THE ACS NEARBY GALAXY SURVEY TREASURY. VIII. THE GLOBAL STAR FORMATION HISTORIES OF 60 DWARF GALAXIES IN THE LOCAL VOLUME^*

Dwarf galaxies have come to play an increasingly important role in understanding how galaxies form and evolve. As the smallest, least luminous, and most common systems in the universe, dwarf galaxies span a wide range of physical characteristics and occupy a diverse set of environments (e.g., Zwicky 1957; Hodge 1971; Koo & Kron 1992; Marzke & da Costa 1997; Mateo 1998; van den Bergh 2000; Karachentsev et al. 2004), making them excellent laboratories for direct studies of cause and effect in galaxy evolution. The low average masses and metallicities of dwarf galaxies suggest that they may be the best available analogs to the seeds of hierarchical galaxy formation in the early universe.

A cohesive picture of the evolution of dwarf galaxies remains elusive. Historically, evolutionary scenarios have often been considered in a dual morphological classification scheme, namely, dwarf spheroidals (dSphs; we include dwarf ellipticals in this general category) and dwarf irregulars (dIs). The former are classified based on their smooth morphology, with no observed knots of star formation (SF), and are generally found to be gas-poor. The latter exhibit morphological evidence for current/recent SF activity and have a high gas fraction. A third, rarer class of so-called transition dwarf galaxies have a high gas fraction yet little to no recent SF activity (e.g., Sandage & Hoffman 1991; Skillman & Bender 1995; Mateo 1998; Miller et al. 2001; Dolphin et al. 2005; Young et al. 2007; Dellenbusch et al. 2008). These galaxies may be an evolutionary link between dIs and dSphs (e.g., Grebel et al. 2003) or simply could be ordinary dIs witnessed between massive star-forming events (e.g., Skillman et al. 2003a). Understanding the relationship between these three types of dwarf galaxies, specifically determining if and how dIs evolve into dSphs, is among the most pressing questions in dwarf galaxy evolution (e.g., Baade 1951; Hodge 1971, 1989; Dekel & Silk 1986; Kormendy 1985; Binggeli 1986; Skillman & Bender 1995; Mateo 1998; Dekel & Woo 2003; Grebel et al. 2003; Ricotti & Gnedin 2005; Mayer et al. 2006; Orban et al. 2008; Kazantzidis et al. 2010).

Resolved stellar populations have proven to be an incredibly powerful tool for observationally constraining scenarios of dwarf galaxy evolution. Past patterns of SF and chemical evolution are encoded in a galaxy's optical color–magnitude diagram (CMD). To extract this information, a number of sophisticated algorithms have been developed to measure the star formation history (SFH), i.e., the star formation rate (SFR) as a function of time and metallicity, by comparing observed CMDs with those generated from models of stellar evolution (e.g., Tosi et al. 1989; Tolstoy & Saha 1996; Gallart et al. 1996; Mighell 1997; Holtzman et al. 1999; Hernandez et al. 1999; Harris & Zaritsky 2001; Dolphin 2002; Ikuta & Arimoto 2002; Cole et al. 2007; Yuk & Lee 2007; Aparicio & Hidalgo 2009; Cignoni & Tosi 2010). The robustness of this approach has become increasingly consolidated with a variety of techniques and stellar models converging on consistent solutions for a range of galaxies (e.g., Skillman & Gallart 2002; Skillman et al. 2003b; Gallart et al. 2005b; Monelli et al. 2010a, 2010b).

Analysis of CMD-based SFHs have become particularly prevalent in studies of the formation and evolution of the Local Group (LG). The LG contains ∼80 dwarf galaxies ranging from highly isolated to strongly interacting (e.g., Mateo 1998; van den Bergh 2000; Tolstoy et al. 2009). Results from CMD-based SFHs of dwarf galaxies in the LG have revealed that both dSphs and dIs feature complex SFHs, typically with dominant stellar components older than 10 Gyr (e.g., Hodge 1989; Mateo 1998; Dolphin et al. 2005; Tolstoy et al. 2009). The SFHs of individual LG dwarf galaxies, as well as aggregate compilations, now serve as the basis for our understanding of the evolution of dwarf galaxies and have significantly advanced our knowledge of galactic group dynamics (e.g., Mayer et al. 2001a, 2001b, 2006; Orban et al. 2008; Tolstoy et al. 2009; Mayer 2010; Kazantzidis et al. 2010).

Beyond the LG, only a small subset of dwarf galaxies have explicitly measured CMD-based SFHs (e.g., Dolphin et al. 2003; Weisz et al. 2008; McQuinn et al. 2009, 2010; Crnojević et al. 2011). Ground-based observations of resolved stellar populations in more distant galaxies are challenging, due to the faintness of individual stars and the effects of photometric crowding. However, observations from the Hubble Space Telescope (HST), particularly the Advanced Camera for Surveys (ACS; Ford et al. 1998), have revolutionized the field of resolved stellar populations, producing stunning CMDs of dwarf galaxies both in and beyond the LG. Outside the LG, past HST observations of resolved stellar populations have been fairly piecemeal, with individual or small sets of galaxies as the typical targets. Subsequent analysis often employed different methodologies or sought different science goals. This lack of uniformity also makes it challenging to place the results from LG studies in the context of the broader universe, as LG dwarf galaxies may not be representative of the larger dwarf galaxy population (e.g., van den Bergh 2000).

The ACS Nearby Galaxy Survey Treasury (ANGST; Dalcanton et al. 2009) was designed to help remedy this situation. Using a combination of new and archival imaging taken with the HST/ACS and Wide Field Planetary Camera 2 (WFPC2; Holtzman et al. 1995), ANGST provides a uniformly reduced, multi-color photometric database of the resolved stellar populations of a volume-limited sample of nearby galaxies (D ≲ 4 Mpc) that are strictly outside the LG. Of the ∼70 galaxies in this sample, 60 are dwarf galaxies that span a range of ∼10 mag in M_B and that reside in both isolated field and strongly interacting group settings, providing an unbiased statistical sample in which to study the detailed properties of dwarf galaxy formation and evolution.

In this paper, we present the uniformly analyzed SFHs of 60 dwarf galaxies based on observations, photometry, and artificial star tests produced by the ANGST project. The focus of this study is on the lifetime SFHs of the sample galaxies, with the recent (<1 Gyr) SFHs the subject of a separate paper (D. Weisz et al. 2011a, in preparation). We first briefly review the sample selection, observations, and photometry in Section 2. We then summarize the technique of measuring SFHs in Section 3. In Section 4, we discuss and compare the resultant SFHs in the context of both dwarf galaxy formation and evolution. We then explore our results with respect to the morphology–density relationship in Section 5. Finally, we discuss the evolution of dwarf galaxies in the context of cosmology in Section 6. In the Appendices, we provide extensive testing of time resolution, photometric depth, and systematic uncertainties from stellar evolution models in the SFH recovery method. Cosmological parameters used in this paper assume a standard WMAP-7 cosmology as detailed in Jarosik et al. (2010).

In this section, we briefly summarize the selection of the ANGST dwarf galaxy sample along with the observations and photometry. A more detailed discussion of the ANGST program can be found in Dalcanton et al. (2009).

2.1. Selection and Final Sample

We constructed the initial list of ANGST galaxies based on the Catalog of Neighboring Galaxies (Karachentsev et al. 2004), consisting exclusively of galaxies located beyond the zero velocity surface of the LG (van den Bergh 2000). We selected potential targets with |b| > 20 ° to avoid observational difficulties associated with low Galactic latitudes. By simulating CMDs and crowding limits, we found that a maximum distance of ∼3.5 Mpc provides the optimal balance between observational efficiency and achieving the program science goals. Because the sample of galaxies within 3.5 Mpc contains predominantly field galaxies, we chose to extend the distance limits in the direction of the M81 Group. This extension added to the diversity of galaxies in the sample, while maintaining the goal of observational efficiency, due to the M81 Group's close proximity to the fiducial distance limit (D_M81 ∼ 3.6 Mpc) and low foreground extinction values. Similarly, we also included galaxies in the direction of the NGC 253 clump (D_N253 ∼ 3.9 Mpc) in the Sculptor Filament (Karachentsev et al. 2003), further extending the range of environments probed by the sample, while maintaining strict volume limits for galaxy selection.

