THE PROBLEM OF BETA LYRÆ.
[Illustration:
FIG. 29.—Light-Curve of β Lyræ (Argelander).
]
On the 10th of September 1784, John Goodricke of York, a deaf-mute
scarcely twenty years of age, perceived the second brightest star in the
Lyre to be variable. He ascertained, further, the main features of its
light-change. They are very peculiar.[659] Four phases of approximately
equal duration are comprised in a period of twelve days and nearly
twenty-two hours. They are portrayed in the symmetrical curve drawn from
Argelander’s observations in Fig. 29. The twin maxima, situated midway
between the principal and secondary minima, are of absolutely constant
brilliancy. Constant, too, is the chief phase of obscurity, so that the
compass of variation, from 3·4 to 4·4 magnitude, is a fixed quantity.
The intermediate minimum, however, is not so immutable. Defect and
excess are occasionally observed in it. But the flow of change is always
smooth and uninterrupted. Nor is there any pause in a slow lengthening
of the period, which has progressed, during the last hundred years, at
the average rate of about one-third of a second at each recurrence. That
the disturbance will prove compensatory can scarcely be doubted; but the
law of restoration is not yet apparent.
The spectrum of β Lyræ is dominated by helium. It includes members of
all the six series emanating from that substance, and they are mostly
composite aggregations of bright and dark rays.[660] The Huggins series
of hydrogen is similarly represented; among metals, calcium and
magnesium are prominent, and ten dark oxygen lines in the ultra-violet
were photographed at Tulse Hill in 1899.[661] But the special
characteristic of this spectrum is its variability. The coupled lines
are neither fixed in position nor constant in structure. They shift,
they split, they flash and fade; they spread into diffuse bands or
contract to definite filaments; and this in obvious, though disturbed,
subordination to the light-period of the star. The two kinds of
variation are, to some extent, mutually dependent; yet they are far from
showing a strict concurrence. The loose and indeterminate nature of
their relations places formidable obstacles in the way of investigating
either.
Already, in 1866, Father Secchi noticed bright lines in the dispersed
light of β Lyræ, and Von Gothard was struck in 1883 with their
unaccountable fluctuations of visibility.[662] But the complexities they
presented wholly baffled direct observation; their unravelment only
began to be possible when spectrographic methods became fully developed.
Through Mrs. Fleming’s examination of the Harvard plates, it was made
evident in 1891 that the emission-rays had dark companions, and were not
stationary with regard to them; and Professor Pickering[663] gathered
from their displacements the probability that the two sets belonged
severally to the unlike components of a close binary, revolving
synchronously with the ebb and flow of total brightness. He estimated
their relative velocity at 300 miles a second in a circular orbit, with
a radius of 50,000,000 miles. This hypothesis is beyond question founded
in fact. The star is composite, and the emissive and absorptive elements
of its spectrum shift, on the whole, oppositely; each battalion, as Mr.
McClean has indicated, moves as a unit, and in a contrary sense to the
other. To distinguish them ought then to be a simple matter. The
differently affected lines ought of themselves, one might expect, to
declare their separate origin. Difficulties well-nigh insuperable,
nevertheless, beset the interpretation of this spectrum. Their main
source is this. The constituent lines do indeed oscillate through
motion, but they are subject to further influences of a more complex
kind, and of a barely conjecturable manner of working. The various
species of change are hence entangled and disguised to a bewildering
extent; and totally divergent views have been expressed as to the proper
apportionment of the spectrum between the bodies jointly originating it.
Sir Norman Lockyer attributes the absorption lines to a pair of “Orion”
stars, unequally advanced in development,[664] with a relative velocity
of 156 miles a second; and the addition of a bright-line companion is an
implied necessity of his scheme. Mr. McClean[665] demands a dark-line
and a bright-line component, mutually circling at a speed of 400 miles a
second. Miss Maury considers that three stars must be engaged.[666] Dr.
