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Mon. Not. R. Astron. Soc. 371, 11591172 (2006) doi:10.1111/j.1365-2966.2006.10638.x

Photoelectric radial velocities, Paper XVII The orbits of 30 spectroscopic binaries in the southern Clube Selected Areas R. F. Griffin

The Observatories, Madingley Road, Cambridge CB3 0HA

Accepted 2006 June 1. Received 2006 May 28; in original form 2006 April 11

A B S T R A C T Three of the six southern Clube Areas that were mainly observed at the European Southern Observatory and whose principal results are given in Paper XVI are marginally observable from Haute-Provence. Additional measurements obtained on several observing runs there enabled orbits to be determined (in most cases rather poorly, owing to the paucity of data) for 30 of the newly discovered spectroscopic-binary systems; they are presented in this paper. One object, HD 33978, seems to be of such significance that special efforts have been made, largely by Drs J. Andersen and H. Lindgren, to obtain additional radial-velocity measurements. That system is shown to be a double-lined binary with a period of only 10.67 d despite one of its components being a late-type giant. The giant star has a projected rotational velocity of almost 40 km s-1; it could be expected to exhibit RS CVn-type photometric variations, which have not yet been observed, in addition to the `ellipsoidal variation', discovered by Hipparcos, which occasioned its designation as VV Lep. Key words: techniques: radial velocities  binaries: spectroscopic  stars: individual: HD 33978 (VV Lep)  stars: late-type.

0 P R E A M B L E Paper XVI of this series (Griffin & Cornell 2006  the paper immediately preceding this one) presents the principal results of a substantial programme of radial-velocity observations of stars in the six southernmost Areas of the Clube survey. Among the 600-odd stars measured, 69 certainly or almost certainly exhibited non-constant radial velocities. The present paper describes efforts to determine orbits for some of those objects. Although the primary source of the observations in the six southern Areas was necessarily in the southern hemisphere, three of the Areas are at declinations (-15 to -30) that put them just about within reach of the Geneva Observatory's 1-m telescope and Coravel radial-velocity spectrometer (Baranne, Mayor & Poncet 1979) at Haute-Provence (  +44). In the 1990s the author was privileged to have a considerable number of observing runs there, and on good nights was sometimes able to supplement the European Southern Observatory (ESO) measurements of stars in the three marginally accessible Areas. The observations were inevitably made at undesirably large zenith distances ranging from 60 to 80, where conditions of transparency, seeing and atmospheric dispersion were less than ideal, to say nothing of the matter of access to the eyepieces of the telescope and its finder. Nevertheless, many observations were ob-

E-mail: rfg@ast.cam.ac.uk

tained in the three Areas at moderate southern declinations, namely Areas 6, 7 and 13. Special attention was paid to the stars for which the ESO survey had yielded discordant velocities; the expectation was that such stars would prove to be spectroscopic binaries, and there was hope that enough radial-velocity measurements could be accumulated for orbits to be derived for some of them. Furthermore, in the course of a complete round of new measurements of the stars in Areas 6 and 13, additional cases of discordance arose, and they were then treated with the same priority as the ESO-discovered velocity variables. This paper presents the results for all the stars for which plausible orbits could be derived. Section 1 describes the stars and the conditions in which they were observed (partly in extenuation for the uncharacteristically preliminary nature of many of the orbits). Section 2 gives the radial velocities and the orbits, while Section 3 provides a brief discussion and notes on some of the stars, only a few of which have attracted any attention whatever in the literature previously. Section 4 then (giving the impression of being `a paper within a paper'!) offers a more thorough treatment of the specially significant object HD 33978 (VV Lep), for which a much more adequate data set has been obtained than for any of the other stars apart from HD 26917, upon which a separate paper based on data analogous to those of HD 33978 has already been published (Griffin et al. 1995). Finally Section 5 amounts to a progress report on certain stars that have definitely shown velocity variations but for which the data are too scanty, or cover too short a total interval, to permit even a preliminary orbit to be deduced.

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1 T H E S TA R S T R E AT E D I N T H I S PA P E R Only a few of the stars that exhibited variations of radial velocity did so on time-scales short enough to make them worth observing more than once in any individual observing run. The orbits of most of the stars that form the subject of this paper, therefore, can at best be delineated by a number of observations equal to the number of observing runs when they were respectively accessible in the sky. The annual observing season on any given star was quite short, since the unfavourable declinations restricted observations to hour angles in the immediate vicinity of the meridian. Many of such orbits as it has been possible to derive, therefore, are much more scantily documented than the writer normally likes to publish; in the majority of cases the number of measurements is only about 15, and it ranges down to (in one case) only 12; it is clear that not many degrees of freedom remain after six orbital elements are fitted to such parsimonious data sets. Inasmuch as he has little prospect of being able to make any further observations of the stars concerned, however, the author is presenting the orbits even in cases where they are obviously preliminary. It is thought that the orbits (with one or two caveats noted in Section 3) are secure, in the sense that the periods are approximations to the correct ones and the general forms of the orbits are correct, but there is clearly a lot of scope for refinement of the elements in many cases. An indication of the writer's own dispassionate assessment of the qualities of the respective orbits is offered in the tabulation in Section 3 of the orbital elements, in the same manner and with what are intended to be the same standards as those assigned by Batten in the Sixth, Seventh and (most recently) the Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Systems (Batten, Fletcher & MacCarthy 1989). Since the Clube Selected Areas observing programme was originally drawn up, additional information has become available for nearly all of the stars that it embraces. Although very few of the objects have been observed photometrically by ground-based observers, nearly all of them feature in the Tycho catalogue [specifically, the Tycho 2 version (Hg et al. 2000)] which represents a sort of bonus from the Hipparcos astrometric satellite; it has provided twocolour photometry that has been transformed by the present author according to the recipes given in the Hipparcos introductory volume (ESA 1997) into an approximation to the Johnson V magnitude and (B - V) colour index. The values are expected to be accurate to a few hundredths of a magnitude.1 Furthermore, Houk and her collaborators have re-classified almost all the southern-hemisphere stars in the Henry Draper (HD) Catalogue (Cannon & Pickering 19181924) on the two-dimensional MK system (Morgan, Keenan & Kellman 1943; Johnson & Morgan 1953; Keenan & McNeil 1989); the volumes relevant to the stars treated in this paper are Volumes 3 and 4 (Houk 1982; Houk & Smith-Moore 1988). Salient data for the 30 stars whose orbits are given in this paper are collected in Table 1. They include the tally of the radial-velocity observations for each star and, as an indication of the observational errors, the rms deviations of the individual velocities (of the primary,

Table 1. Star HD Area 6 88913 92789 93140 94563* 95166* 96402 96818 97574 99584 100306 Area 7 116463 117161* 118116 119011* 119087 119175 120503 120852 124536 125187 125341 Area 13 27600 27871 28426

The 30 stars whose orbits are presented below.

