DRAFTVERSION NOVEMBER 28, 2018 Typeset using LATEX twocolumn style in AASTeX61

PRECISION DISTANCES TO DWARF GALAXIES AND GLOBULAR CLUSTERS FROM PAN-STARRS1 3π RR LYRAE

NINA HERNITSCHEK,1 JUDITH G.COHEN,1 HANS-WALTER RIX,2 EUGENE MAGNIER,3 NIGEL METCALFE,4 RICHARD WAINSCOAT,3 CHRISTOPHER WATERS,5 ROLF-PETER KUDRITZKI,3 AND WILLIAM BURGETT6

1Division of Physics, Mathematics and Astronomy, Caltech, Pasadena, CA 91125 2Max-Planck-Institut fur¨ Astronomie, Konigstuhl¨ 17, 69117 Heidelberg, Germany 3Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA 4Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK 5Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton, NJ 08544, USA 6GMTO Corporation (Pasadena), 465 N. Halstead Street, Suite 250, Pasadena, CA 91107, USA

ABSTRACT We present new spatial models and distance estimates for globular clusters (GC) and dwarf spheroidals (dSphs) orbiting our Galaxy based on RR Lyrae (RRab) in the Pan-STARRS1 (PS1) 3π survey. Using the PS1 sample of RRab stars from Sesar et al.(2017) in 16 globular clusters and 5 dwarf galaxies, we fit structural models in (l, b, D) space; for 13 globular clusters and 6 dwarf galaxies, we give only their mean heliocentric distance D. We verify the accuracy of the period-luminosity (PL) relations used in Sesar et al.(2017) to constrain the distance to those stars, and compare them to period-luminosity-metallicity (PLZ) relations using metallicities from Carretta et al.(2009). We compare our Sesar et al.(2017) distances to the parallax-based Gaia DR2 distance estimates from Bailer-Jones et al.(2018), and find our distances to be consistent and considerably more precise. arXiv:1811.10808v1 [astro-ph.GA] 27 Nov 2018

Corresponding author: Nina Hernitschek [email protected] 2 HERNITSCHEKETAL.

1. INTRODUCTION PL relations for both the RRab and RRc samples as well as In this paper, we exploit the opportunities provided by the for the combined RRab+RRc sample. In their 2017 paper Pan-STARRS1 (PS1) 3π RR Lyrae catalog (Sesar et al. 2017) (Neeley et al. 2017), they also present theoretical mid-IR to explore the . Using that large data set of PLZ relations for RR Lyrae stars at Spitzer and WISE wave- RRab stars covering 3/4 of the sky out to more than 130 kpc, lengths and show that the mid-IR PLZ relations can provide in Hernitschek et al.(2018) we looked at the seemingly distance estimates to individual RR Lyrae stars with uncer- smooth part of the stellar halo. We now focus on the RRab tainties better than 2%. This is comparable to the result by stars in globular clusters (GC) and dwarf galaxies in order to Sesar et al.(2017) derived for the RRab stars with optical determine their distances and constrain their structure. For photometry used in this paper. For the dSph Sculptor, which most of these objects, RRab stars may be the most precise lies outside of the PS1 3π footprint, Garofalo et al.(2018) distance tracers. As shown in Section8, all GC and dwarf derived mid-IR PLZ relations and calculated the distance to galaxies we study here are beyond any parallax precision of the as part of the Spitzer SHMASH project, Gaia DR2, which is according to Bailer-Jones et al.(2018) which targeted in total four dSph (Ursa Minor dSph, Bootes only valid within a heliocentric distance range of about 5 kpc. dSph, Sculptor dSph and Carina dSph). The main advantages of such a study are that due to the large This paper is structured as follows. In Section2, we intro- angular extent and depth of PS1 3π, the source of observa- duce the PS1 3π survey and lay out the properties of the PS1 tional data as well as the methodology are the same for all RRab stars. This is followed in Section3 by a description GC and dSph we analyze. The aim of this paper is to pre- of the spatial area covered by PS1 3π, and the list of GCs cisely constrain the position and extent of each of these over- and dSph that are included in it. In Section4, we present densities from RRab stars, where we determine these prop- the method of fitting a series of parameterized stellar den- erties for 29 GC and 11 dwarf spheroidal (dSph) galaxies, sity models and the probabilistic approach to constrain their and if this is not possible, to at least to give their mean he- model parameters. We describe fitting tests on mock data in liocentric distances. Furthermore, from the globular clusters Section 4.3. In Section5, the position and extent are esti- we demonstrate that the period-luminosity relations used by mated for each GC and dSph. We present various analyses Sesar et al.(2017) to determine the distances of the RRab based on these fitted parameters. In Section6, we calculate stars are precise and their predicted magnitudes well within mean distances for those dwarf galaxies and GC which don’t the claimed uncertainties. have enough sources for the fitting process. We also discuss RR Lyrae stars (RRL) as distance indicators have the ad- the implications on period-luminosity relations in Sec.7, and vantage of being low-mass stars found in both early- and late- compare our distance estimates to those derived using the type stellar systems (van den Bergh 1999). When periods, or second Gaia data release in Sec.8. A discussion and sum- periods and metallicities, for RRL are known, their distances mary of our results is given in Section9. The main part of can be estimated using period-luminosity (PL) or period- the paper is followed by a large Appendix containing figures luminosity-metallicity (PLZ) relations. Visual magnitude- as well as tables. metallicity relations are described for example in Chaboyer 2. RR LYRAE STARS FROM THE PS1 SURVEY et al.(1996), Bono et al.(2003), Cacciari & Clementini (2003). In the infrared, the extinction is smaller and the am- As in our previous papers, e.g. Hernitschek et al.(2017) plitude of variation is smaller. In the near infrared (NIR), and Hernitschek et al.(2018), our analysis is based on a well-defined PL relations can be found (Longmore et al. sample of highly likely RRab stars, as selected by Sesar et al. 1986; Bono et al. 2001, 2003; Catelan et al. 2004; Braga (2017) from the Pan-STARRS1 3π survey. Here, we briefly et al. 2015; Sesar et al. 2017), extending to the mid-infrared describe the pertinent properties of the PS1 3π survey and the with only small scatter (Madore et al. 2013; Klein et al. RR Lyrae light curves obtained, and recapitulate briefly the 2014). process of selecting the likely RRab for the catalog of PS1 These individual distance estimates can then be used to cal- RRab stars, as laid out in Sesar et al.(2017). We also briefly culate distances to and the shape of globular clusters as well characterize the obtained candidate sample. as dwarf galaxies. Dwarf galaxies orbiting our The Pan-STARRS 1 (PS1) survey (Kaiser et al. 2010) col- are not only interesting objects per se, but can also provide lected multi-epoch, multi-color observations undertaking a us with important information to determine the Milky Way’s number of surveys, among which the PS1 3π survey (Cham- total mass and dynamics. bers et al. 2016) is currently the largest. It has ob- ◦ Dambis et al.(2014) used WISE as well as zero-points served the entire sky north of declination −30 in five fil- from HST parallaxes to derive PL relations from 360 RRL ter bands (gP1, rP1, iP1, zP1, yP1) with a 5σ single epoch belonging to 15 globular clusters. depth of about 22.0, 22.0, 21.9, 21.0 and 19.8 magnitudes More recent work on the distances of globular clusters was in gP1, rP1, iP1, zP1, and yP1, respectively (Stubbs et al. carried out by e.g. Neeley et al.(2015) who investigated 2010; Tonry et al. 2012). 9 mid-IR period-luminosity-metallicity (PLZ) relations for the Starting with a sample of more than 1.1 × 10 PS1 3π NGC 6121 (M4), which is not in our sample sources, Hernitschek et al.(2016) and Sesar et al.(2017) as it lies outside of the PS1 3π footprint. Their work contains subsequently selected a sample of 44,403 likely RRab stars, of which ∼17,500 are at Rgc ≥ 20 kpc, by applying PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 3 machine-learning techniques based on light-curve charac- Catalogue of Variable Stars in Globular Clusters. As shown teristics. RRab stars are the most common type of RR Lyrae, in Fig. 12, we find that for each of the 11 globular clusters making up ∼91% of all observed RR Lyrae (Smith 2004), available in both catalogs, our catalog misses most RRab in and displaying the steep rises in brightness typical of RR the globular cluster’s central regions. The dSph galaxies are Lyrae. sufficiently diffuse that this is not a significant issue. The identification of the RRab stars is highly effective, and the sample of RRab stars is pure (90%), and complete 4. DENSITY FITTING (≥ 80% at 80 kpc) at high galactic latitudes. Distances to In this section we lay out a forward-modeling approach to these stars were calculated based on flux-averaged i mag- P1 describe the spatial distribution of RRab stars within and near nitudes, corrected for dust extinction using extinction coeffi- overdensities such as dwarf galaxies and globular clusters. cients of Schlafly & Finkbeiner(2011) and the dust map of We are using a local halo model describing the background of Schlafly et al.(2014). The distance estimates are precise to field stars from the halo as in Hernitschek et al.(2018) and 3%, based on newly derived PL relations for the optical/near- a smooth spheroidal distribution describing the overdensity infrared PS1 bands (Sesar et al. 2017). Overall, this results in itself. Regarding the dwarf galaxies, this approach is similar the widest (3/4 of the sky) and deepest (reaching > 120 kpc) to Martin et al.(2008), who derived structural parameters of sample of RR Lyrae stars to date, allowing us to observe Milky Way satellites from SDSS data. them globally across the Milky Way. Out of these sources, We presume that the local stellar halo distribution can be 1093 exist beyond a Galactocentric distance of 80 kpc, with sensibly approximated by a spheroidal distribution with a 238 beyond 100 kpc, which enables us to estimate distances parameterized radial profile. (See also Hernitschek et al. to and extents of dwarf galaxies and globular clusters. RRc (2018).) The overdensities can be described by multivariate stars, which were also selected by Sesar et al.(2017), are not Gaussians in (l, b, D). Following a number of previous stud- included in our study. ies (e.g. Sesar et al. 2013; Xue et al. 2015; Cohen et al. 2015; Iorio et al. 2017; Hernitschek et al. 2018), we pre- 3. SAMPLE OF GLOBULAR CLUSTERS AND DWARF sume that the overall radial density profile of the halo out- GALAXIES side of overdensities – the distance-dependent “background” PS1 3π, as it covers the entire sky north of declination of field stars in a given direction – can be described by a −30◦ out to more than 130 kpc, gives us access to many power law profile. We attempt to carry out the fit on small globular clusters (GC) and several dwarf galaxies. 5 × 5 deg2 patches on the sky around the assumed position To select those overdensities for which fitting their den- prior (lprior, bprior). We thus neglect the selection effects and sity might be feasible, we started with a list of dwarf galax- halo flattening described in Hernitschek et al.(2018) and ies within 3 Mpc by McConnachie(2012), its update from instead fit for a local stellar halo distribution as a function of 20141 and a list of currently known globular clusters from the a power-law index n only. 2010 update of Harris(1996). We excluded the ones outside We apply a forward-modeling process to fit stellar-density the PS1 3π footprint and made plots of regions on the sky models to the data by generating the expected observed dis- around for each of the remaining ones. If an overdensity is tribution of stars in the RRab sample, based on our model apparent in the PS1 RRab sample from visual inspection, we for the halo background and overdensity. The predicted dis- consider it for further analysis. We ended up with a list of tribution is then automatically compared to the observed 11 dwarf galaxies and 29 globular clusters within PS1 3π, as counts to calculate the likelihood. given in Tables1 and2. Plots of a subset of these overden- sities are found in the Appendix, Fig.1 to 11. For plotting 4.1. Stellar Density Model those overdensities, we chose a Cartesian projection of (l, b) to more easily compare to their marginalized distributions in For the overall radial density profile of the halo stars, we l and b (histograms). With this choice, high-latitude overden- assume a power-law model sities such as NGC 5024, NGC 5053 and NGC 5272 appear n to be elongated in the l direction. ρhalo(X,Y,Z) = ρ RRL (R /rq) (1) We expected that the central regions of the globular clus- ters might be not well represented due to crowding and blend- where ρ RRL gives the number density of RR Lyrae at ing effects that made many RRab stars fail to meet the criteria the position of the Sun, n is the power-law index where for inclusion in the catalogue of PS1 RRab stars (Sesar et al. larger values of n indicate a steeper profile, R the dis- tance of the Sun from the , and rq = 2017). To test that, we compared our sample with the Cat- p alogue of Variable Stars in Globular Clusters from Clement (X2 + Y 2 + (Z/q)2) is the flattening-corrected radius. et al.(2001). There are 11 globular clusters detectable with In Hernitschek et al.(2018), we derived the halo flattening RRab stars both in the catalog of PS1 RRab stars and the on concentric ellipsoids. However, as we deal here with very small patches on the sky, and don’t want to derive a reliable fit for the halo but want to remove any background distribution, 1 https://www.astrosci.ca/users/alan/Nearby_ we decided to set q = 0.75, leaving n the only free parameter Dwarfs_Database.html for the halo component. Also, we are not fitting for ρ RRL. 4 HERNITSCHEKETAL.

