RR Lyrae Variable Stars in the Crater II Dwarf Galaxy
Seok-Joo Joo, Jaemann Kyeong, Soung-Chul Yang, Sang-Il Han, Eon-Chang Sung, Dongwon Kim, Hyunjin Jeong, Chang H. Ree, Soo-Chang Rey, Helmut Jerjen, Hak-Sub Kim, Sang-Mok Cha, Yongseok Lee
aa r X i v : . [ a s t r o - ph . GA ] M a y Draft version May 22, 2018
Preprint typeset using L A TEX style AASTeX6 v. 1.0
RR LYRAE VARIABLE STARS IN THE CRATER II DWARF GALAXY
Seok-Joo Joo , Jaemann Kyeong , Soung-Chul Yang , Sang-Il Han , Eon-Chang Sung , Dongwon Kim ,Hyunjin Jeong , Chang H. Ree , Soo-Chang Rey , Helmut Jerjen , Hak-Sub Kim , Sang-Mok Cha , andYongseok Lee Korea Astronomy and Space Science Institute, Daejeon 34055, Korea; [email protected] Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA Department of Astronomy and Space Science, Chungnam National University, 99 Daehak-ro, Daejeon 34134, Korea Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104, Korea
ABSTRACTWe report the detection of RR Lyrae variable stars in Crater II, a recently discovered large and diffusesatellite dwarf galaxy of the Milky Way (MW). Based on B , V time-series photometry obtained withthe Korea Microlensing Telescope Network (KMTNet) 1.6 -m telescope at CTIO, we identified 83 ab -type and 13 c -type pulsators by fitting template light curves. The detected RR Lyrae stars arecentrally concentrated, which ensures that most of them are members of Crater II. In terms of thedistribution of RRab stars in the period-amplitude diagram, Crater II is clearly different from ultra-faint dwarf (UFD) galaxies, but very similar to the two classical MW dwarf spheroidal (dSph) galaxiesDraco and Carina with Oosterhoff-intermediate (Oo-int) properties. Combined with the mean periodof ab -type variables ( h P ab i = 0 . ± .
004 d) and the c -type fraction ( ∼ Keywords: galaxies: dwarf — galaxies: individual (Crater II) — Local Group — stars: variables: RRLyrae INTRODUCTIONOver the past dozen years, the number of knownsatellite galaxies around the Milky Way (MW)has dramatically increased from 12 to ∼
50 (e.g.,Willman et al. 2005a,b; Belokurov et al. 2006,2007, 2008, 2009, 2010; Grillmair 2006, 2009;Zucker et al. 2006a,b; Sakamoto & Hasegawa 2006;Irwin et al. 2007; Walsh et al. 2007; Bechtol et al.2015; Drlica-Wagner et al. 2015, 2016; Kim et al.2015a,b; Kim & Jerjen 2015; Laevens et al. 2015a,b;Martin et al. 2015; Koposov et al. 2015; Torrealba et al.2016a,b; see also McConnachie 2012, updated 2015;Belokurov 2013, for reviews), thanks to large opticalsurveys such as the Sloan Digital Sky Survey (SDSS;York et al. 2000), the Dark Energy Survey (DES;DES Collaboration 2016), the Pan-STARRS1 Surveys(Chambers et al. 2016), and the VLT Survey Telescope(VST) ATLAS survey (Shanks et al. 2015). Most of these new MW dwarf companions are very faint interms of both total luminosity ( M V & −
8) and surfacebrightness ( µ V &
28 mag arcsec − ), leading to the termultra-faint dwarf (UFD) galaxies. Spectroscopic and/orphotometric follow-up studies (e.g., Mu˜noz et al.2006, 2010; Martin et al. 2007; Simon & Geha 2007;Simon et al. 2011; Kirby et al. 2008; Frebel et al. 2010;Norris et al. 2010; Okamoto et al. 2012; Sand et al.2012; Brown et al. 2012, 2014; Koch & Rich 2014;Kim et al. 2016; Conn et al. 2018) in turn revealed thatthese least luminous galaxies are also most dark matterdominated (mass-to-light ratio, M ⊙ /L V, ⊙ & . − . t &
10 Gyr). It is now naturally expected from thesteep slope of the luminosity function of MW dwarfcompanions (Koposov et al. 2008) that the universe isdominated by these faintest galaxies in number.The UFDs are believed to play an important role in re-
Joo et al. solving the well-known “missing satellite” problem, thediscrepancy between observations and predictions fromthe current ΛCDM hierarchical merging paradigm, forthe number and spatial distribution of satellite galaxies(Kauffmann et al. 1993; Klypin et al. 1999; Moore et al.1999; see also Bullock & Johnston 2005; Simon & Geha2007; Koposov et al. 2009; Bahl & Baumgardt 2014).Hence, not only is a more complete census of MW dwarfsatellites over the entire sky needed, but also detailedstudies of their stellar populations are crucial to betterunderstand their true nature, and thus galaxy formationand evolution via accretion and merger processes (e.g.,Willman et al. 2004; Jerjen 2010; Conn et al. 2018).The Crater II dwarf galaxy is one of the most re-cently discovered MW satellites in the southern hemi-sphere, first reported by Torrealba et al. (2016a) usingthe VST ATLAS survey data. From the total luminosityof M V ≃ − .