V mag (B - V ) mag Sp. type No. of RV obs.  km s-1

9.22 8.71 9.50 8.61 9.70 9.03 10.00 9.71 9.03 8.94 1.08 0.77 0.80 0.88 0.73 0.95 1.19 0.99 1.03 1.14 G8/K0 III G3/5 III K0 III/IV G5 V K0 V G8 IV K0 (III) G8 V G8 III/IV K0 III 27 19 19 24 22 16 13 18 15 16 0.4 0.8 0.4 0.4 0.4 0.3 0.7 0.8 0.3 0.5

9.13 9.84 9.73 9.70 8.98 9.52 9.87 9.50 9.52 10.37 8.87 1.17 0.95 0.82 0.80 1.10 1.18 1.14 1.21 1.06 0.95 1.03 K1 III G6 III/IV G8 III/IV G6 IV/V G8 IV K2 III G8 K1 III K1 III G8/K0 K0 III 19 15 15 24 20 19 13 14 13 15 17 0.5 0.6 1.1 0.9 0.7 0.7 0.5 0.2 0.6 0.6 0.7

8.95 9.50 8.93

31341 B 10.68

33978* 35646 35993 36186 36562

8.31 9.57 9.56 8.87 9.21

1.30 0.90 1.11 0.65 1.03 0.97 1.10 1.51 1.17



K2 III K0/K1 III K0 III -- K1 III G8 III Kp Ba K4 III K1 III 15 15 13 17 42 14 13 13 12 0.5 0.5 0.4 1.4 0.7 0.6 0.3 0.8 0.4

*Double-lined V magnitude from Hipparcos

in the five double-lined cases) from the derived orbits. The total number of measurements is 527. Attention is drawn to the fact that one particularly interesting object, HD 26917, that would otherwise have featured here was the subject of a special investigation that was generously supported by other observers at ESO, and its orbit was published quite a long time ago (Griffin et al. 1995). A second such object, HD 33978, was similarly observed, and a good orbit was obtained but has never been written up and published; the writer is indebted to Dr J. Andersen, who collaborated in the work on that star, for permitting its inclusion in this present paper.

1 Small discrepancies, occasionally amounting to as much as 0.1 mag in the

colour index, between the magnitudes given in Table 1 and those in table 10 of the preceding paper (Griffin & Cornell 2006, Paper XVI) arise because those in the cited paper were taken wholesale by a semi-automatic procedure from SIMBAD, which is believed to quote values based on the original Tycho reductions. The Tycho 2 ones presented here are expected to be superior. Five of the stars, by coincidence all in Area 13, feature in the Hipparcos catalogue itself, and for those stars the V magnitudes derived from the actual Hipparcos photometry rather than from Tycho have been given preference. 2 R A D I A L V E L O C I T I E S A N D O R B I T S The radial-velocity measurements of all the stars were begun in the course of the five observing runs that were allocated to the writer for the use of the Geneva Observatory's `Coravel' photoelectric radial-velocity spectrometer on the Danish 61-inch reflector at ESO. The observing procedure with that instrument has been described in Paper XVI (Griffin & Cornell 2006). Additional observations were

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Photoelectric radial velocities, Paper XVII

Table 31. HD Quality 88913 b

92789 c 93140 c 94563 c

Orbital elements and their standard errors

P (d) T or T0 (MJD)  K e



1161

made during 19 observing runs with the analogous instrument on the dedicated 1-m telescope at the Geneva Observatory out-station at Haute-Provence (hereinafter OHP). Paper XVI, which unlike this one is not largely based on observations made at OHP, is not so forthcoming about the observing procedure there. The operation at OHP was less automated than that at ESO. The telescope was moved by hand and manually clamped up in each coordinate when set; its position was read from circles, and the typical setting accuracy was a quarter of a degree. The observer then used the finder and identified the required star from a chart before bringing its image on to the Coravel entrance slit, where it was thereafter held by the excellent autoguiding system. Late in the observing campaign, the introduction of encoders to indicate the telescope position much more accurately simplified the operation of finding the desired stars. A very few measurements were made with the radial-velocity spectrometer at the coude focus of the 48-inch reflector of the Dominion Astrophysical Observatory (DAO), but the latitude there (nearly 5 higher even than that of OHP) is really too high for observations of stars at the declinations involved here to be a realistic proposition. The journals of radial-velocity measurements for the stars whose orbits have been derived (other than HD 33978, which is treated separately in Section 4) are set out in Tables 230, which are available in the online version of the article on Synergy (see the Supplementary Material section for details). In addition to the dates and velocities, the tables list the phases and residuals of all the observations according to the adopted orbits. Asterisks against the dates identify ESO observations, daggers DAO ones. Weighting of the different sources of observations in the solutions of the orbits presented something of a problem. The ESO telescope, with its 2.4-times larger collecting area and often observing near the zenith, normally provided better data than could easily be obtained at OHP, as has been clearly demonstrated by the statistics in Paper XVI. Those statistics, however, do not apply with full force to the present cases, where the imbalance was deliberately redressed, at least in part, by integrating for longer  sometimes much longer  at OHP than the 1 min that was standard at ESO. The internal assessments of precision that are routinely made for all Coravel traces show in many cases that the ESO measures deserve a relative weight of 2, rather than the 4 that the Paper XVI analysis would suggest. In any case the ESO contribution to the data sets accumulated for the purposes of the present paper rarely amounts to more than two to four observations, and there are serious dangers in attributing too great a weight to just a few data points. Rather than attempting an adjudication of weighting on a case-by-case basis, the writer has adopted in this paper a uniform policy of attributing double weight to all ESO observations. With those preliminaries settled, the orbital elements follow; they are presented in Table 31, which (together with the discovery and discussion of HD 33978) can be seen as encapsulating the principal results of this paper. The second line for each star gives proposed `quality' of the orbit and then the standard errors of the elements, ranged under the elements themselves which appear in the first line. The last column of Table 31 gives the mass functions for single-lined binaries, but for double-lined ones it gives the minimum masses, m sin3 i, in units of solar masses in both cases. The orbits are illustrated in Figs 13.

a sin i f(m) or

(km s-1) (km s-1)

+41.13 .11 -5.80 .22 +4.86 .14 29.15 .12 4.24 .29 6.46 .22

0.131 .004 0.28 .07

(deg) (Gm)

68.8 1.8 106 20

103.367 49201.3

.011 1790 34 1403 9 562.3 1.0 .5 49288 83 48922 54 49063.9 1.5

0.159 154 .026 14

41.07 .18 100 7 123 4

-11.36 17.72 0.470 203.2 120

.20 .017 2.3

95166 c 293.94 .21 49279.5 1.0 +12.69 .15

96402 c 96818 d 97574 c 99584 c 100306 c 3275 70 7000 fixed 318.4 .7 847 9 181.99 .32 50393 26 49902 51 48933.5 2.1 49924 6 49487.1 1.5 +88.12 .12 +2.85 .38 +44.24 .20 +27.20 .12 +14.84 .15

.19 20.4 .4 20.21 .23 21.5 .4 5.34 .13 8.9 .5 6.99 .29 3.57 .24 4.82 .18

0.372 181.5 .014 1.9

0.370 270 .022 4 0.590 336

.023 0 fixed 0.21 .05 0 fixed 7 -- 20 14 --

2 139 3 75.8 1.0 80.8 1.6 223 7 694 38 30.6 1.3 40.7 2.8 12.1 .5

mmin 0.2590 .0033 0.0126 .0027 0.038 .004 1.18 .07 1.03 .05 0.92 .04 0.86 .03 0.0415 .0033 0.27 .05 0.0113 0.0014 0.0037 .0008 0.0021 .0002

116463 b 117161 c 153.88 .03 164.27 .08 48850.3 1.2 48754.2 2.4 -44.46 21.48 0.211 255.3 44.4

.15 +0.44 .28 .008 0.207 .019 2.9 79 7

118116 c 119011 b

1010 14 49621 13 20.85 .36

19.5536 49104.04 +13.29 .0004 .22 .17

119087 c 119175 c 120503 c 124536 c 125187 c 125341 c

185.65 .13 49284.5 1.0

86.945 48977.5

.029 602.0 2.2 346.0 1.1 1753 26 1317 8 .8 49153 17 49631 7 48366 71 49899 69

+35.30 .21 +20.43 .23 +1.35 .23 -38.56 .28 -37.58 .24

.22 23.3 .4 23.6 1.2 5.9 .5 46.8 .3 47.8 .4 18.4 1.0 18.43 .28 6.51 .33 8.6 .6 7.6 .7

0 fixed --

0.073 192 .006 4

0.640 192.9

.016 0.283 .024 0.28 .05 0.36 .07 0.35 .06 0.10 .05 2.5 29 4 232 13 238 8 191 11 253 18

