astrometric search for unseen stellar and sub-stellar ... · a list of the stars known within five...

A S T R O M E T R I C S E A R C H F O R U N S E E N S T E L L A R

A N D S U B - S T E L L A R C O M P A N I O N S TO

N E A R B Y S T A R S A N D T H E P O S S I B I L I T Y

OF T H E I R D E T E C T I O N

S A R A H LEE LIPPINCOTT

Sproul Observatory, Swarthmore College, Swarthmore, Penn. 19081, U.S.A

(Received 10 August, 1978)

Abstract. Unseen companions to nearby stars are found astrometrically through perturbations in the proper motion from photographs taken with long-focus telescopes. The number of known unseen astrometric companions to nearby stars with photocentric orbits has grown by thirty percent in the last few years. Individual cases are discussed and optimum epochs given for resolution of the components. Orbital analysis of the photocentric positions on the photographic plates provides all information for accurate mass determination of the components except for Am and angular separation, p, of the two components which must come from another technique. There are potentially thirty low luminosity stars including some likely sub-stellar objects whose masses could be instantly found with the observations of these additional two parameters.

A list of the stars known within five parsecs as of 1978 July is given and the status of unseen companions to these stars is discussed on the basis of long interval astrometric coverage.

1. Introduction

Mass , w h e t h e r it be s te l lar , in te rs te l la r , galact ic , or that of the Universe , is one of the

mos t i m p o r t a n t p a r a m e t e r s in a s t ronomy. The d e t e r m i n a t i o n of s te l la r mass is

f u n d a m e n t a l to the u n d e r s t a n d i n g of the p rocess of s te l lar fo rma t ion . It p lays a key

ro le in the s tudy of s te l lar in ter iors , and in s te l la r evolu t ion . S te l la r mass is essent ia l to

the s tudy of the mass dens i ty of ou r pa r t of the G a l a x y and of the G a l a x y as a whole .

S te l la r mass can be d e t e r m i n e d accura te ly and d i rec t ly only th rough the s tudy of

o rb i t a l m o t i o n in s te l lar sys tems of known dis tance .

In this p a p e r we will survey stars n e a r e r than five parsecs for ev idence of dupl ic i ty

f rom the a s t rome t r i c d i scovery of unseen compan ions , and we will p lace some l imits

on the exis tence of faint c o m p a n i o n s f rom p h o t o g r a p h i c obse rva t ions thus far

ob t a ined . W e shall also discuss the stars known to have unseen a s t rome t r i c

c o m p a n i o n s and indica te the bes t t imes for visual de tec t ion . Thus this survey m a y

serve as a guide to fu r the r obse rva t ions with new techniques on the g round or f rom

orb i t ing te lescopes . Th rough s tudies of nea rby b ina ry stars we can bes t gain insight

into the f r equency and masses of very low luminos i ty ob jec t s w h e t h e r they be stel lar ,

sub-s t e l l a r or p l ane t - l i ke . Since the vast m a j o r i t y of s tars in our s te l lar n e i g h b o r h o o d

are much fa in ter and less mass ive than ou r Sun, the c o m p a n i o n s d i scove red will

obv ious ly con t r i bu t e to our k n o w l e d g e of the faint end of the luminos i ty funct ion and

even tua l ly to the lower pa r t of the mass - luminos i t y re la t ion .

Space Science Reviews 22 (1978) 153-189. All Rights Reserved Copyright �9 1978 by D. Reidel Publishing Company, Dordrecht, Holland

154 S A R A H LEE LIPPINCOTI"

The direct approach to mass determination is found in Kepler's third Law which provides a statement for the sum of the masses:

a 3 1 ~JJ~A + ~A'~B - -p3 p 2 �9 (1)

Mass is expressed in units of solar mass when a, the semi-axis major of the relative orbit and p, the parallax, are in arc seconds, and P, the period, in years. Mass ratios may be found photographically by referring the observed orbital motion(s) to a reference frame of background stars. These values may be of much higher accuracy than the masses themselves, because the distance does not enter the picture.

Knowledge of duplicity results from a number of observational approaches: (1) The study of radial velocity leads to discovery of spectroscopic binaries, usually stars whose separations are too close for visual resolution. The obtainable knowledge of their orbital motions lies in one observational coordinate only and favors discovery of pairs whose orbital planes are at large angles with respect to the plane of the sky. Because of their faintness red dwarfs are the least studied spectroscopically. (2) Photometric monitoring leads to the discovery of eclipsing binaries; the analysis of the light curve provides relevant information about the stars involved. The separations found are generally in the same realm as for spectroscopic pairs, and the orbital periods likewise are usually counted in days or weeks. Of course there are exceptions viz. VV Cephei and e Aurigae referred to later. Eclipsing binaries may be at any distance, there is no selection effect favoring proximity and there are few in our stellar neighborhood. (3) Binaries found visually have periods upward from one year ranging into hundred of years corresponding to their greater separations. The measurements of position angle and separation commenced over 200 years ago and still continue, while since the beginning of the present century photographic observations for wider pairs play an important role (Hertzsprung, 1920). Thus the necessary data are provided to determine the orbital elements of the longer-period visual binaries found in catalogues today. (4) Photographic studies from astrographs lead to discovery of proper motion pairs- usually systems too widely separated to show significant orbital motion over the covered interval of time. (5) Long-focus photographic studies lead to discovery of duplicity through perturbations and subsequent knowledge of orbital elements through the analysis of the motion of the photocentric image against a background of 'fixed' stars. Because of the absolute smallness of the amplitudes of the orbital motion, discoveries are generally limited to stars in the nieghborhood of the Sun- the group of stars which is the prime consideration in this paper. (6) Techniques involving rapid accumulation of photometric and positional data with high resolution at the telescope give promise of revealing stellar duplicity. Photometry of stars occulted by the moon have revealed additional numbers of close pairs, whose separations may be as small as 0"01. But a single observation yields only a projected separation in one coordinate in the plane of the sky; observations must then be followed up by other available techniques at repeated intervals to gain information on orbital elements. Area scanners and other

A S T R O M E T R I C S E A R C H F O R U N S E E N S T E L L A R A N D S U B - S T E L L A R C O M P A N I O N S ] 5 5

techniques such as speckle interferometry are increasingly playing a role, but as yet

they have limitations which restrict their use (Rakos, 1974; McAlister, 1977).

From a theoretical point of view, stellar masses may range from - 5 0 to -0.06~JJto.

The rigorous requirements for direct mass determination beyond the initial discovery of stellar duplicity, namely, magnitudes, orbital elements, and precise distance, pose a variety of problems. The individual components of close visual binaries

lack photoelectric magnitude precision; generally they are only eye estimates. Ground-based photoelectric magnitude determinations are necessarily combined

magnitudes except for the very widest pairs, those in general with orbital periods so long that accurate masses are as yet unattainable. Determination of orbital elements

requires extended coverage of the relative positions of the components in time appropriate to the orbital period.

A prime prerequisite for determination of masses is knowledge of the parallax of the system, which renders the value for the angular scale of the orbit in linear units of

distance such as the astronomical unit. An error in the parallax enters with the third power in the linear value of the major axis of the orbit so that in practice only nearby binary stars whose trigonometric parallaxes can be accurately measured are available for rigorous mass determinations. The visual orbit thus determined yields the sum of

the masses of the system, but leaves the individual masses undetermined. At the turn of this century photographic programs with long-focus refractors were

established to determine trigonometric parallaxes; and in general they were exten-

ded to follow visual doubles for the purpose of measuring their positions against a background of reference stars. Thus the orbits of the individual components are

measured as they revolve around their common center of gravity, mass ratios then follow from a comparison of the scales of the individual orbits. Programs toward this

goal have continued over a long interval of time at a few observatories in the USA such as Allegheny, McCormick, Sproul, Van Vleck, and Yerkes. Figure 1 shows a photograph of the Sproul telescope which shows the proportions typical of the long-focus refractor.

2. Techniques of Long-Focus Astrometry for Binary Systems and Perturbation Analysis

The resolution capabilities of the optics of a telescope are never achieved at ground level due to the light path through the Earth's atmosphere. With the Sproul refractor where 1 mm= 18':87 in the focal plane, the diameters of acceptable photographic images are about 1" to 2". For photographically resolved binaries we may express each component's geocentric position relative to a field of 'fixed' stars in rectangular equatorial coordinates:

X A = Cx + I~xt + r rP , - B A X , (2)

Xs = Cx +/z~t + ~-P~ - (1 - B ) A X , (3)

156 SARAH LEE LIPPINCOTT

Fig. 1. The 61-cm long-focus Sproul refractor; scale: 1 m m = 18':87. The telescope has been in cont inuous use for astrometric photography since late 1911 except for the interval May 1966-January 1967, when the ins t rument was renovated mechanically and electronically, Nearly 140 000 plates have

been taken with this telescope.

