Homogeneous Photometry VI: Variable Stars in the Leo I Dwarf Spheroidal Galaxy

The nearby dwarf spheroidal galaxies (dSphs, L ≳ 10⁵ L_⊙) are important for understanding the formation and evolution of the Milky Way Galaxy. Their very old ages (≳10 Gyr) and low mean metallicities ([Fe/H] ≲ -1.3 dex) have long been used as evidence for the idea that these systems are fossils from the early Universe: surviving examples of the pregalactic units that formed the Galactic stellar halo, as predicted by hierarchical models of galaxy formation (White & Frenk 1991; Salvadori & Ferrara [2009] and references therein). This view has been widely held for at least the last 20 years, since detailed stellar population studies have been made possible by new deep color-magnitude diagrams (CMDs) and medium and high-resolution spectroscopic analyses (Mateo 1998; Tolstoy et al. 2009). Today, we have at our disposal accurate star-formation histories (Tolstoy & Saha 1996; Gallart et al. 1999; Cole et al. 2007; Monelli et al. 2010a,b; Hidalgo et al. 2011; de Boer et al. 2012a,b) and chemical abundance distributions (Venn et al. 2004; Kirby et al. 2009, 2011; Fabrizio et al. 2012; Lemasle et al. 2012; Kirby et al. 2013) for a large number of nearby dSphs and dwarf irregulars (dIs). However, high-resolution spectroscopy has shown that the [α/Fe] abundance patterns of stars in dSphs do not seem to resemble those of Galactic halo stars (Shetrone et al. 2001; Venn et al. 2004; Pritzl et al. 2005). This could pose some problems for their identification as representative building blocks of the halo. On the other hand, it could also be explained by the fact that present-day dSphs, having not accreted at early epochs, have had a Hubble time to evolve as independent entities under conditions that are different in a variety of ways from those experienced by field halo stars. In support of this interpretation, Font et al. (2006) have argued that differences in the chemical abundances of the Galactic halo and its satellites can be explained within their hierarchical formation model of the halo, which carefully tracks the orbital evolution and tidal disruption of its satellites.

A new source of puzzlement was raised by Helmi et al. (2006), who obtained large samples of low and intermediate-resolution spectra of red giant branch (RGB) stars of the Sculptor, Sextans, Fornax, and Carina dSph galaxies as part of a huge observational effort devoted to the characterization of the chemical abundances of those systems (Tolstoy et al. [2006] and references therein). For the first time, Helmi et al. (2006) noticed a significant lack of extremely metal-poor stars ([Fe/H] ≲ -3 dex) in the galaxies' metallicity distributions when compared with that of the Galactic halo. The most metal-poor stars in a galaxy are likely to be also the oldest ones, so—taken at face value—this evidence again seems to argue against the idea that nearby dSphs are surviving examples of the main contributors to the Milky Way halo. In order to further investigate this issue, Starkenburg et al. (2010) revisited the calibration of [Fe/H] as inferred from the observed strength of the infrared calcium triplet, which has been widely used to estimate the metal content of large samples of RGB stars in nearby dSph galaxies. The initial calibration of this relationship had presumed that it was linear over the relevant range of abundance, but in the new study it turned out to be nonlinear for [Fe/H] ≲ -2 dex, thus modifying the shape of the metallicity distribution in the metal-poor tail. Using the new calibration, Starkenburg et al. suggested that classical dSphs are not as devoid of extremely low-metallicity stars as previously believed. Selecting those stars with [Fe/H] ≲ -3 dex based on this new calibration of the IR calcium triplet, Starkenburg et al. (2013) followed up with high-resolution spectroscopy that confirmed the stars' extremely low metallicities. Today, more than 30 extremely metal-poor stars have been identified in dSphs, and their chemical abundance patterns now seem to more closely resemble those in the Galactic halo (e.g., Kirby et al. 2008; Koch et al. 2008; Kirby et al. 2009; Frebel et al. 2010a,b; Starkenburg et al. 2013).

Furthermore, the discovery of ultra-faint dwarf galaxies (UFDs, L ∼ 10³–10⁵ L_⊙ Willman et al. 2006; Zucker et al. 2006; Belokurov et al. 2006) seems to shed some more light on this intriguing scenario. They are numerous and very old (≳10 Gyr), and they contain extremely metal-poor stars (Kirby et al. 2008). Thus to some investigators they show promise as ideal candidates for the original building blocks of the Galactic halo, that may at the same time help solve the missing-satellite problem (White & Frenk 1991; Salvadori & Ferrara [2009] and references therein). Moreover, spectroscopic investigations of several UFDs provide strong constraints on the dynamical interaction between their baryonic content and their dark matter halos (Mayer 2010; Gilmore et al. 2013).

Tracing the oldest stellar component in a galaxy, RR Lyrae variable stars (RRLs) have the potential to independently test this interesting global picture through their pulsation properties. In particular, RRLs observed in both the Galactic halo and globular clusters (GCs) show a well defined dichotomy in their period distribution (see discussion in Contreras Ramos et al. [2013] and references therein). This behavior was first observed by Oosterhoff (1939) in Galactic GCs; he divided them into two groups according to the mean period of their RRab variable stars. Specifically, Oosterhoff I (OoI) GCs show mean periods around 〈Pab〉 ∼ 0.55 d, whereas OoII GCs show longer periods (〈Pab〉 ∼ 0.65 d). Further observations disclosed that the mean periods of the RRc-type variables are also different—again shorter in OoI clusters—and also that the fraction of RRc variables among RR Lyraes of all types is systematically smaller in OoI (∼17%) than in OoII (∼44%). Many studies have also demonstrated a relationship between the metallicity of the host cluster and the Oosterhoff type of its variable-star population: OoII clusters are typically very metal-poor ([Fe/H] ∼ -2 dex) halo objects, while OoI clusters cover a broader range of generally higher metallicities. At present—75 years later—there is still no full and satisfying explanation for this phenomenology among the GCs.

More recently, major observational surveys have shown that field RRLs in the Milky Way halo show the same period dichotomy as those in the globulars (Bono et al. 1997; ASAS, Pojmanski et al. 2005; LONEOS: Miceli et al. 2008; LINEAR: Sesar et al. 2013, etc.). In contrast, those in nearby Local Group galaxies and their GCs are perversely characterized by mean periods precisely in the range 0.58 d < 〈Pab〉 < 0.62 d—the so-called Oosterhoff gap—that is avoided by the Milky Way halo cluster and field populations (see Bono et al. [1994] and Catelan [2009] for a detailed discussion). However, this comparison, based on the statistical properties of very different samples of stars that may be subject to different selection biases, is not truly decisive in characterizing the differences between GCs, the Galactic halo, and dwarf galaxies.