-30.74 10.0 .24 .4

.5 51.6 0.9 52.2 2.7 82 7 12.56 .08 12.82 .11 36.1 2.1 21.13 .36 52 3 38 3 171 17 181 7

0.148 .005 0.83 .10 0.82 .05 0.022 .006 0.863 .018 0.845 .014 0.054 .009 0.0498 .0025 0.0153 .0024 0.019 .004 0.065 .019 0.135 .015

3 D I S C U S S I O N This discussion takes the form of notes concerning certain individual stars and/or their orbits. The objects are listed in the order in which

27600 c 27871 c 28426 c 31341B d 35646 c 35993 c 36186 c 36562 c 1004 3 7781 835 4037 61 678 3 789 12 2892 34 686 7 2221 44 49315 4 48367 118 50696 68 49309 4 48755 14 50087 82 48779 9 48955 304 +13.55 .15 +19.45 .23 +54.73 .22 -5.4 .5 +24.49 .20 +17.66 .11 +82.16 .24 +1.5 .4 7.50 .19 4.39 .23 10.43 .18 19.0 1.2 3.61 .29 3.84 .16 4.4 .5 5.2 .3

0 fixed 0.38 .07 -- 158 8

0.228 295

.019 0.79 .03 0 fixed 0.20 .04 0 fixed 0.15 .06 8 93 7 -- 193 11 -- 111 44

103.6 2.7 435 54 564 13 109 10 39 3 150 7 42 5 158 11 0.044 .003 0.054 .012 0.439 .025 0.113 .032 0.0039 .0009 0.0160 .0021 0.0061 .0022 0.032 .007

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they appear in Table 31, namely those in Area 6 first, then Area 7, and finally Area 13. HD 88913. The period is short enough to have permitted multiple observations usefully to be made within certain individual observing runs, so there are enough measurements to produce a `perfectly good' orbit. The very large mass function (0.26 M ) makes it certain that the orbital inclination is high and likely that the secondary star is an F-type dwarf, although it has not been apparent in the radialvelocity traces. HD 92789. This G3/G5 giant has the considerable rotational velocity (determined from the Coravel traces, cf. Benz & Mayor 1981) of 10.3  0.7 km s-1. The orbital period (5 yr) is much too long for there to be any question of synchronization. HD 94563. Double-lined, with the secondary component very weak. In cases where the velocity of the primary was close enough to the  -velocity for the two dips to be partly or wholly blended together, but the traces were not good enough to provide a velocity for the secondary, they have been reduced as single-lined and identified in the plot by open diamonds. They were not used in the solution of the orbit, but owing to the dominance of the primary they are very close to the velocity curve of that component. The secondary velocities have been weighted /10 relatively to the

1

primary. The system is classified (Houk & Smith-Moore 1988) as a dwarf of type G5 V. It is to be noticed, however, that the annual proper motion is only 0.019 arcsec (Hg et al. 1998). The colour index of 0.88 mag and the rather generous total dip area would both be consonant with a mean type near K0 V rather than the G5 of the Michigan classification; they would also be satisfactory for a G8 III type. For a K0 V type the distance modulus would be about 3 mag, the distance 40 pc and the parallax 0.025 arcsec, and the known proper motion would correspond to a transverse velocity of less than 4 km s-1. For G8 III, the corresponding figures are 8 mag, 400 pc, 0.0025 arcsec and 36 km s-1. It is known that Tycho parallaxes are none too reliable, and indeed were omitted in Tycho 2, but for what it is worth the Tycho parallax of HD 94563 is -0.0038  0.0086 arcsec. There would, therefore, be little difficulty in arguing that the observed properties of HD 94563 are more consonant with a giant type than with a dwarf. Equally, though, it could be argued that an orbital period of about 18 months, in a very unequal binary system whose photocentric motion could be a substantial fraction of the primary's orbital semi-axis of 0.8 au, is well calculated to vitiate any parallax determination. The areas of the two dips seen in radial-velocity traces have a mean ratio close to 5:1, suggesting a disparity of about 2 mag in the luminosities of the components. The mass ratio of 1.15 is on the low side for a pair of stars with that luminosity difference, if they are on the main sequence; on the other hand it is too high for a pair of stars both to be somewhere within their respective giant-branch evolutions at the same time. The considerable uncertainty in both ratios, particularly that of the mass, might, however, be invoked to make either option appear marginally acceptable. At present no firm decision on the nature of the system seems possible. HD 95166. Another double-lined system. Whereas the previous star is classified G5 and has the colour of K0, this one is classified K0 V and has nearly the colour (0.70 mag) of G5! It has a proper motion of nearly 0.1 arcsec, almost guaranteeing its dwarf status. The ratio of dip areas is 1.9  0.2 to 1, implying a luminosity difference of a little less than one magnitude, which in turn represents a difference of about four spectral sub-types. The mass ratio of 1.066  0.024 would indicate a difference of only two sub-types, or three if

a value increased by 1 were adopted; the agreement is none too good, but the uncertainties are such that the two assessments cannot be said to be in conflict. Secondary velocities have been weighted one-fifth. HD 96402. The classification is G8 IV, but the colour index of 0.95 mag is characteristic of G8 III, a luminosity that is, however, almost ruled out by the annual proper motion of 0.088 arcsec which at the 450-pc distance implied by that type would correspond to a transverse velocity of more than 180 km s-1. A dwarf would have to be much later (K2) to correspond with the colour. The best compromise may be to suppose the type to be about K0 IV, but that is not a common type and would imply a great age for the star. The orbit is of fairly long period (9 yr) and is quite well determined. HD 96818. The form of orbit is certain, but the actual period is longer than the duration of the observing campaign and is indeterminate  any period greater than about 5000 d satisfies the observations almost equally well. For purposes of illustration, the orbit that is listed here has had a period of 7000 d imposed upon it. The standard errors given for the orbital elements refer only to the orbit with that fixed period, so the real uncertainties are in some cases much larger. Comparison with the elements obtained for periods of 5000 and 10 000 d, which probably bracket the true value, shows that the values of T, K and  scarcely vary,  decreases slightly with increasing period, and e varies modestly (by  0.1) in the same sense as the period. The mass function is very large and is insensitive to the adopted period; it betokens a secondary star that is probably in the range of 12 M and could therefore be expected to be an F or early-G dwarf. A couple of fresh observations taken a year or so apart, even now, could define the orbital period reasonably properly. HD 97574. When all six orbital elements are fitted to the data, the computed orbit is nearly circular and its eccentricity is without significance according to the tests given by Bassett (1978), so the value of  is in fact completely indeterminate. This is a dwarf star with a period of nearly a year and there is no reason to suppose that its orbit is likely to be exactly circular; nevertheless, to avoid putting an altogether unreliable value of  into the literature, the circular solution is specified in Table 31. HD 99584. The orbit is secure in the sense that the period and general form must be correct, but it leaves a lot to be desired in terms of phase coverage, especially in the vicinity of the ascending node. There is one OHP velocity that gives an exceptionally bad residual. The orbit listed in Table 31 has been computed without that measure, although there are no grounds except the statistical one for rejecting it, and when it is rejected the fit of the remaining points to the orbit is actually better than is warranted by the internally estimated errors of the individual velocities. When the orbit is computed with the `bad' observation included, the elements are almost unchanged except that  is increased to 64  35 and there is a corresponding increase in T; the standard errors of all the elements are, however, approximately doubled, and the doubled values are probably more realistic than those listed in Table 31. It must also be mentioned that, when the orbit includes the observation that gives the bad residual, the eccentricity is no longer significantly non-zero. HD 100306. Another case where the existence of orbital eccentricity is not immediately clear. The sum of the squares of the residuals is 3.76 (km s-1)2 for a circular orbit and falls to 2.13 when e and  are left free. By the application of Bassett's (1978) second statistical test, whose character and method of application are described more particularly in their application to HD 33978 in Section 4 below, those numbers lead to a variance

ratio F2 ,10  3.82, somewhat short of the 5-per-cent significance

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Photoelectric radial velocities, Paper XVII 1163

