studied by Wolf and Rayet, and named after them. These stars are
characterized by a hydrogen atmosphere of enormous extension, large
enough in some cases, it has been calculated, to fill up the orbit of
Neptune. These stars are evidently either hotter and more strongly
radiating than the red stars, or there is not so much dust in their
neighborhood—the dust may possibly have been expelled by the strong
radiating pressure. They are, therefore, classed with the yellow, and
not with the red stars. Although there is every reason to suppose that
their central bodies are at least as hot as those of the white stars,
the dust is yet able to reduce the color to yellow, owing to the vast
extensions of their atmospheres.
The unequal periods in stars like Mira may be explained by the
supposition that there are several rings of dust moving about them, as
in the case of the planet Saturn. In the case of the inner rings which
have a short period, there has probably been sufficient time during
the uncounted number of revolutions to effect a uniform distribution
of the dust. Hence we do not discern any noteworthy nuclei in them,
such as we observe in the tails of comets; the dust rings only help
to impart to the star a uniform reddish hue. In the outer rings the
distribution of dust will, however, not be uniform. One of the rings
may be responsible for the chief proper period. By the co-operation
of other less important dust rings, the maximum or minimum, we shall
easily understand, may be displaced, and thus the time interval
between the maxima and minima be altered. This alteration of the
period is so strong for some stars that we have not yet succeeded in
establishing any simple periodicity. The best-known star of this type
is the bright-red star Betelgeuse in the constellation of Orion. The
brightness of this star fluctuates irregularly between the magnitudes
1.0 and 1.4.
By far the largest number of variable stars belong to the type of Mira.
Others resemble the variable star Beta in the constellation of the
Lyre, and thus belong to the Lyre type. The variability of the spectra
of a great many of these stars indicates that they must be moving
about a dark star as companion, or rather that they both move about a
common centre of gravity. The change in the light intensity is, as a
rule, explained by the supposition that the bright star is partially
obscured at times by its dark companion. Many irregularities, however,
in their periods and other circumstances prove that this explanation is
not sufficient. The assumption of rings of dust circulating about the
star and of larger condensation centres affords a better elucidation
of the variability of these stars. They are grouped with the white or
yellow stars, in whose surroundings the dust does not play so large a
part as in that of Mira Ceti. The period of their variability is, as
a rule, very short, moreover—generally only a few days (the shortest
known, only four hours)—while the period of the Mira stars amounts to
at least sixty-five days, and may attain two years. There may be still
longer periods so far not investigated.
Nearly related to the Lyre stars are the Algol stars, whose variability
can be explained by the assumption that another bright or dark star is
moving within their vicinity, partially cutting off their light. There
is no dust in these cases, and the spectrum characterizes these stars
as stars of the first class—that is, as white stars—so far as they
have been studied up to the present.
We must presume for all the variable stars that the line of sight from
the observer to the star falls in the plane of their dust rings or of
their companions. If this were not so, they would appear to us like a
nebula with a central condensation nucleus, or, so far as Algol stars
are concerned, like the so-called spectroscopic doubles whose motion
about each other is recognized from the displacement of their spectral
lines.
The evolution of stars from the nebulous state has been depicted by the
famous chief of the Lick Observatory, in California, W. W. Campbell, as
follows (compare the spectra of the stars of the 2d, 3d, and 4th class,
Figs. 59 and 60):
[Illustration:
74 My, in Sun 280
Schjellerup’s Gemini Class 2 Schjellerup’s
Catalogue Class 3 Catalogue
Class 4 Class 4
Fig. 59.—Comparison of spectra of stars of classes 2,
3, 4. After photographs taken at the Yerkes Observatory.
Blue portions of spectrum. Wave-lengths in millionths of a
millimetre]
[Illustration:
280 Sun My, in 74
Schjellerup’s Class 2 Gemini Schjellerup’s
Catalogue Class 3 Catalogue
Class 4 Class 4
Fig. 60.—Comparison of spectra of stars of classes 2, 3, 4.