Recently, extensive variability searches to characterize the RRL populations in UFDs have been carried out (Siegel 2006; Dall'Ora et al. 2006; Kuehn et al. 2008; Greco et al. 2008; Moretti et al. 2009; Musella et al. 2009; Dall'Ora et al. 2012; Musella et al. 2012; Clementini et al. 2012; Garofalo et al. 2013; Boettcher et al. 2013). Given the very small sample of RRL stars observed in most of the cases, it is very difficult even to provide a clear Oosterhoff classification for most UFDs. A few exceptions do exist: Bootes (11 RRLs; see Dall'Ora et al. [2006]) is the sole example of an apparently well-established OoII type, whereas Ursa Major I (7 RRLs, see Garofalo et al. 2013) is classified as Oo-intermediate, resembling the classical dSph galaxies. Indeed, at the present date we might regard the distinction between UFDs and dSphs as largely a matter of semantics: according to the available evidence, the two terms may merely refer to the lower- and higher-mass members of a single family of objects (see, e.g., McConnachie [2012], especially Figs. 6, 7, and 12).

This paper is part of the effort of one of us (PBS) to establish and maintain a database of homogeneous photometry for resolved star clusters and galaxies. This effort seeks the greatest completeness and longest time span possible by exploiting public-domain data currently available from astronomical archives. In this paper we analyse in detail the properties of variable stars that we have identified in the Leo I dwarf spheroidal galaxy. Part of these data have already been presented in Fiorentino et al. (2012), where we focused our attention on understanding the intermediate-age central-helium-burning stellar population (anomalous and/or short-period Cepheids, hereinafter AC/spCs). Here we present the full infrastructure underlying that discussion: identifications and equatorial positions for the complete set of variable star candidates together with their periods and light curve parameters. In § 4 we describe in detail the RRLs of Leo I. In § 5 we perform a slightly more detailed analysis of the AC/spC populations through mass determinations. Next, in § 6 and § 7 we discuss the variable stars in Leo I within the larger context of Milky Way formation and evolution discussed above. In particular, we will compare the period distributions and period-amplitude relations of the RRLs in (1) our data for Leo I and literature data for other classical dSph galaxies with literature data for (2) the Galactic halo field, (3) the Galactic halo GCs, and (4) the new Galactic halo UFDs. A final summary discussion closes the main body of the paper. An appendix addresses the reidentification of previously published variable candidates in Leo I.

The observational material for this study consists of 1884 individual CCD images obtained on 48 nights during 32 observing runs. These data are contained within a much larger data collection (∼400,000 images, ∼500 observing runs) compiled and maintained by the first author. Summary details of all 32 observing runs used here are given in Table 1. In fact, the observing runs designated "23 wfi4" and "24 wfi" were the same run, as were those designated "27 suba" and "28 suba2." However, in each case different subsets of the images had been provided to us through different channels. To avoid any possible unknown differences in the ways the images had been treated before we obtained them, we chose to keep them separate. Considering all the Leo I images together, the median seeing for our observations was 1''.0, the 25th and 75th percentiles were 0''. 8 and 1''.3, and the 10th and 90th percentiles were 0''.7 and 1''.6.

The photometric reductions were all carried out using standard DAOPHOT and ALLFRAME procedures (Stetson 1987, 1994) to perform profile-fitting photometry, which was then referred to a system of synthetic-aperture photometry by the method of growth-curve analysis (Stetson 1990). There were insufficient U-band observations from photometric occasions to establish a reliable U magnitude system in Leo I, and we have made no attempt to calibrate those data photometrically. The few U-band images that we do have, however, were included in the ALLFRAME reductions to exploit whatever information they can provide on the completeness of the star list and the precision of the astrometric positions.

Calibration of these instrumental data to the photometric system of Landolt (1992) (see also Landolt 1973, 1983) was carried out as described by Stetson (2000, 2005). If we define a "dataset" as the accumulated observations from one CCD chip on one night with photometric observing conditions, or one chip on one or more nights from the same observing run with nonphotometric conditions, the data for Leo I were contained within 95 different datasets, each of which was individually calibrated to the Landolt system. Of these 95 datasets, 63 were obtained and calibrated as "photometric", meaning that photometric zero points, color transformations, and extinction corrections were derived from all standard fields observed during the course of each night, and applied to the Leo I observations. The other 32 datasets were reduced as "nonphotometric"; in this case, color transformations were derived from all the standard fields observed, but the photometric zero point of each individual CCD image was derived from local Leo I photometric standards contained within the image itself; these local standards were established by us from the images obtained during photometric conditions. Considering the 95 datasets employed here, the median values for the rms residuals of the observed results for the standard stars relative to their established standard values were 0.029 mag in B (minimum 0.007, maximum 0.079), 0.026 in V (0.011, 0.076), 0.024 in R (0.007, 0.059), and 0.024 in I (0.011, 0.090). The (minimum, median, maximum) numbers of standard-star observations contained in each dataset were (88, 1644, 15084) in B, (79, 2059, 25664) in V, (85, 1440, 8742) in R, and (26, 1526, 14790) in I.

The different cameras employed projected to different areas on the sky, and of course the telescope pointings differed among the various exposures. Furthermore, the Wide-Field Camera on the Isaac Newton Telescope, the Wide-Field Imager on the 2.2 m MPG/ESO telescope on La Silla, Suprime-Cam on the Subaru Telescope, FORS on the VLT on Paranal, and LBC on the Large Binocular Telescope on Mount Graham consist of mosaics of nonoverlapping CCD detectors. The last column of Table 1 gives the number of independent detectors in each camera when this number is greater than one. Therefore, although we have 1884 images, clearly no individual star appears in all those images. In fact, no star appeared in more than 97 B-band images, 240 V images, 51 R images, or 41 I images. The median number of observations for one of our stars is 22 in B, 72 in V, 24 in R, and 16 in I. Since most pointings were centered on or near the galaxy, member stars typically have more observations than field stars lying farther from the galaxy center.