Figure 1. Computed radial-velocity curves plotted with the radial-velocity measurements for the orbits of stars in Area 6. ESO observations are shown as squares, Haute-Provence ones as circles. Open symbols are used for the secondary components of double-lined binaries, except that open diamonds plot observations reduced as single-lined. For HD 99584, the open circle plots the rejected observation.

point (4.10), so for the same conservative reason as is given for HD 97574 the circular solution has been adopted. HD 116463. The mass function is large enough to demand a secondary star of at least 1 M  possibly a white dwarf but much more probably an F- or solar-type star. HD 117161. Double-lined. The secondary dip seen in radialvelocity traces is quite weak, being about 0.3 times the intensity of the primary, and was not discovered until 1993: in the earlier

observations it either was so far separated from the primary as to be beyond the end of the scan, or else, in three cases, was superimposed on the primary dip. In those three cases, observations made at ESO on consecutive nights, the dips were so precisely superimposed that to alleviate the paucity of data they have been treated in the orbital solution as measurements of the primary with the reduced weight of /2, i.e. /4 of the normal weight for ESO observations.

1 1

Secondary velocities have needed to be weighted only /10 in

1

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1164 R. F. Griffin

Figure 2. As Fig. 1, but for the orbits of stars in Area 7. Smaller symbols denote particularly uncertain velocities.

the orbital solution, and three of them (marked with a colon in Table 13 and plotted with smaller symbols in Fig. 2) are particularly uncertain and have had their weights halved (although, perversely, their residuals are on average actually smaller than those of the other secondary measurements). The phase coverage of the data leaves a lot to be desired. The mass ratio is unity to well within its substantial uncertainty, which is only to be expected for a binary system that is classified as a giant and therefore must be supposed to consist of stars that are evolving simultaneously. The substantial disparity in the dips given by the respective components in radial-velocity traces suggests a magnitude difference of rather more than one magnitude, but dip depths are so dependent upon spectral types that in the absence of spectroscopic information no proper estimate can be hazarded. HD 118116. Another case in which it is in all probability the paucity of data rather than the actual circularity of the orbit that prevents the establishment of a significant eccentricity or a meaningful value of . The sum of squares of the residuals from the circular solution listed in Table 31 is 16.57 (km s-1)2, and falls only to 11.12 when e and  are left free; those figures yield

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Photoelectric radial velocities, Paper XVII 1165

Figure 3. As Fig. 1, but for the final orbit from Area 7 (top) and the orbits of stars in Area 13 (with the exception of that of HD 33978 which is discussed in Section 4 and whose orbit is plotted in Fig. 5). The three open circles in the panel for HD 27871 represent recent Haute-Provence observations kindly contributed by Dr J.-M. Carquillat.

F2  2.2 by Bassett's (1978) second statistical test, whereas even ,9

the 10-per-cent point of F2 is about 3. ,9

HD 119011. Double-lined dwarf system with a period of only 20 d and large velocity amplitudes, features that have permitted a good orbit with reasonable phase coverage to be obtained. The orbit has a small but very definite eccentricity. Comparison of the spectral type with the minimum masses given by the orbital elements suggests an orbital inclination in the range 7580. The mass ratio differs from unity by only 2.3  1.1 per cent, suggesting a spectral-

type difference of only about one sub-type between the components; the ratio of dip strengths is 1.26  0.08 to 1, indicating a difference in luminosity of 0.3  0.1 mag that would correspond to about two sub-types. The velocities of the two components have been given equal weights in the orbital solution. HD 119175. This giant star has a period of only 87 d and yet has an orbit of considerable eccentricity ( 0.3). Moreover, it gives wide dips in radial-velocity traces, the projected rotational velocity being 13.0  0.6 km s-1. Upon the assumption that the rotation

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is pseudo-synchronized, the projected radius Rsin i is about 14 R , which is very plausible, although the absence of information that would enable an estimate to be made of the axial inclination means that the actual stellar radius is not determinable. HD 120503. The Michigan classification of G8 does not include a luminosity class; the colour index (1.14 mag) and the smallness of the proper motion (0.011 arcsec yr-1) strongly suggest that the object is a giant. HD 125187. Another star lacking a luminosity classification. Although the proper motion is small (0.018 arcsec yr-1), it cannot be regarded as prescriptive, because the star is particularly faint; even if it were a dwarf it would therefore be at such a distance (80 pc) that the tranverse motion (7 km s-1 in that case) would not be remarkably small. HD 125341. When the orbit is computed with its eccentricity fixed at zero, the sum of squares of the residuals is 14.08 (km s-1)2; when it is left as a free parameter the sum is reduced to 9.35, numcourse very likely that, at the period of nearly 4 yr, the orbit is noncircular, and as the statistical test is so very close to showing modest significance the eccentric solution has been selected for Table 31. HD 27600. A solution with e free gives for that parameter a value that is little more than half its own standard error; it is altogether nonsignificant, so (despite the 1000-d period making an exactly circular orbit improbable) the zero-eccentricity solution is tabulated. HD 27871. This is a case analogous to that of HD 96818 inasmuch as the observations do not cover a complete cycle of the radialvelocity variation. Any period longer than about 5000 d fits the originally available data almost equally well. Dr J.-M. Carquillat, however, has recently (2005/6) made at OHP three additional radialvelocity measurements, which raise the lower limit of the period to about 7000 d and make it probable that the actual value is about 8000 d, although a much longer period still cannot be ruled out with certainty. HD 28426. The observations only just cover an orbital period; there seems no escape, however, from the conclusion that the phase of the final (DAO) measure is after the ascending node, and in that case the orbit is altogether secure. Since no secondary dip has been noticed in the radial-velocity traces, the astonishingly large mass function probably indicates that the secondary object is itself a double system. HD 31341 B. Not itself a Clube star, but a visual companion to one, at a separation of 18 arcsec. The temptation to observe such an obvious companion was irresistible, and the observations have subsequently proved to be of great interest by confirming the physical association between the principal star and the companion. Both components feature in Hipparcos, although they do not do so in any of the normal double-star catalogues. The primary has repeatedly been identified as a barium star (cf. Paper XVI), but was not noticed as such (or was not considered to be such) in the Michigan re-classification of the HD stars (Houk & Smith-Moore 1988); it was there accorded the type K0 II. The Hipparcos parallax is 0.00270 arcsec, a value typical of normal giants at the distances characteristic of stars on the Clube programme, but its standard error is slightly larger still  uncharacteristically large for Hipparcos  so no significance can be read into it at all, apart from its setting an uninteresting lower limit to the distance. If the primary is accepted for the moment as being a normal giant, its distance must be of the order of 400 pc, making its projected linear separation from the companion star as large as 7200 au. If the higher luminosity implied by the Michigan classification is really correct, and not the result of confusion caused by the enhanced ionic lines in a barium-star

