LEO P: AN UNQUENCHED VERY LOW-MASS GALAXY^*

Galaxies at the faint end of the luminosity function (LF) have provided vital tests for our understanding of structure formation and evolution. The dearth of both observable low-mass dwarf galaxies ("missing satellite problem"; e.g., Kauffmann et al. 1993; Klypin et al. 1999; Moore et al. 1999) and of higher surface brightness dwarf galaxies ("too big to fail"; Boylan-Kolchin et al. 2011) compared to simulations based on the ΛCDM model has proven to be a multi-decade challenge. These issues have been partly alleviated with higher resolution simulations that include more baryonic effects (e.g., Brooks et al. 2013; Benítez-Llambay et al. 2014; Oñorbe et al. 2015; Sawala et al. 2015). In addition, large sky surveys have detected an increasing number of satellite systems, providing progressively better agreement between theory and observations for the missing satellite problem (e.g., Koposov et al. 2015). While these results have reduced the inconsistencies, future revisions to structure formation theories will undoubtedly be anchored by observational constraints from studies of very low-mass systems.

Furthermore, galaxies at the faint end of the LF are broadening our understanding of star formation and galaxy evolution. The star formation properties of gas-rich, low-mass galaxies encompass a larger range of parameters for a given stellar mass than more massive, "main-sequence" galaxies (Brinchmann et al. 2004; Bothwell et al. 2009; Huang et al. 2012; McQuinn et al. 2015). It is unclear whether this is due to an inherently stochastic star formation process at low molecular gas column densities and metallicities, or to a variation in the primary processes that regulate star formation.

In the nearby universe, much work has been done to understand the evolutionary history of the rich population of nearby low-mass galaxies (e.g., Skillman et al. 1989; Hunter & Elmegreen 2004; Begum et al. 2008; Dalcanton et al. 2009; Lee et al. 2009; McQuinn et al. 2010, 2015; Cannon et al. 2011; Weisz et al. 2011; Hunter et al. 2012; McConnachie 2012; Lelli et al. 2014; Weisz et al. 2014a; Boyer et al. 2015a, 2015b, among others). The interpretations are often complicated because relative differences between low-mass galaxies can depend significantly on large-scale environmental differences. This latter factor is often described as the morphology–density relation, or the prevalence of gas-poor dwarfs (i.e., dwarf spheroidals or dSphs) to be located in higher galactic density environments whereas gas-rich dwarfs (i.e., dwarf irregulars or dIrrs) are predominantly found in lower density field environments (e.g., Einasto et al. 1974, Binggeli 1987; van den Bergh 1994; Côté et al. 2009). The closest (and most accessible) low-mass galaxies are coevolving with the Milky Way, and thus disentangling the impact of the internal versus external evolutionary processes is a significant challenge. Ideally, one could study the properties of a low-mass system located outside of a group environment. While such low-mass, low-luminosity systems are expected to be numerous, they have generally eluded detection outside of the immediate vicinity in the Local Group (LG) due to their faint and sometimes low surface brightness nature.

An exception is Leo P, a low-luminosity (M_V = −9.27 mag), gas-rich galaxy discovered just outside the zero-velocity boundary of the LG. Leo P's combined properties of extremely low stellar mass (5.6 × 10⁵ M_⊙) and metallicity (3% solar), significant gas content (8.1 × 10⁵ M_⊙), proximity (1.62 Mpc), and isolation (0.4 Mpc from its nearest neighbor and outside of any group environment) present a unique test for our understanding of both structure formation and galaxy evolution. Comparable in luminosity to some of the dSph satellites of the Milky Way and a few of the dIrrs inside the LG, Leo P provides an opportune target for studying evolution at the faint end of the LF in a simplified system. Not only are many complex variables eliminated (e.g., tidal and ram pressure stripping, significant possible merger events, etc. that are present in the majority of galaxies detected in this luminosity regime), but Leo P crosses over into the mass regime where (i) theories of structure formation predict difficulty in galaxies retaining their baryons due to stellar feedback processes (e.g., Larson 1974; Dekel & Silk 1986; Mac Low & Ferrara 1999; Ferrara & Tolstoy 2000) and (ii) theories of the impact of reionization predict the photo-evaporization of the gas content and a sudden and irrevocable quenching of star formation (e.g., Babul & Rees 1992; Efstathiou 1992; Thoul & Weinberg 1996).

In this work, we present a detailed study of the star formation history (SFH) and evolution of Leo P using HST optical imaging of Leo P that reaches ∼2 mag below the red clump (RC). In Section 2 we discuss the observations, data reduction, and variable star identification. In Section 3, we refine the distance measurement to Leo P using analysis of horizontal branch (HB) stellar populations and variable stars. In Section 4, we describe the methodology for deriving the best-fitting SFH, and in Section 5 we present measurements of the SFH and chemical evolution of Leo P. In Section 6 we present a comparison of the evolution of Leo P with previously studied Milky Way dSph galaxy satellites and three LG dIrrs. Our conclusions are summarized in Section 7.

Leo P (AGC 208583; Giovanelli et al. 2013) was discovered through the Arecibo Legacy Fast ALFA survey (ALFALFA; Giovanelli et al. 2005; Haynes et al. 2011). The ALFALFA survey is a blind extragalactic survey in the H i 21 cm line covering over 7000 square degrees of high Galactic latitude sky. Follow-up optical observations at the location of the ALFALFA H i detection, including WIYN 3.5 m BVR and KPNO 2.1 m Hα imaging, confirmed the presence of both a resolved stellar population and a single H ii region (Rhode et al. 2013).

Optical spectroscopy of the H ii region enabled a direct measurement of the auroral [O iii] λ4363 line, yielding an oxygen abundance of 12 + log(O/H) = 7.17 ± 0.04 (Skillman et al. 2013), ∼3% Z_⊙ (based on a solar abundance of 12 + log(O/H) = 8.68; Asplund et al. 2009). This abundance measurement showed that Leo P is the lowest metallicity, gas-rich galaxy known in the Local Volume. Its properties are consistent with the luminosity–metallicity relationship in Berg et al. (2012).