Our complete photometric catalog for Leo I and a stacked image of the field are available at our Web site.⁸

We have used an updated version of the Welch & Stetson (1993) method to identify candidate variable stars on the basis of our multiband photometry of Leo I. We have identified 251 variable star candidates in a luminosity range that goes from the horizontal branch (HB) to the tip of the red giant branch (TRGB). A first guess at the variability period of each star was found using a simple string-length algorithm (Stetson et al. 1998b), then a robust least-squares fit of a Fourier series to the data refined the periods and computed the flux-weighted mean magnitudes and amplitudes of the light curves (Stetson et al. [1998b], Fiorentino et al. [2010], and references therein). The resulting pulsation properties are listed in Tables 2, 3, and 4. This list includes 164 stars that we have classified as RRLs, 55 AC/spCs, and 19 LPVs. There are also 13 more variable candidates whose physical nature is unclear (Table 5). Some of their light curves are shown in Fig. 1, and all are available at our Web site.

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On the basis of the photometric quality of the data and the completeness of the phase coverage, we have divided the pulsating variable candidates into three quality classes, namely: high confidence or "good" (A), uncertain or "fair" (B), and very uncertain or "poor" (C). These grades are given in Tables 2 (RR Lyraes) and 3 (AC/spCs). Among the 164 stars classified as RRL, we have assigned 95 as class A, 47 as B, and 22 as C; among the 55 AC/spCs there are 53 of class A, none of B, and 2 of class C. In the case of a star classified as A we are reasonably confident that our pulsation properties are "essentially" correct; i.e., we believe that the period is correct to better than ∼1%, and the amplitudes are correct to 0.1–0.2 mag. For stars classed B, there is a small (< 25%?) chance that one or more parameters are wrong by more than this, and for stars classed C we feel that the chance of an error larger than this might be as high as 50%. These quantitative likelihoods are purely the educated guesses of a fairly experienced observer. We invite interested readers to examine the light curves and/or download our original data from our web site and judge the reliability of our inferences for themselves. We anticipate that future reinvestigations based upon new data will be able to retroactively establish how meaningful our subjective quality classes truly are.

In Fig. 2, we show the locations in the CMD of these variable star candidates and the theoretical instability strip (IS) derived from radial nonlinear pulsating models for AC/spCs (Marconi et al. 2004; Fiorentino et al. 2006) and RRLs (Di Criscienzo et al. 2004). We have not included here the 13 variables that we have not been able to characterize (see Table 5). The agreement between the locations of "good" RRLs (blue and red dots) and AC/spCs (green squares) and the theoretical boundaries of the IS is excellent with very few exceptions. We also show the possible LPV candidates (stars); they are all located near the TRGB and the upper asymptotic giant branch (see Table 4). Unfortunately, the sampling of our light curves for the LPVs is neither dense nor well distributed over the necessary range of time intervals, and we could not reach any definitive evaluation of their periods. Detailed periods, being related to the LPV's masses and ages, could have provided constraints on the star formation history of the galaxy (see Feast & Whitelock [2013] and references therein). The so-called periods that we give in Table 4 are formal maximum-likelihood values returned by our software, but they should be regarded as purely notional. We provide them only to give some sense of the timescales upon which the variations appear to be occurring. We commend these stars to the attention of individuals having extensive access to telescopes of moderate aperture.

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Our sample of 164 RRL candidates contains 95 good stars (see Table 2), including 24 that apparently either show the Blazhko effect or pulsate in multiple modes. Among the good RRLs we recognize 14 first overtone (FO) and 81 fundamental-mode (FU) pulsators on the basis of their period/amplitude distribution in the Bailey diagram (Fig. 3). The remaining 69 RRL candidates with fair and poor light-curve fits are provisionally divided into 14 FO (12 B and 2 C) and 55 FU (35 B and 20 C) pulsators. The pulsation properties of the RRL sample will be discussed in more detail in the next section.

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The sample of AC/spCs is quite abundant, populating the whole theoretical IS, and consists of 55 objects (Table 3), including two with uncertain or very uncertain periods (V212 and V241). Our sample also includes one possible Blazhko or multiple-mode anomalous Cepheid, V129. The evolutionary classification of these stars has been discussed in a companion paper (Fiorentino et al. 2012) and will not be repeated here, but in § 5 we will place some constraints on their masses and mode classification.

The spatial locations of all our variables are shown in Fig. 4. The (x,y) coordinates in this diagram are referred to an origin (0,0) that we have arbitrarily placed at 10^h08^m16^s.21 + 12°23^'05''.0 (close to the center of an early subset of our images). The y-axis is the great circle x = 0 and is equal to the great circle α = 10^h08^m16^s.21, and the x-axis is tangent to δ = +12°23^'05''.0 at the origin. The photocenter of Leo I has been estimated to lie at (α,δ) = (152.1125,12.30833333) (= 10^h08^m27^s.00 + 12°18^'30''.0) according to Mateo (1998); we ourselves estimate the center of Leo I to lie at 10^h08^m27^s.13 + 12°18^'22''.2[(x,y) = (+160.0,-282.8)], with an uncertainty of order 1'' in each coordinate. This estimate has been derived by determining the median x and y coordinates of probable member stars lying within a range of distances from the center, from 100'' to 850''; the consistency of these values provides our estimate of the uncertainty (see Stetson et al. 1998a, § 3.4). Fig. 4 shows that the RRLs, as representative very old stars, have a larger spatial extent than the younger, more massive stars that we presume the AC/spCs and LPVs to be; the latter appear more centrally concentrated. This supports the idea that AC/spCs in Leo I are of the same nature as those in the Large Magellanic Cloud (LMC), where ACs seem to result from both the intermediate-age stellar population and old binary systems (Fiorentino & Monelli 2012). This is consistent with our provisional classification of these stars as a mix of both ACs and spCs (see Fiorentino et al. [2012] for details).

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The Bailey diagrams are shown in Fig. 3 for the B (top) and V (bottom) photometric bands. As expected, the RRLs separate very cleanly into two different groups, the longer-period FU pulsators (log P ≳ -0.35, P ≳ 0.45 d: RRab or, to some researchers, RR0) and the shorter-period FO pulsators (log P ≲ -0.35: RRc, or RR1). These diagrams are very often used to give an indication of the Oosterhoff class. For this reason, in the V-band (bottom) panel we have also plotted the curves (Cacciari et al. 2005) representative of the Oosterhoff dichotomy shown by RRab stars in Galactic GCs. We note that most of the RRab stars seem to follow the OoI line, reaching a maximum A_V amplitude of about 1.2 mag. However, as discussed in (Fiorentino et al. 2012), based on the mean period of the RRab sample we have classified Leo I as Oo-intermediate, since 〈Pab〉 = 0.596 ± 0.001 d(σ = 0.05), based on only those stars with good light-curve fits. This result does not change when we include the RRab variables with fair or poor periods or when we add the RRc stars with fundamentalized periods (Coppola et al. 2013).