2, Crater II can be classified as either one ofthe brightest UFDs or one of the faintest classical dwarfspheroidal (dSph) galaxies. Interestingly, given the totalluminosity, this galaxy is very large (half-light radius, r h ≈ µ V ≈ . − ).It is currently the fourth largest MW satellite — onlythe Large Magellanic Cloud (LMC), the Small Mag-ellanic Cloud (SMC), and the Sagittarius (Sgr) dwarfgalaxy are larger — and one of the lowest surfacebrightness galaxies known (Torrealba et al. 2016a, seetheir Figure 6). Based on the color-magnitude diagram(CMD) and isochrone fitting, Torrealba et al. (2016a)estimated Crater II to have an old age ( ∼
10 Gyr) andlow metallicity ([Fe/H] ≃ − . ∼
62 red giant branch (RGB) stars in thisgalaxy, and obtained a mean metallicity of h [Fe / H] i ≃− .
98 with a dispersion of σ [Fe / H] ≈ .
22. They alsoshowed that it has an extremely low line-of-sight ve-locity dispersion ( σ v, los ≈ . − , see also McGaugh2016) and a dynamical mass of ∼ . × M ⊙ , suggestinga mass-to-light ratio of ∼ M ⊙ /L V, ⊙ within the half-light radius. Located relatively distant from the Sun( &
100 kpc) and widely distributed on the sky ( r h ≃ ′ ,Torrealba et al. 2016a), there is still a lack of extensivestudies on the stellar population of Crater II.As radially pulsating low-mass horizontal branch (HB)stars in the phase of core helium burning, RR Lyraevariables are good tracers of old ( &
10 Gyr) and metal-poor populations (i.e., population II). Their photometricand pulsation properties including mean magnitude, pe-riod, amplitude, and light curve, are commonly used toderive metallicity, interstellar reddening, and distanceof the system. They can also provide information onthe stellar structure, formation, and evolution of theirhost dwarf galaxies, particularly when compared withthose stars in the Galactic halo or globular clusters (GCs) (e.g., Smith 2004; Catelan 2009; Clementini 2010;Pietrukowicz et al. 2015). Since 2006, about 13 UFDs(with M V > −
7) have been reported to contain RRLyrae variables (Vivas et al. 2016, see their Table 4 fora recent compilation), including Bo¨otes I (holding thecurrent record with 15 RR Lyrae stars) and Segue I,one of the faintest UFDs known (Simon et al. 2011). Itis interesting to note that all dwarf galaxies searchedfor variable stars so far have at least one RR Lyraestar (Vivas et al. 2016; see also Garofalo et al. 2013;Boettcher et al. 2013; Sesar et al. 2014; Medina et al.2017) regardless of the total luminosity.In this paper, we investigate the RR Lyrae populationin the Crater II dwarf galaxy based on time-series ob-servations using the Korea Microlensing Telescope Net-work (KMTNet) 1.6 -m telescope located at the Cerro-Tololo Inter-American Observatory (CTIO). This studyis part of our ongoing southern hemisphere survey forRR Lyrae stars in UFDs using the KMTNet-CTIO. Sec-tion 2 presents the time-series observations and data re-duction process. Section 3 describes our detection of theRR Lyrae stars by applying the template light curve fit-ting routine, RRFIT, developed by Yang & Sarajedini(2012), and the characterization of the stars includingtheir light curves, spatial distribution and metallicityestimates. We discuss the results and draw our conclu-sions in section 4. OBSERVATIONS AND DATA REDUCTIONTime-series B , V observations of the Crater II dwarfgalaxy were carried out using the KMTNet-CTIO 1.6-m telescope during 2016 February 1–4, 6–10, and 2017January 29–30 (UT). The telescope is equipped withthe mosaic CCD camera of 18k ×
18k pixels, provid-ing a wide field of view of 2 ◦ × ◦ and a pixel scale of0.40 ′′ (S.-L. Kim et al. 2016). Our observations covereda total area of ∼ ◦ × ◦ with five largely overlappingfields, which is more than twice the half-light radius ofthe galaxy ( r h ≃ ′ , Torrealba et al. 2016a). With anexposure time of 120 s per image, we obtained in total143 and 145 frames in the B - and V -bands, respectively,which correspond to a total exposure time of ∼ ), and astrometric cali-bration was performed with SCAMP (Bertin 2006) ap- R Lyrae stars in the Crater II dwarf galaxy r h ≃ ′ ) of Crater II,produced by performing PSF photometry on the com-bined images of all our time-series data with SWarp(Bertin et al. 2002). The CMDs were cleaned of poorlymeasured stars and non-stellar objects using the photo-metric errors and the ALLFRAME fitting parameters,CHI and SHARP, as functions of B and V magnitudes(see Kim et al. 2013; Lim et al. 2016). In panel (a), forstars within the half-light radius, we can clearly see theCMD features of Crater II, such as the RGB, red HB,sub-giant branch (SGB), and even main-sequence turn-off (MSTO). Panel (b), for stars outside the half-lightradius, however, shows only weak features of Crater IIsuperimposed on the background contamination, indi-cating that most member stars are within the half-lightradius. Figure 1 generally confirms the CMD propertiesof Crater II presented by Torrealba et al. (2016a, seetheir Figure 1), but our observations are deep enough toreach the MSTO near V ≃
24, which is important forage dating of stellar populations (see Section 4). The reddots represent RR Lyrae stars identified in this study,where their colors and magnitudes are mean values fromour light curve analysis (see Section 3). RR LYRAE VARIABLE STARS3.1.
