The ISLAnds Project. III. Variable Stars in Six Andromeda Dwarf Spheroidal Galaxies^*

RRL stars are low-mass (∼0.6–0.8 ${M}_{\odot }$) and radially pulsating variable stars with periods ranging from 0.2 to 1.0 day and V amplitudes from 0.2 to ≲2 mag. They are found in stellar systems that host an old (t > 10 Gyr) stellar population (Walker 1989; Smith 1995; Catelan & Smith 2015). A total of 870 RRL stars were detected and characterized in the six ISLAndS galaxies. Table 4 summarizes for each galaxy, the number of fundamental (RRab), first-overtone (RRc), and double-mode (RRd) pulsators in both the ACS and WFC3 fields of view. Different types of RRL stars are usually easy to classify on the basis of a visual inspection of the LC and the period. RRab stars are characterized by longer periods (∼0.45–1.0 days) and saw-tooth LCs, with a steep rise up to the maximum and a less steep fall to the minimum. RRc have shorter periods (∼0.2–0.45 days), lower amplitudes (${A}_{V}\lesssim 0.8$), and almost sinusoidal light variations. Conversely, RRd stars usually have periods around 0.4 day, and their LCs are particularly noisy due to simultaneous pulsation in the fundamental mode and first overtone. Figure 5 presents an example RRL LC for each galaxy. Black and gray points are used for data in the $F475W$ and $F814W$ passbands, respectively. Open symbols are used to indicate outlier measurements that have not been taken into account in deriving the pulsational properties. We emphasize that the whole set of LCs is available in the electronic edition of this paper. Additionally, the properties of the individual variable stars can be found in Appendix D.

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Figure 6 presents the period–amplitude (Bailey) diagram for the six galaxies (see caption for details). The plot shows the two different relations for the Oosterhoff types, represented in the plot by the dashed lines (Oosterhoff I and II, or Oo-I and Oo-II Cacciari et al. 2005). As has long been known (Oosterhoff 1939, 1944), the properties of RRab stars divide Galactic GCs into two groups, called Oosterhoff I and Oosteroff II. The mean period of fundamental pulsators of the former group is shorter (P ∼ 0.55 day) than in the latter (P ∼ 0.65). Although the origin of this behavior has not been fully explained, the Oosterhoff dichotomy appears to be related to the metallicity of the clusters, where the Oo-II stars are more metal-poor, on average (e.g., see the review by Catelan 2009). On the other hand, dwarf galaxies do not show a similar behavior, as the mean period of their RRab stars typically locates them in the Oosterhoff gap between the two Oostherhoof groups. For this reason, they have often been considered as Oosterhoff-intermediate types (see e.g., Kuehn et al. 2008; Bernard et al. 2009, 2010; Garofalo et al. 2013; Stetson et al. 2014; Cusano et al. 2015; Ordoñez & Sarajedini 2016).

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Table 5 summarizes the mean pulsational properties for the galaxies in our sample: the mean periods of RRab-type ($\langle {P}_{\mathrm{ab}}\rangle$) and RRc-type ($\langle {P}_{c}\rangle$) stars, the fraction of RRc (f_c) and of RRc+RRd (f_cd) stars, the fraction of Oo-I-like and Oo-II-like stars (defined below in this section), and the apparent mean magnitude in V band (which we use in Section 6 to determine the distance to the galaxy). From the information in the table, the six ISLAndS galaxies could also be considered Oosterhoff-intermediate, since they have $\langle {P}_{\mathrm{ab}}\rangle \sim 0.6$ day. In this respect, the ISLAndS galaxies are similar to the MW dSph satellites. However, an intermediate mean period does not mean that the stars are distributed in the Bailey diagram between the two typical Oosterhoff lines. Figure 6 clearly shows that stars tend to clump around each Oosterhoff group locus, and with a predominance of Oo-I like stars. In fact, if we split the sample using the dotted intermediate line and classify stars as Oo-I like or Oo-II like according to their relative position with respect to this separator, four galaxies (And I, II, III, and XV) present a majority (∼80%) of Oo-I like stars (see Table 6). In the case of And I and II, the same result was found for the variable stars in the parallel WFC3.

Table 5.  Mean Properties of the RRL Stars

Galaxy	$\langle {P}_{\mathrm{ab}}\rangle$	$\langle {P}_{c}\rangle$	fc	fcd	% Oo-I	% Oo-II	$\langle {m}_{V}\rangle$
And I	0.597 ± 0.004 (σ = 0.07)	0.343 ± 0.005 (σ = 0.03)	0.17	0.23	80	20	25.13
And II	0.601 ± 0.005 (σ = 0.07)	0.332 ± 0.006 (σ = 0.04)	0.20	0.25	80	20	24.78
And III	0.622 ± 0.004 (σ = 0.03)	0.344 ± 0.011 (σ = 0.04)	0.15	0.24	89	11	25.04
And XV	0.608 ± 0.006 (σ = 0.05)	0.360 ± 0.009 (σ = 0.04)	0.23	0.32	78	22	25.07
And XVI	0.636 ± 0.010 (σ = 0.02)	0.356 ± 0.019 (σ = 0.04)	⋯	⋯	67	33	24.34
And XXVIII	0.624 ± 0.012 (σ = 0.07)	0.359 ± 0.007 (σ = 0.04)	0.50	0.59	49	51	25.14

Note. Mean periods are given in days. The definition of f_c is $\tfrac{{Nc}}{{Nab}+{Nc}}$, while f_cd is defined as $\tfrac{{Nc}+{Nd}}{{Nab}+{Nc}+{Nd}}$.

