Calibration of stellar evolution using stellar pulsations Marian

Calibration of stellar evolution using stellar pulsations Marian Doru Suran, Nedelia Antonia Popescu Astronomical Institute of the Romanian Academy e-mail: suran@aira. astro. ro Supported by the Romanian Space Agency (ROSA) contract Nr. 124/30. 09. 2004

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.

Calibration method: • Stellar evolution: - CESAM vs. HENYEY (Bucharest); - 1. 8 M track (Figure 1, Table 2). • Evolutive pulsational diagram: - CESAM (osc. ad+nad) +LNANR (linear, nonadiabatic, nonradial, Suran, Bucharest); - 1. 8 M track (l=0 -2, g, f, p, ); - from pms post-ms (Figure 2 a, b); - 3 common points (pms/post-ms): a. , b. , c, (see Figure 1 and Table 1).

Results - HAEBE stars: • Evolutive status: pms vs. post-ms: - V 351 Ori (pt. c. ) t [P=14. 33 (f 2), penetrative post-ms ? !] [BKW, C, M, RP] Table 3, Figure 3 a, b. • Physical parameters: - V 1366 Ori (pts. a. , d. , e. ) Te [A] Table 4, Figure 4 a, b, c.

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. L 11 L 15 [A]; • Balona, L. A. ; Koen, C. ; van Wyk, F. , 2003, M. N. R. A. S. , 333, pp. 923 -931 [BKW]; • Catala, C. , 2003, Astrophysics and Space Science, pp. 53 -60 l [C] • Marconi, M. ; Ripepi, V. ; Palla, F. ; Ruoppo, A. , 2004, Communications in Asteroseismology, 145, pp. 61 -66 [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. 1047 -1055 (2003) [RP].

Table 1. Common pms and post-ms points on the track of 1. 8 M star. Log Te Log L R Age (Myr) Xc rconv M 13 3. 919 1. 050 1. 621 11. 8 0. 7134 0. 186 M 16 3. 920 1. 044 1. 608 300. 0. 6383 0. 204 M 8 3. 897 1. 129 1. 970 8. 25 0. 7142 0. 221 M 19 3. 897 1. 131 1. 978 900. 0. 4355 0. 191 M 4 3. 872 1. 170 2. 319 7. 7 0. 7142 0. 068 M 23 3. 872 1. 167 2. 312 1160. 0. 3132 0. 180 [a]: [b]: [c]:

Table 2. Physical data used in the models of V 351 Ori and V 1366 Ori Model Log(Te) L/L R/R T(Myr) pre/post. MS Xc pre/post. MS rconv pre/post. MS [a] model V 1366 Ori 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] Model V 351 Ori 3. 87 1. 17 2. 31 7. 7/1160 0. 71/0. 31 0. 068/0. 18 [d] Model V 1366 Ori 3. 922 1. 04 1. 58 12. 6/50 0. 71/0. 69 0. 17/0. 20 [e] model V 1366 Ori 3. 924 1. 03 1. 55 13. 0/100 0. 71/0. 66 0. 17/0. 20

Table 3. Pulsational spectra for V 351 Ori. Pobs C [c/d] 0. 145 0. 03 2. 099 11. 780 Pobs RP 12. 754 0. 03 Pobs M 01 1. 89 0. 06 12. 817 Pthpms l=0 l=2 (Pth-Pobs)pms l=0 l=2 Pthpost-ms l=0 l=2 (Pth-Pobs)post-ms l=0 l=2 11. 887 0. 08 ? ? 2. 25 11. 71 10. 60 0. 16 0. 08 1. 18 2. 08 11. 65 11. 58 0. 01 0. 13 0. 21 15. 687 14. 331 15. 687 16. 868 15. 885 15. 49 Pobs BKW. 2 13. 337 12. 14 0. 78 16. 27 14. 33 0. 08 15. 675 14. 153 15. 682 14. 12 15. 16 14. 12? 18. 84 18. 91 0. 79 0. 51 0. 56 -1. 91 -2. 23 13. 07 15. 88 0. 26 0. 59 0. 62 15. 88? 17. 33 -1. 88 -1. 47

Table 4. Pulsational spectra for V 1366 Ori. 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] l=0 l=2 69. 68; 76. 17 68. 66; 75. 83 76. 17; 84. 19 75. 83; 83. 03 71. 38 71. 20 79. 26 77. 93 0. 08 0. 10 0. 25 1. 57 Pobs [c/d] Pth pms Te=3. 924 [e] l=0 l=2 (Pth-Pobs)pms l=0 l=2

Figure 1. Evolutive tracks of 1. 8 M star in the HR diagram. [CESAM(C) vs. HENYEY(H)]. Common points pre/post. MS labeled by a, b, c. In the figure also is indicated the main instability strip.

Figure 2. a. Evolutive pulsational diagram for a star of 1. 8 M [ R] [l = 0 (square), l = 1 (*), l = 2 (+)]

Figure 2. b. Evolutive pulsational diagram for a star of 1. 8 M [ I]. [l = 0 (square), l = 1 (*), l = 2 (+)]

Figure 3. a. Pulsational diagram for V 351 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).

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

Figura 4 a. Pulsational diagram for V 1366 Ori (point a. ). Green points observations. Red and blue points: theoretical model [pms, point a. , l = 0, l = 2] (see table 4)

Figura 4 b. Pulsational diagram for V 1366 Ori (point d. ). Notations as in Figure 4 a.

Figura 4 c. Pulsational diagram for V 1366 Ori (point e. ). Notations as in Figure 4 a.