSph and dE from other early-type morphology such as dS0 and dE_bc, which are dwarf lenticular galaxy and blue-cored dwarf elliptical galaxy, respectively. We confined our sample galaxies to dSphs and dEs for population synthesis studies because morphological features such as disc and lens are observed in dS0s and young stellar populations are dominant in the cores of dE_bc sub-types, which implies that they are not genuine primordial dwarfs although both of them are considered to be early-type dwarfs.

Figure 1 shows the color images of four sample galaxies, the upper row for dSphs and the lower row for dEs. We provide nucleated and non-nucleated dwarfs for each sub-type. Although the sub-types of early-type dwarfs are classified by the morphological characteristics (Ann, Seo & Ha, 2015), there are some difference in luminosity and colors of dSphs and dEs. The luminosity difference between dEs and dSphs is apparent because there is no dEs fainter than $M_{B}\approx-13$, at least in the LG. For the present sample of dSphs and dEs, on average, dSphs are $\sim 1.5$ mag fainter than dEs. However, as shown in Figure 2, there is a range of luminosity, $M_{r}=-13$ $\sim$ $M_{r}=-16$, where a significant fraction of dSphs and dEs are present. The majority of dSphs and dEs are located along the red sequence (Strateva et al., 2001) but some deviate a lot from it. The large spread in the $u-r$ colors of dSphs seems to be due to large photometric errors in $u$-band magnitudes which occurred frequently in faint galaxies.

We used the SDSS spectra of the selected dSphs and dEs which were downloaded from the SDSS DR7. The SDSS spectra are obtained by fibers of $3^{\prime\prime}$ in diameter placed at the focal plane of the 2.5 m telescope of the Apache Point Observatory. The SDSS spectrograph use 320 fibers with exposure time of 45 minutes or longer to achieve a fiducial signal-to-noise ratio. The spectra cover a wavelength range of 3800 to 9200 Åwith a mean spectral resolution of $\lambda/\Delta\lambda\sim 1800$. The wavelength and flux are calibrated using pipeline developed by the SDSS team. Since the average effective radius ($R_{e}$) of the sample galaxies is $\sim 12^{\prime\prime}$ (Seo & Ann, 2022), the spectra we use in the present study reflect the stellar populations in the central regions of sample galaxies, $\sim 13\%$ of $R_{e}$. We could obtain most of the spectra from SDSS DR7 but for a small fraction of sample galaxies ($\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}5\%$), we did not find relevant spectra. We present the spectrum of one of dSphs whose $r-$ magnitude is similar to the median values of the sample galaxies in Figure 3. The spectrum shows the typical features of early type dwarf galaxies. We use the observational data listed in the CVCG such as distance, luminosity ($M_{r}$), color ($u-r$), morphological type as well as coordinates and redshifts.

We applied STARLIGHT (Cid Fernandes et al., 2005) to the SDSS spectra of 200 dSphs and 234 dEs to obtain the most probable mix of stellar populations as a function of stellar age and metallicity. The STARLIGHT, a synthesis code, is well described by Cid Fernandes et al. (2004, 2005) and a recent application is found in Riffel et al. (2021). It fits an observed spectrum with the model spectrum derived from a combination of N simple stellar population (SSP) based on the evolutionary synthesis models of Bruzual & Charlot (2003, BC03). BC03 provides spectral evolution of SSPs of various metallicities (Z = 0.0001, 0.0004, 0.004, 0.008, 0.02, and 0,05) at ages between $1\times 10^{5}$ and $2\times 10^{10}$ yr with a resolution of 3 Åacross the wavelength range from 3200 to 9500 Å. They used the IMF of Chabrier (2003) with lower and upper mass cut-offs $m_{L}=0.1M_{\odot}$ and $m_{U}=100M_{\odot}$. The basic stellar evolutionary tracks are those from Padova groups complemented by Geneva groups with the STELIB library (Le Borgne et al., 2003).

