Spectroscopic Binaries near the North Galactic Pole Paper 6: BD

Transcription

1 J. Astrophys. Astr. (1982) 3, Spectroscopic Binaries near the North Galactic Pole Paper 6: BD R. F. Griffin The Observatories, Madingley Road, Cambridge, England, CB3 OHA Received 1982 July 27; accepted 1982 August 18 Abstract. Photoelectric radial-velocity measurements have confirmed O. C. Wilson s finding that BD , the secondary star in the wide visual binary ADS 8470, is a spectroscopic binary. It has an eccentric orbit with a period of 100 days. Its γ-velocity is close to the constant radial velocity of the visual primary, confirming the physical association of the stars. Key words: radial velocities spectroscopic binaries stars, individual 1. Introduction The multiple system ADS 8470 HD (BD ) is a seventh-magnitude late-type giant, the primary star of the wide visual binary ADS 8470 (Aitken 1932), which was first catalogued by F. G. W. Struve (1827) as Σ1615. The secondary star, a ninth-magnitude solartype object 27 arcsec following the primary, is the spectroscopic system whose orbit is presented now. The separation and position angle of the two visual components have remained virtually unchanged over the century and a half covered by measurements, although the system as a whole has been carried by proper motion across an angular distance of more than 15 arcsec over the same interval. Such relative fixity is a strong indication of the physical association of the stars; indeed the uncertainty arising from the smallness of the relative motion led Stephenson and Sanwal (1979) to infer the improbably high mass of Μ for the system. Aitken (1910) discovered a third visual component, a very faint star almost on the line joining the primary and secondary but much closer to the latter. The pair formed by Σ 1615 Β and the faint star is designated A 2058 or ADS 8470 BC. The few available positional measurements suggest that the faint star, too, shares the proper motion of the wide pair and is therefore a physical member of the system. In what follows, we shall for convenience refer to ADS 8470 simply as the system and to its individual components simply as Α, Β and C. O. C. Wilson is reported by Olsen (1971) as finding that Β is a spectroscopic binary. It is the principal purpose of the present paper to corroborate and amplify

2 384 R.F. Griffin that finding. The system therefore consists of not fewer than four components, probably in an arrangement of hierarchy (Evans 1968) three. Bakos (1974) considers A too to be probably a spectroscopic binary, but we shall show below that the evidence for such a conclusion is weak. 2. Space motion; photometry The proper motion of the system is about 0 11arcsec yr 1 (e.g. Boss 1937; Heckmann and Dieckvoss 1975), and indicates an appreciable space motion transverse to the line of sight. This led Miczaika (1940) to include it in his catalogue of high-velocity stars, defined as those with space motions greater than 63 km s 1 relative to the centroid of the motions of stars near the Sun. Miczaika s catalogue was one of the sources used by Miss Roman in compiling her own list of high-velocity stars (Roman 1955), where she presented photoelectric magnitudes and MK spectral types for the first time for both A and Β; it is rather ironic that she also concluded that the space motion of the system was not, after all, as high as 63 km s 1. The system features in a number of papers by Eggen on photometry and stellar dynamics. At first Eggen (1962) used Miss Roman, s magnitudes, but later he gave his own measurements (Eggen 1963,1968) it would appear that the 1968 magnitudes are merely repeated from the 1963 paper but with a misprint corrected and later still (Eggen 1969,1971a, b) he gave another set. Photometry of the system has also been reported by Tolbert (1964). The various sets of photometry are collected for ease of reference in Table 1, together with the homogenized mean values catalogued by Nicolet (1978). In an early paper, Eggen (1958) claimed that the system is a member of the ζ Herculis group. The distance which membership of the group would necessitate (to obtain the correct space velocity from the known proper motion) required that M V (A) = 1 25 mag. Subsequently he (Eggen 1963) claimed instead that it is a member of the 61 Cygni group, entailing M V (A) = 0 3 mag, a value close to the 0 5 mag that he quoted as having been derived by Adams et al. (1935) from the spectroscopic parallax. [Adams et al. (1935) actually appear to give a value of 0 7 mag.] The assignment to the 61 Cygni group has since been reaffirmed a number of times (Eggen 1969, 1971a, b); in the last of these papers the system appears in a table of certain members of the group. Table 1. Published photoelectric magnitudes for ADS 8470 A and B, with Nicolet s homogenized mean values.

