The Star Formation History of Eridanus II: on the Role of Sne Feedback in the Quenching of Ultra-Faint Dwarf Galaxies

1 1 Draft version January 20, 2021 Typeset using LATEX twocolumn style in AASTeX63

The star formation history of Eridanus II: on the role of SNe feedback in the quenching of ultra-faint dwarf galaxies.

C. Gallart,1, 2 M. Monelli,1, 2 T. Ruiz-Lara,3 A. Calamida,4 S. Cassisi,5, 6 M. Cignoni,6, 7, 8 J. Anderson,4 G. Battaglia,1, 2 J. R. Bermejo-Climent,8, 9, 2 E. J. Bernard,1 C. E. Mart´ınez-Vazquez´ ,10 L. Mayer,11 S. Salvadori,12, 13 A. Monachesi,14, 15 J. F. Navarro,16 S. Shen,17 F. Surot,1, 2 M. Tosi,8 V. Bajaj,4 and G. S. Strinfellow18

1Instituto de Astrof´ısica de Canarias, 38205 La Laguna, Tenerife, Spain 2Departamento de Astrof´ısica, Universidad de La Laguna, E-38200 La Laguna, Tenerife, Spain 3Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands 4Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 5INAF - Osservatorio Astronomico d’Abruzzo, Via M. Maggini, s/n, I-64100, Teramo, Italy 6INFN, Largo B. Pontecorvo 3, 56127, Pisa, Italy 7Department of Physics - University of Pisa, Largo Pontecorvo, 3 Pisa, 56127, Italy 8INAF-Osservatorio di Astrofisica e Scienza dello Spazio, Via Gobetti 93/3, 40129, Bologna, Italy 9INFN, Sezione di Bologna, via Irnerio 46, I-40126 Bologna, Italy 10Cerro Tololo Inter-American Observatory, NSF’s National Optical-Infrared Astronomy Research Laboratory, Casilla 603, La Serena, Chile 11Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland 12Dipartimento di Fisica e Astrofisica, Univerisit degli Studi di Firenze, via G. Sansone 1,Sesto Fiorentino,Italy 13INAF/Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, Firenze, Italy 14Instituto de InvestigaciónMultidisciplinar en Ciencia y Tecnolog´ıa,Universidad de La Serena, RaúlBitrán1305, La Serena, Chile 15Departamento de Astronom´ıa,Universidad de La Serena, Av. Juan Cisternas 1200 Norte, La Serena, Chile 16Department of Physics and Astronomy, University of Victoria, PO Box 3055, STN CSC, Victoria BC V8W 3P6, Canada 17Institute of Theoretical Astrophysics, University of Oslo, Sem Sælands vei 13, 0371, Oslo, Norway 18Center for Astrophysics and Space Astronomy, University of Colorado, 389 UCB, Boulder, Colorado 80309-0389

Submitted to ApJ

ABSTRACT

Eridanus II (EriII) is an ultra-faint dwarf (UFD) galaxy (MV =-7.1) located at a distance close to the Milky Way virial radius. Early shallow color-magnitude diagrams (CMD) indicated that it possibly hosted an intermediate-age or even young stellar population, which is unusual for a galaxy of this mass. In this paper, we present new ACS/HST CMDs reaching the oldest main sequence turnoff with excellent photometric precision, and derive a precise star formation history (SFH) for this galaxy through CMD-fitting. This SFH shows that the bulk of the stellar mass in Eri II formed in an extremely short star formation burst at the earliest possible time. The derived star formation rate profile has a width at half maximum of 500 Myr and reaches a value compatible with null star formation 13 Gyr ago. However, tests with mock stellar populations and with the CMD of the globular cluster M92 indicate that the star formation period could be shorter than 100 Myr.

1 Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs 14224 and 14234. 1 Accepted December 29, 2020 Corresponding author: Carme Gallart [email protected] 2

From the quantitative determination of the amount of mass turned into stars in this early star 5 formation burst (∼ 2 × 10 M ) we infer the number of SNe events and the corresponding energy injected into the interstellar medium. For reasonable estimates of the EriII virial mass and values of the coupling eﬃciency of the SNe energy, we conclude that EriII could be quenched by SNe feedback alone, thus casting doubts on the need to invoke cosmic reionization as the preferred explanation for the early quenching of old UFD galaxies.

Keywords: galaxies: dwarf; galaxies: formation; galaxies: evolution; galaxies: individual (Eridanus II); Local Group

1. INTRODUCTION certain mass range, and particularly in their early star Dwarf galaxies are the most numerous type of galax- formation history (SFH). However, theoretical models ies in the present-day Universe. They are thought to be have made contrasting predictions on what to expect. the first galaxies to form and the basic building-blocks Cosmological models and simulations that include star of the stellar halos of larger galaxies (Helmi 2020). They forming minihalos, i.e. the first galaxies (e.g. Bromm are thus, key astrophysical objects for understanding the & Yoshida 2011), found that owing to SN feedback the most common mode of galaxy formation and how they star formation can be suppressed prior to the end of relate to the build-up of larger structures in the Uni- reionization in small systems with dark matter mass 8 verse. In addition, their relatively simple nature makes < 10 M , which are possibly associated to present-day them ideal test-beds of the physics that goes into galaxy ultra-faint dwarf (UFD) galaxies (e.g. Ricotti & Gnedin formation and evolution models. Processes such as heat- 2005; Bovill & Ricotti 2009; Salvadori & Ferrara 2009; ing by the cosmic UV background and internal feedback Bland-Hawthorn et al. 2015; Jeon et al. 2015). After 4 from SNe are two mechanisms able to dramatically af- reionization the hot intergalactic gas (≈ 2 × 10 K) can- 4 fect the formation and evolution of dwarf galaxies (e.g. not be accreted by these minihalos (Tvir < 10 K), which Mac Low & Ferrara 1999; Ricotti et al. 2002; Kravtsov therefore passively evolve until the present-day unless et al. 2004; Salvadori et al. 2008; Stinson et al. 2009; they experience major mergers (Salvadori et al. 2015) Sawala et al. 2010; Salvadori et al. 2014; Shen et al. 2014; or late accretion events (z < 2) that can fuel new star Cashmore et al. 2017; Fitts et al. 2017; Jeon et al. 2017; formation activity when the intensity of the UV back- Revaz & Jablonka 2018; Romano et al. 2019; Wheeler ground decreases (Babul & Rees 1992; Ricotti 2009). et al. 2019; Katz et al. 2020; Rey et al. 2020; Gelli et al. Conversely, simulations that cannot resolve the star for- 2020). mation in H2-cooling minihalos predict that small dwarf The relative impact of the above effects varies with galaxies are hosted by more massive dark matter halos, the mass of the dwarf, with the largest systems poten- which are less prone to feedback processes and can keep tially unaffected by reionization and less affected by SN on forming stars after reionization in spite of a slow de- feedback in terms of the capability of gas removal (while cline (e.g. Sawala et al. 2010; Wheeler et al. 2015; Ro- feedback might still be able to alter the density profile mano et al. 2019). In conclusion, the hosting halo mass of the inner regions of their dark matter halos). Local seems to be the main driver of the evolution of dwarf effects are also at play if the galaxy is located in a dense galaxies. For example, Ben´ıtez-Llambay et al.(2015) environment or close to a massive galaxy (see Mayer have discussed that the varied SFHs observed in nearby 2010, for a review): not only can the local UV flux be dwarf galaxies may be explained by a combination of the an order of magnitude larger than the cosmic average, diversity of accretion histories and the effects of cosmic but the ram-pressure stripping and the tidal interaction reionization and feedback on the SFH, which critically can profoundly alter the properties of the gaseous, stel- depend on the mass acquired by the object at the time lar and dark matter components of the dwarf galaxy. when reionization is complete. In turn, Gallart et al. However, recent hydro-dynamical zoom-in simulations (2015) have suggested that this may be related to the of massive high-z Lyman Break Galaxies and its dwarf environment where a dwarf galaxy has formed, and that companions (Pallottini et al. 2017), have shown that SN therefore, this is the ultimate origin of the two main feedback is a key physical mechanism driving the evolu- types of SFHs (slow and fast) observed in Local Group tion of dwarf galaxy satellites, even in these extremely dwarf galaxies. dense and biased environments (Gelli et al. 2020). The precise SFHs for Local Group galaxies obtained It is expected that reionization must leave some sig- thanks to deep observations (particularly from the Ad- nature on the stellar content of dwarf galaxies below a vanced Camera for Surveys, ACS on board the Hubble 3

Space Telescope, HST) have been essential in provid- Table 1. Basic data of Eridanus II ing observational constraints to state-of-the-art models of galaxy formation and evolution. The Local Cosmol- Parameter Eri II ref ogy from Isolated dwarfs (LCID) project (see Gallart RA (h:m:s, J2000) 03:44:20.1 (1) et al. 2015, and references therein, for a discussion of DEC (deg:m:s, J2000) -43:32:01.7 (1) global results of the project) pioneered the use of color- MV (mag) -7.1± 0.3 (1) magnitude diagrams (CMDs) reaching the oldest main- (m-M)0 22.87±0.10 (2) sequence turnoﬀs (oMSTO) to obtain precise, complete DMW (Kpc) 375 (2)

