inconceivable amounts of heat every year: 3.8. 10^{33} gramme-calories,
corresponding to 2 gramme-calories for each gramme of its mass. We have
also obtained an idea as to how the enormous storage of heat energy in
the sun may endure this loss for ages. Finally, however, the time must
come when the sun will cool down and when it will cover itself with a
solid crust, as the earth and the other planets—so far, probably, in a
gaseous state—have done long since or will do before long. No living
being will be able to watch this extinction of the sun despairingly
from one of the wandering planets; for, in spite of all our inventions,
all life will long before have ceased on the satellites of the sun for
want of heat and light.
The further development of the cold sun will recall the actual progress
of our earth, except in so far as the sun will have no life-spending,
central source of light and heat near it. In the beginning the thin,
solid crust will again and again be burst by gases, and streams of
lava will rush out from the interior of the sun. After a while these
powerful discharges will stop, the lava will freeze, and the fragments
will close up more firmly than before. Only on some of the old
fissures volcanoes will rise and allow the gases to escape from the
interior—water vapor and, to a less extent, carbonic acid, liberated
by the cooling.
Then water will be condensed. Oceans will flood the sun, and for a
short period it will resemble the earth in its present condition,
though with the one important difference. The extinct sun, unlike
our earth, will not receive life-giving heat from the outside,
excepting the small amount of radiation from universal space and
the heat generated by the fall of meteorites. The temperature fall
will therefore be rapid, and the vanishing clouds of the attenuated
atmosphere will not long check radiation. The ocean will become
covered with a crust of ice. Then the carbonic acid will commence
to condense, and will be precipitated as a light snow in the solar
atmosphere. Finally, at a temperature of about -200° Cent., the gases
of the atmosphere will be condensed, and new oceans, now principally
of nitrogen, will be produced. Let the temperature sink another 20°,
and the energy of the inrushing meteorites will just suffice to balance
a further loss of heat by radiation. The solar atmosphere will then
consist essentially of helium and hydrogen—the two gases which are
most difficult to condense—and of some nitrogen.
In this stage the heat loss of the sun will be almost imperceptible.
Owing to the low thermal conductive power of the earth’s crust,
there escapes through each square mile of this crust scarcely
one-thousand-millionth part of the heat which the sun is radiating
from an equal area of its surface. In future days, when the solar
crust will have attained a thickness of 60 km. (40 miles), its loss
of heat will be diminished to the same degree. The temperature on the
surface of the sun may then still be some 50° or 60° above absolute
zero, and volcanic eruptions will raise the temperature only for short
periods and over small areas. Yet in the interior the temperature will
still be at nearly the same actual intensity, something like several
million degrees, and the compounds of infinite explosive energy will
be stored up there as today. Like an immense dynamite magazine, the
dark sun will float about in universal space without wasting much
of its energy in the course of billions of years. Immutable, like a
spore, it will retain its immense store of force until it is awakened
by external forces into a new span of life similar to the old life. A
slow shrinkage of the surface, due to the progressive loss of heat of
the core and to the consequent contraction, will in the meanwhile have
covered the sun with the wrinkles of old age.
Let us suppose that the crusts of the sun and the earth have the same
thermal conductivity—namely, that of granite. According to Homén, a
slab of granite one centimetre in thickness, whose two surfaces are
at a temperature difference of 1° Cent., will permit 0.582 calorie
to pass per minute per square centimetre of surface. By analogy, the
earth’s crust, with an increase of temperature of 30° per kilometre,
as we penetrate inward, would allow 1.75 .10^{-4} calorie to pass per
minute and per square centimetre (this is 1/3580 of the mean heat
supply of the earth, 0.625 calorie per minute per square centimetre);
while the sun, with a crust of the same thickness as the earth, but
with a diameter 108.6 times larger, would lose 3.3 times more heat per
minute than the earth receives from it at the present time. At present
the sun loses 2260 million times more heat than the earth receives;
consequently, the loss of heat would be reduced to 1/686,000,000 of
the present amount. If the thickness of the solar crust amounted to
1/140 of the solar radius—that is to say, to the same fraction that
the thickness of the earth’s crust represents of the terrestrial
radius—the sun would in 74,500 million years not lose any more heat
than it does now in a single year. This number has to be diminished, on
account of the colder surface which the sun would have by that time,
to about 60,000 million years. Considering that the mean temperature
of the sun may be as high as 5 million degrees Celsius, the cooling
down to the freezing-point of water might occupy 150,000 billion years,
assuming that its mean specific heat is as great as that of water.