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Table 6.  Properties of the Set of RRL Stars in a Sample of 41 LG Dwarf Galaxies of Different Morphological Type within ∼2 Mpc, with at Least Five RRab and with Data Available in the Literature

			RRab				$\langle {P}_{\mathrm{ab}}\rangle$		$\langle {P}_{\mathrm{cd}}\rangle$
Galaxy	$\langle [\mathrm{Fe}/{\rm{H}}]\rangle$ a	RRab	%OoI	%OoII	RRcd	fcd	Median	Mean	Median	Mean	References
MW dwarf satellites
Ursa Major I	−2.18	5	60	40	2	0.29	0.600	0.628 ± 0.031(0.07)	0.407	0.402 ± 0.005(0.008)	Garofalo et al. (2013)
Bootes I	−2.55	7	43	57	8	0.53	0.680	0.691 ± 0.034(0.09)	0.386	0.364 ± 0.016(0.04)	Siegel (2006)
Hercules	−2.41	6	0	100	3	0.33	0.678	0.678 ± 0.013(0.03)	0.400	0.399 ± 0.002(0.003)	Musella et al. (2012)
Canes Venatici I	−1.98	18	72	28	5	0.22	0.610	0.604 ± 0.006(0.03)	0.390	0.378 ± 0.012(0.03)	Kuehn et al. (2008)
Draco	−1.93	211	87	13	56	0.21	0.608	0.615 ± 0.003(0.04)	0.401	0.389 ± 0.004(0.03)	Kinemuchi et al. (2008)
Ursa Minor	−2.13	47	45	55	35	0.43	0.648	0.638 ± 0.009(0.06)	0.383	0.375 ± 0.011(0.07)	Nemec et al. (1988)
Carina	−1.72	71	73	27	12	0.15	0.630	0.634 ± 0.005(0.05)	0.364	0.350 ± 0.013(0.04)	Coppola et al. (2015)
Sextans	−1.93	26	62	38	10	0.28	0.596	0.606 ± 0.010(0.05)	0.352	0.355 ± 0.019(0.06)	Mateo et al. (1995)
Leo II	−1.62	106	63	37	34	0.24	0.615	0.619 ± 0.006(0.06)	0.370	0.363 ± 0.008(0.05)	Siegel & Majewski (2000)
Sculptor	−1.68	289	56	44	247	0.46	0.593	0.610 ± 0.006(0.10)	0.355	0.346 ± 0.002(0.04)	Martínez-Vázquez et al. (2016b)
Leo I	−1.43	136	74	26	28	0.17	0.591	0.599 ± 0.005(0.06)	0.367	0.352 ± 0.007(0.04)	Stetson et al. (2014)
Fornax	−0.99	998	84	16	445	0.31	0.594	0.595 ± 0.001(0.05)	0.380	0.379 ± 0.001(0.07)	Fiorentino et al. (2017)
Sagittarius	−0.40	1636	79	21	409	0.20	0.576	0.575 ± 0.002(0.07)	0.322	0.319 ± 0.002(0.04)	Soszyński et al. (2014)
SMC	−1.00	4961	83	17	1407	0.22	0.598	0.598 ± 0.0008(0.06)	0.366	0.360 ± 0.001(0.04)	Soszyński et al. (2016)
LMC	−0.50	27620	75	25	11461	0.29	0.576	0.580 ± 0.0004(0.07)	0.339	0.333 ± 0.000(0.04)	Soszyński et al. (2016)
M31 dwarf satellites
And XIII	−1.90	8	63	37	1	0.11	0.616	0.648 ± 0.026(0.07)	0.4287	0.4287	Yang & Sarajedini (2012)
And XI	−2.00	10	70	30	5	0.33	0.626	0.621 ± 0.026(0.08)	0.428	0.423 ± 0.013(0.03)	Yang & Sarajedini (2012)
And XXVIII	−1.73	35	49	51	50	0.59	0.622	0.624 ± 0.012(0.07)	0.366	0.361 ± 0.005(0.04)	This work
And XVI	−1.91	3	67	33	5	0.63	0.640	0.636 ± 0.010(0.02)	0.358	0.356 ± 0.019(0.04)	This work
And XIX	−1.80	23	44	56	8	0.26	0.616	0.618 ± 0.007(0.03)	0.401	0.392 ± 0.010(0.03)	Cusano et al. (2013)
And XV	−1.80	80	76	22	37	0.32	0.608	0.608 ± 0.006(0.05)	0.366	0.364 ± 0.006(0.04)	This work
And XXV	−1.80	45	67	33	11	0.20	0.608	0.607 ± 0.007(0.05)	0.370	0.363 ± 0.010(0.03)	Cusano et al. (2016)
And XXI	−1.80	37	49	51	4	0.10	0.619	0.638 ± 0.010(0.06)	0.387	0.343 ± 0.028(0.06)	Cusano et al. (2015)
And III	−1.81	84	89	11	27	0.24	0.620	0.623 ± 0.004(0.03)	0.375	0.375 ± 0.012(0.06)	This work
And VI	−1.30	91	87	13	20	0.18	0.587	0.588 ± 0.006(0.05)	0.386	0.382 ± 0.009(0.04)	Pritzl et al. (2002)
And I	−1.44	229	80	20	67	0.23	0.588	0.597 ± 0.004(0.07)	0.353	0.349 ± 0.004(0.03)	This work
And II	−1.30	187	80	20	64	0.26	0.600	0.601 ± 0.005(0.07)	0.350	0.341 ± 0.005(0.04)	This work
And VII	−1.40	386	75	25	187	0.33	0.571	0.578 ± 0.003(0.06)	0.342	0.338 ± 0.003(0.04)	Monelli et al. (2017)
NGC 147	−1.10	118	70	30	59	0.33	0.577	0.589 ± 0.008(0.09)	0.331	0.325 ± 0.006(0.05)	Monelli et al. (2017)
NGC 185	−1.64	544	63	37	276	0.34	0.580	0.587 ± 0.004(0.09)	0.325	0.322 ± 0.003(0.04)	Monelli et al. (2017)
M32	−0.25	314	80	20	102	0.25	0.564	0.569 ± 0.005(0.08)	0.324	0.323 ± 0.004(0.04)	Fiorentino et al. (2012)
Isolated dwarf galaxies
Tucana	−2.00	216	68	32	142	0.40	0.597	0.604 ± 0.004(0.06)	0.370	0.367 ± 0.003(0.03)	Bernard et al. (2009)
Phoenix	−1.37	95	70	30	26	0.21	0.592	0.602 ± 0.007(0.06)	0.360	0.363 ± 0.014(0.07)	Ordoñez et al. (2014)
LGS3	−2.10	109	69	31	24	0.18	0.607	0.616 ± 0.007(0.07)	0.372	0.360 ± 0.011(0.05)	C. E. Martínez-Vázquez et al. (2018, in preparation)
DDO 210	−1.30	24	92	8	8	0.25	0.606	0.609 ± 0.010(0.05)	0.374	0.359 ± 0.027(0.08)	Ordoñez & Sarajedini (2016)
Cetus	−1.90	506	83	17	124	0.20	0.610	0.613 ± 0.002(0.04)	0.389	0.381 ± 0.003(0.04)	Monelli et al. (2012)
Leo A	−1.40	7	71	29	3	0.30	0.625	0.637 ± 0.014(0.04)	0.372	0.366 ± 0.017(0.03)	Bernard et al. (2013)
IC1613	−1.60	61	64	36	29	0.32	0.606	0.611 ± 0.010(0.08)	0.349	0.339 ± 0.006(0.03)	Bernard et al. (2010)
NGC 6822	−1.00	24	83	17	2	0.08	0.603	0.605 ± 0.007(0.04)	0.406	0.388 ± 0.019(0.03)	Baldacci et al. (2005)
Sculptor Group dwarf galaxies
ESO410-G005	−1.93	224	66	34	44	0.16	0.578	0.589 ± 0.005(0.07)	0.327	0.317 ± 0.010(0.06)	Yang et al. (2014)
ESO294-G010	−1.48	219	62	38	13	0.06	0.589	0.593 ± 0.004(0.06)	0.345	0.330 ± 0.017(0.06)	Yang et al. (2014)

