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					Temp

There are two ways to do this:
! “Broad band”, by taking images with a camera and
a colored filter.
! “High resolution”, by using special optics to
disperse the light and record it.

• Oh Boy, An F Grade Kills Me

5700 K

The flux through the first
sphere is 72 W/m2.
• The surface area of the second
sphere is 4 m2. The flux
through the second sphere is
(72 W)/(4 m2) = 18 W/m2.

Parallax is basically the apparent shifting of
nearby objects with respect to far away
objects when the viewing angle is changes.

For very tiny angles, use the approximation that
tan(p)=p, when p is in radians.
• Then d=B/tan(p) becomes d=B/p.
• B=1 “astronomical unit” (e.g. the Earth-Sun distance).
Define a unit of distance such that d=1/p, if the angle p
is measured in arcseconds.
• This unit is the parsec, which is 3.26 light years

For very tiny angles, use the approximation that
tan(p)=p, when p is in radians.
• Then d=B/tan(p) becomes d=B/p.
• B=1 “astronomical unit” (e.g. the Earth-Sun distance).
Define a unit of distance such that d=1/p, if the angle p
is measured in arcseconds.
• This unit is the parsec, which is 3.26 light years

 Some measure of the temperature is plotted on
the x-axis of the plot, and some measure of the
intrinsic luminosity is plotted on the y-axis.

For a given size, hotter
objects give off more
energy than cooler
objects, and are bluer.
Temperature-Luminosity Diagrams
• Lines of constant
radius go something
like this:
• Cool and luminous
stars: large radii.
• Hot and faint stars:
small radii.
• Most stars are here,
and there is not a large




variation in radius.

A binary system is when two stars are bound
together by gravity. They orbit their common
center of mass.
• In a visual binary, you can see two stars.
• However, for most binary stars, their separation
is very small compared to their distance, and
from Earth they appear to be a single point.

How do you observe these types of binaries?
Use spectroscopy!

A star will appear to “wobble” when it is
orbiting another body.
! If the other body is another star, the wobble
will be relatively large.
! If the other body is a planet, the wobble will be
very small.

Detecting the Wobble
• In Astronomy, any motion can be broken down into two
groups:
! Motion in the plane of the sky (e.g. east-west and north-south
motion).
! Motion towards or away from us (e.g. “radial velocities”).
• Motions in the plane of the sky are usually small, and
typically one has to wait many years to see a relatively
big shift. We can’t detect this motion in most binaries.

Recall that radial velocities can be measured
from Doppler shifts in the spectral lines:
Motion towards us
gives a shorter
observed wavelength.
Motion away from us
gives a longer




observed wavelength.

Center of Mass
• Recall that m1r1=m2r2
• Also, note that velocity of the star is
proportional to the distance to the
center of mass since a star further
from the COM has a greater distance
to cover in the same amount of time.
This implies m1v1=m2v2, or
m1/m2=v2/v1

The ratio of the velocities in inversely
proportional to the mass ratio. Also,
the same is true for radial velocities.

• If you can see both stars in the spectrum, then
you may be able to use Doppler shifts to
measure the radial velocities of both stars. This
gives you the mass ratio, regardless of the
viewing angle (e.g. nearly face-on, nearly edgeon,
etc.). This is usually useful information.
• If you can find the viewing angle, then you can
compute true orbital velocities and use Kepler’s
Laws and Newton’s theory to find the actual
masses.

• An eclipse, occultation, and transit
essentially mean the same thing: one body
passes in front of another as seen from
earth.

! The mass of the Sun is 2x10^30 kg.
! The luminosity of the Sun is 4x10^26 Watts.

Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Nuclear reactions: fission of heavy elements (as
in an atomic bomb), or fusion of light elements
(as in a hydrogen bomb). Fission is not
important in the Sun since the heavy elements
(e.g. uranium) are extremely rare.
! Efficiency = 0.007
! Solar lifetime = billions of years.

• Conduction:
direct contact
• Radiation: via
photons
• Convection: via
mass motions

The 4 “Forces” of Nature
• There are 4 “fundamental forces” in nature:
1. Gravity: relative strength = 1, range = infinite.
2. Electromagnetic: rel. str. = 1036, range = infinite.
3. “Weak” nuclear: rel. str. = 1025, range = 10-10 meter.
4. “Strong” nuclear: rel. str. = 1038, range = 10-15 meter.
• The electromagnetic force can be repulsive (+,+
or -,-) or attractive (+,-). Normal chemical
reactions are governed by this force.