We have also calculated the ratio between the number of RRc and the total number of RRLs, which is considered another indicator of Oosterhoff class, N_c/(N_c + N_ab) = 28/164 ≈ 0.17. This value of the ratio includes the variable candidates with fair and poor light-curve fits; a slightly lower value, 14/95 ≈ 0.15, is obtained when it is based on only the good RRLs. We have a slight preference for the higher value, however, because the very classification "good,", "fair," and "poor" disproportionately assigns the lower quality classes to the c-type variables with their smaller amplitudes. Although those same smaller amplitudes probably mean that the c-type variables are more affected by incompleteness even if we ignore the quality classes, these very small values of the c-to-total ratio still suggest that it would be hard for us to have missed enough c-type variables to push Leo I out of the the OoI class. This conclusion is in line with what has been observed in other nearby dSph galaxies (see § 6 for details).

We take advantage of the good sampling of our light curves, in particular in the B and V bands, to estimate the mean amplitude ratios 〈A_V/A_B〉 = 0.825 ± 0.002 mag (σ = 0.20) and 〈A_R/A_V〉 = 0.763 ± 0.004 mag (σ = 0.24), based on 95 and 63 RRLs respectively (not all stars with A-quality data in B and V have good data in R). This A_V/A_B value is in full agreement with the value discussed in Di Criscienzo et al. (2011) based on 130 RRLs taken from nine GGCs.

4.1. Distance to Leo I from RRLs

In this section, we use the RRL pulsation properties to constrain the distance to Leo I. In particular, we use two independent methods: a linear formulation of the M_V versus [Fe/H] relation (Bono et al. 2003; Cacciari & Clementini 2003) and the first overtone blue edge (FOBE) method (Caputo et al. [2000] and references therein).

For the M_V versus [Fe/H] relation, we consider only the 81 RRab-type variables with light curves of quality class A ("good"), and we compare their measured properties to the following theoretical formulations:

and

(Bono et al. 2003). In order to use these formulae, we must assume a metal abundance for Leo I. Recent measurements of the galaxy's metallicity based on a large (∼850) sample of individual RGB stars studied with medium-resolution spectroscopy have provided a mean metallicity of [Fe/H] ∼ -1.43 (σ = 0.33 dex; Kirby et al. 2011). However, it is worth mentioning that Leo I seems to have a broad metallicity distribution, with iron abundances ranging from ∼-2.15 to ∼-1. RRLs being among the oldest and presumably the metal-poorest stars in a stellar system, we decided to derive two different distance moduli corresponding to both the average Leo I metallicity and the metal poor extreme. We found 〈V〉 = 22.648 ± 0.001 mag (σ = 0.11) for the RRL sample, and assuming E(B–V) = 0.02 mag,⁹ the two distance moduli turn out to be μ₀ = 22.06 ± 0.08 and 22.25 ± 0.07 mag for [Fe/H] = -1.43 and -2.15, respectively. These values are in good agreement with the distance modulus derived by Bellazzini et al. (2004) using the TRGB method¹⁰: μ₀ = 22.02 ± 0.13 mag, corresponding to a heliocentric distance .

Now we use the technique extensively discussed in Caputo et al. (2000), which is a graphical method based on the predicted period-luminosity (PL) relation for pulsators located along the FOBE. It seems quite robust for clusters with significant numbers of RRc variables and is thus applicable to Leo I. The distance modulus is derived by matching the observed distribution of RRc variables to the following theoretical relation:

Here, we assume the same two metallicity values for the RRLs in Leo I and adopt M = 0.7 M_⊙ from the evolutionary HB models for RRc variables, with an uncertainty of the order of 4% (Bono et al. 2003). The comparison between the observed RRLs and the theoretical relation is shown in Figure 5. Given the period-luminosity distribution of our RRc sample and the high uncertainty in the FOBE determination, we decided to use two possible FOBE evaluations, the first defined by the "good" RRc V85 and the other by V80, V141, and V214. Thus, the FOBE method returns a range of possible distance moduli, μ₀ = 21.96 (V85) to 22.14 (V80,V141,V214) assuming [Fe/H] = -2.15 and E(B–V) = 0.02 mag; these decrease by 0.04 mag when using the metal-rich stellar content (-1.43 dex). It is worth noting that the distance evaluation based on the FOBE defined by V85 gives a distance determination that is also in very good agreement with that given by the TRGB method (Bellazzini et al. 2004).

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In a previous paper (Fiorentino et al. 2012), we discussed the evolutionary classification of the Cepheid sample we have detected in Leo I. On the basis of a comparison with a set of evolutionary tracks at different metallicities ([Fe/H] ranging from -1.8 to -1.0) we have concluded that we are dealing with an unprecedented mix of ACs and spCs. In this section, we discuss the pulsation properties of this unique sample of variable stars.

In Figure 6, we show their distribution in the amplitude versus period diagrams in the B (top) and V bands (bottom). It seems clear that the sample can be divided into high and low-amplitude subsamples separated at A_B ∼ 1.1 and A_V ∼ 0.8, with the low-amplitude stars dominating for periods less than one day and the high-amplitude stars dominating at longer periods. Similar behavior seen in other classes of pulsating variables, e.g., RRLs, usually identifies a mode separation between the first overtone (lower amplitudes, shorter periods) and fundamental (higher amplitudes, longer periods) modes of pulsation. However, for ACs, the mode classification is far from trivial and cannot be easily linked to either the period-amplitude distribution or the morphology of the light curves, as discussed in Marconi et al. (2004).

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We note that observational uncertainties probably do not contribute much to the scatter of points in the amplitude versus period diagrams. For the 53 out of 55 candidates to which we have assigned quality class A, we feel that the amplitude uncertainties are probably not worse than 0.1 mag and the period uncertainties are probably not larger than 1% [σ(log P) ∼ 0.004]. These numbers are much smaller than the dispersion seen in Fig. 6. We conclude, therefore, that the spread is real and intrinsic to the stars themselves.

