Download 7/3 Some stars were found in regions above the main sequence

7/3
Some stars were found in regions above the main sequence giant stars and supergiant stars.
Some stars were found in a region below the main sequence white dwarfs.
Once the HR diagram has been plotted with stars whose distances can be measured via parallax
and whose absolute magnitudes can be calculated, we can use the diagram to calculate distances
to more distant stars.
1. Measure the temperature of the star.
2. If a main sequence star, go to the portion of the main sequence with that temperature.
3. Move horizontally over to the absolute magnitude axis and read off its absolute magnitude.
4. Use the distance formula to calculate the distance.
How do we know if a star lies on the main sequence — it could be a giant.
We look at luminosity classes — due to the fact that there are subtle differences between the
main sequence spectra and spectra from giant stars.
Giant stars, while much larger than main sequence
stars, are no more massive. They are much less dense,
and the effect of the low density on the spectrum can be
measured.
Luminosity Classes:
Ia. Bright Supergiants
Ib. Supergiants
II. Bright Giants
III. Giants
IV. Subgiants
V. Main Sequence
We can use the HR diagram to measure the distances to
all the stars.
This procedure is known as spectroscopic parallax.
Finding the masses of stars — use binary star systems.
Binary star systems are classified by how they are
detected:
1. Visual Binary System — one in which we can see both stars in the system.
2. Astrometric Binary System — only one star in the system can be seen visually; the presence of
the second is inferred from a wobbly motion of the visible star.
3. Spectroscopic Binary System — So far away, the two stars cannot be resolved individually; we
infer the presence of the two stars by two separate spectra undergoing opposite Doppler shifts.
4. Eclipsing Binary System — We detect the existence of two stars because the alternately
eclipse one another.
We can use Kepler’s third as modified by Newton to measure the masses of stars in a binary
system.
1. Visual and Astrometric Systems: Plot the orbit and from the orbital parameters, we calculate
the total mass of the two stars. We can get the individual masses of the two stars by using the
center of mass.
2. Spectroscopic Binary Systems: Can’t measure the distance between the stars because they are
imaged as a point. But we can rewrite Kepler’s third law in terms of speed and period rather
than distance and period. We can use the Doppler shift to measure the speeds. But we don’t
measure the actual speed, only the part that is along our line of sight — get only estimates of the
masses in the system.
3. Eclipsing Binary Systems: Analyzed like spectroscopic
systems but, since we are looking in the plane of the
orbit, we measure their actual speeds and get the actual
masses.
We have found:
Lowest mass stars 8% the mass of the Sun = 0.08 MS.
Objects less massive than this are either brown dwarfs or
planets.
The most massive stars found are around 100 solar
masses.
By putting masses on the HR diagram, we can find a
rough relation between the mass of a star and its
luminosity.
Example: Range of Luminosities of Stars:
Lowest mass:
Greatest mass:
We note that there is a factor of 100 billion between the dimmest and brightest stars.
Sizes of Stars — Three ways to find
1. Eclipsing by the Moon — Carefully watch a star as the Moon eclipses it and measure the time
to go from full brightness to zero. We know the speed of the Moon in its orbit and multiplying by
the time gives the distance the Moon travels as it eclipses the star. If we know the distance to
the star: the ratio of the distance to the star to the distance to the Moon is equal to the ratio of
the diameter of the star to the distance the Moon travels while eclipsing the star.
Disadvantages: must know the distance to the star and only those stars along the Moon’s path
through the sky are ever eclipsed. In addition, the smaller the star, the more diffraction effects
mask the time to be measured.
2. Eclipsing Binary System — We can measure the speeds of these stars using the Doppler effect.
We measure the time for one star to pass in front of the
other star (system drops in brightness). Multiplying the
speed of one star by this time gives the diameter of the
other star. In the picture at right, we measure the time
when the brightness begins to dim (point A) and the time
at which it stops dimming (point B). Multiply the
difference between these two times by the speed of the
star to get its diameter d. To get the diameter D of the
large star, use the time at A and the time at C, where
system starts to brighten again. Don’t need to know the
distance to the star, but very few eclipsing binary
systems.
3. Use the Stefan-Boltzmann Law: Written in solar units
Solve for the diameter:
Measure luminosity and temperature to get size.
Example:
This method applies to any star in the sky.
Density of Stars — divide the mass of star by its volume (from the size) to get its density.
