Download (the factor f star in the Drake equation. Recall it

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Astrophysical considerations
(the factor fstar in the Drake equation.
Recall it is the fraction of stars in a typical
galaxy which have the ‘right’ chemistry
for life.
First we need to make a tentative conclusion
concerning what the ‘right’ chemistry might be.
For example in the periodic table in the next
slide I have circled the elements which humans
need to live.
We have little idea how many of these
elements would be required for some
form of life. However we can say the
following:
It is unlikely that the chemistry of just the
FIRST TWO elements (hydrogen and
helium) is complex enough to result
in anything at all lifelike. (Some might
even dispute this conclusion.)
With that assumption, and some
information about how stars form, we
can derive an estimate of fstar
A brief review of the history of the universe,
as currently understood.
About 14 billion years ago, the space of the
Universe was compacted in an extremely
small region and began to rapidly expand.
Roughly one second after the expansion began,
the initial material cooled sufficiently to leave mainly
electromagnetic radiation, two kinds helium nuclear
isotopes, two kinds of hydrogen nuclei (protons
and deuterons) and electrons.
By our assumption, the universe was not yet
chemically complex enough to sustain any kind of life.
About 300,000 years after the initial explosion, the
electrons combined with the nuclei to leave mainly
electrically charge neutral atoms of helium and
hydrogen as well as electromagnetic radiation.
After that, the electromagnetic radiation did not
interact strongly with the matter any more and
it remained in the universe from that time. The
discovery by radio astronomers of this ‘cosmic ray
background’ electromagnetic radiation is one
of the experimental reasons that we believe this
story.
The universe continued to expand and does so to
this day. The expansion was first discovered
by Hubble and coworkers in the 1920’s by measuring
the distances and velocities of distant galaxies.
All the galaxies were found to be moving away from
us and the most distant galaxies were moving away
the fastest. This is what is expected if the universe
is expanding uniformly in all directions.
Hubble used the Doppler effect to measure velocities.
Since the Doppler effect appears several times in
our story, I will take a few minutes to explain how it
works.
Star formation.
The expansion of the universe is fascinating,
but for our purposes, what is more important
is what started happening to the matter
after that 1st 300,000 years.
All massive matter is mutually attracting. Newton
first formulated this idea in his tremendously successful
theory of gravitation, which is still used to
account for the motion of astronomical bodies
and much else. (though for very large masses
and gravitational forces an extension of Newton’s
ideas, due to Einstein, is required.)
If the universe were a perfectly expanding sphere,
the mutual attraction would not matter, but even the
slightest unevenness in the mass distribution will make
the mass of the universe start to clump up.
The clumping of the mass at first resulted in
dust clouds (of helium and hydrogen) but as
it progressed, the centers of the more massive
clouds and the pressure due to the gravitational
attraction got larger and larger in them.
Eventually, the pressure was so great that the
nuclei of the atoms started to get pushed together.
To do this requires a HUGE pressure by earthly
standards and it only occurs inside stars and
in the (fortunately rare) explosion of thermonuclear
weapons. To get an idea how this works requires
some ideas about two other fundamental forces
of nature, namely electromagnetic and strong
nuclear forces.
Electrical repulsion
+
+
Gravitational attraction
If the gravitational attraction becomes large
enough to overcome the electrical repulsion
then the nuclei can get close enough for
the short range attractive nuclear force to
take over. Then ‘nuclear burning’ starts in
which the nuclei can fuse with emission of
large amounts of kinetic energy and rise in
temperature.
Thus the stars ignited and the
resultant ‘nuclear burning’ produces
elements of the periodic table. As you
see from the diagram, this has been
worked out in great detail.
However,from the point of view of
chemistry for building life, there are
two problems:
The elements formed are inside of
high temperature, high pressure
stars.
The chain of reactions stops at iron,
short of many elements essential to
life on earth, at least.
Supernovae: The stars die for life.
For stars of the mass of our sun, the nuclear
burning continues to iron and then stops,
Then the stars slowly die and becoming
white dwarves and then cinders. But more
massive stars (5 stellar masses or more)
die more spectacularly. When the burning
stops, the gravitational pressure results in
catastrophic implosion followed by a
‘bounce' and emission of massive amounts
of material from the star. Two things happen:
1)The elements formed inside the stars are
spread out into the interstellar medium and
2) Reactions producing elements beyond
iron take place during the explosion.
Supernovae occur about once every 100 years
in a typical galaxy. They are observed regularly
in other galaxies by astronomers and were observed
in our own galaxy in 1006,1054,1572 and 1604.
They are the source of the material in the interstellar
medium which is available for formation of planets
with complex chemistry suitable for life, at least
as we know it. In this sense, stars have died for
us.
The last stage of concern is the formation of
new, second generation stars and planets around
them, from this enriched interstellar medium.
The earlier, first generation stars, probably also
formed planets around them as they formed,
but those planets must have been composed only
of hydrogen and helium.
The Crab Nebula in Taurus is the 6-light-year-wide remnant of a supernova explosion
seen in 1054 AD. We know it resulted from the violent death of a massive star, because
the star's collapsed core remains visible as a pulsar — a rapidly rotating, highly
magnetic neutron star — in the nebula's heart. This composite image was assembled
from 24 exposures by the Hubble Space Telescope’s Wide Field and Planetary Camera
2.
Explosion estimated to have occurred in 1681
Science 342,1343 (2014)
Now we want to estimate fstar. which is the
fraction of all the stars which are in this
second generation. For that we need just
a few more facts about how stars evolve.
By making detailed mathematical models using
known facts about the nuclear reactions occuring
inside them, you can predict the lifetimes of
stars if you know their masses. From that information
we will use just a couple of facts:
Stars big enough to be supernovae live about
107 years.
Stars of mass around the mass of our sun live
about 1010 years.
From the first fact we can estimate the number
of stars which will become supernovae in
a typical galaxy like this: Let the number be
Nsuper. . Then since those stars die in about
107 years, the number dying in a galaxy per
year is
Nsuper/ 107 = 1/100
So Nsuper is about 100,000 or one in a million.
From the other fact, we can estimate the
number of second generation stars N2 .
The death rate is equal to the birth rate, giving
N2 /1010 = 5/100, giving N2 about 5x 108
From this we get
fstar= N2/Ngal of about 5x108/1011=5x10-3
This is roughly consistent with estimates
in the scientific literature.