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ASTRO 101
Principles of Astronomy
Instructor: Jerome A. Orosz
(rhymes with
“boris”)
Contact:
• Telephone: 594-7118
• E-mail: [email protected]
• 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 …)
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.
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)
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
• 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.
• 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 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
Stellar Properties
• We can measure the apparent brightnesses of
stars relatively easily (e.g. broad-band
photometry).
• We can measure the color index and/or the
spectral type of stars. This gives us the
temperatures.
• We can measure the distances to the relatively
nearby stars. Thus we can compute intrinsic
brightnesses or luminosities for these stars.
• What do you do with these data?
Temperature-Luminosity Diagrams
• When you have a large number of objects, each
with several observed characteristics, look for
correlations between the observed properties.
Temperature-Luminosity Diagrams
• When you have a large number of objects, each
with several observed characteristics, look for
correlations between the observed properties.
• Henry Norris Russell and Ejnar Hertzsprung
were the first to do this with stars in the early
1900s.
• 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.
Temperature-Luminosity Diagrams
• The stars do not fall
on random locations in
this diagram!
Temperature-Luminosity Diagrams
• The stars do not fall
on random locations in
this diagram!
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Temperature-Luminosity Diagrams
• The stars do not fall
on random locations in
this diagram!
• What does this mean?
• This diagram gives us
clues to inner
workings of stars, and
how they evolve.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Temperature-Luminosity Diagrams
• The stars do not fall
on random locations in
this diagram!
• There is some specific
physical process that
limits where a star can
be on this diagram.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Temperature-Luminosity Diagrams
• The stars do not fall
on random locations in
this diagram!
• Furthermore, the
location of a star on
this diagram is an
indicator of its size.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Black Body Radiation
• The luminosity, radius, and temperature of a
black body are related: measure any two
values, you can compute the third one.
• Since stars are approximately black bodies,
their location in the CMD indicates their
radii.
Temperature-Luminosity Diagrams
• Temperature is on the
x-axis: hotter stars are
on the left, cooler ones
on the right.
• Luminosity is on the
y-axis, more
luminuous ones are at
the top, the less
luminuous ones are at
the bottom.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
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.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Temperature-Luminosity Diagrams
• This diagram shows
some well-known
stars. Most of the
bright stars you see
without a telescope
are giants.
Temperature-Luminosity Diagrams
• These regions in the
H-R diagram are
useful when
considering the
evolution of stars
(more later).
Temperature-Luminosity Diagrams
•
So far, we have found out that:
1. Stars occupy specific regions of the temperatureluminosity or color-magnitude diagram.
2. The inferred radii of stars spans a very wide
range from “white dwarfs” with sizes similar to
the Earth to “supergiants” with sizes equal to the
Sun-Mars distance.
•
This is related to the life cycles of stars. But
first, we must discuss binary stars and stellar
“populations”…
Next:
Other Stellar Properties
Binary Stars
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:





Temperature at the “surface” ---use spectral types
Power output (luminosity) --- flux and distance
Radius
Mass
Chemical composition
Other Stellar Properties
• We can measure the temperature of a star
relatively easily by its spectral type or color. If
the distance is known, then we can measure its
luminosity, and then compute its radius.
Other Stellar Properties
• We can measure the temperature of a star
relatively easily by its spectral type or color. If
the distance is known, then we can measure its
luminosity, and then compute its radius. Note,
however, that the radius measured this way is
not very accurate, owing to the uncertainty in
the distance.
Other Stellar Properties
• We can measure the temperature of a star
relatively easily by its spectral type or color. If
the distance is known, then we can measure its
luminosity, and then compute its radius. Note,
however, that the radius measured this way is
not very accurate, owing to the uncertainty in
the distance.
• Is it possible to measure the radius of a distant
star accurately?
Other Stellar Properties
• We can measure the temperature of a star
relatively easily by its spectral type or color. If
the distance is known, then we can measure its
luminosity, and then compute its radius. Note,
however, that the radius measured this way is
not very accurate, owing to the uncertainty in
the distance.
• Is it possible to measure the radius of a distant
star accurately? Also, are there other properties
we can measure?
Other Stellar Properties
• We can measure the temperature of a star
relatively easily by its spectral type or color. If
the distance is known, then we can measure its
luminosity, and then compute its radius. Note,
however, that the radius measured this way is
not very accurate, owing to the uncertainty in
the distance.
• Is it possible to measure the radius of a distant
star accurately? Also, are there other properties
we can measure? Yes, use binary stars!
Binary Stars
• A binary system is when two stars are bound
together by gravity. They orbit their common
center of mass.
Detour: The Two-Body Problem
• Use Newton’s Laws to describe the
behavior of two objects under the influence
of their mutual gravity.
 We will apply it to binary star systems (e.g. a
system consisting of two stars).
