High-precision 2MASS JHKs light curves and other data for RR Lyrae star SDSS J015450+001501: strong constraints for non-linear pulsation models
R. Szabó, Z. Ivezić, L. L. Kiss, Z. Kolláth, L. Jones, B. Sesar, A. C. Becker, J. R. A. Davenport, R. M. Cutri
aa r X i v : . [ a s t r o - ph . S R ] N ov Draft version October 1, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
HIGH-PRECISION 2MASS JHK S LIGHT CURVES AND OTHER DATA FOR RR LYRAE STARSDSS J R´obert Szab´o , ˇZeljko Ivezi´c , L´aszl´o L. Kiss , Zolt´an Koll´ath , Lynne Jones , Branimir Sesar , AndrewC. Becker , James R.A. Davenport , and Roc M. Cutri Draft version October 1, 2018
ABSTRACTWe present and discuss an extensive data set for the non-Blazhko ab-type RR Lyrae starSDSS J ugriz light curves and spectroscopic data, LINEARand CSS unfiltered optical light curves, and infrared 2MASS JHK s and WISE W1 and W2 light curves.Most notably, light curves obtained by 2MASS include close to 9000 photometric measures collectedover 3.3 years and provide exceedingly precise view of near-IR variability. These data demonstratethat static atmosphere models are insufficient to explain multi-band photometric light curve behaviorand present strong constraints for non-linear pulsation models for RR Lyrae stars. It is a challengeto modelers to produce theoretical light curves that can explain data presented here, which we makepublicly available. Subject headings: stars: variables: RR Lyrae — infrared: stars — techniques: photometric — stars:atmospheres — stars: individual(SDSS J INTRODUCTION
RR Lyrae stars are old low-mass (around half theSun’s) pulsating horizontal branch stars of spectral classA and F. They are important both as stellar evolution-ary probes and as tracers of Galactic structure. Forthese reasons, accurate pulsational models for RR Lyraestars are crucial in a large number of astrophysical ap-plications. Marconi (2009) recently pointed out thata non-local time-dependent treatment of convection innon-linear (i.e., without small oscillation approximation)pulsation models for RR Lyrae are needed to explain themorphological characteristics of the variation along a pul-sation cycle of luminosity, radius, radial velocity, effec-tive temperature and surface gravity: “the comparisonbetween theoretical and observed variations represents apowerful tool to constrain the intrinsic stellar parametersincluding the mass.”Precise multi-band light curves provide strong con-straints for pulsation models. Bono et al. (2000) per-formed simultaneous fitting of multi-band (
U BV K ) lightcurves of an RRc star (U Comae). They transformed thebolometric magnitudes supplied by a hydrocode to stan-dard magnitudes using bolometric corrections and empir-ical color-temperature relations based on
ATLAS9 modelatmospheres (Castelli et al. 1997). Dorfi & Feuchtinger(1999) carried out detailed frequency-dependent radia-tive transfer computations to obtain UBVI light curves Konkoly Observatory, MTA CSFK, Konkoly Thege Mikl´os ´ut15-17, H-1121, Budapest, Hungary; [email protected] Astronomy Department, University of Washington, Box351580, Seattle, WA 98195-1580 Sydney Institute for Astronomy, School of Physics, Universityof Sydney, NSW 2006, Australia ELTE Gothard-Lend¨ulet Research Group, Szent Imre herceg´ut 112, H-9700 Szombathely, Hungary University of West Hungary Savaria Campus, Szombathely,Hungary Division of Physics, Mathematics and Astronomy, Caltech,Pasadena, CA 91125 Infrared Processing and Analysis Center, California Instituteof Technology, Pasadena, CA 91125 of both RRab and RRc stars. Motivated by their re-sults, in this work we present light curves for an RRLyrae star pulsating in the fundamental mode (RRab)obtained over 15 years in ten photometric bandpassesthat span more than a factor of ten in wavelength,and bracket the wavelength range where most of itsluminosity is emitted. Most notably, light curves ob-tained by 2MASS include close to 9000 photometric mea-sures obtained over 3.3 years and, after data averag-ing, provide exceedingly precise view of near-IR variabil-ity. While quasi-continuous, extreme precision opticalligth curves have recently become available thanks to the