ASTROMETRIC S E A R C H FOR UNSEEN STELLAR AND SUB-STELLAR COMPANIONS 157

with similar equations in y. The/x and 7r are proper motion and parallax relative to the mean of the reference stars. The last terms are the orbital displacements, AX, A Y,

in the visual apparent orbit of B - A , and the fractional mass

~tB B = (4)

~ A "-~ ~ B "

In visual double star orbital analysis the relative position may be expressed in rectangular coordinates

A X = B x + Gy , (5)

A Y = A x + F y , (6)

where x and y are elliptical rectangular coordinates in the unit orbit as functions of the dynamical elements P, T, e; B, G, A, F, the Thiele-Innes constants, are the geometric elements expressing the scale and orientation of the orbit in the plane of the sky. The orbits of A and of B are replicas of the visual relative orbit modified by scale which is determined by the mass ratio of the two components; the orientation of the orbits A and B differ in phase by 180 ~ The scales are represented by their semi-axes major where a A q- aB = a ; a A = B a o r A X A = B A X , /~ Y A = B A Y for the orbital displacements at any particular time.

If the components are too close to be resolved photographically, and the secondary is fainter by more than 4 magnitudes, the resulting image is only that of the A component and the above equations hold. But if the A m ~ 4, the image is a blend of the two components, and a photocentric orbit is measured which is generally similar to the relative orbit, diminished in scale. The blending of photographic images is a complicated process depending on the luminosities lA and lB of the two components and their linear separation in the focal plane. In the first approximation the resulting photocentric image may be represented as a weighted light center; the fractional distance/3 of the primary to the photocenter in terms of the distance between the two components being

18 1 /3 -- 1A + IB o r 1 q- 1 0 (0 '4)am " (7)

The last word has not been said on the blending effect of positions of photographically unresolved astrometric binaries (Feierman, 1971), nor of proximity effects of close doubles at or near the limits of resolution on the photographic plate of ground-based telescopes. Whatever functional form is adopted for/3 the blended image may be represented by the modification in the orbital displacement

( B - / 3 ) A X , ( B - / 3 ) A Y . (8)

The scale of semi-axis major of the photocenter is

o~ = (B -/3)a (9)


Figure 2 shows the relative spacing of the component 's primary to photocenter, barycenter and secondary. Additional formulae for analyzing the geocentric position of the photocenter are found elsewhere (van de Kamp, 1967, 1971, 1975).

Fig. 2. The relative photographic positions of primary and companion objects as point sources are shown along with the photocenter and center of mass. For the case of a photographically unresolved binary the

diameter of the blended image fully encompasses those of primary and secondary.

The above discussion of the relation of the components of binary pairs relative to a system of background stars is applicable in the analysis of the photocenter where variable proper motion is interpreted as orbital motion. The principle of discovery of duplicity from perturbation in the proper motion of a star was first demonstrated by

Bessel well over 100 years ago when he correctly interpreted perturbations in the motions of Sirius and of Procyon as due to unseen companions. Since that time there have been many discoveries of unseen companions from studies of proper motion from photographs taken with long-focus telescopes, but as yet only two of the companions have been visually detected, namely the companions of Ross 614 (Lippincott, 1955; Lippincott and Hershey, 1972) and of VW Cephei (Hershey, 1975b).

The photocentric orbital analysis gives information for the most auspicious time for visual observation, i.e., at greatest separation of the components, an estimate of the separation, and the likely range in Am. Through Kepler 's third Law we are able to derive a minimum mass for the companion adopting a value for the sum of the masses which yields a mass appropriate to the visible component and assuming that the

ASTROMETRIC SEARCH FOR UNSEEN STELLAR AND SUB-STELLAR COMPANIONS 159

image is formed solely by the light of the visible component, or that /3 = 0 (from Equation (9)).

~-"~B = o~p-2/3 (~'~ A + ~ B ) 2 /3 . (lO)

In this case, o~ = aA. For further details see van de Kamp (1975). The P, T, e, and the orientation elements may be well-known; the semi-axis major

of the photocentric orbit may have high accuracy in astronomical units, due to well-determined parallax. But until the two parameters, A m and the separation,

which provide the scale of the relative orbit are obtained, rigorous masses for the components cannot be determined. For some of the cases of unseen companions the

A m is great and the separation small, particularly for the short-period orbits. This

situation makes visual detection difficult, if not impossible; also, other techniques

probably cannot help at present for the many faint stars that interest us. It is

anticipated that in the 1980s space telescopes will have the necessary equipment to detect companions and make the required measurements to provide 'instant masses' for those systems whose perturbations have been analyzed.

When/3 is not zero, i.e. the unseen companion contributes light to the photo-

center, Equation (10) becomes

~)Y~B = a P - 2 / S ( ~ A + 9.RB)2/3 +/3 (gJ~A + g)~B). (11)

We may adopt a reasonable mass for the visible component appropriate to its

absolute magnitude, color or spectral type and try various values for A m leading to

corresponding values of/3. Combining Equations (9) and (11) or (1), we find a range in values for the mass of the companion. We may or may not assume that the mass of

the companion must follow the mass luminosity relation. In general the resulting range in mass for ~ s is smaller than the range appropriate to the visible component. Also a range in the values for the sum of the masses leads to values of a.

3. Sproul Astrometric Data as Background for Perturbation Analysis

Before we can turn to a scrutiny of the stars nearer than five parsecs in the search for unseen companions we should discuss the inherent limitations for discovery. In order to detect perturbations of small amplitude, -0"05 , from astrometric data, intensive

observational material is required to reduce the random error, and care must be taken to have homogeneous data as free as possible from systematic errors which change with time. Singe we are dealing with observations spaced over a number of decades, the data are prone to systematic errors from changes in the optics or other aspects of the technique of securing positions of stars relative to one another on the photographic plate. For this reason we must dwell on efforts to recognize systematic errors during the course of the work.

The astrometric programs should go beyond the time interval of traditional trigonometric parallax studies to exploit the discovery of unseen companions to

160 S A R A H L E E L I P P I N C O T T

parallax stars. Traditionally a few plates at large parallax factors in early evening and late morning continued over 3 to 5 yr yield a satisfactory parallax determination. Generally the position of the target star is reduced through a number of reference stars to a standard frame through linear plate constant reduction. These plate mean or night mean positions X, Y are analyzed:

X --- c~ + ~ t + ~rPa (12)

Y = cy + p.yt + 7rP~ (13)

through a least squares solution to yield the parameters c, ix, and ~r. The residuals

from these solutions based on, say, ten or more night means per year are scrutinized for trends in each coordinate.

Perturbation discovery requires a long-range time approach for long-period binary discovery, and intensive short- term coverage for identifying the statistically

small amplitudes which accompany short-period binaries. We have only begun to

detect in the residuals binary characteristics with periods up to about fifty years; for nearby stars this would imply a large Am since the components for a nearby star should have been resolved visually. On the other hand, the shortest period found for an astrometric binary is 0.77 yr.

Not more than about half a dozen observatories have parallax plates taken decades ago with continuing astrometric programs. The Sproul Observatory with its 61-cm

refractor has accumulated about 140 000 plates since 1911, primarily on nearby

stars. In 1937 Peter van de Kamp initiated a long-range program, building upon and

modifying the one already established at the Sproul Observatory, to search for unseen companions to stars with large parallax. Generally stars of the 12th magni-

tude or brighter observable from the latitude of Swarthmore are given intensive coverage over the observing seasons. Special emphasis is given to stars nearer than five parsecs. This program has continued for over forty years, with modificat ions- adding new stars of promise and temporarily dropping certain stars which have been measured and show no orbital motion over an extended period of time. Other observatories are beginning to make more intensive observations on some of these

nearby stars, which will strengthen the interpretations of some of the overlapping data in time.

The amplitudes of some of the suspected perturbations may be just at the 'noise' level. It should not be expected that an unambiguous positive or negative result will always be possible, or at least not only after an interval of time commensurate with a number of likely periods. The attainable accuracy of stellar positions is restricted by random errors due to the light path in the atmosphere through the area of the lens, the optics, the emulsion, and finally, the measurement. But more serious are systematic errors which involve the stability of the telescope behavior over many years. Since this is such an important aspect of the analysis of any astrometric series, some details of the observational data from the Sproul telescope will be given before

A S T R O M E T R I C S E A R C H F O R U N S E E N S T E L L A R A N D S U B - S T E L L A R C O M P A N I O N S 1 6 1

the survey of stars nearer than five parsecs; few intensive studies of this kind have been made thus far at other observatories.

Descriptions and analysis of the plate material obtained with the Sproul refractor have been given elsewhere (Lippincott, 1957, 1971). The subject matter of these two references also deals with the accuracy of Sproul relative photographic positions from statistical studies of night residuals resulting from least squares solutions for c,

/x, ~r and orbital motion when required, in x and in y (R. A. and Decl.), for many series. Analysis of the residuals of over 250 star series covering 4 or more decades when averaged as 'all star' residuals with respect to time provides a monitoring system for the behavior of the lens system over the interval of the time of observations. These averaged residuals indicate the accuracy we are dealing with in the interpretation of trends in series of nearby stars. Yearly means grouped in various ways: size of configuration, magnitude of central star, position in sky, time of night, season, hour angle, etc., give insight on the random and systematic errors with respect to various parameters. The 1971 reference included material up to the year 1968. Subsequent analyses essentially confirm the earlier results. As an example we show in Figure 3a, b the annual averages of 'all star' residuals from 1950 to 1977 grouped with respect to declination, which is part of the continuous larger study of

Decl

> 6 0 ~ -

4 0 L 6 0 ~

2 0 ~ ~

X ALL STAR y ALL STAR Dec l

+ "" , - ~ , o , , -'+ -o > 6 0 ~ -T,_.+.=+ T . , , . . . . . - , ,+ - I / 4 + . o

1950 60 70 80 1950 6 0 70

4._ 4 4- �9 + 4 0 L {

-I /4

+1/4

- r / , ~

T §

8O

,u

< 20 ~ +1/4

- I / . / < i

~ . - ~ + I ~ Meon of moSoee, w- #nmme,~ ; o ~, : . s , ,~ '= . . . MeQI oi l D e c l /

X - ~ - - -I/J- all D �9 = ~ 1 0 0 Y

nights: + =-30 ~ lO0 ~] n i g h t s = o =~30

(a) (b)

�9 ; > 1 0 0 * = 7 3 0 ~ I00 o= ~30

Fig. 3a-b. Residuals from Sproul long-interval series are combined into yearly means in x and y. They serve to monitor the behavior of the optics of the 61-cm refractor in various parts of the sky.


monitoring the long-range telescope behavior. Earlier observations also exist from 1938 and for some star series go back to 1912 which serve to anchor the proper motions. Included in the figure are over twelve thousand night's observations; the number of exposures for each star included varies from 1 to 16 per night, generally distributed on one or two double plates. At present we have about twice the number of night residuals used earlier (Lippincott, 1971), which permits greater diversity in subdividing according to various parameters. Since 1972 nearly all measurements have been made on the Grant two-coordinate machine which yields greater accuracy (Hershey, 1975a), in far less measuring time.