Deeper optical imaging of the resolved stellar populations from the Large Binocular Telescope (LBT) enabled a distance measurement based on the tip of the red giant branch (TRGB) detection of ${1.72}_{-0.40}^{+0.14}$ (McQuinn et al. 2013). The large lower uncertainty is due to the sparseness of the red giant branch (RGB) stars in such a low-mass galaxy. This distance measurement placed Leo P just outside the zero velocity boundary of the LG.

H i spectral line imaging from the VLA shows a small amplitude rotation (V_c = 15 ± 5 km s⁻¹), with no obvious signs of interaction or in-falling gas at larger spatial scales (Bernstein-Cooper et al. 2014). These observations revealed that Leo P has one of the lowest neutral gas mass of any known low-metallicity dwarf, with a mass ratio of gas to stars of 2:1 and total mass to baryonic mass of >15:1. Follow-up high-sensitivity observations with CARMA of the CO (${\text{}}J=1\to 0$) transition did not detect any CO emission, but placed stringent upper limits on the CO luminosity of L_CO < 2930 K km s⁻¹ pc² (Warren et al. 2015). The molecular hydrogen mass remains uncertain as the ratio of CO to H₂ is not well constrained at low-metallicities. In Table 1 we summarize the basic properties measured in Leo P from these previous studies.

Table 1. Leo P Properties and Observations

		Updated Distance-
Parameter	Value	dependent Values
R.A. (J2000)	10:21:45.1	...
Decl. (J2000)	+18:05:17	...
Distance (Mpc)	${1.72}_{-0.40}^{+0.14}$	1.62 ± 0.15
MV (mag)	$-{9.41}_{-0.50}^{+0.17}$	−9.27 ± 0.20
M* (M⊙) from M/L	${5.7}_{-1.8}^{+0.4}\times {10}^{5}$	...
M* (M⊙) from SFH	...	${5.6}_{-1.9}^{+0.4}\times {10}^{5}$
M*/LV	...	1.25
MH i (M⊙)	9.3 × 105	8.1 × 105
Vcirc (kms−1)	15±5	...
Mdyn (M⊙)	2.6 × 107	2.5 × 107
Vsys (km s−1)	260.8 ± 2.5	...
LCO (K km s−1 pc2)	<3300	<2930
12+log(O/H)	7.17 ± 0.04	...
LHα (erg s−1)	6.2 × 1036	5.5 × 1036
SFRHα (M⊙ yr−1)	4.9 × 10−5	4.3 × 10−5
AV (mag)	0.071	...
Semimajor axis (')	1.2	...
Ellipticity	0.52	...
Position angle (°)	335	...
HST Program ID	HST-GO-13376	...
ACS Filters	F475W; F814W	...
Exposure F475W (s)	25,829	...
Exposure F814W (s)	18,496	...

Note. Summary of the properties of Leo P based on measurements reported in Giovanelli et al. (2013), Rhode et al. (2013), McQuinn et al. (2013), Skillman et al. (2013), Bernstein-Cooper et al. (2014) and Warren et al. (2015) and the revised distance measurement from this work (see Table 4). Systemic velocity (V_sys) is in the Local Standard of Rest Kinematic frame. Hα-based SFR is based on the calibration by Kennicutt et al. (1994). Foreground extinction estimate is based on the dust maps from Schlegel et al. (1998) with recalibration from Schlafly & Finkbeiner (2011).

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HST observations of Leo P were obtained using the Advance Camera for Surveys (ACS) instrument (Ford et al. 1998) in the F475W (Sloan g) and F814W (I) filters between 2014 April 23 and 26 (GO 13376; PI McQuinn). The observations were taken over 17 orbits grouped in visits of 2–3 orbits, and followed the ultra-deep field dither pattern between exposures, shifted by 2–3 pixels to aid in the removal of hot pixels and to average-out the detector response. The observations were designed to reach a photometric depth of ∼2 mag below the RC to aid in (i) constraining the SFH at older times and (ii) measuring the distance from the HB stars and RR Lyrae stars.

Similar to the successful Local Cosmology from Isolated Dwarfs ¹⁰ (e.g., Skillman et al. 2014) program, our observation strategy was designed to optimally sample the light curves of short period variable stars (e.g., Bernard et al. 2008, 2009), such as RR Lyrae, which provide independent constraints on the distance to Leo P and the SFH. To achieve this, each orbit was split between the two filters, with an alternating pattern for the exposures (i.e., F475W, F814W, F814W, F475W, etc.). In addition, the visits were executed sequentially and grouped within a 3-day time period, while minimizing orbits with a ∼12 hr cadence. These observations thus maximize sampling within the 17 orbits of a ∼0.6 day period RR Lyrae star across six periods with minimal repetition of sampling at the same point in a light curve. The observational details are summarized in Table 1.

HST Drizzlepac v2.0 was used to create mosaics in each filter. First, the charge transfer efficiency corrected images (i.e., flc files) were processed with Astrodrizzle to remove cosmic-rays (CR), creating a set of CR cleaned images. Second, these CR cleaned images were processed through the task tweakreg to measure the astrometric shifts between the images. Third, the original flc.fits images were processed with Astrodrizzle using the tweakreg shifts to create a combined mosaic in each filter.

In Figure 1, we present a color image of Leo P from the HST ACS observations created using the F475W and F814W mosaics, along with an averaged image of the two filters. As seen in Figure 1, the galaxy has an irregular stellar morphology that is well-resolved and a single H ii region clearly identifiable in the image.

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Point-spread function (PSF) photometry was performed on the flat, charge transfer efficiency corrected images (flc.fits) with the DOLPHOT photometry package, a modified version of HSTPHOT with an ACS specific module (Dolphin 2000). The photometric catalog was filtered for well-recovered stars (i.e., output error flag <8) and with a signal-to-noise ratio ≥5. Point sources with high sharpness or crowding values were rejected (i.e., (V_sharp + I_sharp)² > 0.075; (V_crowd + I_crowd) > 0.8). Sharpness indicates whether a point source is too broad (such as background galaxies) or too sharp (such as cosmic rays). Crowding measures how much brighter a star would be if nearby stars had not been fitted simultaneously; stars with higher values of crowding have higher photometric uncertainties. Spatial cuts were applied to the filtered photometric catalog. These cuts were based on the ellipticity (e = 0.52), semimajor axis (12), and position angle (PA = 335°) of Leo P (McQuinn et al. 2013). The final elliptical parameters are listed in Table 1. We expanded the spatial cuts for variable star identification (see Section 2.4), extending the search to include the halo of the galaxy.

