COMMISSION 27 OF THE I. A. U. INFORMATION BULLETIN ON VARIABLE STARS Number 1841 Konkoly Observatory Budapest 1980 September 10 HU ISSN 0374-0676 IS THERE A MAGNETIC FIELD - PERIOD RELATION FOR THE HOTTER Ap - STARS ? In two recent papers by P. North (1980) and Cramer and Maeder (1980) a new technique is discussed for a photometric way to detect surface magnetic fields. The Z parameter is a linear combination of the Geneva colours U, B1, B2, V1 and G (Cramer and Maeder, 1979) and is nearly independent of T_eff and log g for main sequence stars from about B2 to A5. A linear relation between Z and the surface field Hs is presented. Although no astrophysical argument can be given for the existence of such a relation, there is no doubt that any - even heuristic - photometric technique which allows to pick out candidates for a detailed spectroscopic analysis is highly valuable. S.C. Wolff (1975) brought up some evidence for a correlation between the radius and period for non-Si stars in the sense that larger radii are correlated with larger periods. Her interpretation of this effect was a deceleration due to magnetic braking, with the increasing radius being a consequence of stellar evolution. If this idea is correct, stars with stronger magnetic fields should rotate slower than equally old but weak magnetic field stars. With more data now available for Hs it was interesting to look again into this problem, which is an aspect of the nature of magnetic fields in Ap stars (Weiss et al., 1976). Havnes and Conti (1971) and Strittmatter and Norris (1971) derive a rate of loss of angular momentum too dI/dt = {rho}^{0.5}*v_f*R^3*B_o where rho is the density of matter which is lost from or accreted by the star, v_f is the relative velocity of the star and interstellar medium or the velocity for mass loss, R is the stellar radius and B_o is the magnetic field strength at the stellar surface. The radius R varies even for our subgroup of hot Ap stars, but the observed range in B_o still exceeds the effect of R on dI/dt. Table I Hot magnetic Ap stars HD Hs C BP UF ST pec. p^d 9996 .20 B 3 50 B9p CrEu 36.5 10221 .14 39 A0p SiSr 3.1848 10783 .24 24 A2p CrSr 4.14 11502 .18 D 55 51 B9V+Ap 2.6095 12447 .18 DB 92 87 A0P SiSr 0.7383 18296 .18 22 5 B9p Si 2.88422 21699 .15 59 B8IIIp Mn 2.4761 22470 .15 190 A2V Si 1.9 22920 .16 721 B8IIIp Si 25267 .20 B 34 Ap Si 2.42(5.74,7.4) 25354 .12 17 A0p SrCrEu 3.9001 25823 .20 B 21 27 B9p Si 7.227 27309 .46 46 A0p Si 1.5691-2.7098 32633 .51 23 B9p SiCr 6.43 34452 .48 D 62 44 A0p Si 2.466 34797 .12 80 80 Ap Si 35479 .22 82 B9p Si 43819 .18 55 B9IIIp Si(Cr) 1.0785 54118 .18 0 A0p Si 74521 .35 19 A1p EuCr 4.2359 77653 .12 D 0 Ap Si 3.2 79158 .77 29 B8IIIp Mn 90569 .14 90 A0p CrSr 1.4-7.9 103498 .25 13 <= 25 A1p CrEu(Sr) 112473 .18 D 24 33 A0p SiEuHg 5.46939 120799 .19 20 B9p EuCr 1.3799 125248 .20 B 9 59 A0p CrEu 9.2954 726515 .27 3 A2p CrSr ~ 130 133029 .35 20 B9p SiSrCr 2.8881 134759 .10 D 72 A0p Si 136933 .25 D 0 A0p 140728 .15 75 100 B9p SiCr 1.30488 142884 .15 200 200 B9p (Si) 144667 .13 100: B7IIIp HgMn 145501 .29 D 70 70: B9p 147070 .56 25 <= 50 B9p SiCr 147890 .19 D 25 <= 50 B9p Si 149799 .28 25 <= 50 Ap SiCr 153882 .25 26 B9p CrEu 6.0087 164429 .27 200: B9p SiSr 0.51747 168733 .13 0 B8p 6.3 173650 .14 76 B9p Si(Cr) 9.9748 174933 .15 B 20 20 B9p Hg 6.36247 175362 .18 0 B8IV Si 3.682 [FIGURE 1] Figure 1: Hot Ap stars with known period P (in days) and photometrically determined surface magnetic field (H_S^T) in Tesla (1 T = 10000 Gauss). Asterisks: Si stars, one Hg and one Mn star. Circles: double stars not separated during HS measurement and spectroscopic binaries. Points: hot single Ap stars. [FIGURE 2] Figure 2: Probability function p for all Ap stars (crosses) with known period (P in days), adapted from Catalano and Strazzulla (1976) and for Ap stars with photometrically determined surface magnetic fields (dots). Table I (cont.) HD Hs C BP UF ST pec. p^d 187474 .23 B 4 0 A0p CrEu 192678 .50 5 A4p Cr 18.20, 360? 