The p.e.1 for a series ranges from +0'.'015 to +0':045 and more when the 'central' star is a distant companion, far off the optical center with poor magnitude compensation. If small configurations and ideal magnitude compensation were always possible with 3 to 5 reference stars, a p.e.1 near the minimum in the range quoted above would be generally achieved.

Hershey's studies (1973a, 1977, 1978)with up to twelve reference stars show that the accuracy ranges from no improvement up to but not exceeding the improvement predicted by the ~ / ~ geometric relation; provided that the reference frame is small in area, the improvement becomes minimal when the number of reference stars rises above five. (D is the dependence, a measure of weight of a reference star.) A larger number of reference stars implies a larger configuration and wider range in magnitudes resulting in the introduction of magnitude errors; with a sufficient number of reference stars additional parameters can be introduced and a thorough study of the field made, but this requires some 30 or more reference stars, which is impractical if not impossible in most cases. At Sproul we choose three to six appropriate reference stars with respect to magnitude and position in the field and reduce the position of the central star to a standard frame through linear plate constants. Brighter central stars usually require a rotating sector to reduce the image size to equality with the reference stars. And this in turn excludes possible reference stars near the optical center.

Three instrumental equations might be expected in the optical behavior of the 61-cm objective due to the following: 1941.82, objective adjusted; 1949.21, new objective cell; 1957.9, objective adjusted and recollimated. It has been obvious for a long time (Lippincott, 1957) that the 1941.8 break in the material resulted in a color shift in x, and in y, from 1941.8 - 1942.3, but only gradually has it become clear that the interval 1941.8 to 1949.21 represents a shift in x, which is now allowed for.

The telescope has produced residuals free from long-term systematic errors greater than +0re.m0003 (+0'.'006) in both x and y coordinates since 1957 for all regions of the sky, and for some since 1950 and earlier. Any trends for the various groups in Figure 3 or for smaller groups with respect to position in the sky are helpful in interpreting the normal point residual behavior for individual stars due to unseen companions. However, ultimately each star series must be evaluated on its own. Many stars with strong coverage show no shifts or periodic motions which give evidence for systematic errors over an interval of several decades. There is no clear

A S T R O M E T R I C S E A R C H F O R U N S E E N S T E L L A R A N D S U B - S T E L L A R C O M P A N I O N S 163

foolproof way to judge a field in advance of measurement in order to predict or to

allow for systematic errors. The subtleties in long-term position errors -0':03 or

-1 .5 tz are very elusive; comparisons with other astrometric telescopes are hardly

yet possible because of lack of intensive long-range coverage elsewhere.

4. Stars within 5 parsecs

Table I gives pertinent data on stars known to be within five parsecs from available data in July 1978. We have included systems with parallaxes greater than 0"190. This list supersedes an earlier one of van de Kamp (1971). There is some shifting of order,

deletions and the addition of three newly found systems. The headings are self- explanatory. The m~, spectrum and parallax are taken from Gliese's catalogue (1969)

unless subsequent data warrant a change. In principle, the nearest systems are most likely to be the easiest to detect

accompanying unseen companions. The Sproul Observatory's intensive scrutiny of the nearby stars is necessarily limited to those stars north of approximately -18 ~ declination. Twenty-eight out of forty-six systems in Table I, excluding the Sun, have

been studied at Sproul. The remaining ones are either too far south, too faint, or newly discovered. Table II gives the observational data from the Sproul refractor which form the basis for discussion in many cases for either positive or negative results in the astrometric search for unseen companions. Most of the series date back to 1937 when van de Kamp started the intensive search for unseen companions. Not all the systems within 5 parsecs have been brought up to date with measurement and analysis. Those not measured since 1972 will be remeasured on the Grant machine to

do justice to the photographic material. Some general statements may be made about the limitations of discovery of

duplicity among the stars nearer than 5 parsecs. For a system where Am ~ 2, and the semi-axis major of the relative orbit ~ 1 AU, we should expect visual discovery

already to have been made for stars brighter than the tenth magnitude. For a system of nearly equal magnitudes implying nearly equal masses, astrometric discovery through perturbation is very difficult due to the vanishing size of the photocentric orbit. On the other hand, for a system with Am _> 3 and correspondingly large mass difference, the photographic technique may reveal the orbit of the bright component about the barycenter of the system, while the detection becomes difficult or impossible by visual means. Considering that the majority of the nearby stars are cool main sequence stars, we conclude that their companions will obviously be fainter and

presumably less massive. Short period systems will give rise to small separations while those with long periods, a quarter of a century and more, should yield separations well resolved on the photographic plate, but will show up only if they are sufficiently luminous. Gatewood (1976) has made further comments on the pro-

bability of detection of unseen companions. Out of the 63 individual visual components in Table I twenty-nine are fainter

than M~ = 12.0. The two faintest stars in the list are not as faint as the faintest star


TABLE I

Stars nearer than five parsecs

No. Gliese Name (1950) Proper Position Radial Parallax Distance No. motion angle velocity light

RA Decl. km s -1 years

1 Sun 2 559, c~ Centauri a 14h36m2 -60038 ' 3':68 281 ~ - 2 2 0'.'753 4.3 3 699 Barnard's * 17 55.4 +4 33 10.31 356 -108 0.544 6.0 4 406 Wolf 359 10 54.1 +7 19 4.71 235 +13 0.432 7.5 5 411 BD+36~ 11 00.6 +36 18 4.78 187 - 8 4 0.400 8.2 6 65 Luyten 726-8 1 36.4 -18 13 3.36 80 +30 0.385 8.4 7 244 Sirius 6 42.9 - 1 6 39 1.33 204 - 8 0.377 8.6 8 729 Ross 154 18 46.7 -23 53 0.72 103 - 4 0.345 9.4 9 905 Ross 248 23 39,4 +43 55 1.58 176 -81 0.319 10.2

10 144 e Eridani 3 30.6 -9 .38 0.98 271 +16 0.305 10.7 11 447 Ross 128 11 45.1 +1 06 1.37 153 -13 0.302 10.8 12 866 Luyten 789-6 22 35.7 -15 36 3.26 46 - 6 0 0.302 10.8 13 820 61 Cygni 21 04.7 +38 30 5.22 52 - 6 4 0.292 11.2 14 845 e Indi 21 59.6 -57 00 4.69 123 - 4 0 0.291 11.2 15 71 r Ceti 1 41.7 - 1 6 12 1.92 297 - 1 6 0.289 1~i:3 16 280 Procyon 7 36.7 +5 21 1.25 214 - 3 0.285 11.4 17 725 N2398 18 42.2 +59 33 2.28 324 +5 0.284 11.5 18 15 BD+43~ 0 15.5 +43 44 2.89 82 +17 0.282 11.6 19 887 CD-36~ 23 02.6 - 3 6 09 6.90 79 +10 0.279 11.7 20 G51-15 8 26.9 +26 57 1,26 241 0.273 11.9 21 54.1 L725-32 1 10.1 -17 16 1.22 62 0.264 12.3 22 273 BD+5~ 7 24.7 + 5 23 3.73 171 +26 0.264 12.3 23 825 CD-39~ 21 14.3 - 3 9 04 3.46 251 +21 0.260 12.5 24 191 Kapteyn's* 5 09.7 -45 00 8.89 131 +245 0.256 12.7 25 860 Kriiger 60 22 26.3 +57 27 0.86 246 - 2 6 0,254 12.8 26 234 Ross 614 6 26.8 - 2 46 0.99 134 +24 0.243 1:3.4 27 628 BD-12~ 16 27.5 - 1 2 32 1.18 182 -13 0.238 13-77 28 473 Wolf 424 12 30.9 +9 18 1.75 277 - 5 0.234 13.9 29 35 van Maanen's * 0 46.5 +5 09 2.95 155 +54 0.232 14.0 30 1 CD-37~ 0 02.5 -37 36 6.08 113 +23 0.225 14.5 31 83.1 Luyten 1159-16 1 57.4 +12 51 2.08 149 0.221 14.7 32 380 BD+50~ 10 08.3 +49 42 1.45 249 - 2 6 0.217 15.0 33 674 CD-46~ 17 24.9 - 4 6 51 1.13 147 0.216 15.1 34 832 CD-49~ 21 30.2 - 4 9 13 0.81 185 +8 0.214 15.2 35 682 CD-44~ 17 33.5 -44 17 1.16 217 0.213 15.3 36 687 BD+68~ 17 36.7 +68 23 1.33 194 - 2 2 0.213 15.3 37 G158-27 0 04.2 - 7 48 2.06 204 0.212 15,4 38 G208-44/45 19 53.3 +44 17 0.75 143 0.210 15,5 39 876 BD-15~ 22 50.6 - 1 4 31 1.16 125 +9 0.209 15.6 40 166 40 Eridani 4 13.0 - 7 44 4.08 213 -43 0.207 15.7 41 440 L145-141 11 43.0 - 6 4 33 2.68 97 0,206 15.8 42 388 BD+20~ 10 i6.9 +20 07 0.49 264 +11 0.203 16.0 43 702 70 Ophiuchi 18 02.9 +2 31 1.13 167 - 7 0.203 16.0 44 873 BD+43~ 22 44.7 +44 05 0.83 237 - 2 0.200 16.3 45 768 Altair 19 48.3 +8 44 0.66 54 - 2 6 0.198 16.5 46 445 AC+79~ 11 44.6 +78 58 0.89 57 -119 0.193 16.8 47 G9-38 8 55.4 +19 57 0.89 266 0.190 17.1

