Standard Galactic Field RR Lyrae. I. Optical to Mid-infrared Phased Photometry
Andrew J. Monson, Rachael L. Beaton, Victoria Scowcroft, Wendy L. Freedman, Barry F. Madore, Jeffrey A. Rich, Mark Seibert, Juna A. Kollmeier, Gisella Clementini
aa r X i v : . [ a s t r o - ph . S R ] M a r Draft version March 20, 2018
Typeset using L A TEX twocolumn style in AASTeX61
STANDARD GALACTIC FIELD RR LYRAE. I. OPTICAL TO MID-INFRARED PHASED PHOTOMETRY
Andrew J. Monson, ∗ Rachael L. Beaton, † Victoria Scowcroft, ‡ Wendy L. Freedman, § Barry F. Madore, † Jeffrey A. Rich, † Mark Seibert, † Juna A. Kollmeier, † and Gisella Clementini ¶ ABSTRACTWe present a multi-wavelength compilation of new and previously published photometry for 55 Galactic field RRLyrae variables. Individual studies, spanning a time baseline of up to 30 years, are self-consistently phased to producelight curves in 10 photometric bands covering the wavelength range from 0.4 to 4.5 microns. Data smoothing viathe GLOESS technique is described and applied to generate high-fidelity light curves, from which mean magnitudes,amplitudes, rise-times, and times of minimum and maximum light are derived. 60,000 observations were acquired usingthe new robotic Three-hundred MilliMeter Telescope (TMMT), which was first deployed at the Carnegie Observatoriesin Pasadena, CA, and is now permanently installed and operating at Las Campanas Observatory in Chile. We providea full description of the TMMT hardware, software, and data reduction pipeline. Archival photometry contributedapproximately 31,000 observations. Photometric data are given in the standard Johnson
U BV , Kron-Cousins R C I C ,2MASS JHK, and Spitzer [3.6] and [4.5] bandpasses.
Keywords: stars: variables: RR Lyrae – stars: Population II ∗ The Observatories of the Carnegie Institution for Science, 813 Santa Barbara St., Pasadena, CA 91101, USADepartment of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA † The Observatories of the Carnegie Institution for Science, 813 Santa Barbara St., Pasadena, CA 91101, USA ‡ The Observatories of the Carnegie Institution for Science, 813 Santa Barbara St., Pasadena, CA 91101, USADepartment of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK50th Anniversary Prize Fellow § Department of Astronomy & Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA ¶ INAF-Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy INTRODUCTIONRR Lyrae variables (RRL) are evolved, low-metallicity,He-burning variable stars. They are extremely impor-tant for distance determinations because at infraredwavelengths their period-luminosity relationship showsincredibly small scatter in Galactic and LMC clus-ters (Longmore et al. 1986, 1990; Dall’Ora et al. 2004;Braga et al. 2015). At near-infrared wavelengths thescatter can be as low as σ = 0 .
02 mag, which translatesto ∼
1% uncertainty in distance to an individual star(see detailed discussion in Beaton et al. 2016).While the body of work in Galactic clusters sets thefoundation for exquisite differential distances using theRRL period-luminosity-metallicity (PLZ) relation andyields well-defined slopes, a direct calibration of zero-point, slope, and metallicity parameters using geometricdistance estimates has been elusive since their discoveryover a century ago (based on the work of WilliaminaFleming as published in Pickering et al. 1901) . Whilethere were over 100 RRL in the Hipparcos catalog,RR Lyr itself was the only variable of this class thatwas both sufficiently bright and near enough to deter-mine a parallax with an uncertainty of less than 20 percent (Perryman et al. 1997a; van Leeuwen 2007). Later,Benedict et al. (2011) derived trigonometric parallaxesusing the Fine Guidance Sensor aboard the
HST (HST)for five field RRL with individual quoted uncertainties atthe level of 5%-10%. While the work of Benedict et al.(2011) did provide the first truly geometric foundation,a relatively small sample size still limits the overall sta-tistical accuracy and is not necessarily an improvementover PLZ determinations using Local Group objectswith distances independently derived by other means(e.g., using star clusters and main-sequence fitting ordwarf galaxies with precise distances derived by othertechniques, such as eclipsing binaries). The
Gaia mis-sion (Gaia Collaboration 2016) is poised to provide thefirst opportunity for such a measurement (geometricallybased with a large sample size) and it is our purpose inthis and related works to provide the necessary data tomake full use of the highest-precision
Gaia
RRL sample.In this work, we present optical and infrared data for55 of the nearest and brightest Galactic field RRL stars.These stars span 7 . < h V i < . V magnitude,with the majority of them falling in the magnitude rangefor which Gaia is expected to provide trigonometricparallaxes with a precision better than ∼
10 microarcsec- The introduction to Smith (1995) also provides a detailedhistory of the discovery of RR Lyrae among the variable sourcesdiscovered in globular clusters in the late 19th century. onds ( µ as) (see Table 1 in de Bruijne et al. 2014, for pre-dicted end-of-mission values that will likely be updatedwith the first Gaia-only parallaxes in DR2). These 55RRL were selected as part of the Carnegie RR LyraeProgram (CRRP), which has the primary goal of es-tablishing the foundation for a Population II-based dis-tance scale utilizing the near- and mid-infrared proper-ties of RR Lyrae stars in the Local Group. This worksupports both the Carnegie-Chicago Hubble Program(CCHP; an overview is given in Beaton et al. 2016), aim-ing to produce a completely Population II extragalac-tic distance scale, and the Spitzer
Merger History andShape of the Galactic Halo (SMHASH; V. Scowcroft etal. 2017 in preparation), aiming to construct precisionthree-dimensional maps of the Population II-dominantportions of our Galaxy (e.g., the bulge and stellar halo).These stars were selected to span a large range of metal-licity, have low Galactic extinction, have a moderateincidence of Blazhko stars, and have maximum over-lap with other distance measurement techniques likethe Baade-Wesselink method (Baade 1926; Wesselink1946) .The organization of the paper is as follows. A de-tailed discussion of the properties of the CRRP RRLsample is given in Section 2. Our hardware and tar-geted optical-monitoring campaign are described in Sec-tion 3. Archival studies are described in Section 4. Theprocedures adopted for phasing individual data sets aredescribed in Section 5. Our algorithm (GLOESS) todetermine mean magnitudes and provide uniformly sam-pled light curves is described and applied in Section 6.Finally, a summary of this work is provided in Section7. Appendix A gives the technical details for processingdata from our custom hardware and Appendix B pro-vides detailed information for each star in our sample. THE RR LYRAE CALIBRATOR SAMPLEIn this section we describe the demographics of oursample of 55 stars; a summary of the sample properties isgiven in Table 1. A comprehensive introduction to RRLis given by Smith (1995), with an updated presentationprovided by Catelan & Smith (2015). As we describeour sample we briefly summarize the basics of RRL asneeded for the purposes of this paper.2.1.
Demographics of Pulsation Properties
There are two primary subtypes of RRL, those thatpulsate in the fundamental mode (RRab) and thosethat pulsate in the first overtone mode (RRc; i.e., there A detailed introduction of this method is given in Section 2.6of Smith (1995). −180−90 0 90180 90 60 30 −30 −60 −90 [Fe/H] (dex) −2.6 −2.1 −1.7 −1.3 −0.9 −0.5 −0.1 (a)−2.0 −1.5 −1.0 −0.5 0.0[Fe/H] [dex]0246810 N RR L (b) −0.6 −0.5 −0.4 −0.3 −0.2 −0.1log(P) [dy] N RR L (c) Figure 1.
The sample of RR Lyrae Galactic Calibrators. (a) Distribution of targets in Galactic latitude ( l ) and longitude( b ) color-coded by metallicity. Stars of type RRab are shown as triangles, RRc as circles, and RRd as a diamond. The targetRR Lyrae are largely out of the Galactic plane ( | b | > ◦ ), where variations in line-of-sight extinction due to dust variationsare minimal (e.g., Zasowski et al. 2009). (b) Marginal distribution of [Fe/H] for our targets, demonstrating that the metal-poorend is well populated, but there are stars forming a high-metallicity tail. (c)
Marginal distribution of log( P ) for our targets,emphasizing a relatively uniform distribution. is a pulsational node within the star). A third sub-type pulsates in both modes simultaneously — theseare known as RRd-type variables. Generally, for starsof the same density, the ratio of the fundamental pe-riod ( P F ) and the first-overtone period ( P F O ) is ap-proximately P F O / P F = 0.746 (or ∆[log( P )] = 0 . Kepler in space and OGLE from the ground; see Nemec et al.2013; Smolec et al. 2015, respectively) and some at thelevel of tenths of a magnitude (e.g., those discussed inSmith 1995)—and in their timescales — some with veryshort few-day periods (e.g., Nemec et al. 2013) and somewith very long multi-year periods (e.g., Skarka 2014).The most famous of these is the Blazhko effect Blaˇzko(1907), which is a periodic modulation of the amplitudeand shape of an RRL light curve, with periods of orderof tens to hundreds of pulsation cycles. The amplitudemodulation from the Blazhko effect varies from star tostar (and by passband) with ranges of a few hundredthsto several tenths of a magnitude.In addition, RRL stars can show period changesthought to correspond to the evolutionary path of anindividual star. Such changes can appear to be suddenor gradual, depending on the time sampling of data sets.Recent efforts have combined temporally well-sampled,long-baseline photometric data sets in Galactic star clus-ters to explore these effects and find that most periodchanges ascribed to evolutionary effects are consistentwith being gradual when visualized with semicontinu-ous sampling over very long timescales. Period changesattributed to nonevolutionary origins are also observed,and in contrast to evolutionary effects, these are identi-fied as sudden nonlinear or chaotic evolution of the lightcurve over time (for example see Arellano Ferro et al.2016, for a century-long study of period changes in M5).In our sample, nine stars show the Blazhko effect fromSmith (1995, 16%; their Table 5.2), an additional fourstars show the Blazhko effect from the compilation ofSkarka (2013, 7%;), and two stars show the Blazhko ef-fect in Skarka (2014, 4%), for a total of 15 stars showingthe Blazhko effect. References for the studies demon- strating the Blazhko effect are given for each affectedstar in Appendix B.The total frequency of Blazhko stars in our sample,27%, is comparable to that observed for the full fieldRR Lyrae population and in clusters (e.g., Smith 1995,though recent work has suggested this number couldbe as high as 50% when small amplitude variationsare included; J. Jurcsik, private communication). TheBlazhko periods for our sample (see Table 1) range fromtens of days to several years and have Blazhko ampli-tudes that can be as small as only a few hundredthsof a magnitude or as large as a few tenths of a magni-tude. In our sample, 32% of our RRab stars are Blazhko(12 stars) and 18% of our RRc stars are Blazhko (3stars); these frequencies are similar to but not perfectlymatched to the general statistics for the Galactic RRLpopulation, where ∼
50% of RRab and ∼
10% of RRctype variables show amplitude variations ( though wenote the small number statistics for our RRc stars; fordiscussion see Section 6.5 of Catelan & Smith 2015, andreferences therein). Considering our overall breakdownin RRL subtypes and amplitude modulation effects, thedemographics of our RRL sample are not unrepresenta-tive of the broader field population of Galactic RRL.We note that our discussion has focused on starswith a single pulsation mode. In the era of space-based photometry and top-quality photometry gath-ered from Earth (e.g.