In this paper, we analyze a sample of 60 ANGST dwarf galaxies from both new and comparable quality archival imaging. The galaxies range in M_B from −8.23 (KK 230) to −17.77 (NGC 55) and in distance from 1.3 Mpc (Sex A) to 4.6 Mpc (DDO 165). We have included most galaxies considered dwarf galaxies in the literature in our analysis, although the upper mass/luminosity cutoff for what constitutes a dwarf galaxy is somewhat ambiguous (e.g., Hodge 1971; Skillman 1996; Mateo 1998; Tolstoy et al. 2009). For example, Mateo (1998) chose to exclude the Large Magellanic Cloud (M_B = −17.93) and Small Magellanic Cloud (M_B = −16.35) from the "dwarfs" category. Analogous to Mateo (1998), we have not included NGC 3077 (M_B = −17.44), NGC 2976 (M_B = −16.77), and NGC 300 (M_B = −17.66), which would be among the brightest and most massive galaxies in the sample. Detailed studies of the SFHs of NGC 2976 (Williams et al. 2010) and NGC 300 (Gogarten et al. 2010) are available in the literature. A full list of sample galaxies and their properties are listed in Table 1 with the distances and blue luminosities of the sample shown in Figure 1.

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Table 1. ANGST Dwarf Galaxy Sample

Galaxy	Alternative	Main	MB	Distance	AV	T	Θ	Optical Coverage	Filters	MF814W 50%	HST	Previously
Name	Name	Disturber		(Mpc)				Fraction ($\mathcal {A}_{25}$)		Completeness (mag)	Proposal ID	Measured SFH
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
KK230	KKR3	M31	−8.49	1.3	0.04	10	−1.0	1.00	F606W,F814W	+0.62	9771
BK3N		M81	−9.23	4.0	0.25	10	1.0	1.00	F475W,F814W	−0.32	10915
Antlia		N3109	−9.38	1.3	0.24	10	−0.1	1.00	F606W,F814W	+1.75	10210	McQuinn et al. (2010)
KKR25		M31	−9.94	1.9	0.03	10	−0.7	1.00	F606W,F814W	−0.18	11986
FM1	F6D1	M82	−10.16	3.4	0.24	−3	1.8	1.00	F606W,F814W	+0.11	9884
KKH86		M31	−10.19	2.6	0.08	10	−1.5	1.00	F606W,F814W	−1.3	11986
KKH98		M31	−10.29	2.5	0.39	10	−0.7	1.00	F475W,F814W	+0.46	10915
BK5N–CENTRAL		N3077	−10.37	3.8	0.20	−3	2.4	0.50	F606W,F814W	−0.77	6964
BK5N–OUTER								0.50	F606W,F814W	−0.70	5898
Sc22	Sc-dE1	N253	−10.39	4.2	0.05	−3	0.9	1.00	F606W,F814W	+0.30	10503
KDG73		M81	−10.75	3.7	0.06	10	1.3	1.00	F475W,F814W	−0.38	10915
IKN		M81	−10.84	3.7	0.18	−3	2.7	0.58	F606W,F814W	−0.82	9771
E294-010		N55	−10.86	1.9	0.02	−3	1.0	1.00	F606W,F814W	+1.80	10503
A0952+69		N3077	−11.16	3.9	0.26	10	1.9	1.00	F475W,F814W	−0.23	10915
E540-032		N253	−11.22	3.4	0.06	−3	0.6	1.00	F606W,F814W	+0.10	10503
KKH37		I342	−11.26	3.4	0.23	10	−0.3	1.00	F475W,F814W	+0.12	10915
KDG2	E540-030	N253	−11.29	3.4	0.07	−1	0.4	1.00	F606W,F814W	+0.32	10503
UA292	CVnI-dwA	N4214	−11.36	3.1	0.05	10	−0.4	1.00	F475W,F814W	−0.37	10915
KDG52	M81-Dwarf-A	M81	−11.37	3.5	0.06	10	0.7	1.00	F555W,F814W	+0.37	10605	Weisz et al. (2008)
KK77	F12D1	M81	−11.42	3.5	0.44	−3	2.0	0.83	F606W,F814W	+0.28	9884
E410-005		N55	−11.49	1.9	0.04	−1	0.4	1.00	F606W,F814W	+1.70	10503
HS117		M81	−11.51	4.0	0.36	10	1.9	1.00	F606W,F814W	−0.81	9771
DDO113	UA276	N4214	−11.61	2.9	0.06	10	1.6	1.00	F475W,F814W	+0.08	10915
KDG63	U5428,DDO71	M81	−11.71	3.5	0.30	−3	1.8	1.00	F606W,F814W	+0.31	9884
DDO44	UA133	N2403	−11.89	3.2	0.13	−3	1.7	0.59	F475W,F814W	+0.16	10915
GR8	U8091,DDO155	M31	−12.00	2.1	0.08	10	−1.2	1.00	F475W,F814W	+0.82	10915
E269-37		N4945	−12.02	3.5	0.44	−3	1.6	1.00	F606W,F814W	−1.8	11986
DDO78		M81	−12.04	3.7	0.07	−3	1.8	0.95	F475W,F814W	−0.27	10915
F8D1–CENTRAL		M81	−12.20	3.8	0.33	−3	3.8	0.42	F555W,F814W	−0.77	5898
F8D1–OUTER								0.42	F606W,F814W	−0.90	5898
U8833		N4736	−12.31	3.1	0.04	10	−1.4	1.00	F606W,F814W	−0.23	10210
E321-014		N5128	−12.31	3.2	0.29	10	−0.3	1.00	F606W,F814W	−0.84	8601
KDG64	U5442	M81	−12.32	3.7	0.17	−3	2.5	1.00	F606W,F814W	+0.57	11986	Makarova et al. (2010)
DDO6	UA15	N253	−12.40	3.3	0.05	10	0.5	1.00	F475W,F814W	−0.02	10915
DDO187	U9128	M31	−12.43	2.3	0.07	10	−1.3	1.00	F606W,F814W	+0.40	10210	McQuinn et al. (2010)
KDG61	KK81	M81	−12.54	3.6	0.23	−1	3.9	1.00	F606W,F814W	+0.33	9884	Makarova et al. (2010)
U4483		M81	−12.58	3.2	0.11	10	0.5	1.00	F555W,F814W	−1.36	8769	Dolphin et al. (2001), McQuinn et al. (2010)
UA438	E407-18	N55	−12.85	2.2	0.05	10	−0.7	1.00	F606W,F814W	−1.7	8192
DDO181	U8651	M81	−12.94	3.0	0.02	10	−1.3	1.00	F606W,F814W	−0.31	10210
U8508	IZw60	M81	−12.95	2.6	0.05	10	−1.0	1.00	F475W,F814W	+0.39	10915
N3741	U6572	M81	−13.01	3.0	0.07	10	−0.8	1.00	F475W,F814W	−0.24	10915
DDO183	U8760	N4736	−13.08	3.2	0.05	10	−0.8	1.00	F475W,F814W	−0.46	10915
DDO53	U4459	M81	−13.23	3.5	0.12	10	0.7	1.00	F555W,F814W	−0.05	10605	Weisz et al. (2008)
HoIX	U5336,DDO66	M81	−13.31	3.7	0.24	10	3.3	0.71	F555W,F814W	+0.13	10605	Weisz et al. (2008)
DDO99	U6817	N4214	−13.37	2.6	0.08	10	−0.5	0.58	F606W,F814W	−0.95	10210
SexA	DDO75	MW	−13.71	1.3	0.14	10	−0.6	0.06	F555W,F814W	+0.80	7496	Dohm-Palmer et al. (1997), Dolphin et al. (2003),
N4163	U7199	N4190	−13.76	3.0	0.06	10	0.1	1.00	F475W,F814W	−0.04	10915
SexB	U5373	MW	−13.88	1.4	0.10	10	−0.7	0.10	F606W,F814W	+0.04	11986
DDO125	U7577	N4214	−14.04	2.5	0.06	10	−0.9	0.18	F606W,F814W	−1.3	11986
E325-11		N5128	−14.05	3.4	0.29	10	1.1	0.52	F606W,F814W	−0.58	11986
DDO190	U9240	M81	−14.14	2.8	0.04	10	−1.3	1.00	F475W,F814W	−0.01	10915
HoI	U5139,DDO63	M81	−14.26	3.8	0.15	10	1.5	0.34	F555W,F814W	+0.23	10605	Weisz et al. (2008)
DDO82	U5692	M81	−14.44	4.0	0.13	9	0.9	0.53	F475W,F814W	−0.32	10915
DDO165	U8201	N4236	−15.09	4.6	0.08	10	0.0	0.50	F555W,F814W	−0.7	10605	Weisz et al. (2008), McQuinn et al. (2010)
N3109-DEEP	DDO236	Antlia	−15.18	1.3	0.20	9	−0.1	0.05	F606W,F814W	+0.50	10915
N3109-WIDE2								0.05	F606W,F814W	+0.09	11307
I5152		M31	−15.55	2.1	0.08	10	−1.1	0.10	F606W,F814W	−1.38	11986
N2366–1	U3851	N2403	−15.85	3.2	0.11	10	1.0	0.39	F555W,F814W	−0.16	10605	Weisz et al. (2008), McQuinn et al. (2010)
N2366–2								0.39	F555W,F814W	−0.05	10605
Ho ii–1	U4305	M81	−16.57	3.4	0.10	10	0.6	0.12	F555W,F814W	−0.32	10605	Weisz et al. (2008), McQuinn et al. (2010)
Ho ii–2	U4305							0.12	F555W,F814W	−0.21	10605
N4214	U7278	DDO113	−17.07	2.9	0.07	10	−0.7	0.03	F606W,F814W	−0.48	11986	Williams et al. (2011a)
I2574–SGS	U5666,DDO81	M81	−17.17	4.0	0.11	9	0.9	0.05	F555W,F814W	−0.26	9755	Weisz et al. (2008)
I2574–1	U5666,DDO81							0.05	F555W,F814W	−0.55	10605	Weisz et al. (2008)
I2574–2	U5666,DDO81							0.05	F555W,F814W	−0.15	10605
E383-87		N5128	−17.41	3.45	0.24	8	−0.8	0.25	F606W,F814W	−2.14	11986
N55–CENTRAL		N300	−17.77	2.1	0.04	8	0.4	0.01	F606W,F814W	−1.55	9765
N55–DISK								0.01	F606W,F814W	−0.42	9765