During this time the crust of the sun would increase in thickness and
the cooling would, of course, proceed at a decreasing rate. In any
case, the total loss of energy during a period of a thousand billion
years could, under these circumstances, only constitute a very small
fraction of the total stored energy.
When an extinct star moves forward through infinite spaces of time, it
will ultimately meet another luminous or likewise extinct star. The
probability of such a collision is proportional to the angle under
which the star appears—which, though very small, is not of zero
magnitude—and to the velocity of the sun. The probability is increased
by the deflection which these celestial bodies will undergo in their
orbits on approaching each other. Our nearest neighbors in the stellar
universe are so far removed from us that light, the light of our sun,
requires, on an average, perhaps ten years to reach them. In order
that the sun, with its actual dimensions and its actual velocity in
space—20 km. (13 miles) per second—should collide with another star
of similar kind, we should require something like a hundred thousand
billion years. Suppose that there are a hundred times more extinct than
luminous stars—an assumption which is not unjustifiable—the probable
interval up to the next collision may be something like a thousand
billion years. The time during which the sun would be luminous would
represent perhaps one-hundredth of this—that is to say, ten billion
years. This conclusion does not look unreasonable. For life has only
been existing on the earth for about a thousand million years, and this
age represents only a small fraction of the time during which the sun
has emitted light and will continue to emit light. The probability of
a collision between the sun and a nebula is, of course, much greater;
for the nebulæ extend over very large spaces. In such a case, however,
we need not apprehend any more serious consequences than result when a
comet is passing through the corona of the sun. Owing to the very small
amount of matter in the corona, we have not perceived any noteworthy
effects in these instances. Nevertheless, the entrance of the sun into
a nebula would increase the chance of a collision with another sun; for
we shall see below that dark and luminous celestial bodies appear to be
aggregated in the nebulæ.
From time to time we see new stars suddenly flash up in the sky,
rapidly decrease in splendor again, to become extinguished or, at
any rate, to dwindle down to faint visibility once more. The most
remarkable of these exceedingly interesting events occurred in
February, 1901, when a star of the first magnitude appeared in the
constellation of Perseus. This star was discovered by Anderson, a
Scotchman, on the morning of February 22, 1901. It was then a star of
the third magnitude.[12] On a photograph which had been taken only
twenty-eight hours previous to the discovery of this star, the star
was not visible at all, although the plate marked stars down to the
twelfth magnitude. The light intensity of this new star would hence
appear to have increased more than five-thousand-fold within that
short space of time. On February 23d the new star surpassed all other
stars except Sirius in intensity. By February 25th it was of the first
magnitude, by February 27th of the second, by March 6th of the third,
and by March 18th of the fourth magnitude. Then its brightness began to
fluctuate periodically up to June 22d, with a period first of three,
then of five days, while the average light intensity decreased. By
June 23d it was of the sixth magnitude. The light intensity diminished
then more uniformly. By October, 1901, it was a star of the seventh
magnitude; by February, 1902, of the eighth magnitude; by July, 1902,
of the ninth magnitude; by December, 1902, of the tenth magnitude; and
since then it has gradually dwindled to the twelfth magnitude. When
this star was at its highest intensity it shone with a bluish-white
light. The shade then changed into yellow, and by the beginning of
March, 1901, into reddish. During its periodical fluctuations the hue
was whitish yellow at its maximum and reddish at its minimum intensity.
Since then the color has gradually passed into pure white.