The distribution in the period-luminosity diagram might help in the mode classification. For this reason, in Fig. 7 we show the AC/spC distribution in the reddening-free (V, B–V) Wesenheit magnitude versus period plane. (We have chosen this color combination because the available B and V observations best sample the light curves, resulting in the most accurate mean magnitudes. Uncertainties of a few × 0.01 mag in the adopted mean B and V magnitudes for the stars lead to uncertainties ≲0.1 mag in the derived Wesenheit magnitudes.) For comparison, we have also shown the Wesenheit relations predicted by theoretical models for ACs assuming masses of 1.8 and 3.2 M_⊙ (Marconi et al. 2004; Fiorentino et al. 2006) and metallicities Z from 0.0001 to 0.0004, as well as those for Population II Cepheids (Di Criscienzo et al. 2004). We have assumed μ₀ = 22.11 ± 0.15 with a reddening of E(B–V) = 0.02 mag, values that were used by Fiorentino et al. (2012) to classify our sample of variable stars and that agree quite well with what is found using RRLs (see previous section). Our sample occupies the general region where ACs are expected without defining any tight sequence in this diagram. There are also no distinct subdistributions forming different sequences of AC/spCs such as are typically observed in other galaxies, where abundant samples of ACs (Fiorentino & Monelli 2012) and/or spCs (Bernard et al. 2013) show that both FU and FO pulsators are detected.

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To investigate this behavior, we again use the approach discussed in Fiorentino & Monelli (2012), one that allows us to identify the mode classification within the sample of ACs in the LMC released by OGLE III (Soszyński et al. 2008). This method, detailed in Caputo et al. (2004), returns simultaneously the mode and the pulsation mass for each individual AC. It is based on the use of a theoretically predicted mass- and luminosity-dependent relation between period and V-band amplitude (MPLA) for FU mode pulsators, which is not followed by pulsators in higher modes. Coupling this relation with the mass-dependent period-luminosity-color (MPLC) relation that exists for both modes, we will assign the FU pulsation mode only when the two masses agree within 1σ. We use the following relations:

predicts the visual amplitude from the period, luminosity, and mass for fundamental pulsators, and

predict the luminosity from the period, color, and mass for FU and FO pulsators. These have been derived in (Marconi et al. 2004), and can be inverted to yield

Our application of these equations produces the masses and the classifications given in Table 3 and summarized in Figure 8. In this figure we show the mass distribution (gray histogram) predicted for our sample based on the pulsation relations. This is to be compared with the very peaked mass distribution shown by ACs observed in the LMC. This confirms our interpretation that a continuous spread in masses in Leo I causes the dispersion shown in the Wesenheit plane (Fig. 7), whereas in the LMC you can perceive two distinct sequences in the same plane (Soszyński et al. 2008; Fiorentino & Monelli 2012).

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Three AC/spCs in Leo I show unreasonably high masses, larger than 5 M_⊙ (indicated with crosses in Figs. 6 and 7); in Fig. 7 these stars are the ones deviating the most from the global distribution in the Wesenheit plane due to their very short periods compared to other stars with comparable luminosities and colors. In particular, the star with the highest indicated mass, V241, belongs to our "very uncertain" class (C) and shows a very red color (B–V≥0.6), thus suggesting the possibility of problems in our magnitude, color and/or period determinations for this star. The other two stars, namely V133 and V203, show very small amplitudes (Fig. 6) suggesting that they might be slightly blended. A visual examination of these stars in our stacked image for Leo I suggests that a blending explanation for their anomalous masses is plausible, but not definite.

In Figures 9 and 10, we show the amplitude versus period diagrams (left) and the period histograms (right) for RRL and AC/spC stars in six dSphs ordered by increasing baryonic mass (McConnachie 2012), namely Draco (Kinemuchi et al. 2008), Carina (Coppola et al. 2013), Tucana (Bernard et al. 2009), Sculptor (Kaluzny et al. 1995), Cetus (Bernard et al. 2009; Monelli et al. 2012), and Leo I (this paper). In the top panel of each figure we have also shown all the RRLs and AC/spCs observed in the 11 UFDs surveyed for variability (Dall'Ora et al. 2006; Kuehn et al. 2008; Moretti et al. 2009; Musella et al. 2009; Dall'Ora et al. 2012; Musella et al. 2012; Clementini et al. 2012; Garofalo et al. 2013; Boettcher et al. 2013). For comparison, in Figure 9 we also show the two curves that trace the Oosterhoff dichotomy observed in Galactic GCs as defined by Cacciari et al. (2005). Lying in general between the two Oosterhoff curves, the ab-type RRL distributions for the classical dwarfs in the Bailey diagram are very similar to each other. The only (slight) exceptions are Cetus and Carina, which show a different slope in the period versus amplitude plane as discussed in Bernard et al. (2009) and Monelli et al. (2012). For most dSphs, the period distributions of RRab stars (right panels of Fig. 9) are quite peaked around their mean value with two exceptions, viz., Sculptor and Tucana. In Table 6 we have listed the mean properties of the RRLs according to the catalogs we have adopted; the mean RRab and RRc periods are the same within 1σ. In the last column, we have also listed the total masses and mean metallicities of these galaxies according to the references used in McConnachie (2012). The mean periods of RRLs in UFD galaxies seem to generally follow the same behavior as in classical dwarfs, occupying the same general location in the Bailey diagram with a slightly higher mean period for the RRab stars, very similar to that of Carina (Dall'Ora et al. 2003; Coppola et al. 2013). This suggests that, at least in terms of their RRL properties, there is not a significant difference between classical and ultrafaint dwarf galaxies.

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On the basis of their similar general properties, we decided to build up a single large sample of well-studied RRLs in those dwarf galaxies where the variability surveys do not seem to suffer from strong completeness problems, thus very likely describing the RRL properties of these stellar systems rather well. This initial sample contains 1,726 objects (with 1,299 ab-type variables); we included Cetus and Carina because their inclusion does not bias the mean properties of the sample nor change our final conclusions.

As discussed in Fiorentino et al. (2012), different conclusions result from an inspection of Figure. 10, where it is clear that the AC/spCs have different period distributions and Bailey diagrams. In particular, we note that the period distribution seems to move toward longer periods when the baryonic total mass of the galaxy increases (see Table 6). This is easily understood when one considers that the high masses typical of ACs (Fiorentino et al. 2012, 1.2 ≲ M/M_⊙ ≲ 2.1) may result from either or both the interactions of old binary stellar systems and single-star evolution in purely intermediate-age populations. Thus, their specific frequency could depend on the total mass of the host galaxy and on the relative importance of star formation events at intermediate ages (≲5 Gyr), as extensively discussed by Fiorentino & Monelli (2012).