a The position of c~ Centuri C ('Proxima') is 14h26m3, --62~ 2~ from the center of mass of a Centauri A and B. The proper motion of C is 3':84 in position angle 282 ~ Gliese No. 551.

ASTROMETRIC S E A R C H F O R UNSEEN STELLAR AND SUB-STELLAR COMPANIONS 165

T A B L E I (cont.)

No. Visual apparent magni tude Visual absolute Visual luminosity and spectrum magni tude

A B C A B C A B C

1 - 2 6 . 8 G2 4.8 1.0 2 - 0 . 1 G2 1.5 K0 11.0 M5e 4.4 5.7 1.5.4 1.5 0.44 0.00006 3 9.5 M5 b 13.2 0.00044 4 13.5 M8e 16.7 0.00002 5 7.5 M2 10.5 0.0052 6 12.5 M6e 13,0 M6e 15.4 15.9 0.00006 0.00004 7 - 1 . 5 A1 8,3 D A 1.4 11.2 23. 0.0028 8 10.6 M5e 13.3 0.0004 9 12.3 M6e 14.8 0.00010

10 3.7 K2 c 6.1 0.30 11 11.1 M5 13.5 0.00033 12 12.2 M6 14.6 0.00012 13 5.2 K5e 6.0 K7 c 7.5 8.3 0.083 0.040 14 4.7 K5e 7.0 0.13 15 3.5 G8 5.9 0.39 16 0.4 F5 10.7 2.7 13.0 7.0 0.0005 17 8.9 M4 9.7 M5 11.2 12.0 0.0028 0.0013 18 8,1 M l e S B 11.0 M6e 10.4 13.3 0.0058 0.00040 19 7,4 M2e 9.6 0.012 20 14.8 m 17.0 0.00001 21 11.5 M5e 13.6 0.00030 22 9.8 M4 12.0 0.0014 23 6.7 M0e 8.8 0.025 24 8.8 M0 10.8 0.0040 25 9 .7M4 11.2 M6 11.7 i3.2 0.0017 0.00044 26 11.3 M5e 14.8 13.3 16.8 0.0004 0.00002 27 10.0 M5SB: 11.9 0.0014 28 13.2 M6e 13.4 M6e 15.0 15.2 0.00008 0.00007 29 12.4 DG 14.2 0.00017 30 8.6 M3 10.4 0.00058 31 12.3 M8 14.0 0.00020 32 6.6 K7 8.3 0,040 33 9.4 M4 11.1 0.0030 34 8.7 M3 10.4 0.0058 35 11.2 M5 12.8 0.00063 36 9.1 M3.5SB b 10.8 b 0.0040 b 37 13.7 m 15.4 0.00005 38 13.4 me 14.0 m 15.0 15.6 0.00008 0.00005 39 10.2 M5 11.8 0.0016 40 4.4 K0 9.5 D A 11.2 M4e 6.0 11.1 12.8 0.33 0.0030 0.00064 41 11.4 D G 12.6 0.0008 42 9.4 M4.5 10.9 0.0035 43 4.2 K1 6.0 K5 5.7 7.5 0.42 0.083 44 10.2 M4.5e b 11.7 b 0.0017 b 45 0.8 A7IV,V 2.3 10. 46 10.9 M4 12.3 0.0010 47 14.1 m 14.9 m 15.5 16.3 0.00005 0.000021

u Unseen components . c Suspected.


TABLE II

8proul astrometric coverage of stars nearer than 5 parsecs

No. Plates measured Reference

Interval Nights 1900+

3 16-77 ~ 1000 4 37-74 72 5 12-75 511 6 48-59 38 9 37-74 310

10 38-72 238 11 38-70 88 12 40-74 90 13 12-72 279 15 38-77 71 17 13-66 224 18 37-70 70 21 55-73 36 22 37-72 329 25 38-66 87 26 38-72 252 27 38-78 78 28 38-71 140 29 37-77 208 31 39-74 49 32 38-64 90 36 38-77 287 39 37-67 36 40 37-73 73 42 38-75 284 43 15-71 80 44 37-71 210 46 40-73 51

van de Kamp (1977b) Lippincott and Worth (1976) Lippincott (unpublished) van de Kamp (1959) Lippincott and Worth (1976) van de Kamp (1974), unpublished (1978) Lippincott (1973b) Lippincott and Worth (1976) van de Kamp (1973) Lippincott and Worth (1978), unpublished van de Kamp et al. (1968) Lippincott (1972) Heintz (1973) Lippincott (1973b) Lippincott (1953), unpublished Lippincott and Hershey (1972) Lippincott and Worth (1978), unpublished Heintz (1972) Hershey (1978) Lippincott and Worth (1976) van de Kamp and Lippincott (1949) Lippincott (1977b) Lippincott (1974) Heintz (1974) Lippincott and Worth (1976) Worth and I-Ieintz (1974) van de Kamp (1972) Lippincott (1974)

k n o w n with any ce r t a in ty n a m e l y VB 10 = B D + 4~ B whose M r = 18.9. L u y t e n

(1967) has des igna t ed at leas t four o t h e r s tars which are l ike ly to be in t r ins ical ly

fa in te r than VB 10.

T h e fo l lowing c o m m e n t s on the sys tems in Tab le I a re a i m e d to in form the r e a d e r

of the o b s e r v a t i o n a l s ta te of the search for unseen c o m p a n i o n s and to give p e r t i n e n t

i n fo rma t ion to s t imula t e fu r the r obse rva t ions . R e f e r e n c e s to Sproul s tudies with

some o b s e r v a t i o n a l da t a a re given in Tab le II.

1. S u n . - W e will not t a k e space he re to rev iew the Sun, its a t t e n d a n t p lanets , and the

p e r t u r b a t i o n in the Sun 's m o t i o n caused p r imar i l y by Jup i t e r and Saturn . This and

o the r p e r t i n e n t facts in the con tex t of the Sun as a nea rby s tar are well p r e s e n t e d by

van de K a m p (1971) in his d iscuss ion and list of the n e a r b y stars.


2. A l p h a Centauri. - Little has been done with the nearest stellar system to the Sun since Gasteyer's study (1966). But with current astrometric work in the southern hemisphere, further astrometric studies may be expected. The semi-axis major of the AB orbit is 17"58 or 23 AU with a period of 79.Y92, which does not exclude that A and/or B are close binaries or have planetary systems (Harrington, 1975). The C component is 12 000 AU from the A B system and exhibits flare phenomena. Further astrometric studies and scrutiny of our nearest stellar system are needed.

3. Barnard 's star. - The subdwarf and star with largest proper motion is discussed in the following section on unseen companions.

4. Wol f359 . - T h e limited material from Sproul over thirty-seven years reveals the desirability of a quadratic time term in both coordinates; this is neither called for from the kinematics of Wolf 359 nor from the proper motion of the reference stars. The possibility of orbital motion with a period greater than 40 yr cannot be excluded; further speculation yields a separation of the perturbing body to Wolf 359 of the order of 9 AU. There are no other published studies with long-interval observations of this faint dwarf. Computer analysis reveals no clear evidence of a short periodicity. One of the faintest stars known, Wolf 359 is a flare star.

5. B D + 36~ (Lal 21185).- This star was thought to be an unresolved binary from Sproul studies up to 1963. Subsequent (Lippincott, 1960) Sproul observations do not confirm this interpretation. There remain some trends which do not resemble instrumental origins but do not follow Kepler motion indicative of one perturbing body. Analysis of 56 Allegheny plates from 1934 to 1972 does not reveal variable proper motion (Gatewood, 1974).

6. L 7 2 6 - 8 (UV Ceti) .-Recent studies from the U.S. Naval Observatory (Har- rington and Behall, 1973; Worley and Behall, 1973) indicate P = 26.Y52 with masses 0.115 and 0.109 ~ for this faint pair. A more accurate parallax is desired. A third body has been suspected from the McCormick data, but due to the observing difficulty of this pair its reality must be viewed with great caution. The separation of the two components is currently increasing and will soon reach 2".