Artificial star tests were performed to measure the completeness limits of the images using the same photometry package. Approximately 600 k artificial stars were injected into the individual images following the spatial distribution of all sources in the non-filtered photometric catalog. The final artificial star lists were filtered using the same parameters that were used to produce the final photometry catalog.

Figure 2 shows the CMD from the final photometry plotted to the 50% completeness level as determined from the artificial star tests. Representative uncertainties per magnitude are plotted and include uncertainties from the photometry and uncertainties recovered from the artificial star tests. The photometry was corrected for extinction (A_F475W = 0.086 mag; A_F814W = 0.039 mag) based on the dust maps of Schlegel et al. (1998) with recalibration from Schlafly & Finkbeiner (2011). The main sequence (MS), RGB, HB, and the RC are identifiable in the CMD. In addition, there is a sparse population of red and blue helium burning stars (i.e., blue loop stars with F814W ≲ 25 mag). These stars are intermediate mass stars (2 M_⊙ ≲ M ≲ 15 M_⊙) and are unambiguous signs of recent (t ≲ 500 Myr) star formation activity (Dohm-Palmer & Skillman 2002; McQuinn et al. 2011). We investigate the star-forming properties in Leo P in Section 5.

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Figure 3 shows the spatial distribution of stars separated into course age bins of "young" and "old" stars. Stars were classified as young and old based on their position in the CMD. Specifically, young stars were selected from the upper MS corresponding to a B or O spectral-type classification with lifetimes ≲300 Myr (i.e., F475W < 25.7 mag and F475W−F814W < 0.2 mag), and the blue and red helium burning branch stars which have a similar maximum lifetime. In Figure 4, we overlay an isochrone of 300 Myr to demonstrate the location of young stars in the CMD. The old category is populated with RGB stars identified from the CMD. Despite the coarse time bins, the selection of young versus old stars is robust. In Figure 3, the young stars are more centrally concentrated with an irregular distribution. A small number of young star candidates are located in the outer regions of the galaxy. The locations of the RR Lyrae candidates, identified from the photometry, are also shown (see Section 2.4).

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The area within the one H ii region in the galaxy is resolved into seven individual point sources in the HST images. These sources were blended in previous, ground-based imaging of Leo P, leading to some speculation on the nature of the star(s) responsible for ionizing the surrounding gas (Rhode et al. 2013, see their Section 4.1.2). Figure 4 shows the CMD of Leo P with the F475W magnitude as the ordinate axis. Here, we highlight the stars located at the position of the H ii region in Leo P in red, including the luminous star likely responsible for the ionization of the region. Note that these stars are bluer than expected in the CMD, which is most likely due to contamination by emission lines in the H ii region. The most luminous of these stars has de-reddened F475W and F814W mag of 21.509 ± 0.001 and 21.892 ± 0.002 respectively. Using the calibration of Saha et al. (2011) and an adopted distance modulus of 26.05 ± 0.20 (see Section 2.4 for discussion of the calibration and Section 3.3 for the adopted distance), the ACS filter luminosities transform to an absolute Johnson V mag of −4.43. A star of this magnitude in the upper MS region of the CMD is consistent with an O5V spectral type, according to the empirical catalog of absolute magnitudes of OB stars from Wegner (2000, see their Table 1 of smoothed absolute magnitudes). However, if this star is truly an O5V star, then the star with a similar color but ∼1 mag fainter at F475W = 23.03 mag would correspond to a star with an O9.5 spectral type, which would be hot enough to create a second H ii region. Since no H ii region is found around this fainter star, it is likely that both of these point sources are blended binary stars. High mass stars have been shown to have binary fractions in excess of 50% (Kobulnicky et al. 2014). If we assume each of these MS stars is comprised of equal mass binaries, the brightest source located in the known H ii region could have two constituent O7 or O8 stars. The fainter source constituents would then be B2 or B3 stars, just below the limit for hosting a detectable H ii region.

Rhode et al. (2013) calculated a SFR based on the Hα luminosity of the H ii region of 4.9 × 10⁻⁵ M_⊙ yr⁻¹. Using our adopted distance to Leo P, this SFR is revised downward to a value of 4.3 × 10⁻⁵ M_⊙ yr⁻¹, compared with our SFR derived from the stellar populations over the past 4 Myr of 2.1 × 10⁻⁵ M_⊙ yr⁻¹ (see Section 5). In this regime, the Hα luminosity has been shown to be a poor tracer of the actual star formation activity due, in part, to the incomplete sampling of the high mass end of the initial mass function (IMF) (e.g., Boselli et al. 2009; Goddard et al. 2010; Koda et al. 2012). Weidner & Kroupa (2005) and Pflamm-Altenburg et al. (2007) have suggested there may be an upper limit to the maximum stellar mass that can form at low SFRs. In this scenario, the slope of the upper end of the IMF varies as a function of SFR. Using the framework of Weidner & Kroupa (2005, their Figure 11), and Pflamm-Altenburg et al. (2007, their Figure 4), the maximum stellar mass that would be able to form at a SFR = 10⁻⁵ M_⊙ yr⁻¹ is ∼2.5 M_⊙. This is an order of magnitude lower than the mass of an ∼O8 star (M_* = 25 M_⊙) likely responsible for ionizing the H ii region. Indeed, the mere presence of the H ii region in Leo P provides observational evidence that the maximum stellar mass capable of being formed at low SFRs is significantly greater than 2.5 M_⊙.

