The RR Lyrae of w Centauri: a
theoretical route
(progress report)
Castellani V.1, Degl’Innocenti S.1, Marconi M.2
1
Physics Department, University of Pisa, Italy
2 Capodimonte Astronomical Observatory, Naples, Italy
Omega Centauri,
Cambridge 2001
1
w 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
2
wCen RR Lyrae
Sub-sample of the Kaluzny et al. RR Lyrae for which
the metallicity evaluation from Rey et al. is available
Bearing in mind such a “warning” let us
try to move along a theoretical route….
Omega Centauri,
Cambridge 2001
3
Is theory consistent with observations?
Z peaked at  0.0004
(Rey et al. 2000, Suntzeff & Kraft 1996)
Omega Centauri,
Cambridge 2001
4
Visual magnitude distribution
Kaluzny et al. sample
The bulk of RR Lyrae has a mean visual
magnitude in the range 14.4514.60 mag.
By adopting:
(mv-Mv ) =14.050.11 (Thompson et al. 2001)
<Mv> approximately in the range 0.40.55 mag
Omega Centauri,
Cambridge 2001
5
Evolutionary theory
Consistent with observations…nothing more until
more precise [Fe/H] and <V> will be available
Omega Centauri,
Cambridge 2001
6
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
7
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)
Comparison between theory and observation for
UComae light curve
(Bono, Castellani, Marconi, 2000, ApJ 532, L129)
*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
________________________
(see Bono & Stellingwerf, 1994, for a description of the adopted
non linear, convective, hydrodinamical code)
Omega Centauri,
Cambridge 2001
8
To appreciate the sensitivity of the method: varying
the temperature by 50 oK and <Mbol> by  0.03 mag.
Omega Centauri,
Cambridge 2001
9
w Centauri: a different approach

Let us assume a distance modulus
(DM=14.050.11) 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]= -1.740.05
(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
10
For the given DM (DM=14.05  <Mv>=0.38)
the temperature is fixed mainly by the
required amplitude, in fact:
Te  A  :
For RRab the amplitude increases by increasing
the effective temperature (at fixed period)
One obtains the pulsator mass
Light curves at fixed period and <Mv> but with different Te
Omega Centauri,
Cambridge 2001
11
What happens if DM is changed?
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
modulus
has 2001
been
12
A different distance
applied to each light
curve to obtain the observed <V>14.43 for the light curve 99
Summarising:
By fitting Av
One finds Te
Best fit of the light curve
DM
Best fit
mass
DM=14.05
(In agreement with the DM estimate by Thompson et al. 2001)
…. The fit is not perfect, but satisfactory..
...at least to characterize a method
Note that the estimated stellar mass agrees with
the one predicted by stellar evolution!
In this case pulsational theory is consistent with
observations and stellar evolution
Omega Centauri,
Cambridge 2001
13
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
14
A variation of the distance modulus by  0.15 mag.
can be definitely ruled out
Omega Centauri,
Cambridge 2001
15
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 Z
a 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)
Omega Centauri,
Cambridge 2001
16