In STARLIGHT, stellar motions projected to the line-of-sight are modeled by a Gaussian distribution ($G$) centered at radial velocity $v$ with velocity dispersion $\sigma$. The extinction due to foreground dust is taken into accounted using the V-band extinction $A_{V}$. Thus, the model spectrum $M_{\lambda}$ is expressed as

Since STARLIGHT compares the model spectrum at rest frame, we corrected for the interstellar reddening and redshift before resampling the observed spectrum. The reddening correction was made by multiplying $10^{0.4A_{\lambda}}$ to the observed spectrum where $A_{\lambda}$ is interstellar extinction at $\lambda$. We derived $A_{\lambda}$ by using the reddening law of Cardelli et al. (2010) with E(B-V) obtained from the dustmaps (Schlegel, Finkbeiner & Davis, 1998) by assuming the total-to-selective extinction ratio ($R_{V}$) of 3.1. After reddening correction, we shifted the observed wavelength to the rest frame wavelength using the relation $\lambda_{rest}=\lambda_{obs}/(1+z)$ where $z$ is the redshift. We also applied the dimming of the flux due to cosmic expansion by multiplying $(1+z)^{3}$ to the reddening corrected flux. We resampled the corrected spectrum with a sampling width of $\delta\lambda$ = 1 Å by applying a linear interpolation between the two nearest data points for the STARLIGHT input spectrum.

For the analysis of the star formation histories, STARLIGHT provides luminosity fraction ($x_{j}$) and mass fraction ($\mu_{j}$) for $j$-th stellar population as a function of stellar age. The $x_{j}$ and $\mu_{j}$ are divided into six stellar metallicities (Z = 0.0001, 0.0004, 0.004, 0.008, 0.02, and 0.05), It assumes [$\alpha$/Fe] = 0. The output of STARLIGHT gives two mass fractions, $\mu_{ini}$ and $\mu_{cor}$, which represent initial mass and mass corrected for the mass returned to the interstellar medium, respectively. We used the $\mu_{cor}$ for the mass fraction of stellar populations while we used the $\mu_{ini}$ to derive the star formation rates.

We applied STARLIGHT to the mock spectra to test the robustness of the stellar populations we derived. We constructed the mock spectra using the model fluxes from the STARLIGHT output which fits the observed spectra of sample galaxies. The flux of a mock spectrum is calculated as

Figure 4 shows the mean ages and metallicities of mock galaxies compared with those of model galaxies whose stellar populations were determined from the observed spectra of sample galaxies using STARLIGHT. As shown in Figure 4-(a), the method we employed to determine the stellar populations seems to well reproduce the ages of mock galaxies of which spectra were perturbed by noises proportional to ${S/N}^{-1}$. The metallicities of mock galaxies are also well reproduced except for those from mock spectra with $S/N$ = 5. As shown in Figure 4-(b), they are overestimated by $\sim 0.3$ dex for solar metallicity and $\sim 0.7$ dex for metallicities of log$(Z/Z_{\odot})<-0.5$. It implies that the metallicity determination is more affected than the ages by spectral noises. It seems to be partially due to incomplete templates in BC03 SSPs and the resemblance of the SSP spectra for the old metal-poor populations in BC03.

However, the ill reproduction of metalliciies from the mock spectra that have S/N = 5 is not a severe problem for the present study because most SDSS spectra of the sample galaixes have S/N greater than 5. It is also worth to note that the fluxes at wavelengths with large errors are masked during the fitting process in STARLIGHT so that the best fitted model fluxes are not much affected by the large errors in the observed fluxes which result in the small S/N.

Figure 5 shows a comparison between the present estimates of the total stellar mass and those from SDSS DR12. The total stellar masses provided by SDSS DR12 were derived from multi-band photometric images following Kauffmann et al. (2003) and Brinchmann et al. (2004). About $10\%$ of sample galaxies are missed in the stellar mass table of SDSS DR12. In particular, $\sim 20\%$ of dSphs are missed in the SDSS DR12. There is a good correlation between the two sets of stellar masses. There are some outliers in the stellar masses from SDSS DR12 as well as the present estimates. We suppose that the outliers are mostly caused by large errors in the distances of galaxies because most of the distances are derived from the redshifts. In particular. the stellar masses larger than $10^{10}M_{\odot}$ are thought to be due to the larger distances applied to these galaxies. However, the tight correlation for the majority of sample galaxies is remarkable because the two approaches are completely independent. This confirms the robustness of the population synthesis applied in this study.