Usually, the average properties of RRLs in individual dSphs and UFDs—such as the mean periods of both RRab and RRc stars—are compared to those observed in GCs as representative of the Galactic halo (Catelan [2009], Clementini [2010], and references therein). However, given their different total stellar masses, GCs typically host RRL populations of order a factor 10 smaller than those observed in dwarf galaxies, making a proper statistical comparison frequently difficult. Moreover, in the last 10 years or so, GCs have been demonstrated to be quite complex stellar systems despite what we previously believed in terms of their chemical enrichment histories (Gratton et al. 2004; Piotto et al. 2005; Milone et al. 2012; Monelli et al. 2013), and they may not fairly represent the properties of halo field stars. Even though the net effect of their complex histories on their global average chemical abundances (and therefore on the pulsation properties of their RRLs) may be negligible, this has not yet been demonstrated. Finally, although it seems trivial that the statistical meaning of averaged properties is, by definition, more significant when a large sample of objects is considered, we must remember that small number statistics become quite relevant in those galaxies with very few confirmed member RRLs, as is the case for most UFDs (Moretti et al. 2009; Musella et al. 2009; Dall'Ora et al. 2012; Clementini et al. 2012; Boettcher et al. 2013) where even the term "average" approaches meaninglessness.

The justification for our assembling a large sample of RRLs in classical and ultra-faint dSphs is driven in large part by the opportunity to compare directly, for the first time, their period and amplitude distributions with those of a huge RRL sample representing the Galactic halo. RRLs are ancient stars, older than 10 Gyr. Their younger selves were born during the early millennia of the Universe, and their testimony can provide important information about chemical evolution during the early stages of the assembly of the Galactic halo. Moreover, they are their own robust distance indicators and might also reveal details of the halo's spatial structure (Layden 1994; Kinemuchi et al. 2006; Drake et al. 2013; Zinn et al. 2014).

With this goal in mind, we have collected several catalogs—mainly on the basis of the availability of robust periods and reliable V-band amplitudes—that, taken together, provide about 14,000 RRab stars spanning distances from ∼5 to ∼80 kpc, namely the QUEST (Vivas et al. 2004; Zinn et al. 2014), Northern Sky Variability Survey (NSVS) (Woźniak et al. 2004), All Sky Automated Survey (ASAS) (Szczygieł et al. 2009) and CATALINA surveys (Drake et al. 2013). In cases where a star appeared in multiple surveys, we have retained only those data originating in the most recent and complete study available.

We have computed the three-dimensional Galactocentric position of each individual RRL, first converting (R.A., decl.) to (l, b) coordinates and then assuming for the stars in the very inner part of the Halo (d_G ≲ 7.5 kpc) a mean metallicity of [Fe/H] = -1.3 dex, while for the external part we used -1.6 dex, according to the metallicity gradient reported by Layden (1994). To account for the individual interstellar extinctions we have used the Schlegel et al. (1998) maps, following the prescription given in their website. Finally, we have applied the same magnitude versus metallicity relation for the RRLs as we used in § 4 for [Fe/H] > -1.6 dex (Bono et al. 2003), assuming a distance to the Galactic center of 7.94 kpc (Eisenhauer et al. 2003; Groenewegen et al. 2008; Matsunaga et al. 2011).

In our final catalog, we have not included the samples from Miceli et al. (2008) and Sesar et al. (2013) because amplitudes on their filterless magnitude system must be transformed into V (Landolt) amplitudes using a metallicity and temperature-dependent scale factor that could affect the stars' apparent distribution in the Bailey diagram. On the other hand, we do include the CATALINA sample, while acknowledging that it has a bias in amplitudes; we retain only RRLs with amplitudes A_V larger than 0.4 mag. However, this is the largest, deepest, and most homogeneous catalog at our disposal, and its known bias turns out to have a negligible effect on the following discussion. Finally, we use only ab-type RRLs because they are less affected by both time-sampling and completeness problems. Although not 100% complete, this final huge catalog will allow us to make the most comprehensive analysis of the Galactic halo using field RRLs possible so far.

In order to draw the most complete global view of the globular clusters belonging to the Galactic halo, we have decided to exclude all the RRLs listed in the updated catalog of Clement et al. (2001) that are observed in GCs belonging to the Galactic bulge, i.e., those having both Galactocentric distance d_G ≤ 5 kpc and distance from the Galactic plane Z ≤ 1.5 kpc. Two exceptions to this rule are M62 (NGC 6266) and M28 (NGC 6626) that—even if projected onto the bulge region (Harris 1996)—cannot be considered representative of the bulge population (Casetti-Dinescu et al. [2013] and references therein). We have also excluded NGC 2419 because it is located in a region of the halo not well covered by the field-star surveys considered here. Finally, we have included only GCs for which CCD photometry in V, including amplitudes, is available. The full sample consists of 1,617 RRLs (1,054 ab-type) residing in 35 GCs (see Table 7).

In Figure 11, we show the distributions of RRab stars in period-amplitude diagrams (left) and period histograms (right) for the full set of catalogs we have collected. The first four panels are devoted to the Galactic halo divided into four nonoverlapping regions: (1) the inner halo a, consisting of stars with d_G ≤ 7.5 kpc (Fig. 11a); (2) the inner halo b, stars with 7.5 ≲ d_G ≲ 14 kpc (Fig. 11b); (3) the outer halo a, stars with 14 ≲ d_G ≲ 30 kpc (Fig. 11c); 4) the outer halo b, stars with d_G ≳ 30 kpc (Fig. 11c). The boundary between inner and outer halo (d_G ≳ 14 kpc) has been chosen according to Kinman et al. (2012), whereas the other reference distances are arbitrary. In the last two panels, we have plotted the full distributions obtained for GCs (Fig. 11e) and UFDs+dSphs (Fig. 11f). As in Fig. 9, we have overplotted the Oosterhoff curves given by Cacciari et al. (2005). The average of their two curves (Fig. 11, blue dashed curve) allows us to roughly separate the two populations of OoI (large dots) and OoII (small dots) RRLs. We have computed the ratio between OoI and the total number of RRLs, as given in the last column of Table 7. These numbers are very similar to each other and they are compatible with a global OoI classification, in agreement with recent and independent results from the Robotic Optical Transient Search Experiment (ROTSE) (Miceli et al. 2008) and Lincoln Near-Earch Asteroid Research (LINEAR) (Sesar et al. 2013) surveys.

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We have also used these data to compute the mean periods of the RRLs with log P≥-0.35 (Table 7), and find that 〈Pab〉 is the same within the standard deviations of the distributions. Again, the mean properties of the different RRab samples seem virtually indistinguishable from this statistical point of view.

