SPECTROSCOPIC BINARIES.
Between the old and the new astronomy lies a region claimed by both, yet
belonging by exclusive right to neither. This is the department of
spectroscopically determined, or radial movements. Now the distinction
between radial and transversal movement is purely artificial; it is made
in the interests of our imperfect faculties; nature ignores it. Motion,
although by a geometrical fiction resolvable _ad infinitum_, is
essentially simple. At any given instant it takes place in one direction
only. But if that direction be oblique to our view, we see the line of
travel foreshortened; nor can we tell by direct vision how much
foreshortened. That is to say, the eye perceives one component of
velocity—the tangential component, the component lying square before
it—while of the other component along the visual ray it takes no heed.
Here the spectroscope comes to the rescue. Helpless to deal with
tangential speed, it can measure radial speed by its effects upon the
refrangibility of light. The first method gives one side of the
parallelogram of velocities, the second, the other; combining their
results, we get the diagonal actually traversed by the observed luminous
body. Data obtained by visual means formed the sole materials of the
elder gravitational science; none others were indeed available at the
period of its growth and elaboration; nor, even if they had been, would
they have been of essential service in constructing planetary theories.
In sidereal astronomy they occupy quite a different position. Without
them its progress is crippled, and the possibility of procuring them
fortunately developed just when they began to be urgently needed.
As grist for the mathematical mill, motions determined spectroscopically
serve equally well with motions determined telescopically. The calculus
deals indifferently with either kind. The calculus, however, is an
instrument of precision, and demands minute accuracy in the materials
operated upon. And it is just the effort to satisfy this demand which
has broken down the barrier between celestial mechanics and celestial
physics. For radial velocities cannot be unadvisedly accepted; the
line-displacements significant of them may be otherwise occasioned.
Cases have to be discriminated; conditions scrutinised; recondite
problems attacked. The information within reach is, nevertheless, too
important to be neglected; at any cost of pains it must be extricated
from uncertainty and used for all that it is worth; and so it has come
about that traditional astronomers of the most abstract type find
themselves involved in experimental difficulties, and confronted by
questions answerable only in the laboratory.
Astrophysicists, on their side, have no choice but to cultivate the
spectroscopic branch of dynamical astronomy. Not merely because it
springs from the stem of physical principles and physical experience,
but because the study of its subject-matter is essential to the
furtherance of knowledge respecting stellar constitution and
development. Thus sidereal physics merges into sidereal mechanics; yet
somewhere between them a line of demarcation must, for the purposes of
the present book, be drawn. Arbitrarily drawn in many places it will be;
but there are cases in which it is better to lack logic than limit; and
this is one of them. We shall then regard spectroscopic but not
telescopic binaries as making part of our subject, although fully aware
that the two classes are fundamentally one. Stellar and nebular proper
motions, transversal or radial, must also as such be excluded. Only when
they give evidence, by periodic variability, of the progress of orbital
revolutions, do they fall within our scope. Uniform velocities in space,
in whatever direction, or however determined, do not concern us. Foreign
to our theme as well, is the grand topic of sidereal construction,
prescribed as it is and conditioned by the flittings of the stars.
Something, however, will be said about the physical peculiarities of the
Milky Way, since apart from them the spectroscopic relations of the
various families of stars and nebulæ would remain imperfectly
intelligible.
Spectroscopic binaries are stars telescopically single, but inferred to
be compound from the evidence of a regular flow of spectral change. The
change is of a perfectly definite nature. It consists in the swinging of
all the bright or dark lines to and fro in a fixed period across their
average positions. These, indeed, are not precisely their normal
terrestrial places. They are affected by the motion of the system, as a
whole, towards or from the eye. This constant element of shifting is,
however, easily eliminated, and the circulating pair can then be studied
as if their centre of gravity were at rest relatively to the sun.
Ascribing to them, to begin with, a circular orbit, it is easy to see
that, at two diametrically opposite points—the extremities of the line
of conjunction—radial motion vanishes, the entire measurable velocity
being across the direction of view; while at the corresponding points of
greatest elongation, the radial component represents full speed. In an
elliptic orbit these four points of zero and maximum line-of-sight
movement may be slightly displaced according to the situation of the
major axis; they can, however, be located with the help of exact
observational data, and their positions then serve as an index to the
shape and orientation of the ellipse. One of its elements, nevertheless,
remains incalculable. Unless the revolving stars eclipse one another,
there is no means of determining its plane. It cannot be perpendicular
to the line of sight, for in that case all the motion would be
tangential; no part of it could be spectroscopically apparent. But it
may be inclined at any angle short of a right angle; and the larger the
angle, the smaller the proportion of the orbital velocity directed along
the visual ray. In other words, the measured rates are the true rates
multiplied by the cosine of an unknown angle. They are, accordingly,
minimum values; the actual speed indefinitely exceeds them.