7. Sirius. - The components are just past maximum separation in the 50-yr orbit. In 1980 the separation will be 10'.'3 and will reach a minimum 2"6 in 1993 (Heintz, 1960). Both components have been suspected of duplicity from theoretical consi- derations (Heintze, 1968; Eggen, 1956). Also visual micrometer measurements by some observers (Volet, 1932; Zagar, 1932) have given indications of a perturbation but confirmation is lacking and the interpretation of additional components is doubtful. Sirius B is the nearest known white dwarf to the solar system.

168 S A R A H L E E L I P P I N C O T ' F

8. Ross 154. - No reports of anomalous astrometric behavior; the star is also known as V1216 Sgr., a flare star.

9. Ross 248. - Strong evidence for duplicity has not been forthcoming. The thirty-

seven years of observations with the Sproul telescope give no indication of a long

period. There are some short trends of the order of 6-10 yr of very small amplitude. Observations are being continued. This was the first star to have a small light

variation attributed to spots (Kron, 1950).

10. Epsilon E r i d a n i . - The possibility of a companion of sub-stellar mass has been indicated by van de Kamp (1974) from the Sproul data 1938-72. Subsequent homogeneous measurements on the Grant machine including plates up to 1978 render the interpretation unclear with the amplitude close to the noise level (van de Kamp, unpublished). Further extension of the observations may clarify the situation.

Blazit et al. (1977) have detected a companion at a separation of 0"048 in 143 ~ for 1975.63 with speckle observation. This cannot be the possible astrometric

companion. This star and ~' Ceti, long considered as nearby candidates for planetary systems,

have been monitored in radio wavelength radiation for possible detection of artificial signals.

11. Ross 128. - S o far there is no strong evidence for duplicity from the Sproul plates measured on classical eye bisection long-screw measuring machines; plates await measurement on Grant machine. A companion with period longer than fifty years would have to be very faint not to have been observed as the separation from

the primary could be as much as two seconds of arc or more.

12. L789-6 . - N o strong evidence for duplicity. A companion with period longer than fifty years would have to be very faint not to have been observed; the situation would be similar to that of Ross 128.

13. 61 Cygni. - The analysis of the Sproul long series of plates by van de Kamp does not show the indications of the perturbations found in the Pulkovo series (Deutsch and Orlova, 1977) or from the relative B - A measurement on plates taken with

the Hertzsprung multi-exposure method. Interpretation of trends of residuals at the noise level is always difficult. Due to the brightness of the two visible components the chances of visual detection of a sub-stellar object would be even more difficult

because of the greater Am than for, say, a sub-stellar companion to Barnard's star, or to any red dwarf.

14. l?,psilon Indi. - No recent astrometric work has been reported.

15. Tau Ceti. - T h i s is a difficult star for northern observatories, because of the low


declination. Recent Sproul measurements from limited data do not give clear

indication of a perturbation; there is a hint of a 3 yr period at the 'noise' level.

16. P r o c y o n . - Duplicity was discovered by Bessel from variable proper motion in the same manner as for Sirius; but Procyon presents even greater difficulty in resolving the pair. The minimum separation 2'.'22, was passed in 1968 and is

increasing to 5'.'17 between 1987-1990 (Heintz, 1960). The mass of the faint companion indicates that it is a degenerate star. Because of its closeness to the

primary component an uncontaminated spectrum is difficult to obtain.

17. ~2398 . - T h i s visual binary of two late type dwarfs has a period of 453 yr and a

separation of 15". There is some slight trend in the residuals from the Sproul measurements for the B component which might be interpreted as being due to a third body. Until measurements are made on the Grant machine and brought up to date, little should be said. The behavior of McCormick data (Eichhorn and Alden,

1960) also has given rise to the possibility of additional components in the system.

18. B D + 4 3 ~ (Groombridge 3 4 ) . - T h e components are separated by 33" and a likely period is some 2600 yr. The A component has a range in the radial velocity

determinations indicating that it may be a spectroscopic binary. If this characteristic is confirmed, BD + 43~ would have the distinction of being the nearest known

spectroscopic binary. The B component is known to flare.

19. C D - 3 6 ~ - N o recent astrometric studies reported.

20. G51-15. - This star is a newcomer to the list. The parallax is a mean value from the determinations with the USNO 155-cm astrometric reflector and the Yerkes 102-cm refractor. It displaces Wolf 359 as the faintest star within 5 parsecs. However, it is still brighter than BD + 4~ which is beyond this sample. G51-15 shows a striking emission line spectrum in the Balmer series and in H and K of Ca I1

(Liebert, 1976).

21. L 7 2 5 - 3 2 . - T h i s star is another newcomer since the 1971 list. The large difference in the parallax determination in right ascension and declination from the Sproul data gives inconclusive evidence that this discrepancy is caused by short period orbital motion.

22. B D 4 - 5 ~ - A slight trend has been indicated for an eight to ten year period from the Sproul data. But no clear evidence has been found for Kepler motion.

23. C D - 3 9 ~ - No recent astrometric studies have been reported.

170 S A R A H L E E L I P P I N C O T r

24. Kapteyn's s tar . - This is a high velocity subdwarf, and ranks next to Barnard's star in its large proper motion. No recent astrometric studies have been reported.

25. Kriiger 60. - The B component has been known to flare. No sustained evidence of triplicity. Periastron has been recently passed, and the components are becoming better resolved photographically.

26. Ross 6 1 4 . - This is the classic case of the photographic discovery of an unseen companion subsequently detected visually by Baade. (Reuyl, 1936; Lippincott, 1951, 1955; Lippincott and Hershey, 1972). Ross 614B is the star of smallest known mass. Details of difficulty of observation appear in a later section.

27. B D - 1 2 ~ measurements at the Sproul Observatory give no positive evidence for duplicity; the series is weak due to the low declination and the faintness of the star.

28. W o i [ 4 2 4 . - T h e magnitudes are approximately equal and their masses likely close to 0.06 ~ each found from the Sproul data. A better determination of their separations will give a good mass determination. The system is of obvious interest, as the masses are near the lower limit defining stars. The period is close to fifteen years and the separation >~1". The faintness of the pair makes it difficult for visual observers, and the small separation renders it close to the photographic resolving power.

29. Van Maanen ' s s t a r . -Th i s degenerate star appears single over the interval . . . . . . . 1 1937-1977. Periodic motion m either coordinate greater than the equivalent of 3 AU

or 0"05 should have been detected.

30. C D - 3 7 ~ - N o recent astrometric studies reported.

31. L l159-16 . - No suspicion of variable proper motion with short period over the interval 1963-1973 from the Sproul data, nor long period from the anchor point in 1940. The USNO has no report of a perturbation from their short interval accurate parallax series.

32. B D + 5 0 ~ (Grb 1618). - No recent results reported. Sproul recent data are currently being analyzed.

33. C D - 4 6 ~ 34. C D - 4 9 ~ 35. C D - 4 4 ~ recent astrometric studies reported for these three stars, which can be observed only in the southern hemisphere.


36. B D + 6 8 ~ - is a candidate for sub-stellar mass companion. Details are given

in Table III. The visible component is also likely a spectroscopic binary, unrelated to

the astrometric binary.

37. G158-27. - T h e USNO parallax determination and photometry indicates that

the star is a red dwarf.

38. G 2 0 8 - 4 4 / 4 5 . - T h i s system is a newcomer to the list from the USNO 155-cm

astrometric reflector. The separation of the components is about 8" and photometry indicates a pair of red dwarfs (Harrington et al., 1974) similar to L726-8. The

relative proper motion given in the table is for the brighter member. The cor-

responding value for G208-45 is 0'.'628 in 138.~ The large difference in the proper motions of the two components is due to orbital motion; a period between 400 to

700y r is suggested by the USNO astronomers. Cristaldi and Rodon8 (1976) observed nine flares in an aggregate of twenty hours of observing time from 1975

May 9 to July 11. Both components were included in the 25-inch entrance dia- phragm, so it is unknown which star accounted for the flares. There are no spectra leading to spectral classification or radial velocities of this nearby pair of astrophysical interest.

39. B D - 1 5 ~ - T h e limited material shows no evidence for periodicity. The

low declination limits intensive coverage at the Sproul Observatory.

40. 40 E r i d a n L - T h i s interesting system with yellow, red and white dwarf components appears triple with no further components reported from the Sproul

data. The mass of the white dwarf given by the recent Sproul data is 0.4 ~J~G, one of the four white dwarfs for which a mass determination is available.

41. L145-141 . - N o recent astrometric data reported.

42. B D + 2 0 ~ evidence from McCormick and Sproul plates for duplicity has not been sustained. The star is a flare star.

43. 70 O p h i u c h i . - The possibility of a third body has been often reported from a variety of sources, none of which has been confirmed. The authors of the Sproul analysis state ' the lack of evidence for a third body is sustained'.

44. B D +43~ - This is a flare star known as EV Lacerte. The likely duplicity is discussed under the section on unseen companions.

45. Altair. - One of the brightest stars in the list, has no recent astrometric studies reported.


46. A C + 79~176 - This is a late-type subdwarf star, according to Joy. The Sproul series does not indicate duplicity.

47. G 9 - 3 8 . - A newcomer to the list from the USNO. The relative proper motion is

that of the A component. The corresponding value for the B component is 0"787 in

263 ~ . The separation in 1970.68 is 3';4. The photometry gives indication of late spectral type.

