Download The Family of Stars

Everything you always wanted to
know about stars…
The Spectra of Stars
Inner, dense layers of a
star produce a continuous
(black body) spectrum.
Cooler surface layers absorb light at specific frequencies.
Spectra of stars are absorption spectra.
Spectrum provides temperature, chemical composition
Spectral Classification of Stars (I)
Temperature
Different types of stars show different
characteristic sets of absorption lines.
Mnemonics to remember the
spectral sequence:
Oh
Oh
Only
Be
Boy,
Bad
A
An
Astronomers
Fine
F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known
Me
Me
Mnemonics
Stellar spectra
A
F
G
K
M
Surface temperature
O
B
0
We have learned how to determine a star’s
• surface temperature
• chemical composition
Now we can determine its
• distance
• luminosity
• radius
• mass
and how all the different types of stars
make up the big family of stars.
Distances to Stars
d in parsec (pc)
p in arc seconds
__
1
d= p
Trigonometric Parallax:
Star appears slightly shifted from different
positions of Earth on its orbit
The farther away the star is (larger d),
the smaller the parallax angle p.
1 pc = 3.26 LY
The Trigonometric Parallax
Example:
Nearest star,  Centauri, has a parallax of p = 0.76 arc seconds
d = 1/p = 1.3 pc = 4.3 LY
With ground-based telescopes, we can measure
parallaxes p ≥ 0.02 arc sec
=> d ≤ 50 pc
This method does not work for stars
farther away than about 50 pc
(nearly 200 light-years).
Intrinsic Brightness
The more distant a
light source is, the
fainter it appears.
The same amount of light
falls onto a smaller area at
distance 1 than at distance 2
=> smaller apparent
brightness.
Area increases as square of distance => apparent
brightness decreases as inverse of distance squared
Intrinsic Brightness /
Flux and Luminosity
The flux received from the light is proportional to its
intrinsic brightness or luminosity (L) and inversely
proportional to the square of the distance (d):
L
__
F~ 2
d
Star A
Star B
Earth
Both stars may appear equally bright, although
star A is intrinsically much brighter than star B.
The Size (Radius) of a Star
We already know: flux increases with surface
temperature (~ T4); hotter stars are brighter.
But brightness also increases with size:
A
Star B will be
brighter than
star A.
B
Absolute brightness is proportional to radius squared, L ~ R2.
Quantitatively:
L = 4  R2  T4
Surface area of the star
Surface flux due to a
blackbody spectrum
Example:
Polaris has just about the same spectral type
(and thus surface temperature) as our sun, but
it is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 = 10,000
times more than our sun’s.
The Hertzsprung Russell Diagram
Most stars are
found along the
main sequence
The Hertzsprung-Russell Diagram (II)
Same
temperature,
but much
brighter than
MS stars
 Must be
much larger
 Giant
Stars
Radii of Stars in the
Hertzsprung-Russell Diagram
Rigel
Betelgeuse
Polaris
Sun
100 times smaller than the sun
Ia Bright Supergiants
Ia
Luminosity
Classes
Ib
II
Ib Supergiants
II Bright Giants
III
III Giants
IV
IV Subgiants
V
V Main-Sequence
Stars
Examples:
• Our Sun: G2 star on the main sequence:
G2V
• Polaris: G2 star with supergiant luminosity:
G2Ib
Masses of Stars
in the
HertzsprungRussell Diagram
The higher a star’s mass,
the more luminous
(brighter) it is:
L ~ M3.5
High-mass stars have
much shorter lives than
low-mass stars:
tlife ~ M-2.5
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
Masses in units
of solar masses
Surveys of Stars
Ideal situation:
Determine properties
of all stars within a
certain volume.
Problem:
Fainter stars are
hard to observe; we
might be biased
towards the more
luminous stars.
A Census of the Stars
Faint, red dwarfs
(low mass) are
the most
common stars.
Bright, hot, blue
main-sequence
stars (highmass) are very
rare.