Nevertheless, it can rarely be more than double the seeming amount,
since the chances of discovery manifestly fall off for systems with
highly inclined planes. Thus the scale of orbits computed from
spectroscopic data is indeterminate; but the uncertainty does not extend
to their form, which is as strictly derivable as that of the paths of
visible binary stars.[540] The mass of the revolving bodies, however,
escapes us. It depends upon the compass of their rounds; we can only
assign to it a value less than which it cannot be, although it may be
considerably greater.
Spectroscopic binaries are broadly divisible into three classes: those
that are constant in brightness, those that vary in light through
eclipses, and those that vary in light otherwise than by eclipse. In the
present chapter we shall confine our attention to the first category.
And here again we have to distinguish between stars with bright, and
stars with dark companions. In the spectra of bright pairs the lines
split into doublets twice in the course of each revolution; in those of
bright and dark pairs they execute a complete vibration simultaneously
with the description of a circuit, but remain always single. But these
different conditions are not sharply separated. As usual, the rule of
continuity is observed. Satellites are met with in all gradations of
luminosity. Some shine no less brilliantly than their primaries, in
which case the duplicated lines are exact pairs; others are large but
dim, and show very faint rays periodically appended to the comparatively
intense ones of the greater orb; while the majority, remarkably enough,
are quite obscure, so far at least as spectral indications enable us to
judge.
These marvellous systems have, one and all, been discovered by
spectrographic means. The required consistency and certainty of
measurement are unattainable visually. They have been realised only by
the employment of chemical impressions comparable night by night and
year after year. The first result of the kind was achieved at Harvard
University by the detection as a close double of ζ Ursæ Majoris, the
middle star in the Plough handle. The components are Sirian suns of the
same stamp, and of nearly equal brightness; but they may be to some
extent relatively variable.[541] The nature of their movements was long
an enigma. The period of 104 days at first assigned to them implied
duplication of the spectral lines once in 52 days. Yet this consequence
did not ensue in fact with the inevitableness exacted by theory. Grave
discrepancies became manifest; the anticipated separation of the two
spectra, often non-apparent, was always curtailed in duration, and
repeated attempts were baffled to get rid of these anomalies by adding a
third body to the system, by heightening the eccentricity of the ellipse
traversed, or by shortening the period of its description.[542] At last,
in 1901,[543] by a discussion of a fresh series of Potsdam
spectrographs, Dr. Vogel reached a satisfactory conclusion. He now
assigned to the revolving couple a period of only 20 days 14 hours; the
eccentricity of their orbit came out = 0·5, so that their
periastron-approach is one-half their mean distance; while their least
possible mass proved to be four times that of the sun. Up to the present
they seem inclined to conform to these rules of the road.
The parallax of 0·045″ found by Klinkerfues for Mizar (to give ζ Ursæ
its Arabic name) is likely to be largely erroneous, but erroneous by
excess rather than by defect. If it be correct, the star sends abroad
thirty-eight times more light than our sun. If it be too large, the
star is proportionately brighter; and, judging by Höffler’s
estimate[544]—certainly a most precarious one—it is greatly too large.
Since the components are spectroscopically unlike the sun, the ratio
of the quantity of light they emit to the quantity of matter they
contain must be widely different. Were it the same, a 38-fold
brilliancy would imply their possession of about 160 times the solar
mass; whereas Vogel’s data almost enforce the belief that this value
at least decuples the truth. This may serve to exemplify the
difficulty of deducing massiveness from luminosity. Only in
exceptional cases can any fixed proportionality be safely assumed as
the basis of calculation.
Mizar is attended visibly as well as invisibly. A star of the fourth
magnitude circulates round it at a distance of 14″ with an almost
imperceptible progression. Unless it mends its pace, 10,000 years will
have elapsed before a revolution is completed. It may be worth recalling
that on 18th April 1841, Mädler was unable to find this object,
ordinarily plain to be seen; and the failure seemed so strange that he
endeavoured to account for it by supposing the star subject to sudden
obscurations like those of Algol.[545] No second disappearance is on
record; but phases of the kind are extremely evasive when no time-bill
of their recurrences is at hand. The connection into one system of two
close pairs is not in itself improbable, although no such arrangement
has yet been anywhere verified.