Note.

^aMean metallicity for each galaxy obtained from McConnachie (2012).

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And XXVIII is the exception, with a fraction of Oo-I like stars close to 50%. Moreover, the distribution of RRLs in the Bailey diagram is also different from the other And dSphs; the RRab stars show a broad spread and are not concentrated on either Oosterhoff line. And XXVIII is also peculiar for the large fraction of RRcd-type stars, which represent ∼58% of the total. In the LG, if we exclude low-mass galaxies with very small samples of RRLs (<15, such as Bootes I and And XVI, see Section 5.2), And XXVIII is the only galaxy with more RRcd-type than RRab-type stars. Similar to And XXVIII, the galaxies with a particularly large fraction of RRcd (Ursa Minor: 43%, Nemec et al. 1988; Sculptor: 46%, Martínez-Vázquez et al. 2016b; Tucana: 40%, Bernard et al. 2009) are all also characterized by the presence of a strong blue HB component. This may be connected to a sizable population of very metal-poor stars.

The black vertical line in Figure 6 marks the limit of the high-amplitude short-period (HASP) region, defined by Fiorentino et al. (2015) as those RRab stars with periods shorter than 0.48 day and amplitudes in the V band larger than 0.75 mag. These stars are interpreted as the metal-rich tail of the metallicity distribution of RRL stars ([Fe/H] > −1.5), and have only been found in systems that were dense or massive enough to enrich to this metallicity before 10 Gyr ago (Fiorentino et al. 2017). We confirm this trend with the six ISLAndS galaxies, as HASPs have only been detected in the two most massive satellite galaxies: And I (3)²⁰ and And II (2). A detailed analysis of the chemical properties of RRL stars will be discussed in a forthcoming paper.

It is worth noting that a few stars with HASP properties were already identified in the catalogs by Pritzl et al. (2004) and Pritzl et al. (2005) for And II and And I, respectively. In the case of And I, we confirm the HASP nature of three out of the seven stars, while the period was likely underestimated for the other four, possibly due to aliasing (see Appendix C). However, we do not confirm any of the eight HASP stars in And II (see Appendix C for a detailed comparison with literature values). Nevertheless, we discovered two new HASPs in And I and two in And II, which are both located outside the WFPC2 field studied by Pritzl et al. (2004, 2005).

Five RRLs in And I have mean magnitudes that are a few tenths of a magnitude fainter than the HB (three RRab: AndI-V053, AndI-V110 and AndI-V113; and two RRc: AndI-V257 and AndI-V280). We exclude the possibility that sampling problems of the LC may be causing a bias toward fainter magnitudes. Possible explanations are (i) a significantly higher metal content, or (ii) a distance effect. Assuming they are at the distance of And I, in order to explain such a faint luminosity (0.45 mag fainter), a super solar metallicity is required. This value appears to be unlikely given the morphology of the CMD and the SFH (Skillman et al. 2017).

On the other hand, as indicated in the previous section, the CMD of And I shows that a significant contamination by the GSS is present along the line of sight to And I. In particular, And I is projected on the GSS "Field 3" studied by McConnachie et al. (2003), which is located at 860 ± 20 kpc according to the TRGB determination. To verify whether the faint RRL stars can be associated with the GSS, we first note that two of the three RRab are HASP RRL stars. This suggests that their metallicity is likely to be higher than −1.5 dex. Assuming [Fe/H] = −1.5 and using the PWR described in Section 6.2, we obtain a mean distance modulus of ${\mu }_{0}=24.86$ mag (sys = 0.08; rand = 0.11) for the five stars, corresponding to 937 kpc (sys = 34; rand = 47). This means that they are likely located ∼140 kpc beyond And I (${d}_{\odot }\sim 800\,\mathrm{kpc}$, see Section 6). Given the error bars, we conclude that the five faint RRL stars are compatible with being connected to the metal-poor component of the GSS (Gilbert et al. 2009) rather than members of And I.