To compare these distributions in more rigorous detail, we have performed two more sophisticated statistical analyses. The first is a χ² test on the histograms smoothed with a Gaussian filter (Fig. 11, blue solid curves), and the second is a Kolmogorov–Smirnov test applied to the cumulative period distributions (Fig. 12). For the purposes of these last two tests, only, we take advantage of the large sample of RRLs in the Large Magellanic Cloud that has been provided by the OGLE project (17,693 stars; Soszyński et al. 2009). Although the RRLs in the LMC have been surveyed in the I band by OGLE, we decided to attempt to match the amplitude bias of the CATALINA sample by using only those stars with A_I≥0.26 mag. This corresponds to a scale factor A_V/A_I = 1.58 as found by Di Criscienzo et al. (2011). These two statistical tests returned very similar results, which are listed in Table 8 and can be summarized as follows:

• Inner halo a and b have a likelihood of 30% of being drawn from the same parent populations. This likelihood increases dramatically to 90% when only the CATALINA survey is considered. As shown in Figure 11, these two regions show broad period distributions including the longest-period RRLs.
• Outer halo a and b do not share a common period distribution, with each other or with the inner halo. Each component of the outer halo seems to have a more peaked distribution than that of the inner halo. In particular, outer halo b seems to show a relative deficiency of RRab stars with high amplitudes and short periods (hereinafter, "HASP"). This can not be attributed to a completeness effect because large amplitudes are the easiest ones to detect.
• The GC period distribution mildly resembles that of the RRLs in the inner halo (within ∼14 kpc, a + b). This is reasonable when we consider that 23 out of the 35 GCs considered here belong to this region. We note that this result must be viewed as preliminary because: (1) the GC period distribution strongly depends on the choice of GCs included in the full catalog; (2) GCs have their own space motions that may eventually tell us more about the halo region to which they belong, rather than where they happen to be currently located.
• The UFD+dSph distribution is quite different from the others. It is very peaked around the mean period (Table 7). In particular, this distribution is quite lacking in HASP RRab stars compared to the others: none ¹¹ of the RRLs in dwarfs with high amplitude (A_V≥1.0) reaches periods P ≲ 0.48 d (log P ≲ -0.32). Fundamental-mode RR Lyraes with large amplitudes and periods less than 0.48 d are quite common both in globular clusters and in the halo field. Even the relative deficiency of HASP RRab stars in outer halo b already noted above is not as complete as in the UFD+dSph sample. It is true that at the other extreme, UFDs are seen to help in filling out the long-period tail (cf. Fig. 9a) but—within the limited statistics available—they do not appear to contribute to the short-period tail.
• We find a very low formal likelihood that the LMC sample matches any of the others (Table 8), as is also true for classical dSphs and UFDs. We note here, though, that this result may be affected by the very high temporal and photometric completeness of the OGLE sample for the LMC. In other words, when huge samples are available (as they are here for the LMC and the Milky Way halo), any minor difference in selection biases achieves very high statistical significance and can be mistaken for a real physical difference between the samples. A fair comparison with the LMC sample needs much more complete RRL surveys of the Galactic halo. The same consideration is relevant to the recent result discussed by Zinn et al. (2014) where, on the basis of the OGLE (Soszyński et al. 2009) and their own QUEST RRL samples, the authors declined to exclude the possibility that the smooth Galactic halo may have formed from a combination of LMC-like and Sagittarius-like galaxies. We believe—but are unable to prove—that because our comparisons between the halo, the GCs, and UFD+dSphs are based on samples closer in size, and probably with selection effects more nearly similar to each other than to the OGLE LMC sample, our conclusions regarding the statistical significance of their differences are probably more reliable than similar conclusions relating to the LMC.

Perhaps it is worthwhile to remind the reader that the dwarf galaxies in the Milky Way halo contain stellar populations with some range of ages and metallicities. The classical globular clusters as a class exhibit a broad range of metallicities (-2.5 < [Fe/H] < 0.0, roughly speaking), and a rather limited range of age. The Milky Way field halo also clearly has a broad range of metal abundances, but we have less information as to its range of age. The range of metal abundance in the dwarf galaxies is somewhat narrower than among the GCs, [Fe/H] ≲ -1 or so, but some—including Leo I, Carina, and Fornax, for example—have very broad ranges of age, much greater than the range found among the GCs.pasp_126_941_616tb8

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However, it must also be remembered that the range of age and metal abundance that is conducive to the formation of RR Lyraes is more restricted: the most metal-rich globular clusters contain no RR Lyraes, and the most metal-poor contain few, while moderately metal-poor clusters contain the most. Populations younger than ∼10 Gyr probably cannot produce RR Lyraes by the normal evolution of single stars. The range of metallicities where the globular clusters and the field halo are proficient at producing RR Lyraes, -1.0 ≲ [Fe/H] ≲ -2.0, is very well represented in the dwarf galaxies, and, as we have just mentioned, stars in the dwarf galaxies have—if anything—a broader range of age than those in the globular clusters and the field halo. That being the case, it is remarkable that there exists a class of RR Lyrae star that is present in the globular clusters and the field halo and absent in the dwarf galaxies. One would think that if there were some odd corner of age-metallicity space that is capable of making a particular class of RR Lyrae stars, but is not populated among the globular clusters, that niche would be more likely to be occupied in the dwarf galaxies: if anything, the dwarf galaxies should have more varieties of RR Lyrae stars than the globular clusters, not fewer.

One possible exception to this rule might be if the HASP RR Lyrae stars were uniquely the progeny of stellar collisions or merged gravitational-capture binaries; such stars could then be present in the globular clusters and not in the much sparser dwarf galaxies. But if this is the case, then why are these "special" RR Lyraes also found in the field halo, in roughly the same relative numbers as in the globular clusters? To be consistent, this explanation would suggest that a major fraction of the field halo stars came from globular clusters that were disrupted recently, i.e., only after the globular clusters had had enough time to produce the usual numbers of stellar collisions and gravitational-capture binaries. But even this seems highly unlikely, since halo field red giants do not show the light-element (C, N, O, Na, Mg, Al, etc.) correlations and anticorrelations found among the globular cluster giants.

In conclusion, and for the sake of argument, let us assume that in the early days of the Galactic halo, star formation occurred in one fundamentally indistinguishable family of structures, ranging in mass, that all underwent a common process of internal chemical evolution. During this time the young main sequence stars that grew into today's RR Lyraes were born. During subsequent dynamical evolution most of these structures dissolved or were disrupted, releasing the globular clusters and field stars of today's Galactic halo. At the same time a few of those structures—by random chance—survived, continued evolving internally, and became the classical dSph and UFD galaxies that we see today.