We used the multi-epoch photometry to search for short-period variable stars. As noted in Section 2.2, the spatial cuts were relaxed to include a larger search area as RR Lyrae variable stars can be located in the stellar haloes of galaxies. Variable star candidates were identified first using a series of automated cuts, similar to those used in the study of IC 1613 (Dolphin et al. 2001). Each variable star was required to meet five criteria testing the photometry, variability, and periodicity. First, the object had to have well-measured photometery. While it is possible for a variable star to be part of a blend, our PSF-fitting photometry attempts to fit the profile to that of a single star and thus is unreliable for measuring blended stars. The next cuts were intended to eliminate non-variable or weakly variable stars. The simplest requirement was that the rms scatter of the magnitude measurements,

$$\begin{eqnarray}{\sigma }_{\mathrm{mag}} & = & \left(\displaystyle \frac{1}{{N}_{{\rm{F}}475{\rm{W}}}+{N}_{{\rm{F}}814{\rm{W}}}}\right.\\ & & \ast \;\left(\displaystyle \sum _{i=1}^{{N}_{{\rm{F}}475{\rm{W}}}}{({\rm{F}}475{{\rm{W}}}_{i}-\overline{{\rm{F}}475{\rm{W}}})}^{2}\right.\\ & & +{\left.\left.\displaystyle \sum _{i=1}^{{N}_{{\rm{F}}814{\rm{W}}}}{({\rm{F}}814{{\rm{W}}}_{i}-\overline{{\rm{F}}814{\rm{W}}})}^{2}\right)\right)}^{1/2}\end{eqnarray} \tag{ 1 }$$

had to be 0.14 mag or greater. Next, the overall reduced χ²,

$$\begin{eqnarray}{\chi }^{2} & = & \displaystyle \frac{1}{{N}_{{\rm{F}}475{\rm{W}}}+{N}_{{\rm{F}}814{\rm{W}}}}\\ & & \left(\displaystyle \sum _{i=1}^{{N}_{{\rm{F}}475{\rm{W}}}}\displaystyle \frac{{({\rm{F}}475{{\rm{W}}}_{i}-\overline{{\rm{F}}475{\rm{W}}})}^{2}}{{\sigma }_{i}^{2}}\right.\\ & & +\left.\displaystyle \sum _{i=1}^{{N}_{{\rm{F}}814{\rm{W}}}}\displaystyle \frac{{({\rm{F}}814{{\rm{W}}}_{i}-\overline{{\rm{F}}814{\rm{W}}})}^{2}}{{\sigma }_{i}^{2}}\right)\end{eqnarray} \tag{ 2 }$$

had to be 3.0 or greater. These two cuts eliminate stars that are weakly variable and those for which the photometry signal-to-noise is insufficient to discern variability. We also clipped 1/3 of the extreme points and required that the recalculated reduced ${\chi }^{2}$ exceed 0.5; this was intended to eliminate non-variable stars with a few bad points.

The final test was a modified Lafler–Kinman algorithm (Lafler & Kinman 1965), which tests for periodicity. This was implemented by computing Θ for periods between 0.1 and 4.0 days. The Θ parameter is calculated by determining the light curve for a trial period and using the equation

$$\begin{eqnarray}&&{\rm{\Theta }}=\displaystyle \frac{{\displaystyle \sum }_{i=1}^{N}{({m}_{i}-{m}_{i+1})}^{2}}{{\displaystyle \sum }_{i=1}^{N}{({m}_{i}-\bar{m})}^{2}},\end{eqnarray} \tag{ 3 }$$

where N is the number of exposures for a given filter, m_i is the magnitude at phase i, and $\bar{m}$ is the mean magnitude. If the trial period is the correct period, each magnitude m_i will be close to the adjacent magnitude m_i+1, giving a value of Θ that decreases as 1/N². If the trial period is incorrect, there will be less correlation and consequently larger values of Θ. Because we had data in two filters, we combined the Θ values with:

$$\begin{eqnarray}&&{\rm{\Theta }}=\displaystyle \frac{4}{{(1/\sqrt{{{\rm{\Theta }}}_{{\rm{F}}475{\rm{W}}}}+1/\sqrt{{{\rm{\Theta }}}_{{\rm{F}}814{\rm{W}}}})}^{2}}.\end{eqnarray} \tag{ 4 }$$

For a star to pass the periodicity test, its minimum value of Θ had to be 0.85 or less. For more discussion on the use of the modified Lafler–Kinman algorithm to test for periodicity and specifics on the parameters, see Dolphin et al. (2002, 2004).

Our photometry identified 13,448 total objects, of which 45 passed our automatic selection process. Three of these were clearly RR Lyrae stars by location in the CMD, light curve shape, and period. The χ² criterion was relaxed, and the search was constrained to an area centered on the horizontal branch, and ten more candidates were identified. Of these new ten, three of these candidate variables appeared to not be clean detections upon manual examination of the images and were removed from the list resulting in a final total of ten candidate RR Lyrae stars. The light curves for the ten variable stars are presented in Figure 5; complete photometry in the ACS filters is available in Table 2.

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The absolute magnitudes of RR Lyrae stars have been determined based on the Johnson BVRI filter systems. Therefore, we transform our measured ACS F475W and F814W magnitudes to standard Johnson V and I magnitudes using the calibration from Saha et al. (2011):

$$\begin{eqnarray}&&V=0.026+{\rm{F}}475{\rm{W}}-0.406\ast ({\rm{F}}475{\rm{W}}-{\rm{F}}814{\rm{W}})\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&I=-0.038+{\rm{F}}814{\rm{W}}+0.014\ast ({\rm{F}}475{\rm{W}}-{\rm{F}}814{\rm{W}}).\end{eqnarray} \tag{ 6 }$$

These transformations are an improvement over the previous calibrations from Sirianni et al. (2005) as they were derived based on a larger number of stars down to fainter magnitudes and over a greater range in color. Furthermore, the transformations from Saha et al. (2011) were based on updated corrections for time-dependent charge transfer losses in the ACS detector.

To compute mean magnitudes, we calculated a phase-weighted average using

$$\begin{eqnarray}&&\langle m\rangle =-2.5\mathrm{log}\displaystyle \sum _{i=1}^{N}\displaystyle \frac{{\phi }_{i+1}-{\phi }_{i-1}}{2}{10}^{-0.4{m}_{i}},\end{eqnarray} \tag{ 7 }$$

where ϕ_i is the phase and m_i is the magnitude at each point along the light curve. Finally, the mean magnitudes for all ten stars are computed to be F475W = 26.88 ± 0.02, F814W = 26.18 ± 0.07, and V = 26.62 ± 0.03. Note, these mean magnitudes are not corrected for foreground extinction. Table 3 summarizes the mean magnitudes for each star in the three filters and the final mean magnitudes for all ten stars. The location of the RR Lyrae candidates within Leo P are shown in Figure 3.