The spatial density of an overdensity, i.e. a dwarf galaxy or being the marginal log likelihood for the full data set. globular cluster, is described by a multivariate Gaussian G: To determine the best-fit parameters and their uncertain- ties, we sample the posterior probability over the parame- ρ∗(l, b, D) =G(l, b, D) (2) ter space with Goodman & Weare’s Affine Invariant Markov   2  2  2 Chain Monte Carlo (Goodman et al. 2010), making use of exp −0.5 l−¯l + b−¯b + D−D¯ σl σb σD the Python module emcee (Foreman et al. 2013). = . (3/2) The final best-fit values of the model parameters have been σlσbσD (2π) estimated using the median of the posterior distributions; the uncertainties have been estimated using the 15.87th and The data set D is given as D = (D, δD, l, b). The pa- ¯ ¯ 84.13th percentiles. For a parameter whose pdf can be well- rameters are θ = (l, b, D,¯ σl, σb, σD, f∗, n), composed of ¯ ¯ ¯ described by a Gaussian distribution, the difference between the spatial position of the overdensity (l, b, D), its extent the 15.87th and 84.13th percentile is equal to 1σ. (σl, σb, σD), the fraction of the stars f∗ being in the over- ¯ ¯ Our model has 8 free parameters, θ = (l, b, D,¯ σl, σb, σD, f∗, n), density, and the power-law index n of the halo model. The and each star has three-dimensional coordinates (l, b, D). As heliocentric distance distribution of stars is then character- we attempt to carry out the fit on small 5 × 5 deg2 patches ized by on the sky around the assumed position prior (lprior, bprior), we always have a sufficient number of overdensity and back- p (D|θ) = p (D|θ) + p (D|θ) (3) RRL halo ∗ ground RRab stars for the fit as shown in Fig.1 to 11. The = (1 − f∗) × ρˆhalo(l, b, D, n) overdensity itself is fit by a three-dimensional Gaussian de- ¯ ¯ ¯ ¯ ¯ +f∗ × ρˆ∗(l, b, D, l, b, D,¯ σl, σb, σD), scribing the spatial position of the overdensity (l, b, D) and its extent (σl, σb, σD). Thus a minimum number of two where RRab stars within the overdensity, in addition to the back- ground, is needed for a successful fit, albeit with large uncer- ρhalo(l, b, D, q, n) tainties when the number of RRab is small. All overdensities ρˆhalo(l, b, D, q, n) ≡ R , (4) ρhalo(l, b, D, q, n)dD for which we later claim fitted positions and spatial extents meet these criteria, i.e. the minimum number of RRab stars with an analogous definition of ρˆ∗. is 3. Although we were aware of a distance uncertainty of 3% for RRab stars from Sesar et al.(2017), we have not included 4.2.1. Model Priors it in our calculations yet. The reason for this is that the dis- We now lay out the “pertinent range”, across which the pri- tance uncertainty can easily be taken into account later on, as ¯ ¯ ors for the model parameters θ = (l, b, D,¯ σl, σb, σD, f∗, n) the distance uncertainty D ∼ 0.03D adds in quadrature to ¯ ¯ the (true) width in distance: are given. Based on Table1 and2, we can set priors on l, b, D¯. In general, we allow a rather wide prior, i.e. allow the q on-sky positions to vary around the object’s center by ±5◦, σ = (σ0 )2 + 2 . D D D (5) and the heliocentric mean distance D¯ to vary by ±20 kpc. In cases with a second overdensity nearby (i.e. NGC 5024, We will deal with the distance precision vs. true line of sight NGC 5053), we set more rigid priors on ¯l, ¯b, D¯. As the halo depth later when we evaluate our fitting results. profile tends to vary a lot on such small patches on the sky as are evaluated here, we allow the power-law index n to vary 4.2. Constraining Model Parameters between 1.7 and 5. With the model ρRRL(D|θ) at hand, we can directly calcu- Our complete prior function is then: late the likelihood of the data D given the model ρRRL and the fitting parameters θ. The normalized un-marginalized logarithmic likelihood ln p(θ) =Uniform(0.05 ≤ f∗ < 1) for the i-th star with the observables Di is then + Uniform(1.7 ≤ n < 5.0) ¯ ρRRL(Di|θ)|J| + Uniform(log |l − ltab| < log offset deg) ln p(Di|θ) = RRR (6) ¯ ρRRL(l, b, D|θ)|J|dldbdD + Uniform(log |b − btab| < log offset deg) + Uniform(log |D¯ − D | < log offset kpc) where the normalization integral is over the observed vol- tab ume. The Jacobian term |J| = D2 cos b reflects the transfor- + Uniform(log(0.1) < log(σl) < log(10)) mation from (X,Y,Z) to (l, b, D) coordinates. + Uniform(log(0.1) < log(σb) < log(10)) We evaluate the logarithmic posterior probability of the pa- + Uniform(log(0.1) < log(σD) < log(20)), rameters θ of the halo model, given the full data D and a prior (8) p(θ), ln p(θ|D) = ln p(D|θ) + ln p(θ) with where the index ”tab” denotes the values from Tab.1 and X ◦ ln p(D|θ) = ln p(Di|θ) (7) 2, respectively, and offset deg = 5 , offset kpc = i PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 5