After photographs taken at the Yerkes Observatory. Green and
yellow portions of spectrum. Wave-lengths in millionths of a
millimetre]
“It is not difficult to select a long list of well-known stars which
cannot be far removed from nebular conditions. These are the stars
containing both the Huggins and the Pickering series of bright hydrogen
lines, the bright lines of helium, and a few others not yet identified.
Gamma Argus and Zeta Puppis are of this class. Another is DM +30.3639°,
which is actually surrounded with a spherical atmosphere of hydrogen
some five seconds of arc in diameter. A little further removed from the
nebular state are the stars containing both bright and dark hydrogen
lines—caught, so to speak, in the act of changing from bright-line
to dark-line stars. Gamma Cassiopeiæ, Pleione, and My Centauri are
examples. Closely related to the foregoing are the helium stars. Their
absorption lines include the Huggins hydrogen series complete, a score
or more of the conspicuous helium lines, frequently a few of the
Pickering series, and usually some inconspicuous metallic lines. The
white stars in Orion and in the Pleiades are typical of this age.
“The assignment of the foregoing types to an early place in stellar
life was first made upon the evidence of the spectroscope. The
photographic discovery of nebulous masses in the regions of a large
proportion of the bright-line and helium stars affords extremely
strong confirmation of their youth. Who that has seen the nebulous
background of Orion (Fig. 51) or the remnants of nebulosity in which
the individual stars of the Pleiades (Fig. 52) are immersed can doubt
that the stars in these groups are of recent formation?
“With the lapse of time, stellar heat radiates into space, and, so
far as the individual star is concerned, is lost. On the other hand,
the force of gravity on the surface strata increases. The inevitable
contraction is accompanied by increasing average temperature. Changes
in the spectrum are the necessary consequence. The second hydrogen
series vanishes, the ordinary hydrogen absorption is intensified, the
helium lines become indistinct, and calcium and iron absorptions begin
to assert themselves. Vega and Sirius are conspicuous examples of this
period. Increasing age gradually robs the hydrogen lines of their
importance, the H and K lines broaden, the metallic lines develop, the
bluish-white color fades in the direction of the yellow, and, after
passing through types exemplified by many well-known stars, the solar
stage is reached. The reversing layer in solar stars represents but
four or five hydrogen lines of moderate intensity; the calcium lines
are commandingly permanent, and some twenty thousand metallic lines are
visible. The solar type seems to be near the summit of stellar life.
The average temperature of the mass must be nearly a maximum; for the
low density indicates a constitution that is still gaseous [compare
Chapter VII.].
“Passing time brings a lowering of the average temperature. The
color passes from yellow to red, in consequence of lower radiation,
temperature, and increasing general absorption by the atmosphere.
The hydrogen lines become indistinct, metallic absorption remains
permanent, and broad absorption bands are introduced. In one type
(Secchi’s Type III.), of which Alpha Herculis is an example, these
bands are of unknown origin. In another class (Secchi’s Type IV.),
illustrated by the star 19 Piscium, they have been definitely
identified as of carbon origin.
“There is scarcely room for doubt that these types of stars (Type
IV.) are approaching the last stages of stellar development. Surface
temperatures have been lowered to the point of permitting more complex
chemical combinations than those in the sun.
“Secchi’s Type III. includes the several numbered long-period variable
stars of the Mira Ceti class, whose spectra at maximum brilliancy show
several bright lines of hydrogen and other chemical elements.[17] It
is significant that the dull-red stars are all very faint; there are
none brighter than magnitude 5.5. Their effective radiatory power is
undoubtedly very low.”