Kepler from space and OGLEfrom the ground being two representative examples;see Nemec et al. 2013; Smolec et al. 2015, respectively),a more complicated view of RRL stars has emerged,and they can no longer be considered ‘simple’ radiallypulsating stars. In 200 day continuous coverage forRRL in the M3 star cluster Jurcsik et al. (2015), findthat 70% of RRc stars show multi-periodicity. More-over, nonradial pulsation in RRc stars appears to becommon because 14 out of 15 RRc stars (93%) ob-served from space show evidence for additional nonra-dial modes (e.g., Szab´o et al. 2014; Moskalik et al. 2015;Moln´ar et al. 2015; Kurtz et al. 2016). Similarly, the in-cidence rate in the top-quality ground-based data is alsolarge, with 27% of RRc in the OGLE Galactic bulgedata (Netzel et al. 2015) and 38% in M3 photometry(Jurcsik et al. 2015) showing nonradial modes. Becausemany of these effects are of overall small amplitude,these nonradial modes and additional periodicities likelyhave a negligible effect on the goals of this work – to pro-duce a robust Galactic calibration sample for parallax-based PL determinations – but do suggest that there isgreat complexity to the physical mechanisms at work inRRL stars. With these considerations in mind, an em-pirical approach to calibrating PL or PLZ relations isindeed preferable to theoretically derived relations thattypically do not include the all of the physics drivingthese nonradial and multimode effects.2.2.
Effectiveness of Sample for PL Determinations
Figure 1(a) shows the sky distribution of the CRRPtargets for Galactic coordinates. The stars span thecomplete range of R.A. and cover both hemispheres.The bulk of our sample of Galactic RRL reside out of theGalactic plane, which reduces complications from largeline-of-sight extinction and variations of the reddeninglaw within the disk (e.g., Zasowski et al. 2009, amongothers).bf Figure 1(b) shows the [Fe/H] distribution of our cat-alog, spanning 2.5 dex in metallicity with the most metalpoor star at [Fe/H] = − .
56 (UY Boo) and the mostmetal rich at [Fe/H] = − .
07 (AN Ser). The [Fe/H] val-ues are adopted from the compilation of Fernley et al.(1998a) (as presented in Feast et al. (2008) ) forall but two stars; the [Fe/H] for BB Pup comes fromFernley et al. (1998b) and that for CU Com fromClementini et al. (2000). The values from Fernley et al.(1998a) come from both direct high-resolution measure-ments and the ∆ S method of Preston (1959), with thelatter being calibrated to the former and brought onto auniform scale having typical uncertainties of 0.15 dex .The majority of the sample can be considered metalpoor with 70% (38 stars) of the sample uniformly dis-tributed over a range of 1 dex ( − < [Fe/H] < −
1) witha mean value of h [Fe/H] i = − .
50 dex ( σ = 0 .
24 dex).The other 30% (17 stars) make up a metal rich sam-ple that is itself uniformly distributed over a rangeof 1 dex ( − < [Fe/H] <
0) with a mean value of h [Fe/H] i = − .
50 dex ( σ = 0 .
30 dex).Figure 1(c) shows the period distribution of our sam-ple, with the shortest period being P = 0 .
25 days(DH Peg) and the longest P = 0 .
73 days (HK Pup)(log( P ) = − .
60 and log( P ) = − .
14, respectively).The sample is well designed to uniformly cover the dis-tribution of log( P ) anticipated in RRL populations andprovide the greatest leverage to determine RRL relation-ships with respect to period. We note for the benefit of the reader that this informa-tion on the origin of the [Fe/H] measurement for each staris embedded in the online-only data table associated with themanuscript of Fernley et al. (1998a) and not included in the textof that manuscript. Note 8 in the online notes to the ta-ble provides the references for individual stars as well as themetallicity scale and technique. A direct link to these datais as follows: http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/330/515
With the exception of CU Com and BB Pup, all ofour stars were included in the
Hipparcos catalog (al-beit with fractional errors larger than 30%), whichmeans most stars were included in the
Tycho-
Gaia
Astrometric Solution catalog (TGAS; Michalik et al.2015; Lindegren et al. 2016) as part of Gaia DR1Gaia Collaboration (2016); Gaia Collaboration et al.(2016) . All five RR Lyrae from the Hubble SpaceTelescope-Fine Guidance Sensor parallax program pre-sented in Benedict et al. (2011) are included in our sam-ple. Seventeen stars have distances derived previouslyfrom the Baade-Wesselink (BW) technique in the recentcompilation of Muraveva et al. (2015, and referencestherein). An additional five stars have BW distancesfrom other works (see Table 1). The last three columnsof Table 1 summarize the available distance measure-ments on a star-by-star basis. THE THREE-HUNDRED MILLIMETERTELESCOPEThere are significant complications of a technical andpractical nature when contemplating the use of tra-ditional telescope/detector systems to study GalacticRRL. RRL have typical periods of order a day orless (requiring high-cadence, short-term sampling), butthey can also show significant variations and periodchanges over time, requiring additional long-term sam-pling. These general considerations aside, the 55 Galac-tic RRL in our sample are noteworthy for being amongthe brightest RRL in the sky and are therefore toobright for even some of the “smallest” (i.e., 1 m class)telescopes at most modern observatories. Moreover,bright Galactic RRL are relatively rare and they aredistributed over the entire night sky, which means thatto build a uniform and relatively complete sample ofsuch targets requires a dual-hemisphere effort. In di-rect response to this need, we assembled a devotedrobotic 300mm telescope system to obtain modern, high-cadence, optical light curves for these important tar-gets. In the sections to follow, we describe the telescopesystem (Section 3.1), the observing procedures (Section3.2), and the resulting photometry (Section 3.3), with asummary given in Section 3.4.3.1.
TMMT Hardware
The Three-hundred MilliMeter Telescope (TMMT) isa 300mm f / . on The first
Gaia data release occurred on 2016 September 14: Takahashi FRC-300.
Table 1.
RRL Galactic Calibrators and Ephemerides.
Name P final HJDmax ζ RRL Type P Bl [Fe/H]a π b(days) (days) (days yr −
1) HIP BW HSTSW And 0.4422602 2456876.9206 1.720e-04 RRab 36.8 -0.24 HIP 1,2XX And 0.722757 2456750.915 · · ·
RRab · · · -1.94 HIPWY Ant 0.5743456 2456750.384 -1.460e-04 RRab · · · -1.48 HIP 3X Ari 0.65117288 2456750.387 -2.40e-04 RRab · · · -2.43 HIP 4,5ST Boo 0.622286 2456750.525 · · ·
RRab 284.0 -1.76 HIPUY Boo 0.65083 2456750.522 · · ·
RRab 171.8 -2.56 HIPRR Cet 0.553029 2456750.365 · · ·
RRab · · · -1.45 HIP 1W Crt 0.41201459 2456750.279 -9.400e-05 RRab · · · -0.54 HIP 3UY Cyg 0.56070478 2456750.608 · · ·
RRab · · · -0.80 HIPXZ Cyg 0.46659934 2456750.550 · · ·
RRab 57.3 -1.44 HIP HSTDX Del 0.47261673 2456750.248 · · ·
RRab · · · -0.39 HIP 2,8SU Dra 0.66042001 2456750.580 · · ·
RRab · · · -1.80 HIP 1 HSTSW Dra 0.56966993 2456750.400 · · ·
RRab · · · -1.12 HIP 5RX Eri 0.58724622 2456750.480 · · ·
RRab · · · -1.33 HIP 1SV Eri 0.713853 2456749.956 · · ·
RRab · · · -1.70 HIPRR Gem 0.39729 2456750.485 · · ·
RRab 7.2 -0.29 HIP 1TW Her 0.399600104 2456750.388 · · ·
RRab · · · -0.69 HIP 5VX Her 0.45535984 2456750.405 -2.400e-04 RRab 455.37 -1.58 HIPSV Hya 0.4785428 2456750.377 · · ·
RRab 63.3 -1.50 HIPV Ind 0.4796017 2456750.041 · · ·
RRab · · · -1.50 HIPRR Leo 0.4523933 2456750.630 · · ·
RRab · · · -1.60 HIP 1TT Lyn 0.597434355 2456750.790 · · ·
RRab · · · -1.56 HIP 1RR Lyr 0.5668378 2456750.210 · · ·
RRab 39.8 -1.39 HIP HSTRV Oct 0.5711625 2456750.570 · · ·
RRab · · · -1.71 HIP 3UV Oct 0.54258 2456750.440 · · ·
RRab 144.0 -1.74 HIP HSTAV Peg 0.3903747 2456750.518 · · ·
RRab · · · -0.08 HIP 1BH Peg 0.640993 2456750.794 · · ·
RRab 39.8 -1.22 HIPBB Pup 0.48054884 2456750.102 · · ·
RRab · · · -0.60c 3HK Pup 0.7342073 2456750.387 · · ·
RRab · · · -1.11 HIPRU Scl 0.493355 2456750.296 · · ·
RRab 23.9 -1.27 HIPAN Ser 0.52207144 2456750.334 · · ·
RRab · · · -0.07 HIPV0440 Sgr 0.47747883 2456750.706 · · ·
RRab · · · -1.40 HIP 6V0675 Sgr 0.6422893 2456750.819 · · ·
RRab · · · -2.28 HIPAB UMa 0.59958113 2456750.6864 · · ·
RRab · · · -0.49 HIPRV UMa 0.46806 2456750.455 · · ·
RRab 90.1 -1.20 HIPTU UMa 0.5576587 2456750.033 · · ·
RRab · · · -1.51 HIP 1UU Vir 0.4756089 2456750.0557 -9.300e-05 RRab · · · -0.87 HIP 1,5AE Boo 0.31489 2456750.435 · · ·
RRc · · · -1.39 HIPTV Boo 0.31256107 2456750.0962 · · ·
RRc 9.74 -2.44 HIP 1ST CVn 0.329045 2456750.567 · · ·
RRc · · · -1.07 HIPUY Cam 0.2670274 2456750.147 2.400e-04 RRc · · · -1.33 HIPYZ Cap 0.2734563 2456750.400 · · ·
RRc · · · -1.06 HIP 6RZ Cep 0.30868 2456755.135 -1.420e-03 RRc · · · -1.77 HIP HSTRV CrB 0.33168 2456750.524 · · ·
RRc · · · -1.69 HIPCS Eri 0.311331 2456750.380 · · ·
RRc · · · -1.41 HIPBX Leo 0.362755 2456750.782 · · ·
RRc · · · -1.28 HIPDH Peg 0.25551053 2456553.0695 · · ·
RRc · · · -0.92 HIP 5,7RU Psc 0.390365 2456750.335 · · ·
RRc 28.8 -1.75 HIPSV Scl 0.377356 2457000.479 3.0e-04 RRc · · · -1.77 HIPAP Ser 0.34083 2456750.510 · · ·
RRc · · · -1.58 HIPT Sex 0.3246846 2456750.229 1.871e-03 RRc · · · -1.34 HIP 1MT Tel 0.3168974 2456750.108 5.940e-04 RRc · · · -1.85 HIPAM Tuc 0.4058016 2456750.392 · · ·
RRc 1748.9 -1.49 HIPSX UMa 0.3071178 2456750.347 · · ·
RRc · · · -1.81 HIPCU Com 0.4057605 2456750.410 · · ·
RRd · · · -2.38d a Unless otherwise noted, values are taken from Feast et al. (2008), but the measurements were first compiled byFernley et al. (1998a, and references therein) and are on a metallicity scale defined by Fernley & Barnes (1997, andreferences therein). b Indicates if the star has a parallax derived from
Hipparcos (HIP; Perryman et al. 1997b),
HST (HST; Benedict et al.2011), and/or Baade-Wesselink (BW; source indicated in footnotes). c [Fe/H] comes from Fernley et al. (1998b). d [Fe/H] comes from Clementini et al. (2000). References — (1) Liu & Janes (1990); (2) Jones et al. (1992); (3) Skillen et al. (1993a); (4) Fernley et al. (1989);(5) Jones et al. (1988); (6) Cacciari et al. (1989); (7) Fernley et al. (1990); (8) Skillen et al. (1989) an AP1600 mount. The imager consists of an Apogee D09 camera assembly, which includes an E2V42-40 CCDwith mid-band coatings and an external Apogee nine-position filter wheel containing U, B, V, R c & I c Besselfilters, a 7nm wide H α filter, and an aluminum blankacting as a dark slide. The imaging equipment is con-nected to the telescope via a Finger Lakes InstrumentsATLAS focuser with adapters custom-made by PreciseParts . The short back focal length of the system andthe depth of the CCD in the camera housing precludedthe option of using an off-axis guider. For the programdescribed here, individual exposures were short enoughthat guiding was not required. The mount contains ab-solute encoders, which are able to virtually eliminateperiodic error, and the pointing model program appliesdifferential tracking rates that correct for polar misalign-ment, flexure, and atmospheric refraction.The system was first tested in the Northern Hemi-sphere at the Carnegie Observatories Headquarters (indowntown Pasadena, CA) from 2013 August to 2014 Au-gust. It was later (2014 September) shipped to Chile andpermanently mounted in the Southern Hemisphere in adedicated building with a remotely controlled, roll-offroof at Las Campanas Observatory (LCO). RRL moni-toring observations continued until 2015 July.The TMMT is controlled by a PC that can be accessedremotely through a VNC or a remote desktop sharingapplication. The unique testing and deployment of theTMMT has enabled true full-sky coverage for our RRLcampaign, not just keeping the CCD setup consistentbut also using the same system in both hemispheres soto minimize the effects of observational (equipment) sys-tematics on our science goals.3.2. Observations
ACP Observatory Control Software is used to au-tomate the actions of the individual hardware compo-nents and associated software programs; more specif-ically, MaximDL controls the camera, FocusMax controls the focus, and APCC controls the mount.Weather safety information was obtained via the inter-net from the nearby HAT South facility . Astro-Physics, Inc. Andor Technology plc. Finger Lakes Instrumentation. Precise Parts. ACP is a trademark of DC-3 Dreams. http://acpx.dc3.com MaximDL by Diffraction Limited. FocusMax. For information see http://hatsouth.org/
Table 2.
