ASTRO 101
Principles of Astronomy
Instructor: Jerome A. Orosz
(rhymes with
“boris”)
Contact:
• Telephone: 594-7118
• E-mail: orosz@sciences.sdsu.edu
• WWW:
http://mintaka.sdsu.edu/faculty/orosz/web/
• Office: Physics 241, hours T TH 3:30-5:00
Homework/Announcements
• Homework due Tuesday, April 16: Question 4,
Chapter 8 (Describe the three main layers of
the Sun’s interior.)
• Chapter 9 homework due April 23: Question 13
(Draw an H-R Diagram …)
Next:
How Does the Sun Work?
How Does the Sun Work?
• Some useful numbers:
 The mass of the Sun is 2x1030 kg.
 The luminosity of the Sun is 4x1026 Watts.
 The first question to ask is: What is the energy
source inside the Sun?
Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Chemical energy (e.g. burning wood,
combining hydrogen and oxygen to make
water, etc.).
 Efficiency = 1.5 x 10-10
 Solar lifetime = 30 to 30,000 years, depending on
the reaction. Too short!
Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Gravitational settling (falling material
compresses stuff below, releasing heat).
 Efficiency = 1 x 10-6
 Solar lifetime = 30 million years. Too short,
although this point was not obvious in the late
1800s.
Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Nuclear reactions: fusion of light elements (as
in a hydrogen bomb).
 Efficiency = 0.007
 Solar lifetime = billions of years.
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.
More Nuclear Fusion
• 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).
Nuclear Fusion
• 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
Nuclear Fusion
• The CNO cycle (left) and pp chain (right) are outlined.
Models of the Solar Interior
•
The interior of the Sun is relatively simple
because it is an ideal gas, described by three
quantities:
1. Temperature
2. Pressure
3. Mass density
•
The relationship between these three quantities
is called the equation of state.
Ideal Gas
• For a fixed volume, a hotter gas exerts a higher
pressure:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Hydrostatic Equilibrium
• The Sun does not collapse on itself, nor does it
expand rapidly. Gravity and internal pressure
balance:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Hydrostatic Equilibrium
• The Sun does not collapse on itself, nor does it
expand rapidly. Gravity and internal pressure
balance. This is true at all layers of the Sun.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Hydrostatic Equilibrium
• The Sun (and other
stars) does not collapse
on itself, nor does it
expand rapidly. Gravity
and internal pressure
balance. This is true at
all layers of the Sun.
• The temperature
increases as you go
deeper and deeper into
the Sun!
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).
Models of the Solar Interior
• Solve these equations on a computer:
 Compute the temperature and density at any layer, at
any time.
 Compute the size and luminosity of the star as a
function of the initial mass.
 Etc…….
Solar Structure Models
Solar Structure Models
• Here is the model
of the structure of
the Sun.
• Next: Characterizing Stars
The Sun and the Stars
• The Sun is the nearest example of a star.
• Basic questions to ask:
– What do stars look like on their surfaces? Look
at the Sun since it is so close.
– How do stars work on their insides? Look at
both the Sun and the stars to get many
examples.
– What will happen to the Sun? Look at other
stars that are in other stages of development.
Stellar Properties
• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
measure as many properties about them as we
can:





Power output (luminosity)
Temperature at the “surface”
Radius
Mass
Chemical composition
Observing Other Stars
• Recall there is basically no hope of spatially
resolving the disk of any star (apart from
the Sun). The stars are very far away, so
their angular size as seen from Earth is
extremely small.
• The light we receive from a star comes from
the entire hemisphere that is facing us. That
is, we see the “disk-integrated” light.
Observing Other Stars
• To get an understanding of how a star works,
the most useful thing to do is to measure the
spectral energy distribution, which is a plot of
the intensity of the photons vs. their
wavelengths (or frequencies or energies).
• 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.
Broad Band Photometry
• There are several
standard filters in use
in astronomy.
• The filter lets only
light within a certain
wavelength region
through (that is why
they have those
particular colors).
Color Photography
• The separate images are digitally processed to
obtain the final color image.
Color Photography
Color Photography
Broad Band Photometry
• Broad band photometry has the advantage in
that it is easy (just need a camera and some
filters on the back of your telescope), and it is
efficient (relatively few photons are lost in the
optics).
• The disadvantage is that the spectral resolution
is poor, so subtle differences in photon energies
are impossible to detect.
High Resolution Spectroscopy
• To obtain a high resolution spectrum, light from a star is
passed through a prism (or reflected off a grating), and
focused and detected using some complicated optics.
High Resolution Spectroscopy
• Using a good high resolution spectrum, you
can get a much better measurement of the
spectral energy distribution.
