absolute properties of the eclipsing binary star rt coronae borealis

ABSOLUTE PROPERTIES OF THE ECLIPSING BINARY STAR RT CORONAE BOREALIS

Jeffrey A. Sabby1and Claud H. Sandberg Lacy

1

Department of Physics, University of Arkansas, Fayetteville, AR 72701; [email protected], [email protected]

ABSTRACT

We present an analysis of existing photometric observations in U, B, and V, and a new light curve in V, aswell as spectroscopic observations, of the 5.1 day period, double-lined main-sequence eclipsing binaryRT CrB. From the analysis of the light curves and radial velocity curves, we have determined the masses andradii of the components: 1.343 � 0.010 M� and 2.615 � 0.04 R� for the primary (hotter) component,1.359 � 0.009 M� and 2.946 � 0.05 R� for the secondary (cooler) component. The formal uncertainties inthe masses are both less than 1%, and the formal uncertainties in the radii are both less than 2%. Based on theanalyzed light curves, as well as the combined absolute photometry of the system, we estimate effectivetemperatures of 5781 � 100 K for the primary component and 5134 � 100 K for the secondary component,corresponding to spectral types of G5 and K0, respectively. Projected rotational velocities (v sin i) from thespectrograms are measured as 25 � 2 km s�1 for the primary component and 33 � 3 km s�1 for the secondarycomponent and are consistent with rotation that is synchronous with the orbital motion. Evolutionary tracksfrom the current models are in good agreement with the observations for a system of about age 3.5 � 109 yrwith a slightly nonsolar chemical composition. We also report an approximate DP/P = 3.0 � 10�6 decreasein the orbital period over 37 years.

Key words: binaries: eclipsing — binaries: spectroscopic — stars: evolution —stars: fundamental parameters — stars: individual (RT Coronae Borealis)

1. INTRODUCTION

The discovery of RT Coronae Borealis (=HD 139588,TYC 2039-1337-1, BD +29�2690; V = 10.21, � =15h35m59 9993, � = +29�38059>31, epoch J1960.7 and equi-nox J1950) as a variable star is due to Ceraski (1911).Hoffmeister, from 1914 to 1918, conducted photometricobservations of RT CrB and revealed its eclipsing nature(Beyer 1935). The light elements were analyzed and the starwas classified as an Algol-type binary by Beyer (1935). Thelight curves obtained by Hoffmeister, Beyer, and Rugemerwere published by Beyer (1935). Rugemer noticed a slightvariation in the depth of the secondary eclipse and suggestedthat the system be reclassified as an RR Lyrae type (Beyer1935). Beyer (1943) observed RT CrB for light variation in1935 and 1936, but the results were found to be inconclu-sive. For some time it appears that astronomers were notvery interested in RT CrB; nevertheless, in 1970, RT CrBappeared in a list of 22 close binaries published by Popper(1970). Popper reported that these binaries were showing Hand K emission outside of eclipse in at least one componentand with the primary (hotter) a main-sequence or subgiantstar. Popper (1976) goes on to report that these systems areshowing irregularities in their light curves and that H� emis-sion is absent or weakly present with variable intensity. RTCrB appears in a 1976 list of ‘‘ RS CVn type systems,’’ a defi-nition proposed byHall (1976) for binaries that have the fol-lowing characteristics: orbital periods from 1 to 14 days,strong emission in Ca ii H and K lines, a hot componentwith the spectral type of F or G, and a luminosity class of IVor V. Hall (1976) goes on to state two more characteristicsthat are seen in a large portion (but not all) of the systems:

H and K emission arises from either the cool star or both,and a distortion is present in the light curve outside ofeclipse. Hall & Kreiner (1980) included RT CrB in a paperstudying the period changes and mass-loss rates of 34 RSCVn type binaries, but because of the absence of absoluteproperties, no mass-loss rate for RT CrB was reported.During this period (1970–1984), RT CrB became a renewedtarget of several photometric observational programs, car-ried out by Popper & Dumont (1977) from 1972 June to1973 June; Zhai, Zhang, & Zhang (1982) from 1978 April toJuly; and Ibanoglu et al. (1985) from 1978 April to 1981October. In addition, several spectrograms of RT CrB werecollected by Popper (1990) from 1973May to 1984March.

The photometric data acquired by Zhai et al. (1982)showed the characteristics of a wavelike distortion in thelight curve outside of eclipse, a condition mentioned by Hall(1976). A recent light curve (2001; see x 5) shows these wave-like distortions again. The previous data given by Popper &Dumont (1977) and later data given by Ibanoglu et al.(1985) show no such wavelike distortion. Popper (1990) wasthe first to combine spectroscopic data with his own andprevious photometric data: Popper & Dumont (1977), Zhaiet al. (1982), and Ibanoglu et al. (1985). Analyzing thesedata sets, Popper determined the masses and radii of thecomponents: 1.40 � 0.05 M� and 2.6 � 0.2 R� for the pri-mary (hotter) component, 1.42 � 0.02M� and 3.0 � 0.2R�for the secondary (cooler) component. Other characteristicsof RS CVn type binaries (the analysis of Ca iiH andK emis-sion and H� emission) have been reviewed by Linsky(1984), Montesinos, Gimenez, & Fernandez-Figueroa(1988), Strassmeier et al. (1988), de Castro et al. (1990),Strassmeier et al. (1993), Frasca & Catalano (1994),Fernandez-Figueroa et al. (1994), Montes et al. (1996), andLiu, Huang, & Zhu (1997).

The evolutionary status of RS CVn type binary systemsis far from clear. Hall (1972) argued that the secondarycomponent of the systems may be in a state of

1 Visiting Astronomer, Kitt Peak National Observatory, NationalOptical Astronomy Observatory, which is operated by the Association ofUniversities in Astronomy, Inc., under cooperative agreement with theNational Science Foundation.