SFHs for isolated Local Group dwarf galaxies. The re- rh (arcmin) 2.31 ± 0.12 (1) sults of this project showed that, at least in the Local rh (pc) 252 (1,2) Group environment, reionization alone could not have −1 a vhel (km s ) 75.6±1.3,2.0 (3) halted star formation in dwarf galaxies in the stellar −1 vGSR (km s ) -66.6 (3) 6 7 mass range 10 − 10 M (Monelli et al. 2010a,b; Hi- −1 a µα (mas yr ) 0.159±0.292,0.053 (4) dalgo et al. 2011, 2013). Since 2005, a large number a µ (mas yr−1) 0.372±0.34,0.053 (4) of fainter dwarf galaxies have been discovered (Willman δ V (km s−1) -71±6 (4) et al. 2005; Belokurov et al. 2006; Zucker et al. 2006), rad V (km s−1) 612+526 (4) both as Milky Way (MW) and Andromeda galaxy satel- tan −401 +26 b lites. They were generically named UFDs and they ap- dperi (Kpc) 356−45 (4) pear to be the least luminous, least chemically evolved b dapo (Kpc) >500 (4) and most dark-matter-dominated galaxies known. Their −1 +1.2 σvhel (km s ) 6.9 −0.9 (3) absolute magnitudes range from MV = −1.5 (Segue I) to 5 M∗ (M ) 1.1 × 10 (5) MV ' −8 (Leo T and CVn I). Brown et al.(2014) have 3 MHI (M ) < 2.8 × 10 (1) used ACS HST CMDs reaching well below the oMSTO +0.4 7 M 1 (M ) 1.2−0.3 × 10 (3) in six of these galaxies and concluded that they formed 2 M/L (M /L ) 420+210 (3) 80% and 100% of their stars by z ' 6 (12.8 Gyr ago) −140 and z ' 3 (11.6 Gyr ago), respectively. From the sim- [Fe/H] -2.38 ± 0.13 (3) +0.12 ilar ancient populations of these galaxies, the authors σ[Fe/H] 0.47 −0.09 (3) find support for the hypothesis that star formation in aThe numbers refer to statistical and systematic errors, them was suppressed by a global outside influence such respectively. as cosmic reionization. b For a MW dark matter halo virial mass 12 This conclusion, however, was challenged when the M=1.6×10 M ; very similar values are obtained for Eridanus II (Eri II hereinafter, MV = −7.1) and Hy- a lower mass MW halo. dra II (MV = −4.6) dwarf galaxies were discovered Note— (1) Crnojević et al.(2016); (2) Mart´ınez- (Bechtol et al. 2015; Koposov et al. 2015; Martin et al. Vázquezet al. in prep; (3) Li et al.(2017); (4) Fritz 2015). Their early ground-based CMDs showed possible et al.(2018); (5) This work indications of the presence in them of an intermediate- age, or even, young population like in the case of Leo T, (Clementini et al. 2012; Weisz et al. 2012). What mechanisms may have allowed star formation to substantially to whether a few Gyr old intermediate-age population stretch in time in these extremely small galaxies? The could be present in the galaxy. This work also derived extended SFH in some of them may point to the in- Eri II structural parameters, discussed the presence of a triguing possibility that reionization may not be, after candidate star cluster near its center (which possible ex- all, the cause for the star formation shut down of UFD istence has raised a lot of interest as a potential unique at very early times. probe of the nature of dark matter and of the dark mat- In the case of Eri II, a subsequent paper by Crno- ter density profile of Eri II itself, see Fig.1, Amorisco jevićet al.(2016) presented a ground-based CMD ob- 2017; Contenta et al. 2018; Marsh & Niemeyer 2019; tained with the Magellan telescope, which reached about Zoutendijk et al. 2020), and showed the absence of HI three magnitudes deeper than the discovery CMD, down gas associated to this galaxy (see also Westmeier et al. to the oMSTO (though with relative large photomet- 2015). Subsequently, spectroscopy of 28 member stars ric errors). It clearly excluded the presence of a young was used by Li et al.(2017) to determine their veloc- (' 250 Myr old) stellar component (as had been sug- ities and metallicities, which disclosed a stellar system gested by Koposov et al. 2015), but was inconclusive as with low overall metallicity but considerable metallic- 4 ity dispersion, high mass-to-light ratio, and a negative the dynamical range of our CMD. In this way, we reach velocity with respect to the Galactic standard of rest the oMSTO with good photometric accuracy and preci- (see Table 1) which implies that it is moving toward the sion, while maintaining unsaturated the stars at the tip Milky Way. Finally, Fritz et al.(2018) used Gaia DR2 of the red giant branch (RGB) and any bright blue stars together with the spectroscopic velocity measurements that might be present. The total exposure time was for 12 stars to derive a systemic proper motion, albeit 7,644 s in F475W and 7,900 s in F814W. Even though with large errors due to its large distance and the few six epochs per filter are clearly not sufficient to obtain (faint) stars with the necessary data. The derived or- periods and proper light curves for short period variable bital properties would tentatively indicate that Eri II is stars such as RR Lyrae or Anomalous Cepheids, we did now close to its pericenter and possibly bound to the plan the observations in order to maximize variable star MW. Table1 provides a summary of the basic literature discovery by splitting each orbit in at least one F475W data on Eri II. and one F814W long exposure. Parallel exposures with In this paper we present a detailed and precise SFH the WFC3/UVIS were obtained (R.A.=03:44:18, Dec=– obtained by quantitatively fitting new ACS/HST CMDs 43:26:07, J2000). The CMD resulting from the parallel reaching the oMSTO with high photometric precision exposures does not show any feature that can be asso- with synthetic CMDs. This SFH shows that the bulk of ciated to Eri II. Eri II stellar mass formed in an extremely short burst Another ACS/WFC program was devoted to image of star formation before the epoch of reionization, thus the same galaxy in cycle 23. GO program 14234 (P.I. demonstrating conclusively the absence of any substan- J. Simon) used 13 orbits to observe the central region tial amount of intermediate-age stellar population. of Eri II. Ten and sixteen exposures were collected in The paper is organised as follows: Sec.2 and3 de- the F606W and F814W bands, with individual expo- scribe the observations, data reduction and photome- sure times ranging from 1,220 s to 1,390 s. The total try; Sec.4 discusses the characteristics of the observed integration time was 12,830 s and 20,680 s, respectively. CMD and the hints on the Eri II stellar populations that can be extracted from the comparison with theoretical isochrones; Sec.5 provides a detailed explanation of the SFH derivation procedures, using two independent codes and stellar evolution model sets; Sec.6 discusses the features present in the derived SFH and some tests using mock stellar populations that help further constraining the actual intrinsic duration of Eri II old star formation event. Finally, in Sec.7 we summarise our findings and discuss their implications for dwarf galaxy formation and evolution.