Table 3. Summary of RR Lyrae Candidates in Leo P

	R.A.	Decl.	$\langle {\rm{F}}475{\rm{W}}\rangle$	$\langle {\rm{F}}814{\rm{W}}\rangle$	$\langle {\text{}}V\rangle$	Period
Star ID	(J2000)	(J2000)	(mag)	(mag)	(mag)	(days)
01	10:21:44.388	+18:05:07.63	26.87 ± 0.09	26.04 ± 0.07	26.56 ± 0.14	0.61 ± 0.06
02	10:21:47.080	+18:03:59.16	26.85 ± 0.08	26.22 ± 0.07	26.62 ± 0.12	0.52 ± 0.06
03	10:21:44.324	+18:05:33.73	26.89 ± 0.06	26.11 ± 0.07	26.56 ± 0.09	0.69 ± 0.11
04	10:21:43.240	+18:05:53.13	26.90 ± 0.08	26.16 ± 0.06	26.62 ± 0.12	0.64 ± 0.08
05	10:21:44.722	+18:05:39.91	26.90 ± 0.10	26.25 ± 0.07	26.66 ± 0.15	0.57 ± 0.13
06	10:21:42.750	+18:05:46.47	26.89 ± 0.09	26.17 ± 0.05	26.63 ± 0.13	0.59 ± 0.06
07	10:21:43.704	+18:05:34.37	26.89 ± 0.10	26.25 ± 0.07	26.66 ± 0.15	0.61 ± 0.04
08	10:21:45.227	+18:05:46.86	26.91 ± 0.07	26.11 ± 0.06	26.61 ± 0.11	0.57 ± 0.04
09	10:21:44.633	+18:05:21.31	26.84 ± 0.12	26.27 ± 0.06	26.64 ± 0.18	0.53 ± 0.07
10	10:21:44.087	+18:06:22.92	26.86 ± 0.06	26.24 ± 0.07	26.63 ± 0.10	0.34 ± 0.01
Mean Magnitudes			26.88 ± 0.02	26.18 ± 0.07	26.62 ± 0.03

Note. Ten RR Lyrae variable star candidates were identified as described in Section 2.4. The coordinates, phase-weighted mean magnitudes, and periods of the individual stars are listed, followed by a mean magnitude computed for all ten stars. These magnitudes have not been corrected for foreground extinction.

Machine-readable versions of the table is available.

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Figure 6 shows the location of the ten RR Lyrae candidate variable stars in the CMD. All ten stars were found in a narrow range in luminosity. Because the HB is ∼2 mag above the 50% completeness limit for our observations, we likely did not miss any RR Lyrae stars due to depth of photometry. Also, because of the number and spacing of the epochs, we are likely to have a very high completeness. The data provided excellent coverage for the range of relevant variable star periods. Due to the large number of observational epochs and the fact that the cadence was set to minimize redundancies, the maximum gap in the phase coverage was always less than 0.15 days for periods in the range 0.1–1.0 days (see Figure 5). Consequently, our mean magnitude measurements are robust, as indicated by the very small dispersion (σ_V = ± 0.03) in the sample. Thus, the distance to Leo P derived from the RR Lyrae stars (see Section 3) is limited by the systematic uncertainty of the calibration used.

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As discussed above, the mean V magnitude of the ten RR Lyrae stars is 26.62 ± 0.03 mag. To account for foreground extinction, we subtract A_V = 0.071 mag based on the dust maps of Schlegel et al. (1998) with the re-calibration from Schlafly & Finkbeiner (2011).

There has been significant work done to calibrate the luminosity of the RR Lyrae stars as a function of metallicity, however the zero-point can still vary by ∼0.1 mag between calibrations (for detailed reviews, see Smith 1995; Cacciari 2003; Sandage 2006; Catelan 2009, among others). Some of the differences are due to the difficulty quantifying the luminosity dependence on stellar metallicity. Regardless, the choice of calibration introduces a systematic error to our distance measurement, dominating the uncertainties. We use the calibration from Carretta et al. (2000) which was derived using dozens of RR Lyrae stars in globular clusters and anchored to several independent distance measurements:

$$\begin{eqnarray}&&{M}_{V}=(0.18\pm 0.09)\ast ({\rm{[Fe/H]}}+1.5)+(0.57\pm 0.07).\end{eqnarray} \tag{ 8 }$$

As seen in Equation (8), the RR Lyrae luminosity depends on the metallicity of the population. For an estimate of the metallicity of the oldest stars, we fit Padova–Trieste stellar evolution isochrones (PARSEC; Bressan et al. 2012; Chen et al. 2014; Tang et al. 2014) to the RGB. The PARSEC models are the result of a thorough revision of the previous Padova stellar evolution code with the most up to date input physics. The PARSEC library also includes post-helium core flash phases of evolution and has been adjusted to a revised solar abundance. In Figure 4, we overlay isochrones for a 12 Gyr old population with [Fe/H] values of −1.9, −1.8, and −1.7. The best-fitting isochrone to the mean color of the RGB has a metallicity value of [Fe/H] = −1.8 ± 0.1; the uncertainty is based on the metallicities of the same age isochrones that span the approximate width of the RGB. The −1.8 value seems reasonable as it is lower than the present day gas-phase oxygen abundance measurement of −1.52 (assuming [O/Fe] ∼ 0), and consistent with stellar metallicities spectroscopically measured in low-mass dwarfs (e.g., Kirby et al. 2010). We experimented with using the Dartmouth stellar evolution isochrones which are known to provide a good fit to the RGB in low-metallicity systems. The best-fitting Dartmouth isochrones had a similar metallicity value and range of −1.9 ± 0.1, providing a consistency check on the values from the PARSEC isochrones. Using an [Fe/H] value of −1.8 ± 0.1 in Equation (8) yields M_V = 0.52 ± 0.20, corresponding to a distance modulus of 26.04 ± 0.21 mag.

As noted above, there has been significant work done to calibrate the luminosity of the RR Lyrae stars. For comparison, we consider two additional calibrations from the literature. First, we utilize the calibration from Clementini et al. (2003) based on photometry and spectroscopy of more than 100 RR Lyrae stars in the Large Magellenic Cloud:

$$\begin{eqnarray}&&{M}_{V}=(0.866\pm 0.085)+(0.214\pm 0.047)\ast {\rm{[Fe/H]}}.\end{eqnarray} \tag{ 9 }$$

Using the same [Fe/H] value of −1.8, Equation (9) yields M_V = 0.48 ± 0.12, corresponding to a distance modulus of 26.07 ± 0.13 mag.