[Footnote 12: Stars are classified in magnitude, the order
being such that the most luminous stars have the lowest
numbers. A star of the first magnitude is 2.52 times brighter
than a star of the second magnitude; this, again, 2.52 times
brighter than a star of the third magnitude, and so on. All
this from the point of view of an observer on the earth.]
The spectrum of this star shows the greatest similarity to that of the
new star in the constellation Auriga (Nova Aurigæ) of the year 1892
(Fig. 45).
[Illustration: Fig. 45.—Spectrum of Nova Aurigæ, 1892]
On the whole, it is characteristic of new stars that the spectrum lines
appear double—dark on the violet and bright on the red side. In the
spectrum of Nova Aurigæ this peculiarity is, among others, striking
in the three hydrogen lines C, F, and H, in the sodium line, in the
nebula lines, and also in the magnesium line. In the spectrum of
Nova Persei the displacement of the hydrogen lines towards the violet
is so great that, according to Doppler’s principle,[13] the hydrogen
gas which absorbed the light must have been moving towards us with
a velocity of 700 or more kilometres (450 miles) per second. Some
calcium lines show a similar displacement, which is less noticeable
in the case of the other metals. This would appear to indicate that
relatively cold masses of gas are issuing from the stars and streaming
with enormous velocities towards the earth. The luminous parts of the
stars were either at a stand-still or they were moving away from us.
The simplest explanation of these phenomena would be that a star when
flashing up by virtue of its high temperature and high pressure shows
enhanced (widened) spectral lines, whose violet portion is absorbed by
the strongly cooled masses of gas which are moving towards us and are
cooled by their own strong expansion. These gases stream, of course, in
all directions from the star, but we only become aware of those gases
which absorb the light of the stars—that is to say, those situated
between the star and the earth, and streaming in our direction.
[Footnote 13: When, standing on a station platform, we watch
an express train rushing through the station, the pitch of the
engine whistle seems to become higher as long as the train
is approaching us, and deeper again when the train is moving
away from us. The pitch of a note depends upon the number of
oscillations which our ear receives per second. Now, when the
train is fast approaching us, more vibrations are sent into our
ear than when the train is at a stand-still, and the pitch,
therefore, appears to become higher. The same reasoning holds
for light waves, of which Doppler, of Prague (Bohemia), was in
fact thinking when first announcing his principle in 1842. The
wave-length of a particular color of the spectrum is fixed with
the aid of some Fraunhofer line characteristic of a certain
metal. If we compare the spectrum of a star and the spectrum of
a glowing metal, photographed on the same plate, the stellar
lines will appear shifted towards the violet end (violet light
is produced by nearly twice as many vibrations of the ether per
second as red light) when the star is moving towards us in the
line of sight. This principle has successfully been applied by
Huggins, H. C. Vogel, and others, for determining the motion
of a star in our line of sight. When a star is revolving about
its own axis, the equatorial belt will seem to come nearer to
us (or to recede from us), while the polar regions will seem to
be at a stand-still; the lines will then appear oblique (not
vertical). In this way Keeler proved that the rings of Saturn
consists of swarms of meteorites moving at different velocities
in the different rings.—H. B.]
Gradually the light of the metallic lines and of the continuous
spectrum on which they were superposed began to fade, first in the
violet, while the hydrogen lines and nebular lines still remained
distinct; like other new stars, this star showed, after a while, the
nebular spectrum. This interesting fact was first noticed by H. C.
Vogel in the new star in the Swan (Nova Cygni, 1876). The star P in the
Swan, which flashed up in the year 1600, still offers us a spectrum
which indicates the emission of hydrogen gas. It is not impossible
that this “new” star has not yet reached its equilibrium, and is still
continuing to emit cold streams of gases. Insignificant quantities
of gas suffice for the formation of an absorption spectrum; thus the
emission of gas might continue for long periods without exhausting the
supply.
