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Mem. S.A.It. Vol. 79, 726

SAIt 2008 c

Memoriedella

Modeling M3 RR Lyrae light curves

M. Marconi

1

and S. Degl’Innocenti

2

1

Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Napoli, Via Moiariello 16, I-80131 Napoli, Italy e-mail: marcella@na.astro.it

2

Dipartimento di Fisica, Universit`a di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy e-mail: scilla@df.unipi.it

Abstract.

Nonlinear convective pulsation models of RR Lyrae stars are used to obtain a theoretical fit of the observed light curves for a number of pulsators in the Galactic glob- ular cluster M3, with the purpose of constraining their intrinsic stellar parameters and the cluster distance modulus. The dependence of the fit quality on the input stellar properties is investigated and the self consistency of the adopted theoretical scenario is discussed.

Key words.

Stars: evolution – Stars: variables: RR Lyr – Stars: distances

1. Introduction

An important advantage of nonlinear convec- tive pulsation models is the possibility to pre- dict the time variations of the relevant stellar properties, along a pulsation cycle, and in par- ticular to reproduce the observed light and ra- dial velocity curves of true pulsators.

The model fitting of light curves has been successfully applied to both Classical Cepheids and RR Lyrae (Wood, Arnold and Sebo 1997, Bono, Castellani, Marconi 2000, 2002, Keller & Wood 2006).

In this poster we apply the method to seven RR Lyrae (4 RRc and 3 RRab, see Table 1) belonging to the Galactic globu- lar cluster M3 and observed by Corwin &

Carney (2001). Specific pulsation models with Z=0.001, Y=0.24 were computed by means of the nonlinear nonlocal time-dependent con- vective pulsation code adopted by our group (Bono, Castellani, Marconi 2000 and refer-

Send offprint requests to: M. Marconi

ences therein). A detailed discussion of this investigation can be found in Marconi &

Degl’Innocenti (2007, hereinafter MD07).

2. Fit of V128 light curve: effects of variations in the input model parameters

Isoperiodic model sequences for the observed period of V128 were built. The resulting bolo- metric light curves were transformed into the observational bands by means of the static model atmospheres by Castelli, Gratton &

Kurucz (1997a). The three panels of Fig.1 show the dependence of the model fitting on variations of effective temperature and lumi- nosity at fixed mass (left), of mass and effec- tive temperature at fixed luminosity (middle) and of mass and luminosity at fixed effective temperature (right).

Similar results are obtained in the B and I

bands. This analysis seems to suggest that the

key parameter affecting the light curve mor-

phology is the effective temperature. By ac-

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Marconi & Degl’Innocenti: Modeling M3 RR Lyrae 727 Table 1. Observed properties of the investigated RR Lyrae.

Star Period < V > < B > − < V > Type

V128 0.292 15.620 0.216 c

V75 0.314 15.626 0.240 c

V152 0.326 15.496 0.201 c

V126 0.348 15.609 0.265 c

V72 0.456 15.679 0.247 ab

V6 0.514 15.686 0.285 ab

V120 0.640 15.676 0.384 ab

Table 2. Accepted ranges of the physical parameters (mass,luminosity and effective temperature) for variables V128, V126, V72 and V152, together with the corresponding range of apparent visual distance modulus and intensity weighted (B-V) color. For the V152 variable the range in temperature (color) has not been calculated (see MD07).

Variable Mass log(L/L

) T

e f f

µ

V

<B> - <V>

[M

] [K] [mag] [mag]

V128 0.60÷0.71 1.595÷1.670 7050÷7150 14.92÷15.11 0.227÷0.240 V126 0.60÷0.75 1.683÷1.775 7020÷7080 15.12÷15.35 0.235÷0.244 V72 0.60÷0.73 1.643÷1.710 6900÷7000 15.04÷15.22 0.227÷0.237

V152 0.60÷0.69 1.666÷1.711 14.94÷15.04

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 phase

15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2

V

logL/Lo=1.630 T=7045 K DM=14.99 logL/Lo=1.640 T=7085 K DM=15.02 logL/Lo=1.650 T=7125 K DM=15.05 logL/Lo=1.660 T=7165 K DM=15.09 V128 P=0.292 M=0.67MO α=1.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 phase

15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2

V

M=0.64Mo T=7185 K DM=15.05 M=0.66Mo T=7145 K DM=15.05 M=0.67Mo T=7125 K DM=15.05 M=0.68Mo T=7105 K DM=15.05 M=0.70Mo T=7065 K DM=15.05 P=0.292 logL/LO=1.650

V128

α=1.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 phase

15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2

V

M=0.63Mo logL/Lo=1.630 DM=15.00 M=0.65Mo logL/Lo=1.640 DM=15.02 M=0.67Mo logL/Lo=1.650 DM=15.05 M=0.69Mo logL/Lo=1.660 DM=15.07 M=0.71Mo logL/Lo=1.670 DM=15.11 M=0.75Mo logL/Lo=1.690 DM=15.15 V128 P=0.292 Te=7125 K

α=1.5

Fig. 1. Predicted light curves constrained to the observed period of V128 for the labeled fixed values of mass (left panel), luminosity (middle panel) and effective temperature (right panel).

cepting only the models reproducing the ob- served light curve within 0.05 mag at all the pulsation phases, we obtain the ranges for the distance and the stellar parameters reported in Table 2.