bers yielding F2 ,11  2.79; the 10-per-cent point is 2.86. It is of

spectrum, the separation must be much greater still. The parallax given by Hipparcos for the companion is far more inaccurate even than that of the primary, being -0.00922  0.01060 arcsec; its derivation might very well have been confounded by the orbital motion that is documented here. The Hipparcos proper motions are also very uncertain, with standard errors several times as large as the values themselves, but that situation is retrieved in the Tycho 2 compilation (Hg et al. 2000) which shows that the annual motions of the two stars (close to zero in RA and about -0.012 arcsec in declination) are identical within about 0.003 arcsec, an amount comparable to their standard errors. The radial velocity of the primary star appears to be constant, which is not what is expected for a barium star. The secondary, perversely, is the component that shows radial-velocity variations, which are of quite large amplitude (a range approaching 40 km s-1). They are quite well fitted by an orbit (Table 31) with a very high eccentricity (almost 0.8) and a period a little short of 2 yr. The writer is indebted to Dr A. Kaye for suggesting the period. The ESO and OHP radial velocities have been given equal weights in the orbital solution. Even the ESO ones possess internally computed uncertainties near 1 km s-1, owing to the faintness (10.7 mag) of the star and its rather blue colour (0.6 mag) that leads to its giving only a shallow dip in radial-velocity traces; similar precisions were achieved by OHP measurements, on the nights that were good enough for the object to be observable at all, by relatively extended integration times, typically in the range 510 min. It is noteworthy that the  -velocity found here is almost identical with that of the primary star, although its standard error of 0.5 km s-1 demonstrates that the exactitude of the equality is fortuitous. Nevertheless the agreement reinforces very strongly the conclusion that is warranted by the proper motions that the two stars do constitute a physical binary. The colour index of the secondary star does, however, present some difficulty: if it is supposed that the primary has a type close to K0 III, the colour and relative luminosity of the secondary would seem to demand a type near G0 IV. The colour index, however, may have been diminished by the admixture of the light of a hot companion with that of the principal star in the visual-secondary system; the mass function is large enough to suggest a companion at least as early as solar type, and unless the orbital inclination is quite close to 90 it could be substantially earlier. HD 35646. Another case in which the paucity of data prevents a non-zero eccentricity being reliably documented. The eccentric solution has e = 0.11  0.06, with  = 206  30, but the circular solution results in an an increase that is far from statistically significant in the sum of the squares of the residuals (F2  2.1; the

,8

10-per-cent point is 3.1) and is the one that is listed in Table 31. HD 35993. A barium star, and recognized as such in the Michigan classification. It has an orbit typical of such stars, with a period of several years (in this case about 8), and a modest eccentricity, which is, however, statistically secure; the mass function too is typical and is consistent with the secondary object being the expected white dwarf. HD 36186. The scarcity of observations and the smallness of the radial-velocity amplitude conspire to produce an orbit whose eccentricity is much less than its own uncertainty, so the circular solution has been adopted. HD 36562. This star has the smallest number of observations (12) from which the writer has ever dared to derive an orbit, even in this paper, but the general form of the orbit appears secure and the eccentricity statistics yield F2  6.0, which is significant at the 5-per-cent level (5.14).

,6

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4 H D 3 3 9 7 8 HD 33978, which is fortuitously brighter than most of the Clube stars, appears as an eighth-magnitude star in the constellation Lepus, about 2.4 south-following Leporis. It has long been listed as a visual double star, albeit not seen as such by many people: van den Bos (1928) discovered in 1925 with the Johannesburg 261/2-inch refractor a 13-mag companion little more than 2 arcsec away from the principal star in position angle 293. The system received his discovery designation B 81 and was catalogued by Aitken (1932) as ADS 3804; it has never again been measured. The Vizier ALADIN picture of the field appears to show the image of HD 33978 blended with that of a faint companion at about 8 arcsec, 250. It seems likely to be the van den Bos object, but if so the movement is too great to be orbital, or to be explained by the proper motion (less than 1 arcsec per century) of HD 33978, so most of the relative motion must be ascribed to the proper motion of the faint star. There is a more obvious companion, certainly optical, about 11 mag and probably of something like solar type, 88 arcsec from the principal star and in position angle 337. Its radial velocity was measured twice, at -15.7 km s-1 on 1990 February 15 at ESO and at -16.0 on 1992 January 15 at OHP. SIMBAD reports the inclusion of HD 33978 in a paper on spaceultraviolet observations, but only because it has misidentified the star, which is -24 2915 in the Cordoba Durchmusterung, as the early-type one having the corresponding designation in the Cape Photographic Durchmusterung. No ground-based determinations had been made photoelectrically of the magnitude of HD 33978 before Hipparcos stepped into the breach with V = 8.34, (B - V) = 1.02 mag. Hipparcos detected, moreover, a variation with a peak-to-peak range of 0.078  0.004 mag and a period of 5.3349  0.003 d which we shall show to be precisely half the orbital period. For no reason immediately obvious to the layman (but it is related to the `scanning law' of the satellite and the -47 ecliptic latitude of HD 33978, cf. fig. 3.2.89 in Vol. 1 of the Hipparcos catalogue), the number of Hipparcos photometric data, 241, is approximately twice as large as is available for most stars. The discovery by Hipparcos of its photometric variability led to HD 33978's being accorded the variable-star designation VV Lep (Kazarovets et al. 1999). The combination of the short period and late type of HD 33978 prompted Koen, Laney & van Wyk (2002) to include the star in a short programme of photometric and radial-velocity observations at the South African Astronomical Observatory in the austral summer of 1998/9. They obtained the mean magnitude and colour indices as V = 8.380, (B - V) = 1.063, (U - B) = 0.757 mag; they also confirmed the 5.33-d photometric period found by Hipparcos, finding its amplitude to decline slightly with increasing wavelength from 0.10 mag in U, B and V to 0.09 (R and I) and 0.08 (mean of J, H and K). They were perceptive enough to recognize from their radialvelocity measurements, which were made on six consecutive nights, that the photometric variation must be of `ellipsoidal' character and the orbital period must therefore be exactly twice as great. Then, on the further correct assumption that the radial velocities must chart a sine wave whose period and epoch were fixed by the photometry, they obtained values of  = +28.8  1.2, K = 37.7  1.1 km s-1. They saw the spectrum as single-lined. The Hipparcos parallax of 0.00439  0.00105 arcsec corresponds to a distance modulus of about 6.8  0.5 mag. Rather little interstellar absorption is to be expected over the sight-line of some 200 pc at the Galactic latitude (-32) of HD 33978, so to a sufficient approximation we can use the distance modulus directly to give the

absolute magnitude as +1.5  0.5 mag. That is quite consonant with the spectral type of K1 III given in Houk & Moore's (1988, p. 57) revision of the HD Catalogue; the type in the original Catalogue (Cannon & Pickering 19181924, vol. 92, p. 98), for HD 33978 as for all of the Clube stars (for which it was one of the selection criteria), is K0.

4.1 Radial velocities HD 33978 was first observed with the ESO Coravel in 1987, and immediately drew attention to itself by its excessively wide `dip'. There was no opportunity to re-observe it in that run, but it was observed again in the next one, in 1989, when it gave not only the wide dip but also a velocity that was 11 km s-1 different from before. Two further observations in the following year increased the observed range of variation to more than 70 km s-1, creating great interest in the object. Early in 1992, the writer was fortunate in being able to obtain a connected series of measurements from OHP on seven out of 10 consecutive nights, and was aware from the results that he had seen most of an orbital cycle. He thereupon put out a request to observers at the ESO Coravel to make additional observations before the phasing became lost, in order to fix the period; Dr J. Andersen graciously rose to the occasion and, obtaining lavish integrations with the star practically in the zenith and with a considerably larger telescope than the OHP one, he immediately discovered the existence of a small secondary dip. Not only did he obtain another series of eight observations in a 10-night interval, but he also managed to enthuse his successor at the telescope, Dr H. Lindgren, who very kindly obtained seven more during the ensuing 10 nights and another two a month later. By that time the orbit was already well determined, but in the following three observing seasons the author obtained some additional velocities from Haute-Provence, and three on another visit to ESO, in order to increase the time base and refine the period. It is of interest to record that the photon-counting rates (counts per second per bin, there being 64 bins each about 1.8 km s-1 wide) ranged from less than 2 up to 20 at Haute-Provence and from 7 to 70 at ESO. Altogether there are 42 measurements of the velocity of the primary star and 28 of the secondary. Like the other velocities in this paper, they were reduced by Dr S. Udry and are on the zero-point described by Udry, Mayor & Queloz (1999). They are set out, with the phases and residuals computed according to the adopted orbit, in Table 32, which is available in the online version of the article on Synergy (see the Supplementary Material section for details). Figure 4 illustrates a Coravel radial-velocity trace of HD 33978. In terms of exposure level (about 45 000 counts bin-1, obtained at ESO by Dr Andersen in 22 min) it is one of the very best traces that we have, and it graphically illustrates the difficulties that attended our measurements of the system. In the first place, the width of the primary dip is such as to occupy practically the whole width of the scan. The ESO and OHP Coravels offered a choice of two fixed scanning ranges, and the trace shown was obtained with the longer one. Near the nodes of the orbit, the secondary dip is completely separated from the primary, and then the two can be measured satisfactorily, albeit in separate integrations. When the secondary is well displaced from the primary but not separated from it, however, the only way of measuring them is to centre the scan in such a way as to place the secondary dip right near one end and to lose part of the primary dip off the other  an arrangement that is not conducive to the best results for either of them. Secondly, it will be seen that the model blend drawn in the figure is not a good fit to the observed points on the right-hand side (positive-velocity wing) of