20 kpc for all overdensities except for NGC 5024, NGC 5.1. Comments on Individual Dwarf Galaxies and Globular 5053. For NGC 5024 and NGC 5053, we set the offset to Clusters ◦ offset deg = 1 . We now comment on the fitting results for individual dwarf 4.3. Fitting Tests on Mock Data galaxies and globular clusters. We fitted the five dwarf galaxies Sagittarius dSph, Sex- In order to test the methodology for fitting the density tans dSph, Draco dSph, dE, I as discussed in Section4, we created mock data samples dSph. of RRab stars in the Galactic halo, superimposed Gaussian As the Sagittarius dSph lies at the edge of the PS1 3π foot- mock overdensities with typical distance, extent and star print, we cannot successfully fit its on-sky position (l, b), but count to mimic dwarf galaxies and globular clusters, and fi- we can fit its heliocentric distance D. This can be clearly nally added noise in distance to mimic the distance uncer- seen from Fig.2. For this reason, we don’t give any values tainty of 3%. We then applied our fitting method. dependent on the fitted (l, b) position in the tables. Fig. 13 shows two examples of a simulated distribution of For the other dwarf galaxies, we found that the fit is well halo and overdensity RRab along with a fit, analogous to the defined as these overdensities have typically &100 sources, plots of the GC and dSph shown in Fig.1 to Fig. 11. One of except for Ursa Major I. In the case of the latter, the marginal- them is an overdensity with a high contrast against the back- ized best-fit model for l as given in the lower left panel of Fig. ground of (mock) field stars that resembles a dSph, whereas 3 does not seem to match the histogram well. However, this the other is a sparse overdensity, comparable to typical GC. is only an effect due to the marginalization in the histogram, We give their distribution in (l, b, D) space as well as their as it shows all sources independent of their distance, whereas marginalized distributions, the distribution these mock stars the Gaussian is centered on the fitted (l, b, D). Comparing were drawn from and the best-fit distribution after applying the best-fit model to the map of stars as given in the upper our fitting methodology. left panel reveals the accuracy of the fit. We find results that are consistent with the input model Regarding globular clusters, we have to deal with overden- within reasonable uncertainties, which means that we are sities of fewer sources, given that the central regions are too able to recover the input parameters for the models within crowded for the PS1 RRab catalog (Sesar et al. 2017). Com- their assumed parameter range. paring for example the panel of NGC 5024 in Fig. 12 to the histograms in Fig.5, we clearly see that stars are missing 5. RESULTS FROM FITTING near the assumed center of the globular cluster. However, the When trying to fit all dSph from Tab.1 and globular clus- fit is stable enough to identify a reasonable center position. ters from Tab.2, we found that the data available for some of As for the dwarf galaxy Ursa Minor Dwarf dE, in the case them do not allow for a reasonable fit. For the Crater II dSph of the globular clusters NGC 5024, NGC 5904, NGC 4590, at a distance of ∼120 kpc, the PS1 RRab catalog does not NGC 6864, NGC 7089, the marginalized best-fit model in l contain enough sources for a good fit, not surprising given and b doesn’t seem to match the histogram as well as might the large distance. As Sagittarius dSph lies at the edge of the be expected, as the histogram shows all sources independent PS1 3π footprint, we cannot successfully fit its on-sky posi- of their distance, while the Gaussian is centered on the fitted tion (l, b), but we can fit its heliocentric distance D. Among (l, b, D). Again, comparing the best-fit model to the map of the globular clusters, we have to exclude NGC 4147, NGC stars, we see the fit is reliable. 5634, NGC 5694, NGC 5897, IC 1257, NGC 6093 (M80), In some dSphs and GCs, only 3 - 4 RRab were detected. NGC 6171 (M107), NGC 6356, NGC 6402 (M14), NGC This is the case for Ursa Major I dSph, Ngc 5053, NGC 6864 6426, NGC 7099 (M30), Pal 1, Pal 13, as in those cases, we (M75), NGC 8089 (M2), Pal 3 and Pal 5. In each of those find too few, if any, RRab stars associated with these over- cases, the overdensity is clearly visible in the map of RRab densities picked up by the PS1 3π survey. stars. The histograms might look unconvincing, as they show In Tables3 and4 as well as in Figures1 to 11 we give the all sources independent of their distance and thus are heavily dSph and GC best-fit parameters we get from successfully influenced by field stars. The corresponding best-fit model carrying out the fitting as described in Section4. Tables3 assigns a distance and position (l, b, D) corresponding well and4 list the name, fitted position (l, b, D), fitted angular with the map of RRab stars. However, we expect that the cen- extent σl, σb and depth σD assuming a multivariate Gaussian, ter, (l, b, D), and the extent of the overdensity, (σl, σb, σD) as well as the derived linear extents (∆l, ∆b, ∆D) as can not be determined accurately from only 3 - 4 stars, as there is a high chance that the stars are not representative, i.e. p are at the bright or shallow end or are not located symmetri- ∆l = 2 2((D cos(b))2)(1 − cos(σ )) (9) l cally with respect to the center. ∆b = 2D tan(σb) (10) 5.2. Uncertainty-Corrected Depth of Dwarf Galaxies and ∆D = 2σD. (11) Globular Clusters We give also the axis ratios ∆D/∆l and ∆D/∆b describ- In Table3 and4, we give the axis ratios ∆D/∆l and ing the morphology, as well as the number of sources found ∆D/∆b describing the morphology of each fitted overden- in the dSph or globular cluster in each case. sity. Starting with the dwarf galaxies, we find that all five of 6 HERNITSCHEKETAL. them are found to be quite elongated in the direction of D. In our sample, except Ursa Major I dSph, our estimated extent contrast, their values for ∆D/∆l and ∆D/∆b are compara- from max(σl,σb) matches quite well the core radius. In all ble (except for Sagittarius dSph, where we cannot calculate cases, our estimated extent is below the tidal radius. We don’t them), which is not surprising from Fig.1 and3 showing a pick up sources within or near the core radius for GC. We very round shape in (l, b). We now check if the elongation in attribute this to the fact that in the case of GC, we are losing D direction can be explained by the distance uncertainty. the RRab stars in the cores, as mentioned in Sec.3. For Sextans dSph, Draco dSph, Ursa Minor Dwarf dE4 and Ursa Major I dSph, we find a ∆D/∆l of 9.83, 14.48, 19.77, 6. MEAN DISTANCES TO OTHER GLOBULAR CLUSTERS AND DWARF GALAXIES 4.84, respectively. Using Equ. (5) with D = 0.03D, we calculate the uncertainty-corrected (true) line-of-sight depth For those dwarf galaxies and globular clusters from Table 0 0 p 2 2 p 2 2 (∆D) = 2σD = 2 (σD − D) = 2 (σD − (0.03D) ). 1 and2 which don’t have enough sources to carry out the We find thus (∆D)0 = 4.28 for the Sextans dSph, (∆D)0 = fitting process described in Section4, we derived their mean 1.79 for the Draco dSph, (∆D)0 = 1.41 for the Ursa Minor distances (in the case of finding multiple RRab stars likely Dwarf dE4, (∆D)0 = 0.94 for the Ursa Major I dSph. associated with the overdensitiy in case) or give the distance For the Ursa Major I dSph, D must be .0.027D instead to the single RRab star found within this overdensity. of 0.03D to make the result sensible. With the values for ∆l Tab.5 and6 list the distances, along with the number of given in Tab.3 and D = 0.03D, we calculate ∆D/∆l = RRab stars found in each case. 7.78 for Sextans dSph, 6.36 for Draco dSph, 6.40 for Ursa In total, for each of 13 GC and 6 dSph we found at least Minor Dwarf dE4, 1.44 for Ursa Major I dSph. one RRab star associated with the overdensity. For those with This means that introducing a distance uncertainty, which at least two RRab stars, we give the mean distance, and oth- is appropriate as shown by Sesar et al.(2017), reduces the erwise, the distance from the only RRab star found. In most elongation in D direction, but is still far away from an axis cases, our distance estimate lies well within the 3% uncer- ratio of 1. As the distance uncertainty D and the true line-of- tainty we claim for the PS1 3π sample of RR Lyrae stars. 0 sight extent σD add in quadrature to make the fitted line-of- For some overdensities, we find a lot of stars in the field sight extent σD, a slightly variation in D from the nominal at about the same distance. This is the case for NGC 5897, 3% derived by Sesar et al.(2017) would be able to explain all where one RRab star is very close to the assumed coordinates of the asymmetry. E.g. for the Sextans dSph, D = 0.0396D of this GC, but there are in total up to 4 stars that could be instead of 0.030D would result into a (∆D)0 = 0.55 and associated with that GC. For NGC 6402 (M14), the field is thus (∆D)0/∆l ∼ 1. Similarly, an axis ratio of 1 could be even more crowded; there are many sources in the field at achieved for the Draco dSph with D = 0.0322D, for the that distance without revealing an overdensity. Ursa Minor Dwarf dE4 with D = 0.0316D, and for the In the case of NGC 6356, we find one source close to the Ursa Major I dSph with D = 0.027D. coordinates given for this GC, but at a different distance: The In addition to variations in the distance uncertainties, for RRab star from our catalog is at a heliocentric distance of globular clusters we suggest that fitting uncertainties and es- 11.02 kpc, whereas Harris(1996) gives a heliocentric dis- pecially shot noise are responsible for the non-spherical axis tance of 15.1 kpc for NGC 6356. In the case of Pal 1, we ratios we find. This means, because of the expected small find no RRab stars clearly associated with this GC. For Pal line-of-sight extent, even with a distance uncertainty of 3% 13, we find three RRab stars for which we calculate a mean we cannot say much about the line-of-sight extent for GC and distance of 23.59 kpc, which is about 2.5 kpc lower than the dwarf galaxies at the distances considered here. distance given by the recent compilation of Harris(1996). Siegel et al.(2010) claim a distance of 24.8 kpc, which is 5.3. The Radii of Globular Clusters and Dwarf Galaxies within our distance precision. The same is the case for the We also compared our fitted extent σl, σb to the tidal radius dwarf galaxy Bootes I dSph. We find a mean heliocentric and core radius. distance of 60.61 kpc, which is about 5 kpc off from the dis- For globular clusters, we use the tidal radius rt and core tance given by Okamoto et al.(2012). However, our distance radius rc from the 2010 update of Harris(1996). We use the estimate matches very well the distance of 60.4 kpc by Ham- core radii from Stoehr et al.(2002) for the dwarf galaxies mer et al.(2018). For dSph, it is difficult to identify Draco dSph, Sextans dSph and Ursa Minor Dwarf dE4. A which sources are likely associated with this dwarf galaxy, core radius for Ursa Major I dSph is provided by Simon & as there are many sources in the field at about that distance. Geha(2007). We use tidal radii from Odenkirchen et al. For the farthest dwarf galaxy in our sample, Crater II dSph, (2001) (Draco dSph), Roderick et al.(2016) (Sextans dSph) our heliocentric distance estimate of 105.48 kpc is somewhat and Kleyna et al.(1998) (Ursa Minor Dwarf dE4). A tidal lower than distance estimates in the literature, i.e. the 112 radius for Ursa Major I dSph is not available. kpc claimed by Joo et al.(2018). Tables7 and8 and Fig. 14 summarize these comparisons. We find that for globular clusters, while the distribution 7. PERIOD-LUMINOSITY RELATIONS shows a lot of scatter, our estimated extent from max(σl,σb) In one of our previous papers (Sesar et al. 2017), we represents significant fractions of the tidal radius. We find used the period–absolute magnitude–metallicity (PLZ) rela- sources far beyond the core radius. For the dwarf galaxies in tion known for RR Lyrae stars to calculate the RRab star’s PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 7 distances we use in the paper at hand. The PLZ relation is ∼0.06 mag in the absolute magnitude and thus distance mod- given as (e.g. Catelan et al. 2004; Sollima et al. 2006): ulus (Sesar et al. 2017). As the distance modulus was derived from the iP1 band, in this band, per definition, the observed Mλ = αλ log10(P/Pref )+βλ([Fe/H]−[Fe/H]ref )+Mref,λ+ magnitude and the as predicted without (12) [Fe/H] are the same. We find that for most of the 16 globular where λ denotes the bandpass, P is the period of pulsation, clusters we have evaluated, the predicted apparent magnitude Mref is the absolute magnitude at some reference period and with [Fe/H] (blue markers in the Figures) is a bit brighter than metallicity (here chosen to be Pref = 0.6 days, [Fe/H]ref = - the predicted apparent magnitude without taking into account 1.5 dex), and α, β describe the dependence of the absolute [Fe/H] (black markers), and this is again a bit brighter than magnitude on period and metallicity. The  is a standard the observed dereddened apparent magnitude (orange mark- normal random variable centered on 0 and with a standard ers). NGC 6864 (Fig. 24) is the only GC where the predicted deviation of the uncertainty in Mλ in order to model the in- apparent magnitude with [Fe/H] is higher than the one pre- trinsic scatter in the absolute magnitude convolved with un- dicted without [Fe/H]. It has the highest metallicity in the accounted measurement uncertainties. sample of GC studied here. As PS1 3π itself has no metallicity information available, The offset in the predicted apparent magnitude is depend- we constrained the PLZ relation Equ. (12) in PS1 bandpasses ing on the metallicity of the GC in case. The predicted using metallicities and distance moduli of PS1 RRab stars in apparent magnitudes with [Fe/H] (blue markers in the Fig- the five Galactic globular clusters NGC 6171, NGC 5904, ures) are calculated using Equ. (12) and the distance mod- NGC 4590, NGC 6341, NGC 7078 (Sesar et al. 2017). Table ulus for each RRab star given in the PS1 RRab catalog 1 in Sesar et al.(2017) gives the fitted PLZ relations in all (Sesar et al. 2017). For the black markers, we neglect the bandpasses. The resulting relation in the i band is then P1 term βλ([Fe/H] − [Fe/H] ) from Equ. (12), and again used to constrain distances also for stars where no metallicity ref use the distance modulus. As βλ ranges from 0.06 to 0.09, is available. [Fe/H]ref = −1.5, and [Fe/H], which ranges from -2.33 to In the case of no available metallicity, the expression for -1.29, is < −1.5 for most GC, this term is negative. Thus, for the absolute magnitude in the iP1 band, MiP1 , simplifies to most of the 16 globular clusters we have evaluated, the pre- (Sesar et al. 2017, Equ. (5)): MiP1 = −1.77 log10(P/0.6) + dicted apparent magnitude with [Fe/H] (blue markers in the 0.46, and in general, the expression for the absolute magni- Figures) is a bit brighter than the predicted apparent magni- tude in the λP1 band simplifies to tude without taking into account [Fe/H] (black markers). The offset between observed and predicted apparent mag- M = α log (P/0.6) + M . (13) λP1 λ 10 ref,λ nitudes can be explained by the way the distance to the RRab Distances are then constrained using the dereddened flux- stars was derived. The distance modulus we use here to cal- averaged iP1-band magnitude (this is iF in Sesar et al. culate the predicted magnitudes was derived in Sesar et al. (2017)) and Equ. (13). This equation was used to calcu- (2017) using the flux-averaged iP1-band magnitude. Thus, late the PS1 3π RRab distances we use in this paper. for the i band, the observed magnitude (orange markers) Now, after having fitted the spatial extent and distance of and the magnitude predicted without [Fe/H] agree, while for 16 globular clusters, we are interested in comparing the fitted the other bands, we find the predicted magnitudes to devi- PLZ relation from Sesar et al.(2017) to fits carried out for ate slightly from the observed ones (black vs. orange mark- each cluster using the [Fe/H] from spectra of red giants of ers). This deviation is in the order of the uncertainty claimed Carretta et al.(2009) (Table A1). For each RRab star in each for the distance modulus, 0.06(rnd) ± 0.03 (sys) mag (Sesar GC, we have the period from the RRab catalog, the [Fe/H] – et al. 2017). assumed to be constant for a given GC – from Carretta et al. (2009) and the fitted distance modulus (DM) and distance 8. GAIA DR2 DISTANCES from the RRab catalog. In this section, we compare the PS1 3π distances to those For Fig. 15, we selected the RRab stars for each globular published for the second Gaia data release (hereafter Gaia cluster and plot their dereddended apparent r band magnitude DR2; Gaia Collaboration(2018a)). (rF in the PS1 RRab catalog) vs. their period. The typical According to Bailer-Jones et al.(2018), for the vast ma- trend of a PL relation is clearly visible. jority of stars in Gaia DR2, reliable distances cannot be ob- We then took a closer look at the individual globular clus- tained by inverting the parallax, but should be derived by an ters. For each of them, in each bandpass λ ∈ {gP1, ..., zP1} algorithm that accounts for the nonlinearity of the transfor- we plot each star’s dereddened apparent magnitude mλ mation. Carrying out a probabilistic approach, Bailer-Jones vs. P . We also plot the apparent (unreddened) magni- et al.(2018) published distances to 1.33 billion stars in Gaia tude as expected from the PLZ relation αλ log10(P/Pref ) + DR2. βλ([Fe/H] − [Fe/H]ref ) + Mref + DM vs. P , as well as the To compare our heliocentric distance estimates DPS1 from apparent magnitude as expected from the equation without Sesar et al.(2017) to those of Gaia DR2 Bailer-Jones et al. metallicity αλ log10(P/Pref ) + Mref + DM vs. P . (2018), we cross-matched our PS1 RRab sample of 44,403 This results in Figures 16 to 31. The error bars in the pre- stars with Gaia DR2, and found a cross-match for 43,791 dicted apparent magnitudes correspond to an uncertainty of sources. In Fig. 32, we show the DGaiaDR2 and a rough dis- 8 HERNITSCHEKETAL. tance estimate 1/parallax vs. DPS1 for the RRab stars within timated its distance to 27.24 kpc, in comparison to the 25 kpc DPS1 < 20 kpc. given by Harris(1996). At the present time, we find a rather large scatter in the dis- For the dwarf galaxy Bootes I dSph, we find a mean he- tances, much larger than the PS1 distance uncertainty of 3% liocentric distance of 60.61 kpc, which is about 5 kpc off or an estimate of the distance uncertainty from the parallax from the distance given by Okamoto et al.(2012) and about error. When the parallax error exceeds 10%, which happens 1.5 kpc off from the distance given by Siegel et al.(2006). at a heliocentric distance of about 5 kpc, the distances from However, our distance estimate matches very well the dis- Gaia DR2 become very unreliable. Bailer-Jones et al.(2018) tance of 60.4 kpc given by Hammer et al.(2018). The most already claim quite large uncertainties of their distance esti- distant dwarf galaxy in our sample is Crater II dSph. Our mates. In Fig. 33, we plot the upper and lower 68% confi- heliocentric distance estimate of 105.48 kpc for this dwarf dence interval boundaries of their distance estimates for our galaxy is somewhat off from the 117.5 kpc distance estimate cross-matched sample of RRab stars. According to Bailer- reported by McConnachie(2012), but there are closer dis- Jones et al.(2018), the confidence intervals are asymmetric tance estimates like the 112 ± 5 kpc claimed by Joo et al. with respect to the distance estimate DGaiaDR2 as a conse- (2018), which agrees within the uncertainties with our re- quence of the nonlinear transformation from parallax to dis- sult. For Sagittarius dSph, our distance estimate of 28.18 tance. kpc is slightly larger than, but within the uncertainties of the Up to now, the precision of those distances – which are 26.3 ± 1.8 kpc result obtained by (Monaco et al. 2004). calculated only from geometric principles without any as- For Ursa Minor Dwarf dE4, we find a distance of 68.41 kpc, sumptions on astrophysics such as pulsation or PLZ relation- whereas the distance is given as 76 kpc from Bellazzini et al. ships – is not competitive with the precision of our distances (2002) as well as Carrera et al.(2002). from Sesar et al.(2017), and especially cannot be used for In some cases, it is hard to find stars associated with the the distant GC and dwarfs. However, this might change at overdensities, especially if there are many field stars within least partially for the end-of-mission data. Until then, we the assumed distance range of the dwarf galaxy or GC, and strongly recommend using the RRab distances from Sesar there is no apparent overdensity. This is the case for NGC et al.(2017) and subsequent analysis instead of those from 5897, where one RRab star is very close to the assumed co- Gaia DR2. ordinates of this GC, but there are in total up to 4 stars that could be associated with that GC. For the GC NGC 6402 9. DISCUSSION AND SUMMARY (M14), the field is even more crowded, so many sources in We started our analysis based on a list of dwarf galaxies the field are at its assumed distance without revealing an within 3 Mpc by McConnachie(2012) and a list of currently overdensity. For NGC 6356, we find one source close to known globular clusters from a current online version of the the coordinates given for this GC, but at a different distance: Harris(1996) database. We excluded those outside the PS1 The RRab star from our catalog is at a heliocentric distance 3π footprint and attempted to fit the (l, b, D) distribution of of 11.02 kpc, whereas Harris(1996) give a heliocentric dis- the remaining ones. For the ones for which a fit was not tance of 15.1 kpc for NGC 6356. In the case of Pal 1, we find possible due to only a small number of RRab stars available, no stars clearly associated with this GC. For Segue 1 dSph, we instead selected those stars and give their mean distance. it is difficult to identify the sources that might be associated In Tab.9 and 10, we compare our distances for dwarf with this dwarf galaxy, as there are many sources in the field galaxies and GC to literature distances. For almost all dwarf at about that distance. galaxies and globular clusters, the estimated distances com- For the GC, even though these sources are closer, in most pared to those in the recent literature are well within our dis- cases our distance uncertainties are larger than for dwarf tance precision of 3%. However, there are a few dwarf galax- galaxies. This probably occurs because we are missing ies and globular clusters for which our distances deviate sig- sources near the centers of the GCs as the spatial density nificantly from those given in the literature. of sources is higher that which can be handled by the PS1 In the case of NGC 6356, we find only one source close analysis codes. to the coordinates given for this GC, but at a different dis- In this paper we have computed the extents ∆l, ∆b, ∆D tance: While the RRab star from our catalog is at a helio- and the axis ratios ∆D/∆l and ∆D/∆l for all dwarf galax- centric distance of 11.02 kpc, the updated catalog of Harris ies and GCs in which a sufficient number of RRab were (1996) gives a heliocentric distance of 15.1 kpc for NGC picked up in the PS1 RR Lyr database of Sesar et al.(2017). 6356. For Pal 3, we find three stars within a small distance Our distances to the stellar overdensities we study here, in- range, resulting in a heliocentric distance estimate of 85.05 cluding both GCs and dwarf galaxy satellites of the Milky kpc, whereas Harris(1996) gives a distance of 92.5 kpc. For Way, are accurate to better than 3% when more than 8 RRab Pal 13, we find three RRab stars resulting in a mean distance occur within a system (i.e. a GC or a dSph). of 23.59 kpc, which is about 2.5 kpc off from the distance In the past 5 years many groups have attempted to deter- given by Harris(1996). However, this star might be a mem- mine distances to some of the dwarf galaxies using RRab, but ber of Pal 13, as Siegel et al.(2010) claim a distance of 24.8 they have each used their own procedures and calibrations to kpc, which is within our distance precision. For IC 1257, we convert a mean RRab magnitude into a distance (see Tab.9 have found only 1 RRab star associated with this GC and es- and 10 for references). Our work is unique in that every ob- PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 9 ject, within the large sample we study, is treated identically and comes from the same survey, including the metallicity dependence of the RR luminosity, so that the distances for our large sample of objects are on the same scale across the entire part of the sky covered by the PS1 3π survey, for all halo stellar overdensities within which a sufficient number of RRab could be detected. Thus overall we believe that our distances for the sample of stellar overdensities in the Milky Way halo, i.e. globular clusters and dwarf galaxies, that we study here are more precise and more homogeneous than those in the published literature.