Kepler mission ( e.g. ∼ § § DATA ANALYSIS
We first describe optical SDSS ugriz light curves andspectroscopic data, LINEAR and CSS unfiltered lightcurve data, infrared 2MASS JHK s and WISE W1 andW2 light curve data, and then perform their joint anal-ysis. The temporal coverage and sizes of these data setsare summarized in Table 1.As photometric data for RR Lyrae stars have been his-torically taken predominantly in the UBVRI system, itmight be interesting to note that Ivezi´c et al. (2007) pro-vide a set of non-linear transformation between BVRIand SDSS griz magnitudes. For a linear transformation Szab´o et al. Table 1
Photometric data analyzed in this workSurvey MJD a min MJD b max N epochs c N data d a Earliest MJD in the survey. b Latest MJD in the survey. c The number of photometric epochs. d The number of photometric data points (the number ofepochs times the number of bandpasses). between the U and u magnitudes the interested reader isreferred to Jester et al. (2005). SDSS data
The Sloan Digital Sky Survey (SDSS; Abazajian et al.2009) has repeatedly imaged about 300 sq. deg. largeequatorial strip limited by 309 ◦ < R . A . < ◦ and | Dec | < . ◦ , and known as Stripe 82. The proper-ties of this data set and its impact on variability studiesare discussed in detail by Ivezi´c et al. (2007), Sesar et al.(2007) and Bramich et al. (2008). An extensive study oflight curves for RR Lyrae stars found in Stripe 82 wasundertaken by Sesar et al. (2010).The star discussed here was identified in SDSS Stripe82 data with coordinates (J2000.0): R.A. = 28.709054and Dec= +0.250206 (decimal degrees). Following stan-dard SDSS nomenclature, hereafter we refer to it asSDSS J available, as well as published along withthis paper electronically for convenience. Table 6 showsthe form and content of the data. Images show a dis-tinctively blue isolated point source, with the nearestbrighter object more than 30 arcsec away. Its SDSS r band magnitude varies from ∼ ∼ D = 7 .
59 kpc.
Imaging data
SDSS imaging data for this star were obtained 64 timesand include nearly-simultaneous ugriz photometry pre-cise to 0.01-0.02 mag. In order to construct phased lightcurves, we use the period and epoch of maximum de-termined using better sampled LINEAR data (see § urz light curves are shownin Fig. 1. Following Sesar et al. (2010), we normalizedlight curves by their amplitude (with minimum and max-imum brightness determined using B splines) and shiftedso that minimum brightness is 0 and maximum bright-ness is 1. As evident from Fig. 1, light curves are typicalfor ab RR Lyrae stars and greatly vary with wavelength. Spectroscopic data
SDSS J http://skyserver.sdss3.org/dr9/en/tools/explore/obj.asp?sid=788271533805037568 Figure 1.
Phased and normalized SDSS urz (bottom to top, re-spectively) light curves for SDSS J Table 2
LINEAR light curve for RR Lyrae starSDSS J err Note . — For details see Sesar et al. (2011, 2013). Ta-ble 2 is published in its entirety in the electronic editionof the Journal. A portion is shown here for guidance re-garding its form and content.
Parameter Pipeline (Lee et al. 2011) include [
F e/H ] = − . ± .
03, log(g)=2.97 ± eff =6580 ±
104 K, andradial velocity − . ± − . We note howeverthat the spectrum of this star is a coadd of 5 individualexposures, and the time between the start of the first andthe end of the last exposure is 1.03 days. Thus, the pa-rameters derived from this spectrum might contain muchhigher systematic errors because the individual exposuresspan a wide range of pulsational phases. Figure 2.