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1168 R. F. Griffin

Figure 4. Radial-velocity trace of the double-lined binary HD 33978, obtained by Dr J. Andersen with the ESO Coravel on 1992 March 5. The points represent the observed photon counts in 64 `bins' spaced about 1.8 km s-1 apart, while the full line represents the model curve. The poor fit arises because the model pre-supposes that dip profiles are Gaussian, whereas the principal dip in the case of HD 33978 is greatly broadened by the axial rotation of the star. Rotationally broadened line profiles have wider cores and steeper sides than Gaussians.

the primary dip, where it has too shallow a slope. On the other hand, the left-hand wing, including the blend with the tiny secondary dip, is a tolerably good fit. That fit, however, is illusory and is obtained at the expense of a systematic error in the positioning of the secondary dip in the model trace. All ESO and OHP Coravel traces are reduced by a suite of programs that pre-suppose that all dips are of Gaussian form. That assumption is far from being satisfied in cases such as this one, where the dip is greatly broadened by stellar rotation: rotational profiles have broader cores and steeper sides than the nearest Gaussian approximations. In the same way as the Gaussian model has a slope that is obviously too shallow in the right-hand wing, so it ought to appear on the left, but the reduction program has managed to steepen the left-hand wing of the model trace and make it fit better than it `ought' to do by attributing too positive a velocity to the small and narrow secondary dip. The effect is inevitably systematic: there are in fact six observations in which the secondary is attributed a velocity between 0 and +20 km s-1, and in the solution of the orbit they all give positive residuals, averaging as much as +2.9 km s-1  a quantity far beyond the normal run of radial-velocity residuals from the Coravels. It might well be expected that there would be repercussions on the velocity found for the primary as well, but nothing significant is actually to be seen in the residuals for that component.

less exposure still. The full-weight measurements are so flagged in Table 32, and the three low-weight ones are identified by the colons after the primary velocities. The situation with regard to the secondary is unusual, as outlined above, and it has been concluded that the best result is obtained by rejecting all but the nine observations in which the secondary was observed in isolation, near a node of the orbit, more or less centred in a well-integrated trace. The nine traces have exposure levels ranging from 19 000 to 70 000 counts bin-1; all but one of them were obtained at ESO. Approximate equality with the variance of the primary data is obtained by weighting the nine accepted secondary ones on a par with `full weight' of the primary. Although without any doubt it must seem an abnormally draconian step to reject 19 out of 28 observations, one could point out that the exposure levels of the retained traces would in any case entitle them to high weight, and that measurements made near the nodes have greater leverage in determining the velocity amplitude than those nearer conjunctions, so the nine `good' observations would in any case carry much of the weight in determining K2. Moreover, as has been demonstrated, all the secondary velocities obtained well away from the nodes are likely to be affected by serious systematic errors. The final orbit, computed on the basis described, is illustrated in Fig. 5 and its elements are presented in Table 33. The elements given in the table have been computed with the orbital eccentricity fixed at zero. A solution in which e and  are left as free parameters is naturally able to fit the measurements better, simply through having more degrees of freedom to play with. It gives values of e = 0.008  0.005 and  = 81  42. In such a case, where the eccentricity is appreciably greater than its own standard error, an investigation of its significance is routinely merited, and has been carried out according to one of the statistical tests explained by Bassett (1978). The test uses the sums of the squares of the residuals (or equivalently the apparent variances of the individual observations) in the two solutions of the orbit  those with e fixed at zero, and with e and  left free. In this case the sums of squares are 40.33 and 38.31 (km s-1)2 respectively. In the case with e and  free we have fitted seven orbital elements to a total of 51 observations, leaving 44 degrees of freedom, so the variance per degree of freedom is 38.31/44, or 0.87 (km s-1)2 per degree. With e fixed at zero we

4.2 Orbit In an effort to extract the best orbit from the available data, the residuals given by various trial solutions have been closely examined. The residuals of the primary velocities are tolerably well correlated with exposure levels. The variances of different exposure levels are brought into reasonable accord by a rather cavalier segregation of the data into just three levels. Full (unit) weight has been attributed to the 20 observations having more than 10 000 counts bin-1, weight 0.4 to the 19 with levels between 2000 and 10 000 counts bin-1, and 0.2 to the three (all taken in poor conditions at Haute-Provence in a desperate attempt to maintain the continuity of the initial run of data there at a time when the orbital period was unknown) with

Figure 5. The computed radial-velocity curves corresponding to the orbital elements adopted for HD 33978, with the radial-velocity measurements plotted. As in Figs 13, ESO observations are shown as squares, Haute-Provence ones as circles. The larger symbols identify the observations that were given the maximum (unit) weight; the observations plotted with smaller symbols were attributed weight 0.4 in the case of the primary (filled symbols) and zero in the case of the secondary (open symbols).

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Table 33.

P T0  K1 K2 q e = = = = = = 

Orbital elements for HD 33978. 10.66910  0.00027 d MJD 48837.423  0.010 +26.79  0.16 km s-1 39.27  0.25 km s-1 47.2  0.4 km s-1 1.203  0.013 (= m1/m2) 0

 is undefined in a circular orbit

a1 sin i a2 sin i f(m1) f(m2) = = = = 5.76  0.04 Gm 6.93  0.06 Gm 0.0671  0.0013 M 0.117  0.003 M

m1 sin3 i = 0.392  0.009 M m2 sin3 i = 0.326  0.006 M R.m.s. residual (unit weight) = 0.89 km s-1

have two additional degrees of freedom, and between them they have cost (40.33 - 38.31), or 2.02, (km s-1)2  1.01 per degree, which is 1.16 times as much as the other 44 degrees. That number is so close to unity that it is immediately apparent that there is nothing special about the two extras degrees of freedom that are represented by the exclusion of e and  from the set of elements to be fitted to the data, but for the avoidance of doubt we can appeal to tables of the variance ratio, F, in tables such as those of Fisher & Yates (1948). Even for high as 2.43; the 1-per-cent level is about 5.12. The observed ratio is clearly altogether without significance, and we accordingly adopt the orbital solution whose elements are given in Table 33 above, with e set exactly to zero.

the 10-per-cent significance level the value of F2 ,44 needs to be as

4.3 Discussion Radial-velocity traces of HD 33978 are very reminiscent of those of HD 115781 (Griffin & Fekel 1988), where again there is a K1 III primary star rotating very rapidly and an extremely weak secondary. In the case of HD 115781, however, the two components have, within observational uncertainty, identical masses and must both be evolving, with the primary having climbed to the top of the giant