We find:
Main Sequence Stars all have a density about that of water (1 g/cm 3).
Giant Stars — about the same mass as main sequence stars but much larger — small densities
— range form a hundredth to a tenth of the density of water.
Supergiant Stars — still no more massive than main sequence stars but much much larger —
0.00000001 to 0.001 times the density of water.
White Dwarfs — 2 million times the density of water.
Chapter 9 — The Lives of Stars from Birth through Middle Age
Stars are born as a result of the gravitational contraction of the interstellar medium.
Today there are four types of interstellar medium:
1. HII Regions — hydrogen, helium, and dust — Hot bright stars in the region ionize the gas —
emit light when electrons recombine with ions — hot and low density — we observe them as
emission nebulae and reflection nebulae.
2. HI Regions — Just like an HII region except no hot stars to ionize the gas. Low density but
cool because of the absence of hot stars.
3. Giant Molecular Clouds — denser and much colder than either HI or HII regions. Contain
molecules near their centers protected from radiation from outside.
4. Coronal Gas — very low density, extremely hot, and much like the Sun’s corona — probably
due to supernova explosions.
By weight, about 50% of the interstellar medium is in the form of giant molecular clouds, HI and
HII regions account for nearly 25% apiece, and coronal gas about 2 %.
Stars form from the contraction of this medium, but there are mechanisms that impede the
contraction:
1. Thermal energy — hard to make a hot gas contract.
2. Magnetic fields — will only act on charged particles such as found in HII regions.
3. Rotation — contraction impeded perpendicular to the axis of rotation.
Stars will form in regions that are coolest and densest — giant molecular clouds.
Still, some mechanism must trigger the star formation:
1. Supernova explosion — sends matter through the giant molecular cloud causing density
fluctuations. Where the density fluctuates upward, gravitational contraction into a star can
begin.
2. If star formation has already begun in the cloud, a star entering the main sequence can inject
matter into the cloud to produce additional star formation.
3. If a giant molecular cloud crosses the boundary between spiral arms it can generate density
fluctuations that can cause star formation.
4. If two giant molecular clouds collide, density fluctuations will be produced to cause star
formation — how the first stars were born.
How a star is formed:
1. Density fluctuations are triggered in a giant molecular cloud.
2. A region of high density begins to contract.
3. The region is almost certainly rotating —
as it contracts, the rotation speeds up to
form a disk as we described in talking
about the formation of the solar system.
Planets form in the disk.
4. In the center, the gas continues to
contract and as it contracts it gets hotter.
5. Eventually the gas at the center gets hot
enough to glow — converting gravitational
energy into thermal energy.
6. This glowing object is called a protostar.
7. At this stage, the protostar is much like
a giant star but we can’t see it because it is
enclosed in a cocoon of gas and dust. Can
be viewed in IR.
8. The protostar continues to contract and heat until its center gets hot enough to fuse hydrogen
(H) into helium (He) — at this point the star enters the main sequence.
9. The outgoing stellar wind blows away the cocoon of gas and dust and the star becomes visible
to the universe at large.
Once the star reaches the main sequence, it becomes relatively stable and evolves only slowly.
We can understand the structure of a main sequence star using four principles:
1. Hydrostatic Equilibrium — outflow of energy or the radiation pressure prevents further
gravitational contraction — radiation pressure balances gravity.
2. Energy Transport — imagine breaking the star into spherical shells and energy is driven
across the shell because the inside of the shell is hotter than the outside.
3. Conservation of Mass — the sum of the masses of the shells is equal to the total mass of the
star.
4. Conservation of Energy — summing the energy production in each shell gives the total
luminosity of the star.
What happens to a star depends almost completely on the mass of the star.
Mass Categories:
Low-Mass Stars — 0.2 solar masses and less
Medium-Mass Stars — 0.2 solar masses up to between 2 and 3 solar masses.
High-Mass stars — from 2 to 3 solar masses on up
Main Sequence Lifetime of a Star
The lifetime J of a star is given the energy E available to the star divided by the luminosity L of
the star:
Put this in terms of solar units — the energy available to the star is proportional to its mass
(recall E = mc2) E = M. Recall that, in solar units, L = M3.5, so we get
Example: Range of lifetimes of stars.
Lowest Mass Star: M = 0.08 MS
Highest Mass Star: M = 100 MS
Since a star’s evolution depends so much on its mass, we should note that the mass of a star
changes over time.