Milky Way archaeology using RR Lyrae and type II Cepheids I. The Orphan stream in 7D using RR Lyrae stars
Z. Prudil, M. Hanke, B. Lemasle, J. Crestani, V. F. Braga, M. Fabrizio, A. J. Koch-Hansen, G. Bono, E. K. Grebel, N. Matsunaga, M. Marengo, R. da Silva, M. Dall'Ora, C. E. Martínez-Vázquez, G. Altavilla, H. Lala, B. Chaboyer, I. Ferraro, G. Fiorentino, C. Gilligan, M. Nonino, F. Thévenin
AAstronomy & Astrophysics manuscript no. Stream-Orphan © ESO 2021February 3, 2021
Milky Way archaeology using RR Lyrae and type II Cepheids I.The Orphan stream in 7D using RR Lyrae stars
Z. Prudil , M. Hanke , B. Lemasle , J. Crestani , , , V. F. Braga , , M. Fabrizio , , A. J. Koch-Hansen G. Bono , ,E. K. Grebel , N. Matsunaga , M. Marengo , R. da Silva , , M. Dall’Ora , C. E. Martínez-Vázquez , G. Altavilla , ,H. Lala , B. Chaboyer , I. Ferraro , G. Fiorentino , C. Gilligan , M. Nonino , and F. Thévenin Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12-14, D-69120 Heidelberg,[email protected] Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italy INAF – Osservatorio Astronomico di Roma, via Frascati 33, 00078 Monte Porzio Catone, Italy Departamento de Astronomia, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 6500, Porto Alegre 91501-970,Brazil Space Science Data Center, via del Politecnico snc, 00133 Roma, Italy Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Napoli, Italy Cerro Tololo Inter-American Observatory, NSF’s National Optical-Infrared Astronomy Research Laboratory, Casilla 603, LaSerena, Chile Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy Université de Nice Sophia-antipolis, CNRS, Observatoire de la Côte d’Azur, Laboratoire Lagrange, BP 4229, F-06304 Nice, FranceFebruary 3, 2021
ABSTRACT
We present a chemo-dynamical study of the Orphan stellar stream using a catalog of RR Lyrae pulsating variable stars for whichphotometric, astrometric, and spectroscopic data are available. Employing low-resolution spectra from the Sloan Digital Sky Survey(SDSS), we determined line-of-sight velocities for individual exposures and derived the systemic velocities of the RR Lyrae stars. Incombination with the stars’ spectroscopic metallicities and
Gaia
EDR3 astrometry, we investigated the northern part of the Orphanstream. In our probabilistic approach, we found 20 single mode RR Lyrae variables likely associated with the Orphan stream basedon their positions, proper motions, and distances. The acquired sample permitted us to expand our search to nonvariable stars inthe SDSS dataset, utilizing line-of-sight velocities determined by the SDSS. We found 54 additional nonvariable stars linked to theOrphan stream. The metallicity distribution for the identified red giant branch stars and blue horizontal branch stars is, on average, − . ± .
05 dex and − . ± .
14 dex, with dispersions of 0 .
23 and 0 .
43 dex, respectively. The metallicity distribution of the RR Lyraevariables peaks at − . ± .
06 dex and a dispersion of 0 .
25 dex. Using the collected stellar sample, we investigated a possible linkbetween the ultra-faint dwarf galaxy Grus II and the Orphan stream. Based on their kinematics, we found that both the stream RR Lyraeand Grus II are on a prograde orbit with similar orbital properties, although the large uncertainties on the dynamical properties renderan unambiguous claim of connection difficult. At the same time, the chemical analysis strongly weakens the connection between both.We argue that Grus II in combination with the Orphan stream would have to exhibit a strong inverse metallicity gradient, which to datehas not been detected in any Local Group system.
Key words.
Galaxy: halo – Galaxy: kinematics and dynamics – Galaxy: structure – Stars: variables: RR Lyrae
1. Introduction
The Milky Way (MW) halo holds fossil records of its formationhistory where passing smaller stellar systems were tidally dis-rupted by the Galactic gravitational field and subsequently mixedwith the insitu MW stellar populations. The relics of past merg-ers can be found in the form of stellar streams and overdensities(e.g., Helmi et al. 1999; Belokurov et al. 2006, 2007; Grillmair& Dionatos 2006; Grillmair 2006; Bell et al. 2008; Newberg &Carlin 2016; Shipp et al. 2018; Malhan & Ibata 2018; Helmi2020), with their spatial and kinematical distribution carrying animprint of the underlying MW potential and mass distribution (e.g., Johnston et al. 1999; Ibata et al. 2001; Newberg et al. 2002;Johnston et al. 2005; Law & Majewski 2010; Koposov et al.2010; Küpper et al. 2015; Erkal et al. 2019). The morphology ofstellar streams may also provide insight into the dark matter sub-halos predicted by the Λ cold dark matter ( Λ CDM) cosmology(e.g., Dekel & Silk 1986; Kauffmann et al. 1993; Springel et al.2008). In particular, dynamically cold streams can be utilized inthe search for ”gaps” (de Boer et al. 2020) caused by a streamencounter with a dark matter subhalo (e.g., Ibata et al. 2002;Carlberg 2012; Erkal & Belokurov 2015; Bonaca et al. 2019),and they can possibly provide a lower limit on the size of darkmatter subhalos (e.g., Bode et al. 2001; Hu et al. 2000; Bullock
Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . GA ] F e b &A proofs: manuscript no. Stream-Orphan & Boylan-Kolchin 2017). Yet, a cautious treatment of the gapsis needed since epicyclic motion and giant molecular clouds canproduce such stream features as well (Amorisco et al. 2016; Ibataet al. 2020).The advent of large photometric, spectroscopic, and astro-metric surveys uncovered a wealth of stellar substructures in theMW halo (e.g., York et al. 2000; Abbott et al. 2018; Kaiser et al.2010; Gaia Collaboration et al. 2020; Helmi et al. 2018; Be-lokurov et al. 2018; Malhan & Ibata 2018). Currently, the MWhalo hosts over 60 known tidally disrupted remnants of globularclusters and dwarf galaxies (e.g., Newberg & Carlin 2016; Ma-teu et al. 2018; Ibata et al. 2019). Among the most prominentis the Orphan stellar stream, independently discovered by Grill-mair (2006) and Belokurov et al. (2007) in the Sloan Digital SkySurvey (SDSS, York et al. 2000).The width of the Orphan stream ranges between 1 − ≈
60 kpcin both the southern and northern hemispheres (Koposov et al.2019). The chemical composition of the likely stream mem-bers derived from SDSS low-resolution spectra exhibits a broadmetallicity distribution with a mean at − . − . − . ∼
10 km s − (Newberg et al. 2010). A slightly lower velocity dis-persion was reported by Casey et al. (2013, 6 . − ), whichwas later corroborated by Koposov et al. (2019) and Fardalet al. (2019) placing the velocity dispersion at ≈ − and ≈ − , respectively, still within the boundaries expected fora tidally disrupted, dwarf-like progenitor (e.g., Gilmore et al.2007; Koch 2009; McConnachie 2012). The orbital modeling ofthe Orphan stellar stream suggests a prograde orbit with an ec-centricity of 𝑒 ∼ .
7, a pericentric distance of 16 . 𝑅 -band, through period-luminosity-metallicity relations, PLZ,Catelan et al. 2004; Muraveva et al. 2018; Neeley et al. 2019), andthus RR Lyrae stars serve as excellent distance indicators withinthe MW. In addition, the shape of their light curves reflects theirchemical composition (Jurcsik & Kovacs 1996; Smolec 2005;Hajdu et al. 2018), thereby expanding their potential as trac-ers of the Galactic substructure and chemical composition. Theaforementioned traits of RR Lyrae stars made them invaluable instudies of stellar streams in the MW halo (see, e.g., Sesar et al.2013; Mateu et al. 2018; Hendel et al. 2018; Koposov et al. 2019;Price-Whelan et al. 2019). In our work, we build on studies bySesar et al. (2013), Hendel et al. (2018), Fardal et al. (2019), andKoposov et al. (2019) who used RR Lyrae stars to examine theOrphan stream.We present the first paper of the series focused on the MilkyWay archaeology using old classical pulsators. This paper aims atproviding line-of-sight velocities and metallicities for the mem-bers of the Orphan stream alongside a discussion of a potentialOrphan progenitor. The manuscript is organized in the followingmanner: Section 2 outlines the dataset we built together with thecuts we imposed and the distances that were estimated. Subse-quently, in Section 3, we describe the method we used for estimat-ing the membership probability on basis of Bayesian inference.Section 4 illustrates the spatial and kinematical distribution ofRR Lyrae variables from the assembled catalog associated withthe Orphan stream. From the properties of the RR Lyrae pop-ulation we were also able to recover non-pulsating stars in theSDSS catalog that are likely Orphan members. Both the methodand the properties of these stars are described in Sections 3 and4. In Section 5 we discuss the possible metallicity gradient inthe Orphan stream together with the orbital and chemical prop-erties of Orphan members in context with the proposed Orphanprogenitor. Final remarks are provided in Section 6.
2. Properties of the RR Lyrae sample
As initial sample of RR Lyrae stars, we used the catalog ofpulsating variables from the early second data release of the
Gaia mission (DR2 Clementini et al. 2019) and found matches inthe early third data release of the
Gaia source table (EDR3, GaiaCollaboration et al. 2020) in combination with RR Lyrae starsidentified in the Catalina sky survey (CSS, Drake et al. 2009) toavoid possible misclassification (Molnár et al. 2018). This sampleprovided us with some of the pulsation properties (pulsationperiods) and astrometry (precise coordinates and proper motions;Lindegren et al. 2020) necessary for our study.Subsequently, we cross-matched our RR Lyrae sample withthe spectroscopic part of the fifteenth data release of the SDSS(Aguado et al. 2019). The SDSS provides spectra collectedover two decades using two multi-object fiber-fed spectro-graphs, namely SDSS and BOSS, which share comparably Used for the two phases of the Sloan Extension for Galactic Under-standing and Exploration surveys (SEGUE I and SEGUE II Yanny et al.2009; Eisenstein et al. 2011). Designed for the Baryon Oscillation Spectroscopic Survey (Smeeet al. 2013; Dawson et al. 2013).Article number, page 2 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars low-resolutions ( 𝑅 ∼ ≈ ≈ 𝑔 -band, covering a large portion of the northern sky. Indi-vidual targets are given a specObjID identifier, which is gener-ated based on the Modified Julian Date (MJD) of the observation(midpoint of the exposure), plate, and fiber ID. A fraction of ourRR Lyrae stars has been observed multiple times using differentfibers, plates, and in some cases by both spectrographs. Eachcross-matched RR Lyrae star has one bestObjID identifier,which serves as a reference throughout our study, and one or sev-eral specObjID ’s. We recovered spectroscopic data for the cross-matched sample from the SDSS Science Archive Server . Theretrieved data products contained the co-added (merged acrossepochs and for both channels) spectra together with the individualexposures for both channels (blue and red) and the precise timeof the observation in MJD. The method for obtaining systemicvelocities (corrected for the pulsation velocity) for individualRR Lyrae variables is described in Appendix B.We note that the SDSS provides stellar parameters (e.g.,metallicities, effective temperatures, and radial velocities) thatwere derived by the SEGUE stellar parameter pipeline (SSPP,Lee et al. 2008a,b; Allende Prieto et al. 2008) for a large portionof our sample. These parameters were derived from the co-addedspectra taken over several hours (sometimes across several days).Our targets rapidly change their radius (with radial velocity am-plitudes up to 130 km s − , Liu 1991; Sesar 2012) and effectivetemperatures ≈ Gaia - SDSSsample . The CSS observes a portion of the northern and southernsky in the effort to find and monitor near-Earth objects, and asa by-product provides a large catalog of variable objects (Drakeet al. 2013a,b, 2014; Abbas et al. 2014). The CSS conductsunfiltered observations (with a subsequent calibration to 𝑉 -bandusing Landolt standard star catalog, Landolt & Uomoto 2007;Landolt 2009) to increase the signal-to-noise ratio and detectsfaint objects down to ∼
20 mag with a single 30 s exposure (Drakeet al. 2013a). The number of epochs for each object ranges froma few dozens to almost a thousand with an average uncertainty of0.1 mag. We verified the periodicity of the objects in our initialsample and obtained their ephemerides and pulsation properties.The details of this analysis can be found in Appendix A.