Vogel[667] and Father Sidgreaves,[668] although they have investigated
the spectrum in detail, make no attempts at its analysis. M. Bélopolsky,
by minimising the scope of attack, made a substantial advance towards
the solution of the problem.[669] He dealt with only two lines—the
absorption ray of magnesium at λ 4482 and the brilliant F of hydrogen;
but succeeded in establishing, it might be said, incontrovertibly, their
separate production from conjoined bodies dissimilarly constituted. The
magnesium line is better adapted for measurement than most of the
spectral elements of β Lyræ; it is subject to only moderate alterations
in width and definition, and determinations of its motion-shifts afford,
accordingly, consistent results. From them Bélopolsky has calculated the
orbit of the originating globe, which may be identified with Lockyer’s
Rigel star. He found it to be but slightly eccentric (_e_ = 0·04); the
mean radius (supposing the plane to coincide with the line of sight) is
15,000,000 miles; the system is advancing towards the sun at the rate of
seven miles a second, and the times of zero radial velocity agree so
nearly with the epochs of minimum as to lend countenance to the
eclipse-rationale of light-failure. A second orbit was then
computed—though far less securely—for the component showing bright F,
each being described round the common centre of gravity. It proved to be
about half the size of the former, which implied that the body
travelling in it (designated A) was twice as massive as the companion
(B). It possesses, in fact, the gravitating power of eighteen, the
latter of nine suns. Nevertheless, the principal minimum corresponds to
the obscuration of the minor globe, while at the secondary phase, the
primary star is the one partially occulted. The bright-line star, A,
must then be much less luminous in proportion to the quantity of matter
it contains than the dark-line star, B. This does not appear probable,
but it cannot be pronounced impossible.
On the whole, Bélopolsky’s results are plausible, and the basis they
rest upon is solid, if narrow. Yet the development of their consequences
leads to a network of perplexities. The star A, characterised by
hydrogen-emission, can be no other than Lockyer’s second dark-line
star—that resembling Bellatrix; but if so, “the bright bands,” as Miss
Maury says, “have a residual motion of their own, which places them
sometimes towards the red, and sometimes towards the violet end of their
own system of dark lines, and at other times upon the lines of one, or
both spectra.” Yet the suggested triple combination is inadmissible. The
presence of a third body would require the introduction of a second
period, and of this no trace is discernible. The spectral phenomena are
in many ways abnormal and unaccountable, but in the long run they
conform to the single and nearly uniform time-measure of the system, and
preserve a modified fidelity to the course of its light-change.
Gravitational disturbances, too, might be expected to betray the
influence of an extra member, and none have been detected; for the
slight retardation now going forward is otherwise explicable. We seem
prohibited from carrying the subdivision of β Lyræ any further than into
a pair of globes, exemplifying distinct varieties of the Orion spectral
pattern, one or both vivified by a range of bright lines.
[Illustration:
FIG. 30.—System of β Lyræ (Myers).
]
An effort was made by Mr. G. W. Myers in 1897[670] to bring this star’s
variations within the explanatory scope of the “satellite-theory.” By
suitably combining effects of occultation with effects of tidal
deformation, he showed that the observed periodicity could be
represented with the satisfactory exactitude conveyed in the upper
section of Fig. 30, the lower section of which exhibits his plan of the
supposed orbit and its egg-shaped occupants. Evidently, when they are
seen _broadside on_ there is full light, while a minimum attends an
_end-on_ view of them. And this altogether apart from possible eclipses.
If these occur as well, the effects reinforce each other; while those
due to the gradual turning of the discs soften off the abruptness of
occultation-phases, and thus serve to give the light-curve its smooth
character. The mutually eclipsing spheroids must, however, be extremely
close together, if they do not actually coalesce. Combining, on the
questionable assumption of their congruity, the displacements of F
measured by Bélopolsky with those attributed by Lockyer to three dark
lines, Mr. Myers found the masses of his two stars to be respectively
twenty-one and ten (nearly) in terms of that of the sun, and determined
the radius of their joint orbit at 31,000,000 miles. Their mean density
proved to be lower than that of air at sea-level, and suggested a
“nebulous condition.” Indications were even discerned of a process of
separation between the components, scarcely yet, or just recently
accomplished. “In either case,” Mr. Myers adds, “we seem to have here
the first concrete example of a world in the act of being born.” And it
cannot but be noted with profound interest that “an attempt at a formal
representation of the condition of things prevailing in the system of β
Lyræ leads to the assumption of a single body, such as Poincaré’s or
Darwin’s figures of equilibrium.”