3. Model fitting of the other stars

A similar study is performed for the other se- lected stars. Fig. 2 shows the results at fixed ef- fective temperature for V126, V72 and for the more luminous variable V152 (see Table 1).

We selected this star because a further check

of the reliability of the estimated cluster dis-

tance modulus is to analyze the properties of

pulsators with a different luminosity: as these

stars are also cluster members, the obtained

distance modulus has to be in agreement with

the previous results. One of the possible so-

lutions for variables V75 and V6 is shown in

MD07. No reasonable fit is obtained for the rel-

atively red, long period RRab V120. However

for the very red RR Lyrae, the modeling of

the light curve morphology already appeared

problematic in previous applications (see e.g

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728 Marconi & Degl’Innocenti: Modeling M3 RR Lyrae

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 phase

15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2

V

M=0.60Mo logL/Lo=1.683 DM=15.12 M=0.62Mo logL/Lo=1.694 DM=15.15 M=0.63Mo logL/Lo=1.700 DM=15.16 M=0.64Mo logL/Lo=1.705 DM=15.17 M=0.65Mo logL/Lo=1.710 DM=15.18 V126 P=0.348 α=1.5 Te=7020 K

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 phase

14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5

V

M=0.60 Mo logL/Lo=1.643 DM=15.04 M=0.65 Mo logL/Lo=1.670 DM=15.11 M=0.66 Mo logL/Lo=1.675 DM=15.13 M=0.67 Mo logL/Lo=1.680 DM=15.14 M=0.69 Mo logL/Lo=1.690 DM=15.16 M=0.71 Mo logL/Lo=1.700 DM=15.19 M=0.73 Mo logL/Lo=1.710 DM=15.22 M=0.74 Mo logL/Lo=1.715 DM=15.24 M=0.75 Mo logL/Lo=1.720 DM=15.26 V72 P=0.456

Te=6950 K α=2.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 phase

15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2

V

M=0.60 Mo logL/Lo=1.666 DM=14.94 M=0.61 Mo logL/Lo=1.671 DM=14.95 M=0.63 Mo logL/Lo=1.681 DM=14.97 M=0.65 Mo logL/Lo=1.691 DM=14.99 M=0.67 Mo logL/Lo=1.701 DM=15.03 M=0.69 Mo logL/Lo=1.711 DM=15.04 M=0.71 Mo logL/Lo=1.721 DM=15.06 V152 P=0.326 T=7087 K

Fig. 2. Dependence of the modeling of V126, V72, V152 light curve on the input parameters when the effective temperature is kept fixed.

Marconi & Clementini 2005); this is probably due to the remaining uncertainties in the treat- ment of the coupling between pulsation and convection in the hydrodynamical models. The obtained ranges for all the selected stars are re- ported in Table 2.

4. Conclusions

We have successfully modeled the light curves of six variables (4 RRc and 2 RRab) of the globular cluster M3, covering a significant por- tion of the instability strip and a variety of pe- riods and light curve morphologies. For V128, V152, V126 and V72 the obtained accept- able ranges of stellar parameters (mass, lumi- nosity and effective temperature) and distance modulus are self-consistent and in agreement with stellar evolutionary predictions. Moreover a general agreement can be found with the physical parameters provided by Cacciari et al.

(2005, see MD07 for details) on the basis of a multicolor study. For the other two pulsators (V75 and V6), that show morphological fea- tures similar to the previous ones, the obtained stellar parameters and distance moduli are con- sistent with the already found ranges, confirm- ing the previous estimates. These results rep- resent a cross check for both evolutionary and pulsational theories.

Our final estimate for the distance modu- lus is µ

V

=15.10± 0.1 mag as derived as a mean of the individual determinations, while taking also into account the evolutionary constraints on the pulsator masses (see MD07), one ob- tains a weighted mean value of 15.05±0.02.

Our obtained distance modulus is consis- tent, within the uncertainties, with the results from other methods, for example with the de- termination by Ferraro et al. (1999), obtained from the comparison between the observed and predicted Zero Age Horizontal Branch lumi- nosity, as well as with the results by Marconi et al. 2003, based on additional pulsational meth- ods (see their Table 4). The precision of the technique could be further improved if accu- rate radial velocity curves will be available to- gether with photometric data covering both the optical and the near-infrared bands.

Acknowledgements. We are grateful to V. Castellani who inspired this work and constantly supported us.

We sincerely miss his personality, clearness and en- thusiasm in approaching the different issues of stel- lar astrophysics.

References

Bono, G., Castellani, Marconi, M. 2000, ApJL, 532, 129

Bono, G., Castellani, V., Marconi, M. 2002, ApJL, 565, 83

Cacciari, C., et al., 2005, AJ, 129, 267 Castelli, F., et al., L. 1997, A&A, 318, 841 Corwin, T. M. & Carney, B. W. 2001, AJ, 122,

3183

Ferraro, F. R., et al., 1999, AJ 118, 1738 Marconi, M., et al., 2003, ApJ, 596, 299 Marconi M., Degl’Innocenti S., 2007, A&A,

474, 557

Marconi, M., Clementini, G. 2005, AJ, 129, 2257

Wood, P.R., et al., 1997, ApJ, 485, 25

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