For the purpose of using our catalog to study stellar streams, aprecise astrometric solution including distances and a thoroughtreatment of their uncertainties is essential. In order to carefullyassess the proper motions for individual variables we followed Based on equatorial coordinates with a radius of 10 arcsec. https://dr15.sdss.org/sas/dr15/ Using the web interface: http://nesssi.cacr.caltech.edu/cgi-bin/getmulticonedb_release2.cgi . Hanke et al. (2020) and Prudil et al. (2020), and utilized the valuesprovided by
Gaia ’s EDR3 for proper motions in right ascensionand declination ( 𝜇 𝛼 ∗ , 𝜇 𝛿 ), their uncertainties ( 𝜎 𝜇 ∗ 𝛼 , 𝜎 𝜇 𝛿 ), covari-ances ( 𝜌 𝜇 ∗ 𝛼 , 𝜇 𝛿 ), and re-normalized unit weight error (RUWE ).In the first step, we scaled the covariance matrix, Σ , by theRUWE factor, and diagonalized the resulting scaled covariancematrix by its eigenvectors (resulting in the transformed Σ ∗ ). Usingthe eigenvectors of the covariance matrix, we transformed thevector composed of the stars’ proper motions, V , and required atleast 3 𝜎 confidence in the scaled sum of the transformed propermotions: √︃∑︁ V / tr ( 𝚺 ∗ ) > . . (1)This reduced our sample size from 4247 to 3970 RR Lyrae withat least 3 𝜎 significant proper motions. The connection of the RR Lyrae stars’ pulsation periods, metallic-ities, and luminosities permits us to estimate a distance to a givenRR Lyrae star with an uncertainty on the order of three and tenpercent for infrared and optical data, respectively (Neeley et al.2017). The literature provides many PLZ relations both from thetheoretical (e.g., Catelan et al. 2004; Marconi et al. 2015, 2018),and observational studies (e.g., Muraveva et al. 2018; Neeleyet al. 2019). The importance of metallicity in the PLZ relationsand distance calculation is small as we move from the opticalto the infrared wavelengths, it does not completely disappear,and the absence of a metallicity estimate for an individual starintroduces an additional source of uncertainty on its distanceestimate.Our data set is composed of unfiltered CSS photometry forwhich we estimated the mean magnitude based on a Fourierdecomposition (see Appendix A). Unfortunately, absolute mag-nitudes of RR Lyrae stars in the 𝑉 -band are strongly dependenton metallicity, and not on pulsation period (see Catelan et al.2004; Marconi et al. 2018; Muraveva et al. 2018).To overcome this drawback, one needs to move from the vi-sual wavelengths more toward the near-infrared or rely on theperiod-Wesenheit-metallicity (PWZ) relations, which provide asolid diagnostic for individual RR Lyrae distances due to its lowmetallicity dependence. For this reason, we decided to cross-match our RR Lyrae sample with the PanSTARRS-1 (PS1,Chambers et al. 2016) catalog of RR Lyrae stars (Sesar et al.2017), and utilized their flux-averaged 𝑖 -band magnitudes. ThePLZ in the PS1 𝑖 -passband is strongly dependent on the pulsationperiod and only marginally on metallicity (see table 1 in Sesaret al. 2017). In order to estimate distances to the first-overtonepulsators we needed to transform their pulsation periods ( 𝑃 –pulsation period of the first overtone mode) into the correspond-ing fundamental periods ( 𝑃 F – pulsation period of the funda-mental mode) using the relation from Iben & Huchra (1971) andBraga et al. (2016):log 𝑃 F = log 𝑃 + . . (2)We note that there are several other approaches on how to trans-form the pulsation periods of RRc type stars (e.g., Di Criscienzo The RUWE serves as an informative statistic on the quality ofthe astrometric five-parameter solution. We refer the interested readerto the technical note for more details. Panoramic Survey Telescope and Rapid Response System.Article number, page 3 of 22 &A proofs: manuscript no. Stream-Orphan et al. 2004; Coppola et al. 2015), but their effect on the resultingabsolute magnitude and subsequently distance is only marginal,and is completly covered by the total error budget of the abso-lute magnitude of a given star. To obtain metallicities for the 𝑖 -band PLZ relation, we used samples analyzed by Fabrizio et al.(2019) and Crestani et al. (2020) which largely ( > = − . ± .
51 dex, 2020) for halo RR Lyrae stars. Toaccount for the reddening of the sample stars we utilized theextinction maps from Schlafly & Finkbeiner (2011).To calculate distances, 𝑑 , and their uncertainties, 𝜎 𝑑 , we rana Monte Carlo error analysis where we assumed a Gaussian dis-tribution for the uncertainties on apparent magnitudes of 0 . 𝑖 -band magnitude. We also varied the coefficientsof the PLZ relation (for the 𝑖 -passband as listed in table 1 inSesar et al. 2017), within their errors, together with our assumedmetallicities, reddening coefficients, and their associated uncer-tainties. The resulting distances range from 4 to 100 kpc with theerror budget varying from five to six percent. We note that ouruncertainties are larger than generally reported for the PS1 surveyof RR Lyrae stars (e.g., Sesar et al. 2017, reported uncertaintiesaround three percent). This is mainly due to our assumed error onthe apparent magnitude, which we believe better represents thesparsity of PS1 observations. In Fig. 1 we depict the distributionof our selected RR Lyrae variables with estimated distances. Weshow only the stars whose proper motions satisfy Eq. 1.As a validation check of our derived distances, we cross-matched our sample with the Spitzer
Merger History and Shapeof the Galactic Halo (SMASH) sample of RR Lyrae stars for theOrphan stream assembled by Hendel et al. (2018) and found 17variables in common. We detected a small offset of approximately0 .
3. Membership method
To assess a star’s possible association with a given stellar stream,we employed a probabilistic approach similar to the one used forclassical Cepheids in open clusters by Anderson et al. (2013), anda study of MW globular cluster escapees in the halo (Hanke et al.2020). In our analysis we establish membership probabilitiesbased on the Bayesian framework that states that the posteriorprobability 𝑝 ( 𝐴 | 𝐵 ) of a model for the stream, 𝐴 , and the data, 𝐵 ,is: 𝑝 ( 𝐴 | 𝐵 ) = 𝑝 ( 𝐵 | 𝐴 ) × 𝑝 ( 𝐴 ) 𝑝 ( 𝐵 ) ∝ 𝑝 ( 𝐵 | 𝐴 ) × 𝑝 ( 𝐴 ) , (3)which is a product of the likelihood function 𝑝 ( 𝐵 | 𝐴 ) , our priorbelief in an association, 𝑝 ( 𝐴 ) , and a normalizing constant, 𝑝 ( 𝐵 ) ,representing the probability of observing the data (Bayes &Price 1763). Our analysis focused on connecting our sample ofRR Lyrae variables with the Orphan stellar stream which is suf-ficiently defined in equatorial coordinates 𝛼, 𝛿 , proper motions: 𝜇 𝛼 ∗ , 𝜇 𝛿 , and distances 𝑑 .Thus, we selected the prior to be a uniform probability dis-tribution (with upper and lower boundaries) on the sky position 𝛼 : 𝑝 ( 𝐴 ) = if Min (cid:16)(cid:12)(cid:12) 𝛼 stream − 𝛼 RR ★ (cid:12)(cid:12)(cid:17) < else . (4) For a simple description of stellar streams in a multi-parameterspace, we used the Gaussian process (GP) regressor implementedin the scikit-learn library (Pedregosa et al. 2011). The GPsare a Bayesian nonparametric approach to regression, and theyare a useful tool for nonlinear regression and classification. Inthe GP regressor we predict a continuous variable by specifyinga suitable covariance function (kernel). In our case we selectedthe following set of kernels and their hyperparameters : k e r n e l = ( C o n s t a n t K e r n e l ( ) +W h i t e K e r n e l ( n o i s e _ l e v e l =2) +Matern ( l e n g t h _ s c a l e =2 , nu = 3 / 2 ) ) × · D o t P r o d u c t ( sigma_0 = 1 . 0 ,sigma_0_bounds = ( 0 . 1 , 1 0 . 0 ) ) .
The optimization of the kernels’ hyperparameters is performedinternally by the optimizer based on the maximization of thelog marginal likelihood instead of the computationally expensivecross-validation. We refer the interested reader to Rasmussen &Williams (2005) for a comprehensive and detailed description ofGPs.Using GPs, we fitted the parameters 𝛿, 𝜇 𝛼 ∗ , 𝜇 𝛿 , and 𝑑 as afunction of 𝛼 for the bona fide members of the Orphan stel-lar stream (Koposov et al. 2019), and obtained a GP regressionmodel for the aforementioned parameters. The individual mod-els, when provided with 𝛼 , predict values and covariances for agiven parameter.In order to estimate the conditional likelihood 𝑝 ( 𝐵 | 𝐴 ) , wefollowed the example by Anderson et al. (2013) and Hankeet al. (2020), and utilized the Mahalobis distance (Mahalanobis1936): 𝐷 𝑀 = (cid:16) x RR ★ − x stream (cid:17) T 𝚺 − (cid:16) x RR ★ − x stream (cid:17) , (5)where x RR ★ is a four-component vector composed of equa-torial coordinates, proper motions, and distances ( x RR ★ = { 𝛿, 𝜇 𝛼 ∗ , 𝜇 𝛿 , 𝑑 } ) for a given 𝛼 -coordinate. For obtaining a star’sstream vector x stream we used as an input to the GP regression thestar’s equatorial 𝛼 coordinate. The Gaussian regression modelsin turn yield a prediction for x stream and their variance for thestreams’ covariance matices. The visual depiction of our analysiscan be found in Fig. 2. 𝚺 − represents the inverse sum of covari-ance matrices between an RR Lyrae variable and a given stellarstream scaled by the squared RUWE. The covariance matrix forRR Lyrae stars in our sample was constructed using the variancesand correlation coefficients from Gaia
EDR3. Since our distancescame from an independent source, we set their correlations withother parameters to zero. The stream covariance matrix is builtusing the prediction on the individual parameter from the GPregressor and only contains diagonal entries. To ensure that ourstream quantities are independent of the variable sample (no co-variance between x RR ★ and x stream ) we removed cross-matchedRR Lyrae stars from the parent population of the stream samplefor the GP regression of the stream distributions.Because of the assumption of a multivariate-normal error dis-tribution the resulting 𝐷 𝑀 is chi-squared distributed, in our casewith four degrees of freedom (coordinate, proper motions, anddistance). The likelihood function 𝑝 ( 𝐵 | 𝐴 ) can then be expressed We note that for the individual regressions we varied the individualcovariance functions. The GP models for individual parameters will beprovided at https://github.com/ZdenekPrudil/Orphan2020 . Which in practice is a generalized Euclidean distance (with the iden-tity covariance matrix), and is often used for the identification of outliers(Kim 2000).Article number, page 4 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars l -75 ° -60 ° -45 ° -30 ° -15 ° ° ° ° ° ° ° b
10 20 30 40 50 60 70 80 d [kpc] Fig. 1.