H.-W.R. acknowledges funding from the European Re- search Council under the European Unions Seventh Frame- work Programme (FP 7) ERC Grant Agreement n. [321035]. The Pan-STARRS1 Surveys (PS1) have been made pos- sible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the Univer- sity of Edinburgh, Queen’s University Belfast, the Harvard- Smithsonian Center for Astrophysics, the Las Cumbres Ob- servatory Global Telescope Network Incorporated, the Na- tional Central University of Taiwan, the Space Telescope Sci- ence Institute, the National Aeronautics and Space Adminis- tration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under Grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE) and the Los Alamos National Lab- oratory. 10 HERNITSCHEKETAL.

APPENDIX A. FIGURES PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 11

Draco dSph 40 80 40 best fit parameters ] with 1σ 1

− 35 38 70 n = 3.62+0.17 c 0.18 − 60 p 30 +0.028 ] f = 0.69 k 0.027

36 [ c ∗ − 50 25 +0.18 p D = 74.26 kpc s 0.18 r b 34 k 20 +−0.17 [ 40 a σD = 2.40 kpc

t 0.15 − s 15 +0.01

32 30 D l = 86.37 0.01 deg b −+0.01

a 10 20 σl = 0.13 0.01 deg 30 R − 5 +0.01 10 R b = 34.71 0.01 deg −+0.01 28 0 σb = 0.13 0.01 deg 92 90 88 86 84 82 80 0 10 20 30 40 50 60 70 80 90 − l D [kpc] 800 700 ] ] 1 1

− 700 − 600 g g

e 600 e 500 d d [ [

500

s s 400 r 400 r a a

t t 300

s 300 s

b 200 b 200 a a

R 100 R 100 R R 0 0 92 90 88 86 84 82 80 28 30 32 34 36 38 40 l [deg] b [deg]

(a)

Sextans dSph 48 16 best fit parameters ] with 1σ 105 1

− 14 46 n = 3.79+0.2 c 0.2 − 90 p 12 +0.04

] f = 0.62 k 0.036

44 [ c ∗ − 75 10 +0.41

p D = 81.42 kpc s 0.4 r b 42 60 k 8 +−0.43 [ a σD = 3.24 kpc

t 0.37 − s 6 +0.04

45 D 40 l = 243.55 0.04 deg b +−0.03

a 4 30 σl = 0.26 0.03 deg

38 R − 2 +0.04 15 R b = 42.26 0.03 deg −+0.04 36 0 σb = 0.23 0.03 deg 250 248 246 244 242 240 238 0 20 40 60 80 100 120 − l D [kpc] 200 250 ] ] 1 1 − −

g g 200

e 150 e d d [ [ 150 s s r 100 r a a t t 100 s s

b 50 b a a 50 R R R R 0 0 250 248 246 244 242 240 238 36 38 40 42 44 46 48 l [deg] b [deg]

(b)

Figure 1. The dwarf spheroidals Draco dSph (a) and Sextans dSph (b). For both subfigures, the first panel shows a map of RRab stars near the dwarf galaxy, 270 stars in the figure for Draco dSph, and 157 for Sextans dSph, respectively. The stars are color-coded according to their heliocentric distance. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from4 with the parameters given on the right. 12 HERNITSCHEKETAL.

Sagittarius dSph 8 300 best fit parameters 72 ] with 1σ 1

10 64 − 250 n = 2.20+0.027 c 0.026 − 56 p +0.00085

] f = 0.38 k 0.00038

12 [ 200 c ∗ − 48 +0.093

p D = 28.18 kpc s 0.098 r b 14 40 k 150 +−0.016 [ a σD = 1.01 kpc 0.0082 32 t − s +0.083

16 D 100 l = 7.19 0.078 deg 24 b −+0.052 a σl = 0.69 0.055 deg

16 R 18 50 − +0.18 8 R b = 14.50 0.15 deg − +0.0−94 20 0 σb = 1.30 0.087 deg 11 10 9 8 7 6 5 4 0 10 20 30 40 50 60 70 80 − l D [kpc] 500 300 ] ] 1 1

− − 250 g 400 g e e

d d 200 [ [ 300 s s r r 150 a a t 200 t s s 100 b b

a 100 a

R R 50 R R 0 0 11 10 9 8 7 6 5 4 20 18 16 14 12 10 8 l [deg] b [deg]

Figure 2. The dwarf spheroidal Sagittarius dSph. The first panel shows a map of 1413 RRab stars near the dwarf galaxy; the stars are color-coded according to their heliocentric distance. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. As the Sagittarius dSph lies near the edge of the PS1 3 π footprint, we cannot successfully fit its on-sky position (l, b), but we still can fit its heliocentric distance D. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 13

Ursa Major I dSph 60 2.0 best fit parameters 90 ] with 1σ 1

58 80 − n = 4.47+0.31 c 0.39 − 70 p 1.5 +0.065 ] f = 0.20 k 0.035

56 [ c ∗ − 60 +11

p D = 94.33 kpc s 4.9 r b 54 50 k 1.0 +−5.9 [ a σD = 2.59 kpc 1.1 t − 40 s +2.1

52 D l = 159.38 1.5 deg 30 b +−2.5

a 0.5 σl = 0.34 0.2 deg 50 20 R −+2.8 10 R b = 54.43 0.39 deg −+2 48 0.0 σb = 0.33 0.19 deg 166 164 162 160 158 156 154 0 20 40 60 80 100 − l D [kpc] 20 20 ] ] 1 1 − − g g

e 15 e 15 d d [ [

s s r 10 r 10 a a t t s s

b 5 b 5 a a R R R R 0 0 166 164 162 160 158 156 154 48 50 52 54 56 58 60 l [deg] b [deg]

(a)

Ursa Minor Dwarf dE4 50 72 12 best fit parameters ] with 1σ 1

48 64 − 10 n = 3.55+0.28 c 0.28 − − 56 p +0.054

] f = 0.54 k 0.049

46 [ 8 48 c ∗ − +0.51

p D = 68.41 kpc s 0.51 r b 44 40 k 6 +−3.1 [ a σD = 2.17 kpc 0.59 32 t − s +0.62

42 D 4 l = 105.00 0.06 deg 24 b +−0.86 a σl = 0.16 0.03 deg

16 R 40 2 −+0.36 8 R b = 44.74 0.06 deg −+1.4 38 0 σb = 0.14 0.02 deg 110 108 106 104 102 100 0 10 20 30 40 50 60 70 80 − l D [kpc] 160 160 ] ] 1 1

− − 140 g g

e 120 e 120 d d [ [

100 s s r 80 r 80 a a t t

s s 60

b 40 b 40 a a

R R 20 R R 0 0 110 108 106 104 102 100 38 40 42 44 46 48 50 l [deg] b [deg]

(b)

Figure 3. The dwarf spheroidals Ursa Major I dSph (a) and Ursa Minor Dwarf dE4 (b). The first panel shows a map of RRab stars near the dwarf galaxy, 26 for Ursa Major I dSph, and 98 stars in the figure for Ursa Minor Dwarf dE4, respectively. The stars are color-coded according to their heliocentric distance. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. In the case of Ursa Major I dSph, the best-fit model in the lower left panel doesn’t seem to match the histogram quite well. However, this is only an effect due to the marginalization in the histogram, as it shows all sources independent of their distance, while the Gaussian is centered on the fitted (l, b, D). 14 HERNITSCHEKETAL.

NGC 2419 32 4.0 best fit parameters ] with 1σ

105 1

− 3.5 30 n = 2.91+0.23 c 0.21 90 − p 3.0 +0.046

] f = 0.13 k 0.038

28 [ 75 c ∗ − 2.5 +0.32

p D = 79.70 kpc s 0.37 r b 26 60 k 2.0 +−1.3 [ a σD = 4.24 kpc 1.1 t − s 1.5 +0.03

45 D 24 l = 180.36 0.03 deg b +−0.01

a 1.0 30 σl = 0.11 0.01 deg

22 R − 0.5 +0.04 15 R b = 25.24 0.03 deg −+0.02 20 0.0 σb = 0.11 0.01 deg 186 184 182 180 178 176 174 0 20 40 60 80 100 120 − l D [kpc] 140 120 ] ] 1 1

− 120 − 100 g g

e 100 e d d 80 [ [

s 80 s r r 60 a a

t 60 t s s 40

b 40 b a a

R 20 R 20 R R 0 0 186 184 182 180 178 176 174 20 22 24 26 28 30 32 l [deg] b [deg]

(a)

NGC 4590 (M68) best fit parameters 40 64 9 ] with 1σ 1 8

39 − 56 n = 3.51+0.13 c 0.16 7 − 38 p +0.017

48 ] f = 0.06 k 0.0099

[ 6 c ∗ − 37 +0.26

40 p D = 10.48 kpc s 5 0.28 r b 36 k +−1.3 [ 32 a σD = 0.66 kpc 0.13 t 4 − 35 s +0.12

24 D 3 l = 299.62 0.08 deg b +−0.68

34 a 16 2 σl = 0.15 0.04 deg 33 R −+0.1 8 R 1 b = 36.07 0.11 deg −+0.65 32 0 σb = 0.15 0.04 deg 306 304 302 300 298 296 294 0 10 20 30 40 50 60 70 − l D [kpc] 60 50 ] ] 1 1

− 50 − g g 40 e e

d 40 d [ [ 30 s s r 30 r a a t t 20 s s 20 b b

a a 10

R 10 R R R 0 0 306 304 302 300 298 296 294 32 33 34 35 36 37 38 39 40 41 l [deg] b [deg]

(b)

Figure 4. The globular clusters NGC 2419 (a) and NGC 4590 (M68) (b). The first panel shows a map of RRab stars near the globular cluster, 74 stars in the figure for NGC 2419, and 119 for NGC 4590, respectively. The other three panels show the marginalized histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. For NGC 4590, the best-fit model in the lower left panel doesn’t seem to match the histogram quite well. However, this is only an effect due to the marginalization in the histogram, as it shows all sources independent of their distance, while the Gaussian is centered on the fitted (l, b, D). PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 15

NGC 5024 (M53) 84 12 best fit parameters 80 ] with 1σ 1

70 − 10 n = 3.32+0.29 82 c 0.3 − p +0.078

60 ] f = 0.26 k 0.078

[ 8 c ∗ − 80 +0.13

p D = 18.25 kpc 50 s 0.14 r b k 6 +−0.08 [ a σD = 0.55 kpc 40 0.03 t − 78 s +0.12

30 D 4 l = 332.93 0.12 deg b +−0.12 76 20 a σl = 0.35 0.08 deg R 2 −+0.04 10 R b = 79.74 0.04 deg −+0.02 74 0 σb = 0.11 0.01 deg 338 336 334 332 330 328 326 0 10 20 30 40 50 60 70 80 90 − l D [kpc] 35 100 ] ] 1 1

− 30 −

g g 80 e 25 e d d [ [ 60

s 20 s r r a a t 15 t 40 s s

b 10 b a a 20 R 5 R R R 0 0 338 336 334 332 330 328 326 74 76 78 80 82 84 l [deg] b [deg]

(a)

NGC 5053 84 12 best fit parameters 80 ] with 1σ 1

70 − 10 n = 3.39+0.2 82 c 0.25 − p +0.054

60 ] f = 0.08 k 0.022

[ 8 c ∗ − 80 +0.28

50 p D = 16.66 kpc s 0.26 r b k 6 +−3.7 [ 40 a σD = 0.75 kpc

t 0.2 − 78 s +0.19

30 D 4 l = 335.78 0.18 deg b +−1.1 76 20 a σl = 0.30 0.16 deg R 2 −+0.16 10 R b = 78.93 0.14 deg −+1.1 74 0 σb = 0.18 0.06 deg 342 340 338 336 334 332 330 0 10 20 30 40 50 60 70 80 90 − l D [kpc] 30 100 ] ] 1 1

− 25 − g g 80 e e

d 20 d [ [ 60 s s r 15 r a a t t 40 s s 10 b b

a a 20

R 5 R R R 0 0 342 340 338 336 334 332 330 74 76 78 80 82 84 l [deg] b [deg]

(b)

Figure 5. The globular clusters NGC 5024 (M53) (a) and NGC 5053 (b). The first panel shows a map of RRab stars near the globular cluster, 40 stars in the figure for NGC 5024, and 75 stars for NGC 5272, respectively. The stars are color-coded according to their heliocentric distance. In the Cartesian projection, both NGC 5024 and NGC 5053 appear to be elongated in l direction because of its high latitude. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. 16 HERNITSCHEKETAL.

