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Transcript
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 …)
• Chapter 10 homework due April 30: Question
15 (Explain how and why the turnoff point on
the H-R diagram of a cluster is related to the
cluster’s age.)
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”.
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
Stellar Evolution
• Observational aspects
– Observations of clusters of stars
• Theory
– Outline of steps from birth to death
Stellar Models
Stellar Evolution
• There are several distinct phases in the life
cycle of a star. The evolutionary path
depends on the initial mass of the star.
• Although there is a continuous range of
masses, there are 4 ranges of masses that
capture all of the interesting features.
Stellar Evolution
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.
Points to Remember:
• How to counter gravity:
– Heat pressure from nuclear fusion in the core (no
mass limit)
• Gas pressure proportional to the temperature.
– Electron “degeneracy” pressure (mass limit 1.4
solar masses)
– Neutron “degeneracy” pressure (mass limit 3 solar
masses)
• Stars experience rapid mass loss near the end
of their “lives”, so the final mass can be much
less than the initial mass.
Points to Remember:
• Sources of energy:
– Nuclear fusion:
• needs very high temperatures
• about 0.7% efficiency for hydrogen into helium.
– Gravitational “accretion” energy:
• Drop matter from a high “potential”
• About 10% efficient when falling onto massive bodies
with very small radii.
Stellar Evolution
Star Formation
• The starting point is a giant molecular cloud.
The gas is relatively dense and cool, and usually
contains dust.
• A typical cloud is several light years across, and
can contain up to one million solar masses of
material.
• Thousands of clouds are known.
Side Bar: Observing Clouds
• Ways to see gas:
 By “reflection” of a nearby light source. Blue light
reflects better than red light, so “reflection nebulae”
tend to look blue.
 By “emission” at discrete wavelengths. A common
example is emission in the Balmer-alpha line of
hydrogen, which appears red.
Side Bar: Observing Clouds
• Ways to see dust:
 If the dust is “warm” (a few hundred degrees K)
then it will emit light in the long-wavelength
infrared region or in the short-wavelength radio.
 Dust will absorb light: blue visible light is highly
absorbed; red visible light is less absorbed, and
infrared light suffers from relatively little
absorption. Dust causes “reddening”.
Giant Molecular Clouds
• This nebula is in the belt of Orion. Dark dust lanes
and also glowing gas are evident.
Giant Molecular Clouds
• Interstellar
dust makes
stars appear
redder.
Giant Molecular Clouds
• This images
shows dust
obscuration, an
emission nebula,
and a reflection
nebula.
Giant Molecular Clouds
• Inside many
nebula one finds
very dense cores
called Bok
globules that are
ready to
collapse…
Gravity and Angular Momentum
• There are two important concepts to keep in
mind when considering the fate of giant
molecular clouds:
– Gravity: pulls things together
– Angular momentum: a measure of the spin of
an object or a collection of objects.
Gravity
• There are giant clouds of gas and dust in the
galaxy. They are roughly in equilibrium,
where gas pressure balances gravity.
• Sometimes, an external disturbance can
cause parts of the cloud to move closer
together. In this case, the gravitational
force may be stronger than the pressure
force.
Gravity
• Sometimes, an external disturbance can
cause parts of the cloud to move closer
together. In this case, the gravitational
force may be stronger than the pressure
force.
• As more matter is pulled in, the
gravitational force increases, resulting in a
runaway collapse.
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)
• The angular momentum in a system stays
fixed, unless acted on by an outside force.
Conservation of Angular Momentum
• An ice skater demonstrates
the conservation of angular
momentum:
• Arms held in: high rate of
spin.
• Arms extended: low rate of
spin.
• I = (mass).(radius).(spin rate)
(angular momentum and
mass are fixed here)
Conservation of Angular Momentum
• If an interstellar cloud has some net
rotation, then it cannot collapse to a point.
Instead, the cloud collapses into a disk that
is perpendicular to the rotation axis.
Condensation Theory
• An interstellar cloud
collapsed to a disk.
Friction in the disk drives
matter inward and
outward (conserving
angular momentum).
• Planets may eventually
form in the disk.
Condensation Theory
Image from Nick Strobel’s Astronomy Notes (http://www.astromynotes.com)
The Protostar
• This diagram shows the
steps as computed using a
computer model.
The Protostar
• This diagram shows how a star “moves” through
the temperature-luminosity diagram as it forms.
The Protostar
• This diagram shows how a star “moves” through
the temperature-luminosity diagram as it forms.
The Protostar
• High mass stars simply get bluer, whereas the
lower mass stars contract and become dimmer.
The Protostar
• An external disturbance can cause the cloud to
collapse:
 The material collapses to a rotating disk, and
friction drives material into the center, where it
builds up.
 The central object heats up as the cloud collapses.
Eventually, the temperature gets hot enough for
nuclear fusion to occur.
• We are left with a newly born star surrounded
by a disk of material.
Young Star Systems
• There is strong
evidence for a disk
surrounding the star
Beta Pictoris.
Young Star Systems
• Many stars in the
Orion nebula are
surrounded by disks of
material.
Young Star Systems
• Many stars in the
Orion nebula are
surrounded by disks
of material.
Young Star Systems
• A collapsing cloud can form hundreds of
stars.
 Stars with small masses (less than a solar mass)
are much more common than massive stars
(stars more than about 15 to 20 solar masses).
 The highest mass stars are very hot and
luminous, and can alter the cloud environment.
Young Star Systems
• Infrared images
are useful since
the infrared
light penetrates
deeper into the
dark clouds,
allowing one to
see what is
inside. Often
one sees young
stars.