Spatial distribution of RR Lyrae stars (color-coded based on their distance) in Galactic coordinates. The light blue crosses denote theRR Lyrae stars associated with the Orphan stream by Koposov et al. (2019).
Gaia ’s all-sky star density map is underlaid in the background asillustration.
Image credit: Gaia Data Processing and Analysis Consortium (DPAC); A. Moitinho / A. F. Silva / M. Barros / C. Barata, University ofLisbon, Portugal; H. Savietto, Fork Research, Portugal. as a 𝑝 -value ( 𝑝 val ) of the 𝐷 𝑀 ; 𝑝 ( 𝐵 | 𝐴 ) = − 𝑝 val ( 𝐷 𝑀 ) . (6)The 𝑝 -value is a probability metric for evaluating the null hy-pothesis, which in our case is a hypothesis test whether a star isor is not associated with a given stellar stream. A high 𝑝 -valuein Eq. 6 highlights stars that we considered as outliers from thestream. Thus, our probability calculation mainly tags the stream’soutliers (nonmembers). Conversely, if a high number of exploreddimensions is provided, with strong constraints on the signifi-cance of individual parameters, then the probability of a star’smembership in a given stream increases. We note that just asin any general case, the null hypothesis cannot be proven butonly excluded. Thus, we treat the identified members as likelyassociations.With the goal to distinguish between outliers and possiblemembers, we selected for 𝑝 ( 𝐴 | 𝐵 ) a critical threshold of 0.05.Thus the RR Lyrae stars in our sample with a higher 𝑝 ( 𝐴 | 𝐵 ) willbe treated as tentative stream members.
4. RR Lyrae and non-pulsating stars in the Orphanstream
Since its discovery (Grillmair 2006; Belokurov et al. 2007), theOrphan stream has been targeted by various studies that provided several lists of possible candidates representing a variety of stel-lar types (e.g., F-turnoff stars, BHB stars, RR Lyrae stars, andK-giants, Newberg et al. 2010; Sesar et al. 2013; Koposov et al.2019; Casey et al. 2013). The sample from Newberg et al. (2010)is based on the SDSS photometric and spectroscopic products,providing important spatial, dynamical, and chemical informa-tion about the Orphan stream, especially the metallicities of theBHB stars ([Fe/H] = − . = − .
63 dex) than the BHB stars. We note that in thehigh-resolution spectroscopic study of Casey et al. (2014), threehigh-probable candidates that can be kinematically and astromet-rically associated with the Orphan stream exhibit a slightly loweraverage metallicity [Fe/H] = − .
01 dex.We use the latest sample of possible stream members from thework by (Koposov et al. 2019, and from here on we refer to it asthe K19 reference sample). The K19 sample includes
Gaia
EDR3and variable stars identification from Clementini et al. (2019). Itconsists of 109 RR Lyrae stars (106 fulfilling the condition in
Article number, page 5 of 22 &A proofs: manuscript no. Stream-Orphan − . − . − . − . − . − . . . µ α ∗ [ m a s y r − ] µ RR ?α ∗ − µ stream α ∗ − − µ δ [ m a s y r − ] µ RR ?δ − µ stream δ Koposov et al. (2019)Predicted position from GPTest RR Lyrae ? − δ [ d e g ] δ RR ? − δ stream Prediction from GP68%, 95% and 99% CIs
130 140 150 160 170 180 α [deg] d [ k p c ] d RR ? − d stream Fig. 2.
Visual example of the membership analysis for the Orphan stellarstream using data from Koposov et al. (blue crosses, 2019), with anartificially placed star (black dot), and its stream counterpart (red dot) atthe same 𝛼 and predicted values of 𝛿, 𝜇 𝛼 ∗ , 𝜇 𝛿 , and 𝑑 . Black solid linesand gray shaded regions denote the GP regression and its confidenceintervals (CIs, ± , , 𝜎 ), respectively. Eq. 1) associated with the Orphan stream based on their spatialand kinematical properties. The Orphan reference sample spansboth Galactic hemispheres, with a total coverage of about 210degrees, and distances ranging from ≈
10 kpc to 60 kpc.Our dataset relies on
Gaia
EDR3 astrometric products andmainly on the
Gaia identification of RR Lyrae stars (Clemen-tini et al. 2019) verified using the CSS and PS1 surveys, andcovers primarily the northern Galactic hemisphere due to theSDSS footprint (see Fig. 1). Our dataset offers a re-evaluatedRR Lyrae classification, improved distance estimates, metallici-ties, and systemic velocities for individual RR Lyrae stars. TheRR Lyrae stars from the reference sample only served as aninput for our membership analysis described in the previous sec-tion. From the K19 sample, 20 RR Lyrae stars overlap with ourdataset. The K19 sample does not contain uncertainties on indi-vidual distance estimates, which are based on visual magnitudesof individual RR Lyrae variables, thus we assumed a generaluncertainty of 10 % on the distance estimate for the Gaussianprocess regression.In Figure 3, we show the results of our analysis for our sam-ple of RR Lyrae located in the vicinity of the K19 dataset. In ourinvestigation, we identified 20 RR Lyrae variables (13 RRab and7 RRc-type pulsators) to be associated with the Orphan streambased on their equatorial coordinates, proper motions, and dis-tances. From these stream associates, we recover 12 variables al-ready present in the K19 sample. The remaining eight RR Lyraepulsators consist of three variables that were identified as mem-bers of the Orphan stream by Sesar et al. (2013) and Hendelet al. (2018), while five are new discoveries. The likelihoods ofstars not included in the K19 sample range from 𝑝 ( 𝐴 | 𝐵 ) = . 𝑝 ( 𝐴 | 𝐵 ) = .
8, with only four below 𝑝 ( 𝐴 | 𝐵 ) < .
2. Similarto the K19 sample, we trace the Orphan stream from approx-imately 25 kpc to 47 kpc in distance across 32 deg on the sky.The proper motion ranges are 𝜇 𝛼 ∗ ≈ (− . − . ) mas yr − and 𝜇 𝛿 ≈ (− .
75; 0 . ) mas yr − and follow by construction theranges of the K19 RR Lyrae stars. Based on the likely streammembers, the projected width of Orphan stream varies around1 − = − . ( ) dex witha dispersion of 0 .
25 dex. This is significantly more metal-richthan previously reported by Sesar et al. (2013, average metallic-ity equal to − . RV_ADOP determined by the SSPP pipeline.Expectedly, we found a lower dispersion in our systemic veloc-ities in comparsion to dispersion in
RV_ADOP , 11 . − and19 . − , respectively.Using the calculated distances and estimated systemic veloc-ities, we specifically looked for RR Lyrae stars beyond 50 kpc(the estimated apogalacticon of 90 kpc by Newberg et al. 2010),and we found no RR Lyrae stars in our sample that could beconsidered as a continuation of the Orphan stream. As an ad-ditional corroboration of our Orphan RR Lyrae candidates, welooked at their distribution in the period-amplitude plane andsearched for high-amplitude short-period RR Lyrae variables(HASP, Fiorentino et al. 2015). The HASP RR Lyrae stars arecharacterized by short pulsation periods ( 𝑃 < .
48 day) and highamplitudes (in 𝑉 -band above 0 .
75 mag). They often occur in sys-
Article number, page 6 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars tems with high metallicity (higher than − . > − . Building upon the approach for RR Lyrae stars, we performed asimilar analysis with the remaining stellar sample of the SDSS. Tothis extent, we searched for objects analyzed by the SSPP pipeline,restricting the sample to those objects with determined 𝑇 eff . Uti-lizing SSPP products, we obtained their atmospheric parameters( 𝑇 eff , log 𝑔 , [Fe/H]) together with their heliocentric line-of-sightvelocities. The nonvariable sample, as we refer to it, was sub-sequently cross-matched using equatorial coordinates with the Gaia
EDR3 catalog to acquire their proper motions and photo-metric properties ( 𝐺 , 𝐺 BP , and 𝐺 RP magnitudes). Regarding theproper motion significance, we required the same significance asin the case of the RR Lyrae sample to remove possible outliers.For our nonvariable sample, we proceeded with our methodoutlined in Sect. 3 (using our identified sample of OrphanRR Lyrae stars as the parent population) with two differences.Firstly, instead of using spectrophotometric distances, which canbe prone to many systematics, we substituted the distance in the x ★ vector with the systemic velocity (cid:0) x ★ = (cid:8) 𝛿, 𝜇 𝛼 ∗ , 𝜇 𝛿 , 𝑣 sys (cid:9)(cid:1) ,thus slightly favoring the kinematical over the spatial associa-tion. Secondly, we only looked for tentative members close tothe stream itself, thus narrowing our uniform flat prior from fivedegrees to one degree. As an additional criterion, we adoptedcuts on metallicities and log 𝑔 to select stars above the main se-quence and thus remove the majority of the contributions fromthe Galactic disk:[Fe/H] < − . ∩ log 𝑔 < . . (7)Following this approach, we recovered 54 nonvariable stars likelyassociated with the Orphan stream as traced by our sample ofRR Lyrae variables (listed in Table D.2). We also recovered fourstars that were previously identified as RR Lyrae stars in the Gaia
DR2 and PS1 surveys. Using CSS photometry, we were ableto classify three of them as double-mode RR Lyrae pulsators. Theone remaining variable has an uncertain classification. All fourstars did not enter our initial analysis of single-mode RR Lyraestars and are denoted with an asterisk in Table D.2. The distribu-tions of astrometric and kinematical parameters of the associatednonvariables are depicted in Fig. C.1.Utilizing the spectroscopic products (surface gravities andeffective temperatures) determined by the SSPP pipeline and thedereddened photometry from
Gaia
EDR3, we constructed theKiel diagram (log 𝑔 vs. 𝑇 eff ) and the color-magnitude diagramfor stable stars associated with the Orphan stream (see Fig. 4).To deredden Gaia apparent magnitudes, we used the extinctioncoefficients from Casagrande & VandenBerg (2018, see their ta-ble 2) in combination with the dust maps derived by Schlafly &Finkbeiner (2011). The 𝐺 magnitudes of each stable star werecorrected by the distance modulus estimated from the Gaussianprocess regression of our RR Lyrae sample given its right ascen-sion. In the top panel of Fig. 4 we clearly identify the red giantbranch (RGB, defined as 𝑇 eff < 𝑔 < 𝑝 ( 𝐴 | 𝐵 ) > . 𝑔 ranging from 3 . . − . Gaia data where an isochrone of highermetallicity ( − . 𝑇 eff , log 𝑔 , and [Fe/H] derived by the SDSS and thosefrom high-resolution studies. Similar trends in stellar parametersof the SDSS survey were also independently reported by Hankeet al. (2018) and Hanke et al. (2020, based on monometallicglobular clusters).