2. OBSERVATIONS Deep photometric data for Eri II (R.A.=03:44:21, Dec=–43:32:00, J2000) were obtained with the ACS/WFC (Ford et al. 1998) aboard the HST under program P.ID. 14224 (Cycle 23, P.I. C. Gallart). The observations were designed to obtain a signal-to-noise ratio ' 40 near the magnitude level of the oMSTO, at MF 814W ' +2.75. Following Stetson(1993), the filter choice was based on the analysis of synthetic CMDs Figure 1. Three color image obtained by combining the two in the ACS bands. The (F475W-F814W) pair, due to datasets described in the text (F475W, F606W, F814W im- the large color baseline, is optimal for discriminating ages). The half-light radius of Eri II and that of the possible age and metallicity differences at old age, while the stellar cluster are represented by the solid- and dashed-line relatively large widths of these filters allow keeping ellipses, respectively. NOTE: A higher resolution image will relatively short exposure times. be provided for the final version of the paper. Under this program, the galaxy was observed during six orbits, organised in two visits of three orbits each. Figure1 displays a three-color image created combin- Short and long exposures were taken in order to increase ing the F475W, F606W and F814W images from the two 5 datasets, which are rotated by ' 121 degrees. The ex- posteriori, after correcting the coordinate system for ge- posures for each of the three filters were aligned to Gaia ometric distortions. The final list includes 8,350 and DR2 using TweakReg, and combined into corresponding 12,730 bona-fide stars in common between the F 475W mosaic images using AstroDrizzle 1. The three mosaics and the F 814W filters, and between F 606W and the were then stacked as red, green, and blue channels to F 814W filters, respectively. make the color image in Figure 1. Note the presence In order to have an optimal sample of artificial stars to of a large amount of background extended objects. We simulate the observational errors in the synthetic CMD will use the two datasets to independently derive the used to derive the SFH (see Section5), we adopted a SFH. A detailed analysis of the structural parameters synthetic CMD to create the input artificial stars list. of the galaxy and possible star cluster, together with an Stars were uniformly distributed within a range of ages in-depth analysis of the variable star population of Eri 2.5 < t < 13.5 Gyr and metallicities 0.0001 < Z < II is deferred to a forthcoming paper (Mart´ınez-Vázquez 0.002 to broadly cover the observed range of colours and et al. in prep). magnitudes. Artificial stars tests were performed independently for the two data sets, simulating 106 stars 3. DATA REDUCTION AND PHOTOMETRY per chip in ∼300 iterations, distributing the stars in In order to track down any possible systematic is- a grid of equilateral triangles of side length equal to sues in the SFH results due to the usage of a spe- (2×PSFradius + 1 px) to ensure that the photometry of cific data reduction package, photometry and artificial artificial stars is only affected by neighbour real stars, star tests were performed both with the DAOPHOT in addition to image characteristics and defects (Gal- IV/ALLFRAME suite of codes (Stetson 1987, 1994) lart et al. 1999). The stars are injected in each origi- and ePSF/KS2 (Anderson & King 2006), two commonly nal images scaling for individual zero points using the used programs to perform HST photometry. The details corresponding PSF previously used for the data reduc- of the procedures followed in each case are described be- tion. For a more realistic simulation of the photometric low. process, the recovery of the synthetic stars is not made with the same PSF, which somehow would match per- 3.1. DAOPHOT IV/ALLFRAME photometry fectly the input one and therefore would somehow un- The photometry with DAOPHOT IV/ALLFRAME derestimate the errors. Instead, during the reduction was obtained following the prescriptions of Monelli et al. process the PSF is recalculated assuming the same list (2010a). Briefly, images are individually treated to of stars of the original image but using only a randomly derive optimal point spread functions (PSF) based on selected fraction of stars between 80 and 95%. Moreover, bright stars that are unaffected by cosmic rays and are to take into account possible uncertainties associated to distributed over the full field of view, in order to take the flat-field correction, we added to the input synthetic into account the spatial variations. Original FLC im- magnitudes a Gaussian error with a dispersion of 0.01 ages from the ACS/HST archive pipeline version 8.3.4 mag. This will simulate the ≈ 1% flat-field error of the were used. The input list of sources for the simultaneous observations (Brown et al. 2014). photometry performed by ALLFRAME was generated on a stacked median image. This ensures that most, if 3.2. ePSF/KS2 photometry not all, cosmic rays are filtered out and do not pollute Photometry is performed on the the object lists. The background extended objects were FLC images after efficiently removed using the SHARPNESS parameter correcting them for geometric distortion according to (|sha| < 0.1). The final selected photometric catalog the prescription of Anderson & King(2006). Then, we was calibrated to the VEGAMAG system by using the carried out PSF photometry on the individual images zero points suitable for the observing epoch and avail- with the routine hst2xym and by using standard PSF able on the ACS web page. It is important to note that libraries that account for the spatial variation across the detector (Anderson & King 2006). In addition, we our catalog is calibrated to the HST photometric reference system CALSPEC v10 2. took into account the temporal variation of the PSF Given the rotation between the two datasets, they by calculating a perturbation correction of the standard PSF and an individual PSF for each image. In have been independently reduced, and cross-matched a order to increase the depth of the photometric catalog, we also performed simultaneous PSF-fitting photome- 1 https://www.stsci.edu/scientific-community/software/drizzlepac try on all images from the two datasets with the routine 2 https://www.stsci.edu/hst/instrumentation/reference-data-for- kitchen sync2 (Anderson 2020, in prep.). The final cata- calibration-and-tools/astronomical-catalogs/calspec log includes 13,542 stars with at least one measurement 6 in all the three filters, F 475W , F 606W , and F 814W . of the RGB. An isochrone of the same age and 30 times This photometric catalog was calibrated to the VEGA- more metal-rich (Z=0.0003, [Fe/H]=-1.79, orange line) MAG system by using the same zeropoints used to cal- nicely brackets the red envelope of the same features. ibrate the DAOPHOT/ALLFRAME catalog. However, a much younger (8 Gyr) and even more metal- This code was also used to run artificial star tests with rich (Z=0.0006, [Fe/H]=-1.49, red line) represents well the same input synthetic CMD used for the tests with the turnoff and subgiant-branch shape, and the red part DAOPHOT/ALLFRAME discussed above. We used a of the RGB. The plume of stars bluer and brighter than total of '650,000 stars uniformly distributed on the the oMSTO is well matched by a 2 Gyr old isochrone field. The artificial stars are added to the image and (green). However, as mentioned above, the location of measured by KS2 one at a time, in order of not to affect these blue and bright main sequence stars is also con- the original level of crowding. sistent with a population of BSS. Finally, two zero-age HB (ZAHB) loci, and two He-burning tracks of 1.2 M , 4. THE ERIDANUS II CMD for the lowest and highest metallicity considered in this section, are also displayed. The comparison between Figure2 displays the [( F 475W − F 814W ), F 814W ] the ZAHBs and the observed HB stellar distribution and [(F 606W − F 814W ), F 814W ] CMDs of the cen- shows that the blue HB stars can be accommodated tral region of Eri II covered by the ACS data (left and as belonging to the most metal-poor stellar population central panels, respectively). The diagram spans about in the galaxy while the red HB are consistent with a 10 magnitudes, from the tip of the RGB (F 814W ∼ more metal-rich stellar component, with [Fe/H] up to 18.5 mag) down to the limiting magnitude F 814W ∼ −1.49, consistent with the maximum spectroscopically 28.5 mag, which is about 3 magnitude fainter than the observed metallicity (Li et al. 2017, see also Section6). oMSTO. The plot discloses the features typical of an However, since the ZAHB location of a star strongly de- old population. The bright part presents a remark- pends on its total mass – the larger the mass the redder ably steep RGB, suggestive of mostly metal-poor popu- the ZAHB location – some of the reddest and brightest lations, while the horizontal-branch (HB) is well popu- stars in the HB could be progeny of the BSS population lated, on both the blue and the red part, in the colour mentioned before (see the position of the He-burning range 0 < F 475W −F 814W < 1.1 mag. A blue plume of tracks). stars brighter than the bulk of the main sequence stars In summary, the main sequence locus observed in the has the typical appearance of a population of blue strag- Eri II CMD, can easily accommodate a range of ages gler stars (BSS), commonly observed in globular clusters of up to 5-6 Gyr, and a range of metallicities of over and dSph galaxies. In fact, the logarithmic frequency of 1.5 dex, while a similar range of metallicities can also BSS in Eri II, calculated identically as in Monelli et al. explain the HB morphology. The quantitative analysis (2012) is 0.153, which taking into account the absolute of the SFH presented in Section5 will allow us to disclose magnitude M = −7.1 of Eri II, places this galaxy right V the actual stellar composition of the galaxy: whether in the relationship defined by LG dwarfs containing a star formation extended for a few Gyr, and whether the sequence of BSS in the CMD (see Figure 7 in Monelli blue plume is consistent with a BSS population or, on et al. 2012). the contrary, a young population is necessary to explain In the right panel of Figure2, some isochrones se- it. lected from the BaSTI database (Pietrinferni et al. 2004) are superimposed to the CMD. We adopted the distance modulus derived from the properties of the RR 5. STAR FORMATION HISTORY DERIVATION Lyrae stars (Mart´ınez-Vázquezet al. in prep), (m- The SFH of Eri II has been derived through the com- M)0 = 22.87±0.10 and extinction AF 475W = 0.033 mag, parison of the observed CMDs with synthetic CMDs to and AF 814W = 0.015 mag from Schlafly & Finkbeiner extract the combination of simple stellar populations (2011). The figure discloses that a simple comparison (SSP, that is, synthetic populations with small ranges with isochrones is not enough to assess the age spread of ages and metallicities) which provide the best fit. of the dominant population of Eri II. In fact, the plot The SFH provides a detailed and robust determina- shows that the morphology of the main sequence and tion of the star formation rate (SFR) and metallicity the RGB can be explained by different combinations Z as a function of time. In order to establish the ro- of age and metallicity. A very old (13.5 Gyr) and ex- bustness of the SFH determination, two different stel- tremely metal-poor (Z=10−5 or [Fe/H]=-3.27, blue line) lar evolution model sets (BaSTI and PARSEC) and isochrone matches the blue envelope of the CMD, from two independent SFH derivation procedures (TheStorm the oMSTO to the sub-giant branch and up to the tip and SFERA) have been used. Additionally, the SFH 7

Eridanus II (m-M) = 22.87 mag 18 0 -3.27 /13.5 Gyr E(B-V) = 0.01 mag -1.79 /13.5 Gyr -1.49 / 8 Gyr -1.49 / 2 Gyr 20

22 F814W 24

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 F475W - F814W F606W - F814W F475W - F814W