3 Spectroscopic orbits, paper 6 BD Spectral types and luminosities Roman (1955) gave the MK types of A and Β as K2 III and F9 V, and those remain the generally accepted spectral types. Tolbert (1964), Schild (1973) and Bakos (1974) agreed with Roman s K2 III for A, while Upgren (1962) found K1 III. Tolbert (1964) gave a type of F8 IV, Bakos (1974) F8 V, for B. Tabular values interpolated from Allen (1973) for the absolute visual magnitudes of stars of types K2 III and F9 V are mag and mag. They differ by very considerably more than the 1 9 mag difference in the observed V magnitudes of A and B. It would be easy to argue that the tabular M V (A) is the one more likely to be correct especially as it agrees with the value required if the system is to be a member of Eggen s 61 Cygni group and that the M V (B) of mag that follows from it is evidence in favour of Tolbert s (1964) subgiant classification for B. Moreover, since we now know Β to be itself a binary, Β could well have a composite spectrum not yet recognized as such; in that case any luminosity assigned on spectroscopic or spectrophotometric premises would be liable to error. Unfortunately for such a line of argument, the several modern spectroscopic luminosity estimates in the literature (summarized in Table 2) are unanimous in finding that the primary is somewhat under-luminous for its type, leaving no discrepancy to be explained between the luminosity of the secondary and its main-sequence type. We shall probably not be far wrong in adopting a distance modulus of 5 0 mag, corresponding to a distanceof 100 pc, for the system. It will be difficult to reconcile such a distance with membership of the system in the 61 Cygni group. 4. Radial velocities; discussion 4.1 Component A The radial velocity of A was first determined by Adams et al. (1929), who reported a mean value of 10 3 km s 1 from three plates. Wilson and Joy (1950) gave a mean of 9 8 km s 1 from four plates, noting that theirs was a revision of the earlier value on the basis of additional plates or measurements. In his Radial Velocity Catalogue Wilson (1953) listed A with the Adams et al. (1929) velocity of 10 3 km s 1 but gave the number of plates as four. Subsequently Abt (1973), who published from the card files at Mount Wilson Observatory the individual details of all plates from which the radial velocities had previously been printed merely as mean values, Table 2. Published absolute-magnitude estimates for ADS 8470 A and B. *Values for A and Β are not independent.

4 386 R.F. Griffin only found details of three plates. They are evidently the three used by Adams et al. (1929), because (a) they are all pre1929 and (b) their mean of 9 4 km s 1 agrees exactly with the mean published by Adams et al. when account is taken of the systematic correction of 0 9 km s 1 referred to by those authors. However, the systematic correction used in the Radial Velocity Catalogue for Mount Wilson observations of K-type stars was 0 5 km s 1, so the Catalogue entry of 10 3 km S 1 for A should probably be understood as the Wilson and Joy (1950) value thus corrected, rather than as a citation of the Adams et al. (1929) value whose agreement with it is then fortuitous. Why the card files at Mount Wilson apparently do not contain details of the fourth plate utilized by Wilson and Joy is a question which unfortunately cannot be resolved here. By working backwards from the published mean velocity and the known individual results of the other three plates, we can infer that the velocity given by the missing plate was 11 1 km s 1. Bakos (1974) published two measurements of the radial velocity of A, and concluded that it was probably variable. His own two observations were in tolerable mutual agreement, so Bakos s conclusion must have been based upon the discrepancy between his weighted mean value of 19 1 km s 1 and the Mount Wilson mean. The star has been observed, in the course of the North Galactic Pole survey (Griffin 1981), a total of six times in six different years with the photoelectric radial-velocity spectrometers at Cambridge (Griffin 1967) and Palomar (Griffin and Gunn 1974). The photoelectric measurements are shown in Table 3 along with the historical photographic ones. Table 3 appears to warrant the conclusion that the velocity of A is constant. The only velocities that possibly deviate significantly from the photoelectric ones are those taken from the paper by Bakos (1974); it may be appropriate to recall here that there has been difficulty (Griffin 1975, 1978) in confirming other instances of velocity variations reported in that paper. For present purposes, then, the photoelectric mean value of 11 0 ± 0 4 km s 1 will be adopted as the constant radial velocity of A. Table 3. Radial-velocity measurements of HD (ADS 8470 A). Notes: 1. Published by Abt (1973) from the data by Adams et al. (1935). 2. Velocity inferred from literature (see text), but date unknown. 3. Published by Bakos (1974). 4. Observed by Dr G. A. Radford with the Cambridge photoelectric spectrometer (Griffin 1967). 5. Observed by the author in collaboration with Dr J. Ε. Gunn with the Palomar photoelectric spectrometer (Griffin and Gunn 1974). 6. Observed by the author with the Cambridge spectrometer.