Detection and Characterization
To identify and characterize RR Lyrae stars in thefield of Crater II, we applied the template light curve fit-ting routine, RRFIT, developed by Yang & Sarajedini(2012) on the basis of template fitting methods byLayden (1998) and Mancone & Sarajedini (2008). Fol-lowing the technique of Yang et al. (2010, 2014) andYang & Sarajedini (2012), we first selected stars at theHB luminosity level, i.e., 20 . < V < .
7, and exam-ined their variability using the reduced chi-square, χ ν ,defined as, χ ν = 1 N B + N V × " N B X i =1 ( B i − B ) σ Bi + N V X i =1 ( V i − V ) σ V i , (1)where, for each star in the B - and V -bands, N B and N V are the numbers of the observed frames, B i and V i arethe apparent magnitudes in the i th images with uncer-tainties σ Bi and σ V i , and B and V are the mean magni-tudes for the N B and N V frames. In the calculation ofthe χ ν value, data points further away than 3 σ from themean magnitude were excluded. Variable stars are ex-pected to have larger χ ν values than typical non-variablestars that have values around unity ( χ ν ≈
1) in an idealsituation. We considered the stars with χ ν > . ab -type and 2 c -type templates fromLayden & Sarajedini (2000) and the 17 ab -type tem-plates from Kov´acs & Kupi (2007). By visually inspect-ing the output light curves from RRFIT, we finally iden-tified 96 RR Lyrae stars, including 83 fundamental mode( ab -type) and 13 first overtone ( c -type) pulsators. Fig-ures 2 to 6 present the light curves and the best-fittingtemplates for all the detected RR Lyrae stars. Ta-ble 1 lists their pulsation properties, including coordi-nate, type, period, epoch of maximum light, intensity-weighted mean magnitude ( h B i and h V i ), the numberof observations ( N B and N V ), and amplitude ( A B and A V ). The mean magnitudes are obtained by averagingthe intensity of the best-fit templates over 0.02 phase in-terval. The quantities N B and N V are the actual num-bers of data points used in RRFIT, and some stars, forexample those lying in the gaps between the CCDs, havefewer data points compared to stars detected in all ob-servations.3.2. Synthetic Light Curve Simulation
Time-series analysis may suffer from aliasing (i.e., spu-rious periods), which is mainly caused by the limitednumber of observations, poor phase coverage, and/orphotometric uncertainty. Hence, we need to scrutinizeat what level the aliases affected the pulsation periodsbefore using them to derive metallicity, reddening, anddistance of Crater II. For this purpose we performedsynthetic light curve simulations and statistical tests fol-lowing the prescription of Yang et al. (2014). Based onthe light curve templates of Layden & Sarajedini (2000)for RR Lyrae stars, we first generated 3,000 ab -type and2,000 c -type artificial light curves by applying our obser-vational constraints (such as number of epochs, cadence,observing baseline, and photometric errors) which wereextracted from a few of the good RR Lyrae candidates.The (input) periods and amplitudes were randomly as-signed to each artificial RR Lyrae star within the appro-priate ranges of ab - and c -type variables, respectively. The faintest variable star detected in the field, V97, is notcounted here since it is probably not an RR Lyrae star (see Sec-tion 3.3).
Joo et al.