Second, we consider the calibration from Bono et al. (2003) with uses an updated theoretical prescription of the pulsating modes of RR Lyrae stars:

$$\begin{eqnarray}&&{M}_{V}=(0.718\pm 0.072)+(0.177\pm 0.069)\;\ast \;{\rm{[Fe/H]}}.\end{eqnarray} \tag{ 10 }$$

This calibration yields an absolute magnitude of M_V = 0.40 ± 0.15, corresponding to a distance modulus of 26.16 ± 0.15 mag. The distances from these additional calibrations agree within the uncertainties to the distance calculated based on the calibration from Carretta et al. (2000) above in Equation (8).

The luminosity of the red HB stars can also be used as a distance indicator. Similar to the RR Lyrae stars, the calibration for the HB stars has been done in the Johnson filters. Thus, we use the same transformations described in Equations (5) and (6) to convert the ACS magnitudes to V and I band magnitudes. To measure the luminosity of the HB, we fit a parametric LF to the observed distribution of stars in the magnitude and color range of the HB feature, without any correction for foreground extinction. This is a similar maximum likelihood approach used to measure the TRGB in many systems (e.g., Sandage et al. 1979; Méndez et al. 2002; Makarov et al. 2006; Rizzi et al. 2007), based on a probability estimation that takes into account photometric error distribution and completeness using artificial star tests. We assumed the following form for the theoretical LF:

$$\begin{eqnarray}&&P={\mathrm{exp}}^{(A*(V-{V}_{\mathrm{HB}})+B)}+{\mathrm{exp}}^{(-0.5*{((V-{V}_{\mathrm{HB}})/C)}^{2})}\end{eqnarray} \tag{ 11 }$$

where A, B, and C are free parameters. We selected stars in the HB identified by eye in the CMD to use in the fit. Specifically, stars in the V mag range of 25–28 and within a V − I color range of 0.2–0.6 were used. The HB luminosity was measured to be V = 26.62 ± 0.01 mag, from which we subtracted A_V = 0.071 mag to correct for extinction.

We use the HB calibration from Carretta et al. (2000) to determine the absolute magnitude of the HB:

$$\begin{eqnarray}&&{M}_{V}=(0.13\pm 0.09)\ast ({\rm{[Fe/H]}}+1.5)+(0.54\pm 0.04).\end{eqnarray} \tag{ 12 }$$

In the same manner described for the RR Lyrae stars, we assume an [Fe/H] value of −1.8 ± 0.1. The HB luminosity based on the above calibration yields M_V = 0.50 ± 0.20, in excellent agreement with the range in calibrated magnitudes of the ten RR Lyrae stars. Based on this HB luminosity, the distance modulus is 26.05 ± 0.20.

Table 4 summarizes the distance measurements to Leo P based on the TRGB from the LBT and HST data sets and RR Lyrae and HB measurements from the HST data. The distance moduli determined from the different calibrations and techniques agree within the uncertainties. The calibrations from Carretta et al. (2000) provide consistency across the RR Lyrae, HB, and TRGB distance techniques, allowing us to compare the three methods without introducing a systematic uncertainty. These three techniques yield distance moduli of 26.04 ± 0.21, 26.05 ± 0.20, and ${26.19}_{-0.50}^{+0.17}$ respectively. The consistency of the RR Lyrae and HB distance measurements reinforces the conclusion that the TRGB identified in the CMD from McQuinn et al. (2013), similarly to the HST data presented here, is indeed a false tip. Furthermore, all of the distance measurements are within the uncertainties estimated via Monte Carlo simulations of synthetic populations from McQuinn et al. (2013) supporting this approach for determining uncertainties on the TRGB in this very low-mass regime.

Table 4. Distance Measurements to Leo P

Method	(m − M)o	Distance (Mpc)	Calibration
TRGB (LBT)	${26.19}_{-0.50}^{+0.17}$	${1.72}_{-0.40}^{+0.14}$	Rizzi et al. (2007), Carretta et al. (2000)
TRGB (HST)	${26.19}_{-0.50}^{+0.17}$	${1.72}_{-0.40}^{+0.14}$	Rizzi et al. (2007), Carretta et al. (2000)
Horizontal Branch	26.05 ± 0. 20	1.62 ± 0. 15	Carretta et al. (2000)
RR Lyrae	26.04 ± 0. 21	1.61 ± 0. 16	Carretta et al. (2000)
RR Lyrae	26.07 ± 0.13	1.64 ± 0.10	Clementini et al. (2003)
RR Lyrae	26.16 ± 0.15	1.70 ± 0.12	Bono et al. (2003)

Note. TRGB distance was measured from LBT optical imaging of the resolved stellar populations (McQuinn et al. 2013) and confirmed via the HST data presented here. For the TRGB distance measured from the HST data, we adopt the uncertainties from the Monte Carlo simulations in McQuinn et al. (2013). All values include a correction for foreground extinction of A_V = 0.071 mag. The best distance measurements are highlighted in bold. For the final distance measurement to Leo P, we adopt the HB distance based on the calibration by Carretta et al. (2000) because this measurement agrees with the RR Lyrae distance based on the same calibration but has a slightly lower uncertainty. See Section 3.3 for discussion.

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The HB and RR Lyrae distances based on the calibration from Carretta et al. (2000) are very similar. We adopt the distance modulus of 26.05 ± 0.20 mag from the HB stars due to the slightly lower uncertainty, yielding a distance of 1.62 ± 0.15 Mpc. The refined distance places Leo P in the NGC 3109 association of dwarf galaxies (Tully et al. 2006) including Antlia, Sextans A, and Sextans B as proposed by McQuinn et al. (2013). The closest of these galaxies is Sextans B at a distance of ∼0.4 Mpc. In Table 1, we include updated distance dependent parameters using this revised distance measurement.