Figure 2. Eri II CMDs for the (F475W, F814W) and (F606W, F814W) band combinations. A number of isochrones and ZAHB from the BaSTI library of the ages and [Fe/H] labelled, and two He-burning tracks of 1.2 M and [Fe/H] in the labelled color code, have been superimposed to the [(F475W-F814W), F814W] CMD (see text for details). determination with TheStorm and BaSTI models has The majority of the solutions for the SFH that will been performed using the two independent photometry be discussed in this paper are derived using the code catalogues obtained with DAOPHOT/ALLFRAME and TheStorm presented in Bernard et al.(2015, 2018), ePSF as described in Section3. Finally, to further con- which closely follows the procedures adopted and dis- strain the actual duration of the old star formation burst cussed in detail in previous papers (Aparicio & Hidalgo in Eri II, a number of tests with mock stellar populations 2009; Monelli et al. 2010a; Hidalgo et al. 2011). This have been performed. code uses a ’mother’ synthetic CMD from which the SSP are extracted. We calculated three mother synthetic CMDs adopting the set of BaSTI models accounting for 5.1. SFH with TheStorm core convective overshooting during the core H-burning 8 stage and mass loss during the RGB evolution3. We Table 2. Parameters adopted for the synthetic CMDs have alternatively adopted both the solar-scaled release a of the BaSTI library (Pietrinferni et al. 2004) and the Library Name Set Diffusion IMF β q α-enhanced one (Pietrinferni et al. 2006, see Table2). BaSTI aeb05 ae NO Kroupa (1993) 0.5 0.4 We note that the version of the BaSTI stellar evolution BaSTI ssb05 ss NO Kroupa (1993) 0.5 0.4 library adopted in the present work does not take into BaSTI ssb07 ss NO Kroupa (1993) 0.7 0.1 account the occurrence of atomic diffusion in the evolu- PARSEC parsec ss YES Kroupa (2001) 0.3 0.0 tionary computations - although it has been considered aModel set: ae: α-enhanced chemical composition; ss: solar-scaled in the calibration of the corresponding Solar Standard chemical composition Model (see Pietrinferni et al. 2004, for a detailed discussion on this issue). The impact of atomic diffusion is to decrease the age of the oldest stellar populations by about 1 Gyr (the exact value depending on the absolute Common to all mother synthetic CMDs (with 5 × 107 age and the stellar metallicity) with respect to an age stars) are a flat SFR between ages 14 and 2 Gyr (model dating procedure based on non-diffusive stellar models stars younger than this age have not been included (see e.g. Cassisi & Salaris 2013, for a detailed discussion because there is no evidence that they are present in on this topic). In order to address this issue in detail for Eri II), and the Kroupa et al.(1993) initial mass func- the current problem, we have compared suitable stellar tion (IMF). We have computed three synthetic CMDs models computed on purpose that alternatively account with the stellar evolution models set (solar-scaled or α- or not for atomic diffusion. We have verified that, for a enhanced) and characteristics of the binary star pop- low metallicity such that of Eri II, a 13.5 Gyr diffusive ulation as detailed in Table2. A range in metallicity isochrone mimicks a non-diffusive one about 0.6-0.7 Gyr consistent with that determined in Li et al.(2017) was older. Therefore, in order to account for this character- adopted. This required the use of the lowest metal- istic of the BaSTI models, in computing the synthetic licity stellar models available in the BaSTI database CMDs we included star of ages up to 14 Gyr old (see (Z=0.0001), with an upper Z=0.0004 for the scaled- below). solar models and Z=0.001 for the α-enhanced ones. The For obtaining the synthetic CMDs, we used a cus- metallicity distribution in the mother synthetic CMD is tomized version of the Stellar Population Synthesis Pro- also flat in the whole metallicity range above, that is, gram available at the BaSTI web page4, which allows no other constrains on the metallicity distribution of the the computation of synthetic CMDs with flat age and galaxy are imposed. metallicity distributions within given age and metallic- Observational errors are simulated in the mother syn- ity ranges. This code has been discussed in Cordier et al. thetic CMD to create a model CMD that is directly (2007) and here we will just highlight that a binary star comparable to the observations. A C++ parallel code population is generated according to a binary fraction β called DisPar which follows the strategy detailed in Gal- and minimum mass ratio q specified by the user, with the lart et al.(1996) and discussed in Ruiz-Lara et al.(2020) mass of the secondary selected randomly following the has been used. It takes into account all the observational recipe by Woo et al.(2003). The current version does effects as derived through the artificial stars tests, using not account for any stochastic variation of the mass loss an empirical approach. This is a fundamental step be- efficiency during the RGB evolutionary stage. The effect cause the distribution of stars near the oMSTO is mod- of the occurrence of mass loss is accounted for by assum- ified substantially due to the observational errors, and ing a constant value for the free parameter η = 0.4 in their realistic simulation is fundamental to derive a re- the Reimers formula in the stellar model computations liable and detailed SFH at the oldest age. Even though (see, Pietrinferni et al. 2004, for a detailed discussion DisPAR can take into account possible spatial variations on this issue). Finally the bolometric correction library of the errors derived with the artificial stars tests when for the ACS photometric system adopted in the present simulating them in the mother CMD, we have not used work is that presented by Bedin et al.(2005). this feature in this case, as the crowding is low across the image, and results in very uniform observational errors. The model CMDs have been divided in SSPs using a 3 It is worth noting that the choice between canonical and overshooting models is quite irrelevant for a galaxy such as Eri II number of age and metallicity bins. Age bins are of 0.5 whose bulk stellar population is old. Gyr width in the whole age range considered (14.0 to 4 http://basti.oa-teramo.inaf.it/ 2.0 Gyr ago). The choice of an age bin of width of only 0.5 Gyr even at the oldest ages was made after some 9 testing that showed that wider bins did slightly artifi- brary of “basic” synthetic CMDs (similar to the SSP cially widen the old star formation burst derived for the defined above) is generated using the latest PARSEC- galaxy. To sample the distribution of stars in the CMD COLIBRI isochrones (PAdova and TRieste Stellar Evo- we have defined a number of bundles (a collection of lution Code version 1.2S plus COLIBRI code for AGB non-overlapping regions in color-magnitude space, see thermal pulses; Bressan et al. 2012; Tang et al. 2014; Monelli et al. 2010a), which are shown in Fig.3 for Marigo et al. 2017). Each basic synthetic CMD is a the [(F475W-F814W), F814W] CMD (a similar distri- Monte Carlo realization with constant SFR (in a given bution of bundles was adopted for the[(F606W-F814W), range of ages), Kroupa(2001) IMF (between 0.1 and F814W] CMD). Each bundle was divided in boxes of 300 M ), fixed metallicity (± 0.05 dex). In this work we different size, as indicated in the Figure inset. In this adopted a logarithmic time binning of 0.01 in the inter- case, and after some testing (see also Ruiz-Lara et al. val log(age) = 9.90 − 10.13, and a time binning 0.1 in 2020), we decided to include the whole CMD above the the interval log(age) = 9.50 − 9.90. Concerning metal- 80% completeness limit within the set of bundles, not licity, we allowed the code to use metallicities5 between excluding regions sampling stars in advanced evolution- [M/H] = −2.2 and −1.0 with a resolution of 0.1 dex. ary phases which may be less well described by current The last step concerns the binary population: 30% of stellar evolution models. The influence in the fit of dif- synthetic stars are considered to be part of unresolved ferent regions of the CMD has been instead modulated binary systems and their flux is combined with a com- by the different sizes of the boxes in each bundle, with panion, whose mass is a random fraction between 0 and smaller, thus more numerous boxes in the more popu- 1 of the primary. lated, best theoretically understood (Gallart et al. 2005) Once the library is created, the models are convolved main sequence near the oMSTO. with photometric errors and incompleteness as derived The best-fitting SFH is determined by finding the from the artificial star tests performed on the real images amplitudes of the linear combination of SSP CMDs and described in section 3.1. The linear combination that best match the observed CMD. No a-priori age- of basic CMDs which minimizes the residuals from the metallicity relation is adopted. The number of observed observational CMD (in terms of Poissonian likelihood) and synthetic stars from each SSP, counted in each is searched with a hybrid-genetic algorithm, combining CMD box, serves as the input to the minimization rou- the exploration ability of a genetic algorithm and the tine, which measures the goodness of fit using a Pois- exploitation ability of a local search. son equivalent of χ2 (Dolphin 2002). The minimization process is repeated several times, each one shifting the 6. THE SFH OF ERIDANUS II observed CMD in steps in color and magnitude with re- The SFH of Eridanus II is displayed in Figures4 and6. spect to the synthetic CMDs, in order to account for In Figure4, the results by TheStorm DAOPHOT CMD uncertainties in photometric zeropoints, distance, and fit are shown. Lines of different colors indicate the dif- mean reddening. Once the shift that leads to the best ferent solutions depending on the model CMD (see Ta- solution is located, another set of solutions are calcu- ble2) and the band combination used, as indicated in lated by shifting the bins used to sample the CMD, and the labels (F475W or F606W for the bluest band). The also the age-metallicity bins used to define the SSP in top panel shows SFR(t), the SFR as a function of time, the case of the model CMD. The SFH represented in which is characterized by a strong, narrow episode of Fig.4 is the result of averaging 25 such solutions. The star formation at the oldest possible age, and lasting total uncertainties are assumed to be a combination (in ' 0.5 Gyr (half width at half maximum: this is the quadrature) of the uncertainties due to the effect of bin- maximum possible duration of this early period of star ning in the colour-magnitude and age-metallicity planes, formation; we try to constrain its intrinsic duration in and those due to the effect of statistical sampling in the Section 6.1). After this main star forming period, a sec- observed CMD (see Aparicio & Hidalgo 2009, for de- ond period of possible extremely low level star formation tails). activity, lasting until ' 9 Gyr ago, is found in our solutions. This feature is somewhat more prominent in the 5.2. SFH with SFERA solutions obtained from the (F606W, F814W) CMDs, in which the SFR(t) displays a second small maximum The SFH of Eri II was also recovered using the hybrid- of low significance around 12 Gyr ago. The lower panel genetic algorithm SFERA (Star Formation Evolution Recovery Algorithm). The details of this approach are 5 described in Cignoni et al.(2015) and here we pro- We adopt the approximation [M/H]' log(Z/Z ), with Z = vide only a short description. In this procedure, a li- 0.0152. 10 displays the cumulative mass fraction, which shows that thus likely more metal rich) than the bulk of the Eri II the star formation after the main period ending ' 13 stars. Gyr ago could amount to up to ' 20% of the stellar Figure6 compares the average of the three F475W mass formed by the galaxy. However, note that, in all TheStorm/DAOPHOT solutions (black) shown in Fig- cases, this possible low level SFR is compatible with null ure4, with i) one solution obtained with TheStorm us- star formation after the main burst. The SFHs recovered ing the ePSF (F475W,F814W) CMD (green), and ii) also contain information on the age-metallicity relation a solution obtained with SFERA and a DAOPHOT and metallicity distribution that provide the best fit to (F475W,F814W) CMD (blue). The SFR(t) have been the CMDs. In this case, since the range of age is very normalized to the total area below the curve. Remark- small for a meaningful exploration of the age-metallicity ably, the independent solutions obtained with different relation, we will consider the recovered metallicity dis- SFH derivation codes adopting different stellar evolution tribution. Figure5 displays a number of metallicity his- libraries and stellar populations parameters, such as the tograms derived from the solution CMDs constructed IMF or the binary stars characteristics, present the same from the SFHs, compared with the distribution of metal- key features for the Eri II SFH. Also the solutions with licities measured by Li et al.(2017) for 12 Eri II stars. TheStorm for different photometry sets are consistent. Note the good agreement, particularly for the solutions In the rest of the paper, and for simplicity, we will adopt with the α-enhanced models, in spite of the low number and discuss in more detail the DAOPHOT/TheStorm of spectroscopically measured stars. solution. We will also perform most of the analysis in Figure3 shows the observed CMD (left panel), an ex- relation to the robustness of the features in the Eri II ample solution CMD (middle panel, color coded with SFH using TheStorm. [Fe/H], see below), and the significance of the residuals in units of Poisson σ (right panel). It can be seen that the resulting solution CMD is an overall good realization of the observed CMD: no significant structure is observed in the residual plot, and most CMD bins show residuals under 2σ. One area of the CMD where the discrepancy between observed and solution CMD is particularly apparent is in the HB, which is substantially more extended and more populated toward the blue side in the model. This can be understood by the fact that the RGB mass loss efficiency is parameterized in a simple way and not optimized to provide the best possible match with the data (see Section5; if η = 0.2 in the Reimers formula had been used to parameterize Figure 3. Left panel: Observed [(F475W-F814W), F814W] the mass loss along the RGB, the qualitative agreement CMD of EriII. The bundles used for the SFH derivation have between the observed and the model RGB would have been superimposed, and the size of the boxes in each bundle are given in the inset. Middle panel: Best fit CMD corre- been likely better, as a smaller mass loss results in a HB sponding to the F475ssb07 solution. The synthetic stars in less extended to the blue). In spite of this, in the middle this CMD have been color-coded according to their [Fe/H], panel it can be seen that the HB well populated from as indicated in the upper color bar. Right panel: Significance the blue to the red can be explained by the wide range of of the residuals in units of Poisson σ. metallicity (spanning over 2 dex) in the galaxy. In fact, from the solution CMDs, we calculated that ∼ 5 stars can be expected for the evolved progeny of the bright 6.1. Age accuracy and precision at old ages main sequence stars, and thus their contribution to the In order to assess the robustness of our conclusions star counts in the red part of the HB is small. This panel regarding the key features in the Eri II SFH, and to fur- also shows that the bright main sequence (that we ten- ther constrain the actual intrinsic duration of the main tatively interpreted as a BSS population in Section4) is star formation episode, and the precision in dating this best represented by stars in the whole metallicity range, burst, in the following sections, we will perform a num- with numerous low metallicity stars. This reinforces the ber of tests with simulated CMDs of stellar populations conclusion advanced in that section that this sequence of known age characteristics. is composed by BSS stars and not by stars younger (and 6.1.1. Synthetic mock galaxies 11