Pioneering works by Da Costa et al. (1996, 2000, 2002) based on shallower WFPC2 data disclosed the first hint that the M31 satellites are characterized by a redder HB morphology than MW dwarfs. A similar conclusion was reached by Martin et al. (2017), based on ACS data for 20 M31 galaxies. The analysis was based on a morphological index accounting for the number of blue and red HB stars. In this section we apply a similar approach, and taking advantage of the known number of RRL stars, we can compare the morphology index R_HB²¹ of the six ISLAndS galaxies and of a sample of MW satellites. The latter consists of revised data for Carina, Fornax, Sculptor, Draco, and Leo II from the updated catalogs available in P. B. Stetson's database (P. B. Stetson 2017, private communication). These studies are part of an ongoing series of papers on variable stars in GCs and dwarf galaxies by ourselves and our collaborators (Stetson et al. 2014; Braga et al. 2015, 2016; Coppola et al. 2015; Martínez-Vázquez et al. 2016b; Fiorentino et al. 2017).

The value of the R_HB index was calculated in a homogeneous way considering only stars within one half-light radius, r_h. This was possible for all of the galaxies except for And I and II, since the ACS only covers a fraction of such area (see Figure 3). In the case of the MW satellites, we estimated and subtracted the Galactic field-star contribution using a proper control field in the outskirts of each object. The exact limits in color and magnitude for the selection of HB stars for the R_HB index were defined on a per-galaxy basis because of the variety of CMD morphology, filter bandpasses, and foreground contamination. However, these were carefully chosen to limit contamination from any RGB, AGB, RC, and blue straggler populations present, while also avoiding biases.

Figure 7 shows, as a function of the host galaxy absolute M_V magnitude, the R_HB index calculated inside 1 r_h for the MW (open diamonds) satellites and for the ISLAndS (stars) galaxies. And I and II are calculated over the full ACS area, which is smaller than one r_h. The plot suggests that at least in the innermost regions of the available samples, the M31 satellites have slightly redder HBs than the MW dSph satellites, although the difference is within 2σ. In fact, within one r_h, the mean value of R_HB is more negative in the case of M31 galaxies (${R}_{\mathrm{HB},{\rm{M}}31}=-0.58\pm 0.07$) than for the MW companions (${R}_{\mathrm{HB},\mathrm{MW}}=-0.37\pm 0.06$). However, we emphasize that the latter numbers may be biased due to the small subsample of satellites for which we have data in both MW and M31 systems.

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It is worth mentioning that the present analysis presents several improvements over previous analyses (Harbeck et al. 2001; Martin et al. 2017): (i) the better photometric precision at the HB level, and the filter combination, which provides a better color discriminating power. This allows us to clearly separate the red HB from the blue edge of the RGB, even in the case of And I. (ii) The larger field of view of ACS compared to WFPC2 provided a larger sample. (iii) The up-to-date wide-field homogeneous data available for the MW companions allowed us to perform the comparison in a more homogeneous manner. (iv) Finally, the better phase coverage allowed us to derive better-defined mean colors of RRL stars.

The current data do not allow us to fully explore whether the HB morphology presents significant variation as a function of galactocentric distance, i.e., distance from the center of each galaxy. Nevertheless, when considering the parallel WFC3 field for And I and And II, we derive higher values of the R_HB index, and therefore an indication that the HB morphology becomes bluer when moving to an external region. This is in agreement with what has been found for other LG galaxies (e.g., Harbeck et al. 2001; Tolstoy et al. 2004; Cole et al. 2017), and more in general, with the population gradients commonly found in dwarf galaxies (Hidalgo et al. 2013, and references therein). In fact, when considering the area within two r_h, the six galaxies tend to have bluer HB. Unfortunately, a straight comparison between the two satellite systems is complicated by the fraction of area covered. This leaves open the question whether the HB morphology remains different at larger galactocentric distances, or if M31 and MW satellites tend to be more similar when their global properties are taken into account. More wide-field variability studies, particularly for the M31 satellites, would help solve this problem.

In Section 4 we presented the Bailey diagram of the ISLAndS galaxies and discussed their properties in terms of Oosterhoff classification. Despite the intermediate mean-period, stars in the Bailey diagram still tend to clump around the Oo-type lines, with a predominance of Oo-I-like stars, rather than in between. Therefore, the period distribution provides a more detailed description than the mean period alone (Fiorentino et al. 2015, 2017). In the previous subsection, we have presented evidence that M31 and MW satellites present a slightly different HB morphology. We now focus on the properties of the RRL stars alone.

Table 6 lists the properties of the RRL in a sample of 41 dwarf galaxies (39 LG dwarfs plus 2 Sculptor group dwarfs) of different morphological type within 2 Mpc (column 1): the number of RRab stars (column 2), the percent of Oo-I type and Oo-II type RRab stars (column 3 and 4), the number of RRcd stars (column 5), the fraction of RRcd stars over the total of the RRL (column 6), and the median and mean period of the RRab and RRcd stars (column 7, 8, 9, and 10) derived from the literature (references in column 11).

The left panel of Figure 8 shows the mean period of RRab-type stars, $\langle {P}_{\mathrm{ab}}\rangle$, as a function of the mean metallicity of the host galaxy (left panel), for 16 satellites of M31 (filled orange stars) and 15 MW dwarfs (blue open diamonds). Galaxies with at least 5 known RRab stars have been included. The plot discloses that the mean period of RRab-type stars decreases for increasing mean metallicity of the host system (Sandage et al. 1981), for both the MW and the M31 satellites. The trend presents some scatter, but interestingly, a linear fit to the data provides a very similar slope (0.040 ± 0.008 and 0.038 ± 0.008, respectively), thus suggesting an overall similar behavior in the two satellite systems.

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The decreasing mean period for increasing metallicity can be related to the early chemical evolution of the sample galaxies. On the one hand, the distribution of stars in the Bailey diagram suggests that galaxies tend to progressively populate the RRab short-period range for increasing metallicity (and mass). This translates into a shorter mean period. It may appear intriguing that a property of a purely old stellar tracer correlates with the present-day mean metallicity of the host galaxy. This suggests that galaxies that today are more massive and more metal-rich on average also experienced faster early chemical evolution, which is imprinted in the properties of their RRL stars. This implies that the mass–metallicity relation (e.g., Kirby et al. 2013) was in place at early epoch (Martínez-Vázquez et al. 2016b).