We then ran RRFIT on these synthetic time-series datain the same way as for the observed ones, so that wecan directly compare the assigned (i.e., input) and cal-culated (i.e., output) parameters.The top and bottom panels in Figure 7 present thedifference between input and output periods as a func-tion of the input periods, for RRab and RRc stars, re-spectively. Our simulations show that c -type variablesare more affected by aliasing than ab -type stars in thesense that the output periods are generally longer thanthe input periods. While the input periods of ∼
91% ofthe synthetic RRab stars were recovered within ± ∼
27% of the artificial RRc stars were re-covered within the same period range. Consequently, wehave less confidence in the pulsation parameters calcu-lated for the RRc stars in this study, and decided to usethem only for the the mean magnitude and the c -typefraction (see Section 3.3).We also estimated the systematic error in the mean pe-riod introduced by our period searching method basedon statistical analysis. By employing the synthetic RRLyrae (i.e., 3,000 RRab and 2,000 RRc) stars as a par-ent population, we randomly selected a subsample withthe same number of stars as detected in our observation(i.e., 83 RRab and 13 RRc stars). Since each artificialRR Lyrae has a ∆ P (input - output) value associated,we can calculate an average ∆ P value for the subsam-ple (i.e., h ∆ P i i ). To increase the statistical signifi-cance, we repeated this random sampling 10,000 timesand produced the h ∆ P i distribution for the 10,000 sub-samples. We consider the 1 σ range of the h ∆ P i distri-bution from the best-fit Gaussian as a good estimate forthe systematic error in the mean period of the RR Lyraestars derived by our template light curve analysis. Wefind a systematic error, σ h P ab i = ± CMD and spatial distribution
The panels in Figure 8 present the CMD, spatial dis-tribution, and color-period diagram of the RR Lyraestars we have detected in Crater II. The two grey ver-tical lines in the upper panels denote the empirical in-stability strip, roughly estimated by averaging the blueand red boundaries of 9 Galactic and LMC clusters fromWalker (1998, see his Table 7). The boundaries werereddened by assuming an interstellar extinction valueof E ( B − V ) = 0 .
05 mag (see Section 3.6). It is clearfrom panel (a) and Figure 1 that most RR Lyrae starsare within the appropriate color range of the instabilitystrip at the level of the HB. Panel (a) also shows that theRR Lyrae stars gather on the red side of the instabilitystrip in their color distribution. This further indicatesthat Crater II has a red HB morphology with virtuallyno blue HB stars, which leads the HB morphology in- dex of Lee et al. (1994), ( B − R ) / ( B + V + R ), to beroughly . − .
5, where B , V , and R are the numbers ofblue HB, variable (RR Lyrae) and red HB stars, respec-tively. This red HB morphology naturally explains therelatively small number of c -type variables compared tothat of ab -type stars, yielding the c -type fraction to allRR Lyrae variables, N ( c ) /N ( ab + c ) ≃ . ′ (approximately thehalf-light radius), and about 97% (93 out of 96) of themare within 60 ′ from the center. The CMD and spatialdistribution of the RR Lyrae variables in panels (a) and(b) thus strongly suggest that most of them belong toCrater II. The large heliocentric distance of the galaxy( ∼
112 kpc, see Section 3.6) further ensures this inter-pretation, because the Galactic halo RR Lyrae starsare thought to be rare at distances greater than ∼ ′ ( & r h ) from the center, on the other hand,are also among the brightest (V37, V79) or the reddest(V96) variables in the CMD. These three outliers mightbe field stars, and are denoted as “field?” in Table 1.In panel (c), we plot the fundamental periods (P f )of the RR Lyrae stars as a function of B − V color,where the periods of RRc stars were fundamentalizedassuming the period ratio between the c -type and ab -type stars, P c /P ab = 0.745 (Clement et al. 2001; Nemec1985). While most RR Lyrae stars follow a tight cor-relation between the fundamental period and color,some stars (green symbols) have considerably longer orshorter periods at a given color compared to the otherstars. The two ab -type stars with the longest periods,V1 and V26 (green filled circles), are also the most lumi-nous ( ∼ ab -type stars with longperiods (green open circles) can be seen as evolved RRLyrae stars, since they are also relatively bright in theCMD. The four c -type stars with short periods (greenopen triangles), however, are less certain. They are toored to be c -type stars (V69, V93, and V94) or havesomewhat short periods (V80). These four c -type starsmight be field stars or influenced by other factors suchas photometric errors or aliasing. The 10 outliers inpanel (c) are represented in Table 1 as either “field? R Lyrae stars in the Crater II dwarf galaxy h V RR i = 20 . ± .
01 mag, by fittinga Gaussian profile at the magnitude distribution, wherethe uncertainty is the standard error of the mean. Notethat, even if the 13 outliers (the three and 10 outliersin panels (b) and (c), respectively) are excluded, h V RR i does not change.The faintest variable, V97 (black circle), in panel (a)is also distinct from the other stars. It is not only sep-arated from the rest of the RR Lyrae stars in the CMDby its faint magnitude ( h V i = 21 .
334 mag), but also hasthe shortest period (P ≃ .