The detection of a second spectroscopic binary followed immediately upon
that of the first. Miss Maury announced late in 1889, as a result of her
scrutiny of the Harvard plates, that the absorption lines in the
spectrum of β Aurigæ appear alternately single and double once in
forty-eight hours. Hence the period of revolution is four days, while
the relative velocity of the components, given by the extent to which
their spectral rays separate, is 150 miles a second. Their joint orbit
has been computed by Rambaut,[546] Lehmann-Filhés,[547] and
Schwarzschild[548] so accordantly as to leave little room for
improvement. They find its eccentricity to be somewhat less than that of
the orbit of Mercury; the major axis makes an angle of 32° with the line
of sight, and the periastron is at the end farthest from the earth. The
plane being unknown, its dimensions, as already explained, cannot be
ascertained. If indeed the observed velocity were the true
velocity,—that is, if it lay in a level passing through the eye—the
corresponding orbital radius would be 7,500,000 miles, and the mass of
the system would rather exceed that of 4½ suns;[549] but these are only
the least possible values; they may be greatly surpassed. The components
of β Aurigæ shine with the Sirian quality of light; they are almost
perfectly matched, reciprocal variability, according to Miss Maury,[550]
causing each in turn to appear the brighter. A parallax of 0·062″ was
photographically determined for them by Professor Pritchard. At the
distance indicated, the sun would seem twenty-eight times less bright;
it would sink to the paltry status of a 5·6 magnitude star. If β Aurigæ
were a single globe, constituted like the sun, and giving out a
twenty-eight-fold supply of light, it should be of 147-fold mass.
Neither of these conditions is fulfilled; and allowance for their
realisation might possibly bring into fair agreement calculations of
mass from gravitational and from photometric data. In which case the
plane of revolution would deviate but slightly from that traversed by
the line of sight.
The preceding star of two named μ Scorpii was disclosed as compound in
1896 by Professor Bailey’s notice of the doubling of its spectral lines
on many of the Draper Memorial negatives.[551] The period is only 34
hours 42 minutes; the velocity is correspondingly high. By their wide
separation the lines tell of relative movement at the rate of 286 miles
a second, this being the sum of the opposite velocities of the conjoined
bodies. Their orbit, apart from the foreshortening effect of its
inclination, has a radius of nearly 6,000,000 miles, and they possess at
least fifteen times the gravitating power of the sun. They show a helium
spectrum; and one member of the pair is not only fainter than the other,
but fainter, apparently, in a variable degree.
The spectrographic method employed at Harvard supplies evidence of
line-duplications, but none of the shiftings of solitary lines. This is
easily understood. The dispersing apparatus is placed in front of the
object glass; the stellar images formed at its focus are then ready-made
spectra. Hence no slit is required, and without a slit no
comparison-spectrum can be availed of. Displacements therefore betray
themselves only when the rays furnish standards of mutual reference by
splitting into pairs. The binary nature of stars both bright is,
accordingly, discoverable in this way, but not the association of a
bright with a dark body.
The spectroscopic discovery of these remarkable combinations was
initiated at Potsdam. Dr. Vogel[552] in 1890 found the brilliant Spica
(α Virginis) to have its spectrum shifted to and fro once in four days,
the revolutions thereby intimated proceeding at the rate—apart from
perspective abridgment—of fifty-seven English miles a second. This
implies, if the components be of equal mass, a distance for each from
their common centre of gravity of 3,100,000 miles, and a joint mass 2·6
times that of the sun. The spectrum is of the helium type. Sir David
Gill obtained a null result for the parallax of the star, which must
accordingly be of amazing actual splendour. The attendant of Spica is
not wholly obscure. Traces of its spectrum can be perceived, although
too faintly for purposes of exact measurement. The couple might then be
termed a linking instance between systems composed of twin suns, and
those consisting of a luminous and a non-luminous member. The conditions
of observation are not only more arduous in the latter case, but the
data within reach prove less adequate. They are one-sided; they relate
exclusively to the bright star. All that can be learned about its dark
companion is that it describes, in the same period, a similar orbit. The
size of the orbit is left vague. It is large if the mass of the body
traversing it is small, and _vice versâ_; and the mass of the primary is
involved in the same uncertainty.
A peculiarly interesting bright and dark couple was brought to notice in
1896 through M. Bélopolsky’s work with the thirty-inch Pulkowa
refractor.[553] Castor, the lucida of the constellation Gemini, was the
object of his researches; and it dominates a system no less wonderful
than that of ζ Ursæ Majoris. Two lustrous Sirian stars, of second and
third magnitudes respectively, wheel slowly at an interval of 6″.