Figure 6 and 7 show the mean luminosity and mass fractions of the stellar populations as a function of stellar age for dSphs and dEs, respectively. We applied sigma clipping that excludes galaxies deviate more than $3\sigma$ from the mean. The number of rejected galaxies is less than $\sim 3\%$ of the whole sample. The SFHs of 200 dSphs and 234 dEs are provided in supplemented material as a tabular form, respectively. Some galaxies formed the majority of stars at early epochs of log ($t_{L}$) $\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}10$ where $t_{L}$ is the lookback time in unit of yr, while others form most stars at later times, log ($t_{L}$) $<10$. The general trend of SFHs of the early-type dwarfs is the multiple bursts of star formation with decreasing strength toward the present time. The active periods of star formation ended just after log ($t_{L}$) $\approx 9$ and resumed at log ($t_{L}$) $\approx 8$ with much more reduced strength. The period of quenched star formation between log ($t_{L}$) $\approx 9$ and $8$ is frequently observed in the SFHs of the early-type dwarfs in the LG (Tolstoy, Hill & Tosi, 2009). The recent star formation, which is virtually negligible in stellar mass fractions, is marginally noticeable sin luminosity fractions due to the high luminosity of young massive stars. There is not much difference between dSphs and dEs for the SFHs after log ($t_{L}$) $\approx 8$.

The most notable feature of the SFHs of early-type dwarfs is the presence of two periods of active star formation. The first period is peaked at log ($t_{L}$) $=10$ and the second period occurs at log ($t_{L}$) $=9.4$. There are some differences in the characteristics of the double peaks between dSphs and dEs. In dSphs, the peak of the first period is $\sim 6$ times higher than that of the second period in stellar mass fractions and $\sim 3$ times higher in luminosity fractions, whereas similar strength in stellar mass fractions and reversed fractions in luminosity for dEs. It is apparent that majority of stars in dSphs are the stars formed in the first period. They contribute $\sim 80\%$ of the present stellar mass and $\sim 55\%$ of the present luminosity. More than $80\%$ of their mass is contributed by the stars older than $\sim 10$ Gyr. The difference in the strength of the initial bursts is thought to be due to the difference in the effect of stellar feedback which depends on the mass of galaxies. In our sample of early-type dwarfs, dEs are, on average, 4 times more massive than dSphs.

The difference in the fraction of stars in the second period of active star formation between dSphs and dEs is also related to the mass dependent stellar feedback. The stars formed in the second period of active star formation in dSphs is only half of that in dEs. This difference is thought to be caused by the different influence of stellar feedback due to their mass difference. The strong suppression of star formation after the initial starbursts in dSphs is caused by supernova feedback which heats and expels the gas left to the halo. The almost complete removal of gas in less massive dSphs is due to the explosive starbursts in the early phase of galaxy formation. The lower mass of dSphs also provides a favorable condition for gas removal in the low mass dSphs. The reionization feedback also plays a considerable role for the gas removal in low mass dSphs because reionization feedback is more effective in low mass galaxies (Dawoodbhoy et al., 2018).

The general behavior of star formation after the second period of star formation in dSphs is similar to that of dEs. It is characterized by a short period of quenched star formation until log ($t_{L}$) $\approx 8$ followed by increasing star formation activity toward the present time. However, the total percentage of mass contribution by stars younger than $\sim 0.1$ Gyr is less than $5\%$. The almost quenched star formation between log ($t_{L}$) $\approx 9$ and $0$ resulted in the absence of intermediate-age stars older than $\sim 0.1$ Gyr. This feature of a highly suppressed star formation of intermediate age stars is also observed in some early-type dwarfs in the LG (Weisz et al., 2014a). The suppression of star formation is thought to be caused by stellar feedback such as supernova explosion and stellar wind. The cold gas of galaxies was heated and easily expelled to the halo of early-type dwarfs. After that, star formation was resumed and continued to the present time with multiple starbursts to produce young stellar populations which contribute $\sim 5\%$ of the present luminosity and $\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}0.2\%$ of the stellar mass in total. The resumed star formation at log ($t_{L}$) $\approx 8$ is thought to be driven by the accretion of cold IGM because the metallicities of stars formed just after the period of quenched star formation can be explained if we assume accretion of metal free IGM as described below.