[Footnote 17: This circumstance indicates that the red color of
these stars, as we have already remarked with regard to Mira
Ceti, is not to be traced back to a low temperature, but rather
to the dust surrounding them. The most extraordinary brightness
of some stars, like Arcturus and Betelgeuse, which are redder
than the sun, and whose spectra, according to Hale, resemble
those of the sun-spots, presuppose a very high temperature.
The characteristic lines of their spectra are produced by the
relatively cool vapors of their outer portions.]
The state of evolution, which succeeds that characterized as the
Secchi Type IV., may be elucidated with the aid of the examples of
Jupiter and the earth, with which we are more familiar. These planets
would be invisible if they were not shining in borrowed light.
Jupiter has not advanced so far as the earth. The specific gravity
of Jupiter is somewhat lower than that of the sun (1.27 against
1.38), and, apart from the clouds in its atmosphere, this planet is
probably altogether in a gaseous condition, while the earth, with its
mean density of 5.52, possesses a solid cold crust, enclosing its
incandescent interior. This state of the earth corresponds to the last
stage in the evolution of the stars.
Of the streams of gaseous matter which are ejected when stars collide
with one another, the metallic vapors are rapidly condensed by cooling;
only helium and hydrogen will remain in the gaseous condition and
form nebular masses about the central body. These nebulæ yield bright
lights. Their luminosity is due to the negative particles which are
sent to them by the radiation pressure of near stars, and especially by
the central bodies of the nebula.
With the new stars which have so far been observed, this pressure of
radiation soon diminishes, and the nebular light likewise decreases
in such cases. In other instances, as with the stars characterized by
bright hydrogen and helium lines, the radiation of the central body or
stars in their vicinity seems to be maintained at full force for long
periods.
The nebulous accumulations of helium and hydrogen will gradually escape
and be condensed in near-by stars under the formation of “explosive”
compounds. The tendency to enter into combination seems to be strongest
in the case of helium; it disappears first from the stellar atmosphere.
That helium enters into compounds at high temperatures seems to follow
from the researches of Ramsay, Cooke, and Kohlschütter.
Hydrogen will afterwards be absorbed, and the light of the central body
will then show the predominating occurrence of the vapors of calcium
and of other metals in its atmosphere. Simultaneously with these,
chemical compounds will be noticed, among which the carbon compounds
will play an important part—in the outer portions of the sun-spots, in
the stars of the Secchi Type IV., as well as in the gaseous envelopes
of the comets.[18]
[Footnote 18: The presence of carbon bands in the spectrum
need not be taken as a mark of low temperature. Crew and Hale
have observed that these bands gradually vanished from an arc
spectrum as the temperature was lowered by decreasing the
current intensity.]
Finally a crust will form. The star is extinct.
VII
THE NEBULAR AND THE SOLAR STATES
We will now proceed to a more intimate consideration of the chemical
and physical conditions which probably characterize the nebulæ in
distinction from the suns. These properties differ in many respects
essentially from those which we are accustomed to associate with matter
as investigated by us, which may, from this point of view, be styled
relatively concentrated.
The differences must be fundamental. For the motto of Clausius, which
comprises the sum of our knowledge of the nature of heat, cannot apply
to nebulæ. This motto reads:
“The energy of the universe is constant. The entropy of the
universe tends to a maximum.”
Everybody understands what is meant by energy. We know energy in
many forms. The most important are: energy of position (a heavy body
has larger energy by virtue of its having been raised to a certain
height above the surface of the earth than when it is lying on the
surface); energy of motion (a discharged rifle-bullet has an energy
which is proportional to the mass of the bullet and to the square of
its velocity); energy of heat, which is regarded as the energy of the
motion of the smallest particles of a body; electrical energy, such as
can, for instance, be stored in an accumulator battery, and which,
like all other modifications of energy, may be converted into energy of
heat; and chemical energy, such as is displayed by a mixture of eight
grammes of oxygen with one gramme of hydrogen, which can be transformed
into water under a strong evolution of heat. When we say that the
energy of a system to which energy is not imparted from outside is
constant, we merely mean that the different forms of energy of the
separate parts of this system may be transformed into other forms of
energy, but that the sum total of all the energies must always remain
unchanged. According to Clausius this law is valid throughout the
infinite space of the universe.