Default SDSS visualization of the SDSS spectrum forSDSS J LINEAR and CSS light curve data
The asteroid survey LINEAR was photometrically re-calibrated by Sesar et al. (2011) using SDSS stars actingas a dense grid of standard stars. In the overlappingMASS light curves for SDSS J Table 3
CSS light curve for RR Lyrae starSDSS J err Note . — Table 3 is published in its entirety in theelectronic edition of the Journal. A portion is shown herefor guidance regarding its form and content. ∼ of sky between LINEAR and SDSS, pho-tometric errors for unfiltered (white light) photometryrange from ∼ ∼ r = 18 (here r is the SDSS r band magnitude). LINEAR data provide time domaininformation for the brightest 4 magnitudes of SDSS sur-vey, with 250 unfiltered photometric observations per ob-ject on average. The public access to the recalibratedLINEAR data is provided through the SkyDOT Web site(https://astroweb.lanl.gov/lineardb/) and is also avail-able as auxiliary material with this paper (see Table 2).RR Lyrae stars from this data set have been analyzed bySesar et al. (2013).The Catalina Sky Survey (CSS) uses three telescopesto search for near-Earth objects. Each of the surveytelescopes is run as separate sub-surveys, including theCatalina Schmidt Survey and the Mount Lemmon Sur-vey in Tucson, Arizona, and the Siding Spring Survey inSiding Spring, Australia. CSS is similar to LINEAR inthat it uses unfiltered observations and delivers similarphotometric precision (but is deeper by several magni-tudes). RR Lyrae stars from this data set have beenanalyzed by Drake et al. (2013).SDSS J P = 0 . max = 53675.299080. Based onSesar et al. (2011) photometric transformations betweenLINEAR and SDSS r -band data, a great degree of simi-larity is expected between unfiltered LINEAR/CSS lightcurves and the SDSS r -band light curve. This expec-tation is verified by data, as illustrated in Fig. 3. CSSobservations of SDSS J The most extensive data set presented here comesfrom the 2MASS survey (Skrutskie et al. 2006).SDSS J s bandpasses during each night of the 3.5 yearsurvey. Full details are given in the online ExplanatorySupplement and Cutri et al. (2003). Analysis of variousvariable stars contained in this data set was presentedby Plavchan et al. (2008), Becker et al. (2008) andDavenport et al. (2012), where more technical detailscan be found. Figure 3.
LINEAR (dashed), CSS (dot-dashed) and SDSS r -band (solid) light curves for SDSS J SDSS J gi light curves in Fig. 4. Becausethe 2MASS data set is so large and we see no sign ofBlazhko-modulation in the light curves, data are median-ed in 0.04 wide phase bins, with resulting random errorswell below 0.01 mag. The variation of the light curveshape with bandpass wavelength seen in SDSS data (seeFig. 1), continues into near-IR, but only to the H band– the light curves in the H and K bands are barely dis-tinguishable despite the high precision of 2MASS data.We proceed with a more detailed analysis of the JHK variability which reveals interesting light curve features.
Figure 4.
Phased and normalized SDSS gi and 2MASS JHK (bottom to top, respectively) light curves for SDSS J ∼ H and K lightcurves are barely distinguishable. Phase-resolved near-IR color-magnitude hysteresisloops
The phased
JHK light curves, the J − K color vari-ation with phase, and phased-resolved color-magnitudeand color-color diagrams constructed with median-ed2MASS data are shown in Fig. 5. A notable featureis that the time of maximum light in H and K band-passes does not coincide with the time of maximum light Szab´o et al.at shorter wavelengths, but lags in phase by about 0.25.Unlike the J − K color which varies with an amplitudeof ∼ H − K color does not appear to varyat all: its root-mean-square scatter is only 0.01 mag, andconsistent with photometric noise (compare to 0.075 magfor the J − K color).Perhaps the most interesting feature revealed by thehigh-precision 2MASS data is seen in the J vs. J − K color-magnitude diagram (bottom left panel of Fig. 5). Inaddition to the clearly seen “hysteresis” (for illustrationof a similar behavior in the ugr bandpasses, see Figure 9in Sesar et al. 2010), the J − K color becomes bluer be-tween phases 0.65 and 0.70 despite the decreasing bright-ness (see the middle right and bottom left panels, and ar-row in the latter panel). Given the short duration ( ∼ § Figure 5.
Top four panels display phased and normalized 2MASS
JHK and color J − K light curves for SDSS J ∼ J − K color becomes bluerdespite the decreasing brightness (see the middle right and bot-tom left panels, and arrow in the latter panel). The H − K colordoes not show any variation (rms of ∼ .
01 mag, consistent withmeasurement errors).
WISE light curve data
The Wide-field Infrared Survey Explorer (WISE,Wright et al. 2010) mapped the sky at 3.4, 4.6, 12, and 22 µ m. WISE imaged each point on the sky multiple timesto achieve its sensitivity goals and to reject transientevents such as cosmic rays. SDSS J µ m) and W2 (4.6 µ m) Figure 6.