It is well known that there is a bi-modality in the age of stellar populations of galaxies demonstrated by two peaks in the galaxy age distribution (Gallazzi et al., 2005, 2008). One peak is caused by the old early-type galaxies and the other peak by young star forming galaxies. The distribution of stellar ages presented in Figures 6 - 9 strongly suggests a bi-modality of star formation in early-type dwarf galaxies, especially in dEs. The reason for a weak bi-modality in the SFHs of dSphs seems to be due to feedback of supernova explosion which heats the cold gas to blow out (Dekel & Silk, 1986). Figure 10 shows the distribution of epochs of starbursts. It is clear that star formation in early-type dwarfs is not a single event but multiple episodes of starbursts. The first epoch of starbursts occurs at log ($t_{L}$) $\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}10.1$ for both dSphs and dEs. This epoch includes the first and second bursts shown in Figures 6 - 9. The fraction of galaxies which form stars at the first epoch of starburst is about $30\%$ of dSphs and $43\%$ of dEs, respectively. The first epoch of starburst is the second-high peak in dSphs while it is the highest peak in dEs. The $86\%$ of dSphs and $76\%$ of dEs result in starbursts during the first period of star formation. The highest peak of the second period of star formation in dSphs occurs at log ($t_{L}$) $\approx 9.4$. This peak is made of 10 dSphs only. Thus, the bi-modality of star formation in dSphs is very weak compared to that of dEs of which 44 galaxies ($\sim 20\%$) have starbursts at this epoch. There are some bursts of star formation after the second period of star formation in dSphs, but it occurs in $\sim 2\%$ of dSphs. It is greatly contrasted with the bi-modality of star formation commonly observed in starburst galaxies (Cid Fernandes, 2018).

In past studies of the SFHs of galaxies, it is a common practice to present the characteristics of SFHs in a graphical form such as the figures in the previous sections. Weisz et al. (2014a, b, 2015) introduced a parameter, quenching time $\tau_{90}$, which is defined as the lookback time at which 90% of stellar mass is formed, to quantify the cSFHs of galaxies. Figure 11 shows the histograms of $\tau_{90}$ for the 200 dSps and 234 dEs. As expected from the difference in SFHs of dSphs and dEs shown in the above, there is a clear difference in the distribution of $\tau_{90}$. In particular, a significant fraction of dSphs have log ($\tau_{90}$) > $10$ while only a negligible fraction of dEs have log ($\tau_{90}$) > $10$. The extremely early quenching of $\sim 20\%$ of dSphs is thought to be due to small mass of these galaxies since low mass dwarfs are known to be quenched earlier (Digby et al., 2019; Garrison-Kimmel et al., 2008; Joshi et al., 2021). Besides it, there are two other differences between the dSphs and dEs. One is the highly concentrated distribution of $\tau_{90}$ in dEs compared with the broad distribution of $\tau_{90}$ in dSphs. In both dSphs and dEs, the peak, i.e., the maximum frequency, occurs at log ($t_{L}$) $\approx 9.7$, but the peak height is $\sim 2$ times higher in dEs than dSphs. The other is that virtually no dEs have log ($\tau_{90}$) less than 8. It seems highly probable that the dSphs with log ($\tau_{90}$) > 10 are bona fide primordial objects. The paucity of such early quenched dEs may imply that most of dEs are not primordial objects.

We investigated the dependence of cSFHs on the morphology, stellar mass, and environment of early-type dwarfs. We used the present estimates of the total stellar mass and the local background density derived from the data in the CVCG.

The distinction of dSphs from dEs may help to understand the origin of early-type dwarfs more clearly because their SFHs are significantly different, which implies different origins of dSphs and dEs. The different characteristics of the SFHs of the two sub-types of the early-type dwarfs seems to be closely related to the critical issues on the formation and evolution of galaxies, pre-enrichment and quenching time.