By entropy we understand the quantity of heat of a body divided by its
absolute temperature. If a quantity of heat, of Q calories, of a body
at a temperature of 100° (absolute temperature, 373°) passes over to
another body of 0° (absolute temperature, 273°), the total entropy of
the two will have been decreased by Q/373, and increased by Q/273. As
the latter quantity is the greater, the entropy of the whole will have
increased. By itself, we know, heat always passes, either by radiation
or by conduction, from bodies of higher temperature to bodies of lower
temperature. That evidently implies an increase in entropy, and it is
in agreement with the law of Clausius that entropy tends to increase.
The most simple case of heat equilibrium is that in which we place a
number of bodies of unequal temperatures in an enclosure which neither
receives heat from outside nor communicates heat to the outside. In
some way or other, usually by conduction or radiation, the heat will
pass from the warmer to the colder bodies, until at last equilibrium
ensues and all the bodies have the same temperature. According to
Clausius, the universe tends to that thermal equilibrium. If it be
ever attained, all sources of motion, and hence of light, will have
been exhausted. The so-called “heat-death” (Wärmetod) will have come.
If Clausius were right, however, this heat-death, we may object, should
already have occurred in the infinitely long space of time that the
universe has been in existence. Or we might argue that the world has
not yet been in existence sufficiently long, but that, anyhow, it had a
beginning. That would contradict the first part of the law of Clausius,
that the energy of the universe is constant; for in that case all the
energy would have originated in the moment of creation. That is quite
inconceivable, and we must hence look for conditions for which the
entropy law of Clausius does not hold.
The famous Scotch physicist Clerk-Maxwell has conceived of such a case.
Imagine a vessel which is divided by a partition into two halves, both
charged with a gas of perfectly uniform temperature. Let the partition
be provided with a number of small holes which would not allow more
than one gas molecule to pass at a time. In each hole Maxwell places a
small, intelligent being (one of his “demons”), which directs all the
molecules which enter into the hole, and which have a greater velocity
than the mean velocity of all the molecules, to the one side, and which
sends to the other side all the molecules of a smaller velocity than
the average.[19] All the undesirable molecules the demon bars by means
of a little flap. In this way all the molecules of a velocity greater
than the average may be collected in the one compartment, and all the
molecules of a lesser velocity in the other compartment. In other
words, heat—for heat consists in the movements of molecules—will pass
from the one constantly cooling side to the other, which is constantly
raising its temperature, and which must therefore become warmer than
the former.
[Footnote 19: The kinetic theory of gases imagines all the
molecules of a gas to be in constant motion. The internal
pressure of the gas depends upon the mean velocity of the
particles; but some particles will move at a greater, and some
at a smaller velocity than the average.—H.B.]
In this instance heat would therefore pass from a colder to a warmer
body, and the entropy would diminish.
Nature, of course, does not know any such intelligent beings.
Nevertheless, similar conditions may occur in celestial bodies in
the gaseous state. When the molecules of gas in the atmosphere of a
celestial body have a sufficient velocity—which in the case of the
earth would be 11 km. (7 miles) per second—and when they travel
outward into the most extreme strata, they may pass from the range of
attraction out into infinite space, after the manner of a comet, which,
if endowed with sufficient velocity when near the sun, must escape
from the solar system. According to Stoney, it is in this way that the
moon has lost its original atmosphere. This loss of gas is certainly
imperceptible in the case of our sun and of large planets like the
earth. But it may play an important part in the household of the
nebulæ, where all the radiation from the hot celestial bodies is stored
up, and where, owing to the enormous distances, the restraining force
of gravity is exceedingly feeble. Thus the nebulæ will lose their most
rapid molecules from their outer portions, and they will therefore be
cooling in these outer strata. This loss of heat is compensated by the
radiation from the stars. If, now, there were only nebulæ of one kind
in the whole universe, those escaped molecules would finally land on
some other nebula, heat equilibrium would thus be established between
the different nebulæ, and the “heat-death” be realized. But we have
already remarked that the nebulæ enclose many immigrated celestial
bodies, which are able to condense the gases from their neighborhood,
and which thereby assume a higher temperature.