We have already mentioned (page 116) the peculiar clouds of light which
were observed around Nova Persei. Two annular clouds moved away from
this star with velocities of 1.4 and 2.8 seconds of arc per day between
March 29, 1901, and February, 1902. If we calculate backward from
these dates the time which must have elapsed since those gases left the
star, we arrive at the date of the week—February 8 to 16, 1901—in
satisfactory agreement with the period of greatest luminosity of the
star of February 23d. It would, therefore, appear that these emanations
came from the star and were ejected by the radiation pressure. Their
light did not mark any noticeable polarization, and could not be
reflected light for this reason. We may suppose that the dust particles
discharged their electric charges, and that the gases became thereby
luminous.
In this case we were evidently witnesses of the grand _finale_ of
the independent existence of a celestial body by collision with some
other body of equal kind. The two colliding bodies were both dark, or
they emitted so little light that their combined light intensities
did not equal that of a star of the twelfth magnitude. As, now, their
splendor after the collision was greater than that of a star of the
first magnitude, although their distance has been estimated to be at
least 120 light years,[14] their radiation intensity must have exceeded
that of the sun several thousand times. Under these circumstances the
mechanical radiation pressure must also have been many times more
powerful than on the surface of the sun, and the masses of dust which
were ejected by the new star must have possessed a velocity very much
greater than that of solar dust. Yet this velocity must have been
smaller than that of light, which, indeed, the effect of the radiation
pressure can never equal.
[Footnote 14: One light year corresponds to 9.5 billion
kilometres, and it is the distance which the light traverses in
the course of a year.]
[Illustration: Fig. 46.—Diagram indicating the consequences
of a collision between two extinct suns, A and B ‘moving’ in
the direction of the straight arrows. A rapid rotation in
the direction of the curved arrows results, and two powerful
streamers are ejected by A B, the explosive substances from the
deeper strata of A and B being brought up to the surface by the
collision]
It is not difficult to picture to ourselves the enormous violence
with which this “collision” must have taken place. A strange body—for
instance, a meteorite—which rushes from the infinite universe into
the sun has at its collision a velocity of 600 km. (400 miles) per
second, and the velocity of the two colliding suns must have been
of approximately that order. The impact will in general be oblique,
and, although part of the energy will of course be transformed into
heat, the rest of the kinetic energy must have produced a rotational
velocity of hundreds of kilometres per second. By comparison with
this number the actual circumferential speed of the sun, about 2 km.
(1-1/4 miles) per second on the equator, would vanish altogether; and
the difference is still more striking for the earth, with its 0.465
km. per second at the equator. We shall, therefore, not commit an
error of any consequence if we presume the two bodies to have been
practically devoid of circumferential speeds before their collision. At
the collision, matter will have been ejected from both these celestial
bodies at right angles to the relative directions of their motion in
two powerful torrents, which would be situated in the plane in which
the two bodies were approaching each other (compare Fig. 46). The
rotational speed of the double star, which will be diminished by this
ejection of matter, will have contributed to increase the energy of
ejection. We remember, now, that when matter is brought up from the
interior to the surface of the sun it will behave like an explosive of
enormous power. The ejected gases will be hurled in terrific flight
about the rapidly revolving central portions. We obtain an idea (though
a very imperfect one) of these features when we look at a revolving
pinwheel in a fireworks display. Two pinwheels have been attached
to the ends of a diameter and belch forth fire in radial lines. The
farther removed from the wheel, the smaller will be the actual velocity
and also the angular velocity of these torrents of fire. Similarly with
the star. The streams are rapidly cooled, owing to the rapid expansion
of the gas. They will also contain fine dust, largely consisting of
carbon, probably, which had been bound by the explosive materials.
The clouds of fine dust will obscure the new star more and more, and
will gradually change its white brilliancy into yellow and reddish,
because the fine dust weakens blue-and-green rays more than it does
yellow-and-red rays. At first the clouds were so near to the star that
they possessed a high angular velocity of their own; they then appeared
to surround the star completely. But after March 22, 1901, the outer
particles of the streams attained greater distances and assumed longer
periods of revolution (six days); the star then became more obscured
when the extreme dust clouds of the streams covering it happened to
get between us and the star. As the streams of particles were moving
farther away, their rotational periods increased gradually to ten days.