5. Unseen Astrometric Companions

In 1975 the author drew up a list of nearby stars known to have unseen astrometric companions. The list and the accompanying discussion had a similar goal as this

presentation namely to stimulate interest and technological advances to try to observe some of the companions. The paper was presented at a European Double Star Colloquium in Coimbra, Portugal in 1975 (1977a). Van de Kamp (1975) made a

full discussion of those systems with known and suspected unseen companions. Now

the l!st, given in Table III, has increased by thirty percent in these few years. This list includes the perturbation for stars within five parsecs given in Table I and stars with

unseen astrometric companions found among the stars studied in our stellar neigh-

borhood beyond that limit. Part of the increase in discovery is due to the highly productive and accurate

parallax program of the USNO with its 155-cm astrometric reflector designed for large scale portrayal of a small field as compared to an astrograph. In the fourteen years of operation there have been some 400 trigonometric parallaxes published to

date. The discovery of unseen companions is simply a by-product with serendipity because the program is aimed at securing four year interval series of low luminosity stars placed on the program primarily for their having proper motions in excess of 1'.'0

per year. A fair number of the stars have ttirned out to have parallaxes smaller than

0"05 rendering the chances of detection of short period photocentric Kepler motion slim because of the expected very small amplitudes. However the parallax program, under unfavorable selection effects for revealing perturbations, nevertheless has revealed so far six which have been published and appear in Table III. The average

period for the photocentric orbit is 5.5 yr excluding Stein 2051 which is a special case. Another interesting system not discussed further is G107-69 /70 a red and white dwarf nearby well separated pair. Strand has reported that the degenerate component was discovered to be a close pair on the USNO plates; it is estimated that the period is of the order of 16 yr and with semi-axis major -0 ' :7 (Franz, 1976).

The other primary contribution to the increase in discovery of perturbations is from the Sproul photographs. Since 1972 the Grant impersonal measuring machine, mentioned earlier, has enabled us to measure plates, with greater accuracy, at the rate of approximately 6000 a year, more than four fold the former rate. Also the passage of time at any observatory means greater coverage and longer interval.


Bessel , a f te r his d i scovery of the p e r t u r b a t i o n s in the p r o p e r mo t ions of Sirius and

P rocyon , and his i n t e rp r e t a t i ons of be ing due to unseen compan ions , wro te in a

c o m m u n i c a t i o n to the R o y a l A s t r o n o m i c a l Socie ty (Bessel , 1845):

"But light is no real property of mass. The existence of number less visible stars can prove nothing against the existence of number less invisible ones" ,

and, rea l iz ing the impl ica t ions of his d iscover ies :

"For even, if a change of mot ion can, up to the present time, be proved in only two cases, yet will all other cases be rendered thereby liable to suspicion, and it will be equally difficult, by observations, to free other proper motions from the suspicion of change, and to get such knowledge of the changes as to admit of its amount being calculated".

H o w fars igh ted and how true!

A l t h o u g h severa l dozen p e r t u r b a t i o n s are now well es tab l i shed , and two m o r e

unseen c o m p a n i o n s have subsequen t ly been seen, how m a n y m o r e r ema in to be

found? In pr inc ip le eve ry star is u n d e r suspicion.

The a s t rome t r i c search for unseen c o m p a n i o n s is in its infancy. M a n y d iscover ies

awai t ing us are nea r the t h re sho ld va lue of o b t a i n a b l e obse rva t i ona l accuracy.

Severa l smal l a m p l i t u d e p e r t u r b a t i o n s found thus far have p r o v e d or will p rove to be

spur ious , or smal le r than or ig ina l ly thought . But how m a n y minu te p e r t u r b a t i o n s

have not ye t been found or have been o v e r l o o k e d e i the r because they are be low the

l imits of a t t a inab le accuracy or because of insufficient obse rva t i ona l efforts, which

r ema in a s i n e q u a n o n for the i r a s t rome t r i c d i scovery?

Van de K a m p (1975) has e s t ima ted the f r equency of unseen c o m p a n i o n s to stars

f rom the l imi ted da ta ava i lab le for stat ist ics - the n u m b e r in the i m m e d i a t e vicini ty of

the sun. F r o m this value an e x t r a p o l a t i o n yields an e s t ima ted four h u n d r e d unseen

c o m p a n i o n s to stars with pa ra l l axes over 0'.'040. W e have a long way to go and the

r o a d to d i scovery requ i res t ime, pe r s i s t ence and h o m o g e n e i t y of da t a to ex t rac t the

smal l a m p l i t u d e p e r t u r b a t i o n s jus t a b o u t at the 'no ise leve l ' i nd i ca t ed by res idua l

e r r o r s .

A s van de K a m p once s t a ted in a no te to me

"It cannot be emphasized strongly enough that the ultimate success of perturbation studies depends on both intensive and extensive observations, year after year, decade after decade, etc. Since a priori neither period nor amplitude are known, each object will have to be considered on its own merits as time progresses. If a perturbation is gradually indicated after, say, one decade of observations, a long-period is indicated, and extensive rather than intensive observations may be desirable. If no increasing deviation from uniform rectilinear is indicated, there may very well be a short period perturbation which can be traced with simple analysis, telescoping the material for a range of short periods, say one to five years.

In any or all cases, 'bide your time'. And don't expect quick results from short-interval or scattered material."

The sys tems in T a b l e I I I a re sufficiently s tud ied a s t romet r i ca l ly to have c o m p u t e d

orb i t s and e p h e m e r i d e s with var ious deg rees of re l iab i l i ty f rom which to m a k e

pos i t iona l p red ic t ions . T h e s epa ra t i ons are ca lcu la t ed on a s sumpt ions of the to ta l

masses of the systems, and t h e r e f o r e m a y not be precise . F o r the cases where the

m a x i m u m sepa ra t i on p is not given, e i the r the orb i t is sufficiently open so that the re is

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little variation throughout the period or the prediction beyond a number of periods is

too shaky. Table III has two subsections-one with systems which have been

resolved visually but with insufficient observations to compute a relative orbit.

However, the photographic observations provide a photocentric orbit. Ross 614 and VW Cephei were first known as astrometric binaries with unseen companions. The second subsection contains three systems which are known spectroscopic and/or

eclipsing binaries which have photocentric orbits. There are other nearby stars

suspected of having unseen astrometric companions. Some are listed in Table II of

van de Kamp's (1975) discussion. Frequently suspicions of unseen companions from the behavior of residuals are noted along with parallax determination lists. Only

further observations can settle those in question. Also there is the whole category of known visual binaries suspected of having third

bodies from the deviations in position angle and/or separation, viz. Baize's (1977) study. Another category is the group of spectroscopic binaries with small amplitude

and periods counted in months or years, viz. Abt and Levy's (1976) work. In some of

these cases the separations may be large enough for observers with high resolution receivers to detect each component separately.

The stars in the two above categories may not necessarily be nearby. Therefore we

have limited this study to astrometric unseen companions which are known to be within the range of significant trigonometric parallax determination thus providing the ability to convert the angular scale of the orbit to linear dimensions. Although VV Cephei and e Aurigae are at great distances, their parallaxes are found very accurately from the relation between their orbital scales in seconds of arc found

astrometrically and in km from the radial velocity orbits found spectroscopically (van

de Kamp, 1977a, 1978). The primary components, excluding VV Cephei and e Aurigae, in Table III range

in m~ from +2.0 (c~ Ophiuchi) to 15.1 (G 139-29) and in M~ from 0.7 (Algol) to 14.6 (G139-29). Five primaries have spectral types earlier than F7, there are six G-type

stars, two K-type and fifteen M-dwarfs. Presumably most of the companions have later type spectra than their primaries, and there is a possibility of a number of the

secondaries having masses close to the minimum theoretical limit for stellar mass. Three may have masses of the order of 0.01 ~33~| but Barnard's star remains the only candidate whose observations can be interpreted as due to Jupiter-like masses. These stars are noted with asterisks in Table III.

Following is a description of salient features of the stars in Table III, expecially appropriate to those who contemplate observations. The prime references are given in the Table and are not repeated in the text.

1. B D + 6 6 ~ ( A D S 4 3 3 ) . - The two visible components have m~ = 10.5 and 12.4 with spectra M2.5e and M4.5; P = 3 2 0 y r ; Z~AaB = 0.65 ~| The Sproul Observatory data permit analysis of the photocentric orbit of Aa , with a period of 15.95 yr. The estimated masses of A and a are 0.40 and 0.13 ~| The predicted separation and Am present difficulty for visual detection, viz. Worley's failure to see

178 SARAH LEE LIPP1NCOq'T

the companion with the USNO 155-cm astrometric reflector. The projected orbit is an open one so the range in separation is estimated to be 0"4 to 0'.'5 and the epoch of maximum separation is omitted from the table.

2. M u Cassiopiae. -This nearby star is of special interest as it has a G5sd spectrum with ultra-violet excess. With high velocity and high galactic eccentricitY, 0.59, it fits into the 'halo' population; the time of its formation was of the order of 101~ yr ago (Catchpole et al., 1967). Its mass is of interest to the theoretician for estimating helium abundance. This in turn should lead to information of the primordial helium content of the Universe.