Yet the “formal representation” in question is difficult to accept as a
physical actuality. The extreme tenuity attributed by it to a star
shining with vivid lustre almost defies credence, yet is an inevitable
consequence of the satellite-hypothesis of variability. Where there is
no halt in change, there can be only a transient cessation of eclipse,
and the revolving globes must be virtually in contact. But under these
circumstances, their density, as we have seen, is a function of the
period alone; and thirteen days is long compared with the nine hours of
U Pegasi, for which star the upshot of a similar experimental
investigation has been recorded. This theory, moreover, takes account
only of the optical changes in β Lyræ. Occultation-effects,
distortion-effects, and motion-displacements of spectral lines are of
this kind. They imply no intrinsic alteration. They are compatible with
an absolute constancy in the state of the system; they depend merely
upon the visual relations to ourselves of the bodies forming it. They
are accordingly calculable and measurable. Exactly what sort and amount
of fluctuations they are capable of producing, can be ascertained from
given data. But with the physical influences of close duplicity upon
radiation we have only a speculative acquaintance. And in the present
case, those that might be due to unequal tidal disturbances are excluded
by the circular shape necessarily ascribed to the path of a star noted
for the equal duration of all its phases. Intrinsic variations in its
spectrum are, nevertheless, glaringly apparent, and they tend to recur
cyclically in just thirteen days. We spare our readers the bewilderment
of their minute description, asking them instead to fix their attention
on a few salient points.
Let us consider, for instance, the spectral symptoms at the critical
epoch of chief minimum. Almost as a matter of course, the continuous
radiance has faded; sixty per cent of it is intercepted or otherwise
suppressed. This is, in fact, the essential cause of the falling-off in
brightness. What is distinctive is that the emission-lines have become
narrower, sharper, and fainter than usual; they are considerably shifted
towards the red, and strongly developed dark companions, in their normal
places, are attached to their more refrangible sides. Now the downward
shove of the whole range of bright lines is either due to motion, or it
is not. If it is, the emitting body is travelling rapidly away from the
earth at the time of the supposed eclipse, which must accordingly be
dismissed as fictitious. If, on the other hand, the alteration of
wave-length denotes physical action of some kind in the atmosphere of
the star, then inferences as to its orbital revolution, since they have
only a spectroscopic warrant, are highly precarious. The possibility, to
be sure, may be admitted that the dark lines shift optically, the bright
lines physically _and_ optically; but the distinction has an air of
arbitrariness which does not recommend its confident adoption.
Another significant circumstance is that the spectral appearances at the
secondary minimum and at the ensuing maximum are much alike. The most
characteristic among them is the projection of a black line centrally
upon a wide bright band. Dr. Vogel’s drawings of the first ultra-violet
hydrogen line (Η ζ) at these successive phases are reproduced in Plate
XVI., Figs. 1 and 1a. Here, at any rate, a single light-source is
concerned. A moment’s consideration suffices to show that a dark line in
the spectrum of one star cannot cut a slice out of a brilliant band
proceeding from another. Absorption implies real superposition of the
arresting and absorbing layers. The effect observed is then one of
reversal. It arises through the stoppage by a cooler stratum of hydrogen
of the emissions from a denser and hotter underlying stratum in the same
stellar atmosphere. Fig. 2 in the same Plate represents, from a drawing
by Professor Keeler, the “D lines” in β Lyræ at principal minimum. It
was made with the great Lick refractor, 14th and 15th November 1889, and
shows the sodium pair to the right merged into a dark, hazy band, with
above it D_{3} brilliant and unsymmetrically reversed. Moreover, the
thin dark line constituting the reversal seemed to be nearly, or exactly
in its proper place;[671] the obvious relative shift measured the
lessened refrangibility of the emissive beam. In the gaseous envelope,
then, of one and the same star we find a helium line originating at a
low level moved towards the red, while its repetition by absorption
higher up preserves its wave-length unchanged. The indicated difference
in conditions can here scarcely be anything else than a decrease of
pressure upward from the photospheric surface. The significance of such
an inference hardly needs to be pointed out, and it seems impossible to
avoid drawing it.