The star, therefore, became periodical with a slowly growing length
of period, and its glow turned more reddish at its minimum than at
its maximum of intensity. At the same time, the absorptive power of
the marginal particles decreased, partly owing to their increasing
expansion, partly because the dust was slowly aggregating to coarser
particles; possibly, also, because the finest particles were being
driven away by the radiation pressure. The sifting influence which the
dust exercised upon the light, and owing to which the red-and-yellow
rays were more readily transmitted than the blue-and-green, gradually
became impaired; hence the color of the light turned more gray, and
after a certain time the star appeared once more of a whitish hue.
This white color indicates that the star must still have a very high
temperature. By the continued ejection of dust-charged masses of gas,
probably with gradually decreasing violence, the light intensity of the
star must slowly diminish (as seen from the earth) and the distribution
of the layers of dust around the luminous core will more and more
become uniform. How violent the explosion must have been, we recognize
from the observation that the first ejected masses of hydrogen
rushed out with an apparent velocity of at least 700 km. per second.
This velocity is of the same order as that of the most remarkable
prominences of the sun.
[Illustration: Fig. 47.—Spiral nebula in the Canes Venatici.
Messier 51. Taken at the Yerkes Observatory on June 3, 1902.
Scale, 1 mm. = 13.2 sec. of arc]
It will be admitted that these arguments present us with a faithful
simile even of the details of the observed course of events, and it is
therefore highly probable that our view is in the main correct. But
what has meanwhile become of the new star? Spectrum analysis tells
us that it has been converted into a stellar nebula like other new
stars. The continuous light of the central body has more and more been
weakened by the surrounding masses of dust. By the radiation pressure
these masses are driven towards the outer particles of the surrounding
gaseous envelope consisting principally of hydrogen, helium, and
“nebular matter.” There the dust discharges its negative electricity,
and thus calls forth a luminescence which equals that of the nebulæ.
[Illustration: Fig. 48.—Spiral nebula in the Triangle. Messier
33. Taken at the Yerkes Observatory on September 4 and 6, 1902.
Scale, 1 mm. = 30.7 sec. of arc]
We have to consider next that owing to the incredibly rapid rotation,
the central main mass of the two stars will, in its outer portions,
be exposed to centrifugal forces of extraordinary intensity, and will
therefore become flattened out to a large revolving disk.[15] As the
pressure in the outer portions will be relatively small, the density of
the gases will likewise be diminished there. The energetic expansion
and, more still, the great heat radiation will lower the temperature
at a rapid rate. We have thus to deal with a central body whose inner
portion will possess a high density, and which will resemble the mass
of the sun, while the outer portion will be attenuated and nebular.
Distributed about the central body we shall find the rest of the two
streams of gases which were ejected immediately after the violent
collision between the two celestial bodies. A not inconsiderable
portion of the matter of these spirally arranged outer parts will
probably travel farther away into infinite space, finally to join some
other celestial body or to form parts of the great irregular spots of
nebular matter which are collected around the star clusters. Another
portion, not able to leave the central body, will remain in circular
movement about it. In consequence of this circular movement, which
will be extremely slow, the outlines of the two spirals will gradually
become obliterated, and the spirals will themselves more and more
assume the shape of nebular rings about the central mass.
[Footnote 15: A. Ritter has calculated that when two suns of
equal size collide with one another from an infinite distance,
the energy of the collision is not more than sufficient to
enlarge the volume of the suns to four times the previous
amount. The largest portion of the mass will therefore probably
remain in the centre, and it will only be masses of light gases
which will be ejected.]
[Illustration: Fig. 49.—The great nebula in Andromeda. Taken at
the Yerkes Observatory on September 18, 1901. Scale, 1 mm. =
54.6 sec. of arc]
[Illustration: Fig. 50.—Ring-shaped nebula in Lyra. Taken at
the Yerkes Observatory]