1. Calibration of stellar evolution using stellar pulsations
Marian Doru Suran, Nedelia Antonia Popescu
Astronomical Institute of the Romanian Academy
Supported by the Romanian Space Agency (ROSA) contract Nr. 124/

2. Abstract Close to the main sequence the HR diagram is confusing
as stars of similar global properties but with different stages
of evolution occupy the same position.
Pulsating stars (both pms and post-ms) have been
discovered in this area. In some cases the young pms stars
are recognized through specific characteristics – for
instance the presence of nebulosity or high degree of
activity.
An alternative is to take advantage of the seismological
information whenever it is possible. In this case the discrimination
between pms and post-ms can be made using differences in their
oscillatory frequency distributions in the low frequency range.

3. Calibration method: Stellar evolution: - CESAM vs. HENYEY (Bucharest);
- 1.8M track (Figure 1, Table 2).
Evolutive pulsational diagram: - CESAM (osc.ad+nad) +LNANR
(linear, nonadiabatic, nonradial, Suran, Bucharest);
- 1.8M track (l=0-2, g,f,p,);
- from pms  post-ms (Figure 2a,b);
- 3 common points (pms/post-ms): a.,b.,c,
(see Figure 1 and Table 1).

4. Results - HAEBE stars: Evolutive status: pms vs. post-ms:
- V351 Ori (pt. c.)  t
[P=14.33 (f2), penetrative post-ms ?!]
[BKW,C,M,RP] Table 3, Figure 3a,b.
Physical parameters:
- V1366 Ori (pts. a.,d.,e.)  Te
[A] Table 4, Figure 4 a,b,c.

5. References:
Amado, P. J.; Moya, A.; Suárez, J. C.; Martín-Ruiz, S.; Garrido, R.; Rodríguez, E.; Catala, C.; Goupil, M. J., 2004, M.N.R.A.S.,352, pp. L11-L15 [A];
Balona, L. A.; Koen, C.; van Wyk, F., 2003, M.N.R.A.S., 333,
pp [BKW];
Catala, C., 2003, Astrophysics and Space Science, pp l [C]
Marconi, M.; Ripepi, V.; Palla, F.; Ruoppo, A., 2004, Communications in Asteroseismology, 145, pp [M];
Ripepi, V.; Marconi, M.; Bernabei, S.; Palla, F.; Pinheiro, F. J. G.; Folha, D. F. M.; Oswalt, T. D.; Terranegra, L.; Arellano Ferro, A.; Jiang, X. J., 2003, Astronomy and Astrophysics, v.408, pp (2003) [RP].

6. Table 1. Common pms and post-ms points on the track of 1.8M star.
Log Te
Log L R
Age (Myr) Xc
rconv
[a]:
M13
3.919
1.050
1.621
11.8
0.7134
0.186
M16
3.920
1.044
1.608
300.
0.6383
0.204
[b]: M8
3.897
1.129
1.970
8.25
0.7142
0.221
M19
1.131
1.978
900.
0.4355
0.191
[c]: M4
3.872
1.170
2.319
7.7
0.068
M23
1.167
2.312
1160.
0.3132
0.180

7. Table 2. Physical data used in the models of V351 Ori and V1366 Ori
Log(Te)
L/L
R/R
T(Myr)
pre/postMS Xc
rconv
[a]
model V1366Ori
3.92
1.05
1.58
11.8/300
0.71/0.63
0.18/0.20
[b]
3.89
1.12
1.97
8.25/900
0.71/0.43
0.24/0.19
[c]
V351Ori
3.87
1.17
2.31
7.7/1160
0.71/0.31
0.068/0.18
[d]
V1366Ori
3.922
1.04
12.6/50
0.71/0.69
0.17/0.20
[e]
model
3.924
1.03
1.55
13.0/100
0.71/0.66

8. Table 3. Pulsational spectra for V351 Ori.
Pobs
C [c/d]
0.145
0.03
2.099
11.780
13.337
15.687
16.868 RP
12.754
12.817
14.331
15.885
M01
1.89
0.06
15.49
16.27
BKW
14.33
0.08
15.675
BKW.2
11.887
14.153
15.682
Pthpms
l=0
l=2
(Pth-Pobs)pms ? -
2.25
0.16
11.71
10.60
0.08
1.18
12.14
0.78
14.12
0.79
15.16
14.12?
0.51
0.56
18.84
18.91
-1.91
-2.23
Pthpost-ms
(Pth-Pobs)post-ms
2.08
0.01
11.65
11.58
0.13
0.21
13.07
0.26
15.88
0.59
0.62
15.88?
17.33
-1.88
-1.47

9. Pobs [c/d] 71.3 0.06 79.5 Pthpms Te=3.920 [a] l=0 l=2 67.52;74.64
Table 4. Pulsational spectra for V1366 Ori.
Pobs [c/d]
71.3
0.06
79.5
Pthpms Te=3.920 [a]
l=0
l=2
67.52;74.64
67.08;73.57
80.03
73.56;80.04
Pthpms Te=3.922 [d]
69.68;76.17
68.66;75.83
76.17;84.19
75.83;83.03
Pth pms Te=3.924 [e]
(Pth-Pobs)pms
71.38
71.20
0.08
0.10
79.26
77.93
0.25
1.57

10. Figure 1. Evolutive tracks of 1.8 M star in the HR diagram. [CESAM(C)
vs. HENYEY(H)]. Common points pre/postMS labeled by a,b,c.
In the figure also is indicated the main instability strip.

11. Figure 2.a. Evolutive pulsational diagram for a star of 1.8M [R]
[l = 0 (square), l = 1 (*), l = 2 (+)]

12. Figure 2.b. Evolutive pulsational diagram for a star of 1.8M [I] .
[l = 0 (square), l = 1 (*), l = 2 (+)]

13. Figure 3.a. Pulsational diagram for V351 Ori.
Brown and light brown: observations (see table 3).
Red and green (pms: l = 0,l = 2).
Blue and magenta (post-ms: l = 0,l = 2).

14. Figure 3.b. Zoom of the figure 3.a.

15. Figura 4a. Pulsational diagram for V1366 Ori (point a.).
Green points observations.
Red and blue points: theoretical model [pms, point a., l = 0,l = 2]
(see table 4)

16. Figura 4b. Pulsational diagram for V1366 Ori (point d.).
Notations as in Figure 4a.

17. Figura 4c. Pulsational diagram for V1366 Ori (point e.).
Notations as in Figure 4a.