An astrometric orbit was first published in 1964 from plates taken 1937-63 at the Sproul Observatory. The author has analyzed the plates taken with the Sproul 24-inch refractor up to 1973; the revised orbit has a somewhat longer period. The interpretation remains the same with respect to the probable mass ratio. The companion has recently passed periastron and it seems wise to delay publication of another orbit until the inclusion of another year's observation. A provisional orbit from radial velocity determinations has been computed by Worek and Beardsley (1975); the total range in amplitude appears to be about 5 km s -1. Their orbit can be improved upon with the inclusion of observations over the periastron passage.

There have been a number of contradictory reports of visual detection of the companion by eye, photographic, and by more sophisticated methods. A recent discussion by Feibelman (1976) summarizes the various attempts along with the results of measurement of some elongated photographic images. Partially resolved or even just separated photographic images suffer from proximity effects both as to separation and magnitude and distort the measurements. This problem also renders the measurement of the elongated images of Ross 614 AB on photographs taken with the Hale reflector uncertain. Future attempts at Am and separation must, therefore, involve other techniques.

3. P G C 3 7 2 . - T h i s solar type star was recently found to have a perturbation indicating M dwarf companion with a mass -0.25 ~J)~| The large Am renders this a difficult pair for observing each component separately. No other astrometric study of this star appears to have been made since the parallax solutions in the 1920's.

4. B D § 6~ - This K4V type astrometric binary has common proper motion with a dM6 type star at a distance of 165". Analyses of the McCormick and Sproul Observatory data are in satisfactory agreement. The McCormick orbit is adopted as the more accurate due to the longer time interval covered. The interpl-etations are similar leading to a faint red dwarf companion with mass -0.11 ~A'J~| with large Am. Visual searches for the companion with the current predicted separation of 2" have been in vain, confirming the likely large Am. Rakos, with his area scanner, has not detected the companion (private communication). Atwood and Curott (1975) report that they were unable to detect the companion with the Synchronous Stellar


Area Scanner mounted on the McDonald 91-cm reflector. They conclude that

Amx > 5 assuming a separation ~2':0.

5. A l g o l . - The multiplicity of this classical eclipsing system has been known for many years. A recent Sproul Observatory astrometric study combining spectroscopic and photometric studies confirms the short period orbit of P = 1.Y862 attributed to

the presence of Algol C. But the astrometric amplitude is small, the period so short, that accurate predictions of maximum separation cannot be made. There remains

only weak evidence for a fourth distant companion. Algol C is estimated to have a

mass - 1 . 7 ~J)2| 2 or more magnitudes fainter than Algol A B . Labeyrie and Bonneau (1973) have published a O and 0 for C - A B from speckle interferometry.

6. Stein 2051. - S t r and has made a combined astrometric study of this red, white dwarf pair combining Sproul and USNO photographs. The two visible components m~ = 11.1, 12.4, are now separated by 7". The A component (M5) shows deviations in its path which can be interpreted as due to an unseen companion with a period of 23 yr. Attempts to observe the companion visually with the 223-cm Hawaiian

reflector and with the image scanner of Rakos so far have been unsuccessful. Therefore it seems likely that the A m is large. The minimum mass for Am > 4 for the unseen component is 0.02 ~Y~G. This is a very interesting system with the white dwarf

component being the sixth nearest degenerate star and the fourth white dwarf on

which we have a grasp on its mass.

7. G96-45. - This star, m~ = 12.19, assumed to be a red dwarf from the photometry, has a perturbation with a period of 7.2 yr. On the assumption that the mass of the visible component is 0.27 sj)~| the mass of the invisible component is 0.08 ~Y)2| if the A m ~ 5. If the Am is smaller the mass of the B component may be of the order of 0.10 to 0.16 ~))~G. The semi-axis major of the relative orbit is 60':2. With the negligible value of 0.01 for the eccentricity the orbit has two epochs of maximum separation

half period apart.

8. Chi~ Orionis .- This is the second solar type star to be found to have an unseen companion within two years at the Sproul Observatory (see PGC 372, # 3). A large Am seems likely with the companion's magnitude ~ 10, assuming it to be a red dwarf with mass - 0 . 1 7 ~G. Obviously there would be an advantage of observing in the far red where the A m would be less. The apparent orbit on the sky permits a second near maximum separation near 1987. The photocentric displacement curves and orbit are

given in Figure 4.

9. G a m m a Geminorum. - This early type star was discovered to have variable radial velocity by Keivin Burns in 1904, but a satisfactory period was not obtained until the astrometric study from the Allegheny parallax series 1938-58. The period given in the table is now well determined from the spectroscopic data, and the predicted

+ I/

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separations from the Van Vleck astrometric data. Assuming the mass of the visible

component to be 3 ~JJ~| appropriate for a A0 iv star, and further that Am > 1, since

the star does not show duplicity spectroscopically, Kamper finds a minimum mass of

1 sjj~| for the unseen component . This is indicative of spectral type F or G for A m ~ 4

or more if the companion is a white dwarf. The latter possibility makes visual

resolution even more appealing.

10. Zeta C a n c r i . - T h e well known binary has a distant companion C for which an

unseen companion was established in 1880 from micrometer observations. The D

component remains unseen although the separation of CD remains almost 0"4

throughout the period of revolution. The absolute magnitude of the G2 type C

component is 5.1; the indicated mass is 0.9 ~Js174 for D which is presumably a white

dwarf since the A m must be appreciable. Visual observations of this quadruple

system with a white dwarf component would be of particular interest.

11. B D + 6 7 ~ - T h e orbital motion of this dM1 type star of visual magnitude

9.29 has a period of 23 yr. A A m of two or three at 0"6 maximum separation indicates

a normal late M dwarf star.

12. G146-72. - T h i s is one of the more distant of the stars revealing astrometric

unseen companions. The visible star is assumed to be a red dwarf from the

photometry with a likely mass of 0.35 ~)J~| The minimum mass for the invisible

companion is 0.16 sjs174 assuming no contribution of light to the photographic image.

This would indicate that the B component is subluminous from our present under-

standing of low luminosity stars. Further observations of this system are anticipated

with interest.

13. X i UMa A . - This system is a classical case of the discovery of a third component

from micrometer observations showing a perturbat ion to a component of a well

known double star system. The unseen companion, a, causes the deviation of the A

component with a period of 1.Y832. The B component of the visual binary is also a

spectroscopic binary making the entire system quadruple. Its visual magnitude is

4.80 and it has the same spectral type-GOV as the A component .

14. C C 2 0 , 986, - This red dwarf was on the suspected list for Keplerian deviations

in the proper motion; the period of the orbital motion is now well determined: 3.Y72.

It is difficult to predict the A m ; the range in mass in the unseen component is 0.06 to

0.16 ~| The orbit has a small inclination with the plane of the sky so that the interval near maximum separation is generous. For this system it may not be as difficult to observe each component separately as for many of the others on this list.

15. G 1 3 9 - 2 9 . - T h e photocentr ic motion discovered from the USNO plates indicates a period of about ten years. The orbit is provisional since the interval of

182 S A R A H LEE L I P P I N C O T T

observation represents the length of period; the data look good. The visible component is faint; photometry indicates that it is a red dwarf M star; the My = 14.4. Computations indicate a subluminous companion with respect to the mass luminosity law. The minimum mass for the B component is 0.05 ~J)~| for which the My would be t> 19. Unfortunately, because of the faintness, this is a very difficult system to observe.

16. Alpha Ophiuchi.- The perturbation was found by Wagman from two parallax

series taken with the Allegheny 76-cm refractor. Subsequently a combined analysis of the Allegheny and Sproul plates yielded a period of 8Y.5, T = 1944.2, e = 0.4. The My = +1.0 for the primary corresponds to a likely mass - 3 . 0 ~| A zlrn ~ 2 would

lead to a later-type main sequence companion. This star is among those of earliest spectral type which have unseen companions. It is classified as the standard A5III spectrum on the MKK system. On the Paris 3D classification it is considered a A5V star. If the companion is observed visually yielding separation and Am, we shall have the first direct determination of the mass for a star of this spectral type and class.

17. Ci 18, 2354. -Recent update of Sproul measurements on the Grant machine give indications of an unseen companion with sub-stellar or near sub-stellar mass

with a likely limit of 0.006 to 0.07 9J~| The minimum mass limit presupposes a Am >15. With a period close to twenty six years, T = 1969.4, and e = 0.9. The

apparent orbit gives the comparatively large maximum separation -1" . The perturbation is confined almost entirely to the Y coordinate with a total amplitude of only - 1 . 5 / x . Unfortunately it will not be till the early 1990's before periastron will be reached again where the displacement curves have a sharp slope. The star is also a

likely spectroscopic binary of short period (Wilson, 1967). The radial velocity and astrometric interpretations of additional bodies are not mutually exclusive

(Harrington, 1975).

18. Barnard's Star.- Very intensive Sproul data since 1950 year after year gives strong evidence for a 'short ' period perturbation llY7; the estimated maximum separation is 1':6; an additional 'long' period perturbation 18.Y5 is less well

established. Continued observations in 1976 and 1977 agree with the ephemeris given in the comprehensive report for 1916-1976 by van de Kamp (1977b). Inter- pretation of the Sproul residuals leads to the indication of at least one planet-like object; if the object shines only by the reflected light of the primary, it may be about the 28th magnitude. The Allegheny-Van Vleck material irregularly spaced over the 1916-1971 intervals is discussed by Gatewood (1975, 1976) who states that the compilation of the residuals is 'suggestive of the gravitational interactions of the star and a planetary system'. The U.S. Naval Observatory and the McCormick Obser- vatory over the last decade have been taking plates on Barnard's star which in years to come may clarify the interpretation.