Optical Photometric Parameters for SBS andLCO.
Site v v v b b b i i i σSBS σLCO a The zero-point is relative to 25, which is the default instrumental magnitudezero-point in
DAOPHOT.
For the RRL program, an ACP script was automati-cally generated each day to observe RRL program starsat phases that had not yet been covered. The scriptincluded observations of standard stars spaced through-out the night to calibrate the data. Additional scriptscontrol other functions of the telescope, including: au-tomatically starting the telescope at dusk, monitoringthe weather, monitoring the state of each device andsoftware to catch errors (and restart if necessary), and,finally, to shutting down at dawn. Images were auto-matically pipeline-processed using standard procedures,which are detailed in Appendix A.The goal of the program was to obtain complete phasecoverage for each of the 55 sources. Due to time andobservability constraints, in particular the limited timeavailable for the Northern sample while the telescopewas deployed at the Carnegie Observatory Headquar-ters, there are still phase gaps for most of the stars. Ad-ditional phase sampling was obtained for nearly com-pleted stars only when it was observationally efficientto do so. At the conclusion of the TMMT program,we have photometric observations in the B , V , and I C broadband filters for each of our 55 RRL.3.3. Photometry
Instrumental magnitudes ( m B , m V , m I C ) were ex-tracted from the TMMT imaging data using DAOPHOT (Stetson 1987). Aperture corrections were measured us-ing
DAOGROW (Stetson 1990) and applied to correct theaperture photometry to infinite radius.The magnitudes ( B , V , I C ) and colors ( B − V ) and( V − I C ) for a set of standard stars were adoptedfrom Landolt standard fields (Cousins 1980; Landolt1983; Cousins 1984; Landolt 2009). Photometric cali-brations were determined using the IRAF PHOTCAL pack-age (Davis & Gigoux 1993) with the fitparams and invertfit tasks. Second-order extinction terms werealso measured, but found to be negligible and thereforenot included.The final adopted photometric calibration procedureis as follows: The zero-points are referenced to an air-mass of 1.5 to minimize correlation between airmass( X B , X V , X I C ) and zero-point terms. For the purposesof this work, we provide our calibrations for three of thephotometric bands, m B , m V , m I C . We define relation-ships between these instrumental magnitudes and thetrue magnitudes ( B , V , I C ) and colors ( B − V , V − I C )as follows: V = v + m V − v [( X V ) − .
5] + v ( m V − m I C ) (1) B − V = b − b [0 . × ( X B + X V ) − . b ( m B − m V )(2)and V − I C = i − i [0 . × ( X I C + X V ) − . i ( m V − m I C )(3)The coefficients for the various corrections are: (i) zero-point offset ( b , v , i ), (ii) airmass term ( b , v , i ),(iii) and a color term ( b , v , i ). These three sets ofcoefficients (one set for each filter) are unique for thetelescope and observing site. Median values and 1 σ de-viations for the TMMT at the Carnegie ObservatoriesSanta Barbara Street (SBS) and Las Campanas Obser-vatory (LCO) sites are given in Table 2, and were usedas the starting point for calibrating individual nights orwere adopted as the solution if not enough standardswere observed. Each photometric night has a system-atic zero-point error determined from fitting the stan-dard star photometry, which propagates to each RRLobserved on that night. To reduce the final systematicuncertainty on the mean magnitude of an RRL, eachRRL was observed on as many photometric nights aspossible. DAOMATCH and
DAOMASTER were used to create the lightcurve relative to the first frame by finding and subtract-ing the average magnitude offset (determined from theensemble photometry of common stars in all the frames)relative to the first frame in the series. Figure 2 showsthe zero-point data for V Ind. The average differen-tial magnitude ( δV ) for stars relative to the first frameis plotted with associated error bars. Since each framewas calibrated any frame taken on a photometric nightcould act as the reference, or alternatively, the averageof all the photometrically calibrated frames can be used.The advantage of using the average is that it minimizesrandom fluctuations or poorly calibrated frames. Figure2 illustrates an example where the first frame calibrationdeviated only slightly from the average. The final pho-tometry is corrected by the average offset relative to thereference frame, thus avoiding the problem of choosingthe “best” frame. Since multiple nights were used, eachindependently calibrated, the final systematic error is Figure 2.
An example of the photometric errors over multi-ple nights for V Ind. A total of 326 images were reduced overnine nonconsecutive nights. Each frame is calibrated basedon the transformation equations for that night. The averagedifference magnitude ( δV ) for stars relative to the first frameis plotted in with associated error bars. Four of the nights(black points) were photometric and had good photometricsolutions from observations of standard star. The remainingnights either had poor solutions or used the default trans-formation coefficients. The systematic error of the nightlyzero-point solution is given next to the date of observation;see text for details. reduced. Note that the two nights plotted on the rightof Figure 2 were not photometric and the default photo-metric solution was adopted. The transformation errorson nights such as this may appear discrepant if too fewstars were used, resulting in potentially unrealistic pho-tometric solutions; hence these nights are not used forcalibration. Trends in nonphotometric data may be cor-related with airmass, in which case the airmass termmay be poorly constrained. Dips in the data may bedue to a passing cloud or variable conditions.3.4. Summary
The TMMT is a fully robotic, 300 mm telescope atLCO, for which the nightly operation and data process-ing have completely automated. Over the course of twoyears data were collected on 179 individual nights forour sample of the 55 RR Lyrae in the B , V , and I C broadband filters. Of these nights, 76 were under pho-tometric conditions and calibrated directly. The 103nonphotometric nights were roughly calibrated by us-ing the default transformation equations, but only pro-vide differential photometry relative to the calibratedframes. This resulted in 59,698 final individual observa-tions. Individual data points have a typical photometricprecision of 0.02 mag. The statistical error falls rapidlywith hundreds of observations, with the zero-point un-certainties being the largest source of uncertainty in thefinal reported mean magnitude. ARCHIVAL OBSERVATIONSRR Lyrae variables can show changes in their peri-ods (see discussions in Smith 1995), and can have largeaccumulated effects from period inaccuracies, makingit problematic to apply ephemerides derived from ear-lier work to new observational campaigns. While thesetwo causes— period changes and period inaccuracies—have very different physical meanings (one intrinsic tothe star and one to limited observations) the effect ontrying to use data over long baselines is the same: indi-vidual observations will not “phase up” to form a self-consistent light curve. When well-sampled observationsare available that cover a few pulsation cycles, it is pos-sible to visually see the phase offset and simply alignlight-curve substructure (i.e., the exact timings of min-imum and maximum light), but in the case of sparsesampling the resulting phased data will not necessarilyform clear identifiable sequences (more details will begiven in Section 5).Thus, to compare the results of our TMMT campaignto previous studies of these RRL and to fill gaps inour TMMT phase coverage, we have compiled availablebroadband data from literature published over the past30 years and spanning our full wavelength coverage. Wenote that this is not a comprehensive search of all avail-able photometry. In the following sections, we give anoverview of data sources for the sample, organized bypassband, with star-by-star details given in Appendix B.Optical observations are described in Section 4.1, NIRobservations in Section 4.2, and MIR observations inSection 4.3. Observations are converted from their na-tive photometric systems to Johnson U , B , V , Kron-Cousins R C , I C , 2MASS J, H, K s , and Spitzer µ mand 4.5 µ m, with the transformations given in the text.Section 4.4 presents a summary of the resulting archivaldatasets. 4.1. Optical Data
ASAS
The All Sky Automated Survey (ASAS) is a long-term project monitoring all stars brighter than V ∼ mag (Pojmanski 1997, 2002, 2003; Pojmanski & Maciejewski2004, 2005; Pojmanski et al. 2005). The program cov-ers both hemispheres, with telescopes at Las CampanasObservatory in Chile and Haleakala on Maui, both ofwhich provide simultaneous I and V photometry. Notall photometry produced by the program has yet beenmade public (i.e., only I or V is available and for onlylimited fields and time frames). Moreover, several of ourbrightest targets, for example SU Dra and RZ Cep, bothof which have parallaxes from the HST-FGS program,are not included. We adopt V magnitudes from ASASto augment phase coverage for some of our sample, ifneeded and where available.4.1.2. GEOS
The Groupe Europ e ′ en d’Observations Stellaires(GEOS) RR Lyr Survey is a long-term programutilizing TAROT (Klotz et al. 2008, 2009) at CalernObservatory (Observatoire de la Cte d’Azur, Nice Uni-versity, France). Annual data releases from this projectadd times for maximum light for program stars overthe last year of observations (data releases includeLe Borgne et al. 2005, 2006a,b, 2007a,b, 2008, 2009,2011, 2013, among others). GEOS aims to characterizeperiod variations in RRL stars by providing long-term,homogeneous monitoring of bright RRL stars, albeitonly around the anticipated times of maximum light.The primary public data product from this program arethe times of light curve maxima over a continuous periodsince the inception of the program in 2000. A well ob-served star will have its maximum identified to a preci-sion of 4.3 minutes (0.003 days), but measurements varybetween σ max =0.002 and σ max =0.010 days dependingon local weather conditions. Such data are invaluablefor understanding period and amplitude modulationsfor specific RRL (e.g., RR Lyr in Le Borgne et al. 2014)and for RRL as a population (Le Borgne et al. 2007c,2012). We utilize the timing of maxima provided byGEOS for our common stars, primarily for the phasingefforts to be described in Section 5.4.1.3. Individual Studies
In addition to the large programs previously de-scribed, we use data from individual studies over thepast 30 years. Due to the diversity of such works, wemust determine filter transformations on a study-by-study basis as we now describe. http://tarot.obs-hp.fr/ R J and I J to Cousins R C and I C (noting that V is the same in either), weutilize the following transformations from Fernie (1983): V − R C = − .