The Astronomical Journal, 125:1448–1457, 2003March

# 2003. The American Astronomical Society. All Rights Reserved. Printed inU.S.A.

1448

pre–main-sequence contraction, but neither close nebulos-ity nor the presence of Li lines has been detected. Oliver(1974) suggested a slow mass transfer via an intensified stel-lar wind. In a discussion of the evolutionary status of RSCVn type binaries, Popper &Ulrich (1977) gaveM sin3 i forthe hotter and cooler components as 1.27 and 1.34 M�,respectively. Using this information, Ulrich & Popper(1974) proposed that the components of RS CVn type sys-tems are in their post–main-sequence evolution by normalsingle-star processes; however, the evolution of these stars ismodified by the slow process of mass exchange (�5 � 10�11

M� yr�1; Popper & Ulrich 1977). Mullan (1982) proposedthat the cooler component of the RS CVn type systemscould be undergoing recent, rapid mass loss (�2 � 10�9M�yr�1) due to recent evolution of the secondary (cooler) staracross the velocity dividing line, which separates stars withrapid outflow from stars without rapid outflow. Whateverthe explanation, it is obvious that in order to better under-stand the evolutionary status of RS CVn type binary sys-tems, we must first look at their fundamental properties. Byunderstanding these fundamental properties along with theother characteristics of RS CVn type systems, a workablemodel may be developed. In this paper, we will give adetailed analysis for RT CrB along with some discussion ofthe evolutionary status of this system.

2. SPECTROSCOPIC OBSERVATIONSAND REDUCTIONS

Spectroscopic observations were collected with a varietyof telescopes over a period of 16 years. At KPNO, we usedthe 2.1 m and coude feed telescopes from 1984 to 1999 with

several different CCD detectors. The spectrograms havebeen measured in the visible red region. Those spectra covera range of about 10 nm centered at 642 nm, with a resolutionof about 0.02 nm (2 pixels) during the years 1984, 1989,1990, and 1994. The spectra obtained during 1998 and 1999cover about 32 nm centered at 642 nm and have a resolutionof 0.03 nm. Wavelengths were calibrated with observationsof a ThAr hollow-cathode emission tube. The signal-to-noise ratio was typically 50–100. It should be noted that wewere able to identify seven usable absorption-line pairs perspectrogram. We used the Fe i 640 nm line, Ca ii 646.1 nmline, and five weaker lines.

Rotational velocities (v sin i) were measured from sixKPNO spectra of RT CrB. The high signal-to-noise ratiospectra were obtained from the following sets: one in 1989,one in 1990, one in 1994, one in 1998, and two in 1999. Thesix spectra used for determining rotation were taken whenRT CrB was near quadrature. Measured line widths werecompared with spectra of � Vir (=HR 4540, F9 V), forwhich v sin i = 3 km s�1 (Hoffleit & Jaschek 1982). Thespectrograms of � Vir were synthetically broadened withthe rotational profile of Gray (1992, p. 374) for a range ofrotational speeds until a match was found for the binary starfeatures. The comparison star was chosen to be close to thespectral type of RT CrB and was observed with the sameinstrumental configuration as the binary. The resultant val-ues of v sin i are 25 � 2 km s�1 for the hotter, smaller, moreluminous, and slightly less massive primary star (star A)and 33 � 3 km s�1 for the cooler, larger, slightly more mas-sive secondary star (star B).

Radial velocities were determined from the KPNOspectrograms by cross-correlation of RT CrB spectra with

TABLE 1

Dates of Minimum and Residuals for RT Coronae Borealis

HJD

(2,400,000+)

Error

(days) Typea Year Meth.b Epoch

O�C

(days) Ref.

27,623.393.................. 0.03 1 1934.51 v �2778 �0.03377 1

27,628.504.................. 0.03 1 1934.52 v �2777 �0.03991 1

27,659.221.................. 0.03 1 1934.61 v �2771 �0.02577 1

27,710.369.................. 0.03 1 1934.75 v �2761 �0.04921 1

27,966.219.................. 0.03 1 1935.45 v �2711 �0.05638 1

27,976.480.................. 0.03 1 1935.48 v �2709 �0.02967 1

28,022.494.................. 0.03 1 1935.60 v �2700 �0.06996 1

28,068.492.................. 0.03 1 1935.72 v �2691 �0.12625 1

28,109.416.................. 0.03 1 1935.84 v �2683 �0.13940 1

28,273.281.................. 0.02 1 1936.29 pg �2651 �0.02299 2

36,404.445.................. 0.01 1 1958.55 pp �1062 �0.00001 3

36,675.560.................. 0.01 1 1959.29 pp �1009 �0.09360 3

36,757.435.................. 0.01 1 1959.51 pp �993 �0.09289 3

41,833.7323................ 0.0004 1 1973.41 c �1 �0.00194 4

41,838.8504................ 0.0004 1 1973.43 pe 0 �0.00098 4

43,640.0872................ 0.0004 1 1978.36 pe 352 +0.00131 5

44,433.2412................ 0.0009 1 1980.53 c 508 �0.00193 6

44,791.4423................ 0.0009 1 1981.51 pe 577 �0.00087 6

50,640.3389................ 0.001 1 1997.52 pe 1720 +0.00072 7

52,011.7312................ 0.0009 1 2001.28 pe 1988 �0.00144 8

a Type 1 = primary eclipse.b Method: (pg) photographic; (pp) patrol plate; (v) visual; (pe) photoelectric; (c) calculated from

the phase correction for epoch error in this paper and not used to compute the linear ephemeris stated ineq. (1).

References.—(1) Lause 1936; (2) Beyer 1943; (3) Huth 1964; (4) Popper 1990; (5) Zhai et al. 1982;(6) Ibanoglu et al. 1985; (7) Lacy et al. 1998; (8) Lacy et al. 2002a.

ABSOLUTE PROPERTIES OF RT CrB 1449

https://www.researchgate.net/publication/253413722_The_Observation_and_Analysis_of_Stellar_Photospheres?el=1_x_8&enrichId=rgreq-c32d0f947a3223679f93c251d2e11f3a-XXX&enrichSource=Y292ZXJQYWdlOzIzMTAyMzYyMztBUzoxNTg3MDAxMjc5MjQyMjVAMTQxNDg0ODQ2NzgyOQ==

spectra of � Vir obtained during the same observing run.Spectrograms of � Vir were first synthetically broadened tomatch the width of the appropriate binary star component.The IRAF2 task FXCOR was used in the radial velocityanalysis. The adopted radial velocity for � Vir is +4.3 kms�1 (Mayor & Maurice 1985). Table 2 below presents thevelocity measurements based on the KPNO spectra.