WISE W J K -band light curve (samecurve as in Figure 4). Table 4
WISE light curves for RR Lyrae starSDSS J err W2 W2 err
Note . — Table 4 is published in its entirety in theelectronic edition of the Journal. A portion is shown herefor guidance regarding its form and content. bands: the median photometric errors are 0.05 mag forW1 and 0.15 mag for W2. These two light curves (43data points per band) are compiled in Table 4.Although WISE data are noisy, it is possible to make arough comparison with 2MASS data. As shown in Fig. 6,the phased and normalized light curve in the W1 bandis fully consistent with the corresponding 2MASS lightcurve in the K band (including the amplitude). A moredetailed comparison of data across all ten bandpasses isdescribed next. Simultaneous analysis of optical and infrared data
As shown above, the shape of light curves varies greatlywith wavelength. Another way to look at the same dataset is to construct phase-resolved spectral energy distri-butions (SED). SEDs at minimum and maximum phases,and at phase=0.5, are compiled in Table 5 and shown inthe top panel in Fig. 7. When the SED at phase=0.5 isscaled to a fainter flux level by 0.25 mag, it is indistin-guishable from the SED at minimum phase (0.86). As-suming identical effective temperatures, this scaling fac-tor implies that the effective radius of the star decreasesby 12% between these two phases.The variation of light curve amplitude with wavelengthis shown in the bottom panel in Fig. 7. Between theSDSS g band (0.476 µ m) and the 2MASS H band (1.65 µ m), the amplitude steadily decreases from ∼ ∼ u bandand the g band amplitudes are similar, which impliesthat the u − g color stays approximately constant overthe pulsational cycle. This is easily understood as theconsequence of the fact that the u − g color primarilyMASS light curves for SDSS J F e/H ] = − . T eff = 7500 K (maximum light) and T eff = 6000 K(minimum light). The effective temperature step in themodel library was 250 K. A slight discrepancy betweenthe measured u band magnitude at maximum light andthe best-fit model can be reconciled as due to the impactof the steep SED in that region. u g r i z J H K W1 W2 Figure 7.
Top panel: ten-band spectral energy distributions(SED) at maximum (top) and minimum (bottom) light forSDSS J shifted fainter by 0.25 mag. The SED shape at phase=0.50 is nearly indistin-guishable from the SED at minimum light. The solid lines showKurucz models for [ F e/H ] = − .
5, log(g)=3.0, and T eff = 7500K (top) and T eff = 6000 K (bottom). Bottom panel: light curveamplitude, in magnitudes, as a function of wavelength. Despite this apparent success of static atmospheremodels, it is easy to demonstrate that they cannot pro-vide a complete description of the data. Fig. 8 showsa phase-resolved J − K vs. g − i color-color diagram.Both of these colors are by and large driven by effectivetemperature and Kurucz models show that the impactof log(g) is only minor (at most a few hundredths of amagnitude in the J − K color at a given g − i color, fora detailed discussion see Ivezi´c et al. 2008). Therefore,if static atmosphere models are sufficient to describe thedata, then the data should follow a single line in thisdiagram, with the position along that line controlled bythe effective temperature. In contrast, data in this color-color diagram show a similar hysteresis effect as the J vs. J − K color-magnitude diagram (bottom left panelin Fig. 5). This color-color hysteresis, however, cannotbe described as due to different stellar radii at a giveneffective temperature, as in the case of color-magnitudediagram.To provide a precise quantitative estimate of the dis-crepancy between observed colors and colors predictedby Kurucz models, we compare a set of models for three Figure 8.
The symbols connected by dashed lines show 2MASS J − K color vs. SDSS g − i color for SDSS J g − i = 0, about 0.05 mag difference in J − K color). Note that both colors are essentially constant for phase binsfrom 0.45 to 085. The six thin solid lines are predictions based onKurucz static model atmospheres with effective temperatures in therange 6000–7500 K. At the blue end, they bifurcate into the groupsof three tracks – they correspond to models with [ F e/H ] = − . F e/H ] = − .
0. For each metallicity,the three curves correspond to log(g)=2.5, 3.0 and 3.5. Note thatat the blue end, the models bifurcate according to log(g), ratherthan [
F e/H ] (at J − K ∼ .
13, the g − i color becomes bluer by ∼ values of log(g) and two values of [ F e/H ] that bracket thevalues expected for this star (see Fig. 8). Models providea fairly good agreement, to within a few hundredths of amagnitude) for the descending branch of the light curve(phases between the light curve maximum and minimum,the lower branch in Fig. 8). However, all models fail toexplain the observed colors during the ascending branch,as the light curve goes from the minimum light to themaximum light (note that ascending portion of the lightcurve is about five times shorter than the descending por-tion). At a given J − K colors, the discrepancy can beas large as ∼ J − K = 0 .