235 d), even though classi-fied as ab -type from the shape of the light curve (seeFigure 6 and Table 1). With this short period and pul-sation mode, V97 might be, not an RR Lyrae star, buta dwarf Cepheid (DC) (e.g., Mateo et al. 1998; Breger2000; McNamara 2011) that probably belongs to theMW; it was excluded from our analysis.3.4. Period-Amplitude Diagrams
It is widely recognized that in contrast to the Galac-tic GCs, which present the well-known Oosterhoff di-chotomy in the average period of RRab stars and theirlocation in the period-amplitude (Bailey) diagram, theclassical dSph galaxies have preferentially Oosterhoff-intermediate (Oo-int) properties (e.g., Catelan 2009;Clementini 2010; Smith et al. 2011, for reviews). MostRR Lyrae stars in the UFDs studied so far, on the otherhand, are classified as Oo-int or Oosterhoff group II(Oo II) (e.g., Clementini 2014; Vivas et al. 2016, andreferences therein). Hence, a reliable Oosterhoff classi-fication of Crater II based on the mean period of RRabstars and the Bailey diagram would help to understandthe properties of its stellar population.Figure 9 shows the period distribution and the Baileydiagram of the RR Lyrae stars in Crater II. We see inpanel (a) that the RR Lyrae stars with the two differentpulsation modes are well separated by their periods. Thesolid and dotted lines in panel (b) are the loci of Ooster-hoff group I (Oo I) and Oo II clusters, respectively, ac-cording to the relation given by Zorotovic et al. (2010,see also Cacciari et al. 2005). The average periods of 83 ab -type and 13 c -type stars are h P ab i = 0 . ± .
004 dand h P c i = 0 . ± .
009 d, respectively, where the un-certainties are the standard errors of the means. If the13 outliers (nine RRab and four RRc variables) are ex-cluded, the mean periods of 74 ab -type and nine c -typestars slightly change to h P ab i = 0 . ± .
003 d and h P c i = 0 . ± .
004 d, respectively. Note that these h P ab i values are in the range of Oo II group clusters, overthe Oosterhoff gap (0.58 d ≤ h P ab i ≤ M V < − Data for RR Lyrae variables in the UFDs aretaken from Kuehn et al. (2008, CVn I), Greco et al.(2008, Canes Venatici II, CVn II), Musella et al. (2009,Coma Berenices, ComBer), Siegel (2006, Bo¨otes I,see also Dall’Ora et al. 2006), Vivas et al. (2016, Hy-dra II), Garofalo et al. (2013, Ursa Major I, UMa I),Moretti et al. (2009, Leo IV), Clementini et al. (2012,Leo T), and Boettcher et al. (2013, Segue II). ForBo¨otes II, Bo¨otes III (Sesar et al. 2014), and Ursa Ma-jor II (UMa II) (Dall’Ora et al. 2012), we used the re-vised data by Vivas et al. (2016). For Bo¨otes I, the A B values were converted to A V using equations de-rived by Dorfi & Feuchtinger (1999) in the same way asVivas et al. (2016). In the case of Hercules, we addedthree (1 RRab and 2 RRc) stars recently identified byGarling et al. (2018) to the data of Musella et al. (2012),where the SDSS g -band amplitudes, A g , of these threevariables were transformed to A V , using the equation, V = g − .
59 ( g − r ) − .
01, by Jester et al. (2005, seetheir Table 1). Similarly, without color information, the A g values of three RRab stars in Leo V (Medina et al.2017), were converted to A V , by assuming ( g − r ) = 0 . ∼ h P ab i = 0.631 d),and the c -type fraction ( N ( c ) /N ( ab + c ) ≃ .
14) ofCrater II are comparable to those of CVn I and thetwo classical dSphs, respectively, i.e., h P ab i = 0.60 d and N ( c ) /N ( ab + c ) = 0 .
22 for CVn I, h P ab i = 0.615 d and N ( c + d ) /N ( ab + c + d ) = 0 .
21 for Draco, and h P ab i = 0.634 d and N ( c + d ) /N ( ab + c + d ) = 0.23 for Ca- Joo et al. rina, where we included Blazhko RRab stars and double-mode ( d -type) pulsators (see also Stetson et al. 2014;Baker & Willman 2015, for the several other dSphs).These similarities undoubtedly suggest an Oo-int clas-sification for Crater II, even though it has a somewhatlong h P ab i , which corresponds to the Oo II group. Thisalso leads us to conclude that, based on the RR Lyraeproperties, Crater II is more like a classical dSph ratherthan a UFD. 3.5. Metallicity
RR Lyrae stars can further be used to estimate metal-licity, reddening, and distance of a stellar system in-dependently of other methods, since their pulsationproperties (including period and amplitude) are cor-related with the stellar evolution parameters such asmass, metallicity, temperature, and luminosity (see,e.g., van Albada & Baker 1971; Sandage 1993, 2006;Di Criscienzo et al. 2004; Bono et al. 2007; Jeffery et al.2011). To obtain metallicities for the individual RRabstars of Crater II, we used the empirical period-amplitude-metallicity relation derived by Alcock et al.(2000),[Fe / H] = − .
85 (log P ab + 0 . A V ) − . , (2)where [Fe/H] is on the Zinn & West (1984) scale withan accuracy of σ [Fe / H] = 0.31 dex. The upper panelof Figure 11 shows the metallicity distribution of theRRab stars calculated from this equation and a Gaus-sian fit to the histogram, which gives the mean metallic-ity, h [Fe / H] i = − . ± .