19. Wolf 1062. - T h e analyses of the plates from the USNO and Sproul Obser-

vatories separately indicate the presence of a faint, unseen component which is likely

a red dwarf with a range in mass - 0 . 0 6 to - 0 . 1 5 ~ | lower extreme 4m~/> 5, the

upper Am~ ~ 2.7. The Sproul value for the period is given, since the data covers an interval of 38 yr, while the USNO covers 6 yr. A good value of Am and p will provide additional information on the M-L relation for M-dwarfs.

20. Delta Aquilae. - Discovery of this naked eye star's duplicity is due to Alden from a perturbation found in 1929. The subsequent astrometric study of Osvalds from the analysis of the Yale Southern Station plates 1936-1943 and those taken

with the McCormick refractor 1914 to 1954 yields P = 3.Y42, T = 1934.16, and

e = 0.40. A mass of 1.2 ~ | may be assumed for the primary resulting in an estimated mass of 0.5 ~Y3~| for the unseen companion which presumably is a main sequence

star.

21. G24-I6. -Analys is for parallax from plates taken with the 155-cm USNO astrometric reflector, 1965-1970, revealed a photocentric orbit of short period perturbation for this faint red dwarf. The subsequent Sproul data 1970-76 yield a similar result for a small amplitude photocerltric orbit. The M~ = 13.3 and color photometry of G24-16 are suggestive of an M6 dwarf. The mass range of the unseen companion is likely between 0.07 and 0.11 ~J)~G which would suggest a subluminous dwarf. Figure 5 shows the photocentric displacement curves and orbit for the data

from the two observatories.

22. Ci 1299. - This red dwarf, M0, visual magnitude 9.8, shows orbital motion with a tentative period of forty years. Since the companion has not been detected at a separation of - 0 " 7 the Am is likely four or more; the companion could be a normal late dwarf star.

23. Zeta Aquarii. - A well known long period double (P = 600 y, a = 4"013) whose

fainter component has the unseen companion C, discovered astrometrically by

Strand in 1942. The visible components are of visual magnitudes 4.42 and 4.59 respectively. Estimated mass for the C component indicates a late main sequence

star.

24. BD+43~ - T h i s M4.5e star is also known as the flare star EV Lacertae. The analysis of Sproul astrometric plates can be interpreted to indicate an unseen companion with the minimum mass of - 0 . 0 0 9 ~))~| If the Am is as little as three the mass would be 0.023 ~3"3~| The estimated separation was 1" in the early 1960s but no trace of a companion is evident on the Sproul plates. In any case it appears to be less massive than that of a bona fide star. With a period of revolution of thirty years the separation would be 6 AU for the adopted mass of the visible component equal to 0.25 ~33~| It is possible that the companion is responsible for the flares recorded for

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A S T R O M E T R I C S E A R C H FOR U N S E E N S T E L L A R A N D S U B - S T E L L A R C O M P A N I O N S 185

this star; with a separation of 6 AU it does not seem likely that the flares are related

to the duplicity.

25. Ross 614.-Discovered by Reuyl (1936) to have a perturbation from the McCormick plates. The star has been studied at Sproul (Lippincott, 1951, 1955) and

a definitive photocentric orbit was determined from 252 nights' observations 1938- 1972 with the Sproul refractor (Lippincott and Hershey, 1972). At the time of the writing of the paper there were only four visual observations made with the following telescopes: 508-cm Hale reflector, 91-cm Lick refractor, 152-cm McDonald reflector and the 155-cm USNO astrometric reflector. Since then Kristian has repeated Baade's photographic attempts (Lippincott, 1955)with the Hale reflector

one period later producing another partially resolved image. Measurements suffer from emulsion distortions inherent in the photographic process which affect both the

separation and the image density. In 1974 Atwood and Curott (1975) at tempted an

observation with a photoelectric scanner where a position angle was assumed. This

observation is considered in the discussion by Probst (1977) which includes the analysis of the McCormick plates on Ross 614.

26. Kuiper 84. - The star appears off-center on all the plates of the Barnard's star series. The system has very few visual observations of Am and separation, insufficient for orbital determination. Both the Allegheny and Sproul astrometric plates have

yielded a photocentric orbit with similar interpretations. The mass ratio is better

determined than the masses themselves and both determinations indicate the mass of the secondary more massive than the primary. The mass of A is found to be 0.3 ~Y)2o

and that of B, 0.6 ~Y~| with absolute visual magnitudes 7.4 and 8.0 respectively. According to Bruce Stephenson (private communication), the spectrum is K5V and

both components are dwarfs.

27. Furuhjelm 54.-This close binary whose measured separations are generally equal or less than 1':0 with Am = 2 has only 11 epochs of micrometer measurements

p, 0. The distribution is insufficient to compute an orbit. The photocentric orbit on the other hand is well defined. Using the visual measurements to define the scale of the apparent orbit we find that both red dwarf components are over-massive for their spectral type; ~))~A = 1.5 ~)Y~| and ~)Y~B = 0.4 ~)Y~o. Bopp (private communication) finds that the A component is a spectroscopic binary. This helps explain the excess mass

but not completely. The star is being continued at Sproul to improve the orbit; further measurements of Am, p and 0 are desirable, to strengthen the mass determination. Both components are known to flare.

28. V W Cephei.- This well known eclipsing binary has recently been shown by Hershey from an astrometric study of Sproul plates, to have an astrometric companion with a period of 30 yr. The possibility of a third body had been suspected as early as 1941 from apparent period changes in the eclipsing pair attributed to a


light-time effect due to the orbital motion provided by a third component. However, it turns out that the period changes are real and have nothing whatsoever to do with

the presence of the third body shown by the astrometric study. The resulting light-time changes are very small compared with the intrinsic continuous change in the eclipsing period over the last several decades. As a further result of this study, Heintz looked at VW Cephei through the Sproul 61-cm refractor and visually

detected the third component at 0 =223 ~ and p = 0'.'63, rnv-~ 10.5, for 1974.6 (Heintz, 1975), in good agreement with the astrometric prediction. Further visual

observations will lead to a better mass determination of the components.

29. Epsilon Aurigae.-This well known eclipsing binary has a sufficiently long period, 27.Y08, to give a measurable astrometric orbit. The inclination is near 90 ~ and

therefore there are two equally spaced times of maximum separation. The problem in estimating the maximum separation of the two components is the lack of

knowledge of the masses of the components; in addition it appears that the secondary has no light! The scale of the photocentric orbit in conjunction with the spectroscopic orbit gives a parallax +0'.'001 72 • 0'.'000 08 (p.e.) with far greater accuracy than any

possible trigonometric parallax. This leads to My = - 5 . 9 , not allowing for absorption, for e Aurigae.

30. Chi Dra. - This is an astrometric and spectroscopic binary. The combined data

lead to Am = 2.3 with ~J)C~A = 1.5 + 0.4 ~)Y~| and ~ B = 1.1 + 0.3 ~| The primary fits the M - L relation but the companion appears underluminous for its mass. The Am

indirectly obtained from the astrometric data needs to be improved. The relative positions of the two components are near maximum separation for about half the period centered around 0Y4 past periastron, where T = 1979.5.

31. VV Cephei.-This eclipsing binary with a period of 20Y.4 has a measurable

photocentric orbit from the Sproul data. As with e Aurigae the scale of the photocentric orbit is used with the spectroscopic orbit to yield an accurate parallax +0'.'0014 + 0"0002 (p.e.). This leads to absolute visual magnitudes, not allowing for absorption, - 4 . 0 and -2 .3 for the A and B components. The masses are 18.3 ~JY~| and 19.8 ~332| respectively.

6. Summary

Stars in our stellar neighborhood are prime targets for astrometric studies leading to the discovery of unseen companions and subsequent orbital analysis. Whether the companions be stellar or sub-stellar, they increase our knowledge of low luminosity stars, possible only in the vicinity of the sun, Of the known systems with unseen astrometric companions, approximately one-half of the primaries are late-type main sequence stars. This implies that the secondaries are indeed low luminosity stars for which more observational data are highly desirable. The 'unseen' companions to two


systems, Ross 614, VW Cephei have been detected visually; Ross 614B is the star of smallest known mass. In order to rigorously determine the important astrophysical parameter, namely, mass, from the photocentric orbit the Am and separation of the components are required. They must come from another observational technique requiring high resolution and a highly sensitive detector. Attempts with area scanners, speckle interferometry, the use of diode arrays, etc. give promise and we look forward with anticipation to the observations with the Space Telescope of the 1980's.

Acknowledgements

I wish to express my appreciation and thanks to Drs Peter van de Kamp and John L. Hershey for their helpful comments on the manuscript. The recognition of Dr van de Kamp's contribution to this review goes far beyond the reading and discussions of this manuscript; he was the initiator of the search for unseen astrometric companions to nearby stars and has been the leader during the last forty years. All of us contributing to the field have been influenced by his work and many of us have been his students or members of his staff over the years.

A good part of the results come from the continued support of the National Science Foundation and the present grant #AST77-21315A01 to Swarthmore College.

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