It seems that on the basis of the available RRL samples we can say that this scenario is not supported. Neither the inner (d_G ≲ 14 kpc) nor the outer (d_G ≲ 14 kpc) regions of the Galactic halo, nor any linear combination of the two, can be formed simply from the progenitors of today's classical dSph or UFD galaxies. If present in sufficient numbers, structures like those that became today's UFDs may have contributed to the long-period tail of the Galactic halo RRL period distribution, but—barring a major statistical fluke—neither they nor the dSph progenitors appear to have been capable of producing the kind of main sequence stars that became the HASP RRab variables now found in significant numbers throughout the Galactic halo and in the globular clusters.

Unless it can be shown that a protracted residence within the environment of a dSph or UFD galaxy can somehow alter the internal structure and evolution of an isolated star between the main sequence and RR Lyrae phases of its life, it seems that the simple model—where the dSphs and UFDs are surviving examples of representative protohalo fragments—is disfavored. Instead, it seems that at the time when the future RR Lyrae stars were being born, the milieux that were halo-to-be or UFD/dSph-to-be were already different in some way. In other words, the progenitors of the Milky Way halo and of the surviving dwarf galaxies appear to have been different, nonrepresentative subsamples of the proto-Galactic material, perhaps coming preferentially from distinct ranges of mass or kinematic properties, possessing different typical ratios of baryonic to dark matter, or being distinguished in some other relevant characteristic. Furthermore, the RRLs within the Galactic halo itself seem to have different period distributions when our consideration moves from the inner to the outer regions. This argues that the halo is itself formed from at least two different classes of progenitor or distinct, nonrepresentative subsamples of a continuum of progenitors (Chiappini et al. 2001), as confirmed by kinematical surveys (Carollo et al. 2007; Kinman et al. 2012).

As was pointed out by an astute referee, there is now good evidence that all the known dSph and UFD galaxies—except Hercules—and the "young halo" globular clusters are distributed on a thin, rotationally supported planar structure containing the Galactic poles (the VPOS: vast polar structure; Pawlowski et al. 2012; Pawlowski & Kroupa 2013). It seems far more likely that the VPOS and the distinct star systems located within it result from the disruption of a single infalling object, rather than from the isotropic accretion of a large number of smaller structures. This interpretation is inconsistent with the predictions of classical ΛCDM models for the formation of the halo in its entirety, but is consistent with our inference that the progenitor(s) of the UFD and dSph galaxies were different from the progenitor(s) of the Milky Way field halo stars and normal globular clusters.

As a final remark, since GCs represent only a small fraction of the Galactic halo, and because we now recognize that their histories were probably more complicated than we used to think—and are still not really understood—we would like to suggest that their continued use as representative tracers of the Galactic halo is not necessarily preferable to other comparisons that are now becoming possible.

We plan to extend this work to other dwarf spheroidal and irregular galaxies that are being studied within the homogeneous photometry project; we expect this will provide an opportunity to further test our conclusions.

Leo I was previously surveyed for bright variable stars by Hodge & Wright (1978), who identified candidate anomalous Cepheids and RR Lyraes, and by Menzies et al. (2002), who identified candidate long-period variables.

Hodge & Wright did not publish coordinates for their stars, but they did provide a finding chart. We extracted a JPEG version of their finding chart from the online electronic edition of their article and converted it to FITS format. Using a slightly modernized version of the Stetson (1979) software for astrometry and photometry from digitized photographic plates, we measured the positions of stars within the Hodge & Wright finding chart. We then used quadratic equations to transform those positions to the coordinate system of our Leo I catalog. We were able to match 355 stars within a tolerance of 4'' (the rms residuals were 0''.45 in right ascension and 0''.37 in declination). We were then able to geometrically transform their finding chart and overlay it on our stacked digital image of Leo I. Overall, we feel we are able to recover positions from the Hodge & Wright finding chart with a precision better than 0''.5. We considered stars within several arcseconds of each of the positions indicated in the published chart, basing our identification on (in order of decreasing importance) (1) evidence of variability in our data, (2) relative proximity to the indicated position, and (3) similarity of the mean B-band magnitude. We summarize our resulting cross-identifications in Tables 2 (RR Lyrae stars), 3(AC/spC stars), and 9(stars whose variability we are unable to confirm).

Notes on individual stars:

• The tick marks for HW1 in their chart enclose nothing but blank sky in our image. However, there are two of our variable candidates within 5'' of this position: V66 is a candidate long-period variable with 〈B〉 ≈ 22.1 lying 4''. 2 from the predicted position, and V59 is an AC/spC with P = 1.49328 d, 〈B〉 ≈ 20.7 lying 4''.8 from the predicted position. Despite its greater offset, the latter star more closely resembles HW1 and we accept it as the match.
• HW2 has no detectable star in our image within the tick marks on the finding chart. There is a spot of fuzz most likely representing a galaxy about 1'' southwest of the indicated position, but this is probably too faint to have been detected in Hodge & Wright's photographic material. One of our AC/spC candidates does lie almost 6'' (>10σ) from the indicated position. Since it has approximately suitable period and magnitude, we provisionally make this identification despite the large offset.
• HW20 has at least eleven stars lying closer to the indicated position than our adopted match, but the one we have chosen is clearly the most suitable on the basis of its mean B-band magnitude, and furthermore its Welch/Stetson variability index is not far below the detection threshold that we had imposed. This star may be variable, but we are not confident enough to claim definite confirmation.

Menzies et al. (2002) did not publish a finding chart for their five stars in Leo I. They did publish a table of equatorial coordinates for five luminous red stars in the galaxy field, but unfortunately we have not been able to find any relationship whatsoever between those coordinates and reality: we have marked their coordinates on our digital image of Leo I and we have also marked all the stars that are both luminous and red in our catalog, and we are not able to recognize any correspondence between the two patterns. For example, their stars A and B constitute a pair separated by 29''. 7, slightly inclined with respect to the east-west direction. We have examined our list of luminous red stars for pairs separated by ∼30'', slightly inclined to the east-west direction, and do find a few, but when we accept any of those provisional matches none of the other three stars from Menzies et al. coincides with anything interesting.

Azzopardi et al. (1986) published a finding chart identifing several luminous, red stars in Leo I, and we give cross-identifications with our catalog in Table 10.

As we were reviewing the galley proofs for this article, we were alerted to the fact that we had overlooked a more recent and more complete investigation of the luminous red stars of Leo I by Menzies et al. (2010). This oversight was a mistake on our part. The larger sample (62) of luminous non-variable and variable AGB candidates in this paper does allow us to unambiguously correlate their catalog with ours, with positional agreement of order 1''. A transit table relating their identifications to ours will be provided at our website.