Center of Mass
• For two point masses, the center of mass is
along the line joining the two masses.
• The center of mass is closer to the more
massive body.
Center of Mass
• Why is this useful? Two
bodies acting under their
mutual gravity will orbit
in a plane about their
center of mass.
• Here is the case for
equal masses.
Center of Mass
• Why is this useful? Two
bodies acting under their
mutual gravity will orbit
in a plane about their
center of mass.
• Here is the case for
M1 = 2M2.
Center of Mass
• Why is this useful? Two
bodies acting under their
mutual gravity will orbit
in a plane about their
center of mass.
• Here is the case for
M1 >> M2, for example
the Sun and Earth.
Binary Stars
• A binary system is when two stars are bound
together by gravity. They orbit their common
center of mass.
• In some cases, you can see two stars move
around each other on the sky.
Binary Stars
• A binary system is when two stars are bound
together by gravity. They orbit their common
center of mass.
• In some cases, you can see two stars move
around each other on the sky.
• These are “visual binaries.”
Binary Stars
Binary Stars
• 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!
Center of Mass
• 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”).
• For a binary star, the decomposition depends on the orientation of the orbit:
 For an orbit seen face-on, all motion is in the plane of the sky.
 For an orbit seen edge-on, the motion is also in the radial direction. The
size of the radial velocity variations depend on the inclination of the orbit
(the radial velocity is the true velocity times the sine of the inclination.)
Viewing Angle
• The plane of the orbit
is two dimensional, so
depending on how that
plane is tilted with
respect to your line of
sight you can see
different things.
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.
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. One can see Sirius wobble over the course of
decades (it has a very massive, but dark, companion).
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.
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.
Detecting Radial Velocities
• Recall that radial velocities can be
measured from Doppler shifts in the
spectral lines:
Detecting Radial Velocities
• Recall that radial velocities can be
measured from Doppler shifts in the
spectral lines:
Motion towards us
gives a shorter
observed wavelength.
Detecting Radial Velocities
• 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.
Spectroscopic Binaries
• Recall that radial velocities can be
measured from Doppler shifts in the
spectral lines:
• Here are two spectra of Castor B, taken at
two different times. The shift in the lines
due to a change in the radial velocity is
apparent.
Spectroscopic Binaries
• The radial velocity
of each star
changes smoothly
as the stars orbit
each other.
• These changes in
the radial velocity
can be measured
using high
resolution spectra.
Spectroscopic Binaries
• Recall from that radial velocities can be
measured from Doppler shifts in the
spectral lines:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Spectroscopic Binaries
• In some cases, you can see both stars in the
spectrum.
• In most cases, you can only see one star
changing its radial velocity in a periodic way.
Binary Stars
• A binary system is when two stars are bound
together by gravity. They orbit their common
center of mass.
• In some cases, we can use binary stars to
measure precise masses and radii for stars.
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.
Center of Mass
• 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 edge-on, etc.).
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Center of Mass
• 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 edge-on, etc.).
Stellar Masses
• 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.
Viewing Angle
• The plane of the orbit
is two dimensional, so
depending on how that
plane is tilted with
respect to your line of
sight you can see
different things.
Stellar Masses
• 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. How do you find the viewing angle?
Stellar Masses
• 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. Find eclipsing systems!
Definition
• An eclipse, occultation, and transit
essentially mean the same thing: one body
passes in front of another as seen from
earth.
Eclipsing Systems and Stellar Radii
• Eclipsing systems must be nearly edge-on, since
the stars appear to pass in front of each other as
seen from Earth.
Eclipsing Systems and Stellar Radii
• The relative radii can be found by studying how
much light is blocked, and for how long.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Eclipsing Systems and Stellar Radii
• The “light curve
depends on the relative
sizes and brightnesses
of the stars, and on the
orientation.
Eclipsing Systems and Stellar Radii
• The “light curve
depends on the relative
sizes and brightnesses
of the stars, and on the
orientation.
• Algol was known to
be variable for a long
time, and its periodic
nature was established
in 1783.
Accurate Masses and Radii From
Binary Stars
• The ideal binary systems are ones where
both stars are seen in the spectrum
(“double-lined”), and where eclipses are
seen. Masses and radii accurate to a few
percent can be derived from careful
observations of these systems.
• There are on the order of 100 such wellstudied systems with “main sequence
stars”. What do you do with this
Mass-Luminosity Relation
• The stars form a tight sequence. This is
another clue to the inner workings of stars!
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Mass-Luminosity Relation
• The stars form a tight sequence. This is
another clue to the inner workings of stars!
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:





Temperature at the “surface” ---use spectral types
Power output (luminosity) --- flux and distance
Radius --- eclipsing binary stars
Mass --- eclipsing binary stars
Chemical composition
Next:
• Stellar Evolution.