Figure 6. Hipparcos `epoch photometry' of HD 33978 plotted against phase in the spectroscopic orbit defined in Table 33. The obvious variability led to the assignment of a variable-star designation, VV Leporis, to HD 33978. The double wave with its maxima so exactly phased to the nodes of the orbit (phases .0 and .5) is clear evidence that its cause is the distortion of the star by its close companion (`ellipsoidal variation').

branch in the HertzsprungRussell diagram while the secondary is low down on it. In HD 33978 there is a substantial difference in the masses, the primary being 20.3  1.3 per cent more massive than the secondary. That leads to the expectation that, while the primary is evolving, the secondary is still on the main sequence. The observed `equivalent widths' of the dips seen in Coravel radialvelocity traces have a mean ratio of approximately 14:1; to obtain that ratio in comparison with a K1 III star with a B magnitude of about +2.5 would require the secondary, if on the main sequence, to have a type near F8, being about 2 mag fainter in the B region in which the Coravel operates (2.5 mag fainter in V) and giving a dip that is intrinsically weaker than that of a K1 III star by a factor of about 2. We shall show below that the primary star probably fills or almost fills its Roche lobe and may therefore be spilling matter on to the secondary, but we shall nevertheless suppose that in its gross properties that star is similar to a normal main-sequence star of its current mass. Strictly speaking, we ought now to iterate the above calculation because the absolute magnitude of +1.5 that we have adopted from the Hipparcos parallax and have been using as that of the K1 III primary star is actually that of the whole system; addition of the putative secondary will make the system 0.1 mag brighter than the primary alone. In view of the uncertainty of  0.5 mag in the initial datum, however, it would be specious to tinker with the model at the 0.1-mag level. At a similar level, we should also note that the supposedly much hotter (albeit much fainter) secondary contributes to the integrated colour and spectral type, so we must expect the primary alone to be slightly redder and slightly later than the system appears as a whole. The photometric variations, mentioned in Section 4.1 above, that were discovered by Hipparcos had a period of 5.3349 d, which is to a high degree of exactitude half of the orbital period of 10.669 d. There can scarcely be any doubt that the variations are caused by the distortion of the giant star, which must be elongated along the direction towards the secondary, so it presents a larger surface area to us when we see it `side-on' than `end-on'  although it must be pointed out that we never see it truly end-on, because it is evident from the minimum masses that are required by the orbit and given in Table 33 above that the orbital inclination is well away from 90. The Hipparcos catalogue tabulates an epoch of maximum brightness, MJD 48501.42; the phase of that epoch, in terms of the radialvelocity orbit, is .507  almost exactly at a nodal passage, when the system is seen side-on (phases .000 and .500), a nice confirmation of the distortion hypothesis for the origin of the variations. In Fig. 6 we plot the Hipparcos photometry against phases in the orbit that we have determined, to illustrate the double wave with its maxima at the nodes. The projected rotational velocity, v sin i, of the primary star is given by the Coravels as 38.7  0.6 km s-1, but in view of the illfitting nature of the Gaussian dips used in its derivation the formal precision probably gives a decidedly optimistic impression of the closeness to the true value. The actual rotational velocity must be a good deal more than the projected one, owing to the factor sin i. All the same, since we are certain from the photometric variations that the rotation is synchronized to the orbit and therefore shares the period of 10.67 d, we can obtain a value for the projected radius of the star, Rsin i, simply by multiplying v sin i by the number of seconds in the orbital period and dividing by 2: the result is 5.7 Gm. That may be compared with the (constant) separation of the two stars in their circular orbit, which is shown by Table 33 to be 12.7 Gm, and leads to a ratio R/a of 0.45. The corresponding ratio for the size of the Roche lobe of the primary star is given by Eggleton's

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Figure 7. Radial velocities plotted directly against time for certain stars which show clear evidence of velocity variations but for which the observational data [to be found in the preceding Paper XVI (Griffin & Cornell 2006)] are inadequate for even a preliminary orbital solution.

(1983) expression,

RL a = 0.49q2 0.6q2 + ln (1 + q1 ),

/3

/3

/3

determined mass ratio of the components then leads directly to a mass of 1.38 M for the primary star. Equating those masses to the minimum masses m1 sin3i found from the orbit in Table 33 above

,2

leads to sin3i  0.28, and thus to sin i  0.66, i  41. The primary's actual equatorial rotational velocity, then, is 38.7/sin i, or about 60 km s-1; its radius is nearly 9 Gm (13 R )  a very reasonable value for a K1 III star with MV  +1. The Coravel traces suggest that the secondary dip is practically unbroadened, but the weakness of that dip inevitably prevents an accurate estimate being made of the

which for q = 1.20 yields RL/a  0.40. The best estimate that we can make of the inclination probably comes from attributing a mass of about 1.15 M (under the assumption of normality explicitly made above) to the F8 V star that is proposed as the secondary component in HD 33978. The accurately

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rotational velocity; the observations are consonant with an origin in an F8 V star in synchronous rotation. We have seen that the separation of the components of HD 33978 is about 12.7/sin i Gm, so with the inclination that we have deduced it is some 19 Gm or 0.13 au; at the Hipparcos distance of about 230 pc it will subtend an angle of nearly 0.6 of a millisecond of arc. To judge from the present rate of progress of optical interferometry, we might well hope to see from that quarter, in the reasonably near future, an important advance in our knowledge of HD 33978 (as of almost all other double-lined spectroscopic binaries).

4.4 Probability of RS CVn variation Late-type stars that rotate rapidly mostly exhibit photometric variations, which are known to be caused by `star-spots' or at any rate by what may more non-committally be termed azimuthal variations in surface brightness, although the mechanisms underlying the effect have yet to be agreed upon. Main-sequence examples of stars that show variations of such a character are generally called BY Dra variables, whereas the type star for the giants is RS CVn. HD 33978 must be a strong candidate for RS CVn variability, although the available photometry seems not to show it. It may be significant that the photometric amplitude attributed to the 5.33-d period by Koen et al. (2002) was appreciably greater than that derived by Hipparcos in the same wavelength region; moreover, the mean magnitude found by the 2002 authors was noticeably fainter, and the colour index redder, than the Hipparcos values, as could be explained by a general increase in spot coverage. Photometric monitoring of the star would be worthwhile.

Modified Julian Dates in Fig. 7. The panels in the plot, and the comments below on the stars concerned, are taken as before in order in Areas 6, then 7, and finally 13. (It can be only coincidence that such a majority of them is in Area 13!) HD 97977 B. Not an actual Clube star but a visual companion, this star is relatively faint (10.8 mag), and the velocities typically have internally computed standard deviations close to 1 km s-1. An orbit with a high eccentricity and a period of about 2100 d appears to be a distinct possibility, fitting the data within satisfactory residuals but yielding elements with altogether unacceptable standard errors. HD 114483. The star has a substantial projected rotational velocity, about 14 km s-1, causing the radial velocities to be less accurate than those of most of the Clube stars. Only the two highest points can really be said to differ somewhat significantly from the rest, and even they differ by so little that the writer would not care to express absolute certainty that the velocity varies at all. If it really does, nothing at all can be said about the period, unless it be that it is tempting to see about an 8-yr variation with an uncharted maximum about 1992. HD 123368. It seems clear that a considerable part of a cycle whose period is in excess of 4000 d has been witnessed. A couple of new observations now would probably permit a preliminary orbital solution. HD 30668. The monotonic decline evidently is part of an orbital variation with P 4000 d. HD 33758. The period looks to be less than the duration of the observations; 3000 d is a possibility. HD 34014. The observations rather clearly fail to cover a cycle, whose length must be more than 4000 d. HD 35810. Certainly variable, possibly with a period longer than the duration of the observations. HD 35852. The shortness of the period is evident. The data can be fitted with the acceptable rms residual of only 0.5 km s-1 by a high-eccentricity orbit with a period of 29.6 d, but it could well be objected that such a fit may not be unique and that a high eccentricity is improbable at such a short period. A dense series of measurements within a single observing season is really required. HD 36730. The period may be about 4500 d; a sine wave with that period fits the points within 0.5 km s-1 rms. HD 37044. The period looks to be considerably longer than the 10-yr span of the data. A sine wave with a period of about 8000 d can be fitted, but it yields an improbably high mass function; an eccentric orbit with P  4500 d, e  0.5 and   50 is more plausible but must remain conjectural until further observations can be brought to bear.