Pre-enrichment of interstellar medium (ISM) and IGM by supernovae from Pop III stars have been thought to be present by simulations (e.g., Brommet al., 2009) and observations which show absence of extremely low metallicities below Z $\approx 10^{-3}$ Z_⊙ (Cowie & Songaila, 1998; Helmi et al., 2006). The observations that showed a metallicity floor of $\sim 10^{-3}$ Z_⊙ include the metallicity of the Milky Way halo stars, the LG dSph galaxies (e.g., Helmi et al., 2006), damped Ly${\alpha}$ absorption systems (Wolfe & Prochaska, 1998), and intervening IGM in the line of sight toward quasars (e.g., Cowie & Songaila, 1998). The absence of extremely metal-poor (Z = 0.0001) stars among the oldest stellar populations in the majority of the early-type dwarfs (dSphs and dEs) reported here suggests pre-enrichment of the gas out of which the oldest stars formed. The pre-enrichment resulted in the metallicities of the oldest stellar populations as Z = 0.0004. This level of pre-enrichment is in good agreement with recent simulations (Tassis, Gnedin & Kravtsov, 2012; Wise et al., 2012) in which metals from Pop III supernovae enrich the ISM of the hosting halo and the surrounding IGM.

It is unclear whether the pre-enrichment was made before the collapse of gas into dark matter halo or after the assembly of galaxies. However, the relatively higher metallicity of Z = 0.0004 for the first generation of stars in the early-type dwarfs favors in-situ pre-enrichment during the reionization. This scenario is plausible because the inhomogeneous gas surface density could provide a favorable condition for the formation of Pop III stars in the high density pristine gas pockets (Tassis, Gnedin & Kravtsov, 2012; Pallottini et al., 2014). However, pre-enrichment before galaxy assembly is not completely excluded because the gas out of which a galaxy formed could be pre-enriched by Pop III stars in the neighboring minihalos. It is also possible that pre-enrichment happened in the subhalos that were merged into the host halo. The ages of the oldest stellar population of dSphs and dEs ($\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}10$ Gyr) suggest that star formation started just after the end of reionization which is supposed to occur at z$\approx 6$ (Fan, Carilli & Keating, 2006).

The violent bursts in $\sim 30\%$ of dSphs and $\sim 35\%$ of dEs at log ($t_{L}$) $>10$ imply that their mass is larger than the characteristic mass below which star formation is suppressed by the reionization feedback. For the dark matter halo, this characteristic mass $M_{halo}$ is $\sim 10^{10}M_{\odot}$ (Fitts et al., 2017) which corresponds to the virial temperature of $\sim 10^{4}$ K (Benitez-Llambay et al., 2015). In terms of stellar mass ($M_{\ast}$), it is $\sim 10^{6}M_{\odot}$ based on the extrapolated $M_{\ast}$ - $M_{halo}$ relation and simulations (Fitts et al., 2017, references there in). These mass scales are consistent with the upper limiting mass of ultra faint dwarfs ($\sim 10^{5}M_{\odot}$) whose star formation was quenched by reionization feedback (Rodriguez Wimberlyet al., 2019).

There is a signature of severe suppression of star formation in early-type dwarfs due to the feedback of stellar evolution such as supernova explosions in the initial bursts of star formation. This feedback seems to be strong enough to heat the gas left after the initial bursts of star formation and suppresses star formation somewhat before the second peak of star formation at log ($t_{L}$) $=9.4$. Suppression of star formation after the first period of star formation also seems to be caused by the stellar feedback that heats gas and expels some of them. Removal of gas by supernova feedback seems to be more effective in dSphs because the fraction of stars formed in the second period of star formation is much smaller than those of dEs which show comparable fractions in the first and second period of star formation.

The present sample of early-type dwarfs shows gappy SFHs which are characterized by distinct quiescent periods of star formation (Wright et al., 2019) more frequent than the LG dwarfs (Weisz et al., 2011). In particular, dEs in the present sample show mostly gappy SFHs. Since dEs are, on average, more massive than dSphs, gappy SFHs are likely to be made for galaxies where the supernova feedback is strong enough to heats and expels the gas left to the halos of galaxies but not sufficient to remove the gas to the intergalactic matter. The gas ejected into the halos of galaxies accretes to the galaxies after cooling down and begins to collapse to form next generation of stars. The mass dependent gappy SFH is understandable because the feedback of supernova explosion is more effective in less massive galaxy. In less massive dwarfs, the stellar feedback removes the gas left completely after the first period of star formation.