5. Discussion
The full 7D chemo-dynamical distribution of RR Lyrae starslikely associated with the Orphan stream permits us to exam-ine their orbital parameters with respect to an assumed staticMW potential. Jointly with chemical information in the form of[Fe/H] for nonvariable stars associated with the Orphan stream(see Sect. 4.2) we can search for its possible progenitor. We focuson comparing with the work by K19, who provided a detailedexamination of the properties of a possible Orphan progenitor re-garding the stream RR Lyrae population. K19 also discussedlikely progenitors among several globular clusters and dwarfgalaxies based on the spatial ( 𝛼 , 𝛿 , and distances), and propermotion spaces. The metallicity of RGB and BHB stars centers at − . ± .
05 dex,and − . ± .
14 dex, with dispersions of 0 .
23 and 0 .
43, respec-tively. The average values are in good agreement with previousstudies by Newberg et al. (2010) and Sesar et al. (2013), whofind an average metallicity of − . Gaia astrometry, following the same steps as in the caseof our RR Lyrae sample. From a total of 50 RR Lyrae stars inthe Sesar et al. (2013) catalog we recovered 20 likely membersof the Orphan stream. Following Sesar et al. (2013) we calcu-lated the Kendall’s 𝜏 coefficient (Kendall 1938) for the streamlongitude, 𝜙 (calculated through the coordinates tranformationmatrix from K19), with respect to the metallicity for these 20 sin-gle mode RR Lyrae stars that are likely Orphan members, andwe obtained 𝜏 [ Fe / H ] 𝜙 = − . ± .
11. This is very similar to thevalue reported by Sesar et al. (2013) and also significant . Equatorial coordinates, distances, proper motions, line-of-sight ve-locities, and metallicities. The Kendall’s correlation coefficient, 𝜏 , is a nonparametric correla-tion test, thus independent of any assumptions on the distribution of thetested samples. We note that we calculated the uncertainty on 𝜏 [ Fe / H ] 𝜙 through aMonte Carlo error simulation where we assumed a Gaussian distributionfor errors on the metallicity ( 𝜎 [Fe/H] = . &A proofs: manuscript no. Stream-Orphan α [deg] − . − . − . . . µ α ∗ [ m a s y r − ] [Fe/H] = − . − . − . − µ δ [ m a s y r − ] Sample RR Lyr ? Matched RR Lyr ? Koposov et al. (2019) d [ k p c ] ◦ ◦ ◦ ◦ ◦ α ◦ ◦ ◦ δ Prediction from GP68%, 95% and 99% CIs .
05 0 .
20 0 .
40 0 .
60 0 .
80 1 . p ( A | B ) α [deg] v s y s [ k m s − ] Fig. 3.
Four-parameter association with the Orphan stream defined by the sample of RR Lyrae stars from Koposov et al. (2019, denoted by lightblue crosses) based on the spatial and astrometric properties of the studied sample. The RR Lyrae stars associated with the Orphan stream (witha lower significance threshold set at 0.05) are color-coded based on the conditional probability 𝑝 ( 𝐴 | 𝐵 ) . Gray dots represent rejected RR Lyraestars from our sample. Black lines and gray regions denote the GP fit to the reference sample and confidence intervals of a given interpolation,respectively. The metallicity of each star associated with the Orphan stream is depicted by varying its point size. The error bars in the left cornersrepresent the 15 .
9, 50, and 84 . We explored the existence of a metallicity gradient in theOrphan stream using our nonvariable and RR Lyrae sample .The depiction of the metallicity versus 𝜙 can be found in Fig. 5.In both of our samples (nonvariable and RR Lyrae sample) we donot detect any significant correlation between the sky position 𝜙 and metallicity. A similar outcome holds even when we includeonly stars with a high probability 𝑝 ( 𝐴 | 𝐵 ) > . Δ S method using metallicities determined from high-resolutionspectra (Crestani et al. 2020), while Sesar et al. (2013) relied on We verified, with a sample of 3000 RRL stars, that both the new high-resolution Δ S scale and that of the SSPP pipeline metallicities agreewithin − .
01 dex with a dispersion of 0 .
28 dex without any significanttrend. the calibration of Layden (1994) which is slightly offset comparedto metallicities obtained from high-resolution spectra (see, e.g.,For et al. 2011; Chadid et al. 2017). Another reason could liein the metallicity scale, where Sesar et al. (2013) values lie onthe Zinn & West (1984) scale , while our metallicities are ona different metallicity scale (Chadid et al. 2017; Sneden et al.2017; Crestani et al. 2020). This could shift the metallicities ofSesar et al. (2013) toward the metal-rich end by up to 0 . It is worth mentioning that the Zinn & West (1984) scale exhibitsmild nonlinearity in comparison with the high-resolution studies of theMW globular clusters (see fig. 9 in Carretta et al. 2009).Article number, page 8 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars .
20 0 .
40 0 .
60 0 . p ( A | B ) T eff [K] . . . . . . . . l og g [ d e x ] [Fe/H] [dex] − . − . − . − . . . . . . ( G BP − G RP ) [mag] − − − G − l og ( d p r e d ) + − A G [ m ag ] [Fe/H] [dex] − . − . − . − . [Fe/H]= − . − . Fig. 4.
Kiel diagram (top panel, using quantities from the SSPP pipeline),and the color-magnitude diagram (bottom panel) for stars likely associ-ated with the Orphan stellar stream color-coded based on the probabilityand with varying point size denoting the metallicity. The blue and redlines represent isochrones from the MESA Isochrones & Stellar Tracks(MIST, Dotter 2016; Choi et al. 2016; Paxton et al. 2011, 2013, 2015)database for two different metallicities. The gray contours in the toppanel represent the entire star matched sample of SDSS-
Gaia . In the work by K19, the previously considered candidates for theOrphan progenitors, Segue 1 and UMa II (Fellhauer et al. 2007;Newberg et al. 2010), were excluded based on their distance andproper motions. One viable candidate for the progenitor of theOrphan stream remained, Grus II, a UFD (found in the DES byDrlica-Wagner et al. 2015). Grus II matches with the Orphan stel-lar stream in the coordinates and proper motion space. Recently,line-of-sight velocities and chemical abundances became avail-able for several stars associated with Grus II UFD (Simon et al.2020; Hansen et al. 2020). The line-of-sight velocities center onaverage at − . ± . − for three RGB stars analyzed byHansen et al. (2020), and at − . ± . − for identifiedmembers by (Simon et al. 2020). Combining the distance andsky position of Grus II (Martínez-Vázquez et al. 2019), together . . . . . p ( A | B )
80 90 100 110 120 φ [deg] − . − . − . − . − . − . [ F e / H ][ d e x ] Non-variable ? Orphan RR Lyr ? − . − . − . − . − . [Fe/H] [dex] N Orphan ? RGB ? BHB ? RR Lyr ? Fig. 5.
Stream coordinates, 𝜙 , versus [Fe/H] (top panel), and metallicitydistribution function (bottom panel) for likely variable and nonvariableOrphan stream members. The color-coding of each nonvariable starrepresents the probability of association to the Orphan stream 𝑝 ( 𝐴 | 𝐵 ) ,and the green squares represent RR Lyrae stars associated with theOrphan stream in our study. The histogram in the lower panel representsthe metallicity distribution of the entire sample (black line) the RGBstars (red dashed line), BHB stars (blue dotted line), and RR Lyrae stars(green lines). The red solid line represents the kernel density estimateof the metallicity distribution of the RGB stars. with the proper motions (McConnachie & Venn 2020) and line-of-sight velocities (Simon et al. 2020) allowed us to calculate theorbital properties of Grus II, and to compare them with the orbitalproperties of our RR Lyrae sample associated with the Orphanstellar stream. For the purpose of examining the kinematical distribution ofthe identified Orphan stream members and Grus II, we utilizedthe galpy v1.6 package for Galactic dynamics (Binney 2012;Bovy & Rix 2013; Bovy 2015), and estimated for the entire Available at http://github.com/jobovy/galpy .Article number, page 9 of 22 &A proofs: manuscript no. Stream-Orphan
RR Lyrae sample and Grus II the following quantities: orbitalparameters (eccentricity 𝑒 , excursion from the Galactic plane 𝑧 max , and peri- and apocenters, 𝑟 per and 𝑟 apo ), orbital energy 𝐸 ,actions 𝐽 R , 𝐽 z , and angular momenta 𝐿 z ( 𝐽 𝜙 ) with their respectiveuncertainties and correlations.In our setup, we implemented an MW potential consisting ofa Miyamoto-Nagai disk ( 𝑀 disk = . × M (cid:12) , 𝑎 = . 𝑏 = .
28 kpc, Miyamoto & Nagai 1975) , a Hernquist bulge(Hernquist 1990, 𝑀 bulge = . × M (cid:12) , 𝑎 = . 𝑀 halo = . × M (cid:12) , 𝑟 s =
16 kpc).As a Galactocentric reference frame, we adopted the left-hand annotation with the following values for the Solar positionand motion: The distance to the Galactic center is set to 𝑅 = .
178 kpc (Gravity Collaboration et al. 2019), the Solar system isplaced above the Galactic plane at 𝑧 (cid:12) = . ( 𝑈 (cid:12) , 𝝊 (cid:12) , 𝑊 (cid:12) ) = (− . , . , . ) km s − (Schönrichet al. 2010; Schönrich 2012), where 𝑉 (cid:12) = 𝝊 (cid:12) − 𝑉 c = .
24 km s − .For each star we performed a Monte Carlo simulation taking intoaccount the full covariance between the sky positions 𝛼 , 𝛿 , andproper motions 𝜇 𝛼 ∗ , 𝜇 𝛿 , in combination with errors in systemicvelocities and distances. The estimated values were taken as anaverage of the generated distributions with the standard deviationrepresenting the uncertainties on the given properties. In addition,to robustly assess the distributions of the orbital parameters, wealso recovered the correlations between the individual orbitalproperties. Here we note that 𝐸 and actions often do not followthe multivariate normal distribution, as shown, for example, infigure 6 in Hanke et al. (2020), and here in the bottom panelof Fig. 6. Thus, our assumption based on averages, standarddeviations, and correlations here serves only to guide the eye andgive an intuition on the uncertainties of estimated parameters.The median pericentric distances of RR Lyrae stars associ-ated with the Orphan stellar stream peak at 22 kpc. They reach ontheir orbit a median apocenter equal to 89 kpc, and their averageeccentricity varies around 0 .