3. ORBITAL EPHEMERIS

In order to derive the best possible ephemeris for ourspectroscopic solution, and for our light-curve solutionsfound in x 5, we collected all available times of eclipsefrom the literature. Dates of minima were collected fromHall & Kreiner (1980), Zhai et al. (1982), Ibanoglu et al.(1985), Popper (1990), Lacy et al. (1998), and Lacy,Straughn, & Denger (2002a). We first tried to solve for alinear ephemeris using all eclipse timings collected, butthis showed that there was a noticeable period changeoccurring somewhere between the eclipse timings listedby Hall & Kreiner prior to those of Zhai et al. and allsubsequent eclipse timings listed in this paper. We thensolved for a linear ephemeris based only on the recentminima, adopting errors from the observed times ofeclipse from Zhai et al. (1982), Ibanoglu et al. (1985),Popper (1990), and Lacy et al. (1998, 2002a). Weobtained

Min: I ¼ HJD 2,441,838.85138ð31Þ þ 5:11714349ð41ÞE ;

ð1Þ

where the standard errors of the elements are given inparentheses in units of the last decimal place. The timesof minimum and the residuals are listed in Table 1. TheO�C residuals, computed from the ephemeris in equation(1) and plotted against the epoch number, are presentedin Figure 1. The ephemeris given above was adopted foruse in our spectroscopic and photometric solutionsbelow.

4. SPECTROSCOPIC ORBITAL SOLUTION

With the velocities taken from the spectroscopic observa-tions and reductions of x 2 and the ephemeris given in equa-tion (1), we have derived a spectroscopic orbit for RT CrB.Table 2 gives the radial velocities for each component alongwith their corresponding residuals from the fit. During thederivation of the spectroscopic orbit, the eccentricity ini-tially was allowed to vary and then was fixed at zero. Whenthe eccentricity was allowed to vary, the results were as fol-lows: e1 = 0.0017 � 0.0048 for the primary (hotter) star,e2 = �0.0025 � 0.0042 for the secondary (cooler) star. Theresults show that for purposes of our final derivation, wecan state that the spectroscopic analysis finds the orbitto be circular (e = 0). The elements obtained from the

Fig. 1.—Ephemeris curve for RT CrB. Plotted points are from Table 1.TheO�C residuals were computed from the ephemeris in eq. (1).

Fig. 2.—Radial velocity curves of RT CrB from our final spectroscopicsolution. The open circles are KPNO observations of the primary, and thefilled circles are for the secondary. Phases are from the ephemeris in eq. (1),where zero phase corresponds to conjunction with the hotter primary starbehind.

Fig. 3.—Light curve obtained at Kimpel Observatory with the URSArobotic telescope in the V band along with fitted solution from the NDEmodel. This is a preliminary fit; hence, no solutions will be given here. They-axis is the differentialV-bandmagnitude of RTCrB using the comparisonstar GSC 02039-00004. The ephemeris equation used in this preliminary fitwas taken from Popper (1990) and is as follows: 2,441,838.85104(32) +5.11714489E(60). Phases are given in Table 4.

2 IRAF is distributed by the National Optical AstronomyObservatory.

1450 SABBY & LACY Vol. 125

spectroscopic fit (e = 0) are presented in Table 3, and the fitto the radial velocities is shown in Figure 2.

5. PHOTOMETRIC OBSERVATIONS

No new photometric observations were taken during thetime of the spectroscopic observations. We have recentlyobtained a light curve in the V band during the year 2001

with the URSA robotic telescope (Lacy et al. 2002b). It isshown in Figure 3. The data are listed in Table 4. The lightcurve was obtained by differential photometry, and thecomparison star used for the observations of RT CrB wasGSC 02039-00004. The presence of wavelike distortions dueto spots is apparent. We have not attempted to rectify thelight curve to remove spot variations at this time, althougha preliminary fit with the Nelson-Davis-Etzel (NDE) model

TABLE 2

KPNO Radial Velocity Measurements of RT Coronae Borealis and Residuals

from Final Spectroscopic Orbit

HJD

(2,400,000+)

RVA

(km s�1)

RVB

(km s�1)

(O�C )A(km s�1)

(O�C )B(km s�1)

Orbital

Phase

45,869.7570................ +81.0 �88.0 +1.9 +1.4 0.726

45,870.7312................ +38.3 �45.7 +0.9 +2.4 0.916

45,871.7110................ �57.4 +49.5 +2.5 +1.5 0.108

46,071.0226................ �40.1 +25.7 �3.8 +1.0 0.057

46,072.0700................ �95.7 +77.1 �3.8 �2.6 0.262

46,155.8652................ +57.1 �70.2 �2.3 �0.3 0.637

46,156.8832................ +66.9 �77.8 �0.8 +0.4 0.836

46,247.7195................ +38.0 �50.8 �0.1 �1.0 0.588

46,248.7368................ +76.4 �90.2 �1.4 �2.0 0.787

47,653.8094................ �69.0 +57.3 +0.6 �0.4 0.368

48,015.7844................ �59.6 +48.3 �0.6 +1.1 0.106

48,016.7307................ �90.1 +75.6 �0.7 �1.6 0.291

48,018.8155................ +76.8 �85.9 +1.3 �0.1 0.698

49,487.7543................ +79.8 �91.4 �0.1 �1.2 0.760

49,488.7117................ +24.2 �33.6 +2.1 �0.6 0.947

49,489.7613................ �76.9 +65.6 �0.5 +1.2 0.153

49,490.7547................ �76.2 +66.1 +0.7 +1.3 0.347

50,938.7675................ �82.7 +72.8 +1.5 +0.8 0.320

50,940.8042................ +78.4 �90.0 +0.1 �1.4 0.718

50,941.7182................ +45.9 �56.6 �0.5 +0.5 0.896

50,942.6888................ �50.5 +36.7 �0.4 �1.6 0.086

50,942.7509................ �55.3 +43.2 +0.3 �0.6 0.098

50,943.7566................ �88.3 +77.9 +0.6 +1.2 0.294

51,247.9506................ +80.6 �90.0 +0.7 +0.2 0.741

51,247.9927................ +80.8 �89.6 +0.7 +0.8 0.749

51,249.9984................ �72.6 +61.3 �0.1 +0.8 0.141

51,309.7696................ +71.3 �81.7 �0.4 +0.4 0.821

51,309.8548................ +67.6 �76.5 +0.2 +1.3 0.838

51,309.8983................ +64.2 �76.0 �0.7 �0.7 0.846

51,311.7068................ �87.9 +75.4 �0.05 �0.3 0.200

51,311.7502................ �88.8 +77.0 +0.4 +0.0 0.208

51,312.6994................ �58.2 +45.6 +1.3 �2.0 0.394

51,312.7474................ �53.7 +43.8 +1.7 +0.2 0.403

51,313.8255................ +50.7 �61.8 +0.4 �0.9 0.614

51,314.7557................ +76.0 �87.2 �0.6 �0.2 0.796

51,314.8427................ +73.4 �83.0 �0.2 +0.9 0.813

Note.—The primary is star A (hotter, less massive), the secondary is star B (cooler,more massive).