5 R A D I A L - V E L O C I T Y VA R I A B L E S W I T H

I N D E T E R M I N AT E O R B I T S Fewer than half of the stars whose radial velocities were found, with more or less certainty, to be variable in the course of the southern Clube Selected Areas investigation have had their orbits determined, even in a preliminary fashion. There were simply not enough observing runs at ESO for there to be any hope of obtaining orbits for stars in the far-southern areas, except in the two particularly interesting cases of HD 26917 (Griffin et al. 1995) and HD 33978 (Section 4 above), for which the kind assistance of other ESO observers was enlisted.2 In the three regions at more modest southern declinations, however, most stars that were fairly definitely shown to change velocity were observed between 10 and 20 times, permitting the derivation in some cases of the orbits (albeit mostly of a preliminary character) shown above. In other cases, however, the data remain inadequate for orbit determination. In most cases that appears to be because the cycle length exceeds the duration of the observing campaign, but there are instances in which it is the frequency and not the duration of the observations that is unsatisfactory. In the cases of the 10 stars for which it seems worthwhile, the radial velocities are plotted directly against calendar years and

2

A third object that merits follow-up is HD 37730 B (cf. Paper XVI,

table 8), whose four radial velocities span a range of more than 80 km s-1 and whose v sin i value of about 10 km s-1 suggests an orbital period of the order of 5 sin i d  so most likely about 4 to 5 d  and the likelihood of BY Dra/RS CVn (and perhaps `ellipsoidal') variability. The orbital period could probably, therefore, be determined photometrically without the need for spectroscopy at all, and the four observations in Paper XVI could then be phased to it and should give a preliminary spectroscopic orbit too, albeit having an ambiguous (perhaps no) value of T, still without spectroscopy!

AC K N OW L E D G M E N T S I am grateful to ESO for providing observing time and technical support on the 61-inch Danish telescope at La Silla for this project, and to Dr M. Mayor and the Observatoire de Genev` e for allowing the use of their excellent `Coravel' radial-velocity spectrometers. I am indebted to the SERC and its successor PPARC for defraying the costs of the observing visits, and although now acting in a voluntary capacity I acknowledge with thanks the facilities that are still accorded to me at the Cambridge Observatories. I am grateful too to Dr B. D. Mason of the US Naval Observatory for his prompt and willing assistance in connection with the literature on visual double stars, to Dr J. Andersen for allowing me to include HD 33978  a system in which he has taken much interest  in this paper, to Dr J.-M. Carquillat for radial velocities of HD 27871, and to

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1172 R. F. Griffin

Mrs A. Smith and Mr R. Sword for the concatenation of the individual panels of Figs 1, 2, 3 and 7.

R E F E R E N C E S Aitken R. G., 1932, New General Catalogue of Double Stars Within 120 of the North Pole. Carnegie Institution of Washington, Washington, DC Baranne A., Mayor M., Poncet J. L., 1979, Vistas Astron., 23, 279 Bassett E. E., 1978, Observatory, 98, 122 Batten A. H., Fletcher J. M., MacCarthy D. G., 1989, Publ. Dom. Astrophys. Obs., 17 Benz A., Mayor M., 1981, A&A, 93, 235 Cannon A. J., Pickering E. C., 19181924, Ann. Harv. Coll. Obs., 9199 Eggleton P. P., 1983, ApJ, 268, 368 ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP1200, Vol. 1. ESA, Noordwijk, p. 57 Fisher R. A., Yates F., 1948, Statistical Tables for Biological, Agricultural and Medical Research. Oliver & Boyd, London Griffin R. F., Cornell A. P., 2006, MNRAS, in press (Paper XVI, this issue, doi:10.1111/j.1365-2966.2006.10369.x) Griffin R. F., Fekel F. C., 1988, JA&A, 9, 213 Griffin R. F., Gunn J. E., 1974, ApJ, 191, 545 Griffin R. F., Andersen J., Mayor M., Duquennoy A., 1995, Mon. Not. Astron. Soc. S. Afr., 54, 11 Hg E., Kuzmin A., Bastian U., Kuimov K., Lindegren L., Makarov V. V., Roser S., 1998, [announced in] A&A, 335, L65 Hg E. et al., 2000, [announced in] A&A, 355, L27 Houk N., 1982, Michigan Catalogue of Two-Dimensional Spectral Types for the HD Stars, Vol. 3, Declinations -40.0 to -26.0. Univ. of Michigan Press, Ann Arbor, Michigan Houk N., Smith-Moore M., 1988, Michigan Catalogue of Two-Dimensional Spectral Types for the HD Stars, Vol. 4, Declinations -26.0 to -12.0. Univ. of Michigan Press, Ann Arbor, Michigan Johnson H. L., Morgan W. W., 1953, ApJ, 117, 313 Kazarovets E. V., Samus N. N., Durlevich O. V., Frolo M. S., Antipin S. V., Kireeva N. N., Pastukhova E. N., 1999, Inf. Bull. Variable Stars, 4659, 7 Keenan P. C., McNeil R. C., 1989, ApJS, 71, 245 Koen C., Laney D., van Wyk F., 2002, MNRAS, 335, 223 Morgan W. W., Keenan P. C., Kellman E., 1943, An Atlas of Stellar Spectra with an Outline of Spectral Classification. Univ. Chicago Press, Chicago Udry S., Mayor M., Queloz D., 1999, in Hearnshaw J. B., Scarfe C. D., eds, ASP Conf. Ser., Vol. 185, Precise Stellar Radial Velocities. Astron. Soc. Pac., San Francisco, p. 367 van den Bos W. H., 1928, Ann. Leiden Obs., 14, part 4

Table 4. Radial-velocity observations of HD 93140. Table 5. Radial-velocity observations of HD 94563. Table 6. Radial-velocity observations of HD 95166. Table 7. Radial-velocity observations of HD 96402. Table 8. Radial-velocity observations of HD 96818. Table 9. Radial-velocity observations of HD 97574. Table 10. Radial-velocity observations of HD 99584. Table 11. Radial-velocity observations of HD 100306. Table 12. Radial-velocity observations of HD 116463. Table 13. Radial-velocity observations of HD 117161. Table 14. Radial-velocity observations of HD 118116. Table 15. Radial-velocity observations of HD 119011. Table 16. Radial-velocity observations of HD 119087. Table 17. Radial-velocity observations of HD 119175. Table 18. Radial-velocity observations of HD 120503. Table 19. Radial-velocity observations of HD 120852. Table 20. Radial-velocity observations of HD 124536. Table 21. Radial-velocity observations of HD 125187. Table 22. Radial-velocity observations of HD 125341. Table 23. Radial-velocity observations of HD 27600. Table 24. Radial-velocity observations of HD 27871. Table 25. Radial-velocity observations of HD 28426. Table 26. Radial-velocity observations of HD 31341 B. Table 27. Radial-velocity observations of HD 35646. Table 28. Radial-velocity observations of HD 35993. Table 29. Radial-velocity observations of HD 36186. Table 30. Radial-velocity observations of HD 36562. Table 32. Radial-velocity observations of HD 33978.

This material is available as part of the online article from http://www.blackwell-synergy.com

S U P P L E M E N TA RY M AT E R I A L The following supplementary material is available for this article online: Table 2. Radial-velocity observations of HD 88913. Table 3. Radial-velocity observations of HD 92789.

This paper has been typeset from a TEX/LTEX file prepared by the author. A

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