To provide context for Leo P's properties, we compile a comparison sample of very low-mass, low-luminosity galaxies in the nearby universe, listed in Table 6. By both necessity and design, the sample is heterogeneous, including both gas-poor dSphs satellites of the Milky Way and gas-rich dIrrs that lie outside the virial radius of the Milky Way but still inside the LG zero velocity boundary. On the one hand, there are very few known gas-rich, star-forming galaxies in this mass range, despite predictions that they should be the most common galaxy structure in the nearby universe (e.g., Haynes et al. 2011). As noted in the Introduction, these galaxies have proven elusive observationally. Thus, to build a larger sample of galaxies in this mass regime, we must include some of the gas-poor low-mass dSphs detected in close proximity to the Milky Way. On the other hand, the dSphs present very different environment-driven histories than Leo P and other dIrrs. Thus, these galaxies provide a contrast to evolution in isolation allowing us to explore possible environmental differences on evolution in this mass regime.

As an extension to our comparison, we also include three dSphs with even lower lumnosities. The discovery and study of a population of very low-mass Milky Way satellite dSph galaxies, colloquially called "ultra-faint dwarf" galaxies, have extended the constraints of structure formation and evolution in the universe. These galaxies are very low-luminosity (M_V ≳ −8; Martin et al. 2008) with little gas content and a predominantly old, metal-poor, stellar population (e.g., de Jong et al. 2008b; Hughes et al. 2008; Martin et al. 2008; Okamoto et al. 2008, 2012; Sand et al. 2009, 2010; Frebel et al. 2010; Kirby et al. 2010, 2011a; Norris et al. 2010; Brown et al. 2014; Weisz et al. 2014a). The M/L of these systems indicate that they are dark matter dominated (i.e., M/L ≳ 100 Kleyna et al. 2005; Muñoz et al. 2006; Martin et al. 2007; Simon & Geha 2007), setting them apart from globular clusters of similar luminosity. Discovered from slight over-densities in the SDSS data set, it appears that these very low surface brightness galaxies are an extension of dSphs to lower masses (Belokurov et al. 2007; Clementini et al. 2012).

From Table 6, the present-day luminosities of the dIrrs and dSphs span close to four magnitudes; this range increases to seven magnitudes when including the very low-mass dSphs. The dSphs are all located within ∼200 kpc of the Milky Way, well inside the virial radius. The three comparison dIrrs reside outside of this boundary, but still inside the LG (McConnachie 2012).

Another way to compare these low-mass galaxies is to consider the evolution of their luminosities with time based on their SFHs (e.g., Weisz et al. 2014b). This can allow one to compare the initial properties of the sample and study whether subsequent changes are correlated with environment. Such a comparison can be made by converting the SFHs into luminosity evolution profiles. The SFHs from resolved stellar populations of various low-mass galaxies have been published by a number of authors (e.g., Cole et al. 2007, 2014; Kirby et al. 2011a; Clementini et al. 2012; Brown et al. 2014; Weisz et al. 2014a, among others).

Because our analysis requires tabulated results of the fraction of stars as a function of time, we utilize the results on eight galaxies in our comparison sample derived from HST optical imaging from Weisz et al. (2014a), and similarly obtained results on one galaxy (DDO 210) from Cole et al. (2014). The SFH solutions from Weisz et al. (2014a) were derived using the Padova isochrones, and the solution for DDO 210 from Cole et al. (2014) was derived using the PARSEC isochrones. However, the CMDs in both of these previous studies have photometric depths reaching below the old main sequence turn-off (oMSTO), which provides robust constraints on the ancient star formation. SFH solutions derived from different stellar evolution libraries using data with photometry extending below the oMSTO have shown excellent agreement with each other (e.g., Gallart et al. 2005; Monelli et al. 2010a, 2010b; Hidalgo et al. 2011; Weisz et al. 2011). Thus, the systematic uncertainties between members of our comparison sample should be small. For completeness in our qualitative comparison, we also include the luminosity evolution of Leo P based on the SFH from the Padova, PARSEC, and BaSTI models, which provides a sense of the systematic uncertainties.

The SFHs were used as input to the stellar population synthesis technique from Bruzual & Charlot (2003) which builds a synthetic galaxy spectrum as a function of time, assuming a constant metallicity and an IMF. Because the SFHs from Weisz et al. (2014a) and Cole et al. (2014) were derived from HST data which do not encompass the full optical disks of the galaxies, a correction is necessary. While the SFHs are generally assumed to be representative of the galaxy as a whole, the stellar mass only traces the stars (and luminosity) in the field of view. As a result, the modeled present-day luminosities from the SFHs are less than the measured luminosities. The exception to this is the luminosity for Leo P whose stellar disk is contained within the observational footprint. To account for the disparate fields of view between SDSS imaging used to determine the luminosities and data used to measure the SFHs from Weisz et al. (2014a) and Cole et al. (2007), we normalized the results from Bruzual & Charlot (2003) by the present-day measured luminosity. This scaled the modeled luminosities while preserving relative changes as a function of time.

In the left panel of Figure 9, we present a comparison of the luminosity evolution (M_V (t)) for Leo P based on the three stellar evolution libraries. Because the best-fitting solution from the Padova models has 50% of the stellar mass formed in the earliest epochs, compared to 10%–20% from the BaSTI and PARSEC libraries respectively, the Padova luminosity profile also shows the highest luminosity at earliest times. Regardless of the absolute magnitude, all three solutions show a peak in brightness at early times followed by a slow fading in luminosity.

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The right panel of Figure 9 presents a comparison of M_V (t) for Leo P using the PARSEC models with six gas-poor dSphs and three gas-rich dIrrs. We chose to highlight the Leo P solution using the PARSEC models which provided the best-fitting modeled CMD to the data, but our overall interpretation is valid for the profiles derived from all three stellar libraries. Two of the very low-mass dSphs (CVn II and Leo IV) lie 2–4 mag below the rest of the sample in both initial and present-day luminosity. Excluding these two systems, the rest of the sample shows a much narrower range in their initial luminosities than their present day luminosities (i.e., ΔM_V ∼ 2 versus ΔM_V ∼ 5). The larger range at the present-epoch is mainly driven by changes in three galaxies. On the bright end are DDO 210 and Leo A which show dramatic increases in star formation in the last 6 Gyr (Cole et al. 2007, 2014). On the faint end is Hercules which has formed far fewer stars at recent times than the initially comparable low-luminosity dIrr, Leo T.