TABLE 3

Spectroscopic Orbital Elements (Circular) for RT Coronae Borealis

Parameter Symbol

Primary

(Star A, Hotter)

Secondary

(Star B, Cooler)

Center-of-mass radial velocity (km s�1)................ � �6.02 � 0.23 �5.24 � 0.20

Radial velocity semiamplitudes (km s�1) .............. K 86.12 � 0.29 85.16 � 0.24

Mass ratio............................................................ q 1.011 � 0.004

Minimummasses (M�) ........................................ M sin3 i 1.325 � 0.007 1.340 � 0.007

Projected semimajor axis (Gm) ............................ a sin i 6.060 � 0.020 5.993 � 0.017

Number of observations (KPNO) ........................ Nobs 36 36

Standard error for KPNO (km s�1) ...................... � 1.38 1.18

No. 3, 2003 ABSOLUTE PROPERTIES OF RT CrB 1451

TABLE 4

Photometric Observations in V of RT Coronae Borealis

Phasea DV Nb Phasea DV Nb Phasea DV Nb Phasea DV Nb

0.75264 .... �1.896 25.00 0.00813 .... �1.302 25.00 0.15605 .... �1.869 25.00 0.39460 .... �1.906 25.00

0.75719 .... �1.879 25.00 0.00940 .... �1.328 25.00 0.15801 .... �1.881 25.00 0.39710 .... �1.894 25.00

0.75990 .... �1.876 25.00 0.01098 .... �1.357 25.00 0.15999 .... �1.885 25.00 0.39957 .... �1.888 25.00

0.76193 .... �1.871 25.00 0.01261 .... �1.393 25.00 0.16177 .... �1.875 25.00 0.40337 .... �1.888 25.00

0.76419 .... �1.865 25.00 0.01424 .... �1.422 25.00 0.16347 .... �1.878 25.00 0.40825 .... �1.895 25.00

0.76651 .... �1.873 25.00 0.01587 .... �1.447 25.00 0.16570 .... �1.875 25.00 0.41330 .... �1.898 25.00

0.76853 .... �1.887 25.00 0.01750 .... �1.487 25.00 0.16830 .... �1.878 25.00 0.41829 .... �1.901 25.00

0.77102 .... �1.877 25.00 0.01919 .... �1.520 25.00 0.17086 .... �1.884 25.00 0.42192 .... �1.891 25.00

0.77405 .... �1.884 25.00 0.02091 .... �1.543 25.00 0.17501 .... �1.882 25.00 0.42535 .... �1.902 25.00

0.77908 .... �1.887 25.00 0.02269 .... �1.582 25.00 0.18032 .... �1.890 25.00 0.43017 .... �1.897 25.00

0.78419 .... �1.901 25.00 0.02507 .... �1.615 25.00 0.18334 .... �1.905 5.00 0.43483 .... �1.896 25.00

0.78910 .... �1.890 25.00 0.02703 .... �1.648 25.00 0.20967 .... �1.899 25.00 0.43912 .... �1.906 25.00

0.79213 .... �1.879 25.00 0.02894 .... �1.684 25.00 0.21453 .... �1.904 25.00 0.44316 .... �1.899 25.00

0.79461 .... �1.895 25.00 0.03066 .... �1.709 25.00 0.22219 .... �1.886 25.00 0.44564 .... �1.908 25.00

0.79743 .... �1.883 25.00 0.03227 .... �1.745 25.00 0.22703 .... �1.883 25.00 0.44839 .... �1.911 25.00

0.80199 .... �1.863 25.00 0.03441 .... �1.769 25.00 0.22952 .... �1.884 25.00 0.45290 .... �1.896 25.00

0.80766 .... �1.850 25.00 0.03681 .... �1.793 25.00 0.23199 .... �1.888 25.00 0.45756 .... �1.889 25.00

0.81511 .... �1.852 25.00 0.03921 .... �1.819 25.00 0.23529 .... �1.888 25.00 0.45992 .... �1.858 25.00

0.81997 .... �1.878 25.00 0.04161 .... �1.842 25.00 0.23985 .... �1.898 25.00 0.46133 .... �1.858 25.00

0.82482 .... �1.870 25.00 0.04404 .... �1.865 25.00 0.24521 .... �1.904 25.00 0.46255 .... �1.842 25.00

0.82968 .... �1.855 25.00 0.04600 .... �1.877 25.00 0.25139 .... �1.888 25.00 0.46378 .... �1.839 25.00

0.83466 .... �1.861 25.00 0.04769 .... �1.882 25.00 0.25620 .... �1.893 25.00 0.46500 .... �1.836 25.00

0.83958 .... �1.857 25.00 0.04944 .... �1.875 25.00 0.26209 .... �1.896 25.00 0.46628 .... �1.823 25.00

0.84353 .... �1.871 25.00 0.05109 .... �1.875 25.00 0.26528 .... �1.915 25.00 0.46757 .... �1.807 25.00

0.84597 .... �1.858 25.00 0.05264 .... �1.881 25.00 0.26799 .... �1.913 25.00 0.46926 .... �1.791 25.00

0.84899 .... �1.867 25.00 0.05400 .... �1.881 25.00 0.27040 .... �1.906 25.00 0.47159 .... �1.776 25.00

0.85188 .... �1.867 25.00 0.05530 .... �1.880 25.00 0.27282 .... �1.900 25.00 0.47405 .... �1.768 25.00

0.85432 .... �1.865 25.00 0.05678 .... �1.881 25.00 0.27523 .... �1.899 25.00 0.47651 .... �1.749 25.00

0.85677 .... �1.872 25.00 0.05845 .... �1.866 25.00 0.27765 .... �1.895 25.00 0.47861 .... �1.721 25.00

0.85925 .... �1.872 25.00 0.06013 .... �1.878 25.00 0.28047 .... �1.894 25.00 0.48028 .... �1.711 25.00

0.86203 .... �1.873 25.00 0.06199 .... �1.866 25.00 0.29428 .... �1.892 25.00 0.48172 .... �1.708 25.00