5 Spectroscopic orbits, paper 6 BD Component Β A mean velocity of 44 km s 1, based on four observations, was published by Wilson and Joy (1950). Abt (1973) gives details of five plates, all pre-1950; they are listed as the first five entries in Table 4. By a comparison of the published mean with the five individual velocities, it can be deduced that the one that Wilson and Joy did not include in the mean was that of 1947 February 1. There is no means of knowing now whether it was deliberately rejected or merely overlooked; it does not give an especially large residual, either from a straight mean or from the orbit derived below. Bakos (1974) has one velocity, of 8 4 km s 1, for B. He notes that the velocity of Β is probably variable ; that conclusion is presumably based on the range of the Mount Wilson measurements (Abt 1973). The observational basis of O. C. Wilson s discovery of velocity variations (Olsen 1971) has not been published. Dr Wilson has kindly informed me that unfortunately the details of that work are no longer extant, and that the plates themselves cannot at present be located. Although B, owing to its early spectral type (which causes it to be observable only with some inefficiency with the photoelectric spectrometer), is not formally eligible for inclusion in the photoelectric survey of Galactic, Pole radial velocities (Griffin 1981), it was observed simply out of the interest attaching to its proximity to A, which is on the survey programme. The velocity of Β has been determined 44 times, with the results given in Table 4. All entries not otherwise noted in Table 4 are photoelectric measures made at Cambridge (Griffin 1967). The orbit derived from the photoelectric observations is plotted in Fig. 1 and has the following elements: Although the published photographic observations were not included in the orbital solution, they may be seen from Fig. 1 to be in reasonable accord with the orbit found from the photoelectric measurements alone. In particular, they do not strongly suggest that the period needs adjustment. However, the uncertainty of the phases of the Mount Wilson observations, which were made about 140 cycles before the photoelectric ones, is about 140 (P)/P or 0 03 cycles; this quantity is too small in relation to the accuracy of the Mount Wilson results for the latter to be very helpful in reducing it further. The γ-velocity of Β differs from the constant radial velocity of A by 1 1 ± 0 4 km s 1, a probably significant quantity. The projected separation of A and B, 27 arcsec at 100 pc, is 2700 AU. Let us suppose, first, that the actual distance between A and Β is similar to the projected distance equivalent to assuming that the line joining A and B lies in the plane of the sky and, secondly, that the total mass of

6 388 R.F. Griffin Table 4. Radial-velocity measurements of BD (ADS 8470 B). *Mount Wilson Observatory photographic observation (Abt 1973); not utilized in orbital solution, but plotted in Fig. 1. David Dunlap Observatory photographic observation (Bakos 1974); not utilized in orbital solution, but plotted in Fig. 1. Observed, in collaboration with Dr J. Ε. Gunn, with the 200inch telescope (Griffin and Gunn 1974).

