Seismology of "Little Rainer" (HD209775)
A. Moya, M.J. Goupil and M. A. Dupret
•Observational data
•Instability and histogram of differences
•Rotational splitting
•Statistical constraints
•Conclusions
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Observational data
Teff=7490 Klog Teff=3.872
L/LΘ=6.92log L/LΘ=0.84
v sin i=75km/s
[6.6071 c·d-1,33.8648 c·d-1]= [77.62 μHz,391.54 μHz]
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Observational data
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and histogram of differences
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and histogram of differences
Direct comparison
Theoretical – Observed spectra
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Stable
Overstable
Instability and histogram of differences
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and histogram of differences
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and histogram of differences
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Subtracting the rotational splittings
• We search for candidate multiplets in the observed spectrum
• For each multiplet, we keep the central frequency
and drop the others
• About 30 frequencies are dropped
• We compare the histogram with theoretical ones
without splittings (m=0)
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Subtracting the rotational splittings
Old histogram with splittings
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Subtracting the rotational splittings
New histogram without splittings
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Subtracting the rotational splittings
New histogram without splittings
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Rotational splitting
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Rotational splitting
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Rotational splitting
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
10 models per HR position
*000 αMLT=1.8, αov=0.2 and [Fe/H]=0
*001
*002
*003
[Fe/H]=
0.1
[Fe/H]=
0.2
[Fe/H]= [Fe/H]=-0.1
0.2
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
*004
*010
*020
*030
*100
*200
σov=0
σov=0.1
σov=0.3
σMLT=2.1
σMLT=1.5
Statistical constrains
Construct the χ2 defined as
n
 
2
N obs (i)  N theor (i) 
i 1
2
N obs (i )  N theor(i )
Nx= Number of differences in binning i
n= Number of binning
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
χ2<37.7Accept > 90%
1000 1001 1002 1020 1030 1100 1200 2000 2002 2030
χ2
31.7
24.4
32.7
37.2
23.0
31.1
34.2
37.8
%
accept
98
>99.5
97.5
90
>99.5
98.5
95
90
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
27.7
23.9
99.5 >99.5
Statistical constrains
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
0000 0001 0002 0030 0100 0200 1002 1100
χ2
36.8
28.9
26.6
31.0
33.6
33.7
32.2
31.7
%
accept
96
99.4
>99.5
98
96.5
96
95
98
4000 4001 4003 4010 4020 4030 4100 4200
χ2
27.3
29.5
33.8
24.9
25.6
29.3
27.4
27.3
%
accept
99.5
99.3
96
>99.5
>99.5
99
99.5
99.5
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
 dyn 
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
R3
GM
Statistical constrains
Without models with [Fe/H]=-0.1 and -0.2
and αov=0
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
Δν=52 μHz
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Statistical constrains
Without models with [Fe/H]=-0.1 and -0.2
and αov=0
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Conclusions
•Histogram of differences gives a
necessary but not sufficient condition for
modelling.
•We need further constraints or theoretical
techniques
•Better computational tools including
rotation for a direct comparison with the
observed frequencies
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Conclusions
Global characteristics
M/MΘ
Age
(My)
αov
[Fe/H]
Xc
MAX
1.9
1166
0.1
0.2
0.47
MIN
1.6
786
0.3
0
0.34
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Conclusions
Through the instability and histogram of
differences study:
1. The models matching observations have luminosity
larger than observed
2. No accepted models with [Fe/H]<0 or αov=0
3. The rotational rate is observed and then the angle i
is predicted in the range [70º,50º]
4. All the acceptable models have a similar dynamical
time, directly related with observed large separation
5. Largest amplitude mode is never predicted as radial
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Consequences for COROT
•Procedure for the systematic modelling of massive
photometric data
•We can estimate the non-linear effects Q, where
dA
3
 A  QA
dt
To understand if Q is mode and/or model
dependent we need similar result from many
stars, that is... COROT
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Growth rates:
Comparison between TDC and FC results
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Instability and difference’s histogram
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
Return
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005
The chi-square probability function Q(χ2|ν)
is the probability that the sum of the
squares of ν random normal variables of
unit variance (and zero mean) will be
grater than χ2.
This is the meaning of the accepted
percentage of the histogram.
Seismology of "Little Rainer" (HD209775)
COROT week 9, ESTEC 07/12/2005