0.87567 .... �1.838 25.00 0.06448 .... �1.857 25.00 0.30343 .... �1.882 25.00 0.48293 .... �1.694 25.00

0.88544 .... �1.830 25.00 0.06703 .... �1.873 25.00 0.30681 .... �1.884 25.00 0.48413 .... �1.680 25.00

0.89078 .... �1.829 25.00 0.06907 .... �1.883 25.00 0.30932 .... �1.893 25.00 0.48537 .... �1.665 25.00

0.89511 .... �1.849 25.00 0.07077 .... �1.884 25.00 0.31257 .... �1.886 25.00 0.48659 .... �1.659 25.00

0.89849 .... �1.855 25.00 0.07245 .... �1.885 25.00 0.32034 .... �1.874 25.00 0.48780 .... �1.658 25.00

0.91692 .... �1.844 25.00 0.07400 .... �1.881 25.00 0.32890 .... �1.887 25.00 0.48923 .... �1.647 25.00

0.92172 .... �1.844 25.00 0.07532 .... �1.877 25.00 0.33212 .... �1.884 25.00 0.49089 .... �1.642 25.00

0.92667 .... �1.837 25.00 0.07658 .... �1.873 25.00 0.33384 .... �1.881 25.00 0.49265 .... �1.641 25.00

0.93168 .... �1.859 25.00 0.07785 .... �1.867 25.00 0.33545 .... �1.882 25.00 0.49434 .... �1.627 25.00

0.93442 .... �1.858 3.00 0.07924 .... �1.873 25.00 0.33741 .... �1.879 25.00 0.49597 .... �1.619 25.00

0.95793 .... �1.821 25.00 0.08109 .... �1.879 25.00 0.33975 .... �1.881 25.00 0.49767 .... �1.614 25.00

0.96304 .... �1.762 25.00 0.08278 .... �1.879 25.00 0.34149 .... �1.880 25.00 0.49931 .... �1.620 25.00

0.96834 .... �1.675 25.00 0.08439 .... �1.873 25.00 0.34313 .... �1.875 25.00 0.50085 .... �1.622 25.00

0.97422 .... �1.555 25.00 0.08601 .... �1.875 25.00 0.34477 .... �1.887 25.00 0.50217 .... �1.637 25.00

0.97750 .... �1.529 25.00 0.08769 .... �1.883 25.00 0.34645 .... �1.886 25.00 0.50378 .... �1.637 25.00

0.98013 .... �1.479 25.00 0.08980 .... �1.881 25.00 0.34817 .... �1.881 25.00 0.50542 .... �1.647 25.00

0.98394 .... �1.388 25.00 0.09164 .... �1.899 25.00 0.34994 .... �1.880 25.00 0.50707 .... �1.652 25.00

0.98681 .... �1.342 25.00 0.09377 .... �1.891 25.00 0.35163 .... �1.887 25.00 0.50917 .... �1.667 25.00

0.98938 .... �1.299 25.00 0.09799 .... �1.906 25.00 0.35378 .... �1.884 25.00 0.51295 .... �1.698 25.00

0.99185 .... �1.278 25.00 0.11177 .... �1.853 25.00 0.35926 .... �1.876 25.00 0.51800 .... �1.741 25.00

0.99433 .... �1.254 25.00 0.11678 .... �1.857 25.00 0.36092 .... �1.881 25.00 0.52198 .... �1.753 25.00

0.99694 .... �1.226 25.00 0.12132 .... �1.865 25.00 0.36263 .... �1.874 25.00 0.52625 .... �1.783 25.00

0.99961 .... �1.229 25.00 0.12411 .... �1.865 25.00 0.36434 .... �1.892 25.00 0.52888 .... �1.807 25.00

0.00150 .... �1.245 25.00 0.12656 .... �1.882 25.00 0.36629 .... �1.893 25.00 0.53147 .... �1.823 25.00

0.00314 .... �1.247 25.00 0.12901 .... �1.882 25.00 0.36799 .... �1.888 25.00 0.53530 .... �1.847 25.00

0.00442 .... �1.263 25.00 0.13282 .... �1.885 25.00 0.36970 .... �1.894 25.00 0.53802 .... �1.861 25.00

0.00565 .... �1.275 25.00 0.13741 .... �1.898 25.00 0.37140 .... �1.895 25.00 0.54002 .... �1.879 25.00

0.00689 .... �1.284 25.00 0.14020 .... �1.908 25.00 0.37311 .... �1.890 25.00 0.54166 .... �1.876 25.00

0.00813 .... �1.302 25.00 0.14288 .... �1.897 25.00 0.37458 .... �1.895 25.00 0.54331 .... �1.889 25.00

0.00150 .... �1.245 25.00 0.14544 .... �1.899 25.00 0.37611 .... �1.901 25.00 0.54563 .... �1.897 25.00

0.00314 .... �1.247 25.00 0.14821 .... �1.892 25.00 0.37773 .... �1.896 25.00 0.54834 .... �1.894 25.00

0.00442 .... �1.263 25.00 0.15078 .... �1.885 25.00 0.38051 .... �1.895 25.00 0.55094 .... �1.902 25.00

0.00565 .... �1.275 25.00 0.15264 .... �1.868 25.00 0.38519 .... �1.889 25.00 0.55313 .... �1.893 25.00

0.00689 .... �1.284 25.00 0.15433 .... �1.883 25.00 0.39071 .... �1.903 25.00 0.55492 .... �1.894 25.00

(Etzel 1981; Popper & Etzel 1981) is not very different fromthe adopted orbit below. Given these circumstances, itappears worthwhile to reanalyze Popper & Dumont’s(1977) excellent U-, B-, and V-band photometric observa-tions, along with Zhai et al.’s (1982) V-band and Ibanogluet al.’s (1985) B- andV-band photometric observations.

Popper & Dumont’s and Ibanoglu et al.’s photometricdata were taken when spot activity appeared to be absent,whereas Zhai et al.’s were taken when spot activity appearedto be present. The photometric observations of Popper &Dumont, Zhai et al., and Ibanoglu et al. were fitted with theNDE model. The fit allowed the simultaneous adjustmentof the following six parameters: Js (surface brightness of thesecondary star, where the primary [hotter] component iseclipsed at phase zero), rp (radius of primary), k (ratio ofradii), i (orbital inclination), Dh (phase correction for epocherror), and SFACT (luminosity scaling factor). The ephem-eris presented in equation (1) was used in reanalyzing thelight curves.