15 (0 . − . ± . h [Fe/H] i = − . ± .
1) by Caldwell et al. (2017). Notehowever that, as Caldwell et al. (2017) already stated,their estimation might be systematically metal-poorprobably due to the zero-point uncertainty of metallic-ity. While the relation of Alcock et al. (2000) which we CVn I is often considered to be a classical dSph rather thana UFD, because of its classical-dSph-like properties such as thetotal magnitude, broad RGB, Oo-int classification, half-lightradius, and distribution of alpha-elements (e.g., Simon & Geha2007; Kuehn et al. 2008; Martin et al. 2008; Sand et al. 2012;Vargas et al. 2013). Leo T is probably not bound to the MW,located at a large heliocentric distance of ∼
409 kpc (Irwin et al.2007; de Jong et al. 2008; Clementini et al. 2012; McConnachie2012). Segue 1 is not included here. While one or two RRLyrae stars are detected by Simon et al. (2011), their periodsand amplitudes are not accurately measured (see also Vivas et al.2016). adopt here is more reliable than the other methods basedonly on the mean period of RRab stars (e.g., Sandage2006; Sarajedini et al. 2006), it should be noted that thederived [Fe/H] value has also intrinsically a large disper-sion and uncertainty. For example, it can be affected bythe luminosity (evolution) effect on the period of RRabstars (Yang et al. 2010) and/or the selection of calibra-tion cluster (Jeffery et al. 2011; Bono et al. 2007).3.6.
Reddening and Distance
Sturch (1966) has shown that ab -type RR Lyrae starshave nearly identical intrinsic colors, ( B − V ) , in thephase interval from 0.5 to 0.8 (i.e., at minimum light),only weakly correlated with period and metallic-lineblanketing. By combining the Sturch’s formula withthe calibration between metallicity and line blanketingeffect from Butler (1975), Walker (1990) presented thefollowing relation for the interstellar extinction, E ( B − V ) = ( B − V ) min − . P ab − .
056 [Fe / H] − . , (3)where ( B − V ) min is the average color at the mini-mum light (phase between 0.5 and 0.8) and the metal-licity scale is that of Zinn & West (1984). Adoptingthe metallicities from the previous subsection, we ob-tain reddening values of the individual RRab stars.The distribution of E ( B − V ) values and a Gaussianfit at the histogram are plotted (black solid lines) inpanel (b) of Figure 11, which yields h E ( B − V ) i =0 . ± .
02 (0 . . − .
03 mag. If this effectis taken into account, h E ( B − V ) i would be reduced to ∼ h E ( B − V ) i = 0.034 for r < ′ and h E ( B − V ) i = 0.037 for r < ′ areas around thecenter of Crater II (see solid and dotted grey circles inFigure 8b).Another independent estimation for the interstellarreddening can be made using the B -band amplitude(A B ), metallicity, and period of RRab stars, namely,the amplitude-color-metallicity (ACZ) and/or period-amplitude-color-metallicity (PACZ) relations derived byPiersimoni et al. (2002),( B − V ) = 0 . − . A B + 0 .
012 [Fe / H] , (4)( B − V ) = 0 . − . A B +0 .
223 log P ab +0 .
036 [Fe / H] . (5)The E ( B − V ) values are then calculated by subtractingthese intrinsic colors, ( B − V ) , from the magnitude-mean colors, ( B − V ) m . The histograms of reddening R Lyrae stars in the Crater II dwarf galaxy h E ( B − V ) i = 0 . ± .
02 (0 . − M V (RR) − [Fe / H] relation, but some discrepanciesstill remain between the methods (see, e.g., Chaboyer1999; Cacciari & Clementini 2003; Catelan 2009, forreviews). We adopt here the slope of the relation,∆ M V (RR) / ∆[Fe / H] = 0 .
23 ( ± . M V = 0 .
56 ( ± .
12) at [Fe / H] = − .
6, from Chaboyer(1999, see his equation 8). The relation is then, M V (RR) = 0 .
23 [Fe / H] + 0 . , (6)and yields the absolute magnitude M V (RR) = 0 . ± .
07, by applying the mean metallicity of RRab starsderived above, h [Fe / H] i = − . ± .
15 (0 . M V was propagated from the intrinsicdeviation of the Alcock et al. (2000) relation.Combining this with the reddening estimated aboveand the mean apparent V -magnitude, h V RR i = 20 . ± .
01, we finally obtain a distance modulus of ( m − M ) =20 . ± .
10 and a distance of d ⊙ = 112 ± m − M ) isthe quadratic sum of the errors in the M V (RR) andthe V -band extinction, ∼ . E ( B − V ). Note thatthis distance estimate agrees with the suggestion byTorrealba et al. (2016a, d ⊙ = 117 . ± . DISCUSSIONUsing the 1.6m wide-field KMTNet-CTIO telescope,we performed time-series B , V photometry of Crater II,one of the largest and lowest surface brightness dwarfsatellites of the MW. We have detected and character-ized 96 RR Lyrae stars (83 RRab and 13 RRc) withthe template light curve fitting routine, RRFIT, byYang & Sarajedini (2012) and Yang et al. (2010, 2014).The mean period of RRab stars, h P ab i = 0 . ± .