The lost molecules of gases may also stray into the vast atmosphere of
these growing stars, and the condensation will then be hastened under a
continuous lowering of the entropy. By such processes the clock-work of
the universe may be maintained in motion without running down.
About the bodies which have drifted into nebulæ, and about the remnants
of new stars which lie inside the nebulæ, the gases will thus collect
which had formerly been scattered through the outer portions of the
nebula. These gases originate from the explosive compounds which had
been stored in the interior of the new stars. Hydrogen and helium
are, most likely, the most important of these; for they are the most
difficult to be condensed, and can exist in notable quantities at
extremely low temperatures, such as must prevail in the outermost
portions of the nebulæ, in which gases of other substances would be
liquefied. Even if the nebulæ had an absolute temperature of 50° (-223°
C.), the vapor of the most volatile of all the metals, mercury, would
even in the saturated state be present in such a small quantity that
a single gramme would occupy the space of a cube whose side would
correspond to about two thousand light-years—that is to say, to 450
times the distance of the earth from the nearest fixed star. One gramme
of sodium, likewise a very volatile metal, and of a comparatively high
importance in the constitution of the fixed stars, would fill the side
of a cube that would be a thousand million times as large. Still more
inconceivable numbers result for magnesium and iron, which are very
frequent constituents of fixed stars, and which are less volatile than
the just-mentioned metals. We thus recognize the strongly selective
action of the low temperatures upon all the substances which are less
difficult to condense than helium and hydrogen. As we now know that
there is another substance in the nebulæ, which has been designated
nebulium, and which is characterized by two spectral lines not found in
any terrestrial substance, we must conclude that this otherwise unknown
element nebulium must be almost as difficult to condense as hydrogen
and helium. Its boiling-point will probably lie below 50° absolute,
like that of those gases.
That hydrogen and helium, together with nebulium, alone seem to occur
in the vastly extended nebulæ is probably to be ascribed to their
low boiling-points. We need not look for any other explanation. The
supposition of Lockyer that all the other elements would be transformed
into hydrogen and helium at extreme rarefaction is quite unsupported.
In somewhat lower strata of the nebula, where its shape resembles
a disk, other not easily condensable substances, such as nitrogen,
hydrocarbons of simple composition, carbon monoxide, further, at deeper
levels, cyanogen and carbon dioxide, and, near the centre, sodium,
magnesium, and even iron may occur in the gaseous state. These less
volatile constituents may exist as dust in the outermost strata. This
dust would not be revealed to us by the spectroscope. In the strongly
developed spiral nebulæ, however, the extreme layers, which seem
to hide the central body, appear to be so attenuated that the dust
floating in them is not able to obscure the spectrum of the metallic
gases. The spectrum of the nebula then resembles a star spectrum,
because the deepest strata contain incandescent layers of dust clouds,
whose light is sifted by the surrounding masses of gases.
It has been observed that the lines of the different elements are
not uniformly distributed in the nebulæ. Thus Campbell observed,
for instance, when investigating a small planetary nebula in the
neighborhood of the great Orion nebula, that the nebulium had not the
same distribution as the hydrogen. The nebulium, which was concentrated
in the centre of the nebula, probably has a higher boiling-point than
hydrogen, therefore, and occurs in noticeable quantities in the inner,
hotter parts of the nebula. Systematic investigations of this kind may
help us to a more perfect knowledge of the temperature relations in
these peculiar celestial objects.