The Sun is a star. Stars appear much fainter because they are much further away.
The distance to the nearest stars was found in the mid-18th century using parallax. The
Earth's orbit acted as the baseline, so a star had to be observed at different times of
the year.
A new unit of measurement was defined: the distance required to give a parallax of 1
arcsec using a baseline of 1 AU, a parsec. This is the standard distance measurement to
stars. 1 parsec = 206265 AU = 3.1 x 1018cm.
Greater distances have smaller parallax, so the parallax angle alpha = 1/d, where alpha
is measured in arcseconds and d is measured in parsecs e.g.. A star with a parallax of 0.1
arcsec's is 10 parsecs away.
The nearest star beyond the Sun is Alpha Centauri, 1.3pc away.
Modern measurements are good to 0.02 arcsec (@50 parsecs), although the Hipparcos
satellite is improving this to 0.002 arcsec (@500 parsecs).
Another unit of distance measure is the lightyear, the distance light travels in a
single year. One parsec is 3.26 lightyears. B. Luminosity and
Color
The luminosity is the total light energy emitted. L = Flux x A = sigma T4 x
4xpi R2
The luminosity depends on both the size and temperature of the object.
As you get further from a star, the amount of light per unit area from the star (i.e.
the brightness), b is proportional to 1/d2.
If we were 1pc from the Sun, its brightness would drop 1/2062652 = 2.5 x 10-11.
Stellar luminosities range from 10000 to 0.0001 times the Sun.
Different stars have different colors, hence, different surface temperatures. We can
categorize stars by their colors: spectral
class. For historical reasons, these classes are: O B A F G K M
Each letter class is broken up further from 0 to 9, with 0 being the hottest.
The Sun is a G2 star.
In the early 20th century, a diagram of luminosity and
color was developed: The
Hertzsprung-Russell diagram.
Stars were generally found in certain parts of the diagram, called luminosity classes.
Most stars lie along a single band called the main sequence (Class V).
Other classes are supergiants (Class I), bright giants (Class II), giants (Class III),
and the subgiants (Class IV).
Different luminosity classes have different line strengths, so they can be told apart.
Giants have much more extended atmospheres, and hence stronger lines.
White dwarfs are very small (Earth-sized), very hot stars with little or no hydrogen.
In a distance limited survey (nearby stars), the vast majority are red dwarf stars (K
and M Class V).
If we can place a star on the H-R diagram (from colors
and lines), then we can estimate
its luminosity and hence its distance. The brighter the star, the further away we can see
it. This works best for clusters of stars. C. Binaries and Stellar Mass
We know the Sun's mass because of the planets orbiting it. We need orbiting companions
in order to measure masses.
Fortunately, most stars are really binaries or multiple star systems.
Visual binaries can be seen as two separate objects. We measure the angular separation,
relative brightness's and colors, sometimes the orbital period and the mass ratio (from
the proper motions).
Spectroscopic binaries are systems in which we can see the spectral lines move back and
forth due to Doppler shift. In single-line binaries, we can only see the lines from one
star, while in double-line systems both stars' lines are visible. We can measure the
velocity (with an uncertainty from the inclination of the system) and period, and for
double-line systems the mass ratio from the velocity ratio.
In eclipsing binaries one star passes in front of the other. Light curves give radii,
periods, relative brightness's and colors.
An individual system can be any combination of these.
Orbital periods can be hours to 1000's of years.
From Kepler's 3rd Law: T2 = 4 pi/G(M1 + M2) a3.
If we know T and a, we can measure the sum of the masses. We can often measure T directly,
and a can be estimated from the velocities or the separations.
The mass ratio is needed to determine the individual masses.
Systematic trends are seen on the main sequence. Hot stars are more massive. O stars are
more than 20 Mo (solar masses), while M stars are less than 0.2Mo.
Giants are less obvious, although supergiants have masses greater than 5Mo.
White Dwarfs have masses of 0.5 to 1.2Mo. D. Stellar Evolution
Most stellar evolution occurs over timescales which are much longer than human
experience, so models are needed to determine how stars change.
Stellar evolution is driven by the fight against gravity. At different stages different
forces hold the star up.
A star begins as a dense core (104 particles/cm3) inside a cloud
of dust and gas. Initially, the thermal motions of the gas support the cloud.
If gravity becomes too strong, collapse begins. The transition occurs when the orbital
speed becomes greater than the thermal gas velocity.
Collapse occurs as an ``inside first'' freefall until collisions between molecules
become important and the gas starts trapping light. This slows the collapse down, but it
doesn't stop it.
The star moves horizontally on the H-R diagram until it reaches 4000K. At this point
ionizing hydrogen holds the surface at a constant temperature, while the contraction
reduces the star's luminosity. A star evolving this way is said to be on a Hayashi track.
During these early phases, the stars energy comes entirely contraction.
Eventually, the core reaches 107K, and hydrogen fusion can occur. Further
contraction increases the surface temperature. As the core temperature increases, the
luminosity increases (because reactions occur faster), and the star settles onto the main
sequence.
Evolution onto the main sequence takes 3 x 107 years for a 1 Mo
star. A 20 Mo star only requires 106 years.
For most stars, the main sequence is where the spend the bulk of their active (energy
producing) lives. Hydrogen fusion occurs in the core either through the p-p chain (for M
< 1.5Mo) or the CNO cycle (for M > 1.5Mo). The Sun will last
1010 years in this phase. Higher mass stars deplete their cores much more
quickly.
During the main sequence, the star changes very slightly (becomes brighter and cooler).
As the core runs out of hydrogen, fusion moves out to a shell around the core.