From the analysis of SFHs of dSphs and dEs, it seems apparent that the morphology of early-type dwarfs is closely related to their SFHs. As shown in Figure 13, the cSFH of dSphs is clearly different from that of dEs, regardless of their mass. It implies that the morphology dependence of cSFHs seems to be most important in the SFHs of early-type dwarfs (Figures 13 and 14). Thus, dSphs are not merely a faint sub-sample of dEs but are distinct objects. The morphology difference seems to be due to their different origins. The majority of dSphs are likely to be primordial objects while most dEs are likely to be transformed ones. It is more likely that most faint dSphs are originated from the primordial objects some of which are collapsed before reionization while the majority of bright dEs are transformed from the late-type galaxies as implied by the embedded spiral arms in a number of dEs (Lisker, Grebel & Binggeli, 2006; Seo & Ann, 2022). However, it is highly plausible that some fractions of dEs are primordial objects, in particular, the dEs of which quenching of star formation occurred before log ($t_{L}$) $\approx 10$. On the other hand, the origin of some dSphs whose star formation quenched after log ($t_{L}$) $\approx 9.7$ is not clear. They can be primordial objects as well as transformed ones, If they are primordial objects, the delayed quenching of star formation needs to be explained.

The terminology of fast dwarfs and slow dwarfs were introduced by Gallart et al. (2015) to distinguish cSFHs of dwarf galaxies. On average, the present sample of dSphs and dEs are said to be slow dwarfs because the mean cSFHs at log ($t_{L}$) $\approx 10$ are 0.65 and 0.54 for dSphs and dEs, respectively. However, there are a number of fast dwarfs in the present sample. In particular, a significant fraction of dSphs are fast dwarfs if we consider that dwarfs that quenches at log($t_{L}$) $\approx 10$ or redshift of $z\sim 2$, are fast dwarfs. Since most star formation occurred before log ($t_{L}$) $=10$, fast dwarfs are thought to be primordial objects.

There seems to be a trend between the mass of a galaxy and $\tau_{90}$. Less massive dwarfs are likely to be fast dwarfs (Weisz et al., 2014a, b) and they are considered to be fossils of reionization which formed the bulk of its stars prior to reionization (Weisz et al., 2014b). The dependence of $\tau_{90}$ on the mass of a galaxy is consistent with the recent simulations of Digby et al. (2019). The fact that fast dwarfs are more frequent in dSphs than in dEs is consistent with the dependence of quenching time on the stellar mass because dEs are on average $\sim 4$ times more massive than dSphs, Some fast dSphs could be fossils of reionization if the bulk of their stars were formed prior to reionization. The suppression of star formation which resulted in almost complete quenching of star formation in the majority of dSphs after log ($t_{L}$) $\approx 10$ is caused by the feedback from supernova explosions. But, the suppression after the initial bursts in dSphs and dEs at log ($t_{L}$) $>10$ could be caused by reionization or feedback from supernova explosions because both of them depend on the galaxy mass. It is well known that suppression or quenching of star formation by reionization are thought to be effective for lower mass dwarfs (Gnedin, 2000; Bovill & Ricotti, 2009; Benitez-Llambay et al., 2015; Jeon, Besla & Bromm, 2017; Dawoodbhoy et al., 2018). The difference between the SFHs of the two sub-types of early-type dwarfs are thought to be mainly due to their difference in origin.

The pronounced differences in SFHs between dSphs and dEs are the paucity of moderately old ($\sim 2.5$ Gyr) stars in dSphs. It is thought to be caused by the effects of reionization and feedback from supernova explosion which expel gas left into the halo of the galaxy. It is also the reason why the chemical evolution of dSphs was suppressed. These ejected gas evaporated from the halo and some remained there. Since the gas ejected into the halo was enriched before being expelled, this enriched gas can be mixed with the IGM around the galaxy. The rapid chemical evolution in dEs was possible due to the relatively large mass which prevented the removal of gas at early epochs when reionization and supernova feedback were strong. During the second period of star formation between log ($t_{L}$) $\approx 9.7$ and $9$, the metal content of gas out of which the moderately old stars were formed increased monotonically. The monotonic increase of metallicity in the second period of star formation can be explained by a simple chemical evolution model which assumes a closed box with a reservoir such as that of Hartwick (1976). Here, the halo played the role of a reservoir.