Notes. Properties of the sample of ANGST dwarf galaxies—Columns 1 and 2: names; Column 3: most gravitationally influential neighbor (Karachentsev et al. 2004); Column 4: absolute blue magnitude (Karachentsev et al. 2004); Column 5: TRGB distance (Dalcanton et al. 2009; K. Gilbert et al. 2011, in preparation); Column 6: foreground extinction (Schlegel et al. 1998); Column 7: morphological T Type (de Vaucouleurs et al. 1991; Karachentsev et al. 2004); Column 8: tidal index (Karachentsev et al. 2004); Column 9: optical coverage fraction: angular area of ACS/WFPC2 coverage divided by angular area of the galaxy measured at a level of ∼25 mag arcsec⁻² or ∼26.5 mag arcsec⁻² for "KK" galaxies (Karachentsev et al. 2004); Column 10: filter combination; Column 11: 50% completeness limit (M_F814W); Column 12: HST Proposal ID, note new ANGST ACS (ID 10915) and WFC2 (11307, 11986) observations; Column 13: studies in the literature that have previously used the same HST imaging to measure a quantitative, CMD-based SFH.

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Although the sample of ANGST dwarf galaxies is extensive, it is not complete within a fixed distance limit. Galaxies at low Galactic latitudes have been intentionally excluded from the original volume selection to avoid complications associated with high degrees of reddening. While SFHs can still be derived from CMDs of such galaxies (e.g., IC 4662; McQuinn et al. 2009, 2010), the effects of extreme reddening can lead to larger uncertainties and can require special analysis techniques (e.g., individual stellar line-of-sight reddening corrections), which detracts from a uniform approach to the data reduction. In addition there have been a number of recently discovered dwarf galaxies in the M81 Group (Chiboucas et al. 2009), which were not discovered in time to be included in the original ANGST sample. The recent distance reassignment of UGC 4879 to the periphery of the LG (Kopylov et al. 2008; Jacobs et al. 2010) meant that this galaxy has also been excluded from the ANGST sample. Further, the ANGST sample is likely to be missing any faint dSphs which might be located in close proximity to M81, i.e., analogs to Milky Way satellites such as Draco and Ursa Minor, as such galaxies have not yet been detected due to their inherent faintness. At a distance of M81 (3.6 Mpc) Draco and Ursa Minor would have apparent blue luminosities of 18.98 and 20.13, respectively. In comparison, Sc22 (m_B = 17.72) has the faintest apparent magnitude in the ANGST sample. As a consequence, we caution that the results in this study are not necessarily applicable to the extremely low luminosity systems.

In this paper, we initially divide the sample of dwarf galaxies according to morphological type, T, (de Vaucouleurs et al. 1991; Karachentsev et al. 2004) resulting in 12 dwarf galaxies with T ⩽ 0 (dSphs), 5 with T = 8 or 9 (dwarf spirals; dSpirals), and 43 with T = 10 (dIs). For ease of direct comparison with well-studied LG dwarf galaxies, we have adopted nomenclature consistent with Mateo (1998), in which dwarf ellipticals (e.g., NGC 147, NGC 185) are found to be rare, and dSphs are more common. Among the dIs, there could be some ambiguity between bright dIs and dSpirals. For consistency, we defer to the T-type morphological classification scheme, but note that the distinction between a bright dI and dSpiral is not always clear. Morphological type T = 10 further includes transition dwarf galaxies (dTrans), galaxies with reduced recent SF but high gas fractions (e.g., Mateo 1998), and tidal dwarf galaxy candidates (dTidals), which appear to be condensing out of tidally disturbed gas. We classify dTidal and dTrans subtypes as follows: the three dTidals are Holmberg ix, A0952+069, and BK3N, and are all located in the M81 Group. For dTrans, we adopt the definition of Mateo (1998), namely, that a galaxy has detectable gas but very little or no Hα flux. The final sample of dTrans was classified based on H i and Hα measurements in the literature (Côté et al. 1997; Skillman et al. 2003a; Karachentsev et al. 2004; Karachentsev & Kaisin 2007; Begum et al. 2008; Bouchard et al. 2009; Côté et al. 2009). We find 12 ANGST dwarf galaxies that satisfy the dTrans criteria: KK 230, Antlia, KKR 25, KKH 98, KDG 73, ESO294-10, ESO540-30, ESO540-32, KDG 52, ESO410-005, DDO 6, and UGCA 438, leaving the final tally of true dIs at 28.

Throughout this paper, we adopt the tidal index, Θ (Karachentsev et al. 2004), as a measure of a galaxy's isolation. Θ describes the local mass density around galaxy i as

$$\begin{equation} \Theta _{i} = \max\big[\log\big(M_{K}/D^{3}_{ik}\big)\big] + C, \phantom{1} i = 1,2,\cdots, N, \end{equation} \tag{ 1 }$$

where M_k is the total mass of any neighboring galaxy separated from galaxy i by a distance of D_ik. The values of Θ we use in this paper have been taken from Karachentsev et al. (2004). Negative values correspond to more isolated galaxies, and positive values represent typical group members (see Table 1).

2.2. Observations and Photometry

To ensure uniformity in the SFHs of the ANGST dwarf galaxies, we selected one SFH code (Dolphin 2002) and one set of stellar evolution models (Padova; Marigo et al. 2008). The SFH code of Dolphin (2002) provides the user with robust controls over critical fixed input variables, e.g., initial mass function (IMF), binary fraction, time resolution, and CMD bin sizes, as well as the ability to search for the combination of metallicity, distance, and extinction values that produce a model CMD that best fits the observed CMD. The models of Marigo et al. (2008) combine updated asymptotic giant branch (AGB) evolution tracks with the models of Bertelli et al. (1994) (M ⩾ 7 M_☉) and Girardi et al. (2002) (M < 7 M_☉). As with any models, there may be inevitable systematic biases associated with these particular choices (cf., at some metallicities the Padova model red giant branches (RGBs) have color offsets from observations; e.g., Gallart et al. 2005b). However, these systematic effects will be shared by all galaxies in the sample, making for a robust relative comparison within the sample. We discuss systematic uncertainties due to choice of isochrones in Appendix B.