How to get energy from atoms
• Fission: break apart the nucleus of a heavy
element like uranium.
• Fusion: combine the nuclei of a light element
like hydrogen.
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
! Rate ~ (temperature)4 for p-p chain.
! Rate ~ (temperature)15 for the CNO cycle.
! Small changes in the temperature lead to large
changes in the fusion rate.
• Suppose the fusion rate inside the Sun increased:
! The increased energy heats the core and expands the
star. But the expansion cools the core, lowering the
fusion rate. The lower rate allows the core to shrink
back to where it was before.



Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
! Rate ~ (temperature)4 for p-p chain.
! Rate ~ (temperature)15 for the CNO cycle.
! Small changes in the temperature lead to large
changes in the fusion rate.
• Suppose the fusion rate inside the Sun increased:
! The increased energy heats the core and expands the
star. But the expansion cools the core, lowering the
fusion rate. The lower rate allows the core to shrink
back to where it was before.

Models of the Solar Interior
• The pieces so far:
! Energy generation (nuclear fusion).
! Ideal gas law (relation between temperature,
pressure, and volume.
! Hydrostatic equilibrium (gravity balances pressure).
! Continuity of mass (smooth distribution throughout
the star).
! Continuity of energy (amount entering the bottom of
a layer is equal to the amount leaving the top).
! Energy transport (how energy is moved from the
core to the surface).

Stellar Groupings
• One way to get around sample biases is to
study groups of stars bound by gravity.
Why?
1 The distance across a group is relatively
small, which means the stars in the group
have roughly the same distance from us. This
in turn means that ratios in apparent
brightness are the same as the ratios of
intrinsic luminosities.

Star Clusters
• The physical size of a cluster is only a few
dozen light years, compared to typical
distances of several hundred or a few
thousand light years. All of the cluster stars
have the same distance from us to an
accuracy of a few percent.
• You can plot the apparent brightness instead
of the intrinsic luminosity on the
temperature-luminosity diagram.

Mass-Luminosity Relation
• The luminosity of a star represents the amount of
energy emitted per second. There must be a
source of this energy, and it cannot last forever.
• The amount of “fuel” a star has is proportional to
its initial mass.
• The length of time the fuel can be spent is equal
to the amount of fuel divided by the consumption
rate.
• Age ~ mass/luminosity = mass/(mass)4=1/(mass)3

Mass-Age Relation
• Age ~ 1/(mass)3 (“age” means time on the
main sequence, “mass” means initial mass).
• More massive stars “die” much more
quickly than less massive stars. For
example, double the mass, and the age
drops by a factor of 8.
• On the main sequence, O and B stars (the
bluest ones) are the most massive. Their
lifetimes are relatively short.

Mass-Luminosity Relation
• The luminosity of a star is related to its
mass: L ~ Mp, where p is almost 4.

Mass-Luminosity Relation
• The luminosity of a star represents the amount of
energy emitted per second. There must be a
source of this energy, and it cannot last forever.
• The amount of “fuel” a star has is proportional to
its initial mass.
• The length of time the fuel can be spent is equal
to the amount of fuel divided by the consumption
rate.
• Age ~ mass/luminosity = mass/(mass)4=1/(mass)3

Stellar Evolution
• The basic steps are:
! Gas cloud
! Main sequence
! Red giant
! Rapid mass loss (planetary nebula or supernova
explosion)
! Remnant
• The length of time spent in each stage, and the
details of what happens at the end depend on
the initial mass.

Nuclear Fusion in the Sun
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• Why does this produce energy?
! Before: the mass of 4 protons is 4 proton masses.
! After: the mass of 2 protons and 2 neutrons is 3.97
proton masses.
! Einstein: E = mc2. The missing mass went into
energy! 4H ---> 1He + energy

• Fusion of elements
lighter than iron can
release energy (leads to
higher BE’s).
• Fission of elements
heaver than iron can
release energy (leads to
higher BE’s).

After the Main Sequence: Low Mass
• After the core hydrogen is used up, internal
pressure can no longer support the core, so it
starts to collapse. This releases energy, and
additional hydrogen can fuse outside the core.
• The excess energy causes the outer layers of the
star to expand by a factor of 10 or more. The
star will be large and cool: these are the red
giants seen in the temperature-luminosity
diagram.

After the Main Sequence: Low Mass
• The excess energy causes the outer layers of the
star to expand by a factor of 10 or more. The
star will be large and cool: these are the red
giants seen in the temperature-luminosity
diagram.
• The core continues to collapse, and helium can
fuse into carbon for a short time. The star
expands further. The outer layers eventually
may be ejected to form a “planetary nebula”.
The outer parts of the star expand by large
amounts, and eventually escape into space,
forming a planetary nebula. Matter is recycled
back into space.