Young Star Systems
• Infrared
observations often
reveal hundreds of
newly-formed
stars embedded in
molecular clouds.
Young Star Systems
• Infrared observations
often reveal hundreds
of newly-formed stars
embedded in
molecular clouds.
Young Star Systems
• Infrared observations
often reveal hundreds
of newly-formed stars
embedded in
molecular clouds.
• In this particular case,
many of the stars have
not arrived on the
main sequence.
Young Star Systems
• Newly-formed hot stars can alter their
environment.
Hubble Anniversary
Star Formation Summary
Stellar Evolution
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.
The Main Sequence
• A star that is fusing hydrogen to helium in its
core is said to be on the main sequence.
• A star spends most of its “life” on the main
sequence; the time spent is roughly proportional
to 1/M3, where M is the initial mass.
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 energy from fusion in
the core ultimately
provides the pressure
needed to stabilize the star.
Stellar Evolution
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.
After the Main Sequence
• On the main sequence, the star is in hydrostatic
equilibrium where internal pressure supports the
star against gravitational collapse. Nuclear
fusion (hydrogen to helium) is the energy
source.
After the Main Sequence
• On the main sequence, the star is in hydrostatic
equilibrium where internal pressure supports the
star against gravitational collapse. Nuclear
fusion (hydrogen to helium) is the energy
source.
• What happens when all of the hydrogen in the
core is converted to helium?
After the Main Sequence
• On the main sequence, the star is in hydrostatic
equilibrium where internal pressure supports the
star against gravitational collapse. Nuclear
fusion (hydrogen to helium) is the energy
source.
• What happens when all of the hydrogen in the
core is converted to helium? The details depend
on the initial mass of the star…
After the Main Sequence
• Stars with masses
between 0.1 and 0.4
solar masses
convert their entire
mass into helium.
• This can take
hundreds of billions
of years or more.
After the Main Sequence
• Stars with masses
between 0.1 and 0.4
solar masses
convert their entire
mass into helium.
• Stars with higher
mass don’t mix
new fuel into their
cores…
Points to Remember:
• Sources of energy:
– Nuclear fusion:
• needs very high temperatures
• about 0.7% efficiency for hydrogen into helium.
– Gravitational “accretion” energy:
• Drop matter from a high “potential”
• About 10% efficient when falling onto massive bodies
with very small radii.
• After a stage of nuclear fusion is complete in a
stellar core, it will collapse and get hotter.
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).
• Extremely high temperatures and densities are
needed (the Sun’s core is about 15,000,000 K).
Images from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
The 4 “Forces” of Nature
•
Both gravity and the electromagnetic force are
“inverse square” forces where the strength of
the force depends on 1/d2.
–
–
Fgrav = product of masses divided by distance
squared.
Felec = product of charges divided by distance
squared. Higher concentrations of (like) charges
need stronger forces to bring them together (recall
like charges repel).
More Nuclear Fusion
• Fusion of elements lighter than iron can release energy (leads to
higher BE’s).
• As you fuse heavier elements up to iron, higher and higher
temperatures are needed since more and more electrical charge
repulsion needs to be overcome.
–
–
–
–
Hydrogen nuclei have 1 proton each temperature ~ 10,000,000 K
Helium nuclei have 2 protons each
temperature ~ 100,000,000 K
Carbon nuclei have 6 protons each temperature ~ 700,000,000 K
…..
• After each stage of fusion is complete, the core collapses and heats
up.
• More mass in the core --> higher core temperature --> fusion of
heavier elements …
• For a given core mass, there is a limit to how hot it can become.
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.
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.
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 red giants are
stars that just finished
up fusing hydrogen in
their cores.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
After the Main Sequence: Low Mass
• Some red giants are as
large as the orbit of
Jupiter!
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
After the Main Sequence: Low Mass
• Some red giants are as
large as the orbit of
Jupiter!
• The Sun will reach
approximately to the
orbit of the Earth
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.
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.
After the Main Sequence: Low Mass
• Helium fusion starts in
a “shell” around the
core, then after a
“helium flash” the
helium fusion starts in
the core.
After the Main Sequence: Low Mass
• Helium fusion starts in
a “shell” around the
core, then after a
“helium flash” the
helium fusion starts in
the core.
In Brief: Evolution of Close Binaries
• The evolution of stars in a close binary can be
drastically altered. In many cases, one star transfers
mass to the other, thereby changing its evolution.
In Brief: Evolution of Close Binaries
• In Algol and in many other similar systems, the less
massive star is a red giant, and the higher mass star is on
the main sequence. Shouldn’t the higher mass star have
evolved first?
In Brief: Evolution of Close Binaries
• In Algol and in many other similar systems, the less
massive star is a red giant, and the higher mass star is on
the main sequence. Shouldn’t the higher mass star have
evolved first? Mass transfer messed things up…
In Brief: Evolution of Close Binaries
• In b Lyrae and other similar systems, the shapes of the
eclipses can only be explained by the presence of an
“accretion disk” around one of the stars. Mass transfer
is taking place in these systems.
In Brief: Evolution of Close Binaries
• In W Ursae Majoris and other similar systems, the two
stars apparently share a common atmosphere. When
one eclipse ends, the other begins.
After the Main Sequence: Low Mass
• As core hydrogen
fusion stops, low mass
stars become more
luminous and red (e.g.
cooler), higher mass
stars tend to just get
redder while keeping
the same luminosity.
• In all cases, the star
gets larger in size.
Next:
• The “deaths” of stars.