Here, we briefly summarize the technique of measuring an SFH based on the full methodology described in Dolphin (2002). The user specifies an assumed IMF and binary fraction, and allowable ranges in age, metallicity, distance, and extinction. Photometric errors and completeness are characterized by artificial star tests. From these inputs, many synthetic CMDs are generated to span the desired age and metallicity range. For this work, we have used synthetic CMD sampling stars with age and metallicity spreads of 0.05 and 0.1 dex, respectively. These individual synthetic CMDs are then linearly combined along with a model foreground CMD to produce a composite synthetic CMD. The linear weights on the individual CMDs are adjusted to obtain the best fit as measured by a Poisson maximum likelihood statistic; the weights corresponding to the best fit are the most probable SFH. This process can be repeated at a variety of distance and extinction values to solve for these parameters as well.

Monte Carlo tests were used to estimate uncertainties due to both random and systematic sources. For each Monte Carlo run, a Poisson random noise generator was used to create a random sampling of the best-fit CMD. This CMD was then processed identically to the original solution, with additive errors in M_bol and log (T_eff) introduced when generating the model CMDs for these solutions. Single shifts in M_bol and log (T_eff) are used for each Monte Carlo draw, and the errors themselves were drawn from normal distributions with σ(M_bol) = 0.41 and σ[log (T_eff)] = 0.03. These distributions were designed to mimic the scatter in SFH uncertainties obtained by using alternative isochrone sets to fit the data; we prefer to use this approximation of the model uncertainties rather than directly fitting a variety of isochrone sets because few alternatives exist that fully cover the range of ages, metallicities, and evolutionary states required to adequately model our CMDs. We found that the uncertainties were stable after 50 Monte Carlo tests, and thus conducted 50 realizations for each galaxy. This technique of estimating error on SFHs will be described in greater detail in A. E. Dolphin (2011, in preparation).

To minimize systematic effects when comparing between galaxies, we selected consistent parameters for measuring SFHs of the sample. All SFHs were measured using a single slope power-law IMF with a spectral index of −1.30 over a mass range of 0.1–120 M_☉, a binary fraction of 0.35 with a flat secondary mass distribution, 71 equally spaced logarithmic time bins ranging from log (t) = 6.6–10.15, color and magnitude bins of 0.05 and 0.1 mag, and the Padova stellar evolution models (Marigo et al. 2008). We note that the difference between our selected IMF and a Kroupa IMF (Kroupa 2001) is negligible, as the ANGST CMDs are limited to stellar masses ≳0.8 M_☉.

We designated the faint photometric limit to be equal to the 50% completeness limit in each filter (see Table 1) as determined by the artificial star tests run for each galaxy. The SFH program was initially allowed to search for the best-fit distance and extinction values without constraints. Initial values for the distances were taken from the tip of the red giant branch (TRGB) distances measured in Dalcanton et al. (2009), while foreground extinction values were taken from the Galactic maps of Schlegel et al. (1998). We found no significant discrepancies between the assumed values and the best CMD fit distance and foreground extinction values, i.e., all were consistent within error. Final solutions were computed using the TRGB distances from Dalcanton et al. (2009) and K. Gilbert et al. (2011, in preparation) and foreground extinction values from Schlegel et al. (1998).

We placed an additional constraint on the CMD fitting process, namely, that the mean metallicity in each time bin must monotonically increase toward the present. The deepest ANGST CMDs do not reach the ancient main-sequence (MS) turnoff, a requisite feature for completely breaking the age–metallicity degeneracy of the RGB only using broadband photometry (e.g., Cole et al. 2005; Gallart et al. 2005b). As a result, SFHs derived from shallow CMDs without a metallicity constraint can often have accompanying chemical evolution models that are unphysical (e.g., a drop in metallicity of several tenths of a dex over subgigayear timescales). A more robust analysis of the chemical enrichment of dwarf galaxies would need to include the ancient MS, measured gas phase abundances, and/or individual stellar spectra (e.g., Cole et al. 2007; Monelli et al. 2010a, 2010b; Kirby et al. 2010). We therefore consider analysis of the metallicity evolution of the ANGST sample beyond the scope of this paper.

As an example of a typical CMD fit made by the SFH code, we compare the observed and synthetic CMDs of a representative ANGST dTrans, DDO 6 (Figure 2). Dalcanton et al. (2009) determined the TRGB distance of DDO 6 to be 3.31 ± 0.06 Mpc while the foreground extinction maps of Schlegel et al. (1998) give values of A_B = 0.07 and A_V = 0.06. Allowing the SFH code to search for the best-fit CMD, we find best-fit values of D = 3.31 ± 0.07 Mpc and A_F475W = 0.05 ± 0.04, both in excellent agreement with the independently measured values. Examining the residual significance CMD, i.e., the difference between the data and the model weighted by the variance (panel (d) of Figure 2), we see a good, although not perfect, fit. Notably, the area between the blue helium-burning stars and young MS appears to be too cleanly separated in the model, which could be due to differential extinction affecting young stars in the observed CMD. Additionally, the model red helium-burning stars are too blue compared to the data, likely due to uncertainties in the massive star models (e.g., Gallart et al. 2005b). However, even the most discrepant regions are fit within ±5σ, which are indicated by black or white points. Overall, the model CMD appears to be in good agreement with the observed CMD, indicating that we have measured a reliable SFH. See Dolphin (2002) for a full discussion of the quality measures of this CMD fitting technique.

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In general, uncertainties in the absolute SFHs generally are somewhat anti-correlated between adjacent time bins, such that if the SFR is overestimated in one bin, it is underestimated in the adjacent bin. However, cumulative SFHs, i.e., the stellar mass formed during or previous to each time bin normalized to the integrated final stellar mass, do not share this property, and thus present a more robust way of analyzing SFHs. Uncertainties on the individual cumulative SFHs represent the 16th and 84th percentiles of the distribution of SFHs as determined by Monte Carlo tests.

In the following sections, we consider absolute and cumulative SFHs plotted versus two different time binning schemes. The cumulative SFHs are shown at the highest time resolution possible. Errors in the cumulative SFHs presented at this resolution indicate both the uncertainty in the fraction of total stellar mass formed prior to a given time, and the inherent time resolution for the SFH of that particular galaxy. For clarity in each of the relevant cumulative SFH figures, we have only plotted the error bars in every other time bin.

A coarser time binning scheme is used for the absolute SFHs of the individual galaxies, and the specific SFHs across the ANGST sample. The broader time bins allow us to securely average the best-fit SFHs from individual galaxies. For the absolute SFHs of individual galaxies, broader time bins tend to minimize covariant SFRs between adjacent time bins. Thus, applying a broader time binning scheme to the absolute SFHs of individual galaxies provides for more secure measurements of the SFRs. In Appendix A, we determine that six broad time bins of 0–1, 1–2, 2–3, 3–6, 6–10, and 10–14 Gyr provide an optimal balance between photometric depths and age leverage contained in the CMDs of the ANGST dwarfs.

In this paper, we often consider the mean cumulative SFHs and associated error in the mean. While computing the mean cumulative SFH is a straightforward exercise, appropriately calculating the uncertainties in the mean cumulative SFHs is non-trivial. In addition to independent random errors for the SFH of each galaxy in an ensemble, one must consider the inherent spread in the mean, as well a correlated systematic component, shared by all galaxies. To this effect, in Appendix C, we provide a detailed derivation of the uncertainty in the mean cumulative SFH, which accounts for all sources of error that contribute to the mean SFH of an ensemble of galaxies.

The ANGST dwarf galaxies exhibit a wide variety of complex SFHs. In Figure 3, we show the absolute SFHs, i.e., SFR(t), and the cumulative SFHs of the individual galaxies, sorted in order of increasing blue luminosity. A cursory inspection of the 60 SFHs reveals that often galaxies with similar luminosities, morphologies, or chemical compositions, do not have comparable SFHs, confirming the complexity of dwarf galaxy SFHs previously found in studies of the LG (e.g., Mateo 1998; Dolphin et al. 2005; Tolstoy et al. 2009). The wide variety of SFHs underlines the importance of having a large sample; conclusions based on the SFH of a single galaxy may not be representative of the population as a whole. Although we generally do not consider individual galaxies in this paper, in Table 2 we provide data on the SFHs of individual galaxies considered in this sample, which may be useful for specific studies.