NGC 5272 (M3) 84 70 best fit parameters ] with 1σ 90 1 82 − 60 n = 4.36+0.43 c 0.38 − 75 p +0.059 ] 50 f = 0.74 k 0.09

80 [ c ∗ −

+0.07

p D = 10.48 kpc 60 s 40 0.07 r b 78 k +−0.02 [ a σD = 0.51 kpc 0.01 45 t 30 − s +0.08

76 D l = 42.20 0.07 deg 30 b 20 −+0.05 a σl = 0.45 0.05 deg 74 R 10 −+0.02 15 R b = 78.71 0.02 deg −+0.01 72 0 σb = 0.10 0.002 deg 48 46 44 42 40 38 36 0 20 40 60 80 100 120 − l D [kpc] 90 300 ] ] 1 80 1 − − 250 g 70 g e e

d 60 d 200 [ [

s 50 s r r 150 a a

t 40 t s s 30 100 b b

a 20 a

R R 50

R 10 R 0 0 48 46 44 42 40 38 36 72 74 76 78 80 82 84 l [deg] b [deg]

(a)

NGC 5466 80 10 best fit parameters ] with 1σ 90 1 78 − n = 4.07+0.33 c 8 0.29 − 75 p +0.073

] f = 0.27 k 0.064

76 [ c ∗ − 6 +0.14

p D = 15.76 kpc 60 s 0.14 r b 74 k +−0.07 [ a σD = 0.54 kpc

t 0.03 45 − s 4 +0.04

72 D l = 42.13 0.04 deg 30 b −+0.03 a 2 σl = 0.12 0.02 deg 70 R −+0.04 15 R b = 73.59 0.03 deg −+0.02 68 0 σb = 0.11 0.01 deg 48 46 44 42 40 38 36 0 20 40 60 80 100 120 − l D [kpc] 70 80 ] ] 1 1

− 60 − g g

e 50 e 60 d d [ [

s 40 s r r 40 a a

t 30 t s s

b 20 b 20 a a

R 10 R R R 0 0 48 46 44 42 40 38 36 68 70 72 74 76 78 80 l [deg] b [deg]

(b)

Figure 6. The globular clusters NGC 5272 (M3) (a) and NGC 5466 (M5) (b). The first panel shows a map of RRab stars near the globular cluster, 75 in the figure for NGC 5272, and 36 for NGC 5904, respectively. In the Cartesian projection, both NGC 5272 and NGC 5466 appear to be elongated in l direction because of its high latitude. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 17

NGC 5904 (M5) 52 72 30 best fit parameters ] with 1σ 1

50 64 − 25 n = 2.54+0.13 c 0.13 − 56 p +0.028

] f = 0.14 k 0.038

48 [ 20 48 c ∗ − +0.19

p D = 7.87 kpc s 0.19 r b 46 40 k 15 −+0.08 [ a σD = 0.53 kpc 0.02 32 t − s +0.03

44 D 10 l = 3.88 0.04 deg

24 b −+0.04 a σl = 0.13 0.02 deg

16 R 42 5 −+0.03 8 R b = 46.77 0.02 deg −+0.02 40 0 σb = 0.11 0.005 deg 9 8 7 6 5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 − l D [kpc] 120 200 ] ] 1 1

− 100 − g g

e e 150

d 80 d [ [

s s r 60 r 100 a a t t s s 40 b b 50 a a

R 20 R R R 0 0 9 8 7 6 5 4 3 2 1 0 40 42 44 46 48 50 52 l [deg] b [deg]

(a)

NGC 6229 46 8 best fit parameters ] with 1σ 56 1

− 7 44 n = 3.34+0.17 c 0.18 − 48 p 6 +0.027

] f = 0.08 k 0.021

42 [ c ∗ − 40 5 +0.17

p D = 29.94 kpc s 0.19 r b 40 k 4 +−0.19 [ 32 a σD = 0.61 kpc 0.08 t − s 3 +0.04

38 24 D l = 73.64 0.04 deg b −+0.02

a 2 16 σl = 0.11 0.01 deg

36 R − 1 +0.04 8 R b = 40.31 0.04 deg −+0.03 34 0 σb = 0.11 0.01 deg 80 78 76 74 72 70 68 0 10 20 30 40 50 60 70 − l D [kpc] 120 70 ] ] 1 1

− 100 − 60 g g

e e 50 d 80 d [ [

s s 40 r 60 r a a

t t 30 s s 40

b b 20 a a

R 20 R 10 R R 0 0 80 78 76 74 72 70 68 34 36 38 40 42 44 46 l [deg] b [deg]

(b)

Figure 7. The globular clusters NGC 5904 (M5) (a) and NGC 6229 (b). The first panel shows a map of RRab stars near the globular cluster, 177 in the figure for NGC 5904, and 104 for NGC 6229, respectively. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. For NGC 5904, the best-fit model in the lower left panel doesn’t seem to match the histogram quite well. However, this is only an effect due to the marginalization in the histogram, as it shows all sources independent of their distance, while the Gaussian is centered on the fitted (l, b, D). 18 HERNITSCHEKETAL.

NGC 6864 (M75) 23.5 72 7 best fit parameters ] with 1σ 24.0 1 64 − 6 n = 2.96+0.055 c 0.054 24.5 − 56 p +0.0027

] 5 f = 0.05 k 0.0011

25.0 [ c ∗ −

48 +0.32

p D = 20.79 kpc 25.5 s 4 0.35 r b 40 k +−4.3 [ a σD = 1.59 kpc 0.93 26.0 t 32 3 − s +0.25

26.5 D l = 20.28 0.23 deg 24 b 2 −+1.5 27.0 a σl = 0.25 0.13 deg

16 R 1 − +0.2

27.5 R 8 b = 25.76 0.28 deg − +2.7− 28.0 0 σb = 0.34 0.21 deg 23 22 21 20 19 18 0 10 20 30 40 50 60 70 80 − l D [kpc] 80 50 ] ] 1 1

− 70 −

g g 40

e 60 e d d [ [ 50 30 s s r 40 r a a t t 20 s 30 s

b 20 b a a 10 R 10 R R R 0 0 23 22 21 20 19 18 28 27 26 25 24 23 l [deg] b [deg]

(a)

NGC 6934 12 25 best fit parameters 90 ] with 1σ 1

14 80 − n = 3.38+0.067 c 20 0.065 − 70 p +0.0046

16 ] f = 0.05 k 0.0028 [ c ∗ − 60 15 +0.21

p D = 16.77 kpc 18 s 0.21 r b 50 k +−0.16 [ a σD = 0.57 kpc 0.05 20 t − 40 s 10 +0.04

D l = 52.12 0.04 deg 22 30 b −+0.03 a 5 σl = 0.11 0.01 deg

20 R 24 − +0.03 10 R b = 18.87 0.04 deg − +0.0−2 26 0 σb = 0.11 0.01 deg 58 56 54 52 50 48 46 0 20 40 60 80 100 − l D [kpc] 120 120 ] ] 1 1

− 100 − 100 g g e e

d 80 d 80 [ [

s s r 60 r 60 a a t t s s 40 40 b b a a

R 20 R 20 R R 0 0 58 56 54 52 50 48 46 24 22 20 18 16 14 l [deg] b [deg]

(b)

Figure 8. The globular clusters NGC 6864 (M75) (a) and NGC 6934 (b). The first panel shows a map of RRab stars near the globular cluster, 81 in the figure for NGC 6864, and 378 for NGC 6934, respectively. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. For NGC 6864, the best-fit model in the lower left panel doesn’t seem to match the histogram quite well. However, this is only an effect due to the marginalization in the histogram, as it shows all sources independent of their distance, while the Gaussian is centered on the fitted (l, b, D). PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 19

NGC 6981 (M72) 28 30 best fit parameters ] with 1σ 90 1 − 25 n = 3.14+0.077 30 80 c 0.084 − p +0.012

] f = 0.06 70 k 0.007

[ 20 c ∗ − 32 60 +0.15

p D = 17.51 kpc s 0.17 r b 50 k 15 +−0.11 [ a σD = 0.56 kpc 0.05 t − 34 40 s +0.03

D 10 l = 35.16 0.03 deg 30 b −+0.01 36 a σl = 0.11 0.01 deg

20 R 5 − +0.03 10 R b = 32.70 0.03 deg − +0.0−1 38 0 σb = 0.11 0.01 deg 30 32 34 36 38 40 0 20 40 60 80 100 − l D [kpc] 160 120 ] ] 1 1

− 140 − 100 g g

e 120 e

d d 80 [ [

100 s s r 80 r 60 a a t t

s 60 s 40 b 40 b a a

R 20 R 20 R R 0 0 42 40 38 36 34 32 30 38 36 34 32 30 28 26 l [deg] b [deg]

(a)

NGC 7006 14 14 best fit parameters ] with 1σ

80 1 − 12 n = 3.33+0.092 16 70 c 0.09 − p +0.012

] 10 f = 0.06 60 k 0.0084 [ c ∗ − 18 +0.16

p D = 40.12 kpc 50 s 8 0.15 r b k +−0.11 [ a σD = 0.59 kpc 0.06 40 t 6 − 20 s +0.03

30 D l = 63.78 0.03 deg b 4 −+0.01 22 20 a σl = 0.11 0.004 deg R 2 − +0.03 10 R b = 19.39 0.03 deg − +0.0−1 24 0 σb = 0.11 0.01 deg 70 68 66 64 62 60 58 0 10 20 30 40 50 60 70 80 90 − l D [kpc] 160 ] ]

1 1 120

− 140 −

g g 100 e 120 e d d [ [

100 80 s s r 80 r a a 60 t t

s 60 s 40 b 40 b a a

R 20 R 20 R R 0 0 70 68 66 64 62 60 58 24 22 20 18 16 14 l [deg] b [deg]

(b)

Figure 9. The globular clusters NGC 6981 (M72) (a) and NGC 7006 (b). The first panel shows a map of RRab stars near the globular cluster, 271 in the figure for NGC 6981, and 278 for NGC 7006, respectively. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. 20 HERNITSCHEKETAL.

NGC 7078 (M15) 22 18 best fit parameters ] with 1σ 90 1 16 − n = 3.46+0.099 24 80 c 0.086 14 − p +0.014

] f = 0.06 70 k 0.0081

[ 12 c ∗ − 26 60 +0.24

p D = 11.07 kpc s 10 0.22 r b 50 k +−2.7 [ a σD = 0.60 kpc

t 8 0.08 − 28 40 s +0.11

D 6 l = 65.03 0.08 deg 30 b −+1.1 30 a 4 σl = 0.15 0.04 deg 20 R − +0.07

R 2 10 b = 27.32 0.08 deg − +0.9−5 32 0 σb = 0.13 0.03 deg 70 68 66 64 62 60 0 20 40 60 80 100 − l D [kpc] 80 100 ] ] 1 1

− 70 −

g g 80

e 60 e d d [ [ 50 60 s s r 40 r a a t t 40 s 30 s

b 20 b a a 20 R 10 R R R 0 0 60 62 64 66 68 70 34 32 30 28 26 24 22 l [deg] b [deg]

(a)

NGC 7089 (M2) 30 9 best fit parameters 80 ] with 1σ 1 8 32 − n = 3.24+0.11 70 c 0.11 7 − p +0.0077

] f = 0.06 60 k 0.0044

34 [ 6 c ∗ −

+0.39

p D = 12.11 kpc 50 s 5 0.28 r b 36 k +−6.3 [ a σD = 1.47 kpc 0.84 40 t 4 − s +0.22

38 30 D 3 l = 53.46 0.25 deg b −+2.4 20 a 2 σl = 0.35 0.21 deg 40 R − +0.29 10 R 1 b = 35.81 0.29 deg − +3.6− 42 0 σb = 0.62 0.47 deg 58 56 54 52 50 48 0 10 20 30 40 50 60 70 80 90 − l D [kpc] 80 60 ] ] 1 1

− 70 − 50 g g

e 60 e

d d 40 [ [

50 s s r 40 r 30 a a t t

s 30 s 20 b 20 b a a

R 10 R 10 R R 0 0 58 56 54 52 50 48 42 40 38 36 34 32 30 l [deg] b [deg]

(b)

Figure 10. The globular clusters NGC 7078 (M15) (a) and NGC 7089 (M2) (b). The first panel shows a map of RRab stars near the globular cluster, 211 in the figure for NGC 7078, and 163 for NGC 7089, respectively. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. For NGC 7089, the best-fit model in the lower left panel doesn’t seem to match the histogram quite well. However, this is only an effect due to the marginalization in the histogram, as it shows all sources independent of their distance, while the Gaussian is centered on the fitted (l, b, D). PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 21

Pal 3 44.0 2.0 best fit parameters ] with 1σ 80 1 43.5 − n = 3.65+0.92 c 1.2 − 70 p 1.5 +0.18

43.0 ] f = 0.32 k 0.18 [ c ∗ − 60 +0.32

p D = 85.05 kpc 42.5 s 0.34 r b k 1.0 +−1.8 [ 50 a σD = 1.76 kpc 1.1 42.0 t − s +0.1

40 D l = 240.14 0.09 deg 41.5 b +−0.17

a 0.5 30 σl = 0.14 0.03 deg 41.0 R −+0.21 20 R b = 41.95 0.18 deg −+0.31 40.5 0.0 σb = 0.34 0.17 deg 243 242 241 240 239 238 237 0 10 20 30 40 50 60 70 80 90 − l D [kpc] 50 30 ] ] 1 1

− − 25 g 40 g e e

d d 20 [ [ 30 s s r r 15 a a t 20 t s s 10 b b

a 10 a

R R 5 R R 0 0 243 242 241 240 239 238 41.041.542.042.543.043.544.0 l [deg] b [deg]

(a)

Pal 5 48.0 64 4.0 best fit parameters ] with 1σ 47.5 1

− 3.5 56 n = 2.68+0.098 c 0.11 47.0 − 48 p 3.0 +0.0074 ] f = 0.06 k 0.0038

46.5 [ c ∗ − 2.5 +0.33

40 p D = 21.66 kpc 46.0 s 0.3 r b k 2.0 +−7.5 [ 32 a σD = 1.61 kpc

45.5 t 0.98 − s 1.5 +0.29

45.0 24 D l = 0.87 0.27 deg b −+2.8

a 1.0 44.5 16 σl = 0.58 0.43 deg R 0.5 −+0.26 44.0 R 8 b = 45.80 0.28 deg −+2.4 43.5 0.0 σb = 0.31 0.19 deg 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 0 10 20 30 40 50 60 70 − l D [kpc] 30 50 ] ] 1 1

− 25 − g g 40 e e

d 20 d [ [ 30 s s r 15 r a a t t 20 s s 10 b b

a a 10

R 5 R R R 0 0 3.0 2.5 2.0 1.5 1.0 0.5 0.0 43 44 45 46 47 48 l [deg] b [deg]

(b)

Figure 11. The globular clusters Pal 3 (a) and Pal 5 (b). The first panel shows a map of RRab stars near the globular cluster, 8 in the figure for Pal 3, and 28 for Pal 5, respectively. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted is the best-fit model from Sec.4 with the parameters given on the right. 22 HERNITSCHEKETAL.