024 + 0 . × ( V − R J ) for ( V − R J ) ≤ . .
218 + 0 . × ( V − R J ) for ( V − R J ) > . R C − I C = +0 .
034 + 0 . × ( R J − I J ) for ( R J − I J ) ≤ . − .
239 + 1 . × ( R J − I J ) for ( R J − I J ) > . V − I C = +0 .
004 + 0 . × ( V − I J ) for ( V − I J ) ≤ . − .
507 + 1 . × ( V − I J ) for ( V − I J ) > . Near-Infrared Data
Multi-Epoch data in the NIR are particularly sparse,but owing to numerous RRL campaigns in the 1980sand 1990s to apply the BW technique to determine dis-tances to these stars, there are some archival data inthese bands. Care, however, must be taken in usingthese archival data directly with more recent data, be-cause (i) they must be brought onto the same photomet-ric system (filter systems and detector technology havechanged) and (ii) RRL are prone to period shifts overrather short time-scales. While the former concern canbe characterized statistically, the latter concern presentsa serious limitation to the use of archival data. Contem-poraneous optical observations are necessary to properlyphase the NIR data with our modern optical data. Thus,only data that could be phased, owing to the availabil-ity of contemporaneous optical data, could ultimatelybe used for our purposes.4.2.1.
Single-epoch photometry is available from 2MASS(Skrutskie et al. 2006) in J , H , and K s . Phasing ofthese data was accomplished primarily using data fromGEOS (Section 4.1.2).4.2.2. Individual Studies
Data from Sollima et al. (2008) are adopted and al-ready on the 2MASS system. To convert from the CIT systems to 2MASS we usethe following transformations: ( J − K ) = 1 . × ( J − K ) CIT − . H − K ) = 1 . × ( H − K ) CIT + 0 . K s = K CIT − .
019 + 0 . × ( J − K ) CIT (4)This was required for data presented in Liu & Janes(1989), Barnes et al. (1992) and Fernley et al. (1993). Ifno color was provided, then the average color for RRLof ( J − K ) CIT = 0.25 was adopted.The data in Skillen et al. (1989) and Fernley et al.(1990) required conversion from the UKIRT system asfollows:( J − K ) = 1 . × ( J − K ) UKIRT − . H − K ) = 1 . × ( H − K ) UKIRT + 0 . K s = K UKIRT + 0 .
003 + 0 . × ( J − K ) UKIRT (5)The average colors for RRL of ( J − K ) UKIRT = 0.3 and( H − K ) UKIRT = 0.1 were adopted if no color informationdata were available.Data from Fernley et al. (1989) and Skillen et al.(1993a) required conversion from the SAAO systemto 2MASS as follows:( J − K ) = 0 . × ( J − K ) SAAO − . H − K ) = 0 . × ( H − K ) SAAO + 0 . K s = K SAAO − .
024 + 0 . × ( J − K ) SAAO (6)The average colors for RRL of ( J − K ) SAAO = 0.2 and( H − K ) SAAO = 0.2 were adopted if no color data wereavailable. 4.3.
Mid-Infrared Data
Spitzer
The mid-infrared [3.6] and [4.5] (hereafter also S1and S2, respectively) observations were taken using
Spitzer /IRAC as part of the Warm–
Spitzer
ExplorationScience Carnegie RR Lyrae Program (CRRP; PID 90002Freedman et al. 2012). Each star was observed a min-imum of 24 times (with additional observations pro-vided by the
Spitzer
Science Center to fill small gaps inthe telescope’s schedule). The
Spitzer images were pro-cessed using SSC pipeline version S19.2. Aperture pho-tometry was performed using the SSC-contributed soft-ware tool irac aphot corr , which performs the pixel- http://irsa.ipac.caltech.edu/data/SPITZER/docs/dataanalysistools/tools/contributed/irac/iracaphotcorr/ WISE
WISE (Wright et al. 2010) or
NEOWISE (Mainzer et al.2011, 2014) photometry is available for each of our stars(Wright et al. 2010). This is the only MIR data forthree RRL. We opt to tie the
WISE photometric sys-tem to that defined for
Spitzer . For our RRL stars, wefind an average offset of W − [3 .
6] = − . ± .
010 (7)and W − [4 .
5] = − . ± .
010 (8)This offset is applied to all of the
WISE or NEOWISE data used in this work.4.4.
Summary of Archival Data
We have compiled a heterogeneous sample of data inorder to build well sampled light curves from the opticalto mid-infrared. We have homogenized these diversedata sets to the following filter systems: Johnson
U BV ,Kron-Cousins RI , 2MASS J, H, K s , and Spitzer [3 . . < φ < Spitzer ) and open symbols representingdata taken from the literature. Single-epoch 2MASSdata are represented by open pentagons. NIR data fromFernley et al. (1993) are available for many stars butonly for a few epochs; these data are represented byopen triangles. All other literature data in the NIR arerepresented by open squares.
Visualizations of this type are provided foreach of our 55 stars as a figure set associatedwith Figure 4. RECONCILING PHASE Due to their short periods, RRL experience hundredsto over one thousand period cycles over a single year (be-tween 500 and 1460 cycles per annum for our longest-and shortest-period RRLs, HK Pup and DH Peg, re-spectively). On these long timescales RR Lyrae canshow physical changes in their periods due to their ownstellar evolution that may appear gradual/smooth orsudden or they can show sudden changes with unex-plained origins (i.e., changes not based on evolution).Over our 30 year baseline, a period uncertainty of 1 sresults in maximal offsets of 0.17 day or a 0.24 phasefor HK Pup (longest period) and 0.50 day or 1.95 fullcycles for DH Peg (shortest period). Each individual ob-servation taken within this time span would have its ownphase offset. In this section, we describe our proceduresto merge the data described in the previous section byupdating the ephemerides for each star.For clarification, we define several terms for the dis-cussions to follow. A data set is either a single or a setof individual photometric measurement(s) for a givenstar and the associated date of observation taken withthe same instrument setup and transformed into ourstandard photometric systems. We define the
HJD max asthe
HJD at maximum light measured from our TMMTdata, which means that the quantity is defined uni-formly for all stars in our sample. Our term ( ϑ ) is theoffset in days between our HJD max and the date of ob-servation, which is defined mathematically as follows: ϑ i = HJD i, obs − HJD max (9)for each individual data point ( i ). Then, we define theinitial phase ( φ ) for each data point ( i ) as follows: φ i = ϑ i P archival − int (cid:18) ϑ i P archival (cid:19) , (10)where the P archival is adopted from Feast et al. (2008).As we merge data, the initial phase ( φ ) may be modi-fied by adjustments to the period, HJD max , and inclusionof higher-order terms, which are fixed for an individualstar. The final phase ( φ ) for any given data point isdefined as: φ i = ϑ i P final − int (cid:18) ϑ i P final (cid:19) + ζ (cid:18) ϑ i . (cid:19) , (11)where P final is the final period, and ζ is an optionalterm (quadratic in ϑ ) that is used to describe changesin period in recent times, where ζ = 0 for a star with This involves using the GLOESS light curves for those datathat are not fully sampled at maximum. The process for makingthese light curves is described in Section 6.1. Figure 3.
Data from GEOS (Sec 4.1.2) demonstrating of phasing solutions in the O-C diagram (see Section 5.1 for details) for the four cases described in the text. The solid vertical line highlights the epoch of the TMMT data and the vertical dashedline is at the epoch of the 2mass observations. (a) – top left
Flat O-C behavior (for AN Ser) implies that no updates toperiod are required. (b) – top right
Linear O-C behavior over the last 30 years (for DX Del) implies that the period is slightlylonger than originally determined. (c) – bottom left
Quadratic O-C behavior (for X Ari) implies that the period itself hasbeen changing over time. (d) – bottom right
Chaotic O-C behavior (for RR Lyr) implies that neither adding precision to theperiod nor applying a shift in period is sufficient to phase all of the individual data-sets analytically. In this case, each data-setgets a custom phase offset for alignment to the current TMMT epoch.
3a stable period. The
HJD max measured from our TMMTdata and ζ and P final , determined by the analyses tofollow, are given in Table 1 for each of the stars in oursample.Our goal for this work is to build multi-wavelengthlight curves, and as such our goal for phasing is to makeall of the data sets for a given star conform to a singleset of HJD max , P final and ζ that self-consistently phaseall of the data-sets for a star (see Appendix B). Whilethis seems straightforward, in practice it is quite difficultowing both (i) to the nature of the observational dataand (ii) to the nature of finding phasing solutions.Based on the sampling, each observational data setcan be placed into one of three categories: • Case 1 —well sampled light curves, • Case 2 —sparse coverage (or single points) forwhich there is a contemporaneous data set in theprevious category (sparse data become ‘locked’ tothe data in
Case 1 ), and • Case 3 —sparse coverage (or single points) withwide time baselines from well sampled curves.
Case 1 and
Case 2 can be analyzed and evaluated inthe O-C diagram, which compares the observed (O) andcomputed or predicted (C) time of maximum or mini-mum light as a function of time (here we will use ϑ ).The Case 2 data-sets become ‘locked’ to their contem-poraneous
Case 1 data sets. Usually the well sampleddata sets can be merged by visual examination of theirlight curves. For
Case 3 , the ephemerides for the ma-jority of the well sampled data must be complete (e.g.,the analyses for
Case 1 and
Case 2 ) before the data setcan be fully evaluated for consistency with the phaseddata sets. Usually, the
Case 3 data set is ‘locked’ tothe nearest GEOS maxima observation and phased toother data via small shifts in φ .5.1. The O-C Diagram
Full evaluation of the ephemerides occurs withinthe context of the O-C diagram (see Figure 3 ofLiska & Skarka 2015, for good demonstrations of vari-ous behaviors). O-C diagrams have a long history, be-ginning with Luyten (1921) and Eddington & Plakidis(1929), and are utilized for a number of time-domaintopics in astronomy. An excellent general introductionto O-C diagrams and their application for various sci-ence goals, as well as detailed discussion of misuse ofsuch diagrams, is provided by Sterken (2005) and werefer the interested reader to that text. We now describeour use of the O-C diagram in the context of the goalsof this work. The O-C diagrams for stars in our study could beclassified into four characteristic behaviors, which aredemonstrated in the panels of Figure 3: flat, linear,quadratic, and chaotic/jittery. These behaviors are ap-plied to when the the data directly used in this studywere taken. DX Del (Figure 3(b)), for example, wasflat and then became (positive) linear; the linear por-tion applies to all available data analyzed in this work.None of the stars exhibited high-order periodic behaviorthat could be associated with a close companion or othercomplicated physical scenario (for examples of thesecases see discussions in Sterken 2005; Liska & Skarka2015). We discuss the implications for each of the situ-ations in the sections to follow.