Auxiliary quantities needed in the analysis were calcu-lated. Absolute photometric observations in the uvby� sys-tem are available in the works of Reglero et al. (1987) andHilditch & Hill (1975), summarized by Gimenez et al.(1991). We have applied to these values the prescription ofCrawford (1975) to determine the interstellar reddening,and the prescription of Olsen (1984) to determine theeffective temperature. The absolute photometric values arepresented in Table 5. Convective gravity-brightening coeffi-cients were calculated using the method of Martynov (1973)(0.427 inU, 0.355 in B, and 0.286 inV for the primary; 0.480in U, 0.399 in B, and 0.320 in V for the secondary). Optimalvalues of the limb-darkening coefficients were determinedby varying their values to achieve the minimum residuals,keeping the differences between the limb-darkening coeffi-cients of the primary (hotter) star and secondary (cooler)star at the values given by Dıaz-Cordoves, Claret, & Gime-nez (1995). The values are 0.839 in U, 0.788 in B, and 0.679in V for the hotter star, 0.908 in U, 0.853 in B, and 0.754 inV for the cooler star. The mass ratio was fixed at the spectro-scopic value (1.011). The results of the photometric analysespreviously published by Popper & Dumont (1977), Zhai etal. (1982), and Ibanoglu et al. (1985) are listed in Table 6.The individual U-, B-, and V-band light curves were reana-lyzed; then the mean values of the geometric quantities wereadopted, and the radiative quantities were determined fromthese. The results are listed in Tables 7, 8, and 9.

6. ABSOLUTE DIMENSIONS

The absolute dimensions and masses result from the com-bination of spectroscopic results in Table 3 and the light-curve results in Table 9. The masses are determined with aprecision of 0.7% and the radii are good to about 1.7%, asignificant improvement over the results of Popper (1990).The results for the absolute dimensions of RT CrB are givenin Table 10. The difference in the visual surface brightnessparameter (DFv) is related to the central surface brightnessof the secondary star (normalized to that of the primarystar) and limb-darkening coefficients, as discussed by Lacy,Frueh, & Turner (1987). The corrected difference in the visu-al surface brightness is DFv = 0.0614 � 0.0007 calculated

TABLE 4—Continued

Phasea DV Nb Phasea DV Nb Phasea DV Nb Phasea DV Nb

0.55668 .... �1.896 25.00 0.59541 .... �1.912 25.00 0.63374 .... �1.887 20.00 0.70776 .... �1.892 25.00

0.55834 .... �1.904 25.00 0.59799 .... �1.910 25.00 0.65678 .... �1.896 25.00 0.71175 .... �1.897 25.00

0.56045 .... �1.899 25.00 0.60051 .... �1.910 25.00 0.66184 .... �1.898 25.00 0.71471 .... �1.881 25.00

0.56372 .... �1.909 25.00 0.60421 .... �1.899 25.00 0.66679 .... �1.896 25.00 0.71806 .... �1.881 25.00

0.56671 .... �1.910 25.00 0.60842 .... �1.912 25.00 0.66980 .... �1.898 25.00 0.72289 .... �1.887 25.00

0.57001 .... �1.897 25.00 0.61096 .... �1.906 25.00 0.67347 .... �1.897 25.00 0.72794 .... �1.883 25.00

0.57377 .... �1.910 25.00 0.61338 .... �1.899 25.00 0.67601 .... �1.893 25.00 0.73173 .... �1.891 25.00

0.57786 .... �1.917 25.00 0.61573 .... �1.895 25.00 0.67783 .... �1.894 25.00 0.73478 .... �1.900 25.00

0.58041 .... �1.909 25.00 0.61748 .... �1.894 25.00 0.67961 .... �1.895 25.00 0.74473 .... �1.893 25.00

0.58288 .... �1.909 25.00 0.61910 .... �1.896 25.00 0.68194 .... �1.895 25.00 0.74943 .... �1.896 6.00

0.58536 .... �1.909 25.00 0.62081 .... �1.894 25.00 0.68494 .... �1.910 25.00 0.70776 .... �1.892 25.00

0.58783 .... �1.911 25.00 0.62312 .... �1.898 25.00 0.68934 .... �1.897 25.00

0.59034 .... �1.911 25.00 0.62555 .... �1.892 25.00 0.69434 .... �1.893 25.00

0.59289 .... �1.908 25.00 0.62939 .... �1.886 25.00 0.69795 .... �1.896 25.00

a Ephemeris equation used to compute phases: 2,441,838.85104(32) + 5.11714489(60)E. Phases are before the phase correction for epoch error stated inTable 1.

b Weight of normal points.

TABLE 5

Absolute Photometric Analysis

Symbol Value Ref.

b�y (observed).............. 0.459 � 0.009 1

m1 (observed) ................ 0.201 � 0.016 1

c1 (observed) ................. 0.365 � 0.020 1

H� ................................ 2.584 � 0.015 1

m1 (standard) ................ 0.287 � 0.002 2

c1 (standard) ................. 0.241 � 0.002 2

�m1................................ 0.086 � 0.005 2

�c1 ................................. 0.124 � 0.007 2

u�b ............................... 1.680 � 0.024 3

[u�b] ............................. 0.993 � 0.008 3

(b�y)0 ........................... 0.451 � 0.002 3

Eb�y .............................. 0.008 � 0.003 3

EB�V ............................. 0.011 � 0.004 3

Teff (K) .......................... 5445 3

References.—(1) Initial values taken from Table3 of Reglero et al. 1987 and Table 1 of Hilditch &Hill 1975, then averaged; (2) interpolated from Table6 of Olsen 1984; (3) calculated in this paper.


TABLE 6

Previous Photometric Analyses of RT Coronae Borealis

Author Band Na �b Wavec Meth.d rh rc

i

(deg) Lh

Zhai et al. 1982............................ V 254 0.07 0.06 R-M 0.164 0.169 84.86 0.639

B 335 0.017 0 NDE 0.149 0.159 85.05 0.663Ibanoglu et al. 1985.....................

V 335 . . . . . . . . . 0.163 0.149 85.52 0.694

U 239 0.008 0 NDE 0.136 0.177 84.6 0.507

B 252 . . . . . . . . . 0.148 0.170 84.5 0.567

Popper &Dumont 1977 ..............

V 252 . . . . . . . . . 0.160 0.160 84.7 0.632

a Number of observations given.b Standard deviation of nightly means outside eclipse.c Photometric wave amplitude (semiamplitude of a wave approximated by a sine wave) caused by starspot activity.d (R-M) Russell-Merrill method; (NDE)Nelson-Davis-Etzel method.