004 d,is somewhat longer than the Oosterhoff gap, but the c -type fraction is low ( ∼ ab -typevariables in the period-amplitude diagram is close to thelocus of Oo I group clusters. In terms of these Ooster-hoff properties, Crater II is very similar to CVn I and the two classical dSph, Draco and Carina. This not onlysuggests an Oo-int classification for this galaxy, but alsoleads us to conclude that it can be categorized as a clas-sical dSph rather than a UFD.These similarities in RR Lyrae stars between Crater IIand the classical dSphs indicate that the RR Lyrae prop-erties are independent of the surface brightness of thegalaxy. Instead, given the fact that Crater II and CVn I,with M V ≈ − . − .
6, respectively, are much moreluminous than typical UFDs and are comparable tothe faint classical dSphs, like Draco and Carina with M V ≈ − . − . , respectively (Martin et al. 2008;Sand et al. 2012; McConnachie 2012; Torrealba et al.2016a), the RR Lyrae properties appear to be morerelated to the total luminosity of the galaxy. Thisinterpretation also agrees well with the luminosity-metallicity (or mass-metallicity) relation of (dwarf)galaxies (e.g., Grebel et al. 2003; Kirby et al. 2008;Willman & Strader 2012; Conn et al. 2018; see alsoYang et al. 2014, for a recent compilation of nearbydwarfs), in the sense that stellar population propertiesare correlated with the luminosity (stellar mass) of thesystem.We have then constructed stellar population models,to investigate the star formation history of Crater II,following the techniques outlined by Lee et al. (1990,1994) and Joo & Lee (2013). We used Yonsei-Yale(Y ) isochrones and HB evolutionary tracks (Yi et al.2008; Han et al. 2009a), and employed the stellarmodel atmospheres by Castelli & Kurucz (2003) fortemperature-color transformations. Readers are referredto Joo & Lee (2013) and references therein for detailsof the model construction. In Figure 12, our syntheticmodel is compared with the observed CMDs for r < ′ .In this model, we first adopted the metallicity, red-dening, and distance modulus from the RR Lyrae stars,under the assumptions of [ α /Fe] = 0.3 and the standardhelium-enrichment parameter (∆ Y / ∆ Z = 2 . Y = 0.23+ Z (∆ Y / ∆ Z )). The age value was then adjusted un-til the best match between the model and the observedCMD was obtained, while those parameters from RRLyrae stars were mostly fixed. The input parametersused in our best simulation are listed in Table 3. Fig-ure 12 shows that there is no clear sign of young stellarpopulations, in addition to the old stellar populationreproduced by our model in panel (b), indicating that Unlike the other dwarfs considered here, Carina has a sizeableamount of intermediate-age population with a red HB that cannotproduce RR Lyrae stars (Monelli et al. 2003). If we assume thatroughly half of the population in Carina are old enough to hostRR Lyrae stars, then the total magnitude of the old populationonly would be M V ≃ − . Joo et al.
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R Lyrae stars in the Crater II dwarf galaxy Table 1 . Pulsation Properties of RR Lyrae Stars in Crater II
ID R.A. Dec. Type Period Epoch (max) h B i a h V i a N B b N V b A B c A V c Note(2000) (2000) (days) ( − − d V2 11:48:59.49 − − − − − − − − − − − − − − − − − − − − − − − − − d V27 11:50:26.35 − − − − − − − − − − − − − − − − − − − − − − − − Table 1 continued Joo et al.
Table 1 (continued)
ID R.A. Dec. Type Period Epoch (max) h B i a h V i a N B b N V b A B c A V c Note(2000) (2000) (days) ( − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Table 1 continued
R Lyrae stars in the Crater II dwarf galaxy Table 1 (continued)
ID R.A. Dec. Type Period Epoch (max) h B i a h V i a N B b N V b A B c A V c Note(2000) (2000) (days) ( − Table 2 . Metallicity, Reddening, and Distance of Crater IIDerived from the RRab Stars
Properties Values
Metallicity, h [Fe / H] i − . ± .
15 (0 . a Reddening, h E ( B − V ) i . ± .
02 (0 . a Distance Modulus, ( m − M ) (mag) 20 . ± . Distance, d ⊙ (kpc) 112 ±
5a The uncertainty is the standard deviation and the number in paren-theses is the standard error of the mean.
Table 3 . Input Parameters Used in Our Best Simulationof the Crater II Stellar Population Z [Fe/H] a Y b Age Mass-loss c σ M d (Gyr) ( M ⊙ ) ( M ⊙ )0.00071 − α /Fe] = 0.3.b From the standard helium-enrichment parameter, i.e., ∆ Y/ ∆ Z =2 . , Y = 0 .