7 Spectroscopic orbits, paper 6 BD Figure I. The computed radial-velocity curve for BD , with the measured radial velocities plotted. photoelectric observations are represented by filled circles. The earlier photographic observations, which were not used in solving the orbit, are represented by open symbols circles for Mount Wilson Observatory (Abt 1973) and a triangle for David Dunlap Observatory (Bakos 1974). the three stars in the A B system is 3M.Then, working in solar-system units of distance, mass and orbital velocity (d = 1 AU, Μ =1Μ, V 30 km s 1 ) and recalling that, from Kepler s third law, V 2 is proportional to M/d, we find that a relative velocity of 1 km S 1 is to be expected between A and B. Thus the observed difference of radial velocity is entirely consistent with membership of A and Β in a physical system, even if the difference is accepted at face value, without the need to invoke the presence of C or of other, invisible, companions to explain it. 4.3 The Gravitational Redshift A Digression Notwithstanding the above argument which shows that there is no difficulty in reconciling the true association of A and Β with the observed difference in their radial velocities, there is a good reason why that observed difference should not be taken at face value: the gravitational red-shifts of the two stars are different. The gravitational redshift of the Sun, which is typical of that of main-sequence stars in general and is similar to the value to be expected in the particular case of ADS 8470 B, is km s 1. It is proportional to the gravitational potential at the stellar surface, and therefore scales directly as the mass and inversely as the radius. Since giant stars are many times as big as dwarfs but are at most a few times the mass, their redshifts are much less than the solar redshift. Thus any comparison of radial velocities between dwarf stars and giants in binary systems or star clusters is likely to involve a systematic bias the velocities measured for dwarfs will be too positive in relation to those found for giants. The approximate magnitude of the differential effect is 0 5 km s 1 a quantity that is by no means negligible at the level of accuracy of the best modem radial-velocity measurements. If we allow for such an effect in the case of present interest, the difference in the centre-of-mass velocities of A and Β is reduced from 1.1 to 0,6 ± 0 4 km s 1, i.e. to insignificance,

8 390 R.F. Griffin Because this matter seems not to have been discussed explicitly before in its application to normal stars as opposed to white dwarfs, it seems useful to present a brief tabulation (Table 5) of the gravitational redshifts expected from stars of different types. The entries in the table follow directly from the values of mass and radius quoted by Allen (1973). The entries for late-type giants must be regarded as upper limits, since Allen gives masses for such stars in the range 3 Μ (G5 III)to 6Μ (M0 III).There is (not universally accepted) dynamical and spectroscopic evidence for the existence of giant stars of sub-solar mass (cf. Wilson 1967; Mäckle et al. 1975), as well as the seemingly incontrovertible fact that in globular and old galactic star clusters with main-sequence turn-off points near to solar type the giants can hardly be much more massive than the Sun. Thus in individual cases the redshifts from giant stars may be only a fraction of the values derived from Allen (1973) and listed in Table 5. On the other hand, the values tabulated for main-sequence stars should be fairly reliable. It would not require an observational accuracy much higher than that obtained in the present work before a realistic comparison of giant and dwarf radial velocities would necessitate a full discussion not attempted here of the relationship between the measured velocities and the true velocities of the centres of mass. Such a discussion would need to take into account not only the gravitational redshift but also the complex effects of mass motions and of variations of brightness and spectral-line strengths on both large and small scales over the complete hemisphere whose integrated light is observed. 4.4 Spectroscopic Companion of Β The mass function of B, together with the mass of Μ inferred from the spectral type of the spectroscopic primary (Allen 1973) points to a minimum mass of about 0 55Μ for the secondary in the 100-day orbit. If the secondary is a mainsequence star, its type can be no later than late Κ and its luminosity in the blue must be within four magnitudes of that of its primary. Its presence has not been noticed on the radial-velocity traces, so it must be considerably fainter than the F9 V primary: it is more likely to be a Κ star than a G. Table 5. Gravitational redshift (km s 1 ) as a function of spectral classification.