Although they have been wards of science since Bradley’s measure of them
in 1719, their orbit is not yet, in any strict sense, calculable. It is,
however, certainly very eccentric, and takes many centuries to describe.
A small, distant star shares the proper motion of this majestic pair,
and is hence known to form with them a ternary combination, which the
spectroscope has rendered quaternary by assigning an invisible satellite
to the minor component of the original binary. Its revolutions are
rapid; they have a period of not quite three days, and its gravitative
power suffices to impart a radial velocity of 22 miles a second to the
luminous orb in its vicinity. The corresponding distance from the centre
is 1,800,000 miles; but this, as in all such cases, is a minimum value.
The ellipse traversed is slightly more eccentric than the path of
Mercury round the sun. And here arose a curious complication.[554]
Obviously, the interval between two periastron passages should, if the
major axis remained fixed in space, be identical with the time occupied
in making the circuit from node to node. It proved, nevertheless, to be
notably longer, and the hypothesis was, so to speak, compulsorily
adopted that the major axis shifts forward as the stars revolve. The
period of the inequality, as determined by Bélopolsky in 1899, is 2100
days. In four years and forty days the orbital axis makes a complete
gyration, and is once more directed as at first. The cause assigned for
the disturbance is the spheroidal form impressed upon the conjoined
bodies by their reciprocal tide-raising power. A flattening of
one-seventh would suffice to produce the observed effect, admitting that
the system has the same dimensions as that of Algol. This special kind
of perturbation, long theoretically recognised, has been found
practically operative only within the narrow precincts of close stellar
systems. Its continued study in them may lead to important developments.
The disclosure of a duplex character in Capella was eminently
unexpected. Its reputation as an exemplary solar star, irreproachably
regular in its movements, had been established at Potsdam, where the
spectrographic investigation of radial velocities was set on foot in
1888.[555] But the instrumental resources then at Professor Vogel’s
command were inadequate to bring out certain deviations from the
Fraunhofer pattern lately noticed. The spectrum is indeed both
oscillatory and compound; but a powerful and perfect apparatus is
required for the manifestation of these singularities. The discovery
was, nevertheless, made in duplicate by Professor Campbell at Lick,[556]
and by Mr. Newall at Cambridge.[557] It is of unique interest.
Capella is one of the very few spectroscopic binaries at a determined
distance from the earth. The carefully revised parallax of 0·081″,
implying a light-journey of forty years, assigned to it by Dr. Elkin in
1897, has every mark of authenticity. Located thus remotely, our sun
would appear as a star below the fifth magnitude; 102 orbs like it
should be combined to give the light of Capella. Hence the joint volume
of the components, assuming them to be equal globes of solar intrinsic
brilliancy, must be just 730 times that of the sun. And their joint mass
should be even proportionately greater, unless the tremendous force of
internal compression proper to bodies so gigantic were counterbalanced
by exorbitant heat. There is strong, if not convincing evidence that
this is actually the case.
The members of the Capellan system are unequally luminous, and differ in
their absorptive qualities. One is spectroscopically indistinguishable
from the sun, the other, of about half its brightness, is more akin to
Procyon. It has, accordingly, been found possible to measure separately
the swing of each set of lines, and they have proved to be of much the
same amplitude. This means that the two bodies are animated by
equivalent movements, and are hence nearly equal in mass. Their
revolutions proceed in a slightly eccentric orbit, the mean radius of
which, if seen edgewise, would measure 52,000,000 miles. It is not,
however, seen edgewise; very far from it. Capella possibly makes an
exception to the rule that the circulatory plane of non-eclipsing
spectroscopic pairs is unascertainable; and for this reason, that it may
be, to some extent, a visual pair as well. Mr. Newall adverted to the
probability, based upon the star’s parallax and conditions of movement,
that the distance between its components would subtend from the earth an
angle of nearly one-tenth of a second. Telescopic observations might
then have a successful issue; and the opportunity for testing the powers
of great instruments was, at any rate, too tempting to be neglected.
Those of the Lick refractor, strange to say, though employed with all
Professor Hussey’s skill, failed to answer the demand made upon them.