Flat O-C Diagram . If the data sets are in phase withthe literature period and TMMT
HJD max , then the O-Cdiagram will show flat behavior as in the example inFigure 3a. Physically, this means that the period itselfhas been stable over the time frame of the data set. Ifthe TMMT
HJD max is correct, then h O − C i = 0; if itis incorrect, then there will be a zero-point offset. Toreconcile, we adjust HJD max , where a positive (negative)offset implies that the observed
HJD max is occurs later(earlier) than the value predicted by Equation 10.
HJD max is then adjusted such that the h O − C i = 0. Linear O-C Diagram . If the data sets show linearbehavior (with nonzero slope) in the O-C diagram thenobserved maxima occur earlier (later) than predicted byEquation 10. This is typically an indication that theperiod is incorrect in a way that accumulates over time,i.e., a constant difference between the true period andthat initially used for phasing. The magnitude of theslope provides the amount of period mismatch and thesign of the slope indicates whether the period should belengthened (negative) or shortened (positive).
Quadratic O-C Diagram . RRL with historical orcurrent constant period changes (most likely due to evo-lution) will have parabolic behavior in the O-C diagram.An upward (downward) parabola represents a periodthat is lengthening (shortening) at a constant rate overtime. Since the period is still evolving, we describe theevolution of the period with an additional term in lieu ofproviding the period for the current epoch (if the periodbecame constant, then we would see discontinuity froma parabola to linear). An example is given in Figure3c. The quadratic shape can be fit, resulting in an addi-tional coefficient for phasing the data, which we call ζ inEquation 10. Values of ζ are given in Table 1, with ‘nodata’ indicating that no quadratic term was required. Chaotic/Jittery O-C Diagram . Chaotic/jittery O-C diagrams could have many causes, including unre-4solved high-order variations due to companions, suddenperiod changes due to stellar evolution or other physi-cal processes, typographical or computational errors inliterature observations, and/or a combination of effectsthat cannot be identified individually (see some exam-ples of individual effects in Liska & Skarka 2015). Ad-ditionally, both sudden and prolonged chaotic and/ornonlinear effects could have causes unrelated to thephysical evolution of the star. Merging data in thesecases is quite complex. Our general approach is to fitonly the recent behavior in the O-C diagram to adjustthe ephemerides (the last decade is usually covered byGEOS). Older data sets are then treated individually,often requiring individual phase shifts for merging. Anexample chaotic/jittery O-C diagram is given in Figure3d and for this demonstration we use RR Lyr itself,which appears chaotic/jittery in this visualization be-cause of its strong Blazhko effect with a variable period(see Section B.33 for details).5.2.
Final Ephemerides
Making the data sets align to a single set ofephemerides is a multi-step process. Data are con-verted to an initial phase ( φ ) based on the literatureperiod ( P archival ) and TMMT HJD max using Equation 10.Iteration on the parameters occurs via visual inspec-tion of the light curves from multiple data sets and theO-C Diagram.
Case 1 and
Case 2 data-sets providethe most leverage on the ephemerides and are, as such,merged first, with
Case 3 data-sets being tied to theclosest GEOS epoch and folded in last. Flat, linear,and quadratic O-C behaviors constrain adjustments tothe ephemerides, which are also evaluated in the lightcurves. An additional term, ζ , may be added as inEquation 11 to describe period changes in a quadraticO-C diagram. Final ephemerides are reported in Table1, with some star-specific notes for chaotic/jittery O-Cdiagrams included in Appendix B.Our final data sets report the final derived phase foreach data point ( φ i ) using our adopted ephemerides aswell as the original HJD of observation. Our processhas generally preserved phase differences between fil-ters. We note that our goal in this process was to buildmulti-wavelength light curves for the eventual multi-wavelength calibration of period-luminosity relation-ships and not to find the highest-fidelity ephemeridesfor these stars. Thus, while our solutions are adequatefor our goal (as will be shown in the next section), theymay not be unique solutions and may require furtheradjustment for other applications. LIGHT CURVES AND MEAN MAGNITUDES The light curves constructed from the newly acquiredTMMT data and phased archival data are shown in Fig4. The complete figure set (55 images) is available in Ap-pendix B. The process of creating a light curve throughthe data using the GLOESS technique is described in thefollowing sections. From the evenly sampled GLOESSlight curve the intensity mean magnitude is determinedas a simple average of the intensity of the GLOESS datapoints and converted to a magnitude. Table 3 containseach new TMMT measurement along with all phasedarchival data included in this study. The full table isavailable in the online journal and a portion is shownhere for form and content.
Fig. Set 4. Multi-Wavelength phased RRLyrae light curves
GLOESS Light Curve Fitting
Nonparametric kernel regression and local polyno-mial fitting have a long history, dating as far back asMacaulay (1931); in particular they have been exten-sively applied to the analysis of time series data. Morerecently popularized and developed by Cleveland (1979)and Cleveland & J. (1988), this method has been giventhe acronym LOESS (standing for LOcal regrESSion),or alternatively and less frequently
LOWESS (stand-ing for LOcally WEighted Scatterplot Smoothing). Ineither event, a finite-sized, moving window (a kernel offinite support) was used to select data, which were thenused in a polynomial regression to give a single interpo-lation point at the center of the adopted kernel (usuallyuniform or triangular windows). The kernel was thenmoved by some interpolation interval determined by theuser and the process repeated until the entire data setwas scanned. Instabilities would occur when the win-dow was smaller than the largest gaps between consec-utive data points. To eliminate this possibility one ofus (BFM) introduced GLOESS, a Gaussian-windowedLOcal regrESSion method, first used by Persson et al.(2004) to fit Cepheid light curves. In its simplest formGLOESS penalized the data, both ahead of and be-hind the center point of the window, by their Gaussian-weighted distance quadratically convolved with their in-dividual statistical errors. Instabilities are guaranteedto be avoided given that all data contribute to the poly-nomial regressions at every step.GLOESS light curves were created for our stars foreach band independently, the goal being to create uni-formly interpolated light curves from nonuniformly sam-pled data. In this way, for example, color curves and/orother more complicated combinations of colors and mag-nitudes can be derived from multi-wavelength data setsthat were collected in different bands at disparate and5
Figure 4.
Example light curves from the final data sets. Data and GLOESS fits for the RRab types SW And (top left)and WY Ant (top right) and the RRc types RZ Cep (bottom left) and T Sex (bottom right). From top to bottom in eachpanel, the bands are S S K s (orange), H (dark green), J (purple), I C (red), R C (brown), V (light green), B (blue), and U (purple). Filled points are newly acquired data from TMMT (circles) and Spitzer (squares). All open symbols areadopted from the literature. Large open pentagons are J , H , K s from 2MASS, open triangles are NIR data from Fernley et al.(1993) and open squares are NIR data from the remaining literature sources. For the MIR data, open symbols are from WISE and filled symbols are from
Spitzer . The GLOESS light curve fit for each band is shown as the solid line (3 σ outliers wererejected during creation of the GLOESS light curve). The dotted line is constructed from the V and I GLOESS light curvesfor each band. The process of generating this faux curve and using it as a template is the topic of a future paper, but is brieflydemonstrated here. Table 3.
TMMT Photometry and Phased Archival Data
Star Filter mag σ phot σ sys HMJD
Phase ( φ ) ReferenceSW And I 9.170 0.010 0.009 56549.3206 0.390 0SW And I 9.168 0.010 0.009 56549.3216 0.392 0SW And I 9.173 0.010 0.009 56549.3222 0.394 0SW And I 9.174 0.010 0.009 56549.3229 0.395 0SW And I 9.171 0.010 0.009 56549.3235 0.397 0
Note — The Heliocentric Modified Julian Day (HMJD = HJD - 2400000.5) is provided.The photometric error for each measurement is included as well as the systematicerror in the zero-point determination. Table 3 is published in its entirety in themachine-readable format. A portion is shown here for guidance regarding its formand content.
References — (0) TMMT This work; (1)
Spitzer
This work; (4) Skillen et al.(1993a); (5) Barnes et al. (1992); (7) Liu & Janes (1989); (8) Liu & Janes (1989);(9) Barcza & Benk˝o (2014); (10) Paczy´nski (1965); (11) 2MASS Skrutskie et al.(2006); (17) ASAS Pojmanski (1997); (15) Jones et al. (1992); (19) IBVSBroglia & Conconi (1992); (31) Fernley et al. (1990); (41) Fernley et al. (1989);(98) Clementini et al. (1990); (99) Clementini et al. (2000); (999) TMMT modifiedfor Blazhko effect. x (usually phase), could be either set to aconstant or allowed to vary as the density of availabledata points changes. The latter allows for finer detail tobe captured in the interpolation in regions where thereare more densely populated data points. Our implemen-tation has been extended further by also weighting in ∆ y (magnitude). By doing a first-pass linear interpolationthe data points are weighted by an additional factor of e − ∆ y /σ y . In this way, regions near the top and bottom ofa steeply rising feature are “shielded” from each other.In this case, σ y is the scatter in the data within the ∆ x window. Outliers are clipped by performing a second it-eration and rejecting points outside 3 σ . For some stars,it proved useful to partition the data into discrete re-gions to further isolate steeply changing features fromone another.The results of the GLOESS fitting are shown for eachof the light curves given in Figure 4 as the solid graylines. In comparison to the data points (shown for0 < φ < . . < φ < .
0) accurately traces the natural structureof the light curves with no a priori assumptions of thatshape. There are two types of cases in our current sam-ple that require special attention. These are (i) thosestars exhibiting the Blazhko effect in our sampling (typ-ically only visible in TMMT data) and (ii) those starswith large phase gaps.6.1.1.
Treatment of the Blazhko Effect
The Blazhko effect is a modulation of the amplitudeand shape of the RRL light curve with periods rangingfrom a few to hundreds of days. The search for a physi-cal basis for the Blazhko effect remains unclear globallyand is beyond the scope of this paper. The average lu-minosity of Blazhko stars remains constant from cycle tocycle; however; data that nonuniformly sample the lightcurve from different Blazhko cycles may lead to an incor-rect determination of the mean, biased in the directionwhere most of the data were obtained. For the purposesof this paper, we did the following: If the observationscould be separated cleanly into distinct Blazhko cycles,then the two cycles were shifted and scaled to one an-other if necessary for the purposes of GLOESS fitting(for example, SV Hya and RV UMa). Data displayed inthese figures are the original photometry with the mod-ified photometry displayed in gray. If the observationscould not readily be separated, then the GLOESS algo-rithm was left to average between the cycles.6.1.2.