2, the difference in the g − i color at the descending and ascending branches is over0.2 mag. Similarly, at a fixed g − i = 0 color, the J − K color differs by ∼ DISCUSSION AND CONCLUSIONS
Essentially by coincidence, the non-modulated (non-Blazhko) RR Lyrae star SDSS J Table 5
Spectral energy distribution data for RR Lyrae star SDSS J λ eff ( µ m) mag min err mag max err amplitude mag φ =0 . extinction corr.u 0.3540 16.96 0.02 15.72 0.02 1.24 16.70 0.179g 0.4760 15.78 0.01 14.51 0.01 1.27 15.52 0.139r 0.6280 15.50 0.01 14.58 0.01 0.92 15.24 0.099i 0.7690 15.38 0.01 14.66 0.01 0.72 15.14 0.075z 0.9250 15.35 0.02 14.69 0.02 0.66 15.10 0.056J 1.25 15.42 0.01 14.95 0.01 0.47 15.18 0.031H 1.65 15.62 0.01 15.28 0.01 0.34 15.36 0.020K 2.17 16.04 0.01 15.72 0.01 0.32 15.79 0.013W1 3.4 16.80 0.05 16.46 0.05 0.34 16.56 0.008W2 4.5 17.50 0.10 17.20 0.10 0.30 17.24 0.007 Note . — The table lists 2MASS and WISE magnitudes on AB scale. The following Vega-to-ABmagnitude offsets (m AB =m Vega +offset) were used: 0.89, 1.37, 1.84 in
JHK , and 2.6, 3.3 in W W
2. Magnitude values are not corrected for ISM dust extinction. Plausible extinction corrections(Schlegel et al. 1998) are listed in the last column and are derived using the SFD value for the r -bandextinction quoted by SDSS for this star: A r = 0.099, and coefficients listed in the first row of Table1 from Berry et al. (2012) for the ugrizJHK bands. For the WISE bands, the coefficients taken fromYuan et al. (2013) (A W1 /A r = 0.084, A W2 /A r = 0.074). ability. A data set of similar completeness, precision, andwavelength and temporal coverage likely does not existfor any other RR Lyrae star.The data for SDSS J ugriz RR Lyrae light curvesobtained by SDSS and theoretical light curve predictionsfrom Marconi et al. (2006). Here, we further demon-strated that static atmosphere models are insufficientto explain multi-band photometric light curve behav-ior. Indeed, Barcza (2010) demonstrated that the quasi-static approximation is not valid for all phases during anRR Lyrae pulsational cycle. Pulsation models computedby Fokin & Gillet (1997) with a large number of massshells in the stellar atmosphere show that the s3’ and/orthe merging s3+s4 shock waves might be at work at thepulsational phase range of 0.65-0.70, where we found the’kink’ in the J − K color progression (Fig 5). We cau-tion however that a large model survey should be con-ducted in a broad range of RR Lyrae physical parametersin order to verify the existence and the influence of theseshock waves, in particular in SDSS J ACKNOWLEDGMENTS J Szab´o et al.
Table 6
SDSS ugriz light curves for RR Lyrae star SDSS J a Dec a MJD u u u err MJD g g g err MJD r r r err (deg) (deg) (day) (mag) (mag) (day) (mag) (mag) (day) (mag) (mag)28.709058 0.250204 51075.379381 16.603 0.008 51075.381047 15.412 0.005 51075.377714 15.161 0.00628.709058 0.250204 51818.349055 16.921 0.009 51818.350721 15.715 0.006 51818.347388 15.447 0.006... ... ... ... ... ... ... ... ... ... ... Note . — Magnitudes are not corrected for ISM dust extinction and set to -99.999 if unreliable. See Sesar et al. (2010) for moredetails. Table 6 is published in its entirety (including the iz photometry) in the electronic edition of the Journal. A portion is shownhere for guidance regarding its form and content. a Equatorial J2000.0 right ascension and declination.
Table 7
JHK light curves for RR Lyrae star SDSS J a Dec a BJD
J J err J q b H H err H q b K K err K q b (deg) (deg) (mag) (mag) (mag) (mag) (mag) (mag)10038165 28.709000 0.250413 51003.4463211 14.257 0.030 A 14.007 0.041 A 13.947 0.075 A10038255 28.708985 0.250394 51003.4466211 14.219 0.031 A 13.949 0.040 A 13.941 0.077 A... ... ... ... ... ... ... ... ... ... ... ... ... Note . — Table 7 is published in its entirety in the electronic edition of the Journal. A portion is shown here for guidance regardingits form and content. a Equatorial J2000.0 right ascension and declination. b Reliability flag. Single character flag that is related to the probability (P) that the extraction is a valid detection of a near infraredsource on the sky at the time of the observation. ”A” means P >>