61. These values are similar to theorbital properties estimated by Newberg et al. (2010), who esti-mated eccentricities of Orphan stream stars to be 0 . ≈
90 kpc, and 16 kpc,respectively. In the case of Grus II, the UFD reaches apocentricand pericentric distances of 66 kpc, and 27 kpc, respectively. Ourcalculated orbital parameters are by a construction similar to or-bital properties obtained by Simon et al. (2020) since we usedthe same the distance and line-of-sight velocity of the Grus II.Its orbit has an eccentricity of 0 .
44, somewhat different from the20 RR Lyrae stars associated with the Orphan stream in our study.In addition, looking at the best-fitting model of the Orphan orbitobtained by Erkal et al. (2019, see their figure 3 for reference)Grus II at 𝜙 = − . 𝐸 – 𝐿 z plane and are displayed in Fig. 6.All of Orphan RR Lyrae stars clusters on positive values of 𝐿 z denoting its prograde orbit (thus confirming previous findingsby, e.g., Newberg et al. 2010), and high-energy region. Grus IIfalls right in the middle of our distribution of RR Lyrae stars,partially supporting the hypothesis of Grus II being the progenitorof the Orphan stellar stream. Unfortunately, large uncertaintiesin actions and energies prohibit a sensible comparison in the For details on the disk potential see Bovy (2015). − − − . − . − . − . − . − . − . − . E [ k m s − ] × Retrograde Prograde
All RR Lyr ? Orphan RR Lyr ? Grus II − − L z [kpc km s − ] × − . − . − . − . − . − . − . − . E [ k m s − ] × bestObjID − . − . − . − . Fig. 6.
Distribution of the orbital energy 𝐸 vs. the 𝑧 -component of theangular momentum 𝐿 z (top panel). The bottom panel shows an exampleof the multivariate non-normal distribution of energies 𝐸 vs. angularmomenta for one of the stars from our sample (represented with bluesquares) and Grus II (denoted with red circles). The underlying graypoints in the upper panel represent the entire RR Lyrae sample fulfillingthe condition in Eq. 1. The blue squares represent the RR Lyrae variablesassociated with the Orphan stellar stream. Each point is accompaniedwith an error ellipse estimated based on our Monte Carlo simulation.The position of Grus II is marked with the red dot and dashed linesaccompanied by error ellipses representing the covariances. multivariate parameter space between Orphan RR Lyrae starsand Grus II. At the current error budget, multivariate analysis inthe action space would lead to a large number of false-positivecandidates for membership with Grus II. The broad [Fe/H] distribution of the Orphan stream supportsits likely origin from a dwarf-like galaxy as was pointed outby several previous studies (e.g., Sesar et al. 2013; Casey et al.2013, 2014; Koposov et al. 2019; Fardal et al. 2019). The work byCasey et al. (2013, 2014) used low- and high-resolution spectra ofK-giants to study the chemical and kinematical properties of the
Article number, page 10 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars
Orphan stream. Using
Gaia proper motions, we were able to cleanthe K-giants sample from the obvious outliers using our methoddescribed in Sect. 3 and the K19 RR Lyrae sample as a reference.We note that we did not use the radial velocities determined inour study, since they do not cover the coordinate region examinedby Casey et al. (2013, 2014), thus our membership probabilitiesare only based on coordinates and proper motions.We found that from both studies (Casey et al. 2013, 2014)only two stars can be considered as likely members (having setthe 𝑝 ( 𝐴 | 𝐵 ) > .
05 threshold). Similarly to the proper motionmembership provided by Fardal et al. (2019), we associate starOSS-8 with the Orphan stream. Unlike Fardal et al. (2019) wedo not associate OSS-6 and OSS-14 with the stream given theirlow 𝑝 ( 𝐴 | 𝐵 ) = .
02 and 𝑝 ( 𝐴 | 𝐵 ) = .
0, respectively. This doesneither significantly affect the observed metallicity spread, northe assumed peak in its distribution. The two stars associatedwith the Orphan stream in our analysis exhibit very differentmetallicities namely; − . , − .
62 dex (based on tab. 1 in Caseyet al. 2013) covering the entire metallicity domain described inSesar et al. (2013) or covered by our sample of nonvariable stars(see Sect. 4.2 and Fig. 5 for details).The spectroscopic study by Hansen et al. (2020) providesa detailed abundance analysis for three likely Grus II mem-bers located on the RGB. The low number of stars with ex-tensive abundance patterns associated both with the Orphan stel-lar stream and the Grus II dwarf galaxy prohibits any detailedchemical tagging. Nevertheless, the iron abundance [Fe/H] = (− . − . − . ) dex for three red giants linked with Grus IIpermits a tentative discussion about their possible connectionwith the Orphan stream on the basis of its metallicity distribu-tion. The metallicities of the three Grus II giants fall onto themetal-poor end of Orphan’s metallicity distribution as traced byseveral independent sources: K-giants, RR Lyrae stars (Caseyet al. 2013; Sesar et al. 2013), and our RR Lyrae and nonvariablestellar sample.In general, the UFDs are almost exclusively old and metal-poor. On the other hand, considering a rather massive dwarfgalaxy, it is expected to undergo a few episodes of star formation.This will result in stars with higher metallicities being centrallyconcentrated (due to past and/or ongoing star formation), whilethe more metal-poor stars are distributed all over the galaxy(Harbeck et al. 2001; Grebel et al. 2003; Crnojević et al. 2010;Lianou et al. 2010; Hendricks et al. 2014). Thus, when a givendwarf enters a parent galaxy potential, it is subdued by the stronggravitational forces, which inevitably results in a tidal disrup-tion of its peripherals, and later the dwarf itself. The outlinedparadigm leads to the formation of a metallicity gradient, wheremetal-poor stars are stripped first followed by the metal-rich core.Such a metallicity gradient has been reported, for example, in theSagittarius dwarf and stream (see, e.g., Bellazzini et al. 1999;McDonald et al. 2013; Hayes et al. 2020). We note that dwarfgalaxies with inverse metallicity gradients have been observedin other galaxy systems and at higher redshifts (e.g., Wang et al.2019; Grossi et al. 2020) but so far not in the Local Group.Concerning the presumed metallicity distribution betweenthe stream and its progenitor, we assessed the probability ofobserving three metal-poor red giants with respect to the metal-licity distribution of the Orphan stream. We employed the Gaus-sian kernel density estimate (KDE) from the scikit-learn library (Pedregosa et al. 2011) to describe the aforementionedmetallicity distribution. Using the GridSearchCV module fromthe scikit-learn library, with 10-fold cross-validation, we se- Marked as OSS-7 and OSS-8 in Casey et al. (2013, 2014). lected the most suitable bandwidth (0 . < − . . = − . ± .
11 dex from Simon et al. (2020) based onmetallicities estimated from the Calcium triplet. Thus, connect-ing the Grus II with the Orphan stream is rather unlikely. Takinginto consideration the discrepancy between metallicities in high-resolution studies and SDSS stellar parameters (Smolinski et al.2011), we would expect this probability to go even lower.
6. Summary
In this study, we presented our sample of 4247 halo RR Lyraestars with an available 7D chemo-dynamical distribution basedon the SDSS survey, mapping mainly the northern hemispherefrom four out to 100 kpc. We employed our dataset to studythe Orphan stellar stream with which we found 20 single modeRR Lyrae stars spatially and kinematically associated. We pro-vide the full spatial and kinematical distribution for the identifiedstream members together with their spectroscopic metallicities.The average metallicity of our Orphan RR Lyrae members centersat − . ( ) dex, thus yielding a higher metallicity than previouslyreported for RR Lyrae variables linked to the Orphan stream (e.g.,Sesar et al. 2013). A higher average metallicity and the extendedmetallicity distribution could potentially shift the predicted massof the Orphan progenitor from 10 to 10 M (cid:12) (using the mass-metallicity relation from Kirby et al. 2013). Unfortunately, largeuncertainties in systemic velocities of our RR Lyrae sample pre-vent us from exploring the progenitor mass for the Orphan stellarstream by means of its velocity dispersion.Using the newly identified stream members and their line-of-sight velocities, we searched for additional nonvariable membersusing the spectral catalog of the SDSS survey processed by theSSPP pipeline. We found additional 54 nonvariable stars that aremainly RGB and BHB stars exhibiting different metallicity distri-butions − . ± .
05 dex, and − . ± .
14 dex, with dispersionsof 0 .
23 and 0 .
43 dex, respectively.The 7D chemo-dynamical distribution of the associatedRR Lyrae and nonvariable stars permitted us to carry out com-parison between likely Orphan stream members and a possi-ble Orphan progenitor, Grus II, a UFD discovered in the DES(Drlica-Wagner et al. 2015; Abbott et al. 2018). Kinematically,RR Lyrae members and Grus II match in action and energy space,albeit with large uncertainties in the aforementioned parameters.The orbital properties also fit, both Orphan stream stars andGrus II follow a prograde orbit with mildly different eccentrici-ties (0 . − . . M (cid:12) , Grossi et al. 2020) have Article number, page 11 of 22 &A proofs: manuscript no. Stream-Orphan been observed outside the Local Group. Dwarf galaxies with aninverted metallicity gradient have been found in, for example,the Virgo cluster (Grossi et al. 2020) or at high redshifts (Cresciet al. 2010; Queyrel et al. 2012; Wang et al. 2019). Thus, linkingGrus II with the Orphan stream on metallicity alone is dubious.For the reasons above we conclude that the link between Grus IIand the northern part of the Orphan stream is rather unlikely.This conclusion leaves us with two possible options to con-template about the Orphan’s stream’s progenitor. One suggeststhat it has been already dissolved during its passage through theMW halo while the second option points toward the progenitorcurrently being located in the Galactic plane where high extinc-tion severely hampers the efforts in search for MW satellites.Using our Gaussian process regressor between the equatorialcoordinate 𝛼 and the heliocentric distance, we looked at the ex-pected orbit of the Orphan stream. It passes behind the Galacticplane around 𝑑 = ( ± ) kpc which places the stream righton the edge of the assumed MW disk. Although the currentlyassumed mass of the Orphan progenitor (from 10 to 10 M (cid:12) )is not enought to warp the MW disk (Burke 1957; Westerhout1957), the model passes through the strong negative vertical dis-placement traced by the Classical Cepheids in the outer disk (seethe left-hand panel of figure 7 in Skowron et al. 2019). Acknowledgements.