• The disadvantage is that the efficiency is lower
(more photons are lost in the complex optics).
Also, it is difficult to measure more than one
star at a time (in contrast to the direct imaging
where several stars can be on the same image).
Stellar Properties
• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
measure as many properties about them as we
can:





Power output (luminosity)
Temperature at the “surface”
Radius
Mass
Chemical composition
The Luminosity
• Luminosity (or power) is a measure of the
energy emitted at the surface of the star per
second.
– We are not at the surface of the star, so we need to
extrapolate from measurements we can do.
– We can measure the energy received from the star
at the Earth.
– If we can measure the distance to the star, then we
can figure out the energy that the star emitted.
The Distance
• How can you measure the distance to
something?
 Direct methods, e.g. a tape measure. Not good
for things in the sky.
 Sonar or radar: send out a signal with a known
velocity and measure the time it takes for the
reflected signal. Works for only relatively
nearby objects (e.g. the Moon, certain
asteroids).
The Distance
• How can you measure the distance to
something?
 Direct methods, e.g. a tape measure. Not good
for things in the sky.
 Sonar or radar: send out a signal with a know
velocity and measure the time it takes for the
reflected signal. Works for only relatively
nearby objects (e.g. the Moon, certain
asteroids).
 Triangulation: the use of parallax.
The Parallax
• Parallax is basically the apparent shifting of
nearby objects with respect to far away
objects when the viewing angle is changes.
• Example: hold out your finger and view it
with one eye closed, then the other eye
closed. Your finger shifts with respect to
the background.
The Parallax
• Example: hold out your finger and view it
with one eye closed, then the other eye
closed. Your finger shifts with respect to
the background.
The Parallax
• A better example: place an object on the
table in front of the room and look at its
position against the back wall as you walk
by. In most practical applications you will
have to change your position to make use of
parallax.
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
• The length B and the
angle p can be
measured, so the
distance can be
computed: d=B/tan(p)
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
• This technique can be
applied to nearby
stars.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
• Here is another
diagram showing the
technique. This
technique can be
applied to other stars!
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• The largest baseline one can obtain is the orbit of the
Earth!
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
Triangulating the Stars
• The largest baseline one can obtain is the orbit of the
Earth!
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• The largest baseline one can obtain is the orbit of the
Earth!
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• Here are two neat Java tools demonstrating parallax:
http://www.astro.ubc.ca/~scharein/a310/Sim.html#Oneover
http://spiff.rit.edu/classes/phys240/lectures/parallax/para1_jan.html
Triangulating the Stars
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
• The angle p for the nearest star is 0.77 arcseconds.
One can currently measure angles as small as a few
thousands of an arcsecond.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• 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.
Triangulating the Stars
• 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.
Triangulating the Stars
• 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.
Distances and Brightness
• What do we do with the distance
measurement?
Distances and Brightness
• What do we do with the distance
measurement? We need the distance to
compute the star’s luminosity.
• Note the distinction between how bright a
star appears and how luminous it actually is.
• Let’s review how to quantify brightness…
Magnitudes as a Measure of
Brightness
• Historically (e.g. Hipparcos in the First
Century), the brightness of stars as seen by
the eye have been measured on a magnitude
scale:
– The brightest stars were “first magnitude”.
– The faintest stars were “sixth magnitude”.
• Brighter objects have smaller magnitudes.
Magnitudes as a Measure of
Brightness
• In modern times, it was discovered that the
human eye has a nonlinear response to light:
if one source of light has twice the photons
as a second source, then the first source
would not appear by eye to be twice as
bright.
• The response of the eye is logarithmic, so
that differences of magnitudes correspond
to ratios of flux.
The Magnitude Scale
• The modern of the
magnitude scale is set
up so that a difference
of 5 magnitudes
corresponds to a ratio
of brightnesses of 100.
• Bright objects can
have negative apparent
magnitudes.
The Magnitude Scale
• The modern of the
magnitude scale is set
up so that a difference
of 5 magnitudes
corresponds to a ratio
of brightnesses of 100.
• Bright objects can
have negative apparent
magnitudes.
The Luminosity of Stars
• An important physical characteristic of a star is
its luminosity, which is a measure of the amount
of energy emitted by the star at its surface per
unit time.
• We can measure the amount of energy received
from the star per unit time (we call this the
flux).
• How do we relate the luminosity to the flux?
The Inverse Square Law
• Imagine a source emitting light uniformly over all
directions. Also imagine a series of concentric spheres
centered on the light source.
• The energy passing through each sphere is the same!
The Inverse Square Law
• The energy passing through each
sphere is the same.
