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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
• 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) Measure distance and flux
Temperature at the “surface” color or spectral type
Radius
Mass
Chemical composition
Next:
• Temperature-Luminosity diagrams
• Binary stars
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!
• 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
• 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
•
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. 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!
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.
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!
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.).
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.
Stellar Evolution
• Observational aspects
– Observations of clusters of stars
• Theory
– Outline of steps from birth to death
Stellar Groupings
• To understand how stars evolve, one must
study groups of stars since an individual star
takes a very long time to change.
Stellar Groupings
• To understand how stars evolve, one must
study groups of stars since an individual star
takes a very long time to change.
• One must choose samples of stars very
carefully to avoid bias and to eliminate
“variables”.
An Example of Bias
• Suppose we had two
samples of stars, one
with the nearest stars,
and one with the
apparently brightest
stars. What to the
CMDs look like?
An Example of Bias
• Suppose we had two
samples of stars, one
with the nearest stars,
and one with the
apparently brightest
stars. What to the
CMDs look like?
• Here are the nearest
stars.
An Example of Bias
• Suppose we had two
samples of stars, one
with the nearest stars,
and one with the
apparently brightest
stars. What to the
CMDs look like?
• Here are the nearest
stars.
• Here are the brightest
stars.
An Example of Bias
• Suppose we had two
samples of stars, one
with the nearest stars,
and one with the
apparently brightest
stars. What spectral
types do the stars
have?
An Example of Bias
Image from Nick Strobel’s Astronomy Notes
(http://www.astronomynotes.com)
• Suppose we had two
samples of stars, one
with the nearest stars,
and one with the
apparently brightest
stars. What spectral
types do the stars
have?
• The nearby stars tend
to be cooler, whereas
the bright stars are
hotter.
An Example of Bias
Image from Nick Strobel’s Astronomy Notes
(http://www.astronomynotes.com)
• Suppose we had two
samples of stars, one
with the nearest stars,
and one with the
apparently brightest
stars. What spectral
types do the stars
have?
• Which sample is more
representative?
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.
Stellar Groupings
•
One way to get around sample biases is to
study groups of stars bound by gravity.
Why?
2
The groups are loosely bound, meaning that
the stars must have formed together, rather
than being “captured” after formation.
Stellar Groupings
•
One way to get around sample biases is to
study groups of stars bound by gravity.
Why?
2
The groups are loosely bound, meaning that
the stars must have formed together, rather
than being “captured” after formation. This
means the stars in the group all have the same
age and the same chemical composition.
Star Clusters
• Star clusters can be roughly classified based
on how “tight” they are.
Star Clusters
• Star clusters can be roughly classified based
on how “tight” they are.
 “Open” clusters are less compact, and generally
have relatively small numbers of stars (a few
hundred).
Star Clusters
• Star clusters can be roughly classified based
on how “tight” they are.
 “Globular” clusters are more compact, and
generally have relatively large numbers of stars
(a few hundred thousand).
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.
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.
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.
Star Clusters
• Here is a plot of
apparent magnitude
vs. the color. No
pattern is seen since
each star is at a
different distance.
Figure from Michael Richmond (http://spiff.rit.edu/classes/phys230/phys230.html)
Star Clusters
• Here is a plot of
luminosity
(expressed as
absolute
magnitude) vs. the
color. A clear
pattern is seen since
the luminosity is a
physical property.
Figure from Michael Richmond (http://spiff.rit.edu/classes/phys230/phys230.html)
Star Clusters
• Here is a plot of
luminosity
(expressed as
absolute
magnitude) vs. the
color. A clear
pattern is seen since
the luminosity is a
physical property.
Comparing Stellar Properties
• Sometimes in order to understand how stars work, it is
useful to compare two or more stars.
• Note you can sometimes compare properties without
knowing the actual values, as in “The female rabbit of
this species is larger than the male rabbit of the same
species.”
• A simple question to ask is “Which star is more
luminous than the others?”
Comparing Stellar Properties
• This large-area
photograph shows the
constellations of Orion,
Canis Major, Canis
Minor Taurus, and a
few others.
• Which star is more
luminous:
Rigel
or
Sirius
Comparing Stellar Properties
Comparing Stellar Properties
• Looking up the
distances, we find
• Rigel
– d = 240 pc
– L = 66,000 Lo
• Sirius
– d = 2.64 pc
– L = 25.4 Lo
• The ratio of the fluxes is
not the ratio of the
luminosities since the
distances are different.
Comparing Stellar Properties
Comparing Stellar Properties
• A cluster is a group of
stars bound by their
own gravity. The size
of the cluster is small
compared to its distance
from Earth.
• Which star is more
luminous:
Star A
or
Star B
Comparing Stellar Properties
Comparing Stellar Properties
•
Comparing the
apparent brightnesses
does not help if the
stars have different
distances.
Figure from Michael Richmond (http://spiff.rit.edu/classes/phys230/phys230.html)
Comparing Stellar Properties
•
•
Comparing the
apparent brightnesses
of stars in a cluster
does help since each
star in that cluster has
the same distance from
the Earth.
The distance is still
needed to compute the
actual luminosities,
and not just the relative
ones.
Figure from Michael Richmond (http://spiff.rit.edu/classes/phys230/phys230.html)
Star Clusters
• Let’s plot the stars
from several different
clusters on the diagram
and draw “tracks”
where the stars are to
clean it up…
Figure from Michael Richmond (http://spiff.rit.edu/classes/phys230/phys230.html)
Star Clusters
• The “sequences”
occupied by cluster
stars changes from
cluster to cluster
(within certain
bounds).
Star Clusters
• The “sequences”
occupied by cluster
stars changes from
cluster to cluster
(within certain
bounds). WHY????
Star Clusters
• The “sequences”
occupied by cluster
stars changes from
cluster to cluster
(within certain
bounds). WHY????
• This is related to the
life cycles of stars.
The Life Cycles of Stars
• To understand why different star clusters
have different tracks in the temperatureluminosity diagram, we must return to a
result found from eclipsing binaries…
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.
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.
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.
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-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).
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.
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-Age Relation
• Detailed computations show:
Star Clusters
• Large radii
• Small radii
• High mass (main
sequence)
• Low mass (main
sequence)
Star Clusters
• The “sequences”
occupied by cluster
stars changes from
cluster to cluster
(within certain
bounds).
Star Clusters
• Some clusters have
“lost” only the bluest
main sequence stars.
Star Clusters
• Some clusters have
“lost” only the bluest
main sequence stars.
• Others have lost main
sequence stars down
to type F.
Star Clusters
• Some clusters have
“lost” only the bluest
main sequence stars.
• Others have lost main
sequence stars down
to type F.
• The differences in the
tracks are due to age
differences of the
clusters!
Star Clusters
• Here is an animation showing how a cluster
ages:
http://spiff.rit.edu/classes/phys230/lectures/clusters/hr_anim_slow.gif
Star Clusters
• Here is a temperature
luminosity diagram for
the Hyades cluster.
• This one is relatively
young.
Star Clusters
• Here are the
temperature
luminosity diagrams
for a three clusters.
• These diagrams and
others can be used to
make a “movie” on
how stars evolve.
Star Clusters
• Here is a
schematic
diagram showing
a cluster age
from zero years
(formation) to
several billion
years.
Stellar Evolution
• Observational aspects
– Observations of clusters of stars
• Theory
– Outline of steps from birth to death