Gaia ( ), processed by the Gaia
Data Process-ing and Analysis Consortium (DPAC, ). Funding for the DPAC has been provided by nationalinstitutions, in particular the institutions participating in the
Gaia
MultilateralAgreement. The CSS survey is funded by the National Aeronautics and SpaceAdministration under Grant No. NNG05GF22G issued through the Science Mis-sion Directorate Near-Earth Objects Observations Program. The CRTS survey issupported by the U.S. National Science Foundation under grants AST-0909182and AST-1313422. This research made use of the following Python packages:
Astropy (Astropy Collaboration et al. 2013, 2018), dustmaps (Green 2018), emcee (Foreman-Mackey et al. 2013), galpy (Bovy 2015),
IPython (Pérez &Granger 2007),
Matplotlib (Hunter 2007),
NumPy (Harris et al. 2020), scikit-learn (Pedregosa et al. 2011), and
SciPy (Virtanen et al. 2020).
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Article number, page 13 of 22 &A proofs: manuscript no. Stream-Orphan
Appendix A: Processing the photometric data fromCSS
Appendix A.1: Processing known RR Lyrae in CSS and
Gaia
Our initial step in the verification of our sample was to establishthe dominant pulsation period. Thus, we retrieved the pulsationperiods for stars in our sample that were identified as RR Lyraestars both in CSS and
Gaia
EDR3 (Drake et al. 2013a,b, 2014; Ab-bas et al. 2014; Clementini et al. 2019), and compared their pul-sation periods. When the difference between periods in
Gaia andCSS was larger than 0.005 days, we performed a period analysisusing the
Period04 software (Lenz & Breger 2004) on the CSSdata in order to establish the dominant period. Once the vari-ability periods 𝑃 were secured, we focused on the determinationof the time of brightness maxima 𝑀 . We proceeded iteratively:first, we phased the retrieved CSS light curves using the deter-mined periods and as a time of brightness maxima we selectedthe brightest point on the light curve. In the second step wedecomposed the light curves using the Fourier decomposition: 𝑚 ( 𝑡 ) = 𝐴 + 𝑛 ∑︁ 𝑖 = 𝐴 𝑖 · cos ( 𝜋𝑘 ( MJD − 𝑀 ) / 𝑃 + 𝜑 𝑖 ) , (A.1)where 𝜑 𝑖 and 𝐴 𝑖 stand for phases and amplitudes, and MJDrepresents the Modified Julian Date at the time of observation,and 𝐴 represents the mean magnitude. The optimal degree, 𝑛 , ofthe Fourier decomposition was estimated by gradually increasingthe order until the condition on Fourier amplitude was broken 𝐴 𝑖 / 𝜎 𝑖 >
4. From the Fourier fit, we determined the phase ofthe brightest point and added its period-corrected value from theinitial 𝑀 init0 creating a new, updated 𝑀 upd0 which entered again inthe first step (see an example in Fig. A.1). After a few iterations(usually up to 5) we derived a final time of brightness maxima.We note here that for the subsequent spectroscopic analysis (seeSect. B) we favored 𝑀 determined from the analysis of CSS datadue to a larger number of observations (as compared to Gaia ),and because the CSS photometric observations were conductedroughly at the same time as the SDSS observations. This ensureda consistent classification of our sample since RR Lyrae starscan rapidly change their pulsation mode within a few years (see;e.g., Soszyński et al. 2017). Furthemore, strong period changes(especialy in the first-overtone pulsators, see, i.e., Jurcsik et al.2001; Szeidl et al. 2011) can introduce an additional source ofuncertainty in the determination of 𝑀 .In the next step, we visually verified the variability of theindividual phased light curves using the CSS photometry, and weremoved stars with no signs of luminosity variation. Alongsidethis step, using a Fourier decomposition, we determined basiclight curve parameters for the RR Lyrae sample, for example,pulsation amplitudes Amp 𝑉 CSS , rise time RT 𝑉 CSS , amplituderatios ( 𝑅 , 𝑅 ) and phase differences ( 𝜑 , 𝜑 ) defined asfollows: 𝜑 𝑖 = 𝜑 𝑖 − 𝑖𝜑 𝑅 𝑖 = 𝐴 𝑖 𝐴 . (A.2)The estimated photometric parameters allowed us to robustlyassess the pulsation subclasses (RRab, RRc, and RRd) of thestudied RR Lyrae stars. Based on their position in the period-amplitude diagram and amplitude ratio vs. pulsation period, we Defined as a magnitude difference between the faintest and brightestpoint of the Fourier fit. Determined from the Fourier fit as a phase difference between thebrightest and faintest point. − . − . . . . Phase . . . . . . . B r i g h t n e ss [ m ag ] M new0 = M old0 + Phase(mag min ) × P Fourier fit bestObjID
Fig. A.1.
Example of the 𝑀 determination based on CSS photometryfor one of the sample stars. The blue and red dots represent erroneous 𝑀 that were subsequently corrected by a phase shift of the time ofbrightness maxima (determined from the Fourier fit) multiplied by thepulsation period. divided them into the two categories RRab and RRc . Variableson the borderline between both classes were examined furtherusing an automated routine that removed the dominant pulsationmode and searched for signs of an additional mode that wouldcoincide with a period ratio typical for double-mode RR Lyraestars ( 𝑃 / 𝑃 F from 0 .
68 to 0 .
76, Smolec et al. 2015; Soszyńskiet al. 2016; Prudil et al. 2017). In the end, variables with signs ofdouble-mode behavior were removed from our sample.
Appendix A.2: Searching for new RR Lyrae stars in CSS data
Taking advantage of the extensive SDSS sample and availableCSS photometry, we conducted a new search for RR Lyrae stars,similar to the one performed in Hanke et al. (2020). As an initialstep, we removed stars that did not have an effective temperaturedetermined using the SSPP pipeline, assuming that they are ex-tragalactic sources. In a second step, we looked at the color spaceof our confirmed RR Lyrae sample, using SDSS multi-band pho-tometry. Based on their color distribution, we applied rectangularcolor cuts on the entire SDSS spectral sample: − . < ( 𝑢 − 𝑔 ) < . − . < ( 𝑔 − 𝑟 ) < .
35 (A.4) − . < ( 𝑟 − 𝑖 ) < .
15 (A.5) − . < ( 𝑖 − 𝑧 ) < . . (A.6)We note that our color conditions are similar to the ones used bySesar et al. (2010) and Abbas et al. (2014), only more restricted.In addition, we did not use dereddened magnitudes.Using the sample selected on the SDSS products, we retrievedtheir CSS photometry and searched for signs of variability us-ing the upsilon software package (Kim & Bailer-Jones 2016).This software searches for variability in the provided photomet-ric data and yields a classification (and class probability) of thevariable objects based on the shape of their light curves. To en-sure a correct classification, we selected for further examinationonly stars marked as RR Lyrae stars with a class probability We note that we identified some RRd pulsators but they were not usedin our study. Accessible at: https://github.com/dwkim78/upsilon .Article number, page 14 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars . . . . . . . Period [day] . . . . . . . . A m p li t ud e [ m ag ] RRab = 2826RRc = 1421
Fig. A.2.
Period-amplitude diagram for the studied sample of RR Lyraestars. Blue and red dots represent the fundamental and first overtonepulsators, respectively. above 50 %. Then, using the determined pulsation periods fromthe upsilon package we determined 𝑀 (as described above),visually verified their periodicity in the phased light curves andremoved the misclassified stars. For the final (pure) sample, wedetermined the Fourier coefficients and classified RR Lyrae insubclasses.As a last step, we cross-matched our sample of RR Lyraestars with the PanSTARRS-1 (PS1) survey catalog of RR Lyraestars (Sesar et al. 2017), where their mean magnitudes were laterused for the distance estimation (see Sect. 2.2). In the end, ourtotal sample consists of 4247 RR Lyrae stars (2826 RRab and1421 RRc) with photometric, astrometric, and spectroscopic datathat entered our analysis. In Fig. A.2 we depict the distributionof the final sample in the period-amplitude diagram. Appendix B: Processing the spectroscopic datafrom SDSS
Obtaining a precise systemic velocity 𝑣 sys for a given RR Lyraevariable is hampered by the entanglement of the measured line-of-sight velocity, 𝑣 los , and the motion of the atmosphere due topulsation. The amplitude variation of the line-of-sight velocitycurves depends on the atmosphere depth. Therefore, lines formedin the upper levels of the atmosphere (e.g., the Balmer lines H 𝛼 ,H 𝛽 , etc.) yield larger amplitude variation, in contrast to metalliclines from elements like Fe or Sr, which are formed lower andthereby expose smaller variations in line-of-sight velocities. Theline-of-sight velocity curves measured from lines in the upperand lower layers of the atmosphere vary not only in amplitudebut also in shape (see, e.g., figure 1 in Sesar 2012). Thus, toestimate precisely the systemic velocity of a given RR Lyrae starone needs to follow the entire pulsation cycle or utilize line-of-sight velocity templates defined for individual spectral lines(metallic lines, H 𝛼 , H 𝛽 , H 𝛾 , H 𝛿 , see Liu 1991; Sesar 2012; Braga2021, for instance). The aforementioned templates scale with thephotometric amplitudes, hence one can determine the systemicvelocity using a single spectral line, the time of the observation,ephemerides, and amplitude information from photometry.The available spectra from the SDSS are of low resolution( ≈ Wavelength [˚A] F l u x [ − e r g/ c m / s / ˚A ] H β H γ H δ Ca ii H line + H ε Ca ii K lineH ζ H η Na D , O i Mg b , , lines Ca ii tripletregion bestObjID specObjID H α .
131 0 .
260 0 . pulsation phase Fig. B.1.
Example of an SDSS co-added spectrum (black line) for anRR Lyrae variable from our sample with the most prominent lines anno-tated. The individual exposures around the H 𝛼 line are depicted in theinset and color-coded based on the pulsation phase. Server , and consist of the co-added spectra and individual ex-posures in both SDSS spectral windows (blue and red). Eachexposure contains a header with information about the time ofthe observation and data composed of vacuum wavelengths in the heliocentric frame, flux-calibrated spectra (in units of10 − erg s − cm − Å − ), and their associated errors (Stoughtonet al. 2002).To consistently estimate the systemic velocities of ourRR Lyrae sample, we proceeded in the following way. We sepa-rated the individual exposures (blue and red part of the spectrum)and selected four prominent Balmer lines (H 𝛼 , H 𝛽 , H 𝛾 , H 𝛿 )for which we determined their line-of-sight velocities by cross-correlation with a synthetic spectrum using the iSpec package(Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019). The syn-thesized spectra for each line were obtained through a pythonwrapper of the radiative transfer code MOOG (February 2017version, Sneden 1973), using the ATLAS9 model atmospheres(Castelli & Kurucz 2003), a solar reference scale from Asplundet al. (2009), and a line list from VALD , all of which are imple-mented in iSpec . The synthesized spectra were calculated withrespect to a set of typical stellar parameters of RR Lyrae stars(For et al. 2011; Sneden et al. 2017; Preston et al. 2019): – 𝑇 eff = – log 𝑔 = .