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We first consider the unweighted mean specific SFHs (i.e., an SFH divided by the total integrated stellar mass formed) of the ANGST sample, grouped by morphological type (Figure 4). Comparison between the specific SFHs shows that all morphological types sample a comparable range of SFHs for times ≳1 Gyr ago, with the exception of dTidals.¹⁴ Qualitatively, we find that a typical dwarf galaxy exhibits dominant ancient SF (>10 Gyr ago), and lower levels of SF at intermediate times (1–10 Gyr ago). The only consistent difference between the morphological types is within the last 1 Gyr, where dSphs exhibit a significant drop in SFRs relative to the other types. This suggests that many of the dSphs in the ANGST sample could have been gas-rich as recently as 1 Gyr ago, implying that the process of gas loss can occur relatively quickly and at late times, as seen in the LG galaxies Leo i and Fornax (e.g., Gallart et al. 1999, 2005a; Dolphin et al. 2005). Naively, one might associate the sharp drop in the SFR of a typical dSph ∼ 1 Gyr ago with rapid gas loss. However, large uncertainties in the AGB models (e.g., Girardi et al. 2010; Marigo et al. 2010) make the precise age for the drop in dSph SFRs and the degree of synchronization uncertain. In addition, some of the dSphs do appear to have dramatically lower SFRs at more intermediate ages.

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Cumulative SFHs allow us to readily compare galaxies of different masses. Like the absolute SFHs, the cumulative SFHs plotted in Figure 5 show significant diversity within each morphological class, yet converge on mean values that are broadly consistent among the morphological types. Considering the morphological ensemble of galaxies, in Figure 6 we see that the typical dwarf galaxy formed the bulk of its stellar mass prior to z ∼ 1, virtually independent of morphological type. Taken at face value, the amplitude of the difference in SFHs between morphological types is significantly smaller than found in typical models, for example, those which assume that dSphs are dominated by ancient stellar populations and dIs exhibit constant SF over their lifetimes (e.g., Hunter & Gallagher 1985; Binggeli 1994; Skillman & Bender 1995; Grebel et al. 2003).

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The mean cumulative SFHs hint at divergence between the morphological types within the last few Gyr (Figure 6). This may be consistent with suggestions that present-day morphological types of luminous galaxies only began to emerge more recently than z ∼ 1–2 (e.g., Brinchmann & Ellis 2000). However, as we discuss below, the uncertainties on mean ancient and intermediate SFHs in the ANGST sample are relatively large, preventing a precise interpretation.

We identify clear differences in the mean SFHs within the most recent 1 Gyr. At these times, luminous MS and core blue and red helium-burning stars provide excellent age leverage (e.g., Dohm-Palmer et al. 1998), and the SFHs clearly illustrate differences between the morphological types. Specifically, the typical dSph, dI, dTrans, and dSpiral formed ∼2%, 8%, 4%, and 5% of their total stellar mass within the most recent 1 Gyr. This suggests that present-day morphological typing is strongly influenced by SF that occurred in the most recent 1 Gyr.

The combined findings from intermediate and recent SFHs suggest that morphological differences in dwarf galaxies can be relatively recent phenomena, at least within the Local Volume. dSphs that are strictly old, i.e., have no AGB star populations, are known to exist in the LG (e.g., Mould et al. 1982; Mateo 1998; Dolphin et al. 2005; Tolstoy et al. 2009), but appear to only represent a minority of all known dSphs in the larger volume we analyze here. We caution that this conclusion is only applicable to more luminous dSphs, which are likely analogs to LG dSphs such as Fornax and Leo i. As discussed in Section 2.1, the ANGST sample does not include faint dSphs such as Ursa Minor or Draco.

We mention that results based on SFHs with look back times ≳2 Gyr ago should be treated with appropriate caution. At these times, uncertainties on the mean cumulative SFHs, due to both the shallow nature of the data and accuracies of the stellar models of evolved stars as detailed in the Appendices, can be broad. For example, while the average SFH of the dSph population shows relatively modest uncertainties at most times, the dI sample has noticeably larger uncertainties. The contrast in error bars is largely due to the average photometric depth of the sub-population, e.g., the dIs typically have the shallowest CMDs, and the age–metallicity degeneracy on the RGB. Increasing the precision on the SFHs at ancient times requires continued improvement in the stellar models of evolved stars, and, perhaps more importantly, increased depth in the observed CMDs.

Galaxies in clusters, groups, and the field follow similar morphology–density relationships. Namely, gas-poor galaxies, i.e., ellipticals, are generally found to be less isolated than gas-rich galaxies, i.e., spirals (e.g., Oemler 1974; Dressler 1980; Blanton et al. 2005). A comparable morphology–density relationship has been found for dwarf galaxies (e.g., Einasto et al. 1974; Mateo 1998; van den Bergh 2000; Skillman et al. 2003a; Geha et al. 2006), such that gas-poor dwarfs are found primarily near massive galaxies.

The observed change in the relative fraction of gas-rich and gas-poor galaxies with environment provides a simple test for various models of dwarf galaxy evolution. As illustrated in Figure 7, the ANGST dwarf galaxies clearly adhere to the morphology–density relationship, when using tidal index (Equation (1)), Θ, as a proxy for local density. Typically, dIs are significantly more isolated than dSphs, in spite of having similar mean total stellar masses. dTrans, on average, have a distribution of tidal indices closer to dIs than dSphs (see Section 5.3), and have a lower mean stellar mass than either dIs or dSphs. dSpirals are the most massive galaxies in the sample and are typically more isolated than dSphs. These findings are in general agreement with earlier studies of LG dwarf galaxies (e.g., Mateo 1998; van den Bergh 2000; Tolstoy et al. 2009).

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When combined with measured SFHs, the morphology–density relationship can be used to assess dwarf galaxy evolution models, particularly those that include gas loss. Scenarios favoring internal mechanisms (i.e., stellar feedback) as the primary driver of gas loss (e.g., Dekel & Silk 1986; Dekel & Woo 2003) can reproduce a number of observed dwarf galaxy properties (e.g., surface brightness, rotation velocities, metallicities, etc; Woo et al. 2008). However, such models are generally unable to account for the morphology–density relationship (e.g., Mayer 2010) and often predict that gas-rich and gas-poor dwarf galaxies may have different patterns or efficiencies of SF (e.g., Dekel & Silk 1986; Skillman & Bender 1995). In contrast, some models that factor in additional external effects (e.g., gravitational interactions, ram pressure stripping) have been able to reproduce a wide range of dwarf galaxy properties, including a canonical morphology–density relationship (e.g., Mayer et al. 2006; Mayer 2010; Kazantzidis et al. 2010). In the following sections, we discuss results from the ANGST SFH analysis within the context of physical processes that can affect the evolution of dwarf galaxies.

5.1. Comparing Stellar and Gas Masses

The relative masses of the gas and stellar components can provide clues to dwarf galaxy evolution. For the ANGST sample, we consider the gas mass and baryonic gas fraction as functions of total stellar mass and tidal index. The gas masses are based on the H i masses in Karachentsev et al. (2004), corrected by a factor of 1.4 to account for helium content. The baryonic gas fraction, M_gas/M_baryonic, is defined to be M_gas/(M_gas+M*₂₅) and does not account for the contribution due to warm/hot baryons. The stellar masses, M*₂₅, are derived from integrating the SFHs over time and applying the areal normalization, $\mathcal {A}_{25}$.

We first consider the relationship between the total gas mass and integrated stellar mass, shown in Figure 8, where the dot-dashed line denotes a gas fraction of 50% (i.e., M_gas = M*₂₅). In this context, the most massive galaxies occupy the upper right portion of the plot, while lower mass dwarfs are located to the left. Galaxies without detectable gas are located in the lower portion of the plot and have been placed at log (M_gas/M_☉) = 3 for convenience. To illustrate the range of stellar mass covered by the ANGST dSphs relative to the LG dSphs, we have included select LG dSphs in gray (placed using stellar mass-to-light values from Mateo 1998).