RRab stars Clement+2001 RRab stars Sesar+2017b

80.0 79.2 79.1 NGC 5024 (M53) NGC 5053 79.0 NGC 5272 79.9 79.1 78.9 79.8 79.0 78.8 b b b 79.7 78.9 78.7 78.6 79.6 78.8 78.5 79.5 78.7 78.4 334.0 333.5 333.0 332.5 332.0 337 336 335 45 44 43 42 41 40 39 l l l

36.3 73.7 NGC 4590 NGC 5466 47.4 NGC 5904 (M5) 36.2 73.6 47.2 36.1

b b 73.5 b 47.0 36.0 46.8 73.4 35.9 46.6 35.8 73.3 299.8 299.7 299.6 299.5 299.4 42.3 42.2 42.1 42.0 41.9 41.8 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 l l l

40.40 18.75 32.60 40.38 NGC 6229 NGC 6934 NGC 6981 (M72) 18.80 32.65 40.36 40.34 18.85 32.70

b 40.32 b b 40.30 18.90 32.75 40.28 18.95 32.80 40.26 40.24 19.00 32.85 73.8 73.7 73.6 52.20 52.15 52.10 52.05 52.00 35.3 35.2 35.1 35.0 l l l

19.25 27.20 NGC 7006 NGC 7078 (M15) 19.30 27.25

19.35 27.30 b b 19.40 27.35

19.45 27.40

19.50 27.45 63.80 63.75 63.70 65.2 65.0 64.8 l l

Figure 12. Comparison of the RRab stars available in our PS1 RRab catalog (Sesar et al. 2017) as used for this work, to the RRab stars in the Catalogue of Variable Stars in Galactic Globular Clusters (Clement et al. 2001). For the 11 globular clusters available in both catalogs, we find that our catalog misses most RRab in the central regions of the globular clusters. These regions are too compact, and thus most stars did not pass the quality criteria for the PS1 RRab catalog. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 23

mock dSph with halo background 42 25 best fit parameters ] with 1σ 72 1

40 − n = 4.64+0.2 64 c 20 0.23 − 38 p +0.036

56 ] f = 0.59 k 0.037 [ c ∗ − 36 48 15 +0.2

p D = 74.07 kpc s 0.2 r b 34 40 k +−0.16 [ a σD = 2.09 kpc 0.15 32 t − 32 s 10 +0.012

D l = 86.01 0.012 deg

24 b −+0.0086

30 a 16 5 σl = 0.12 0.0084 deg 28 R −+0.013 8 R b = 35.00 0.012 deg −+0.0087 26 0 σb = 0.12 0.0082 deg 92 90 88 86 84 82 80 0 20 40 60 80 100 120 − l D [kpc] 350 350 input parameters ] ] 1 1 n = 4.50 − 300 − 300

g g f = 0.60 e 250 e 250 ∗

d d D = 74.00 kpc [ [ σD = 2.00 kpc s 200 s 200 r r l = 86.00 deg a a t 150 t 150 σ = 0.13 deg s s l

b 100 b 100 b = 35.00 deg a a σb = 0.13 deg R 50 R 50 R R 0 0 92 90 88 86 84 82 80 28 30 32 34 36 38 40 l [deg] b [deg]

(a)

mock gc with halo background 42 30 best fit parameters 54 ] with 1σ 1

40 − 48 25 n = 4.35+0.25 c 0.3 − 38 42 p +0.057

] f = 0.21 k 0.057

[ 20 c ∗ − 36 36 +0.12

p D = 20.08 kpc s 0.08 r b 34 30 k 15 +−1.9 [ a σD = 0.41 kpc 0.09 24 t − 32 s +0.081

D 10 l = 86.00 1.2 deg

18 b −+1.8

30 a 12 σl = 0.14 0.026 deg R 5 − 28 +1.4 6 R b = 34.96 0.07 deg −+0.78 26 0 σb = 0.16 0.034 deg 92 90 88 86 84 82 80 0 20 40 60 80 100 120 − l D [kpc] 70 100 input parameters ] ] 1 1 n = 4.50 − 60 −

g g 80 f = 0.20 e 50 e ∗

d d D = 20.00 kpc [ [ 60 σD = 0.50 kpc s 40 s r r l = 86.00 deg a a t 30 t 40 σ = 0.13 deg s s l

b 20 b b = 35.00 deg a a 20 σb = 0.13 deg R 10 R R R 0 0 92 90 88 86 84 82 80 28 30 32 34 36 38 40 l [deg] b [deg]

(b)

Figure 13. Fit to two mock overdensities, where the one in subfigure (a) resembles a typical dSph with 166 sources, and the one in subfigure (b) resembles a typical GC with 91 sources. We used mock overdensities to test the methodology for fitting overdensities, as well as estimate typical error ranges. The best-fit set of parameters along with their 1σ intervals, as well as the input parameters used to generate the mock overdensities and background distribution of halo stars, are given in the right part of each panel. In each case, the first panel shows a map of the star distribution near the overdensity, where the stars are color-coded according to their heliocentric distance. The other three panels show the histograms in l, b, D for the stars from the first panel. Overplotted are both the distribution the mock stars were drawn from (red) and the best-fit model from Sec.4 (blue). We find results that are consistent with the input model within reasonable uncertainties, which means that we are able to recover the input parameters for all models in their assumed parameter range. 24 HERNITSCHEKETAL.

globular clusters globular clusters 45 45 40 40

] 35 ] 35 n n i i

m 30 m 30 c c r r a a

[ 25 [ 25

) ) b b σ σ

, 20 , 20 l l σ σ ( (

x 15 x 15 a a

m 10 m 10 5 5 0 0 5 10 15 20 25 30 35 40 45 0 0 2 4 6 8 10 rt [arcmin] rc [arcmin]

dwarf galaxies dwarf galaxies 175 45 40 150 ] ] 35 n n i 125 i m m 30 c c r r a a

[ 100 [ 25

) ) b b σ σ

, , 20 l 75 l σ σ ( (

x x 15

a 50 a

m m 10 25 5 0 0 0 25 50 75 100 125 150 175 0 5 10 15 20 25 30 35 40 45

rt [arcmin] rc [arcmin]

Figure 14. Comparison between the estimated extent of the overdensities (here we take the maximum of σl and σb, max(σl,σb)) in the present study and the tidal radii rt and core radii rc for globular clusters (Harris 1996, no uncertainties are available) and for dwarf galaxies (from different sources, see Table7; uncertainties are partially available). For all of our remote globular clusters and for three of our dwarf galaxies, we were able to look up rt, rc. The dwarf galaxy Ursa Major I lacks a published tidal and core radius. The diagonal line represents the one-to-one relation.

We find that for globular clusters, whereas the distribution shows a lot of scatter, our estimated extent from max(σl,σb) represents significant fractions of the tidal radius. We find sources ways out of the core radius. For dwarf galaxies, our estimated extent from max(σl,σb) matches quite good the core radius. We don’t pick up sources being as distant as the tidal radius. Tables7 and8 list the data used for this Figure. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 25

14 NGC 5904 (M 5) NGC 5272 (M 3) NGC 4590 (M 68) NGC 7078 (M 15) 15 NGC 6864 (M 75) Pal 5 NGC 6934 F

r NGC 5466

e NGC 5024 (M 53) d 16 u

t NGC 5053 i

n NGC 6981 (M 72) g a Pal 3 m

d NGC 6229

n 17

a NGC 7006 b

r NGC 2419

t

n NGC 7089 (M 2) e r a

p 18 p a

d e n e d d

e 19 r e d

20

21 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05

log10(P/days)

Figure 15. We plot the dereddened apparent r band magnitude (rF in the PS1 RRab catalog) for each of the RRab in our sample for each globular cluster vs. their period. The typical trend of a PL relation is clearly visible. 26 HERNITSCHEKETAL.

NGC 2419 g 19.6 g 19.6 a observed a m 19.7 m 19.7

predicted without [Fe/H] d 19.8 predicted with [Fe/H] d 19.8 n n a 19.9 a 19.9 b b

g 20.0 r 20.0

t 20.1 t 20.1 n n e e

r 20.2 r 20.2 a a

p 20.3 p 20.3 p p

a 20.4 a 20.4 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 19.6 19.6 a a m m 19.7 19.7

d d 19.8 19.8 n n a a 19.9 19.9 b b

i 20.0 z 20.0

t t

n 20.1 20.1 n e e r 20.2 r 20.2 a a p 20.3 p 20.3 p p a

20.4 a 20.4 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 16. In this and the following plots, we select the RRab stars for each globular cluster and plot their dereddended apparent g, r, i, z magnitudes (gF ,...,zF in the PS1 RRab catalog) vs. their periods. These are the orange points in each panel. Along with that, we plot the apparent magnitude one would get from the PLZ or PL relation for each of the periods. The grey points describe the predicted apparent magnitude based on period without any assumption on metallicity (Equ. (13)) whereas the blue points describe the predicted apparent magnitude based on period when taking the metallicity [Fe/H] from Equ. (12) into account. We find that for most of the 16 globular clusters we have evaluated, the predicted apparent magnitude with [Fe/H] (blue markers in the Figures) is a bit brighter than the predicted apparent magnitude without [Fe/H] (black markers), and this is again a bit brighter than the observed dereddened apparent magnitude (orange markers). This Figure was made for the globular cluster NGC 2419. In the following figures, we show similar plots for all the globular clusters discussed in this paper. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 27

NGC 5024 (M53) g 16.5 g 16.5 a observed a m m

16.6 predicted without [Fe/H] 16.6 d predicted with [Fe/H] d n 16.7 n 16.7 a a b 16.8 b 16.8

g r

t 16.9 t 16.9 n n

e 17.0 e 17.0 r r

a 17.1 a 17.1 p p p p

a 17.2 a 17.2 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 16.5 16.5 a a m m

16.6 16.6

d d n

n 16.7 16.7 a a b b 16.8 16.8

i z

t 16.9 t 16.9 n n e 17.0 e 17.0 r r a 17.1 a 17.1 p p p p a

17.2 a 17.2 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 17. Observed and predicted apparent magnitudes for the globular cluster NGC 5024 (M53). See Fig. 16 for a detailed description.

NGC 5053 g 16.2 g 16.2 a observed a m m

16.3 predicted without [Fe/H] 16.3 d predicted with [Fe/H] d n 16.4 n 16.4 a a b 16.5 b 16.5

g r

t 16.6 t 16.6 n n

e 16.7 e 16.7 r r

a 16.8 a 16.8 p p p p

a 16.9 a 16.9 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 16.2 16.2 a a m m

16.3 16.3

d d n

n 16.4 16.4 a a b b 16.5 16.5

i z

t 16.6 t 16.6 n n e 16.7 e 16.7 r r a 16.8 a 16.8 p p p p a

16.9 a 16.9 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 18. Observed and predicted apparent magnitudes for the globular cluster NGC 5053. See Fig. 16 for a detailed description. 28 HERNITSCHEKETAL.

NGC 5272 (M3) g 15.2 g 15.2 a observed a m m

15.4 predicted without [Fe/H] 15.4 d predicted with [Fe/H] d n n a 15.6 a 15.6 b b

g r

t 15.8 t 15.8 n n e e r 16.0 r 16.0 a a p p p p

a 16.2 a 16.2 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 15.2 15.2 a a m m

15.4 15.4 d d n n a a 15.6 15.6 b b

i z

t 15.8 t 15.8 n n e e r r

a 16.0 16.0 a p p p p a

16.2 a 16.2 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 19. Observed and predicted apparent magnitudes for the globular cluster NGC 5272 (M3). See Fig. 16 for a detailed description.

NGC 5466 g 16.0 g 16.0 a observed a m m

predicted without [Fe/H] d 16.2 d 16.2 predicted with [Fe/H] n n a a b b

16.4 16.4 g r

t t

n 16.6 n 16.6 e e r r a a

p 16.8 p 16.8 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 16.0 16.0 a a m m

d

d 16.2 16.2 n n a a b b

16.4 16.4

i z

t t n 16.6 n 16.6 e e r r a a p 16.8 p 16.8 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 20. Observed and predicted apparent magnitudes for the globular cluster NGC 5466. See Fig. 16 for a detailed description. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 29

NGC 5904 (M5) g 14.4 g 14.4 a observed a m m

14.6 predicted without [Fe/H] 14.6 d predicted with [Fe/H] d n n a 14.8 a 14.8 b b

g r

15.0 15.0 t t n n

e 15.2 e 15.2 r r a a

p 15.4 p 15.4 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 14.4 14.4 a a m m

14.6 14.6 d d n n a a 14.8 14.8 b b

i z

15.0 15.0 t t n n e 15.2 e 15.2 r r a a p 15.4 p 15.4 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 21. Observed and predicted apparent magnitudes for the globular cluster NGC 5904 (M5). See Fig. 16 for a detailed description.