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• The flux through the first
sphere is 72 W/m2.
• The energy passing through each
sphere is the same.
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• The flux through the first
sphere is 72 W/m2.
• The surface area of the second
sphere is 4 m2.
• The energy passing through each
sphere is the same.
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• 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.
• The energy passing through each
sphere is the same.
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• 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.
• The surface area of the third
sphere is 9m2.
• The energy passing through each
sphere is the same.
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• 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.
• The surface area of the third
sphere is 9m2. The flux
• The energy passing through each
through the third sphere is (72
sphere is the same.
2) = 8 W/m2.
W)/(9
m
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• 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.
• The surface area of the third sphere is
9m2. The flux through the third
sphere is (72 W)/(9 m2) = 8 W/m2.
• The flux decreases as the square of
• The energy passing through each
the distance.
sphere is the same.
• Suppose the light source has a
luminosity of 72 watts.
• Suppose the inner sphere has a
surface area of 1 m2. Recall the
area of a sphere is 4 p R2.
The Inverse Square Law
• The car’s headlights
give off the same
amount of light no
matter where you
stand.
• Obviously you will
see more light if you
are closer.
The Inverse Square Law
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
The Inverse Square Law
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
The Inverse Square Law
• The received flux from a source depend
inversely on the square of the distance.
The Inverse Square Law
• Here is a neat Java tool demonstrating the inverse
square law:
http://www.astro.ubc.ca/~scharein/a310/Sim.html#Oneover
The Inverse Square Law
• The received flux from a source depend
inversely on the square of the distance.
• If you want to know the intrinsic luminosity
of your source, you must measure the flux
and the distance.
Stellar Properties
• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
measure as many properties about them as we
can:





Power output (luminosity) Measure distance and flux
Temperature at the “surface”
Radius
Mass
Chemical composition
Stellar Properties
• There are two ways to measure the temperature
of a star:
 Measure its “color”.
 Measure its absorption line spectrum.
Stellar Temperatures
• Recall from the discussion of black bodies that a
hotter black body looks bluer than a cooler black
body. This works for stars also…
Stellar Temperatures
• The redder stars
in this image are
relatively cool,
and the bluer
stars are
relatively hot.
Stellar Temperatures
• As the temperature goes up, the peak of the
spectrum goes towards the blue.
Stellar Properties
• There are two ways to measure the temperature
of a star:
 Measure its “color”.
 Measure its absorption line spectrum.
High Resolution Spectroscopy
• To obtain a high resolution spectrum, light from a star is
passed through a prism (or reflected off a grating), and
focused and detected using some complicated optics.
Spectral Classification
• In the early 1800s, Joseph Fraunhofer observed the
solar spectrum. He saw dark regions, known as
spectral lines (these tell us what elements are there).
• Starting in the late 1800s, it became possible to take
the spectra of stars with similar detail.
Spectral Classification
• At first, there was no physical understanding.
• The earliest classification scheme was based
on the strength of the hydrogen lines, with
classes of: A, B, C, D, E, F, G, H, I, J, K, L,
M, N, O.
• Class A had the strongest hydrogen lines, class
O the weakest.
• Later on, only a few of these classes were kept.
Then, subclasses were added (e.g. G2), based
on other elements.
Spectral Classification
• At first, there was no physical understanding.
• The earliest classification scheme was based
on the strength of the hydrogen lines, with
classes of: A, B, F, G, K, M, O.
• Eventually, physical understanding came. It
was discovered that the spectral type was a
temperature indicator. As a result, a more
natural ordering of the spectral types became:
O, B, A, F, G, K, M (the old classes were
retained).
Spectral Type Sequence Mnemonics
• Oh Boy, An F Grade Kills Me
• Oh, Be A Fine Girl, Kiss Me
http://www.astro.sunysb.edu/fwalter/AST101/mnemonic.html
Spectral Classification
• Here are digital plots
of representative stars
in the spectral
sequence.
• Note the variation in
the strength of the
hydrogen lines.
Spectral Classification
• This is a computer simulation of the different types.
Spectral Classification
• A measurement of the spectral type gives the
“surface” temperature of the star.
• O-stars are the hottest, with surface
temperatures of up to 60,000 K.
• M-stars are the coolest, with temperatures of
only 3000 K.
• The temperature of the Sun (a G2 star) is 5770
K.
Stellar Properties
• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
measure as many properties about them as we
can:





Power output (luminosity) Measure distance and flux
Temperature at the “surface” color or spectral type
Radius
Mass
Chemical composition
Next:
• Temperature-Luminosity diagrams
• Binary stars