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Figure 8 provides a concise snapshot of the current evolutionary state of nearby dwarf galaxies. For large stellar masses, this view illustrates the morphological ambiguity between dIs and dSpirals; galaxies from both classes are gas-rich and can have stellar masses ≳10⁸ M_☉. H i surface density maps of some dIs even reveal hints of spiral gas structure (e.g., Puche et al. 1992). In this same mass regime, however, there is a conspicuous absence of dSphs. In the ANGST sample, we do not find dSphs more massive than ∼10⁸ M_☉, which is in agreement with the lack of massive gas-poor galaxies in the LG (e.g., Mateo 1998; Tolstoy et al. 2009). dTrans are predominantly located at low stellar masses, yet have relatively large gas supplies. These properties suggest that some dTrans may not be significantly different from low-mass dIs; we return to this point in Section 5.3.

Plotting the baryonic gas fractions for the ANGST dwarfs allows us to readily compare to similar analysis from previous studies (Figure 9). The general trend for dwarf galaxies mirrors that of massive counterparts on the Hubble sequence (e.g., Roberts & Haynes 1994), namely that spiral galaxies typically have lower gas fractions than irregulars. The typical gas fractions of galaxies in the ANGST sample are slightly lower than those found in other studies of nearby dwarfs (e.g., Geha et al. 2006). This difference likely arises from two sources. First, stellar masses in other studies are derived using M/L ratios whose value is typically fixed by the galaxy color. These colors will be luminosity weighted to favor younger stellar ages, leading to artificially small mass-to-light ratios. These luminosity-weighted biases do not affect the resolved CMD determinations used here. Second, the stellar masses computed from the SFHs are the total mass of stars formed over the lifetime of the galaxy. The present-day stellar masses are likely to be smaller, however, due to stellar evolution. Accounting for this effect would result in higher gas fractions for the ANGST dwarf galaxies.

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There also appear to be a handful of outliers to the general trends in Figure 9. The two most conspicuous low-mass outliers, HS 117 and DDO 113, may simply be morphological misclassifications. HS 117 is classified as a dI, but has a very low gas content, with an upper limit of $M_{ \rm H\,{\mathsc{i}}}$ ∼ 10⁵ M_☉ (Huchtmeier et al. 2000) and error bars consistent with zero. Interestingly, Karachentsev & Kaisin (2007) detect low levels of Hα in HS 117, which reinforces the dI classification, but based on the lack of H i, they classify this as a dSph. Morphologically, inspection of the HST image further reveals that it appears to be superimposed on an H ii region located in the outskirts of M81, leading to an erroneous dI classification. We therefore suggest that HS 117 is best classified as a dSph or possibly a dTrans. DDO 113 is likewise classified as a dI with negligible gas content, but has a possible Hα detection (Karachentsev & Kaisin 2007). Inspection of the HST-based CMD suggests that DDO 113 resembles a prototypical dSph, with a handful of relatively faint blue stars, suggesting it is also likely a dSph or a dTrans.

Additional putative outliers are three dTrans (ESO294-010, ESO410-005, ESO540-032), which have low gas masses relative to other dTrans. These three dTrans have confirmed blue horizontal branch populations (Da Costa et al. 2010), which helps constrain their ancient SFHs. However, none of these galaxies shows any unique features in their SFHs that would explain their outlier status. We discuss these galaxies in the context of dTrans in Section 5.3.

Examining the gas fraction as a function of isolation (Figure 10), we see that isolated galaxies tend to have high gas fractions, while those in high-density environments have low gas fractions. Interestingly, there appear to be no galaxies with any appreciable gas in dense environments (Θ ≳ 1.5; HS 117 and DDO 113 have uncertain gas measurements as described above).

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5.2. Mechanisms for Complete Gas Loss

5.3. The Nature of Transition Dwarf Galaxies

As the smallest and most pristine galaxies in the universe, dwarf galaxies occupy a critical, but poorly constrained, role in cosmological models of galaxy formation and evolution (e.g., Moore et al. 1999; Klypin et al. 1999). Because of their intrinsic faintness, dwarf galaxies have been difficult to directly detect at cosmologically significant redshifts (e.g., Mathews et al. 2004), and we are left to infer high-redshift evolution from the properties of their descendants. To do so, we present a comparison between the mean cumulative SFHs of the ANGST sample dwarfs and the cosmic SFH, as derived from observed UV fluxes in high-redshift galaxies (e.g., Reddy et al. 2008). In the top panel of Figure 11, we have plotted the cosmic SFH (gray shaded region) along with results from the present study.

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The uncertainties in the ANGST SFHs at ancient times are relatively large, limiting precise interpretation at epochs older than z ∼ 1. However, at z ≲ 0.7, we see clear separation between the cosmic and ANGST cumulative SFHs. At these redshifts, dwarf galaxies in the ANGST sample of all morphological types appear to have formed a lower percentage of stellar mass than the more luminous galaxies that dominate determinations of the cosmic SFH. This finding is generally consistent with the expectations of galaxy "downsizing," where high-mass galaxies preferentially stop forming stars at higher redshifts (e.g., Cowie et al. 1996). The precise role of dwarf galaxies in theories of downsizing is highly uncertain, making this result difficult to interpret in the context of current models (e.g., Mouri & Taniguchi 2006). We also caution that the physical significance of this finding is still ambiguous due to a several factors including uncertain AGB star models and redshift-dependent dust corrections applied to the cosmic SFH (e.g., Girardi et al. 2010; Marigo et al. 2010; Reddy et al. 2010). A comparison of SFHs from the entire ANGST sample (including the more massive spiral galaxies) and the cosmic SFH is presented in Williams et al. (2011b).

The cumulative SFHs can also provide insight into the validity of model SFHs often used to describe the evolution of dwarf galaxies. As an illustrative example, we have selected a simple exponentially declining SF model (SFR ∝ e^−t/τ; a τ model), and show the cumulative SFHs for a range of τ values (gray shading) in the lower panel of Figure 11. Visual inspection suggests that the best-fit SFHs show significant deviations from the predicted smooth curve of single τ valued models. A χ² test between the best-measured cumulative SFHs and exponentially declining SFH models (with τ varying from 0.1 to 14.1 Gyr) confirms that any single value of τ does not accurately represent the data. Similarly, the mean measured SFHs also are not well matched by a constant SFH (i.e., τ → ∞ Gyr) or by a single ancient epoch (τ ≲ 0.1 Gyr) of SF followed by passive galaxy evolution. Instead we suggest that a more representative SFH of dwarf galaxies can be made through a τ plus constant SFH model. As we show in Figure 11, a model SFH with an initial burst with τ = 1.25 Gyr that produces 65% of the stellar mass prior to z ∼ 0.7 (6.5 Gyr ago), followed by a constant SFH at intermediate and recent times that produces 35% thereafter. This combined model provides a better representation of the data than either a simple τ model or constant SFH model does independently. Although the relatively large errors at ancient times do not make for tight constraints on τ models at all epochs, we nevertheless suggest that more complex and multi-component models may be a better representation of the lifetime SFHs of dwarf galaxies.

We have uniformly analyzed SFHs of 60 dwarf galaxies in the nearby universe based on observations and data processing done as part of the ANGST program. While the SFHs of individual galaxies are quite diverse, we find that the mean SFHs of the different morphological types are generally indistinguishable earlier than the most recent ∼1 Gyr. On average, the typical dwarf galaxy formed the bulk of its stars prior to z ∼ 1, although the uncertainties are relatively large, particularly for dIs, which have a diverse set of SFHs.

Among the morphological types, the SFHs hint at divergence within the past few Gyr, although assigning a precise time to this phenomenon is challenging due to uncertainties in AGB star modeling and the modest time resolution afforded by the data. The clearest differences between the morphological types can been seen in the most recent 1 Gyr, where the typical dSph, dI, dTrans, and dSpiral formed ∼2%, 8%, 4%, and 5% of their total stellar mass, respectively.

The dwarf galaxies in the ANGST sample show a strong morphology–density relationship. This suggests that internal mechanisms that lack an environmental dependence, e.g., stellar feedback or gas consumption, cannot solely account for gas loss in dwarf galaxies. Instead, we find qualitative consistency with the model of "tidal stirring" (e.g., Mayer et al. 2001a, 2001b, 2006), which can broadly explain the extended SFHs as well as the observed morphology–density relationship.