NGC 4590 (M68) g 15.3 g 15.3 a observed a m m

15.4 predicted without [Fe/H] 15.4 d predicted with [Fe/H] d n 15.5 n 15.5 a a b 15.6 b 15.6

g r

t 15.7 t 15.7 n n

e 15.8 e 15.8 r r

a 15.9 a 15.9 p p p p

a 16.0 a 16.0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 15.3 15.3 a a m m

15.4 15.4

d d n

n 15.5 15.5 a a b b 15.6 15.6

i z

t 15.7 t 15.7 n n e 15.8 e 15.8 r r a 15.9 a 15.9 p p p p a

16.0 a 16.0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 22. Observed and predicted apparent magnitudes for the globular cluster NGC 4590 (M68). See Fig. 16 for a detailed description. 30 HERNITSCHEKETAL.

NGC 6229 g 17.4 g 17.4 a observed a m

17.5 m 17.5

predicted without [Fe/H] d 17.6 d 17.6 predicted with [Fe/H] n 17.7 n 17.7 a a b b

17.8 17.8 g r 17.9 17.9 t t

n 18.0 n 18.0 e e

r 18.1 r 18.1 a a

p 18.2 p 18.2 p p

a 18.3 a 18.3 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 17.4 17.4 a a

17.5 m 17.5 m

d

d 17.6 17.6 n n 17.7 17.7 a a b b

17.8 17.8

i z

17.9 17.9 t t n 18.0 n 18.0 e e r 18.1 r 18.1 a a p 18.2 p 18.2 p p a

18.3 a 18.3 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 23. Observed and predicted apparent magnitudes for the globular cluster NGC 6229. See Fig. 16 for a detailed description.

NGC 6864 (M75) g 16.8 g 16.8 a observed a m m

predicted without [Fe/H] d 17.0 predicted with [Fe/H] d 17.0 n n a a b b

g 17.2 r 17.2

t t n n e e

r 17.4 r 17.4 a a p p p p

a 17.6 a 17.6 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 16.8 16.8 a a m m

d d 17.0 17.0 n n a a b b

i 17.2 z 17.2

t t n n e e r 17.4 r 17.4 a a p p p p a

17.6 a 17.6 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 24. Observed and predicted apparent magnitudes for the globular cluster NGC 6864 (M75). See Fig. 16 for a detailed description. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 31

NGC 6934 g 16.4 g 16.4 a observed a m m

16.5 predicted without [Fe/H] 16.5 d predicted with [Fe/H] d n 16.6 n 16.6 a a b 16.7 b 16.7

g r

t 16.8 t 16.8 n n

e 16.9 e 16.9 r r

a 17.0 a 17.0 p p p p

a 17.1 a 17.1 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 16.4 16.4 a a m m

16.5 16.5

d d n

n 16.6 16.6 a a b b 16.7 16.7

i z

t 16.8 t 16.8 n n e 16.9 e 16.9 r r a 17.0 a 17.0 p p p p a

17.1 a 17.1 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 25. Observed and predicted apparent magnitudes for the globular cluster NGC 6934. See Fig. 16 for a detailed description.

NGC 6981 (M72) g g a observed a m

16.4 m 16.4

predicted without [Fe/H] d predicted with [Fe/H] d n 16.6 n 16.6 a a b b

g r 16.8 16.8 t t n n e e

r 17.0 r 17.0 a a p p p p

a 17.2 a 17.2 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g a a

16.4 m 16.4 m

d d n n 16.6 16.6 a a b b

i z

16.8 16.8 t t n n e e r 17.0 r 17.0 a a p p p p a

17.2 a 17.2 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 26. Observed and predicted apparent magnitudes for the globular cluster NGC 6981 (M72). See Fig. 16 for a detailed description. 32 HERNITSCHEKETAL.

NGC 7006 g 18.3 g 18.3 a observed a m m

18.4 predicted without [Fe/H] 18.4 d predicted with [Fe/H] d n 18.5 n 18.5 a a b 18.6 b 18.6

g r

t 18.7 t 18.7 n n

e 18.8 e 18.8 r r

a 18.9 a 18.9 p p p p

a 19.0 a 19.0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 18.3 18.3 a a m m

18.4 18.4

d d n

n 18.5 18.5 a a b b 18.6 18.6

i z

t 18.7 t 18.7 n n e 18.8 e 18.8 r r a 18.9 a 18.9 p p p p a

19.0 a 19.0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 27. Observed and predicted apparent magnitudes for the globular cluster NGC 7006. See Fig. 16 for a detailed description.

NGC 7078 (M15) g g a 15.4 observed a 15.4 m m

predicted without [Fe/H] d predicted with [Fe/H] d n 15.6 n 15.6 a a b b

g 15.8 r 15.8

t t n n

e 16.0 e 16.0 r r a a

p 16.2 p 16.2 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g a a 15.4 15.4 m m

d d n n 15.6 15.6 a a b b

i 15.8 z 15.8

t t n n e 16.0 e 16.0 r r a a p 16.2 p 16.2 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 28. Observed and predicted apparent magnitudes for the globular cluster NGC 7078 (M15). See Fig. 16 for a detailed description. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 33

NGC 7089 (M2) g g a 15.7 observed a 15.7 m m

predicted without [Fe/H] d 15.8 predicted with [Fe/H] d 15.8 n n a 15.9 a 15.9 b b

g r

16.0 16.0 t t

n 16.1 n 16.1 e e r r

a 16.2 a 16.2 p p p p

a 16.3 a 16.3 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g a a 15.7 15.7 m m

d d 15.8 15.8 n n a a 15.9 15.9 b b

i z

16.0 16.0 t t n n

e 16.1 16.1 e r r a 16.2 a 16.2 p p p p a

16.3 a 16.3 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 29. Observed and predicted apparent magnitudes for the globular cluster NGC 7089 (M2). See Fig. 16 for a detailed description. 34 HERNITSCHEKETAL.

Pal 3 g 20.0 g 20.0 a observed a m m

20.1 predicted without [Fe/H] 20.1 d predicted with [Fe/H] d n n a 20.2 a 20.2 b b

g r

20.3 20.3 t t n n

e 20.4 e 20.4 r r a a

p 20.5 p 20.5 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 20.0 20.0 a a m m

20.1 20.1 d d n n a a 20.2 20.2 b b

i z

20.3 20.3 t t n n e 20.4 e 20.4 r r a a p 20.5 p 20.5 p p a 0.4 0.3 0.2 0.1 a 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 30. Observed and predicted apparent magnitudes for the globular cluster Pal 3. See Fig. 16 for a detailed description.

Pal 5 g 17.0 g 17.0 a observed a m m

17.1 predicted without [Fe/H] 17.1 d predicted with [Fe/H] d n n a 17.2 a 17.2 b b

g r

t 17.3 t 17.3 n n e e r 17.4 r 17.4 a a p p p p

a 17.5 a 17.5 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days) g g 17.0 17.0 a a m m

17.1 17.1 d d n n a a 17.2 17.2 b b

i z

t 17.3 t 17.3 n n e e r r

a 17.4 17.4 a p p p p a

17.5 a 17.5 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 log10(P/days) log10(P/days)

Figure 31. Observed and predicted apparent magnitudes for the globular cluster Pal 5. See Fig. 16 for a detailed description. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 35

) 20 20 8

1 < 10% parallax error 0 2

] + c s 15 15 p e k n [

o J 2 - R r D e a l i i a a 10 G 10 x B ( a

l ] l c a r p a k [ p 5 5 / 2 1 R D a i a G

D 0 0 0 5 10 15 20 0 5 10 15 20

DPS1 [kpc] DPS1 [kpc]

Figure 32. To compare our distance estimates DPS1 from Sesar et al.(2017) to those of Gaia DR2 (Bailer-Jones et al. 2018), we cross- matched our PS1 RRab sample with Gaia DR2, and found a cross-match for 43,791 sources. The plot shows the DGaiaDR2 and a rough distance estimate 1/parallax vs. DPS1 for the RRab stars within DPS1 < 20 kpc. Blue points indicate RRab stars with parallax errors of <10%. We find a rather large scatter in the distances, ways larger than the PS1 distance uncertainty of 3% or an estimate of the distance uncertainty from the parallax error. Beyond about 5 kpc, where also the parallax error exceeds 10%, the distances from Gaia DR2 become very unreliable.

20 < 10% parallax error

15

10

5

confidence interval boundaries [kpc] 0 0 5 10 15 20

DGaiaDR2 [kpc] (Bailer-Jones+2018)

Figure 33. Bailer-Jones et al.(2018) claim quite large uncertainties of their distance estimates. The plot shows the upper and lower 68% confidence interval boundaries of their distance estimates for our cross-matched sample of RRab stars. Again, blue points indicate RRab stars with <10% parallax error (blue points). For those RRab stars with a parallax error of ∼10%, we find that the uncertainty is about 10%, and otherwise, can increase to as much as 50% for many RRab stars. 36 HERNITSCHEKETAL.

B. TABLES PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 37

Table 1. Dwarf Galaxies, attempted

◦ ◦ name (lprior [ ], bprior [ ], Dprior [kpc])

Aquarius II dSph 55.0 -53.0 108 Bootes I dSph 358.036 69.642 60 Crater II dSph 282.9084 42.0276 117.5 Draco dSph 86.3747 34.7171 79 Sagittarius dSph 5.6081 -14.0858 26.3 Segue 1 dSph 220.488 50.420 23 dSph 149.433 -38.1352 35 Sextans dSph 243.4981 42.2721 86 Ursa Minor Dwarf dE4 104.9527 44.8028 63 Ursa Major I dSph 159.4311 54.4143 100 Ursa Major II Dwarf 152.464 37.443 30

NOTE—The list of dwarf galaxies within the PS1 3π footprint for which we want to determine their distance. Their (l, b, D) coordi- nates are from McConnachie(2012). 38 HERNITSCHEKETAL.

Table 2. Globular clusters, attempted

◦ ◦ name (lprior [ ], bprior [ ], Dprior [kpc])

IC 1257 16.54 15.15 25 NGC 2419 180.37 25.24 82.6 NGC 4147 252.85 77.19 19.3 NGC 4590 (M68) 299.63 36.05 10.3 NGC 5024 (M53) 332.96 79.76 17.9 NGC 5053 335.7 78.95 17.4 NGC 5272 (M3) 42.22 78.71 10.2 NGC 5466 42.15 73.59 16 NGC 5634 342.21 49.26 25.2 NGC 5694 331.06 30.36 35 NGC 5897 342.95 30.29 12.5 NGC 5904 (M5) 3.86 46.8 7.5 NGC 6093 (M80) 352.67 19.46 10 NGC 6171 (M107) 3.37 23.01 5.4 NGC 6229 73.64 40.31 30.5 NGC 6356 6.72 10.22 15.1 NGC 6402 (M14) 21.32 14.81 9.3 NGC 6426 28.09 16.23 20.6 NGC 6864 (M75) 20.3 -25.75 20.9 NGC 6934 52.1 -18.89 15.6 NGC 6981 (M72) 35.16 -32.68 17 NGC 7006 63.77 -19.41 41.2 NGC 7078 (M15) 65.01 -27.31 10.4 NGC 7089 (M2) 53.37 -35.77 11.5 NGC 7099 (M30) 27.18 -46.84 8.1 Pal 1 130.06 19.03 11.1 Pal 3 240.15 41.86 92.5 Pal 5 0.85 45.86 23.2 Pal 13 87.1 -42.7 26

NOTE—The list of globular clusters within the PS1 3π footprint for which we want to determine their distance. Their (l, b, D) coordinates are from a current update of Harris(1996). PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 39

Table 3. Fitted Dwarf Galaxies

name fitted fitted ∆l [kpc] ∆b [kpc] ∆D [kpc] ∆D/∆l ∆D/∆b sources

◦ ◦ ◦ ◦ (l [ ], b [ ], D [kpc]) (σl [ ],σb [ ],σD [kpc])

+0.01 +0.01 +0.18 +0.01 +0.01 +0.17 Draco dSph 86.37−0.01, 34.71−0.01, 74.26−0.18 0.13−0.01, 0.13−0.01, 2.40−0.15 0.28 0.33 4.81 14.48 14.66 191 +0.10 +0.02 Sagittarius dSph -,-, 28.18−0.10 -, -, 1.01−0.01 2.02 - - - - 538 +0.04 +0.04 +0.41 +0.03 +0.04 +0.43 Sextans dSph 243.55−0.04, 42.26−0.03, 81.42−0.40 0.26−0.03, 0.23−0.03, 3.24−0.37 0.55 0.66 6.49 9.83 9.87 99 +2.07 +2.79 +10.80 +2.53 +2.05 +5.90 Ursa Major I dSph 159.38−1.48, 54.43−0.39, 94.33−4.94 0.34−0.20, 0.33−0.19, 2.59−1.11 0.65 1.07 5.18 4.84 4.84 4 +0.62 +0.36 +0.51 +0.86 +1.45 +3.10 Ursa Minor Dwarf dE4 105.00−0.06, 44.74−0.06, 68.41−0.51 0.16−0.03, 0.14−0.02, 2.17−0.59 0.22 0.33 4.35 19.77 13.11 53

NOTE—The best-fit positions (l, b, D) and extent (σl, σb, σD ) of dwarf galaxies from Table1, along with their 1 σ uncertainties. Assuming an ellipsoidal shape for each dwarf galaxy, we calculate their axis ratios by first translating their angular extent (σl, σb) into a linear extent (∆l, ∆b) as given by Equ. (9) and Equ. (10), and then use the line-of-sight depth ∆D = 2σD (11) to calculate the axis ratios ∆D/∆l, ∆D/∆b. In this table, Sagittarius Dwarf dSph and Crater II dSph from Table1 are missing, as we were not able to determine reasonable fits for them. For details on this, see Sec.4.