The central panel of Figure 8 shows the mean period as a function of the fraction of Oo-I type stars, as defined in Section 4. While there is no clear correlation for either satellite system, we find that the vast majority of galaxies host a larger fraction of Oo-I type stars, between 60% and 90% of the total amount of RRab stars. Nevertheless, the mean period of fundamental pulsators would classify them as Oo-intermediate system. Again, this suggests that the RRL stars in complex systems such as galaxies are not properly represented by a single parameter.

Finally, the right panel of Figure 8 shows the mean period distribution for the RRab in MW satellites (blue) and in M31 satellites (orange). Apparently, the two are similar, and their peaks agree within 1σ.

This analysis reveals that if we limit the comparison to strictly old and well-defined populations such as that of RRL stars, there are no obvious differences between the RRL populations of the satellite systems of M31 and the MW.

Figure 9 shows the behavior of $\langle {P}_{\mathrm{ab}}\rangle$ versus [Fe/H], but comparing a sample of 41 galaxies (black circles, including MW and M31 satellites, isolated dwarfs, and 2 galaxies in the Sculptor group) with GCs (magenta bowtie symbols). We use here the compilation from Catelan (2009), including all the GCs with more than 10 RRL stars. Galactic GCs are shown together with clusters from the LMC and the Fornax dSph galaxy. The plot shows that a few Oo-intermediate clusters overlap with galaxies in the Oosterhoff gap, but most of the Oo-I clusters (i.e., with ${P}_{\mathrm{ab}}\lt 0.58$) occupy a region of the parameter space where no galaxies are present—this holds even when we restrict the GC sample to those with 30 RRL or more. This is even more evident in the right panel of Figure 9, which shows the mean period distributions of the two samples. It clearly shows that the peak for the galaxy distribution occurs at a period typical of Oo-intermediate systems, while the peak of the GCs occurs in the Oo-I regime.

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The metallicity estimates available in the literature for the ISLAndS galaxies are all based on CaT spectroscopy of bright RGB stars.²² As the RGB can be populated by stars of any age older than ∼1 Gyr, the derived metallicity distribution may not be representative of the RRL stars, since relatively young and/or more metal-rich populations may exist on the RGB, but may not have counterparts among RRL stars (Martínez-Vázquez et al. 2016a). As a consequence, assuming a mean metallicity that may be too high by 1.0 dex for the RRL stars would introduce a systematic error in the distance modulus estimates at the level of ∼0.2 mag.

Table 7 lists literature values for the mean metallicity (column 2) of ISLAndS galaxies, the σ of the metallicity distribution (column 3), and the number of RGB stars (column 4) used in these studies (references in column 5). Relatively low values were found for And III, And XV, And XVI, and And XXVIII, on average close to [Fe/H] ∼ −1.8 or lower. On the other hand, in the case of And I and And II, different authors (Kalirai et al. 2010; Ho et al. 2012) agree on a much higher mean metallicity ([Fe/H] ∼ −1.4), and a relatively large metallicity spread (${\sigma }_{\mathrm{And}{\rm{I}}}=0.37$ dex, ${\sigma }_{\mathrm{And}\mathrm{II}}=0.72$ dex). Nevertheless, the small number of HASP stars (see Section 4) suggests that even if the tail of the RRL metallicity distribution reaches such relatively high values, the bulk of the RRL stars must have a lower metallicity ([Fe/H] < –1.5, Fiorentino et al. 2015). Therefore, as representative values of the metallicity for the RRL population, we adopted—in agreement with their SFHs (Skillman et al. 2017)—[Fe/H] = –1.8 for And I and And II, while for the rest of the galaxies, we assumed that the metallicity of the old population must be quite similar to that obtained by the spectroscopic studies (see column 8).

Table 7.  Metallicity Studies with the Largest Samples of RGB Stars

	RGB stars						RRL Stars
Galaxy	$\langle [\mathrm{Fe}/{\rm{H}}]\rangle$	${\sigma }_{\langle [\mathrm{Fe}/{\rm{H}}]}\rangle$	Nstars	References	Metallicity Scalea	$\langle [\mathrm{Fe}/{\rm{H}}]{\rangle }_{{\rm{C}}09}$ b	${[\mathrm{Fe}/{\rm{H}}]}_{\mathrm{old}\mathrm{pop}.}$
And I	−1.45 ± 0.04	0.37	80	Kalirai et al. (2010)	ZW84	−1.44	−1.8
And II	−1.39 ± 0.03	0.72	477	Ho et al. (2012)	G07	−1.30	−1.8
And III	−1.78 ± 0.04	0.27	43	Kalirai et al. (2010)	ZW84	−1.81	−1.8
And XV	−1.80 ± 0.20	⋯c	13	Letarte et al. (2009)	C09	−1.80	−1.8
And XVI	−2.00 ± 0.10	⋯d	12	Collins et al. (2015)	G07	−1.91	−2.0
And XXVIII	−1.84 ± 0.15	0.65e	13	Slater et al. (2015)	C09	−1.84	−1.8

Notes.

^aMetallicity scales: ZW84—Zinn & West (1984), G07—Grevesse et al. (2007), and C09—Carretta et al. (2009). ^bWe have either converted the metallicity into the C09 scale when possible or shifted the metallicity value assuming the same solar iron abundance (log(Fe) = 7.54). The C09 scale was chosen as the homogeneous scale because it is the most recent scale. ^cLetarte et al. (2009) did not publish ${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}$. Instead, they provide an interquartile range of 0.08, with a median metallicity of [Fe/H] = –1.58 dex. ^dCollins et al. (2015) did not publish ${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}$. However, Letarte et al. (2009) published for And XVI an interquartile range of 0.12, with a median of [Fe/H] = –2.23 dex. By stacking the spectra of the member stars (eight, in this case), they found [Fe/H] = –2.1 with an uncertainty of ∼0.2 dex. This value agrees with that obtained by Collins et al. (2015) (shown in the table). ^eAs this σ is obtained from a small number of individual measurements, it may not be representative of the actual distribution.