25 dex – [Fe/H] = − . – Microturbulence velocity 𝜉 turb = . − .A region ( ±
100 Å) around each Balmer line was cross-correlatedwith the synthetic spectrum. To account for the uncertaintiesin the flux we employed a Monte-Carlo simulation by varyingthe flux within its errors (assuming that they follow a Gaussiandistribution). This allowed us to identify problematic spectra andto assign their 𝑣 los larger uncertainties than they would have usinga single cross-correlation procedure.Using this approach, we discarded line-of-sight velocities thatfailed at least one of the following conditions: (cid:12)(cid:12) 𝑣 los / 𝜎 𝑣 los (cid:12)(cid:12) > ∪ 𝜎 𝑣 los <
10 km s − . (B.1) https://dr15.sdss.org/sas/dr15/ We note that for the determination of line-of-sight velocities we con-verted SDSS vacuum wavelengths to the air wavelength frame using aformula from Ciddor (1996). http://vald.astro.uu.se/ Article number, page 15 of 22 &A proofs: manuscript no. Stream-Orphan
To determine the systemic velocities of our RR Lyrae sample, weused a new set of line-of-sight velocity templates for the Balmerlines from Braga (2021), and scaled them by the provided linearscaling relations between the line-of-sight velocity amplitudesand the light curve amplitudes (see Braga 2021, for details).The systemic velocity for each Balmer line was estimatedby minimizing the offset between the amplitude-scaled line-of-sight velocity templates and the measured line-of-sight veloc-ities. For this process, we utilized the Markov Chain MonteCarlo (MCMC) sampler implemented in the emcee package( v.3.0.2 , Foreman-Mackey et al. 2013) where we maximal-ized the posterior probability defined in the following way: 𝑝 ( 𝜽 | 𝐷 ) ∝ 𝑝 ( 𝜽 ) × 𝑁 (cid:214) 𝑝 ( 𝐷 𝑛 | 𝜽 𝑛 ) , (B.2)where 𝐷 𝑛 represents data for an individual star in the form: 𝐷 𝑛 = (cid:110) 𝑃 𝑛 , 𝑀 ,𝑛 , 𝑣 H 𝛼 los ,𝑛 , 𝑣 H 𝛽 los ,𝑛 , 𝑣 H 𝛾 los ,𝑛 , 𝑣 H 𝛿 los ,𝑛 (cid:111) , (B.3)and 𝜽 the model consisting of an amplitude scaled line-of-sightvelocity template for the individual Balmer line (from Braga2021), each shifted by the systemic velocity. In our MCMC setupwe therefore sampled the following model parameters: 𝜽 𝑛 = (cid:110) Δ 𝑀 ,𝑛 , 𝑣 H 𝛼 sys ,𝑛 , 𝑣 H 𝛽 sys ,𝑛 , 𝑣 H 𝛾 sys ,𝑛 , 𝑣 H 𝛿 sys ,𝑛 (cid:111) , (B.4)with Δ 𝑀 ,𝑛 representing the shift in the time of maximum light.This offset has been included since the photometric quality de-grades at the faint end of our sample and the estimation of 𝑀 be-comes challenging. This is particularly true for the first-overtonepulsators, where symmetrical light curves with lower amplitudesand larger photometric errors hamper the precise determinationof 𝑀 . The uncertainty of 𝑀 can affect the systemic veloc-ity determination for stars with observations around the time ofthe brightness maxima, where the line-of-sight velocities changerapidly. Thus, the offset parameter, Δ 𝑀 ,𝑛 , can compensate forsuch an eventuality. As a prior for our model parameters, weadopted uniform ( U ) priors: 𝑝 ( 𝜽 𝑛 ) = U (− . < Δ 𝑀 ,𝑛 < . ) ∩ (B.5) U ( ¯ 𝑣 H linelos − , ¯ 𝑣 H linelos + ) , (B.6)where ¯ 𝑣 H linelos represents the median velocity for all lines, withthe value 130 km s − characterizing the maximal line-of-sightvelocity amplitude for an RR Lyrae star with Amp 𝑉 CSS ≈ . 𝑝 ( 𝐷 𝑛 , 𝜽 𝑛 ) represents the likelihood for each line of a given star: 𝑝 ( 𝐷 𝑛 , 𝜽 ) = N ( 𝑣 H linelos , 𝜎 𝑣 Hlinelos | 𝑣 H modellos ) , (B.7)where 𝑣 H modellos represents a velocity value for a given phase ofthe observation 𝜗 = ( MJD − 𝑀 + Δ 𝑀 )/ 𝑃 , from the amplitude-scaled line-of-sight velocity template shifted by 𝑣 H linesys .To estimate the posterior distribution of our model parame-ters, we ran emcee with 48 walkers for an initial 200 steps asburn-in and then restarted the sampler for an additional 2200steps. Fig. B.2 depicts the posterior likelihood distribution of themodel parameters 𝜽 for a given RR Lyrae star from our sample.While examining the systemic velocities determined fromindividual lines, we noticed a non-negligible offset in systemicvelocities between individual lines, where values determined onthe blue end of the spectrum showed on average smaller values https://github.com/dfm/emcee/ . than the lines on the red end. We further examined this discrep-ancy in nonvariable stars associated with three star clusters(M 13, M 15, and M 67), where we performed a piecewise cross-correlation in the following way: for each exposure of a given star,we divided the spectrum into three sections based on wavelength; 𝜆 = ( ) (B.8) 𝜆 = ( ) (B.9) 𝜆 = ( ) . (B.10)These three wavelength regions approximately represent spec-tral regions covering H 𝛿 and H 𝛾 ( 𝜆 ), H 𝛽 ( 𝜆 ), and H 𝛼 ( 𝜆 ).For each part of the spectrum, we determined the line-of-sightvelocity using a synthesized template spectrum generated usingthe SSPP pipeline-derived quantities for 𝑇 eff , log 𝑔 , and [Fe/H].We found that the average line-of-sight velocities from individ-ual exposures are decreasing as we move from the red, 𝜆 , tothe blue part, 𝜆 , of the spectrum. The difference between thebluest and reddest regions is on average −
13 km s − . In addi-tion, a difference between the second bluest region, 𝜆 , and thereddest, 𝜆 , region was found as well (on average −
10 km s − ).The comparison between the known line-of-sight velocities ofthe three star clusters (using literature values, Geller et al. 2015;Baumgardt et al. 2019) showed that the line-of-sight velocitiesdetermined in the red region match very well literature values,while the line-of-sight velocities from the blue regions showedthe aforementioned offsets.We decided to include this systematic offset in the determinedsystemic velocities for H 𝛾 , H 𝛿 (shift by +
13 km s − ) and H 𝛽 (shiftby +
10 km s − ). The final systemic velocity value, 𝑣 sys , for a givenRR Lyrae star was estimated through a weighted average usingall four Balmer lines. For its uncertainty, we adopted a weightedstandard deviation 𝜎 𝑣 sys . On average, our weighted uncertaintiesare on the order of 14 km s − . We note here that we chose todetermine the systemic velocities for each line separately insteadof combining them, since this approach leads to uncertaintieson the systemic velocities that are considerably lower than theprecision of the SDSS wavelength calibration ( < − , Leeet al. 2008b; Allende Prieto et al. 2008).As a test for our determined systemic velocities, we comparedour results ( 𝑣 sys ) with the heliocentric line-of-sight velocities, RV_ADOP . As expected, our systemic velocities linearly followthe values from the SSPP with a substantial scatter ( ≈
29 km s − )which is mainly caused by the pulsations of our targets and orig-inate from erroneous estimates on the basis of coadded spectra.In Fig. B.3, we see that stars with low amplitudes and short pul-sation periods (first-overtone pulsators) exhibit a dispersion of25 km s − and cluster around unity (black solid line in the toppanel). In contrast, stars at the other end of the period-amplitudedistribution exhibit a larger scatter since the chances of observingthem around the time of mean line-of-sight velocity are lower.Fundamental pulsators exhibit a dispersion of 31 km s − . Appendix C: Additional figuresAppendix D: Additional tables In total 162 stars covering a broad range of log 𝑔 ≈ ≈ ≈ − . . − . − . − . − . H α [ k m s − ] − . . − . − − − H β [ k m s − ] − . . − . − − − v H linesys [km s − ] H α H β H γ H δ − − H γ [ k m s − ] > CI − . . − . − . − . − . ∆ M [day] − − − H δ [ k m s − ] − − H α [km s − ] − − − H β [km s − ] − − H γ [km s − ] − − − H δ [km s − ] − . . − . Fig. B.2.
Posterior probability distribution for parameters of our model for a given RR Lyrae star in our sample ( bestObjID = 𝛽 , H 𝛾 ,and H 𝛿 in comparison with a systemic velocity determined through the H 𝛼 line (see color histogram on the right-hand side of the figure).Article number, page 17 of 22 &A proofs: manuscript no. Stream-Orphan . . . . . . . Period × Amplitude [day mag] − − RVADOP [ k m s − ] − −
200 0 200 400 v sys [km s − ] − ∆ [ k m s − ] Fig. B.3.
Comparison between line-of-sight velocities
RV_ADOP derivedby SSPP and our systemic velocities calculated using the line-of-sightvelocity templates (top panel) and the residuals of their difference (bot-tom panel) with a color coding that is based on the product of pulsationperiod and amplitude.Article number, page 18 of 22. Prudil et al.: The Orphan stream in 7D using RR Lyrae stars − . − . − . . µ α ∗ [ m a s y r − ] − . − . . . . µ δ [ m a s y r − ] Our sample of RR Lyr ? Sample of stable ? Matched stable ? α [deg] δ [ d e g ] Prediction from GP68%, 95% and 99% CIs α [deg] v s y s [ k m s − ] .
05 0 .
20 0 .
40 0 .
60 0 .
80 1 . p ( A | B ) Fig. C.1.
Four-parameter association of nonvariable stars with our identified sample of RR Lyrae variables (blue crosses) in the Orphan stellarstream. Similar to Fig. 3, the color coding denotes the membership probabilities 𝑝 ( 𝐴 | 𝐵 ) in coordinate (bottom left panel), proper motion (upperpanels), and systemic velocity (bottom right panel) space. The gray lines and shading represent the Gaussian process regression and confidenceintervals (CIs), respectively. The three error bars at the bottom of each panel denote the 15 .
9, 50, and 84 . & A p r oo f s : m a nu s c r i p t no . S t r ea m - O r ph a n Table D.1.