Looking at the early evolution of the profiles in Figure 9, Leo P's initial luminosity is similar to one very low-mass dSph (Hercules) and lower than three other dSphs (CVn I, Draco, Ursa Minor). This similarity suggests that Leo P may be what a dSph would look like if it evolved in isolation and retained its gas. One of the arguments against a dIrr evolving into a dSph is based on conservation of angular momentum; dIrrs are typically rotation supported whereas dSph are pressure supported (e.g., Grebel et al. 2003). However, analysis of the gas velocity field in Leo P shows that the gas velocity dispersion approaches the rotation speed. As discussed in detail in Bernstein-Cooper et al. (2014), there is significant random motion of the gas in Leo P superposed on the bulk rotation signature. This agrees with previous findings of little evidence of rotational support in other very low-mass dIrrs such as Leo A and DDO 210 (Lo et al. 1993; Young & Lo 1997). In contrast to higher-mass dIrrs with clearly defined rotation curves, the transformation of a very low-mass galaxy like Leo P to a dSph would not require a drastic loss of angular momentum.

From Figure 9, the patterns in luminosity profiles within the two morphological groups are quite similar over the last ∼7 Gyr. The dIrrs show fairly steady or increasing luminosities whereas the dSphs show declining luminosities. This more recent evolution in luminosity is presumably dictated by environment, described by the morphology–density relation (i.e., the isolated low-mass galaxies which retain their gas continue forming stars while those in closer proximity to a massive galaxy do not retain their gas and begin to fade). This is indirect evidence that the removal of gas in the dSphs is driven by environment—not internal stellar feedback—although feedback may be necessary to oust the gas from the inner, denser parts of the galaxies into an enveloping diffuse gaseous halo (see, e.g., Mayer et al. 2006; Simpson et al. 2013; Milosavljević & Bromm 2014, and references therein) for more swift and efficient removal. Previous authors have attributed the removal of gas and metals in Draco, CVn I, and Ursa Minor to stellar feedback processes (Kirby et al. 2011b), but additional factors must be involved to explain the distinct retention of gas in comparably low-mass systems such as Leo P and Leo T.

Despite the heterogeneity and general divergence of the profiles between the morphological types at more recent times, there is a similarity in the first 6 Gyr regardless of present-day morphological classification. As seen in Figure 9, there is a peak in luminosity at early epochs followed by a decrease. As suggested by previous studies (Cole et al. 2007, 2014; Brown et al. 2014), this pattern is consistent with a quelling of star formation post-reionization. In this scenario, ionizing photons from the first epochs of star formation (z = 11.3 ± 1.1; Planck Collaboration et al. 2014), may heat the outer disks of the galaxies in the mass and distance ranges probed, slowing or halting further gas accretion and causing an eventual (although sometimes temporary) decline in star formation (e.g., Oñorbe et al. 2015). As noted above, the galaxies at closer distances to the hostile environment of a massive galaxy are more likely to have the hot coronal gas removed by stripping mechanisms. The more distant, isolated galaxies retain the gas heated by reionization, which is likely at extended radii in the dark matter halo. Through atomic line cooling processes over Gyr-long timescales, this hot coronal gas may eventually condense onto the disk and reignite star formation, consistent with the increases noted for the more isolated galaxies (Leo P, Leo A, DDO 210, Leo T).

The impact of reionization on an individual galaxy is likely dependent on the distance to the local source of the ionizing photons, however it is unclear what distance scales are involved (e.g., Weinmann et al. 2007, and references therein). Excluding Leo P, the distances probed by our comparison sample range from 76–1000 kpc; within this range, the early evolution of the luminosity profiles do not show differences that can be obviously tied to present-epoch distances. For example, contrary to the idea that galaxies closer to the ionizing source should be more impacted by reionization, the galaxies closest to the Milky Way (Draco, Ursa Minor, CVn II, Leo IV) show smaller fractional increases in luminosity between ∼8–12 Gyr ago; the more distant galaxies do not, suggesting additional variables (e.g., mass) must be considered. The literature SFHs used to model the luminosity evolution have similarly small uncertainties at old look back times. Thus, the luminosity profiles should be robust. The exception, of course, is Leo P, which at the larger distance of 1.6 Mpc, limits the accuracy of the ancient SFH with the current data set. The best-fitting SFH suggests star formation was damped even at the larger distance of Leo P. However, given the uncertainties at older times, the SFH of Leo P does not preclude a fairly constant SFR as an alternative evolution for Leo P. If true, this would imply the damping of star formation occurs inside of ∼1.5 Mpc scales for a LG-type environment.

The impact of reionization on early star formation is also predicted to be dependent on the mass of a galaxy. Theoretical simulations fine-tune a "filtering mass" below which reionization universally quenches star formation. While the "filtering mass" generally falls within the mass range probed here (e.g., Gnedin 2000; Susa & Umemura 2004), we do not see evidence of universal quenching, in agreement with previous results (e.g., Grebel & Gallagher 2004; Monelli et al. 2010b; Hidalgo et al. 2011; Weisz et al. 2015). Yet, observational studies have reported something akin to this "knife-edge" in star formation within the temporal limitations of the CMD analysis in a few dSphs of even lower-masses (i.e., M_* ≲ 10⁴ M_⊙ Brown et al. 2014). There is still continuing debate on whether the cessation of star formation in the aforementioned systems can be solely attributed to photoevaporization from reionization (Brown et al. 2014) as these galaxies are also susceptible to environmentally driven removal of gas, and possibly stellar feedback (Kirby et al. 2011b).

Finally, we note that while Leo P has initial luminosity properties similar to the dSphs Hercules, Draco, CVn I, and Ursa Minor, the overall evolution of Leo P, based on the best-fitting SFH, is most similar to Leo T (shifted to brighter magnitudes). Leo T lies just outside the virial radius of the Milky Way, but is thought to have been only recently accreted (t_infall < 1 Gyr; Rocha et al. 2012). The similarities in the luminosity profiles support this hypothesis as tidal stripping of gaseous material in a galaxy as low-mass as Leo T becomes important at ∼1.5 times the virial radius of the Milky Way, or ∼450 kpc (Milosavljević & Bromm 2014). Thus, it is unlikely that Leo T would have retained its gas if it had been in residence around the Milky Way for a cosmically significant time. Previous authors have suggested that Leo T, as well as Leo A, fit in the general scenario outlined above for Leo P where star formation is quelled by reionization and reignited by late phase cold gas accretion (Cole et al. 2007; Ricotti 2009; Clementini et al. 2012; Weisz et al. 2012).