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The adopted mean metallicities for each ISLAndS galaxy are summarized in the penultimate column of Table 7. We note that the values have been homogenized to the scale of Carretta et al. (2009). Column 2 reports the value in the original scale, which is specified in column 6. In the cases that are based on theoretical spectra, we applied a correction to take into account the different solar iron abundance (from $\mathrm{log}{\epsilon }_{\mathrm{Fe}}=7.45$ to 7.54), which translates into a distance modulus change between 0.01 mag in the case of the FOBE and 0.04 in the case of the LMR.

PWRs are a powerful tool for distance determination, because they are reddening-free by construction and are only marginally metallicity dependent. They are theoretically described by

$$\begin{eqnarray}&&W(X,X-Y)=\alpha +\beta \mathrm{log}P+\gamma [\mathrm{Fe}/{\rm{H}}],\end{eqnarray} \tag{ 1 }$$

where X and Y are magnitudes and W($X,X$–Y) denotes the reddening-free Wesenheit magnitude (Madore 1982) obtained as W($X,X\mbox{--}Y$) = X–R(X–Y), where R is the ratio of total-to-selective absorption, R = A_X/E(X–Y).

An updated and very detailed analysis of the framework of the PWRs is provided by Marconi et al. (2015). Their Tables 7 and 8 give a broad range of optical, optical-NIR, and NIR PWRs, along with their corresponding uncertainties. In particular, in this work, we use their PWR in the ($I,B\mbox{--}I$) filter combinations²³ :

$$\begin{eqnarray}W(I,B\mbox{--}I) & = & -0.97(\pm 0.01)+(-2.40\pm 0.02)\mathrm{log}P\\ & & +(0.11\pm 0.01)[\mathrm{Fe}/{\rm{H}}],\end{eqnarray} \tag{ 2 }$$

which has an intrinsic dispersion of σ = 0.04 mag. For this relation, a metallicity change of 0.2 dex translates into a change in the distance on the order of 0.03 mag.

The theoretical W($I,B$–I) was obtained from the individual stars assuming a metallicity for the old population (see column 8 in Table 7 and the discussion of Section 6.1). We next calculated the individual apparent Wesenheit magnitude as: w($I,B$–I) = I–0.78(B–I). We report the distance moduli obtained by averaging individual estimates for the global sample (RRab + fundamentalized RRc: log P_fund = log P_RRc + 0.127; Bono et al. 2001) in columnn 2 of Table 8. For comparison, if we independently use the sample of RRab and RRc, the values from the different determinations agree on average within ±0.04 mag. Column 2 of Table 8 reports the true distance moduli obtained for each galaxy using this method.

The LMR is another simple, widely used approach to determine distances, in this case, using the mean V magnitude of RRL stars. Although both theoretical and empirical calibrations suggest that the relation is not linear (it is steeper in the more metal-rich regime (see e.g., Caputo et al. 2000; Sandage & Tammann 2006; Cassisi & Salaris 2013 and references therein)), most examples in the literature use one of the different linear relations proposed.

In the present work, we adopted the following relations:

$$\begin{eqnarray}&&\langle {M}_{V}\rangle =0.866(\pm 0.085)+0.214(\pm 0.047)[\mathrm{Fe}/{\rm{H}}]\end{eqnarray} \tag{ 3 }$$

from Clementini et al. (2003) and

$$\begin{eqnarray}&&\langle {M}_{V}\rangle =0.768(\pm 0.072)+0.177(\pm 0.069)[\mathrm{Fe}/{\rm{H}}]\end{eqnarray} \tag{ 4 }$$

from Bono et al. (2003).²⁴

The latter is valid only for a metallicity lower than [Fe/H] = –1.6, which is appropriate for the six ISLAndS galaxies (where the metallicity of the old population is considered to be [Fe/H] = –1.8 or lower). Columns 3 and 4 of Table 8 show the true distance moduli obtained using the two relations. They are in excellent agreement with each other and with those derived previously using the PWR.

Another method that can be used to estimate the distance is based on the predicted period–luminosity–metallicity relation for pulsators located along the FOBE of the IS (see Caputo et al. 2000):

$$\begin{eqnarray}{M}_{V,\mathrm{FOBE}} & = & -0.635-2.255\mathrm{log}({P}_{\mathrm{FOBE}})\\ & & -1.259\mathrm{log}(M/{M}_{\odot })+0.058\mathrm{log}(Z),\end{eqnarray} \tag{ 5 }$$

which has an intrinsic dispersion of ${\sigma }_{V}=0.07$ mag.

This is considered a particularly robust technique for stellar systems with significant numbers of first-overtone RRL (RRc) stars, especially if the blue side of the IS is well populated. Thus, it can be applied safely to five of our six galaxies²⁵ (see Figure 6). The distance modulus is derived by matching the observed distribution of RRc stars to Equation (5). That is, for a given metallicity and a mass corresponding to the typical effective temperature for RRL stars, we shift the relation until the FOBE matches the observed distribution of RRc stars.

For the adopted metallicity listed in Table 7 and using the evolutionary models from BaSTI (Pietrinferni et al. 2004), we obtain masses at log ${T}_{\mathrm{eff}}\approx 3.86$ of M ∼ 0.7 ${M}_{\odot }$. True distance moduli obtained for each galaxy using this method are shown in column 5 of Table 8, and are in good agreement with those described in the previous section.

It is well established that the TRGB is a good standard candle thanks to its weak dependence on age (Salaris et al. 2002), and in the I band in particular, on the metallicity (at least for relatively metal-poor systems; Da Costa & Armandroff 1990; Lee et al. 1993). The TRGB is frequently used to obtain reliable distance estimates to galaxies of all morphological types in the LG and beyond (e.g., Rizzi et al. 2007; Bellazzini et al. 2011; Wu et al. 2014). However, determining the cutoff in the luminosity function at the bright end of the RGB is not straightforward in low-mass systems because more than about 100 stars populating the top magnitude of the RGB are required to reliably derive the location of the tip (Madore & Freedman 1995; Bellazzini et al. 2002; Bellazzini 2008). This condition is fulfilled only in And I (>200), And II (>150), and nearly so in And III (∼90). The low number of stars in the other three galaxies prevents us from deriving a reliable measurement of the apparent magnitude of the TRGB.