Where it Stops
• For large masses (initial mass greater than
about 30 solar masses):
– The core ends up with a substantially more than
1.4 solar masses. The temperature gets hot enough
to fuse elements all the way up to iron.
– The fusion of iron takes energy rather than
liberating it. The core collapses, but it is too
massive to be supported by electron degeneracy
pressure and neutron degeneracy pressure. No
known force can halt the collapse, and the core
collapses to a point. A black hole is born.

Einstein’s Theory
• In Newton’s theory of gravity, gravity is a force
between two objects.
– The “force” travels instantly through space by some
unspecified mechanism.
– Space is the ordinary 3 dimensional “Euclidean
space.”
• In Einstein’s theory:
– Nothing travels faster than light.
– Matter causes space to “warp”, and gravity is a
manifestation of curved space.

Black Holes
• A black hole is an object with a gravitational
field so strong that nothing, not even light, can
escape.
• All of the matter is compressed to a point.
• There is no physical surface. However, one can
define a radius within which nothing can escape:
this is called the “event horizon” or the
“Schwarzchild radius” .
• Once matter or light crosses the event horizon, it
is gone forever.

Black Holes
• A black hole is an object with a gravitational
field so strong that nothing, not even light, can
escape.
• Black holes have only three properties:
– Mass
– Angular momentum (if it is spinning)
– Electric charge (not astrophysically important since
macroscopic objects are neutral)
• Black holes cannot have magnetic fields, or a
temperature, or a color, etc.

• If the black hole is
close to another
star, it can pull
material off that
star. As the
matter falls into
the black hole, it
gets very hot, and
emits X-rays.

Results
• There are 21 cases where there is good
evidence that there is a black hole:
– Strong X-ray sources (usually flares).
– Optically dark objects (that is, only one star is
seen in the spectrum, and it is the mass-losing
one).
– Masses too large to be a white dwarf or a
neutron star.

A Sense of Scale
• The Sun (and its planets) and these nearby stars
are part of a vast collection of stars bound by
gravity:
! Such a collection of stars is called a “galaxy”.
! This structure contains roughly 1011 stars and is
100,000 light years across.
• There are about 50 billion galaxies similar to our
own in the observable universe!

Interstellar Dust
• Light passing through an
interstellar dust cloud will
be dimmed.
• However, the amount of
dimming depends on the
wavelength of the light:
blue light is scattered
more easily than red light.
The object appears
redder.

Why is the Sky Blue?
• Blue light travels a relatively short distance before
it is scattered by molecules in the air. Red light
goes much further before being scattered.

then the Sun is well off the center!
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Finding the Structure
• Counting individual stars in the optical
leads to biases if interstellar dust is not
accounted for. One has the illusion that we
are at the center.
• The globular clusters give a much more
unbiased view. The center of the galaxy is
roughly 25,000 light years away in the
direction of Sagittarius.

• There are three main parts:
– The bulge/nucleus at the center (roughly spherical with a
radius of about 3000 light years).
– The disk which is about 100,000 light years across and about
2000 light years thick. It contains the young stars, the gas,
and the dust. The Sun is in the disk about 2/3 the way out.
– The halo, which is a roughly spherical and relatively diffuse
region a few hundred thousand light years across. The halo
contains very old stars and the globular clusters.
The 21 cm line of Hydrogen
• For the study of Galactic structure, radio
observations have some advantages:
! Radio photons can easily penetrate the
interstellar dust. You can essentially see every
part of the disk.
! Neutral hydrogen, which is the most abundant
element in the universe, has an emission line at
21.1 cm, so you can measure radial velocities
from Doppler shifts

The 21 cm line of Hydrogen
• In quantum mechanics, electrons and
protons have a property called “spin”,
although it is really not the same as a
spinning ice skater.
• This “spin” has only two values: “up” or
“down”.

– Angular momentum: a measure of the spin of
an object or a collection of objects.

Angular Momentum
• Angular momentum is a measure of the spin
of an object. It depends on the mass that is
spinning, on the distance from the rotation
axis, and on the rate of spin.
• I = (mass).(radius).(spin rate)

History of Milky Way
• The galaxy formed from a
single large cloud of gas over
13 billion years ago. The first
stars were metal poor.
• In the second stage, the disk
formed. The metal abundance
gradually built up as the earlier
generations of stars enriched
the gas with metals.
• Many details remain to be
worked out…

				
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posted:11/27/2011
language:English
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