The star was seen persistently round.[558] Yet Messrs. Dyson and Lewis
were persuaded of its genuine elongation with the Greenwich
twenty-eight-inch equatorial. The components were never seen clearly
divided; no thread of dark space was perceptible between them; but they
formed together an oval image, and the direction of lengthening changed
consistently with the period of their mutual circulation.[559] The
visual data thus procured even served for the calculation of a
provisional orbit, and the missing element of its inclination proved to
have a value of 30°. The stars, if this be so, travel in a plane making
an angle of 60° with the line of sight, and the actual radius of their
path is double that derived from spectroscopic velocities. It measures
104,000,000 miles; these immense bodies are not much farther apart than
the earth is from the sun. Their mass can hence be arrived at; together
they contain somewhat more matter than seventeen suns. This result,
though in many ways plausible, is extraordinarily discrepant from what
we may call the light-value of the same element. If they gravitated in
the proportion of their luminosity, these orbs, as we have seen, should
outweigh the sun 730 times; in point of fact, they seem to possess no
more than seventeen times the solar mass. Even apart from the Greenwich
results, we seem here to find evidence that stars differing enormously
in density may show spectra of the same stamp, and that large bodies
traverse the various stages of development more rapidly than small. The
members of the Capellan pair, admitting the alleged facts, are some
forty times more rarefied than the sun; liquid hydrogen is a heavy
substance compared with them. They are, accordingly, at an early epoch
of their career as radiant globes, while their spectra indicate full
maturity. Confirmation is thus afforded to the inference, already drawn
from the spectral diversities of double stars, that mass accelerates
evolution.
Late in 1896 Professor Campbell undertook at the Lick Observatory a
comprehensive investigation of stellar radial motion. The adjustment of
the fine apparatus known as the “Mills spectrograph” to the great
refractor made this feasible; and among its “bye-products,” the analysis
of visually single stars into revolving pairs is particularly important,
first, because of the individual interest of the facts collected, next,
on account of their significance in the scheme of the Cosmos. The
abundance with which such systems occur is quite unexpected, and very
remarkable. Professor Campbell finds that, of 285 stars observed by him,
more than one in nine is a spectroscopic binary.[560] And this excludes
several objects suspected, but not demonstrated to belong to the same
class, and makes no allowance for those cases in which the orbital plane
is so nearly vertical that movement in it makes no appreciable
spectroscopic effect. He has then good reason for holding it probable
“that at least one star in five or six will be found to be a
spectroscopic binary,” and he is quite prepared “to see a still larger
ratio established. The proven existence,” he adds, “of so large a number
of stellar systems differing widely in structure from the solar system
gives rise to a suspicion, at least, that our system is not of the
prevailing type of stellar systems. The new field of astronomical
research thus opened up is of great richness, and may well occupy the
attention, for an indefinite period, of the large number of observers
and institutions now engaging in its development. It is perhaps
unnecessary to say that the measure of success attainable is dependent
upon the degree of accuracy realised in the observed velocities.”
The Lick results in this branch are in several respects noteworthy.[561]
They show the wide diffusion of arrangements strange to experience, if
admissible in speculation. They serve, by the variety of periods which
they indicate, to narrow the lacuna between stars directly seen, and
stars inferred from Doppler’s principle to be revolving. They have
rendered it obvious that no generic distinction separates the two
classes. A pair revolving in 2½ years, like η Pegasi, cannot be set
apart fundamentally from δ Equudei, with its period of 5·7 years. It is,
indeed, clear that spectroscopic and telescopic binaries differ only in
the mode of their observation; not what they are in themselves, but the
aspect under which we regard them, has caused them to be artificially
disconnected. Already, however, a tentative beginning has been made with
Capella in the telescopic observation of spectroscopic couples; and
spectroscopic determinations of orbital speed, long a desideratum for
visual pairs, have been tried with good promise of success.
Individually, too, the detections announced from Mount Hamilton are
frequently curious and suggestive. Thus Polaris claims the attendance of
two dark companions; while the bluer component of κ Pegasi, besides
circulating visibly in a period of 11·4 years, circulates invisibly in
six days. Again, the primary of the classic pair, ξ Ursæ Majoris, proves
to have a variable radial movement, the conditions of which invite
investigation. The duplicity of υ Sagittarii is significant for a
different reason. The spectrum of this star includes bright hydrogen
lines; it was noted by Miss Maury[562] as compound, and perhaps mutable.
Motion-displacements, giving a velocity-range of about twenty-five miles
a second, were measured in it by Professor Campbell in 1899; but their
period remains undetermined, as well as the extent to which they are
shared by the responsive lines of the companion-spectrum.[563] For in
this case both the stars are luminous, and both show absorption of the
helium type. The exceptional constitution of υ Sagittarii, indicated by
its emissive symptoms, accentuates the interest of its systemic
relations. It should accordingly be an object of particular and
persevering attention. Indeed, each of these wonderful pairs may be
expected to develop peculiarities of its own, demanding study by varied,
and perhaps recondite methods.