We applied the same method from Bernard et al. (2013) to determine the magnitude of the TRGB. We convolved the $F814W$ luminosity functions with a Sobel kernel of the form [1, 2, 0, 2, 1]. From the filter response function, we obtain the center of the peak corresponding to the TRGB of each galaxy: $F814{W}_{0,\mathrm{And}{\rm{I}}}=20.45\pm 0.09$, $F814{W}_{0,\mathrm{And}{\rm{I}}}=20.05\pm 0.12$, and $F814{W}_{0,\mathrm{And}\mathrm{III}}=20.25\pm 0.19$ mag, where the uncertainty is the Gaussian rms width of the peak of the Sobel filter response.

The distances were obtained from the TRGB magnitudes using three calibrations:

(i) the empirical calibrations in the HST flight bands from Rizzi et al. (2007, R07):

$$\begin{eqnarray}{M}_{\mathrm{TRGB}}^{F814W} & = & -4.06+0.15{(F555W-F814W)}_{0}\\ & & -1.74]\,(\sigma =0.10),\end{eqnarray} \tag{ 6 }$$

(ii) the empirical calibration reported in Bellazzini (2011, B11), derived by Bellazzini (2008) from the original calibration as a function of [Fe/H] obtained in Bellazzini et al. (2001) and revised in Bellazzini et al. (2004):

$$\begin{eqnarray}{M}_{\mathrm{TRGB}}^{F814W} & \approx & {M}_{\mathrm{TRGB}}^{I}=0.080{(V-I)}_{0}^{2}\\ & & -0.194{(V-I)}_{0}-3.93\,(\sigma =0.12),\end{eqnarray} \tag{ 7 }$$

(iii) the theoretical calibration ${{\rm{M}}}_{\mathrm{TRGB}}^{F814W}$, as a function of the color ($F475W$–$F814W$)₀, obtained in this work by fitting the BaSTI predictions (Pietrinferni et al. 2004, 2006) for the TRGB brightness for an old (∼12 Gyr) stellar population, a wide metallicity range, and an α-enhanced heavy-element distribution:²⁶

$$\begin{eqnarray}{M}_{\mathrm{TRGB}}^{F814W} & = & -4.11+0.07[{(F475W-F814W)}_{0}-2.5)\\ & & +0.09{[{(F475-F814)}_{0}-2.5]}^{2}\,(\sigma =0.02).\end{eqnarray} \tag{ 8 }$$

In the case of the Rizzi et al. (2007) calibration, we considered that $F555W$–$F814W$ ∼V–I.²⁷ In fact, for both this calibration and that of Bellazzini et al. (2011), we used the following equation to determine the expected (V–I)₀ color: (V–I)${}_{\mathrm{TRGB},0}=0.581$[Fe/H]²+2.472[Fe/H]+4.013 (Bellazzini et al. 2001). Since this last equation is based on the Zinn & West (1984, ZW84) scale, in order to use it properly, we have to apply the conversion scales provided by Carretta et al. (2009): [Fe/H]_ZW84 = ([Fe/H]_C09–0.160)/1.105. Columns 6, 7, and 8 in Table 8 give the values of the true distance moduli calculated using the previous relations for And I, And II, and And III. All three calibrations lead to distances that are in good agreement with each other and with the previously calculated RRL-based distances.

As show in Table 8, all the distances obtained from the different methods are in agreement within less than 1σ with each other. The inclusion of the TRGB method in this study was mainly to check the distances we obtained using the properties of the RRL stars with those assessed with this method. In fact, it is worth mentioning that since the TRGBs of these galaxies are not densely populated (we have ≳200 only for And I), this technique is secondary in our study, but it serves to show that the metallicity we have assumed for the old population is robust. The good sampling of our LCs together with the large amount of RRL stars in all these galaxies (with exception of And XVI) make them the best distance indicators that we have in these galaxies so far.

We adopt the distances obtained with the PWR as preferred because (i) they are obtained with the RRL stars, (ii) the PWR used to derive them come from the most recently updated study (Marconi et al. 2015), and (iii) the systematic uncertainties are the smallest (see Table 8).

Figure 10 summarizes the distance determinations derived in this work. In particular, the filled circles together with the dotted line show the adopted final distance measurement coming from the PWR (Section 6.2). Open circles show the results from the RRL-based methods presented in previous sections (see Table 8), while the open squares show the TRGB distances. The plot shows that the agreement between the different methods presented here is remarkably good, as most of the derived distances agree within 1σ. Taking as reference the PWR distance, some general trends can be noted for the results of the different methods we adopted. The distance derived using the LMR with the Bono et al. (2003) calibration provides marginally larger distances with respect to both the Clementini et al. (2003) calibration (in agreement with the difference in the zero-point) and the distance obtained from the PWR. The FOBE distance is larger than the PWR distance in three cases (And III, XV, and XVI) and is shorter for And II. Nevertheless, this method is the most sensitive to the sampling of the IS, and in particular, the lack of RRL close to the blue edge of the IS introduces a bias toward larger distances. The TRGB technique could only be applied to the three most massive systems. Interestingly, in the case of And II and And III, the derived distance seems to be, on average, marginally smaller, independent of the calibration adopted. We note that in the case of And I, the agreement between different indicators and methods is remarkably good. This is possibly linked to the fact that it presents the largest sample of RRL stars and the most populated TRGB region, thus suggesting that statistical fluctuations have a minimal effect.

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Figure 11 displays a comparison with distance estimates available in the literature and derived with different techniques: RRL stars (open triangles: Pritzl et al. 2004, 2005), the HB luminosity (open diamonds: Da Costa et al. 1996, 2000; Slater et al. 2015), and the TRGB (open stars: Mould & Kristian 1990; Koenig et al. 1993; McConnachie et al. 2004, 2005; Letarte et al. 2009; Conn et al. 2012). This figure shows an overall good agreement with our estimates within the uncertainties. We note that the TRGB tends to provide closer distances than the RRL and the HB luminosity, although it is still compatible within 1.5σ. Several discrepant cases (And XV and XVI from Conn et al. 2012) can be ascribed to the sparsely populated bright portion of the RGB in these galaxies.