Light-curve Partitioning
One feature of GLOESS is that points ahead of or be-hind the current interpolation point are downweighted.In the optical bands, the light curves can have very rapidrise times, and even with the the weighting functionsometimes the data on the ascending or descending sideof the light curve still influence the local estimation ofthe others. Here we briefly discuss the general modifi-cation of GLOESS for these situations.For the purposes of this work, the phase between min-imum light and just past maximum light was often ‘par-titioned’ such that the points on either side of the max-imum could not influence each other. This partitioningwas particularly necessary for the optical light curves ofRRab variables. This was done by setting the weightsof those points outside the fitting partition to zero. Toprevent discontinuities at or near the partition point,data from within 0.02 in phase were allowed to con-tribute from the opposite side. In this way, there werealways data to interpolate and GLOESS did not have toextrapolate.Another feature of GLOESS is that at each point of in-terpolation a quadratic function locally fits the weighteddata. This low-order function has the advantage ofnot overfitting the data and generally changes slowlyat adjacent interpolation points, thus providing a rel-atively smooth and continuous curve through the datain the end. At the timing of the ‘hump’ in the ascend-ing branch of the light curve for RRabs in the optical(see Chadid et al. 2014, Figure 6 for a visualization), thefunction is allowed to use the best χ result for a first-,second-, or third-order order polynomial. Because the‘hump’ happens so quickly there are often not enoughdata to capture the subtlety of the feature. Allowing fora third-order polynomial in this region avoids losing thisand similar features in the light curves. RRcs are rela-tively smooth (in comparison to RRabs) and we alwaysuse an underlying quadratic function.6.2. Light-curve Properties
Mean magnitudes were determined by computing themean intensity of the evenly sampled GLOESS fit pointsto the light curve, then converting back to a magni-tude. The light curve must be sampled with enoughdata points to capture all the nuances of the shape foran accurate mean; in our case we sampled with 256 datapoints spaced every 1/256 in phase. Generally, GLOESSfits were determined only for those stars and bands thathad more than 20 individual data points over a reason-able portion of phase (i.e., 20 data points only spanning φ ∼ Table 4.
GLOESS light curves.
Star Name Filter φ GLOESS Mag.SW And U 0.00000 9.562SW And U 0.00391 9.559SW And U 0.00781 9.560SW And U 0.01172 9.563SW And U 0.01562 9.571
Note —Table 4 is published in its entirety in themachine-readable format. A portion is shownhere for guidance regarding its form and content. curve. The full table is available in the online journaland a portion is shown here for form and content.The random uncertainty of the GLOESS-derivedmean magnitude is simply the error on the mean ofdata points going into GLOESS fitting. Thus, starswith more data points will have a smaller uncertainity inGLOESS mean magnitude. The systematic uncertaintyis determined by the photometric transformations, ei-ther in transforming our TMMT photometry onto anabsolute system (see Figure 2) or as reported in theliterature and in transforming from other filter systems(as described in Section 4). The final reported erroris σ = 1 / P (1 /σ phot ) + 1 / P (1 /σ sys ), where the sumover σ sys includes only the unique entries from eachreference, i.e. it is not counted for every measurement.These results are given in Table 5. A technique to bet-ter utilize sparsely sampled data will be presented ina future companion paper (R. L. Beaton et al. 2017,in preparation) and no mean magnitudes are reportedhere for data with too few measurements to construct aGLOESS light curve.In addition to the mean magnitudes, we provide am-plitudes ( a λ ), rise times ( RT λ ), and magnitudes at HJD max in Table 6 as measured from the GLOESS lightcurves. We define ( a λ ) and ( RT λ ) as the difference inmagnitude and phase, respectively, between the mini-mum and maximum of the GLOESS light curve. Wenote that at the longer wavelengths these terms becomeless well defined due to the less prominent ‘saw-tooth’shape and overall smaller amplitudes, both of which aretypical changes for RRL stars at these passbands.6.3. Comparison with Literature Values
The difference between the intensity means in the V band determined here and literature values is shown inFigure 5. In most cases B photometry is available forcomparison with respect to V (i.e. B − V ), but I C is not,which was part of the motivation for this work. Notable outliers are labeled in Figure 5 and it is worth notingthat three out of the five RRL with HST parallaxes areconsidered outliers. Both RV UMa and ST Boo exhibitthe Blazhko effect (our treatment of these stars was dis-cussed in Section 6.1.1) and differences are likely due tohaving sampled different parts of the Blazhko cycle.We compare our GLOESS-derived apparent meanmagnitudes for 53 stars to those presented in Feast et al.(2008), which were originally derived in Fernley et al.(1998a) from
Hipparcos
Fourier fitting to H P magni-tudes (converted to intensity). A correction was usedin Fernley et al. (1998a) to transform the RRL fromthe H P system onto the standard Johnson V systemby adopting an average color for each subtype of star;the corrections were − .
09 mag for the RRabs and − .
06 mag for the RRcs. Some of the scatter fromFeast et al. (2008) and Fernley et al. (1998a) in Figure 5is due to reddening, since the corrections were not basedon apparent color but rather by adopting a mean colorfor each type of star. RZ Cep (type RRc), for example, ishighly reddened and has an apparent color redder thanmost RRabs (which should be intrinsically redder thanRRcs). Thus RZ Cep’s (and the others’) color correctionwas likely underestimated when transforming from H P to V . Both XZ Cyg and RR Lyr are also offset, perhapsdue to their Blazhko cycle. The mean magnitude fromFernie (1965) for RR Lyr is in agreement with the valuedetermined here. For 51 stars in common (two rejected)we find an average offset of ∆ V = − . ± .
021 mag.Piersimoni et al. (1993) provide photometry for twostars (AB UMa and ST Boo). There is good agreementon AB UMa, but the reported mean magnitude reportedfor ST Boo (a Blazhko star) differs by 0.07 mag.There are a number of stars with BW analysis; theresults of Skillen et al. (1993b, 1989) and Fernley et al.(1989, 1990) are grouped together in Fig 5 as ”Skillen1993.” For the seven stars in common (one rejected),we find an average offset of ∆ V = − . ± .
009 mag-nitudes. W Crt was discussed in Skillen et al. (1993b)as perhaps having an offset from observations betweendifferent telescopes.We have 10 stars in common with Liu & Janes(1990) and we we find an average offset of ∆ V = − . ± .
007 mag. For the 10 stars in com-mon with Fernie (1965) we find an average offset of∆ V = − . ± .
016 mag. For three stars in commonwith Cacciari et al. (1987, we exclude V0440 Sgr), wefind an average offset of ∆ V = − . ± .
001 mag.Simon & Teays (1982) adopted photometry for a num-ber of stars from earlier sources to generate Fourier fitsto the light curve for each star. The fits were performedin magnitudes so the Fourier parameters provided were9
Feast 2008 / Fernley 1998Piersimoni 1993Skillen 1993Liu 1990Fernie 1965Cacciari 1987Simon 1982
Figure 5.
Difference between the current intensity meanvalues ¡ V ¿ and values published in the literature as describedin the text. used to generate light curves from which the intensity-averaged magnitudes were determined. For the 23 starsin common with Simon & Teays (1982), we find an av-erage offset of ∆ V = − . ± .
024 mag.Overall, the average offsets in the Johnson V bandbetween the literature intensity mean values in the lit-erature and our current results fall between 1% and2%. On average this would indicate that the currentphotometry is about 1% brighter than previous esti-mates. To check potential systematics, random standardstars observed with TMMT were processed like the RRLsample and the final mean magnitudes did not deviatefrom their standard values. Additionally, to check theGLOESS method, literature data was passed throughthe GLOESS algorithm and their final mean magnitudesagreed with their published values. The source of anysystematic remains unclear and a full investigation intothe potential systematics involved in the complete as-similation of other data from the literature is beyondthe scope of this paper. SUMMARY AND FUTURE WORKWith the upcoming
Gaia results, we will soon beable to calibrate the period–luminosity relationship di-rectly using trigonometric parallaxes for a large sam-ple of nearby Galactic RR Lyrae variables. In antici-pation of the
Gaia data releases, we have prepared adata set spanning a wavelength range from 0.4 to 4.5microns in 10 individual photometric bands for a sam- ple of 55 bright, nearby RR Lyrae variables that willbe in the highest-precision
Gaia sample. Moreover, 53of the 55 stars appear in the
Hipparcos catalog, anda large fraction were a part of the
Gaia first data re-lease with the
Tycho-Gaia Astrometric Solution (TGAS;Michalik et al. 2015; Lindegren et al. 2016). Our sam-ple spans a representative range of RRL properties, con-taining both RRab and RRc type stars, a wide rangeof metallicity, and several stars showing short-term andlong-term Blazhko modulations.In this paper, we described the TMMT, an automated,small-aperture facility designed to obtain high-precision,multi-epoch photometry for calibration sources. We pre-sented a multi-site and multi-year campaign with theTMMT that produced well-sampled optical light curvesfor our (55-star) sample. Additionally, we utilize MIRlight curves obtained in the CRRP. Furthermore, wepresent an extensive literature search of the photome-try to expand our phase coverage at all wavelengths.We described our efforts to merge these data sets toconform to a single set of ephemerides (
HJD max , period,and higher-order terms) and explicitly include both ourfilter transformations and phasing solutions.With multi-wavelength merged data sets, we apply theGLOESS technique to produce well-sampled, smoothedlight curves for as many stars and bands as possible.GLOESS produces light curves that are not scaled tem-plates or analytic functions, but are generated from astars’ actual data and thereby preserve the details oftheir often unique light-curve sub-structure. We de-scribe adaptations of this technique required for appli-cation to stars with large amplitude modulations due tothe Blazhko effect, and with other light -curve featuresthat can present challenges. The GLOESS light curvesare then used to determine high-precision intensity meanmagnitudes and mean light-curve properties includingamplitudes, rise times, and magnitudes at minimum andmaximum light.While our study is as complete as possible, many starshave observational data that are currently not well sam-pled enough for the direct application of GLOESS. Wehave GLOESS light curves for 22 (40%) stars in the U ,55 (100%) stars in B , 55 (100%) stars in V , 20 (36%)stars in R , 55 (100%) stars in I , 19 (35%) stars in J , 9(16%) stars in H , 20 (36%) stars in K s , 55 (100%) in[3.6], and 55 (100%) in [4.5]. Our sample is particularlylimited for the near-infrared, where high-cadence obser-vations of bright stars are challenging or observationallyexpensive. A companion paper will present a technique,schematically described in Beaton et al. (2016), thatuses the TMMT-derived GLOESS optical light curvespresented in this work to produce star-by-star predic-0tive templates capable of making use of single-phase orsparsely sampled data sets for RR Lyrae.ACKNOWLEDGMENTSWe thank the anonymous referee for helpful commentson the manuscript. We acknowledge helpful conversa-tions with George Preston.This publication makes use of data products from theTwo Micron All Sky Survey, which is a joint projectof the University of Massachusetts and the InfraredProcessing and Analysis Center/California Institute ofTechnology, funded by the National Aeronautics andSpace Administration and the National Science Foun-dation.This work is based (in part) on observations madewith the Spitzer
Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute ofTechnology under a contract with NASA.This publication makes use of data products from the
Wide-field Infrared Survey Explorer , which is a jointproject of the University of California, Los Angeles,and the Jet Propulsion Laboratory/California Instituteof Technology, funded by the National Aeronautics andSpace Administration. This publication also makes useof data products from
NEOWISE , which is a projectof the Jet Propulsion Laboratory/California Institute ofTechnology, funded by the Planetary Science Division ofthe National Aeronautics and Space Administration.