Figure 6. Comparison between the average of the SFR(t) solutions from the DAOPHOT (F475W,F814W) CMD obtained with TheStorm displayed in Figure4, one solution obtained with TheStorm using the ePSF (F475W,F814W) CMD, and with a solution obtained with SFERA and a DAOPHOT (F475W,F814W) CMD. The SFR(t) plots have been normalized by the area below the curve. Note the excellent agreement between all the solutions.

Figure 4. SFH of Eri II derived with TheStorm. The The synthetic CMDs have been calculated with the same upper panel shows the SFR while the lower panel shows synthesis program used to compute the mother synthetic the cumulative mass fraction as a function of the look- CMDs, adopting the solar-scaled BaSTI stellar evolution back time. Different lines indicate different solutions combining the DAOPHOT photometry of the two datasets library, a gaussian metallicity distribution with mean (F475W+F814W or F606W+F814W), different BaSTI stel- [Fe/H]=-2.38 and σ[Fe/H]=0.47 (as observed for Eri II by lar evolution model sets (ss or ae), and binary stellar popu- Li et al. 2017) and a binary fraction β = 0.7 with mass lation properties (binary fraction β=0.7 or 0.5). See Table2 ratios q>0.1. The difference between these four mock for details. galaxies is the age distribution of their stellar populations: two of them were calculated with an age range of 100 Myr (between 13.5 and 13.4 Gyr old, and 12.5 and 12.4 Gyr old) and the other two with an age range of 1 Gyr (13.5-12.5 Gyr old, and 12.5-11.5 Gyr old). The shape of these input SFR(t) are represented as thin black lines in Figure7. These tests were performed using both the (F475W,F814W) and (F606W,F814W) band combinations. After simulating the observational errors in these synthetic populations using the corresponding artificial star tests, a number of stars comparable with the observed CMDs of Eri II was randomly selected to fully mimic the observed CMD properties. The CMDs of the four mock galaxies were treated in the same way as the observed Eri II CMD to retrieve their SFH with TheStorm. The same three model CMDs used to re- Figure 5. Normalized metallicity histograms derived for trieve the SFH of Eri II (see Table2) were also used for Eri II from a number of DAOPHOT/TheStorm solutions in the mock galaxies, in order to mimic the fact that the Figure4, compared with the metallicities derived by Li et al. (2017). assumptions that go into the model CMD creation (e.g. stellar evolution, binaries) are different to the parameters of the actual galaxy. The recovered SFR(t) for the We have created four ’synthetic mock galaxies’ from mock galaxies are displayed in Figure7 (colored lines), synthetic CMDs in which observational errors have been together with the Eri II SFR(t) (thick black solid line). simulated using DisPar and the Eri II artificial star tests. 12

The results for the mocks calculated with the two band combinations are basically identical, and in the Figure we show those for the (F475W, F814W) band combination, while for the Eri II solution we show the average of the F475aeb05 and F606ssb05 solutions. It can be seen that the recovered SFR(t) do not depend strongly on the adopted model CMD (with slightly worse recovery for ’aeb05’, that is, when the stellar evolution model set used to compute the mother CMD not matches the one used to calculate the mock galaxy: α- enhanced for the model CMD and solar scaled for the mock galaxy), and that the age of the population is well recovered in all cases. The true width of the star formation episode is not well recovered in the 100 Myr case. This indicates that we cannot resolve a narrow star formation event occurred ' 13.5-12.5 Gyr ago with these data. However, note that only the mock galaxy with the narrow and old age range (13.5-13.4 Gyr) results in a recovered SFH similar to the one derived for Eri II, which is actually in the narrow side of the three SFR(t) derived for the mock. This indicates that the Eri II main star forming epoch occurred at the earliest possible age, Figure 7. Results of the test with synthetic mock galax- and might have been very narrow, possibly not lasting ies described in the text. The black thin lines indicate the SFR(t) of the mock galaxy, while the thick black line indi- longer than 100 Myr. On the other hand, for the old- cates the SFR(t) inferred for Eri II (average of the F475aeb05 est, best fitting mock SFHs, the period of very low star and F606ssb05 solutions). The colored lines indicate the formation activity extended to ' 9 Gyr ago that is ob- SFR(t) derived for the corresponding mock galaxy, using the served in the Eri II SFR(t) is not observed, except in the (F475W, F814W) band combination and different mother case in which there is a mismatch between the param- synthetic CMDs (see Table2). eters used to compute the model CMD and the mock galaxy (green lines). In this case, a local maximum of them the Eri II observational errors using the Eri II ar- low intensity, similar to the one observed in the original tificial stars tests. We also selected a similar number F606W solutions, is recovered at an look back time of ' of stars as in the Eri II observed CMDs. After that, 11.5 Gyr ago. This is an indication that these low level the SFH was obtained identically as for Eri II. Figure8 features in the SFR(t) are likely spurious. shows the SFR(t) obtained for the M92 mock, using either the [F475W, F814W] (blue line) or the [F606W, 6.1.2. Retrieving the SFH of a M92 mock F814W] (red line) CMDs and adopting the model synthetic CMD computed with the α-enhanced model set It could be argued that the tests with mock galax- and b = 0.5, compared to the Eri II SFH. The width ies presented in the previous section are idealized cases of the main star forming period of Eri II is basically in which the same stellar evolution model set has been identical to that derived for M92, thus reinforcing the used to calculate the input mock stellar population and conclusion in the previous section that the early Eri II the model synthetic CMD used to retrieve its SFH. We star formation burst must have had a very narrow times- have performed a further test with a mock stellar pop- pan, possibly even narrower than 100 Myr. In this case, ulation created using the CMD of the old, metal poor the period of star formation extended to ' 9 Gyr ago is ([Fe/H] = –2.3) Milky Way globular cluster M92 (Di clearly not found. Cecco et al. 2010; VandenBerg et al. 2016, NGC6341), as observed with the ACS under HST programs ID. 10505 (1 orbit in each F475W, F814W) and ID. 10775 (1 or- 7. DISCUSSION bit in each F606W, F814W). Since these data are much The SFHs of Eri II presented in Section6, obtained us- deeper in the absolute magnitude planes than the Eri II ing different photometry tables and CMD-fitting meth- CMD, we have assumed that the photometric errors are ods, and constrained further with tests using mock stel- negligible, and degraded the M92 CMDs to the pho- lar populations all agree in that Eri II has formed the tometric quality of the Eri II CMDs, by simulating in bulk of its stars in a very early and extremely short (pos- 13