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AC stars are variable stars in the core He-burning evolutionary phase at a luminosity that is higher than that of RRL stars. Their periods range from ∼0.5 to ∼2.0 days and their masses are thought to be higher than 1 ${M}_{\odot }$. In order to have ACs with such masses, two different channels are likely (Bono et al. 1997; Gallart et al. 2004; Cassisi & Salaris 2013). They can be the progeny of coalesced binary stars, that is, evolved blue straggler stars (BSS) tracing the old population (Renzini et al. 1977; Hirshfeld 1980; Sills et al. 2009). Alternatively, they can be an evolutionary stage of single stars with mass between ∼1.2 and ∼2.2 ${M}_{\odot }$ and age between 1 and 6 Gyr (Demarque & Hirshfeld 1975; Norris & Zinn 1975; Castellani & Degl'Innocenti 1995; Caputo et al. 1999; Dolphin et al. 2002; Fiorentino et al. 2006). In both scenarios, they trace the existence of a metal-poor (Z < 0.0006) stellar population, thus providing sound constraints to the metal enrichment of the galaxy.

Typically, purely old (age $\gtrsim 10$ Gyr) nearby LG dwarf galaxies host a few ACs. However, they are very rare in GCs; so far, only one candidate has been confirmed in the metal-poor ([Fe/H] ∼ −2 dex) cluster NGC 5466 (Zinn & Dahn 1976), and a few others have been suggested (Corwin et al. 1999; Arellano Ferro et al. 2008; Kuehn et al. 2011; Walker et al. 2017). On the other hand, large samples of ACs have been collected in the LMC (141) and in the SMC (109) in the framework of the OGLE-IV project (Soszyński et al. 2015). In this context, it is worth mentioning that the work of Mateo et al. (1995)—updated by Fiorentino & Monelli (2012), who collected data from nearby dwarf galaxies with an established SFH and in which ACs have been found (see their Figure 7)—noted a correlation between the frequency of ACs and the total luminosity of the host galaxy; the frequency of ACs decreases for increasing luminosity of the host galaxy. Another parameter that seems to impact the ACs frequency is the SFH of the host system, with primarily old systems, or fast galaxies (as defined by Gallart et al. 2015) having a lower specific frequency of ACs than systems containing many intermediate-age and young populations (slow galaxies).

Figure 1 shows the presence of a few variable stars located 1 to 2 mag above the HB. Given their pulsation properties, their position in the period-Wesenheit diagram (see e.g., Figure 1 in Fiorentino & Monelli 2012), and the shape of their LCs, we classify them as ACs. In particular, a total of 15 ACs have been detected in the ACS field of And II, III, XV, and XXVIII. No ACs have been detected in And I, in agreement with Pritzl et al. (2005), or in And XVI. The lack of ACs in And I can be a hint of the fast chemical enrichment of this galaxy. This is supported by the high metallicity of this galaxy when compared with the remaining ISLAndS galaxies. On the other hand, And XVI has the proper mean low metallicity, but its low total mass is the most probable cause for the lack of ACs. Interestingly, And XVI shows active star formation until about 6 Gyr ago, thus not extended enough to produce ACs through the single-star channel.

As none of the four ISLAndS galaxies where ACs have been detected shows evidence of star formation younger than 2 Gyr (Skillman et al. 2017), it is unlikely that ACs come from the evolution of a young metal-poor star. The sequence of blue objects between the oldest MSTO and the HB are most likely BSS descending from primordial binary stars of the old population, in agreement with the SFHs obtained by Skillman et al. (2017). Therefore we assume that the AC we detected here are the progeny of coalesced binary stars (evolved BSS), thus tracing the old population (Renzini et al. 1977; Hirshfeld 1980; Sills et al. 2009).

From our sample, only four ACs were previously known²⁸ : AndII-V083 (V14 by Pritzl et al. 2004), AndIII-V073, AndIII-V075, and AndIII-V105 (V01, V07, and V06 by Pritzl et al. 2005). The LCs of all the detected ACs are shown in Figure 12. The different shapes are an indication of different pulsational modes. However, the classification of the pulsation mode of ACs is not trivial and cannot be easily determined from the morphology of the LCs alone (Marconi et al. 2004).

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Figure 13 shows the period-Wesenheit plane for the reddening-free index W($I,B$–I)—which reduces the scatter due to the interstellar reddening and the intrinsic width of the IS—for the ACs of the LMC (open symbols) published by the OGLE collaboration (Soszyński et al. 2015). This plot shows a clear separation between fundamental (F, black dots) and first-overtone (FO, open circles) pulsators for ACs. Therefore, ACs are defined by different PL relations, and fundamental and first-overtone pulsation can also be distinguished in this way. We therefore overplot the 15 ACs found in this work with the aim of checking their nature and identifying their pulsation modes. The four ACs found in And II are represented by red circles, the four in And III by green squares, the four in And XV by orange diamonds, and the three in And XXVIII by blue triangles. First, Figure 13 supports their classification as ACs. We note that only one star (And XXVIII-V068) is somewhat distant from the bulk of the F mode ACs of the LMC. From an inspection of the LC of this star (see Figure 12), the lack of phase points close to the maximum light is evident. Therefore, the measurement of the mean magnitude of this star may be biased to brighter magnitude, as the fit with templates tends to overestimate the amplitude. Figure 13 indicates that the majority of the ACs (12) are pulsating in the F mode, and only three of them (And III-V075, And III-V105, and And XXVIII-V060) are FO pulsators.

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For the sake of completeness, we report the detection of three EBs, one in And I and two in And II. Figure 14 shows their LCs, which in all cases show a minimum. For the three candidates, the minimum occurs at the same phase in the two bands. This feature, together with the flat bright part of the LCs, the periods, and their position in the CMD, supports the classification as EBs.

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The fact that only such a small number of candidate EBs was detected is due to both the relatively small number of points per LC taken, the non-optimal time sampling for this type of variable, and the limited region of the CMD that was searched for variables.