TABLE 7

Photometric Reanalyses of Popper & Dumont Data for RT Coronae Borealis

Parameter Symbol U B V

Surface brightness of secondary star.................. Js 0.430 � 0.006 0.511 � 0.004 0.598 � 0.004

Radius of primary (hotter) star (R�).................. rp 0.1466 � 0.0077 0.1562 � 0.0046 0.1470 � 0.0050

Radius of secondary (cooler) star (R�) .............. rs 0.1724 � 0.0090 0.1685 � 0.0049 0.1736 � 0.0061

Ratio of radii .................................................... k 1.176 � 0.093 1.079 � 0.053 1.181 � 0.064

Orbital inclination (deg).................................... i 84.50 � 0.11 84.40 � 0.08 84.36 � 0.06

Normalized luminosity of primary star ............. Lp 0.633 � 0.068 0.634 � 0.037 0.552 � 0.039

Standard error (mag) ........................................ � 0.01420 0.00849 0.00843

Number of observations.................................... N 239 252 252

TABLE 8

Photometric Reanalyses of Zhai et al. and Ibanoglu et al. Data for RT Coronae Borealis

Zhai et al. Ibanoglu et al.

Parameter Symbol V B V




Ratio of radii .................................................... k 1.173 � 0.084 1.134 � 0.100 0.960 � 0.130



Standard error (mag) ........................................ � 0.00965 0.01723 0.02131

Number of observations.................................... N 254 335 335

TABLE 9

Adopted Photometric Elements of RT Coronae Borealis

Parameter Symbol U B V




Ratio of radii .................................................... k 1.176 � 0.093 1.132 � 0.010 1.149 � 0.047



from Js (cooler) in the V band, translated into a color differ-ence D(B�V ) = 0.178 � 0.002 (Table 1 of Popper 1980).The color difference, along with the adopted value for inter-stellar reddening, gives the intrinsic color indexes and effec-tive temperatures in Table 10. The intrinsic colorscorrespond to stars of spectral type G5 and K0. An accuratedetermination of the metal content of RT CrB has not beengiven, but an estimate can be made from the uvby� photom-etry of the combined light cited in Table 5. We obtain avalue of [Fe/H] = �0.4 with an uncertainty of about 0.16dex by using the formula of Schuster & Nissen (1989),implying a metallicity about 40% of the solar value. In addi-tion, the projected rotational velocities adopted from mea-surements of our spectrograms are consistent with the

synchronous values resulting from the calculation ofabsolute dimensions.

7. DISCUSSION

The information from the analysis of the ephemeriscurve, light curves, and radial velocity curves for RT CrBare consistent. We have adopted weighted averages of theparameters in common for the photometric solutions andpresent them in Table 9. The absolute dimensions andmasses result from the combination of the spectroscopicand photometric orbits presented. The results are given inTable 10. These values are compared with the zero-age stel-lar evolutionary model of Schaller et al. (1992) in Figures 4and 5. The absolute visual magnitudes were calculated fromthe color indexes via the visual surface brightness parame-ters of Popper (1980, Table 1). The components of RT CrBfall above the main-sequence band. Our determinationshave formal errors smaller than 1% in the masses and 2% in

TABLE 10

Absolute Properties of RT Coronae Borealis

Property Symbol

Primary

(Star A, Hotter)

Secondary

(Star B, Cooler)

Mass (M�) ............................................................ M 1.343 � 0.009 1.359 � 0.010

Radius (R�) .......................................................... R 2.615 � 0.044 2.946 � 0.051

Surface gravity (cm s�2)......................................... log g 3.731 � 0.014 3.632 � 0.015

Measured rotational velocity (km s�1)................... v sin i 25.0 � 2.0 33.0 � 3.0

Synchronous rotational velocity (km s�1).............. Vsyn 25.9 � 0.4 29.1 � 0.5

(b�y)0 0.417 � 0.007 0.492 � 0.007Intrinsic color index ..............................................

(B�V )0 0.660 � 0.007 0.838 � 0.007

Surface temperature (K)........................................ T 5781 � 100 5134 � 100

Luminosity (L�).................................................... log L 0.838 � 0.032 0.736 � 0.036

Visual surface brightness....................................... F0v 3.748 � 0.007 3.684 � 0.007

Absolute bolometric magnitude ............................ Mbol 2.66 � 0.01 2.92 � 0.09

Absolute visual magnitude .................................... Mv 2.69 � 0.08 3.07 � 0.08

Eb�y 0.008 � 0.003Color excess ..........................................................

EB�V 0.011 � 0.004

Distance modulusa,b.............................................. V � Mv,tot � Av 8.05 � 0.08

Distance (pc)......................................................... d 408 � 15

a V-bandpass absorption taken fromTable 12 of Crawford&Mandwewala 1976.b ApparentV-bandpass magnitude (combined light of both stars) taken from SIMBAD database.

Fig. 4.—Absolute visual magnitude vs. logarithmic mass. Thecomponents of RT CrB are shown with error bars. Other components ofeclipsing binaries with well-determined properties are shown as open circles(Andersen 1991). The curve is the ZAMS of Schaller et al. (1992) forX = 0.68 andZ = 0.02. Fig. 5.—Same as Fig. 4, but for log (radius) vs. log (mass)


the radii. We proceed in this section to compare observa-tions with evolutionary models.

The evolutionary models we compared were those ofClaret (1995), Claret & Gimenez (1995), Schaller et al.(1992), and Schaerer et al. (1993). Details of the inputphysics are described by Claret & Gimenez (1992) andSchaller et al. (1992). Convection in these models istreated with a fixed mixing-length parameter of 1.52Hp

for Claret (1995) and Claret & Gimenez (1995), and1.60Hp for Schaller et al. (1992) and Schaerer et al.(1993). These values give the best fit between a stellarmodel and the observed properties of the Sun. A moder-ate amount of core overshooting is assumed (�ov =0.20Hp). The result of [Fe/H] = �0.4 implies Z = 0.008and points to the system’s having roughly half the metal-licity of the Sun. An acceptable fit of the fundamentalobservational data in Table 10 to the theoretical modelsof Claret (1995), Claret & Gimenez (1995), Schaller et al.(1992), and Schaerer et al. (1993) was found for an initialchemical composition of Y = 0.27 and Z = 0.013 at alogarithmic age of 9.54 � 0.02 (years). These models indi-cate the stars are in the terminal-age main sequence, justbeyond core hydrogen exhaustion.