Facility:
Spitzer (IRAC)
Software:
DAOPHOT (Stetson 1987), DAOGROW(Stetson 1990), PHOTCAL (Davis & Gigoux 1993)1
Table 5.
Intensity Mean Magnitudes from GLOESS light curves
Name
U B V RC IC J H Ks [3.6] [4.5]SW And 10.287 0.020 10.097 0.006 9.692 0.006 9.433 0.020 9.169 0.008 8.757 0.020 8.590 0.013 8.511 0.009 8.485 0.009 8.472 0.008XX And · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Table 6 . Amplitudes, minimum magnitude and rise times from GLOESS light curves
Name
U B V RC IC J H Ks [3.6] [4.5]SW And 1.265 10.823 0.191 1.264 10.630 0.176 0.930 10.096 0.164 0.740 9.757 0.191 0.578 9.457 0.156 0.406 8.998 0.168 0.312 8.802 0.332 0.304 8.725 0.344 0.280 8.680 0.387 0.279 8.665 0.406XX And · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
Table 6 continued Table 6 (continued)
Name
U B V RC IC J H Ks [3.6] [4.5]T Sex 0.469 10.693 0.438 0.534 10.596 0.465 0.411 10.262 0.465 0.330 10.051 0.441 0.257 9.815 0.465 0.201 9.427 0.500 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
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L., Eisenhardt, P. R. M., Mainzer, A. K., et al.2010, AJ, 140, 1868 Wunder, E. 1990, BAV Rundbrief - Mitteilungsblatt derBerliner Arbeits-gemeinschaft fuer Veraenderliche Sterne,39, 9Zasowski, G., Majewski, S. R., Indebetouw, R., et al. 2009,ApJ, 707, 510 Zhou, A.-Y., & Liu, Z.-L. 2003, AJ, 126, 2462 A. IMAGE PROCESSINGThe following section discusses the data reduction procedure under the following prescription: I ∗ ( x, y ) i = B ( x, y ) + D ( x, y )( E i ) + ( G ) F ( x, y ) i ( S ( x, y ) i ( E ( x, y ) + E i )) (A1) where I ∗ ( x, y ) i is the ideal (linear response) raw image and G is the average gain (ADU/photon) of the detector.In the case of a nonlinear detector the actual raw image, I ( x, y ) i , approximately becomes I ( x, y ) i = I ∗ ( x, y ) i (1 − L ( x, y )( I ∗ ( x, y ) i )) (A2)where L ( x, y ) i is the nonlinearity of the pixel. Typically this is a small number, resulting in a reduction in countsby only a few per cent. The ultimate goal is to produce an image that contains the source count rate S ( x, y ) i of thetarget being imaged: S ( x, y ) i = I ( x, y ) i (1 + L ( x, y ) I ( x, y ) i ) − B ( x, y ) − D ( x, y )( E i )( G ) F ( x, y ) i (( E ( x, y ) + E i )) (A3) where each component of Equation A3 is described in one of the following subsections.A.1. Bias and Dark Frames: B ( x, y ) and D ( x, y )A bias frame is the intrinsic count level on the detector and it can be single-valued or have a spatial structure. Inour system the bias pattern has noticeable column structure, which actually changes when the shutter is actively heldopen versus closed. The origin of the effect is not understood ; however, calibrations can be taken with the shutteropen by placing a “dark” blocking filter in the light path. We typically obtain thirty 5 s “light” frames with the darkfilter in place. To construct the 2D bias these frames were averaged together (with sigma-clipping to reject cosmicrays or other outliers).A dark frame is a map of how many counts each pixel produces due to its own heat or electrical characteristics.Our dark frame is produced in much the same way as our bias. We typically take five 605 s “light” frames with thedark filter in place. To construct the 2D dark these frames are averaged together (with sigma-clipping to reject cosmicrays or other outliers). The reason for taking long dark frames is because dark counts are typically low and shortexposures are dominated by read noise, so getting enough dark signal requires longer exposures. One could average alarger number of shorter dark frames, but that requires more overhead in the form of read-out time and data transfer.The average bias is subtracted from the average dark, which removes the bias component and leaves only the darkrate for a 600 s exposure (605 s - 5 s) since the average bias contains 5 s of dark counts. The master dark ( D ( x, y ))is then normalized to counts per second. The scaled master dark frame is then subtracted from the original bias tocreate the dark-subtracted master bias frame, B ( x, y ).A.2. Exposure correction image: E ( x, y )The camera uses a 63 mm Melles-Griot iris shutter, which has a finite opening and closing time, meaning that thecenter of the CCD is exposed slightly longer than the edges. As a result, the true exposure time is the sum of the setexposure time E i and the inherent shutter correction E ( x, y ). To find the shutter correction, pairs of exposures (shortand long) at various exposure times were taken while viewing a flat-field screen. Each image pair was processed up tothe current point, A ( x, y ) i = I ( x, y ) i (1 + L ( x, y ) I ( x, y ) i ) − B ( x, y ) − D ( x, y )( E i )( G ) F ( x, y ) i (A4) and the shutter correction constructed from the following relation: E ( x, y ) = A E − A E A − A . (A5)Multiple pairs of exposure times and flat-field intensities were used to construct an average shutter correction. Thebest result is obtained by using a uniform screen bright enough to get a good signal-to-noise ratio, with a short shuttertime ( E ) just longer than the open/close time of the shutter; in this case E = 0 . s . A corresponding long shuttertime ( E ) is enough to avoid saturation at the same light level as ( E ). Since the shutter correction is a relativelylow-order smooth feature the image was smoothed using a wavelet transform to remove the pixel noise; see Figure 6. The camera has since been repaired by E2V for a shutter power problem, which also fixed the bias problem. Figure 6.
The TMMT shutter correction image. The six blades of the iris shutter open outwards and close in a finite amountof time, resulting in an uneven illumination pattern. The resulting map of exposure time varies radially from 0.07 to 0.02s. Starting from the center, the contours represent: 60, 55, 50, 45, 40, 35, 30, and 25 additional milliseconds to the originalexposure time.
Flats Frames and Linearity: F ( x, y ) and L ( x, y )Flat-field frames were taken by using an 18” Alnitak electroluminescent flat-field panel. The illumination wasadjusted for each filter to reach 30,000 ADU in 30 s. The relatively long exposure time was designed to minimize theimpact of the shutter correction, which at 30 s was already less than a 0.2% correction. To reduce the effect of straylight, exposures were taken with the panel on and off; the images were processed and then differenced to produce a flatfield. To determine the linearity a series of exposures of increasing time were taken of the flat-field screen. The imagecounts versus exposure time for each pixel were fit with a second-order polynomial. The first term in the polynomialis the linear response component and the linearity term is the ratio of the second coefficient to the first. For thiscamera there is no significant pixel-to-pixel variation, and a constant value of 10 − was adopted for the entire arraycorresponding to a 5% correction at 50,000 ADU. To place the final image in more meaningful (Poisson) units theimage was divided by the average gain; G =1.4 in this case as adopted from the manufacturer and confirmed frommeasurements of variance versus flux. B. NOTES ON INDIVIDUAL STARSIn this appendix, we organize discussions relating to specific stars in our sample, incorporating our literature searchand analysis. More specifically, we provide rationales regarding the adopted parameters for the stars when there aredisagreements in the literature (i.e., the values given in Table 1), any notes regarding the behavior of the star, specialtechniques required to phase data sets widely separated in time, and any other individual star concerns. By separatingthese discussions from the main body of the paper we hope to be as streamlined as possible in the example schematicpresented in the main text, while also providing as complete documentation of our efforts as possible.Unless otherwise noted, all 55 stars have data from the following sources: (i)
B, V, I c multiphase optical observationsfrom the TMMT (Section 3 in the main text), (ii) one J, H, K s phase point from 2MASS (Section 4.2.1), and (iii)[3.6] & [4.5] multiphase data from Spitzer (Section 4.3.1) and
WISE (Section 4.3.2). Filter transformations or othermodifications required for the entire body of a study were given in the appropriate subsections of Section 4, withstar-by-star specifics reserved for the following subsections.B.1.
SW And
SW And shows the Blazhko effect with P Bl = 36 . B , V , I from Barnes et al. (1992), B , V , I from Barcza & Benk˝o (2014), B , V , K from Jones et al. (1992), B , I , R , U , V , J , K from Liu & Janes (1989), and J , H , K s from Barnes et al. (1992).B.2. XX And
XX And is a non-Blazhko RRab. Supplementary data in
J, H, K s from Fernley et al. (1993).B.3. WY Ant
WY Ant is a non-Blazhko RRab. Supplementary data come from the following sources: U , B , V , R , I fromSkillen et al. (1993b), V from ASAS, and J, H, K s from Skillen et al. (1993a).B.4. X Ari
X Ari is a non-Blazhko RRab. Supplementary data come from the following sources: V from ASAS and B , V , R , I , J , H , and K from Fernley et al. (1989). B.5. AE Boo
AE Boo is a non-Blazhko RRc. There are no supplementary data for this star.B.6.
ST Boo
ST Boo is a RRab showing the Blazhko effect P Bl = 284 .
09 days (Smith 1995). Owing to this long period, we onlysee hints of two distinct amplitudes in our light curve. Supplementary
J, H, K s data come from Fernley et al. (1993). Optec Inc.
TV Boo
TV Boo is a RRc showing the Blazhko effect (Smith 1995). Skarka & Zejda (2013) showed the star to have twoBlazhko periods of P = 9 .
737 days and P = 21 . U , B , V , R , I , J , K s from Liu & Janes (1989), J, H, K s from Fernley et al. (1993), and U , B , V from Paczy´nski (1965).B.8. UY Boo
UY Boo is a RRab showing the Blazhko effect with P Bl = 171.8 days (Skarka 2014). Between φ = 0.1 and φ = 0.2in our data, we see clearly see two distinct amplitudes for the light curve. Supplementary data in J, H, K s come fromFernley et al. (1993). B.9. UY Cam
UY Cam was only observed for one night with the TMMT. The light curve is supplemented in B and V with datafrom Broglia & Conconi (1992). An offset of 0.03 mag and phase offset of φ =0.02 were required to align the data tothe modern epoch. There appears to be some slight modulation of the amplitude that may account for the offset.Zhou & Liu (2003) studied this star in much greater detail, and as a result they determine this star to be an analogto a high-amplitude Delta Scuti (HADS), SX Phoenicis, and type RRc variable. For the purposes of this paper wecontinue to classify it as type RRc and provide the photometry.B.10. YZ Cap
YZ Cap is a non-Blazhko RRc. Supplementary data in U , B , V , R , I from Cacciari et al. (1987).B.11. RZ Cep
RZ Cep is a non-Blazhko RRc and the only RRc with an
HST parallax from Benedict et al. (2011), in which twovalues are given for the parallax of RZ Cep: π = 2.12 and π = 2.54 mas, the former being the final and preferred adoptedvalue (Benedict et al. (2011), private communication). New multi-wavelength PL relations suggest, however, that π =2.54 mas provides a better solution (Monson et al. in prep). This is also consistent with results from Kollmeier et al.(2013), which find the absolute magnitude of RRc from statistical parallax to be M V = 0 . ± . ± .
