Omega Centauri, Cambridge 2001

1

The RR Lyrae of The RR Lyrae of Centauri: a Centauri: a

theoretical route theoretical route

(progress report)

Castellani V.1, Degl’Innocenti S.1, Marconi M.2

1 Physics Department, University of Pisa, Italy2 Capodimonte Astronomical Observatory, Naples, Italy

Omega Centauri, Cambridge 2001

2

Cen RR Lyrae Rich sample by Kaluzny et al. (1997) Metallicity by Rey et al. (2000)

An exciting possibility……However :

<V> ?

[Fe/H]?

Omega Centauri, Cambridge 2001

3

Bearing in mind such a “warning” let us try to move along a theoretical route….

Sub-sample of the Kaluzny et al. RR Lyrae for whichthe metallicity evaluation from Rey et al. is available

Cen RR Lyrae

Omega Centauri, Cambridge 2001

4

Is theory consistent with observations?

Z peaked at 0.0004 (Rey et al. 2000, Suntzeff & Kraft 1996)

Omega Centauri, Cambridge 2001

5

Visual magnitude distribution

The bulk of RR Lyrae has a mean visual

magnitude in the range 14.4514.60 mag.

By adopting:

(mv-Mv ) =14.050.11 (Thompson et al. 2001)

Kaluzny et al. sample

<Mv> approximately in the range 0.40.55 mag

Omega Centauri, Cambridge 2001

6

Evolutionary theory

Consistent with observations…nothing more until more precise [Fe/H] and <V> will be available

Omega Centauri, Cambridge 2001

7

Pulsational theory

The strongest constraint:

Light curve

(P,31, A are only a partial parametrization of the light curve)

Let us recall the scenario:

UComae : a field RRc

observations: P=0.29 days, E(B-V) 0

Omega Centauri, Cambridge 2001

8

(Bono, Castellani, Marconi, 2000, ApJ 532, L129)

________________________(see Bono & Stellingwerf, 1994, for a description of the adoptednon linear, convective, hydrodinamical code)

Comparison between theory and observation for UComae light curve

by assuming the mass in the range predicted by evolutionary theory for the observed P the fitting exists L, Te

*

(in agreement with independent evaluations available in the literature)

*We recall the Bono et al. (1997) relations:LogPF =11.627 +0.823 LogL -0.582 LogM -3.506 LogTe

LogPFO=10.789 +0.800 LogL -0.594 LogM -3.309 LogTe

Omega Centauri, Cambridge 2001

9

To appreciate the sensitivity of the method: varying the temperature by 50 oK and <Mbol> by 0.03 mag.

Omega Centauri, Cambridge 2001

10

Centauri: a different approach Let us assume a distance modulus

(DM=14.050.11) and thus <Mv> for RR Lyrae

Given the period, for each Te, one finds a mass and a light curve morphology

RR ab type light curve 99B P=0.627 days, [Fe/H]= -1.740.05

(however the results are barely sensitive to the metallicity value within the metal poor range*)

*see e.g. Bono, Incerpi & Marconi 1996, Bono et al. 1997

Omega Centauri, Cambridge 2001

11

For the given DM (DM=14.05 <Mv>=0.38) the temperature is fixed mainly by the required amplitude, in fact:

Light curves at fixed period and <Mv> but with different Te

Te A : For RRab the amplitude increases by increasing

the effective temperature (at fixed period)

One obtains the pulsator mass

Omega Centauri, Cambridge 2001

12

What happens if DM is changed?

A different distance modulus has been applied to each lightcurve to obtain the observed <V>14.43 for the light curve

99

The amplitude is almost constant

..but the light curve shape changes

Light curves at fixed period and Te but with different <Mv>

Omega Centauri, Cambridge 2001

13

Best fit

In this case pulsational theory is consistent withobservations and stellar evolution

DM=14.05

…. The fit is not perfect, but satisfactory.. ...at least to characterize a method

Summarising:

By fitting Av One finds Te

DMBest fit of the light curve

(In agreement with the DM estimate by Thompson et al. 2001)

Note that the estimated stellar mass agrees with the one predicted by stellar evolution!

mass

Omega Centauri, Cambridge 2001

14

If one changes the DM by about 0.1 mag. the light curve fit appears less satisfactory upper limit for a DM variation

Omega Centauri, Cambridge 2001

15

A variation of the distance modulus by 0.15 mag. can be definitely ruled out

Omega Centauri, Cambridge 2001

16

This is the “theoretical truth”… ….how true is this truth?

Pulsational computations are quite sophisticated: one has to account for difficult mechanisms as eddy viscosity, overshooting and so on....

The true truth: we were already surprised of the rather beautiful agreement….

We would like to test deeper the theory:

Firmer Te Better [Fe/H] Velocity curve

A strong test! Details of LC depend on Za further prediction

Goal*: a well tested and well calibrated theory promises to provide reliable distance modulus from just one (or few) RR!

…the work is in progress...

________

*These results confirm a similar analysis on a LMC bump Cepheid by Wood et al. (1997)