As stated earlier, RS CVn type binary systems followseveral criteria given by Hall (1976): orbital periodbetween 1 and 14 days, strong emission lines in Ca ii Hand K, hot component having spectral type F or G, andluminosity class IV or V. Hall (1981) reported some sys-tems with orbital periods greater than 14 days; as aresult, Montesinos et al. (1988) no longer consider orbitalperiods to be a defining characteristic for RS CVn typesystems. Two more characteristics seen in a large numberof systems (but not all) also given by Hall (1976) includeH and K emission arising either from the cool compo-nent or from both components of the system, and distor-tions in the photometric light curves outside of eclipse.The general term chromospherically active binaries, cata-loged by Strassmeier et al. (1988, 1993), is used todescribe detached systems that show levels of chromo-spheric activity that are greater than that observed on theSun (Hilditch 2001, p. 286). When discussing the activitythat arises from the observed Ca ii H and K emission,Hilditch (2001) remarks that RS CVn type systems canbe included in this category (Strassmeier et al. 1988,1993), since they show characteristics of rapid axial rota-tion and deep convective envelopes, resulting in enhancedmagnetic activity (Montes et al. 1996). The magneticactivity demonstrates itself as photospheric starspots,strong emission lines from the chromosphere, andincreased X-ray emission from active coronae (Montes etal. 1996).

In considering this, we report an evolved system withnearly the same masses, 1.343 � 0.010M� for the (G5 class)hotter, and 1.359 � 0.009M� for the (K0 class) cooler. Themore massive of the two, the (K0) cooler star, is the moreevolved of the system (luminosity class IV). Refer to Figure5, where the components of RT CrB are shown with errorbars. Other components of eclipsing binaries with well-determined properties are shown as open circles (Andersen1991). The curve is the zero-age main sequence (ZAMS) ofSchaller et al. (1992) for X = 0.68 and Z = 0.02. Note thatthis system follows the typical RS CVn type pattern—thediagram confirms that the hotter component lies closer tothe ZAMS, while the cooler component is the more evolved.

The low surface gravities and rapid rotation of both stars(the more evolved being more active) in the RT CrB systemimply the presence of deep convective motions in the outerenvelopes, as described by Thomas (1967). This shouldresult in substantial magnetic activity, according to themodels of Belvedere (1983). The magnetic activity manifestsitself as photospheric starspots, noted by Zhai et al. (1982)and in this paper, detected through the presence of a wave-like distortion in the light curve of RT CrB outside ofeclipse. Furthermore, the magnetic activity manifests itselfthrough the detection of Ca ii H and K emission lines fromthe chromosphere, as noted by de Castro et al. (1990) andMontes et al. (1996). This leads us to conclude that at leastone component of RT CrB is chromospherically active andhence may be undergoing mass exchange through stellarwinds. Other indications (de Castro et al. 1990) point to thefact that both components of RT CrB are undergoing chro-mospheric activity, which is quite possible given the factthat both are so close in all physical attributes.

With regard to the possibility of mass exchange, RT CrBis detached by a wide margin and should not be undergoingmass exchange—at least not by Roche lobe overflow.Nevertheless, when we compare the orbital period given inequation (1) of this paper with that given by Hall & Kreiner(1980), we see an approximate DP/P = 3.0 � 10�6 decreasein the orbital period for RT CrB. The period decrease is evi-dent in Figure 6 (all dates of minimum listed in Table 1,excluding those calculated from the phase correction forepoch error, were used). In calculating the mass transfer forthe RT CrB system, we consider the conservative masstransfer model prescribed by Hilditch (2001, p. 163). In thissimple model, we assume that all of the mass lost by the sec-ondary (cooler, more massive star) is gained by the primary(hotter, less massive star). The total mass and the totalangular momentum of the binary system are conserved.This points to a conservative mass transfer of approxi-mately 1.15 � 10�4 M�. The time span between the orbitalperiods given in equation (1) of this paper and that given byHall & Kreiner (1980) is approximately 37 yr. This wouldlead to a conservative mass transfer rate of approximately3.11 � 10�6 M� yr�1, which is far beyond the enhanced rate

Fig. 6.—Ephemeris curve for RT CrB, showing a period decrease for thesystem. All dates of minimum listed in Table 1, excluding those calculatedfrom the phase correction for epoch error, were plotted. TheO�C residualswere computed from the ephemeris in eq. (1).

1456 SABBY & LACY Vol. 125

of �2 � 10�9 M� yr�1 put forth by Mullan (1982). There isa more likely alternative mechanism for explaining abruptperiod changes (alternating increases and decreases) indetached binaries that contain at least one convective star.The Applegate mechanism (Hall 1991) involves redistribu-tion of rotational angular momentum in one of the two starsand its reflex action on the orbital angular momentum.These changes supposedly are driven by magnetic cycles inthe convective star. Mass transfer (or mass loss) plays norole.

We thank the National Science Foundation for the grantsfor observation time at KPNO. We are also grateful toDaryl Willmarth at KPNO for assistance with the spectro-scopic observations there. Amber Straughn is thanked forher initial investigation of the URSA light curve of RT CrB.This research has made use of the SIMBAD database, oper-ated at CDS, Strasbourg, France, and of NASA’s Astro-physics Data System bibliographic services. We would alsolike to thank the referee of this paper for his diligence inproofreading our paper.

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No. 3, 2003 ABSOLUTE PROPERTIES OF RT CrB 1457



https://www.researchgate.net/publication/252355310_An_Introduction_to_Close_Binary_Stars?el=1_x_8&enrichId=rgreq-c32d0f947a3223679f93c251d2e11f3a-XXX&enrichSource=Y292ZXJQYWdlOzIzMTAyMzYyMztBUzoxNTg3MDAxMjc5MjQyMjVAMTQxNDg0ODQ2NzgyOQ==

https://www.researchgate.net/publication/252355310_An_Introduction_to_Close_Binary_Stars?el=1_x_8&enrichId=rgreq-c32d0f947a3223679f93c251d2e11f3a-XXX&enrichSource=Y292ZXJQYWdlOzIzMTAyMzYyMztBUzoxNTg3MDAxMjc5MjQyMjVAMTQxNDg0ODQ2NzgyOQ==

absolute properties of the eclipsing binary star rt coronae borealis

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