A comparison of dwarf galaxy SFHs with the cosmic SFH determined from in situ measurements of high-redshift galaxies find significant discrepancies for z ≲ 0.7, such that the ANGST dwarf population has been forming a larger fraction of their stellar mass in the most recent several Gyr. However this, in part, results from the ANGST SFHs showing a slower rate of SF at intermediate epochs, where broad uncertainties in extinction corrections and AGB star models may be able to explain the offset. The mean measured SFHs are inconsistent with single-valued exponential models of SF (i.e., τ models), and may require more complex or multi-component models.

We also identify 12 dTrans in the sample, based on the literature definition of present-day gas fraction and SF as measured by Hα (e.g., Mateo 1998). We find that most dTrans in the ANGST sample have lower characteristic stellar masses than other morphological types, but have properties that are consistent with dIs in all other respects. This suggests that most dTrans ANGST sample are simply low-mass dIs galaxies that do not have detectable levels of Hα, but have sufficient gas with which to form stars. Three dTrans in the ANGST sample (E294-10, E410-5, and E540-32) appear to have extremely low gas fractions and may indeed be in the last throes of SF.

The authors thank the anonymous referee for preceptive and insightful comments that have helped to improve the paper. D.R.W. is grateful for support from the University of Minnesota Doctoral Dissertation Fellowship and Penrose Fellowship. Support for K.M.G. is provided by NASA through Hubble Fellowship grant HST-HF-51273.01 awarded by the Space Telescope Science Institute. I.D.K. is partially supported by RFBR grant 10-02-00123. The authors thank Stephanie Côté for fruitful discussions on the nature of transition dwarf galaxies, and Oleg Gnedin for his insightful suggestions on measures of photometric quality. This work is based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. Support for this work was provided by NASA through grants GO-10915, DD-11307, and GO-11986 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made extensive use of NASA's Astrophysics Data System Bibliographic Services.

Meaningful comparison of absolute SFHs across the ANGST sample requires a uniform time binning scheme. This necessitates balancing the wealth of information about the ancient and intermediate epochs from the deepest CMDs (e.g., Antlia; 50% completeness of M_F814W ∼ +1.75) with the course leverage of the shallower CMDs (e.g., UGC 4483; 50% completeness of M_F814W ∼ −1.7; see Table 2). As a compromise between the two extremes, we fixed a sample-wide time binning scheme using a galaxy with a 50% completeness value near the median of the sample (DDO 6; M_F814W ∼ 0). To test for the optimal time resolution, we constructed CMDs of single age stellar populations, convolved the simulated photometry with the artificial stars and photometric limits of DDO 6, and ran the SFH recovery program on each of these simulated CMDs. This process was conducted on single age CMDs of 0.5, 1.5, 2.5, 4.5, 8, and 12 Gyr in age.

The purpose of this exercise is to provide a simple test for the robustness of the final time bins. While coarser time bins encompass a larger fraction of the input SF, there are fewer of them, which provide less information about patterns of SF over time. In this test, we deemed a good recovery as one in which the input SFH was within the uncertainties of the recovered SFH. In Figure 12, we show the cumulative SFHs, where the input SF is indicated by the dashed magenta line and the recovered SFH by the solid black line. Uncertainties were computed using 50 Monte Carlo realizations as described in Section 3.

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Initial tests suggested that six broad time bins of 0–1, 1–2, 2–3, 3–6, 6–10, and 10–14 Gyr would provide suitable time resolution across the ANGST sample. As shown in Figure 12, the general agreement between the input and recovered SFHs is good and falls within the uncertainties. Clearly, the best recovery is seen in the 0–1 Gyr bin, where the young MS and massive core and blue helium-burning stars provide secure leverage on recent SF. The oldest bin also shows similarly robust results.

The results in the intermediate bins are generally reasonable, although not as reliable as the youngest and oldest bins. Much of the variation at intermediate ages can be attributed to uncertainties in AGB star models (e.g., Girardi et al. 2010; Marigo et al. 2010). Although we used the same models to generate and recover the single age populations, there are many other sources of uncertainties in the recovered SFH, including photometric depth, systematic stellar model uncertainties, and blurring of distinct features due to observational effects (see Appendix B). AGB populations of different ages often have similar colors and magnitudes on optical CMDs (e.g., Gallart et al. 2005b; Weisz et al. 2008), thus it can be difficult to confidently determine the epoch of SF at intermediate ages (1–10 Gyr ago). This limitation is clearly illustrated in Figure 12, which shows broad uncertainties on the recovered SFHs during intermediate times. However, we still find that the input SFHs are generally within the recovered SFH error bars. Additionally, ≳50% of the SF is recovered in the correct time interval. Although it would be possible to combine bins at intermediate times to increase the accuracy of the recovered SFRs, we believe that this scheme will permit future comparisons with SFHs derived using improved AGB star models (e.g., Girardi et al. 2010).

For this time binning scheme, we find that reported uncertainties in the SFRs typically decrease for CMDs deeper than DDO 6, and increase for shallower CMDs, in agreement with expectations. We thus conclude that this scheme is nearly optimal for comparison of lifetime SFHs derived from CMD with typical depths of the ANGST sample.

Photometric depth strongly affects the accuracy of a measured SFH. Increasing photometric depth increases both the number of stars on a CMD and the visibility of age-sensitive CMD features (e.g., ancient MS turnoff, horizontal branch, red clump). Intuitively, a CMD with a brighter photometric limit has less information available than a deeper CMD, and the derived SFH is thus more uncertain. However, quantifying the precise impact of these uncertainties, such as the amplitude and ages affected, is challenging as varying photometric depths can amplify effects of uncertainties in the stellar models used to measure SFHs. In this appendix, we explore the effects of photometric depth on the accuracy of SFH recovery. We demonstrate the effects in two regimes: one where the only variable is photometric depth, and the other where we vary both photometric depth and stellar evolution models.

We first analyze the accuracy of recovered SFHs as a function of only photometric depth. That is, we construct synthetic CMDs at select photometric depths, then attempt to recover the input SFH using identical parameters (e.g., IMF, binary fraction, filter combination) and, in this case, the same stellar evolution models. More concretely, we constructed CMDs at six different photometric depths (M_V = +4, +2, +1, 0, −1, −2), using a constant SFH (log (t) = 7.4–10.15, with a time resolution of ∼0.1 dex), a fixed metallicity, and the BaSTI stellar evolution models. Each CMD was populated with ∼10⁶ stars to minimize the contribution of random uncertainties due to the number of stars used to measure the SFR in each time bin; the uncertainties for Poisson sampling of the CMD are already well characterized by our Monte Carlo tests for SFHs measured from observed CMDs. We then recovered the SFH of each CMD using the BaSTI stellar evolution models, to ensure that the only variable being tested is photometric depth.

In Figure 13, we compare the input (black lines) and recovered (colored lines) cumulative SFHs at each photometric depth. Overall, the recovered cumulative SFHs are in excellent agreement with the input SFHs at all photometric depths. The maximum deviation between the input and recovered SFHs at any photometric depth is ∼4%, which is consistent with the expected Poisson precision of 1/$\sqrt{N}$, where N is the number of stars used to measure the SFR in a given time bin. This exercise demonstrates that if all the underlying stellar models are known exactly, then the accuracy of the recovered SFH only depends on the number of stars in the CMD, and not the photometric depth. The same results are found when using different stellar evolution models, e.g., Padova, Dartmouth (Dotter et al. 2008), to conduct this exercise. This test is extremely promising for the future of SFH recovery methods, suggesting that as the stellar modeling improves, the accuracy of the recovered SFHs will steadily increase.

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Unfortunately, stellar evolution models are still uncertain, especially for the evolving stars that dominate the brighter regions of the CMD. Therefore, additional systematic uncertainties are introduced into SFH measurements by uncertainties in the selected stellar models. The luminosity, color, and number density of specific CMD features provide leverage on the SFR at different epochs. However, stellar models are not always self-consistent when trying to model multiple observed features (e.g., reproducing colors consistent with observations for both the horizontal branch and RGB; e.g., Gallart et al. 2005b). The effect on a measured SFH is that the SFR may be systematically shifted into a particular time bin, depending on the stellar model used and photometric depth of the CMD (i.e., which particular age-sensitive CMD features are available). We refer the reader to Gallart et al. (2005b) for a comprehensive review on the adequacy of stellar evolution models for reproducing CMD features.