List of RR Lyrae variables in our sample associated with the Orphan stream based on our analysis. The first two columns denote the SDSS and
Gaia
EDR3 object IDs followed by theirequatorial coordinates in columns three and four. Columns 5, 6, 7, and 8 list the estimated distances and systemic velocities with associated uncertainties. The parameters estimated on basis of theCSS photometry are listed in columns 9, 10, 11, 12, and 13, starting with mean magnitudes, pulsation periods, time of brightness maxima, and pulsation amplitude. The following two columns listthe RR Lyrae pulsation type and its conditional probability. The last columns flag stars that were associated with the Orphan stream by Koposov et al. (marked with K19, 2019) as parent population.The asterisk at bestObjID indicates a star that was not used as reference sample in Sec. 4.2. bestObjID (SDSS)
Gaia
EDR3 ID 𝛼 𝛿 𝑑 𝜎 𝑑 𝑣 sys 𝜎 𝑣 sys 𝑉 CSS 𝜎 𝑉 CSS
𝑃 𝑀 Amp 𝑉 CSS
Type [Fe/H] 𝑝 ( 𝐴 | 𝐵 ) Note[deg] [deg] [kpc] [kpc] [km s − ] [km s − ] [mag] [mag] [day] [day] [mag] [dex]1237660635454701712 801408324401633664 146.05782 40.22071 39.7 2.2 144.742 18.081 18.453 0.135 0.711533 54588.22739 0.57071 RRab -1.680 0.272 K191237660635453718722 812926670775689984 143.48258 39.13402 42.5 2.3 172.430 15.680 18.582 0.145 0.527852 55198.25415 0.64537 RRab -1.880 0.111 K191237667734496018571 625033259008713344 153.80169 19.05096 26.3 1.5 199.518 6.169 17.703 0.100 0.400190 54769.47305 0.44528 RRc -2.030 0.915 —1237657770706600085 1011841380940809344 140.40968 48.01452 45.4 2.5 109.058 1.139 18.922 0.158 0.367648 56402.27718 0.37343 RRc -2.030 0.592 —1237667782285131881 625042020741726976 153.99639 19.22272 25.8 1.4 214.922 7.709 17.667 0.098 0.645172 55563.40418 0.60377 RRab -1.720 0.799 —1237668290157281403 623982645584012928 154.82491 18.22602 28.0 1.6 194.632 10.047 17.870 0.108 0.578450 54628.16950 0.77584 RRab -1.670 0.239 K191237657606967459944 1011263007760611456 139.35631 46.72456 42.3 2.3 86.520 12.399 18.762 0.155 0.388203 54862.20461 0.35120 RRc -1.870 0.194 —1237657773935624421 814812268794932608 144.29504 43.42943 41.5 2.3 140.578 6.938 18.824 0.156 0.366009 54535.33735 0.37174 RRc -1.380 0.358 K191237658203425341674 813632316722202112 145.61867 41.56253 42.1 2.3 157.187 17.406 18.489 0.134 0.604208 55505.50362 0.58930 RRab -2.190 0.188 K191237661851456962762 800283700102935808 147.37900 38.73692 37.6 2.1 166.666 6.772 18.135 0.117 0.286424 55212.30609 0.20096 RRc -1.910 0.105 K191237664870825918615 793317812902061568 147.81260 32.49737 39.3 2.2 171.941 13.919 18.533 0.134 0.552830 54035.50252 0.65775 RRab -1.290 0.195 —1237665099002937435 744466232107315712 148.36049 30.02346 38.0 2.1 208.007 4.582 18.392 0.128 0.591062 53677.59556 0.40989 RRab -2.150 0.265 K191237665129604317276 744807802266002432 148.91221 30.42627 34.8 1.9 197.726 35.431 18.390 0.129 0.360622 54574.20862 0.37578 RRc -1.450 0.756 —1237660634916913359 ∗ A r ti c l e nu m b e r , p a g e ff
Type [Fe/H] 𝑝 ( 𝐴 | 𝐵 ) Note[deg] [deg] [kpc] [kpc] [km s − ] [km s − ] [mag] [mag] [day] [day] [mag] [dex]1237660635454701712 801408324401633664 146.05782 40.22071 39.7 2.2 144.742 18.081 18.453 0.135 0.711533 54588.22739 0.57071 RRab -1.680 0.272 K191237660635453718722 812926670775689984 143.48258 39.13402 42.5 2.3 172.430 15.680 18.582 0.145 0.527852 55198.25415 0.64537 RRab -1.880 0.111 K191237667734496018571 625033259008713344 153.80169 19.05096 26.3 1.5 199.518 6.169 17.703 0.100 0.400190 54769.47305 0.44528 RRc -2.030 0.915 —1237657770706600085 1011841380940809344 140.40968 48.01452 45.4 2.5 109.058 1.139 18.922 0.158 0.367648 56402.27718 0.37343 RRc -2.030 0.592 —1237667782285131881 625042020741726976 153.99639 19.22272 25.8 1.4 214.922 7.709 17.667 0.098 0.645172 55563.40418 0.60377 RRab -1.720 0.799 —1237668290157281403 623982645584012928 154.82491 18.22602 28.0 1.6 194.632 10.047 17.870 0.108 0.578450 54628.16950 0.77584 RRab -1.670 0.239 K191237657606967459944 1011263007760611456 139.35631 46.72456 42.3 2.3 86.520 12.399 18.762 0.155 0.388203 54862.20461 0.35120 RRc -1.870 0.194 —1237657773935624421 814812268794932608 144.29504 43.42943 41.5 2.3 140.578 6.938 18.824 0.156 0.366009 54535.33735 0.37174 RRc -1.380 0.358 K191237658203425341674 813632316722202112 145.61867 41.56253 42.1 2.3 157.187 17.406 18.489 0.134 0.604208 55505.50362 0.58930 RRab -2.190 0.188 K191237661851456962762 800283700102935808 147.37900 38.73692 37.6 2.1 166.666 6.772 18.135 0.117 0.286424 55212.30609 0.20096 RRc -1.910 0.105 K191237664870825918615 793317812902061568 147.81260 32.49737 39.3 2.2 171.941 13.919 18.533 0.134 0.552830 54035.50252 0.65775 RRab -1.290 0.195 —1237665099002937435 744466232107315712 148.36049 30.02346 38.0 2.1 208.007 4.582 18.392 0.128 0.591062 53677.59556 0.40989 RRab -2.150 0.265 K191237665129604317276 744807802266002432 148.91221 30.42627 34.8 1.9 197.726 35.431 18.390 0.129 0.360622 54574.20862 0.37578 RRc -1.450 0.756 —1237660634916913359 ∗ A r ti c l e nu m b e r , p a g e ff . P r ud il e t a l . : T h e O r ph a n s t r ea m i n7 D u s i ng RR L y r ae s t a r s Table D.2.
List of nonvariable stars associated with the Orphan stellar stream based on our RR Lyrae sample. The first two columns list the identifiers from the SDSS and
Gaia
EDR3, the followingtwo columns the objects equatorial coordinates. Columns 5 and 6, contain the line-of-sight velocities determined by the SSPP pipeline, and the subsequent two columns provide their 𝑔 -bandmagnitudes together with their uncertainties. Columns 9, 10, 11, 12, 13, and 14 list the stellar parameters derived by the SSPP pipeline. The last column represents the conditional probability for theindividual star. The asterisk at bestObjID marks stars that are classified as RRd type stars or their classification in RR Lyrae subtypes is uncertain. bestObjID (SDSS) Gaia
EDR3 ID 𝛼 𝛿
RV_ADOP RV_ADOP_UNC 𝑔 𝜎 𝑔 𝑇 eff 𝜎 𝑇 eff [Fe/H] 𝜎 [Fe/H] log 𝑔 𝜎 log 𝑔 𝑝 ( 𝐴 | 𝐵 ) [deg] [deg] [km s − ] [km s − ] [mag] [mag] [K] [K] [dex] [dex] [dex] [dex]1237667537471144142 628696866112455168 151.60904 21.04929 221.210 14.141 19.493 0.025 8311 253 -1.86 0.38 3.69 0.10 0.1371237667211053498537 738657310314238720 152.20035 25.46991 198.841 3.985 17.955 0.019 8349 68 -1.64 0.08 3.33 0.39 0.4021237667211590566073 738839309553409536 152.65131 26.09226 185.870 9.608 20.035 0.025 5162 216 -2.04 0.09 2.43 0.54 0.2421237667549803446363 628835095339982976 153.21074 21.01953 197.102 2.124 17.954 0.022 5046 11 -2.03 0.08 1.92 0.17 0.8931237667430635143257 630353112875731840 151.01106 23.71998 201.503 2.698 16.792 0.018 6107 102 -1.91 0.05 2.17 0.29 0.2851237667736106369165 625374592944708864 152.97943 20.03164 223.173 5.468 18.203 0.017 5178 25 -2.36 0.08 2.05 0.14 0.5391237667551413796866 629200481092312064 152.26792 22.22917 199.110 1.543 16.744 0.026 4681 105 -2.02 0.01 1.50 0.08 0.8301237667537471930559 628871997698600704 153.51826 21.40729 193.410 3.993 18.198 0.021 5182 55 -2.27 0.06 2.01 0.07 0.8241237667252929167431 726590372062626944 152.22576 24.81725 200.607 3.832 17.953 0.026 8139 139 -2.24 0.10 3.21 0.20 0.4901237667253466103892 738656996781344128 152.20437 25.42895 209.124 5.578 17.728 0.019 8359 47 -1.97 0.08 3.41 0.35 0.7601237667210516562002 738630681517008000 152.19512 25.11815 197.252 4.560 17.599 0.017 5184 50 -2.18 0.03 2.42 0.21 0.2491237667736106303744 625388813581465856 152.80820 20.13625 207.441 8.433 18.030 0.025 8733 295 -1.90 0.08 3.09 0.50 0.6451237660343936090311 812965188042058752 143.88747 39.66263 130.608 11.815 18.741 0.024 8381 214 -1.24 0.14 3.19 0.65 0.1811237667430635536640 630417842327675776 152.07167 23.92788 183.996 4.831 18.144 0.018 7219 113 -1.70 0.10 3.22 0.25 0.8851237657776082518150 817873957704595328 141.36492 44.12217 113.810 3.612 18.336 0.014 5042 44 -2.09 0.07 1.46 0.13 0.1241237667735570088150 625510618853633152 154.46992 19.93856 207.081 5.169 18.514 0.022 5324 44 -1.94 0.16 2.40 0.09 0.6581237661383846920453 796532505729010048 147.39971 36.55098 151.613 3.837 18.422 0.017 5039 44 -2.11 0.04 2.11 0.08 0.1731237664667895398511 ∗ Continued on next page A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . S t r ea m - O r ph a n Table D.3.
Continued from previous page bestObjID (SDSS)
Gaia
EDR3 ID 𝛼 𝛿
RV_ADOP RV_ADOP_UNC 𝑔 𝜎 𝑔 𝑇 eff 𝜎 𝑇 eff [Fe/H] 𝜎 [Fe/H] log 𝑔 𝜎 log 𝑔 𝑝 ( 𝐴 | 𝐵 ) [deg] [deg] [km s − ] [km s − ] [mag] [mag] [K] [K] [dex] [dex] [dex] [dex]1237657628979757237 815002102051985536 143.05483 43.85158 105.393 7.243 18.967 0.015 7892 106 -1.83 0.10 3.46 0.25 0.3551237667254540173418 738864082924453888 152.62750 26.39346 194.872 4.968 19.065 0.020 5414 35 -2.33 0.05 2.60 0.14 0.5011237667253466431572 726732209062781056 152.88857 25.52055 195.383 6.763 18.022 0.029 8132 61 -1.95 0.03 3.33 0.20 0.5091237661384383266935 799481881247354496 145.68937 36.40120 150.277 2.854 17.956 0.018 4970 57 -2.10 0.06 1.23 0.32 0.3031237664338242896034 ∗ ∗ ∗ A r ti c l e nu m b e r , p a g e ff