014 at[Fe/H]=-1.5 dex. For RZ Cep the value of M V is 0.25 mag or 0.64 mag using 2.12 or 2.54 mas, respectively (adopting h V i = 9 .
398 mag and A V of 0.78 mag).Supplementary data for this star come from U , B , V in Paczy´nski (1965) and J, H, K s from Fernley et al. (1993).The data presented for RZ Cep in Feast et al. (2008) appear to contain a discrepancy. While Fernley et al. (1989)have E ( B − V ) = 0.25 mag, Feast et al. (2008) claim E ( B − V ) = 0.078 mag. Benedict et al. (2011) found A v ∼ V -[Fe/H] relations and iterating to find E ( B − V ). As pointed out in Sec 6.3 their adopted mean V magnitude for RZ Cep was transformed from the Hipparcos H P magnitude using an adopted mean color correctionfor type RRc RRL. Since RZ Cep is highly reddened, this color correction would cause the distance modulus in theM V -[Fe/H] relation to be overestimated and the resulting estimate of E ( B − V ) to be underestimated.B.12. RR Cet
RR Cet is a non-Blazhko RRab. Supplementary data come from Liu & Janes (1989) in the U , B , V , R , I , J , and K s bands. B.13. CU Com
CU Com is the only double-mode pulsator in our sample. Clementini et al. (2000) used
B, V, I c photometry with an11 year baseline, finding that CU Com has to have periods P = 0.5441641 days and P = 0.4057605 ( P /P = 0.7457).The HJD data for the B observations presented in Clementini et al. (2000) and those available from the online catalogdiffer by 2231 days, which was rectified for the data in this study.B.14. RV CrB
RV CrB is a non-Blazhko RRc. Additional
J, H, K s data come from Fernley et al. (1993).1B.15. W Crt
W Crt is a non-Blazhko RRab. U , B , V , R , I data were adopted from Skillen et al. (1993b), but required a correctionof δM λ = -0.04 mag. J, H, K s data were adopted from Skillen et al. (1993a).B.16. ST CVn
ST CVn is a non-Blazhko RRc. Additional
J, H, K s data were adopted from Fernley et al. (1993).B.17. UY Cyg
UY Cyg is a non-Blazhko RRab. Additional
J, H, K s data were adopted from Fernley et al. (1993).B.18. XZ Cyg
XZ Cyg is an RRab showing the Blazhko effect with P = 57 . J, H, K s data were adopted from Fernley et al. (1993). Our TMMT light curveclearly shows the Blazhko effect from φ = 0 . φ = 1 .
0. To remedy problems in the smoothed light curve from theBlazhko effect, the GLOESS light curve sampled the data at 50 phase points and then the GLOESS light curve wasup-sampled to 200 phase points. We note that the mismatch in the MIR and NIR data points is likely due to beingon different parts of the Blazhko phase. B.19.
DX Del
DX Del is a non-Blazhko RRab. Supplementary data are adopted from Skillen et al. (1989) in V , J, H, K s .B.20. SU Dra
SU Dra is a non-Blazhko RRab. Supplementary data are adopted from Liu & Janes (1989) in U , B , V , R , I , J and K s . B.21. SW Dra
SW Dra is a non-Blazhko RRab. Supplementary data in U , B , V , R , I are from Cacciari et al. (1987).B.22. CS Eri
CS Eri is a non-Blazhko RRc. There are no supplementary data for this star.B.23.
RX Eri
RX Eri is a non-Blazhko RRab. Additional data are adopted from Liu & Janes (1989) in U , B , V , R , I , J , and K s .B.24. SV Eri
SV Eri is a non-Blazhko RRab Additional data in
J, H, K s come from Fernley et al. (1993).B.25. RR Gem
The light curve for RR Gem is classified as ‘stable or contradictory,’ meaning that it does not always show a Blazhkomodulation, but has at times (Jurcsik et al. 2009, and references therein). The most recent characterization is fromJurcsik et al. (2005), finding a short period, P Bl = 7 .
23 day, and a small 0.1 mag modulation. Our data show a clearBlazhko effect over the full phase cycle. Supplementary data are adopted from Liu & Janes (1989) in U , B , V , R , I , J , and K s . B.26. TW Her
TW Her is a non-Blazhko RRab. No additional data were adopted.B.27.
VX Her
VX Her is an RRab showing a very long-period Blazhko effect with P Bl = 455 .
37 days (the Blazhko period wasfirst published in Wunder (1990), but the associated data are much more easily accessed in the compilation of Skarka(2013)). Owing to this long period, we see no evidence of a Blazhko effect in our data. Supplementary data areadopted in
J, H, K s from Fernley et al. (1993).2 B.28. SV Hya
SV Hya is an RRab showing a Blazhko effect with P Bl = 63 .
29 days (Smith 1995). Visible discontinuities in ourlight curve can be attributed to this effect. Supplementary data are adopted from Fernley et al. (1993) in
J, H, K s and from Warren (1966) in U , B , V .To construct a light curve without a large discontinuity, the data on MJD 57160 were shifted by -0.12 mag. Thedata being presented are unaltered in the primary catalog, but the modified data used to build the GLOESS lightcurve are available under the ID code 999 for B , V , I .B.29. V Ind
V Ind is a non-Blazhko RRab. We supplement the TMMT data with B , V , R , I data from Clementini et al. (1990)and V data from ASAS. B.30. BX Leo
BX Leo is a non-Blazhko RRc. No supplementary data are adopted for this star. This star was unusually difficultto phase properly. Phasing of the
Spitzer epochs required an offset of ∆ φ =0.15.B.31. RR Leo
RR Leo is a non-Blazhko RRab. Supplementary data are adopted from Liu & Janes (1989) in U , B , V , R , I , J and K . B.32. TT Lyn
TT Lyn is a non-Blazhko RRab. Supplementary data are adopted from Liu & Janes (1989) in U , B , V , R , I , J and K and from Barnes et al. (1992) in B , V , I . B.33. RR Lyr
RR Lyr is an RRab star that is well known to exhibit the Blazhko effect (Smith 1995). Moreover, RR Lyr has atime-variable Blazhko cycle with a variation from P Bl = 38 . P Bl = 40 . K epler field and its time variations are explored in detail within K epler by Kolenberg et al. (2011) and compared to an abundance of historical data by Le Borgne et al. (2014). Supplementary data in J, H, K s are adoptedfrom Sollima et al. (2008) and Fernley et al. (1993).B.34. RV Oct
RV Oct is a non-Blazhko RRab. Supplementary data are adopted from Skillen et al. (1993b) in B , V , R , I andSkillen et al. (1993a) in J, H, K s . B.35. UV Oct
UV Oct is an RRab showing the Blazhko effect with P Bl = 143 .
73 days (Skarka 2013). We see bifurcation in ourlight curve indicative of seeing the Blazhko effect. Supplementary data are adopted in V from ASAS.B.36. AV Peg
AV Peg is a non-Blazhko RRab. Supplementary data are adopted from Liu & Janes (1989) in U , B , V , R , I , J , and K .B.37. BH Peg
BH Peg is an RRab showing the Blazhko effect with P Bl = 39 . J, H, K s from Fernley et al. (1993).B.38. DH Peg
DH Peg is a non-Blazhko RRc. Additional data are adopted from the following sources: Fernley et al. (1990) in V , J , K UKIRT , Barcza & Benk˝o (2014) in B , V , I , and Paczy´nski (1965) in U , V , B . There are no Spitzer data for thisstar.3B.39.
RU Psc
RU Psc is an RRc showing the Blazhko effect with P Bl = 28 days (Smith 1995). We see evidence of amplitudemodulation in our light curve. Supplementary data are obtained from Paczy´nski (1965) in U , B , V and Fernley et al.(1993) in J, H, K s . Phasing of the Spitzer epochs required an offset of ∆ φ =0.12.B.40. BB Pup
BB Pup is a non-Blazhko RRab. Supplementary data from Skillen et al. (1993b) in U , B , V , R , I , Skillen et al. (1993a)in J, H, K s , and V from ASAS. There are no Spitzer data for this star.B.41.
HK Pup
HK Pup is a non-Blazhko RRab. Supplementary data in V from ASAS.B.42. RU Scl
RU Scl is an RRab showing the Blazhko effect with P Bl = 23.91 days (Skarka 2014). We see some modulation inour light curve at maximum light. Supplementary data in J, H, K s are adopted from Fernley et al. (1993). There areno Spitzer data for this field. B.43.
SV Scl
SV Scl is a non-Blazhko RRc. Supplementary data are adopted in
J, H, K s from Fernley et al. (1993) and in V fromASAS. B.44. AN Ser
AN Ser is a non-Blazhko RRb. Supplementary data are adopted in
J, H, K s from Fernley et al. (1993) and in V from ASAS. B.45. AP Ser
AP Ser is a non-Blazhko RRc. There are no additional data for this star.B.46.
T Sex
T Sex is a non-Blazhko RRc. Supplementary data are adopted from the following sources: Barnes et al. (1992) in B , V , I , Liu & Janes (1989) in U , B , V , R , I , J , and K , and V from ASAS.B.47. V0440 Sgr
V0440 Sgr is a non-Blazhko RRab. Supplementary data are adopted from Cacciari et al. (1987) in U , B , V , R , I andFernley et al. (1993) in J, H, K s . B.48. V0675 Sgr
V0675 Sgr is a non-Blazhko RRab. Supplementary data in
J, H, K s are adopted from Fernley et al. (1993).B.49. MT Tel
MT Tel is a non-Blazhko RRc. Additional V data are adopted from ASAS.B.50. AM Tuc
AM Tuc is a RRc that has a long-period Blazhko modulation with P Bl = 1748 .
86 days Szczygie l & Fabrycky (2007).This period is much longer than the span of our observations. No additional data are adopted for this star.B.51.
AB UMa
AB UMa is a non-Blazhko RRab. No additional data are used for this star, although there is good agreementbetween the average found here and that of Piersimoni et al. (1993).4 B.52.
RV UMa
RV UMa is an RRab showing the Blazhko effect (Smith 1995). Hurta et al. (2008) note a time-variable Blazhkoperiod from P Bl = 89 . P Bl = 90 .
63 days. Supplementary data are adopted in
J, H, K s from Fernley et al. (1993).We see evidence for modulation in our light curve. In order to construct a GLOESS light curve without a largediscontinuity, the amplitudes of the light curves from MJD 56786, 56793, and 56796 were scaled by a factor of 1.6around the B,V,I means of 11.2, 10.9, 10.4, respectively. The data are presented unaltered in the primary table, butthe scaled data are available under the ID code 999 for B , V , I .B.53. SX UMa
SX UMa is a non-Blazhko RRc. Supplementary data are adopted in
J, H, K s from Fernley et al. (1993).B.54. TU UMa
TU UMa is an RRab. As discussed in Barnes et al. (1992, and references therein), Fernley & Barnes (1997), andLiˇska et al. (2016), this might be in a binary system, which causes slight delays in the phasing of the time of maximumlight for the light curve. Supplementary data are adopted in B , V , I , J, H, K s from Barnes et al. (1992) and U , B , V , I , R , J and K from Liu & Janes (1989). B.55. UU Vir
UU Vir is a non-Blazhko RRab. Supplementary data are adopted from the following sources: U , B , V , I , R , J and K from Liu & Janes (1989), V from ASAS, and J, H, K ss