in Eri II happened before z ∼ 6 and calculate the competing gravitational potential of the dark matter halo at this redshift. According to Woo et al.(2008), we consider that this kind of dwarf galaxies with a very fast SFH (Gallart et al. 2015) present a stellar mass-to-light ratio close to ∼ 2, and we derive the present-day stellar mass from the luminosity by Crnojevićet al.(2016). We 5 link the resulting stellar mass (∼ 1.1 × 10 M ) to the z = 0 virial halo mass using the abundance-matching (AM) relations by Brook et al. 2014 (B14) and Moster et al. 2013 (M13). We evolve these virial halo masses back to z = 6 following Fakhouri et al.(2010) and we 8 8 obtain halo masses of 3.4 × 10 M and 2.1 × 10 M for the B14 and M13 AM relations, respectively. Then, Figure 8. Comparison between the SFR(t) obtained for we derive the gravitational potential of the dark mat- the M92 mock described in the text, and for Eri II. The ter halo and relate it to the gaseous component ac- blue and red line refer to the mocks constructed with the counting for the baryon fraction (fb ∼ 1/6). We fi- [F475W,F814W] and [F606W,F814W] M92 data, respec- nally obtain that the competing gravitational potential tively. The gray and black lines represent the average of z=6 52 z=6 52 the F475W and F606W SFR(t) solutions for Eri II shown in is ∆Wgas /2 = 4.8×10 erg and ∆Wgas /2 = 2.2×10 Figure4. erg for the B14 and M13 AM relations, respectively. This means that Eri II could have removed its gaseous component with a coupling efficiency of the SNe energy sibly shorter than 100 Myr) star formation burst. As 2%, which is well compatible with the maximum discussed in the Introduction, three main mechanisms . values of this parameter in the literature; for example in are usually debated as potentially able to remove gas and Bermejo-Climent et al.(2018) the coupling efficiency is halt star formation in small galaxy halos, namely i) ram- constrained to be smaller than ∼ 10%. pressure stripping and tidal interactions with a nearby The above estimates are of course an order of magni- larger galaxy, ii) cosmic reionization, and iii) SNe feed- tude calculation since i) we are assuming that all SNe back associated to the early star formation in the dwarf explode at once, thus producing a much powerful explo- galaxy itself. Since we have a quantitative determina- sion than if they were spread out in time, and ii) we are tion of the amount of mass turned into stars in Eri II relying on a dark matter halo mass derived from abun- early star formation burst, and stringent constraints on dance matching relations. However, the very low star the duration of this burst, we will investigate whether formation rate of Eri II, hΨi ≈ 10−3M /yr, is perfectly Eri II could have removed its own gaseous component at consistent with what is predicted for inefficiently star early times just by stellar feedback caused by supernovae forming mini-halos with relatively small virial halo mass, (SNe) explosions. For this, we follow the methodology ≈ 107M , which can rapidly lose all their gas thanks by Bermejo-Climent et al.(2018). We first integrate to SN feedback and then are permanently switched off the SFH of Eri II and correct the result by the miss- because reionization is preventing further gas accretion ing stellar component in the HST /ACS observations, (e.g. Salvadori & Ferrara 2009, Rossi et al. submit- which cover ∼ 55% of the galaxy, taking into account ted). In conclusion, the short history of star formation the galaxies stellar profile derived by (Crnojevićet al. of Eri II, lasting < 100 Myr combined with its low star 2016). We obtain that the total mass transformed into formation rate, strongly support the idea that we are stars is ∼ 1.9 × 105M . Assuming the IMF by Kroupa observing the living relic of one of the first star forming (2001) and a stellar mass threshold of 6.5 M for ex- H -cooling minihalos, which hosted the first stars. plosions of SN II, we get that Eri II had ∼ 2700 SNe 2 In absence of quantitative estimates of the actual early events, which considering a typical energy ∼ 1051 erg star formation rate (in units of solar masses per year), per SN would have injected an energy ∼ 2.7×1054 erg and thus of the SNe energy ejected to the interstellar to the medium. We note that when adopting a higher medium, and noting the very similar quenching times in mass threshold, like 8 M for the SN II explosions, the a number of UFD, previous works (e.g. Brown et al. energy budget would be ∼ 75% the value obtained for 2012, 2014) favoured the conclusion that an outside 6.5 M . global influence such as cosmic reionization was the most To evaluate whether this energy could or could not plausible cause of the synchronized quenching. The re- push away the gas, we assume that all the SNe events 14