Giants and
supergiants
are extremely
rare.
Shocks Triggering
Star Formation
Henize 206
(infrared)
0
The Contraction of a Protostar
Protostellar Disks and Jets –
Herbig-Haro Objects
Disks of matter accreted onto the protostar (“accretion
disks”) often lead to the formation of jets (directed
outflows; bipolar outflows): Herbig-Haro objects
Herbig-Haro 34 in Orion
• Jet along the
axis visible as
red
• Lobes at each
end where jets
run into
surrounding gas
clouds
Motion of Herbig-Haro 34 in Orion
Hubble Space Telescope Image
• Can actually see the knots in the jet move with time
• In time jets, UV photons, supernova, will disrupt
the stellar nursery
The Source of Stellar Energy
Stars produce energy by nuclear fusion of
hydrogen into helium.
In the sun, this
happens
primarily
through the
proton-proton
(PP) chain
The Deaths and End States
of Stars
The End of a Star’s Life
When all the nuclear fuel in a star is used up,
gravity will win over pressure and the star will die.
High-mass stars will die first, in a gigantic
explosion, called a supernova.
Less massive stars will
die in less dramatic
events.
Evolution off the Main Sequence:
Expansion into a Red Giant
Hydrogen in the core
completely converted into He:
 “Hydrogen burning”
(i.e. fusion of H into He)
ceases in the core.
H burning continues in a
shell around the core.
He core + H-burning shell
produce more energy than
needed for pressure support
Expansion and cooling of
the outer layers of the star
 red giant
Expansion onto the Giant Branch
Expansion and
surface cooling during
the phase of an
inactive He core and
a H-burning shell
Sun will expand beyond Earth’s orbit!
HR Diagram of a Star Cluster
High-mass stars
evolved onto the
giant branch
Turn-off point
Low-mass stars
still on the main
sequence
Red Dwarfs
Recall:
Stars with less
than ~ 0.4
solar masses
are completely
convective.
 Hydrogen and helium remain well mixed
throughout the entire star.
 No phase of shell “burning” with expansion to giant.
Star not hot enough to ignite He burning.
Sunlike Stars
Sunlike stars
(~ 0.4 – 4
solar masses)
develop a
helium core.
 Expansion to red giant during H burning shell
phase
 Ignition of He burning in the He core
 Formation of a degenerate C,O core
White Dwarfs
Degenerate stellar remnant (C,O core)
Extremely dense:
1 teaspoon of white dwarf material: mass ≈ 16 tons!!!
Chunk of white dwarf material the size of a beach
ball would outweigh an ocean liner!
white dwarfs:
Mass ~ Msun
Temp. ~ 25,000 K
Luminosity ~ 0.01 Lsun
Low luminosity; high temperature => White dwarfs are found in
the lower center/left of the H-R diagram.
The Chandrasekhar Limit
The more massive a white dwarf, the smaller it is.
 Pressure becomes larger, until electron degeneracy
pressure can no longer hold up against gravity.
WDs with more than ~ 1.4 solar masses
can not exist!
The Final Breaths of Sun-Like Stars:
Planetary Nebulae
Remnants of stars with ~ 1 – a few Msun
Radii: R ~ 0.2 - 3 light years
Expanding at ~10 – 20 km/s ( Doppler shifts)
Less than 10,000 years old
Have nothing to do with planets!
The Helix Nebula
The Formation of Planetary Nebulae
Two-stage process:
The Ring Nebula in Lyra
Slow wind from a red giant blows
away cool, outer layers of the star
Fast wind from hot, inner
layers of the star overtakes
the slow wind and excites it
=> planetary nebula
The Fate of our Sun
and the End of Earth
• Sun will expand to a red
giant in ~ 5 billion years
• Expands to ~ Earth’s orbit
• Earth will then be
incinerated!
• Sun may form a planetary
nebula (but uncertain)
• Sun’s C,O core will
become a white dwarf
The Deaths of Massive Stars: Supernovae
Final stages of fusion
in high-mass stars (>
8 Msun), leading to the
formation of an iron
core, happen
extremely rapidly: Si
burning lasts only for
~ 1 day.