Table 4. Fitted Globular Clusters

name fitted fitted ∆l [kpc] ∆b [kpc] ∆D [kpc] ∆D/∆l ∆D/∆b sources

◦ ◦ ◦ ◦ (l [ ], b [ ], D [kpc]) (σl [ ],σb [ ],σD [kpc])

+0.03 +0.04 +0.32 +0.01 +0.02 +1.33 NGC 2419 180.36−0.03, 25.24−0.03, 79.70−0.37 0.11−0.01, 0.11−0.01, 4.24−1.14 0.28 0.30 8.47 30.25 27.81 8 +0.12 +0.10 +0.26 +0.68 +0.65 +1.29 NGC 4590 (M68) 299.62−0.08, 36.07−0.11, 10.48−0.28 0.15−0.04, 0.15−0.04, 0.66−0.13 0.04 0.05 1.32 33.0 24.15 5 +0.12 +0.04 +0.13 +0.12 +0.02 +0.08 NGC 5024 (M53) 332.93−0.12, 79.74−0.04, 18.25−0.14 0.35−0.08, 0.11−0.01, 0.55−0.03 0.04 0.07 1.09 15.57 15.31 12 +0.19 +0.16 +0.28 +1.08 +1.10 +3.69 NGC 5053 335.78−0.18, 78.93−0.14, 16.66−0.26 0.30−0.16, 0.18−0.06, 0.75−0.20 0.03 0.10 1.50 50.0 14.54 4 +0.08 +0.02 +0.07 +0.05 +0.01 +0.02 NGC 5272 (M3) 42.20−0.07, 78.71−0.02, 10.48−0.07 0.45−0.05, 0.10−0.002, 0.51−0.01 0.03 0.04 1.02 34.0 27.05 56 +0.04 +0.04 +0.14 +0.03 +0.02 +0.07 NGC 5466 42.13−0.04, 73.59−0.03, 15.76−0.14 0.12−0.02, 0.11−0.01, 0.54−0.03 0.02 0.06 1.08 54.0 17.76 10 +0.03 +0.03 +0.19 +0.04 +0.02 +0.08 NGC 5904 (M5) 3.88−0.04, 46.77−0.02, 7.87−0.19 0.13−0.02, 0.11−0.005, 0.53−0.02 0.02 0.03 1.05 52.5 36.01 24 +0.04 +0.04 +0.17 +0.02 +0.03 +0.19 NGC 6229 73.64−0.04, 40.31−0.04, 29.94−0.19 0.11−0.01, 0.11−0.01, 0.61−0.08 0.09 0.12 1.22 13.5 10.31 12 +0.25 +0.20 +0.32 +1.46 +2.70 +4.27 NGC 6864 (M75) 20.28−0.23, −25.76−0.28, 20.79−0.35 0.25−0.13, 0.34−0.21, 1.59−0.93 0.16 0.24 3.17 19.8 13.01 4 +0.04 +0.03 +0.21 +0.03 +0.02 +0.16 NGC 6934 52.12−0.04, −18.870.04 , 16.77−0.21 0.11−0.01, 0.11−0.01, 0.57−0.05 0.06 0.07 1.14 19.00 17.14 10 +0.03 +0.03 +0.15 +0.01 +0.01 +0.11 NGC 6981 (M72) 335.16−0.03, −32.70−0.03, 17.51−0.17 0.11−0.01, 0.11−0.01, 0.56−0.05 0.06 0.07 1.12 18.70 16.90 15 +0.03 +0.03 +0.16 +0.01 +0.01 +0.11 NGC 7006 63.78−0.03, −19.39−0.03, 40.12−0.15 0.11−0.004, 0.11−0.01, 0.59−0.06 0.15 0.15 1.17 7.80 7.87 16 +0.11 +0.07 +0.24 +1.07 +0.95 +2.69 NGC 7078 (M15) 65.03−0.08, −27.32−0.08, 11.07−0.22 0.15−0.04, 0.13−0.03, 0.60−0.08 0.05 0.05 1.21 24.20 23.42 10 +0.22 +0.29 +0.39 +2.38 +3.60 +6.28 NGC 7089 (M2) 53.460.25 , −35.81−0.29, 12.11−0.28 0.35−0.21, 0.62−0.47, 1.47−0.84 0.12 0.26 2.95 24.58 11.24 4 +0.10 +0.21 +0.32 +0.17 +0.31 +1.77 Pal 3 240.14−0.09, 41.95−0.18, 85.05−0.34 0.14−0.03, 0.34−0.17, 1.76−1.08 0.31 1.01 3.53 11.39 3.50 3 +0.29 +0.26 +0.33 +2.82 +2.37 +7.52 Pal 5 0.87−0.27, 45.80−0.28, 21.66−0.30 0.58−0.43, 0.31−0.19, 1.61−0.98 0.31 0.24 3.23 10.41 13.56 3

NOTE—The best-fit positions (l, b, D) and extent (σl, σb, σD ) of globular clusters from Table2, along with their 1 σ uncertainties. Assuming an ellipsoidal shape for each globular cluster, we calculate their axis ratios by first translating their angular extent (σl, σb) into a linear extent (∆l, ∆b) as given by Equ. (9) and Equ. (10), and then use the line-of-sight depth ∆D = 2σD (11) to calculate the axis ratios ∆D/∆l, ∆D/∆b. In this table, NGC 4147, NGC 5634, NGC 5694, NGC 5897, IC 1257, NGC 6093 (M80), NGC 6171 (M107), NGC 6284, NGC 6356, NGC 6402 (M14), NGC 6426, NGC 7099 (M30), Pal 1 and Pal 13 from Table2 are missing, as we were not able to determine reasonable fits for them. For details on this, see Sec.4. 40 HERNITSCHEKETAL.

Table 5. Dwarf Galaxies with too few RRab stars

name mean sources comment

D¯ [kpc]

Aquarius II dSph 107.87 1 Bootes I dSph 60.61 2 Crater II dSph 105.48 2 Segue 1 dSph 23.24 1 up to 2 additional sources nearby Segue 2 dSph 33.31 1 Ursa Major II Dwarf 33.02 1

NOTE—The mean positions (l, b, D) of those dwarf galaxies from Table1 which don’t have enough sources in the PS1 catalog of RR Lyrae stars for carrying out the fitting process described in Sec.4.

Table 6. Globular Clusters with too few RRab stars

name mean sources comment

D¯ [kpc]

IC 1257 27.24 1 NGC 4147 18.54 1 NGC 5634 25.81 1 NGC 5694 33.96 1 NGC 5897 12.91 1 up to 3 additional sources nearby NGC 6093 10.74 2 NGC 6171 (M107) 6.01 7 NGC 6356 11.02 1 NGC 6402 (M14) many field stars at this distance NGC 6426 19.83 5 NGC 7099 (M30) 8.41 2 Pal 1 nothing detected at this position: mean D = 10.08 kpc Pal 13 23.59 3

NOTE—The mean positions (l, b, D) of those globular clusters from Table2 which don’t have enough sources in the PS1 catalog of RR Lyrae stars for carrying out the fitting process described in Sec.4.

Table 7. Radii of Dwarf Galaxies

name rt [arcmin] rc [arcmin] max(σl,σb) [arcmin]

Draco dSph 40.1 ± 0.9 (Odenkirchen et al. 2001) 8.33 (Stoehr et al. 2002) 7.8 Sextans dSph 83.2 ± 7.1(Roderick et al. 2016) 14.14 (Stoehr et al. 2002) 16.5 Ursa Minor Dwarf dE4 34 ± 2.4 (Kleyna et al. 1998) 10.5 (Stoehr et al. 2002) 9.6 Ursa Major I dSph 7.28 (Simon & Geha 2007) 20.4

NOTE— Comparison of tidal radii rt and core radii rc to the angular extent max(σl,σb) from our analysis for the four fitted dwarf galaxies. Ursa Major I dSph lacks a published tidal radius. We give uncertainties as far as provided. See also Fig. 14. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 41

Table 8. Radii of Globular Clusters

name rt [arcmin] rc [arcmin] max(σl,σb) [arcmin]

NGC 2419 8.74 0.35 6.6 NGC 4590 (M68) 30.34 0.69 9.0 NGC 5024 (M53) 21.75 0.36 21 NGC 5053 13.67 1.98 18 NGC 5272 (M3) 38.19 0.55 27 NGC 5466 34.24 1.64 7.2 NGC 5904 (M5) 28.40 0.42 7.8 NGC 6229 5.38 0.13 6.6 NGC 6864 (M75) 7.28 0.10 20.4 NGC 6934 8.37 0.25 6.6 NGC 6981 (M72) 9.15 0.54 6.6 NGC 7006 6.34 0.24 6.6 NGC 7078 (M15) 21.50 0.07 9.0 NGC 7089 (M2) 21.45 0.34 37.2 Pal 3 4.81 0.48 20.4 Pal 5 16.28 3.25 34.8

NOTE—Tidal radius rt, core radius rc from the 2010 version of Harris (1996), as well as the angular extent max(σl,σb) from our analysis for all the fitted globular clusters. See also Fig. 14.

Table 9. Distance Comparison for Dwarf Galaxies

name D [kpc] method literature D [kpc] method and reference

Aquarius II dSph 107.87 1 RRab 107.900 ± 3.300 BHB stars (Torrealba et al. 2016) Bootes I dSph 60.61 mean of 2 RRab 65.3 (BHB + RR Lyr) HSC/Subaru imaging (Okamoto et al. 2012) 62 ± 4 15 RR Lyr (Siegel et al. 2006) 60.4 (Hammer et al. 2018) Crater II dSph 105.48 mean of 2 RRab ∼120 CMD (Torrealba et al. 2016a) 112 ± 5 RR Lyr (Joo et al. 2018) 117.5 ± 5 (McConnachie 2012) +0.18 Draco dSph 74.26−0.18 fit 71 ± 7 SDSS photometry (Odenkirchen et al. 2001) 75.8 ± 5.4 94 RR Lyr (Bonanos et al. 2004) +0.10 Sagittarius dSph 28.18−0.10 fit 26.3 ± 1.8 RGB tip (Monaco et al. 2004) Segue 1 dSph 23.24 1 RRab 23 ± 2 CMD fitting, esp. horizontal branch (Belokurov et al. 2007) Segue 2 dSph 33.31 1 RRab 35 from 4 BHB stars (Belokurov et al. 2009) +0.41 Sextans dSph 81.42−0.40 fit 84.2 ± 3.3 RR Lyr from Dark Energy Camera imaging (Medina et al. 2018) +0.51 Ursa Minor Dwarf dE4 68.41−0.51 fit 76 RR Lyr and HB (Bellazzini et al. 2002) 76 ± 4 distance from HB, considering metallicity of UMi (Carrera et al. 2002) +10.80 Ursa Major I dSph 94.33−4.94 fit 96.8 ± 4 V mag of HB, HSC/Subaru imaging study (Okamoto et al. 2008) +6.0 97.3−5.7 variable stars in UMa 1 (Garofalo et al. 2018) +2.0 Ursa Major II Dwarf 33.02 1 RRab 34.7−1.9 1 RR Lyr (Dall’Ora et al. 2012)

NOTE—Comparison of our distance estimates (column D [kpc]) to reference values from literature. For our distance estimates, we give whether they are a result from the fitting process or are determined as a mean distance from a small number of RRab stars. For literature values, we give the method used to obtain the distance and the reference. 42 HERNITSCHEKETAL.

Table 10. Distance Comparison for Globular Cluster

name D [kpc] method literature D [kpc]

IC 1257 27.24 1 RRab 25 +0.32 NGC 2419 79.70−0.37 fit 82.6 NGC 4147 18.54 1 RRab 19.3 +0.26 NGC 4590 (M68) 10.48−0.28 fit 10.3 +0.13 NGC 5024 (M53) 18.25−0.14 fit 17.9 +0.28 NGC 5053 16.66−0.26 fit 17.4 +0.07 NGC 5272 (M3) 10.48−0.07 fit 10.2 +0.14 NGC 5466 15.76−0.14 fit 16 NGC 5634 25.81 1 RRab 25.2 NGC 5694 33.96 1 RRab 35 NGC 5897 12.91 1 RRab 12.5 +0.19 NGC 5904 (M5) 7.87−0.19 fit 7.5 NGC 6093 (M80) 10.74 2 RRab 10 NGC 6171 (M107) 6.01 7 RRab 5.4 +0.17 NGC 6229 29.94−0.19 fit 30.5 NGC 6356 11.02 1 RRab 15.1 NGC 6426 19.83 5 RRab 20.6 +0.32 NGC 6864 (M75) 20.79−0.35 fit 20.9 +0.21 NGC 6934 16.77−0.21 fit 15.6 +0.15 NGC 6981 (M72) 17.51−0.17 fit 17 +0.16 NGC 7006 40.12−0.15 fit 41.2 +0.24 NGC 7078 (M15) 11.07−0.22 fit 10.4 +0.39 NGC 7089 (M2) 12.11−0.28 fit 11.5 NGC 7099 (M30) 8.41 2 RRab 8.1 +0.32 Pal 3 85.05−0.34 fit 92.5 +0.33 Pal 5 21.66−0.30 fit 23.2 Pal 13 23.59 3 RRab 26

NOTE—Comparison of our distance estimates (column D [kpc]) to refer- ence values from literature. For our distance estimates, we give whether they are a result from the fitting process or are determined as a mean distance from a small number of RRab stars. For literature values, we use the 2010 online version of the (Harris 1996) catalog. PRECISIONDISTANCESTODWARFGALAXIESANDGLOBULARCLUSTERSFROM PAN-STARRS1 3π RRLYRAE 43

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