Table 3. Properties of Eridanus II compared to Leo T around two orders or magnitude lower than the one we a have inferred for Eri II, that would have not been able to Parameter Eri II Leo T ref(LeoT) quench it by SNe feedback. However, apparently reion- MV (mag) -7.1± 0.3 -7.1 (1) ization was not able to quench it either: the highest rh (pc) 252 166 (1) temporal resolution SFR(t) for this galaxy published in DMW (Kpc) 375 409 (2) both Clementini et al.(2012) and Surot et al. (in prep) −1 vGSR (km s -66.6 -58.4 (3) −1 show a continuous SFR(t) which increases substantially σvhel (km s ) 6.9 7.5 (3) 3 5 after 10 Gyr ago, with no apparent gap after reioniza- MHI (M ) < 2.8 × 10 2.8×10 (4) +0.4 7 7 tion. M 1 (M ) 1.2−0.3 × 10 8.2 ± 3.6 ×10 (3) 2 What may be the physical reasons for the radically M/L (M /L ) 420+210 138 ± 71 (3) −140 different SFHs for Eri II and Leo T, two otherwise quite [F e/H] -2.38 ± 0.13 -2.29 (3) similar dwarf galaxies (Table3)? Rey et al.(2020) σ[F e/H] 0.47 0.35 (3) use cosmological high resolution hydrodynamical sim- a The corresponding references for Eri II are given in Table1 ulations of field dwarf galaxies encompassing the Eri II Note—(1) Irwin et al.(2007); (2) Clementini et al.(2012); (3) and Leo T mass range to explore the mechanisms that Simon & Geha(2007) (4) Ryan-Weber et al.(2008) allow some of these small galaxies, all quenched after reionization in their simulations, to reignite star formation at a late time. They find that these galaxies have been able to replenish their interstellar medium maining candidates, tidal interactions or ram-pressure by slowly accreting gas until high enough densities are stripping, would result in quenching times that depend reached to self-shield the gas from the UV background. on the accretion time of each dwarf galaxy into the Milky These models could explain the extended Leo T SFH, Way. In a paper that was accepted and posted in ArXiv even if reionization would have affected it early, at a after this one was submitted, Simon et al.(2020) ana- level not clearly detected by the measured SFHs. It is lyzed the same Eri II (F 606W −F 814W , F 814W ) CMD also possible that the coupling between reionization and with the methodology used in Brown et al.(2014). They SNe feedback results in enough energy for a complete reach a conclusion on the age and duration of the star removal of gas in Eri II, but not in Leo T. In fact, Jeon formation in Eri II that is totally compatible with our et al.(2017) find that while reionization plays an im- scenario. The main difference between our conclusion portant role in inhibiting star formation, SNe feedback and theirs is in the interpretation of the results. While is crucial for the ultimate quenching of UFDs. In ad- they focus their discussion on possible reionization and dition, UFDs have such shallow potential wells that the tidal effects, and conclude that the former is the most SF, and thus the feedback, might be very sensitive to the plausible explanation for the early quenching of Eri II, local environment and to the details of the ISM/CGM our quantitative estimate of the star formation rate al- physics. For example, SNe feedback and outflow from lows us to argue that SN feedback is a main driver of a nearby dwarf galaxy can also quench star formation the star formation quenching in Eri II. Note that if the directly in these low mass systems(Mina et al. 2020). very early star formation events in UFDs as reported in But one may still ask the further question of what is Brown et al.(2014) were intense enough to result in suf- the actual origin of the different early SFR of these two ficiently large feedback energy to remove the gas as in galaxies. Gallart et al.(2015) use precise, time-resolved the case of Eri II, they would also result in apparently SFHs of Local Group classical dwarf galaxies derived synchronized quenching. from CMDs reaching the oMSTO and find that they can That reionization may not have been the main or only be assigned to two basic types: fast dwarfs that started cause of the star formation quenching in Eri II is sup- their evolution with a dominant and short star formation ported by the fact that another UFD galaxy of similar episode, and slow dwarfs that formed a small fraction of properties such as Leo T (in terms of mass, metallicity, their stars early and have continued star formation ac- distance and velocity with respect to the Milky Way; tivity until, or almost, the present time. Given their see Table3) has been able to retain gas and sustain star SFHs, Eri II and Leo T would allow extending this defi- formation until (almost) the present time (Clementini nition to the UFD regime. Gallart et al.(2015) hypoth- et al. 2012; Weisz et al. 2012, Surot et al., in prep; other esized that the distinction between fast and slow dwarfs gas-rich UFDs are discussed by McQuinn et al. 2015 reflected the characteristic density of the environment and Janesh et al. 2019). The available SFHs of Leo T all where they formed, with fast dwarfs assembling quickly −5 −1 agree on a low early star formation rate, ∼10 M yr , in high density environments where interactions trigger- 15 ing star formation were common, leading to a high SFR We present new ACS/HST CMDs reaching the oM- before reionization, and resulting in strong gas loss due STO with excellent photometric precision for the ultra- to the combined effects of reionization and SNE feed- faint dwarf galaxy Eri II and derive a detailed and back (see also Ben´ıtez-Llambay et al. 2015). On the precise SFH for this galaxy by fitting these CMDs contrary, slow dwarfs would have resulted from a slower with synthetic CMDs. The photometry, obtained from mass assembly in lower density environments, implying two independent datasets providing (F475W, F814W) lower initial SFR and ability to retain gas. The proper and (F606W, F814W) measurements, has been ob- motions and orbit estimated for Eri II (Fritz et al. 2018) tained using two commonly used programs, DAOPHOT do not totally preclude that Eri II was close to the Milky IV/ALLFRAME (Stetson 1994) and ePSF/KS2 (Ander- Way at early times (see also Buck et al. 2019, for a pos- son et al. 2008), and the CMD-fitting has been per- sibility of Eri II being a backsplash galaxy that has had formed using two different codes and stellar evolution close encounter with M31 before being accreted onto the model sets: TheStorm (Bernard et al. 2018) with the Milky Way), while the 3D movement of Leo T in the BaSTI stellar evolution models (Pietrinferni et al. 2004, Local Group is still highly uncertain. Therefore more 2006) and SFERA (Cignoni et al. 2015) with the PAR- precise information on the orbits of Eri II and Leo T SEC isochrones (Bressan et al. 2012). The SFHs derived would help understand whether they can provide fur- using different combinations of photometry tables and ther support to the hypothesis by Gallart et al.(2015) CMD-fitting methods all agree in that Eri II has formed on the origin of the dichotomy in the slow/fast dwarf the bulk of its stars in a very early (ending before 13 galaxy types, and its extension to even lower masses. Gyr ago) and extremely short star formation burst: pos- Finally, the finding that the bulk population of Eri II sibly shorter than 100 Myr, as indicated with tests with formed before 13 Gyr ago makes this galaxy one of the mock stellar populations, and compared with the SFH oldest among the faint dwarfs in the Local Group, and derived for the globular cluster M92. Though up to 20% hence the ideal testbed for dark matter scenarios alter- of its stars could have been formed in an extended pe- native to CDM that imply a delayed start of star forma- riod lasting a few Gyr after the main burst, the signal tion in the lowest mass halos. This applies, for example, corresponding to this possible extended star formation to Warm Dark Mater models (WDM) and the currently is very low, and the error bars make the star formation popular Fuzzy Dark Matter (FDM) models. Chau et al. after the main burst compatible with zero. Similarly, (2017) have shown how stringent constraints on the ther- no significant signal is detected in the SFH from the mal velocity of the WDM particle candidate can be im- blue plume extended to bright magnitudes above the old posed based on how early the largest fraction of the stars main sequence. This, together with the low metallicity in the lowest mass subhalos have formed. Their analysis inferred for these stars among other indicators, point to did not include an object as old as Eri II and yet, using the fact that, like in many other dwarf galaxies (Monelli less stringent star formation history data on some of the et al. 2012), this feature corresponds to a population of UFD, they were able to exclude WDM models with par- BSS. This result conclusively shows that Eri II is an ex- ticle masses lower than 3 keV, as they would suppress tremely old galaxy, with no young or intermediate-age excessively the collapse of halos below virial masses be- star formation, as the earliest observations of this galaxy 9 low 10 M . Eri II’s current mass estimate (within the suggested (Bechtol et al. 2015; Koposov et al. 2015). half mass radius) is well below this limit (Li et al. 2017). From the quantitative determination of the amount of Therefore, a similar analysis based don Eri II could help mass turned into stars in this early star formation burst 5 to constrain WDM models with energies in the range (∼ 2 × 10 M ), we infer the number of SNe events and 3-5 keV, which is the territory where other probes, such the corresponding energy injected into the interstellar as the Lyman alpha forest and gravitational lensing by medium. For reasonable estimates of the Eri II early halo substructure, are reaching their limits (see Bullock virial halo mass (evolved from the current virial mass & Boylan-Kolchin 2017, for a review). The delayed SFH calculated using the present day stellar mass and pub- in low mass halos has been recently shown to be a dis- lished abundance matching relations) and appropriate tinctive feature of Fuzzy Dark Matter models because values of the coupling efficiency of the SNe energy, we halo collapse is delayed due to the quantum pressure conclude that Eri II could have been quenched by SNe of the underlying Bose-Einstein condensate (Mocz et al. feedback alone. This short history of star formation, 2020). Of course for these applications determining the combined with the low star formation rate, support the virial mass of Eri II before infall is crucial. idea that Eri II is the relic of one of the first star forming H2-cooling minihalos, which hosted the first stars. 8. SUMMARY AND FINAL REMARKS 16

Our results cast doubts on the need to invoke cosmic ACKNOWLEDGMENTS reionization as the preferred or only explanation for the early quenching of old UFD galaxies. This conclusion We thank the anonymous referee for a careful read- is indirectly supported by the fact that another UFD ing of the manuscript and many useful suggestions that galaxy of similar properties to Eri II such as Leo T (in have helped to improve the paper. This study was terms of mass, metallicity, distance and velocity with supported by NASA through grant GO-14224 from the respect to the Milky Way) has sustained star formation Space Telescope Science Institute, which is operated until just a few hundred million years ago. This pair by AURA, Inc., under NASA contract NAS5-26555. of galaxies, particularly when their orbits will be avail- CG, MM, TRL, GB and FS acknowledge financial able, are key to understand the origin of the dichotomy support through grants (AEI/FEDER, UE) AYA2017- between fast and slow dwarfs (Gallart et al. 2015), ex- 89076-P, AYA2016-77237-C3-1-P (RAVET project) and tended to the lowest mass regime. AYA2015-63810-P, as well as by Ministerio de Cien- cia, Innovacióny Universidades (MCIU), through Juan de la Cierva - Formacióngrant (FJCI-2016-30342) and the State Budget and by Consejer´ıade Econom´ıa,In- dustria, Comercio y Conocimiento of the Canary Is- lands Autonomous Community, through Regional Bud- get. SS acknowledges support from the ERC Start- ing Grant NEFERTITI H2020/808240 and from the PRIN-MIUR2017, “The quest for the first stars”, prot. n. 2017T4ARJ5. TRL acknowledges support from a Spinoza grant (NWO) awarded to A. Helmi. AM acknowledges financial support from FONDECYT Regu- lar 1181797 and funding from the Max Planck Society through a Partner Group grant. M.C. acknowledges the support of INFN iniziativa specifica TAsP.

Facilities: HST(ACS) Software: Astrodrizzle, DAOPHOT (Stetson 1987, 1994), TheStorm (Bernard et al. 2018), numpy (Har- ris et al. 2020), scipy (Virtanen et al. 2020), astropy (Astropy Collaboration et al. 2018, 2013), matplotlib (Hunter 2007).