9 Spectroscopic orbits, paper 6 BD Component C ADS 8470 C, whose magnitude was estimated by Aitken (1932) to be 14 0, must have an absolute magnitude of about 9 0 if it is physically related to A and B. It may therefore be expected to have a spectral type close to MO V. On 1979 June 6.16 a brief attempt was made at Palomar to determine its radial velocity, and a result of 6 ± 2 km s 1 was obtained a difference of 4 ± 2 km s 1 from the γ-velocity of its putative primary, B. This result tends to support the association of C with AB. Unfortunately the velocity of Β (5 magnitudes brighter than C and only 2 7 arcsec distant) was found on the same occasion to be 4.3 km s 1. Although or perhaps because there was no doubt at the time that the velocity of C had been measured, no test integrations were recorded to provide complete conviction in retrospect that the feature seen in the radial-velocity trace of C was not partly (or even wholly) due to scattered light from B. It would be reassuring to make a further measurement at a time when the radial velocity of Β is well removed from the γ-velocity, but no opportunity to do so has yet arisen. Acknowledgements It is a pleasure to thank Dr J. Ε. Gunn for his collaboration in radial-velocity observations made with the Palomar 200-in telescope, and Dr O. C. Wilson for helpful correspondence. References Abt, H. A. 1973, Astrophys. J. Suppl. Ser., 26, 365. Adams, W. S., Joy, A. H., Humason, M. L., Brayton, A. M. 1935, Astrophys. J., 81, 187. Adams, W. S., Joy, A. H., Sanford, R. F., Strömberg, G. 1929, Astrophys. J., 70, 207. Aitken, R. G. 1910, Lick. Obs. Bull., 5, 166. Aitken, R. G. 1932, New General Catalogue of Double Stars within 120 of the North Pole, Carnegie Institution of Washington. Allen, C. W. 1973, Astrophysical Quantities, Athlone Press, London, pp. 206, 209. Bakos, G. A. 1974, Astr. J. 79, 866. Boss, B. 1937, General Catalogue of Stars for the Epoch 1950, Carnegie Institution of Washington, 4, 12. Boyle, R. J., McClure, R. D. 1975, Publ astr. Soc. Pacific, 87, 17. Eggen, Ο. J. 1958, Observatory, 78, 21. Eggen, Ο. J. 1962, R. Obs. Bull., No. 51. Eggen, Ο. J. 1963, Astr. J., 68, 483. Eggen, Ο. J. 1968, R. Obs. Bull., No Eggen, Ο. J. 1969, Publ. astr. Soc. Pacific, 81, 553. Eggen, Ο. J. 1971a, Astrophys. J., 165, 317. Eggen, Ο. J. 1971b, Astrophys. J. Suppl. Ser., 22, 389. Evans, D. S. 1968, Q. J. R. astr. Soc., 9, 388. Griffin, R. F. 1967, Astrophys. J., 148, 465. Griffin, R. F. 1975, Astr. J., 80, 245. Griffin, R. F. 1978, Astr. J., 83, Griffin, R. F. 1981, J. Astrophys. Astr., 2, 115. Griffin, R. F., Gunn, J. E. 1974, Astrophys. J., 191, 545. Hansen, L., Kjaergaard, P. 1971, Astr. Astrophys., 15, 123.

10 392 R. F. Griffin Heckmann, Ο., Dieckvoss, W. 1975, AGK 3, Hamburger Sternwarte, Hamburg-Bergedorf, 4, 245. Mäckle, R., Holweger, Η., Griffin, R., Griffin, R. 1975, Astr. Astrophys., 38, 239. Miczaika, G. 1940, Astr, Nachr., 270, 249. Nicolet, B. 1978, Astr. Astrophys. Suppl. Ser., 34, 1. Olsen, Ε. Η. 1971, Astr. Astrophys., 15, 161. Roman, N. G. 1955, Astrophys. J. Suppl. Ser., 2, 195. Schild, R. E. 1973, Astr. J., 78, 37. Stephenson, C. B. 1960, Astr. J., 65, 60. Stephenson, C. B., Sanwal, N. B. 1969, Astr. J., 74, 689. Struve, F. G. W. 1827, Catalogus Novus Stellarum Dupliciuim et Multiplicium, Senatus Universitatis Dorpatensis, Dorpat, p. 41. Tolbert, C. R. 1964, Astrophys. J., 139, Upgren, A. R. 1962, Astr. J., 67, 37. Wilson, O. C. 1967, in Modern Astrophysics, A Memorial to Otto Struve, Ed. M. Hack, Gauthier- Villars, Paris, p Wilson, O. C. 1976, Astrophys. J., 205, 823. Wilson, R. E. 1953, General Catalogue of Stellar Radial Velocities, Carnegie Institution of Washington, p Wilson, R. E., Joy, A. H. 1950, Astrophys. J., 111, 221.