The red ray of hydrogen is particularly brilliant in β Lyræ; but since
it lies beyond the ordinary spectrographic range it has of late received
little attention. Yet the history of the modifications which it
assuredly undergoes, and of the modes of their correlation with those of
its associates in the spectrum, must be learned, unless knowledge of
this wonderful star is to remain essentially incomplete.
[Illustration:
PLATE XVI.
THE ALTERNATING SPECTRUM OF NOVA PERSEI STONYHURST COLLEGE
OBSERVATORY.
1. Hζ Line in Spectrum of β Lyræ at Secondary Minimum.
1a. Hζ Line in Spectrum of β Lyræ at Second Maximum.
2. D-Lines in β Lyræ (Keeler).
3. D-Lines in Nova Persei (Hale).
4. Spectra of Nova Sagittarii.
5. Alternating Spectrum of Nova Persei (Sidgreaves).
]
We may now endeavour to sum up our conclusions regarding its nature,
tentative and fragmentary though they be. A finished theory on the
subject cannot at present be formulated; but the ground may be prepared
for it by the removal of inadmissible hypotheses and by the
clarification of thought.
(1) The system of β Lyræ is binary. Two stars, and no more, are
concerned in producing the observed changes in the quantity and quality
of its light. Both show strong hydrogen and helium absorption; one is
distinguished besides by oxygen absorption, and it is this latter which,
in all probability, emits the more conspicuous set of bright lines.
There are indications, too, that a second set is occasionally
sub-apparent, and that the spectrum really consists of two separate
ranges of dark, and two accompanying ranges of vivid rays.
(2) The dark lines are in their normal positions at minima; they are
shifted from them at maxima, when some of their number open out into
doublets. The conjunctions at times of least light, and elongations at
intervening epochs, of two bodies giving absorption spectra are thus
presumably signified.
(3) At chief minimum, the more prominent bright lines are shifted
towards the red, so as to lie beside the corresponding dark lines. The
spectrum has then the coupled aspect distinctive of “Novæ” and of
certain other emission-stars. The change of refrangibility during this
phase cannot be due to motion; it may be due to pressure.
(4) During the second half of the period, reversals are a leading
feature of the spectrum, which thus affords evidence, not only of
orbital revolution, but also of a course of physical vicissitudes
comprised in the same cycle.
(5) Finally, the cause of variability has to be considered. Is it to be
found in mutual occultations? The geometrical conditions are such as to
admit of an affirmative reply; the physical conditions are adverse. They
involve a rarefaction of the circling bodies so extreme as to repel
assent unless under the stress of rigid demonstration. And that is by no
means at hand. Evidence on the subject could perhaps more easily be
collected from objects with analogous light-curves, than from β Lyræ
itself. The endless complications which embarrass research in the
“problem star” would not, for instance, be likely to present themselves
in _d_ Serpentis. Another variable, highly desirable to be included in
such a comparative study, is R Sagittæ. This remarkable object has a
period of seventy days, symmetrically divided by two unequal minima, and
two slightly disparate maxima. The light-curve, however, underwent a
curious change in 1874. A reversal of the minima was perceived.[672]
Equalisation first took place. Then the secondary minimum gradually
gained emphasis at the expense of the primary; and the exchange of
relative values was not redressed until 1883, when the pristine state
was restored. An arrested tendency towards such a transformation is
sometimes shown by β Lyræ in the fluctuating accentuation of its
subordinate phase, but it has never reached so far as a bisection of the
period. A suggestion is, nevertheless, irresistibly conveyed that the
two stars form similarly constructed systems. When the spectra of R
Sagittæ, _d_ Serpentis, and U Pegasi have been examined, and their
changes tabulated and collated, we shall be in a better position to
interpret those manifest in the Lyre variable.