23 + Z (∆ Y/ ∆ Z ).c Mean mass-loss on the RGB for Reimers (1977) mass-loss param-eter, η = 0.53.d Mass dispersion on the HB. Joo et al.
Figure 1 . CMDs of stars within and outside the half-light radius ( r h ≃ ′ , Torrealba et al. 2016a) of Crater II, obtained fromthe combined images of our time-series data. The CMD features of Crater II such as the red HB, RGB, SGB, and MSTO, areclearly visible in panel (a). The 96 RR Lyrae stars we detected are highlighted as red points. See also Figure 8(b) for theirspatial distribution. R Lyrae stars in the Crater II dwarf galaxy Figure 2 . Light curves of RR Lyrae stars for B - and V -bands (blue and red points), respectively, together with our best-fittingtemplates (solid lines). The B -band data are shifted by +0.2 mag to separate from the V -band. The variable ID, type, period(day), and V -band amplitude (mag) are denoted in each panel. The error bars in the upper left corner represent the meanphotometric errors for each band. Joo et al.
Figure 3 . Continued from Figure 2.
R Lyrae stars in the Crater II dwarf galaxy Figure 4 . Continued from Figure 3. Joo et al.
Figure 5 . Continued from Figure 4.
R Lyrae stars in the Crater II dwarf galaxy Figure 6 . Continued from Figure 5. Joo et al.
Figure 7 . Our synthetic light curve simulations for Crater II, showing the differences between the input and output periods(∆ P in − out ) as a function of the input period (left panels) and their distributions (right panels), for the two different pulsationmodes. The simulations indicate that c -type RR Lyrae stars are much more affected by aliasing compared to ab -type variables. R Lyrae stars in the Crater II dwarf galaxy Figure 8 . (a) CMD zoomed around the HB region, (b) spatial distribution, and (c) color-period diagram of the RR Lyraestars, showing that most of them belong to Crater II. Circles and triangles denote ab - and c -type variables, respectively. Thetwo vertical grey lines in panels (a) and (c) represent the empirical instability strip estimated from the nine Galactic and LMCclusters in Walker (1998), which are also reddened by 0.05 mag (see the text). The three variables (cyan circles) outside 60 ′ fromthe center of the galaxy (grey cross) might be field RR Lyrae stars. The periods of RRc stars in panel (c) are fundamentalizedassuming P c /P ab = 0.745 (Clement et al. 2001; Nemec 1985). The dotted line in panel (c) is the robust linear fit to the data,where 10 RR Lyrae stars are outside the 3 σ range. The two brightest variables with the longest periods (green filled circles)might be either field RR Lyrae stars, highly evolved RR Lyrae stars, or ACs. The four RRab stars (green open circles) withlong periods appear to be evolved RR Lyrae stars, while the four RRc stars (green triangles) with short periods are less certain.A probable non-RR Lyrae variable, V97, is marked as a black circle in panels (a) and (b). Joo et al.
Figure 9 . (a) Period distribution and (b) period-amplitude diagram of the RR Lyrae stars in Crater II. The solid and dottedlines in panel (b) represent the loci of the MW Oo I and Oo II GCs, respectively (Zorotovic et al. 2010; Cacciari et al. 2005).Symbols are the same as in Figure 8.
R Lyrae stars in the Crater II dwarf galaxy Figure 10 . (a) Same as Figure 9(b), but here the RR Lyrae stars in Crater II (red circles) are compared with those in the MWhalo (grey dots), CVn I (green crosses), and the other 13 UFDs (blue symbols). Note that this is just an update of Figure 10in Vivas et al. (2016). Numbers in parentheses are the numbers of ab - and c -type variables separated by plus signs. (b) Sameas panel (a) but compared with those in the two classical dwarfs, Draco (green) and Carina (blue). Numbers in parentheses arethe numbers of variables. Joo et al.
Figure 11 . (a) Metallicity distribution of individual RRab stars derived from the equation of Alcock et al. (2000) and aGaussian fit (solid curve). (b) Reddening distributions of RRab stars obtained from the equations of Walker (1990, W90, basedon Sturch 1966, S66) and Piersimoni et al. (2002, P02, ACZ and PACZ) and Gaussian fits to the data (solid curves). Note thatthe Sturch’s method tends to overestimate the reddening by ∼ < ′ and r < ′ regions around the center of the galaxy.Dotted lines indicate the peaks of the distributions. The peak values of metallicity and reddenings hardly change even if thenine ab -type outliers (i.e., the three stars outside 2 r h and the six stars with long periods) are excluded. Figure 12 . Comparison of our population models with the observations of Crater II. (a) Observed CMD, similar to Figure 1(a)with red open circles for the RR Lyrae stars. (b) Our population models (green lines and points) on the observed CMD (greypoints). Red crosses denote the model RR Lyrae stars. Parameters used in our simulation are listed in Table 3. Adoptedreddening and distance modulus are E ( B − V ) = 0 .
05 and ( m − M ) = 20 .
30 mag, where ( m − M )0