193722 .13 250 B9p Si 1.13254 196502 .20 8 0 A0p SrCrEu 20.2754 203006 .24 48 A2p CrEuSr 2.1219 204411 .10 32 A6p Cr(Eu) ~ 360 ? 215038 .39 31 A3p Si 2.03763 215441 .51 3 A0p Si 9.4877 220825 .14 35 42 A0p CrSr 0.5805 223640 .22 64 B9p SiSrCr 3.73 224801 .18 38 70: Ap SiEu 3.73975 HD...HD number, Hs...surface magnetic field in Tesla (1 T = 10000 Gauss), C... Comments (D photometrically unresolved double star, B spectroscopic binary) BP...v.sin i from Bernacca and Perinotto (1971), UF...v.sin i from Usuegi and Fukuda (1970) in km/s, ST, pec...spectral type and peculiarity from North (1980), P...period in days. Table I gives a subset of stars from Cramer and Maeder (1980, op.cit.) for which v. sin i and/or a rotational period is determined. F. Catalano (Catania) kindly contributed 5 periods from his catalog. Double stars not separated during the measurements and spectroscopic binaries (circles in Figure 1) obviously do not differ systematically from single Ap stars. Therefore all objects from Table I are used for the following discussion. A comparison of the integral probability distribution for all Ap stars with known rotational period (adapted from Catalano and Strazzulla, 1976) with those for which Hs is measured by the Geneva group give no evidence for a different parent distribution for both samples (Figure 2). We can therefore hope that the objects from Table I are characteristic at least for the group of hot Ap stars. The median rotational period is 2.56 days. Large Hs values are found in Figure 1 for all periods almost equally frequent. This result does not change even if all pure Si stars from Table I are excluded, as did S. Wolff for her investigation (Figure 3). Hs obviously does not correlate with the period. On the basis of the still rather limited material it can be concluded: [FIGURE 3] Figure 3: Mean photometrically determined surface magnetic fields (H_S^T in Tesla, 1 T = 10000 Gauss) for Ap stars within a given period interval (P in days). Filled symbols: arithmetic mean, open symbols: individual stars. i) The quantity Hs, as determined by Cramer and Maeder photometrically, shows the same distribution for P (and v.sin i) as is known to be typical for Ap stars. ii) No evidence can be found for a correlation of Hs with the rotational period. Thus, at least for the hotter Ap stars, magnetic braking needs further investigation. iii) Only 34 more or less reliable periods are known for more than 740 bright magnetic Ap stars from the list of Cramer and Maeder. Much more telescope time should be devoted to the determination of basic Ap star parameters, such as is the rotational period. W.W. WEISS Institute for Astronomy University of Vienna, A-7180, Vienna Tuerkenschanzstr. 17, Austria References: Bernacca, P.L., Perinotto, M.: 1971, Contrib.Oss.Astrof.Padova No. 250 Catalano, F.A., Strazzulla, G.: in "Physics of Ap Stars", IAU-Coll. No.32. W.Weiss et al., edts.,Vienna 1976 Cramer, N., Maeder, A.:1979, Astron.Astrophys. 78, 306 [BIBCODE 1979A&A....78..305C ] Cramer, N., Maeder, A.: 1980,Astron.Astrophys. 88, 135 [BIBCODE 1980A&A....88..135C ] Havnes, O., Conti, P.S.: 1971, Astron.Astrophys. 14, 1 [BIBCODE 1971A&A....14....1H ] North, P.: 1980, Astron.Astrophys. 82, 230 [BIBCODE 1980A&A....82..230N ] Strittmatter, P.A., Norris, J.: 1971, Astron.Astrophys. 15, 239 [BIBCODE 1971A&A....15..239S ] Usuegi, A., Fukuda, I.: 1970, Contrib. Inst. Astrophys. Kwasan Univ., Kyoto, No. 189 [BIBCODE 1970crvs.book.....U ] Weiss, W.W., Jenker, H., Wood, H.J.: 1976, 'Physics of Ap Stars" IAU-Coll. No. 32. edts., Vienna Observatory [BIBCODE 1976paps.coll.....W ] Wolff, S.C.: 1975, Astrophys. J. 202, 121 [BIBCODE 1975ApJ...202..121W ]