Iron core ultimately collapses,
triggering an explosion that
destroys the star:
Supernova
The Crab Nebula–Supernova from 1050 AD
• Can see expansion between 1973 and 2001
–
Kitt Peak National Observatory Images
The Famous Supernova of 1987:
Supernova 1987A
Before
At maximum
Unusual type II supernova in the Large
Magellanic Cloud in Feb. 1987
Type I and II Supernovae
Core collapse of a massive star:
type II supernova
If an accreting white dwarf exceeds the
Chandrasekhar mass limit, it collapses,
triggering a type Ia supernova.
Type I: No hydrogen lines in the spectrum
Type II: Hydrogen lines in the spectrum
Neutron Stars
A supernova
explosion of an
M > 8 Msun star
blows away its
outer layers.
The central core Pressure becomes so high
will collapse into that electrons and protons
combine to form stable
a compact object
neutrons throughout the
of ~ a few Msun.
object.
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density:  ~ 1014 g/cm3
 Piece of neutron
star matter of the
size of a sugar cube
has a mass of ~ 100
million tons!!!
Discovery of Pulsars
Angular momentum conservation
=> Collapsing stellar core spins up
to periods of ~ a few milliseconds.
Magnetic fields are amplified
up to B ~ 109 – 1015 G.
(up to 1012 times the average
magnetic field of the sun)
=> Rapidly pulsed (optical and radio) emission from some
objects interpreted as spin period of neutron stars
The Crab Pulsar
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun),
there is a mass limit for neutron stars:
Neutron stars can not exist
with masses > 3 Msun
We know of no mechanism to halt the collapse
of a compact object with > 3 Msun.
It will collapse into a single point – a singularity:
=> A black hole!
Escape Velocity
Velocity needed to
escape Earth’s gravity
from the surface: vesc
≈ 11.6 km/s.
Now, gravitational force
decreases with distance (~
1/d2) => Starting out high
above the surface =>
lower escape velocity.
If you could compress
Earth to a smaller radius
=> higher escape velocity
from the surface.
vesc
vesc
vesc
The Schwarzschild Radius
=> There is a limiting radius
where the escape velocity
reaches the speed of light, c:
2GM
Rs = ____
c2
G = gravitational constant
M = mass
Rs is called the
Schwarzschild radius.
Vesc = c
Schwarzschild Radius
and Event Horizon
No object can travel faster
than the speed of light
=> nothing (not even light)
can escape from inside
the Schwarzschild radius
 We have no way of
finding out what’s
happening inside the
Schwarzschild radius.
 “Event horizon”
“Black Holes Have No Hair”
Matter forming a black hole is losing
almost all of its properties.
black holes are completely
determined by 3 quantities:
mass
angular momentum
(electric charge)
Gravitational
Potential
The Gravitational Field
of a Black Hole
Distance from
central mass
The gravitational potential
(and gravitational attraction
force) at the Schwarzschild
radius of a black hole
becomes infinite.
General Relativity Effects
Near Black Holes
An astronaut descending down
towards the event horizon of
the black hole will be stretched
vertically (tidal effects) and
squeezed laterally.
General Relativity Effects
Near Black Holes (II)
Time dilation
Clocks starting at
12:00 at each point.
After 3 hours (for an
observer far away
from the black hole):
Clocks closer to the black
hole run more slowly.
Time dilation
becomes infinite at
the event horizon.
Event horizon
General Relativity Effects
Near Black Holes (III)
gravitational redshift
All wavelengths of emissions
from near the event horizon
are stretched (redshifted).
 Frequencies are lowered.
Event horizon
Observing Black Holes
No light can escape a black hole
=> Black holes can not be observed directly.
If an invisible compact
object is part of a binary,
we can estimate its
mass from the orbital
period and radial
velocity.
Mass > 3 Msun
=> Black hole!