To test for systematic effects on measured SFHs, one ideally wants to test for differences between the stellar models and "truth," that is, stellar population characteristics based on the exact physics governing stellar evolution in Nature. However, current stellar evolution models represent the best physical descriptions we have of Nature. By measuring how different stellar models influence a measured SFH, we can get a sense of the amplitude of systematic uncertainties for SFH recovery.

To examine the magnitude of systematic effects, we use the same CMDs as in Figure 13. However, the SFHs are now recovered with the Padova stellar models. In this case, the differences between the input and recovered SFHs are indicative of the systematic effects introduced by choice of stellar model.

In Figure 14, we see that the differences in the input (black lines) and recovered (colored lines) mean cumulative SFHs are more substantial than when identical models were used, as expected. For the deepest CMD considered (M_V = +4), the agreement between the input and recovered CMD is excellent. Here, the ancient MS turnoff provides a reliable constraint on the ancient SFH, reducing the systematics in progressively younger time bins as well. For shallower CMDs that do not include the ancient MS turnoff, we see significant deviations between the recovered and input SFHs. These differences arise primarily in the treatment of such features of the horizontal branch, red clump, and RGB (see Gallart et al. 2005b for a more detailed discussion), all of which are intrinsically difficult to model due to mass loss and complicated stellar atmospheres.

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Of interest are the general order-of-magnitude variations, and not a specific point-by-point analysis. In the case of the shallowest CMDs (M_V  =  −2, −1, 0), the ancient SF is preferentially recovered at intermediate ages, with a typical magnitude in the difference of input and recovered SFH of ∼20%. For the deeper CMDs (M_V  =  +1, +2), SF at the oldest times tends to be overestimated by up to ∼40%. At all photometric depths, the systematic effects within the last ∼2 Gyr are ≲10%. These trends would likely have the opposite sign if reality is closer to the Padova model, and SFHs were recovered with the BaSTI models.

The exercises we have conducted demonstrate the importance of systematic uncertainties in SFH recovery. We caution that our results are actually measuring the systematic differences between the Padova and BaSTI models, and only serve as a proxy for the difference between a given model and "truth," i.e., observed CMDs. That being said, the methodology of this type of analysis provides a framework for exploring the effects of systematic uncertainties. The primary limitation to this type of analysis is the number of models available that span the entire age/metallicity range needed to derive SFHs in nearby galaxies. As the number of models that sample a broader parameter space increases, it will be possible to gain more leverage on the effects of systematic uncertainties.

Propagating systematic uncertainties of the measured SFHs into the mean SFH of an ensemble, e.g., the mean cumulative SFH of all dSphs, is non-trivial. Unlike random uncertainties, which can be treated as statistically independent, systematic uncertainties share an unknown degree of correlation. Because this violates a common assumption of statistical independence, we must consider a more involved approach to appropriately folding the random and systematic SFH uncertainties into a sample average. In this section, we outline the mathematical framework we employed to combine uncertainties of individual SFHs into the mean of an ensemble of SFHs.

We begin by considering an ensemble of N galaxies, for which we want to determine the mean SFH and associated errors. If we consider the SFH as a set of measured SFRs in discrete time bins, we can write the SFR per time bin of the ith galaxy, x_i, as

$$\begin{equation} x_{i} = \mu \pm \sigma * random_{1} \pm r_{i}*random_{2} + \alpha *s_{i}, \end{equation} \tag{ C1 }$$

where μ is the true mean of the ensemble and σ is the dispersion of the SFHs of the ensemble. We define r_i to be the random uncertainty component and s_i to be the systematic uncertainty component contributed by the ith galaxy. Each galaxy contributes some uncorrelated fraction to the σ and r_i terms, which we designate as random₁ and random₂. We assume that there is an unknown systematic error in the measurement that is shared by all systems, which we denote as α.

Given the equation for x_i, we can write the probability of measuring a set of particular values of x_i given μ, σ, α, s_i, and r_i as

$$\begin{equation} P(x_{i} | \mu, \sigma, \alpha, s_{i}, r_{i}) = \prod \frac{1}{\sqrt{2\pi }} e^{\frac{-0.5(\mu + x_{i} + s_{i} \alpha)^{2}}{(\sigma ^{2} + r_{i}^{2})}}. \end{equation} \tag{ C2 }$$

The degree of correlation attached to s_i is the constant α. Given that α is an unknown, we must marginalize over α using its probability distribution function (PDF). For simplicity, we assume the form of the PDF to be a Gaussian, with μ_α = 0 and σ_α = 1, which can then be written as

$$\begin{equation} P(\alpha) =\frac{1}{\sqrt{2\pi }} \int e^{-0.5(\frac{\alpha }{\sigma _{\alpha }})^{2}}d\alpha. \end{equation} \tag{ C3 }$$

Setting up the integral, we now have

$$\begin{eqnarray} && P(x_{i} | \mu, \sigma, s_{i}, r_{i}) = \frac{1}{\sqrt{2\pi }}\nonumber\\ && \quad \times \int \left(d\alpha \ e^{-0.5\alpha ^{2}} \prod \frac{1}{\big(\sigma ^{2} + r_{i}^{2}\big)} e^{\frac{-0.5(\mu + x_{i} + s_{i} \alpha)^{2}}{(\sigma ^{2} + r_{i}^{2})}} \right), \end{eqnarray} \tag{ C4 }$$

which reduces to

$$\begin{equation} P(x_{i} | \mu, \sigma, s_{i}, r_{i}) = C*e^{\frac{-0.5*(\mu -(X+X*SS-S*SX)/(I+I*SS-S^{2}))^{2}}{((1+SS)/(I+I*SS-S^{2}))}}, \end{equation} \tag{ C5 }$$

where C is a constant of integration, and we have defined the terms I, S, X, SS, and SX to be

$$\begin{equation} I = \sum \left(\frac{1}{\sigma ^{2} + r_{i}^{2}} \right) \end{equation} \tag{ C6 }$$

$$\begin{equation} S = \sum \left(\frac{s_{i}}{\sigma ^{2} + r_{i}^2} \right) \end{equation} \tag{ C7 }$$

$$\begin{equation} X = \sum \left(\frac{x_{i}}{\sigma ^{2} + r_{i}^2} \right) \end{equation} \tag{ C8 }$$

$$\begin{equation} SS = \sum \left(\frac{s_{i}^{2}}{\sigma ^{2} + r_{i}^2} \right) \end{equation} \tag{ C9 }$$

$$\begin{equation} SX = \sum \left(\frac{s_{i}*x_{i}}{\sigma ^{2} + r_{i}^2} \right). \end{equation} \tag{ C10 }$$

Per our assumption of Gaussian distributions, we can then use these identities and Equation (C5) to write the mean SFR per time bin as

$$\begin{equation} \langle \rm SFR \rangle \ = \frac{X+X*SS-S*SX}{I+I*SS-S^{2}} \end{equation} \tag{ C11 }$$

and the uncertainty in the mean SFR (not the standard deviation) as

$$\begin{equation} \sigma _{\rm Mean}(\rm SFR) = \sqrt{\frac{1+SS}{I+I*SS-S^{2}}}. \end{equation} \tag{ C12 }$$

In the limit that the systematic uncertainties do not contribute to the overall uncertainty, i.e., s_i = 0, we see that Equations (C11) and (C12) reduce to the expected form for statistically independent uncertainties, i.e., random errors:

$$\begin{equation} \langle \rm SFR \rangle \ = \frac{X}{I} \end{equation} \tag{ C13 }$$

$$\begin{equation} \sigma (\rm SFR) = \frac{1}{\sqrt{I}}. \end{equation} \tag{ C14 }$$

The uncertainties on the average cumulative SFHs per morphological type (e.g., Figure 6) have been computed using Equation (C12).

For the purposes of simplified mathematics, we have assumed Gaussian distributions for the uncertainties. However, it is often the case that the distribution of uncertainties is not well approximated by a Gaussian. In the case of this analysis, we have therefore computed the upper and lower uncertainties independently, resulting in asymmetric errors bars. A more detailed treatment of combining correlated systematic effects will be explored in A. E. Dolphin (2011, in preparation).

Facility: HST (ACS, WFPC2) - Hubble Space Telescope satellite