REFERENCES

Amorisco, N. C. 2017, ApJ, 844, 64 Belokurov, V., Zucker, D. B., Evans, N. W., et al. 2006, Anderson, J., & King, I. R. 2006, PSFs, Photometry, and ApJL, 647, L111 Astronomy for the ACS/WFC, Instrument Science Ben´ıtez-Llambay, A., Navarro, J. F., Abadi, M. G., et al. Report ACS 2006-01, , 2015, MNRAS, 450, 4207 Anderson, J., King, I. R., Richer, H. B., et al. 2008, AJ, Bermejo-Climent, J. R., Battaglia, G., Gallart, C., et al. 135, 2114 2018, MNRAS, 479, 1514 Aparicio, A., & Hidalgo, S. L. 2009, AJ, 138, 558 Bernard, E. J., Ferguson, A. M. N., Chapman, S. C., et al. Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., 2015, MNRAS, 453, L113 et al. 2013, A&A, 558, A33 Bernard, E. J., Schultheis, M., Di Matteo, P., et al. 2018, Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz,B. M., MNRAS, 477, 3507 et al. 2018, AJ, 156, 123 Bland-Hawthorn, J., Sutherland, R., & Webster, D. 2015, Babul, A., & Rees, M. J. 1992, MNRAS, 255, 346 ApJ, 807, 154 Bechtol, K., Drlica-Wagner, A., Balbinot, E., et al. 2015, Bovill, M. S., & Ricotti, M. 2009, ApJ, 693, 1859 ApJ, 807, 50 Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, Bedin, L. R., Cassisi, S., Castelli, F., et al. 2005, MNRAS, 427, 127 357, 1038 Bromm, V., & Yoshida, N. 2011, ARA&A, 49, 373 17

Brook, C. B., Cintio, A. D., Knebe, A., et al. 2014, The Hidalgo, S. L., Aparicio, A., Skillman, E., et al. 2011, ApJ, Astrophysical Journal, 784, L14 730, 14 Brown, T. M., Tumlinson, J., Geha, M., et al. 2012, ApJL, Hidalgo, S. L., Monelli, M., Aparicio, A., et al. 2013, ApJ, 753, L21 778, 103 —. 2014, ApJ, 796, 91 Hunter, J. D. 2007, Computing in Science & Engineering, 9, Buck, T., Macciò,A. V., Dutton, A. A., Obreja, A., & 90 Frings, J. 2019, MNRAS, 483, 1314 Irwin, M. J., Belokurov, V., Evans, N. W., et al. 2007, Bullock, J. S., & Boylan-Kolchin, M. 2017, ARA&A, 55, ApJL, 656, L13 343 Janesh, W., Rhode, K. L., Salzer, J. J., et al. 2019, AJ, 157, Cashmore, C. R., Wilkinson, M. I., Power, C., & Bourne, 183 M. 2017, MNRAS, 468, 451 Jeon, M., Besla, G., & Bromm, V. 2017, ApJ, 848, 85 Cassisi, S., & Salaris, M. 2013, Old Stellar Populations: Jeon, M., Bromm, V., Pawlik, A. H., & Milosavljević,M. How to Study the Fossil Record of Galaxy Formation 2015, MNRAS, 452, 1152 Chau, A., Mayer, L., & Governato, F. 2017, ApJ, 845, 17 Katz, H., Ramsoy, M., Rosdahl, J., et al. 2020, MNRAS, Cignoni, M., Sabbi, E., van der Marel, R. P., et al. 2015, 494, 2200 ApJ, 811, 76 Koposov, S. E., Belokurov, V., Torrealba, G., & Evans, Clementini, G., Cignoni, M., Contreras Ramos, R., et al. N. W. 2015, ApJ, 805, 130 2012, ApJ, 756, 108 Kravtsov, A. V., Gnedin, O. Y., & Klypin, A. A. 2004, Contenta, F., Balbinot, E., Petts, J. A., et al. 2018, ApJ, 609, 482 MNRAS, 476, 3124 Kroupa, P. 2001, MNRAS, 322, 231 Cordier, D., Pietrinferni, A., Cassisi, S., & Salaris, M. 2007, Kroupa, P., Tout, C. A., & Gilmore, G. 1993, MNRAS, 262, AJ, 133, 468 545 Crnojević,D., Sand, D. J., Zaritsky, D., et al. 2016, ApJL, Li, T. S., Simon, J. D., Drlica-Wagner, A., et al. 2017, ApJ, 824, L14 838, 8 Di Cecco, A., Becucci, R., Bono, G., et al. 2010, PASP, Mac Low, M.-M., & Ferrara, A. 1999, ApJ, 513, 142 122, 991 Marigo, P., Girardi, L., Bressan, A., et al. 2017, ApJ, 835, Dolphin, A. E. 2002, MNRAS, 332, 91 77 Fakhouri, O., Ma, C.-P., & Boylan-Kolchin, M. 2010, Marsh, D. J. E., & Niemeyer, J. C. 2019, PhRvL, 123, Monthly Notices of the Royal Astronomical Society, 406, 051103 22672278 Martin, N. F., Nidever, D. L., Besla, G., et al. 2015, ApJL, Fitts, A., Boylan-Kolchin, M., Elbert, O. D., et al. 2017, 804, L5 MNRAS, 471, 3547 Mayer, L. 2010, Advances in Astronomy, 2010, Ford, H. C., Bartko, F., Bely, P. Y., et al. 1998, in Proc. SPIE, Vol. 3356, Space Telescopes and Instruments arXiv:0909.4075 V, ed. P. Y. Bely & J. B. Breckinridge, 234–248 McQuinn, K. B. W., Skillman, E. D., Dolphin, A., et al. Fritz, T. K., Battaglia, G., Pawlowski, M. S., et al. 2018, 2015, ApJ, 812, 158 A&A, 619, A103 Mina, M., Shen, S., Keller, B. W., et al. 2020, arXiv Gallart, C., Aparicio, A., & Vilchez, J. M. 1996, AJ, 112, e-prints, arXiv:2009.06646 1928 Mocz, P., Fialkov, A., Vogelsberger, M., et al. 2020, Gallart, C., Zoccali, M., & Aparicio, A. 2005, ARA&A, 43, MNRAS, 494, 2027 387 Monelli, M., Hidalgo, S. L., Stetson, P. B., et al. 2010a, Gallart, C., Freedman, W. L., Mateo, M., et al. 1999, ApJ, ApJ, 720, 1225 514, 665 Monelli, M., Gallart, C., Hidalgo, S. L., et al. 2010b, ApJ, Gallart, C., Monelli, M., Mayer, L., et al. 2015, ApJL, 811, 722, 1864 L18 Monelli, M., Cassisi, S., Mapelli, M., et al. 2012, ApJ, 744, Gelli, V., Salvadori, S., Pallottini, A., & Ferrara, A. 2020, 157 MNRAS, 498, 4134 Moster, B. P., Naab, T., & White, S. D. M. 2013, MNRAS, Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 428, 3121 2020, Nature, 585, 357 Pallottini, A., Ferrara, A., Bovino, S., et al. 2017, MNRAS, Helmi, A. 2020, ARA&A, 58, 205 471, 4128 18

Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, Stetson, P. B. 1993, in Astronomical Society of the Pacific ApJ, 612, 168 Conference Series, Vol. 48, The Globular Cluster-Galaxy —. 2006, ApJ, 642, 797 Connection, ed. G. H. Smith & J. P. Brodie, 14 Revaz, Y., & Jablonka, P. 2018, A&A, 616, A96 —. 1994, PASP, 106, 250 Rey, M. P., Pontzen, A., Agertz, O., et al. 2020, MNRAS, Stinson, G. S., Dalcanton, J. J., Quinn, T., et al. 2009, 497, 1508 MNRAS, 395, 1455 Ricotti, M. 2009, MNRAS, 392, L45 Tang, J., Bressan, A., Rosenfield, P., et al. 2014, MNRAS, Ricotti, M., & Gnedin, N. Y. 2005, ApJ, 629, 259 445, 4287 Ricotti, M., Gnedin, N. Y., & Shull, J. M. 2002, ApJ, 575, VandenBerg, D. A., Denissenkov, P. A., & Catelan, M. 49 2016, ApJ, 827, 2 Romano, D., Calura, F., D’Ercole, A., & Few, C. G. 2019, Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, A&A, 630, A140 Nature Methods, 17, 261 Ruiz-Lara, T., Gallart, C., Monelli, M., et al. 2020, Weisz, D. R., Zucker, D. B., Dolphin, A. E., et al. 2012, MNRAS, arXiv:2012.07863 ApJ, 748, 88 Ryan-Weber, E. V., Begum, A., Oosterloo, T., et al. 2008, Westmeier, T., Staveley-Smith, L., Calabretta, M., et al. MNRAS, 384, 535 2015, MNRAS, 453, 338 Salvadori, S., & Ferrara, A. 2009, MNRAS, 395, L6 Wheeler, C., Oñorbe, J., Bullock, J. S., et al. 2015, Salvadori, S., Ferrara, A., & Schneider, R. 2008, MNRAS, MNRAS, 453, 1305 386, 348 Wheeler, C., Hopkins, P. F., Pace, A. B., et al. 2019, Salvadori, S., Skúladóttir, A.,´ & Tolstoy, E. 2015, MNRAS, MNRAS, 490, 4447 454, 1320 Willman, B., Dalcanton, J. J., Martinez-Delgado, D., et al. Salvadori, S., Tolstoy, E., Ferrara, A., & Zaroubi, S. 2014, 2005, ApJL, 626, L85 MNRAS, 437, L26 Woo, J., Courteau, S., & Dekel, A. 2008, Monthly Notices Sawala, T., Scannapieco, C., Maio, U., & White, S. 2010, of the Royal Astronomical Society, MNRAS, 402, 1599 doi:10.1111/j.1365-2966.2008.13770.x Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103 Woo, J.-H., Gallart, C., Demarque, P., Yi, S., & Zoccali, M. Shen, S., Madau, P., Conroy, C., Governato, F., & Mayer, 2003, AJ, 125, 754 L. 2014, ApJ, 792, 99 Zoutendijk, S. L., Brinchmann, J., Boogaard, L. A., et al. Simon, J. D., & Geha, M. 2007, ApJ, 670, 313 2020, A&A, 635, A107 Simon, J. D., Brown, T. M., Drlica-Wagner, A., et al. 2020, Zucker, D. B., Belokurov, V., Evans, N. W., et al. 2006, arXiv e-prints, arXiv:2012.00043 ApJL, 650, L41 Stetson, P. B. 1987, PASP, 99, 191