Meanwhile, the helium core contracts and heats up. This heat up of the core causes the
outer layers of the star to expand and the overall luminosity to go up. The star evolves
up through the subgiant and giant branches.
Eventually, the core reaches 108K (in 108 years). so He nuclei can
fuse.
There are no stable nuclei with 5 or 8 nucleons (protons and neutrons) so He much go
through the triple alpha reaction.
4He + 4He + 4He -> 12C + gamma
By the time He burning occurs, the core is degenerate. The electrons have been squeezed
together as tightly as they can get.
A degenerate core keeps the same temperature throughout, so the whole thing stars fusion
at once. This is called the helium flash.
He flash causes the core to expand, and the total luminosity to drop. The star enters
the horizontal branch (bright giant star).
He fusion is less efficient than H fusion, and the luminosity is much larger, so He core
burning lasts only 5x 107 years.
The C core starts to contract, so it heats up. The outer layers of the star expand, and
the star's luminosity increases and its surface temperature decreases, so it becomes a
supergiant. H and He fusion continue in shells around the core.
At this point core contraction stops because the core has once again become degenerate,
and there isn't enough material above it to heat it up to 6 x 108K for carbon
fusion.
He shell burning becomes unstable, and the star's luminosity pulsates. Since the outer
layers are cool and far from the center of the star, they can be removed by radiation
pressure when the luminosity is high.
Eventually, the star's hydrogen and helium envelope separates from the core and forms a
``planetary nebula''.
The planetary nebula is a spherical shell of hot, glowing gas around the central core.
The gas glows due to emission lines.
The nebula looks like a ring because it is optically thin. Only along the edges do we
look through enough material to see it.
The hot core becomes a white dwarf star (density 107g/cm3), while
the nebula expands out into space. The white dwarf gradually cools over hundreds of
billions of years.
At higher mass, the main sequence lifetime is much shorter. For a 5Mo star,
the lifetime is 3 x 108 years. For 10Mo, it's 107 years.
High mass stars also lose mass due to stellar winds. A 20Mo star can lose up
to 1Mo in only 106 years.
In stars with mass > 4Mo, the core gets to He fusion before it becomes
degenerate, so no He flash occurs.
The core also reaches C burning, so it can make heavier elements.
After C, the star fuses O, Ne, Mg, Si. Each of these forms a shell around the next
layer. Si burning only lasts 1 week, and leaves an ash of iron.
Iron is the most stable nucleus, so changing it to anything else costs energy, and the
core no longer supports the star.
Core contraction raises the temperature to 1010K, where photons can
dissociate the iron nuclei. The Fe breaks down into p+, n, and e-
(where p+ = proton and n = neutron), and still more energy is lost.
When the core mass gets bigger than 1.4Mo (the Chandrasekhar mass) electron
degeneracy can no longer hold the star up. Further contraction brings on neutronization: p+
+ e- -> n + nu. This accelerates the collapse.
The core collapse ends when the star reaches a density of 1014g/cm3
(the density of an atomic nucleus) and neutron degeneracy pressure becomes important. This
occurs at a radius of 15km.
The core tries to rebound, but it runs into the infalling material.
A shock wave pushes up through the star, blowing most of it apart in a Type II
supernova.
A supernova releases 1046 Joules in a few seconds. Most of this is in the
form of neutrinos, although around 1044Joules comes out as light and mechanical
energy (motion).
A supernova releases metals into space. These are formed both in the star before the
explosion and during the explosion itself (including all material heavier than iron).
The debris forms a supernova remnant. This expanding cloud of gas is heated by
radioactive decay, ram pressure, and synchrotron radiation.
The synchrotron radiation is powered by the remnant core, a neutron star. The neutron
star retains a very strong magnetic field which accelerates electrons, especially near the
magnetic poles.
The neutron star rotates very rapidly (initially its period is 10-3 seconds).
If its magnetic poles aren't exactly lined up with the rotation poles, then the stars
brightness will change each orbit period. This is a pulsar.
As the pulsar slows down, its radiation gets less energetic, and it gradually
disappears.
If the star is too massive (M > 25Mo), the neutron star gets larger than
3Mo before the rebound can occur. At this mass, neutron star degeneracy can no
longer hold the star up, so it collapses rather than rebounds.
When the density gets up to 2 x 1015g/cm3, the escape velocity
becomes larger than the speed of light, and a black hole is formed.
In general relativity, gravity is an illusion. Instead, mass actually curves space. The
effect of this curvature is an apparent acceleration on all things.
The most important new effect of GR is that light is affected by gravity. Light can be
bent by a strong gravitational field, and if it encounters a strong enough field, it can
be prevented from escaping. This is a black hole.
Much of the mass of the star falls into the black hole, where it is lost forever
(nothing can move faster than light).
The matter all falls to the a point in the center (a singularity) while all of this is
hidden by an event horizon (the Schwarzchild radius), which is defined as the radius at
which the escape velocity is the speed of light: R = 2GM/c2.
A black hole's major connection with the universe is its gravity. One way to observe a
black hole would be to look for a binary system with 1 star orbiting a compact, dark
object with mass > 3Mo.
Alternatively, we can look for gas being heated as it spirals into a compact object.
See
Solar Physics E.
Stellar Populations
Another way to describe stars is by their `metallicity', the percentage of metals in
their mass.
Our Sun, and most other nearby stars, have around 2% metals. These are population I
stars.
Some stars have metallicity of < 0.2%. These are population II stars.
Metallicity is correlated with age. There are no young Pop II stars in our galaxy.
updated:
|