a1199 are we alone? the search for life in the...
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A1199Are We Alone?
The Search for Life in the UniverseSummer 2019
Instructor: Shami Chatterjee
Web Page: http://www.astro.cornell.edu/academics/courses/astro1199/HW 2 posted – due Wednesday 10 July
So far: Big Bang, cosmology, galaxiesNow: Stars
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What is needed to form a star?
• A star typically means an object that shines because nucleosynthesis occurs in its core.
• Initial reactions for “main sequence” stars: 4H à He (CNO cycle, proto-proton chain).
• Later: He à C à … other heavier elements … à Fe.
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What is needed to form a star?• Requirements:
• Collapse of a gas cloud that contains H.• Sufficient mass in protostar so that central temperature
is high enough to drive nuclear reactions.
• Collapse of gas clouds is constrained by the temperature and density of the gas cloud.
• Jeans radius and Jeans mass are measures of whether an object (a gas cloud) is susceptible to collapse.
RJ ~ sound speed x free-fall time~ (Tgas / ρ)1/2.
• Stars form with a large range of masses: Initial mass function.
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Jeans Scale and Mass
r
FP
FG
Compare: Free-fall time for a cloud to collapse:
vs.Time for pressure wave to propagate:
tP = R/Cs.
If tff < tP, then the region will collapse faster than pressure can push back.
Jeans Scale RJ ~ Cs / √(Gρ)
tff =
✓2R3
GM
◆1/2
⇠ 1pG�
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Gravitational stability: The case of B68 Optical Near-Infrared
Starless Bok GlobuleGravitationally stable, or at the verge of collapse.
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Example• In the Milky Way there are cold dense clouds that are
actively forming stars today.• Typical temperatures are 10 K and densities 10-22 g/cm3.• Evaluating RJ ~ (kT/m)1/2 (1 / (Gρ))1/2 ~ 3 pc.• We can also calculate the Jeans mass as
MJ ~ ρ RJ3
and we get about 50 M¤.
• Interpretation: Relatively large mass regions collapse. Sub-regions inside them fragment as their temperatures fall and their densities increase.
à A wide range of stellar masses.
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Initial mass function of stars = distribution of masses at birth
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Populations of Stars: I, II, III
• Population I stars: stars like the Sun; later generation, higher metal content.
• Population II stars: low metallicity, older stars like those found in globular clusters.
• Population III stars: the hypothetical first stars formed from pure H and He.
Mass fractions of elements in the Sun
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Globular cluster M80
Stars mostly older than the Sun.
The Pleiades
Newborn stars, “only” ~ 108 yrs old.
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Stars: Birth, Life, and DeathBIRTH: Gravitational Collapse of interstellar
clouds. “Hayashi Contraction.”
LIFE: Stability on Main Sequence.Energy from nuclear reactions in stellar cores(E = mc2).
DEATH: Lack of nuclear fuel. Instability, variability, expansion (giants, supergiants). Spectacular explosions!
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H-R Diagrams
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H-R
diag
ram
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Entrance of a star into the HR Diagram
At equilibrium core T ≈ 15´106 K.Nuclear reactions create energy Þ E = mc2.
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Stellar Evolution
Interstellar Cloud è Proto-StarèHayashi Contraction è Main Sequence
è Red Giant è Variable Starèè Explosion è White Dwarf
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Evolution of a star like the SunContraction/collapse of a fragment of an interstellar cloud
• Density and temperature in core rise.• Star has large radius (R) but cool temperature (T)
so it is bright (high luminosity L) but very red (infrared).• Short-lived phase.• Collapses along axis of rotation; formation of disk possible.• When the core becomes hot enough, hydrogen burning ignites.
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HK Tau –young stars (5 Myr) in binary system.
ALMA imagingreveals misaligned disks.
Star formation and protoplanetary disks
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HK Tau –young stars (5 Myr) in binary system.
ALMA imagingreveals disks.
Doppler shift of emission from molecular gasà Get rotation, and infer disk axis.
Disks are misaligned!
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H-R
diag
ram
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The Main Sequence• Stars on the “Main
Sequence” are burning hydrogen into helium in their cores.
• The mass of a star determines its location on the Main Sequence of the H-R diagram.
• Sirius A, Altair, Procyon A are more massive than the Sun. Sirius B, Proxima Cen are less massive than the Sun.
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Main Sequence: the Hydrogen-burning phase of a star’s lifetime
• Different stars have different masses.
• The time a star spends on the Main Sequence depends on its mass.
• A more massive star converts all its H into He quicker than a less massive star!
• A more massive star has a shorter “Main Sequence lifetime” than a less massive star.
L µ M4
on the M.S.
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Stars don’t shine forever• The “fuel” in stars is proportional to the mass, M.• The luminosity of stars on the main-sequence varies
with mass as: Luminosity µ (Mass)4
Assuming all stars “consume” the same fraction of their mass (M), the lifetime is given by:
Lifetime µ =Amount of fuel Rate of using fuel
Star’s mass, M*Star’s luminosity, L*
M*L*
MassMass4
1Mass3
==µtLifetime of star
High mass stars have SHORTER lifetimes!
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Stellar Evolution
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H-R
diag
ram
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Globular Clusters: Older Populations
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Virial Theorem and Stellar TemperaturesThe virial theorem says that in a stable object the internal and gravitational energy are balanced:
2 x KE + PE = 0.Example: a planet of mass m orbiting a star of mass M
The KE and PE are:
• So the VT is satisfied. The same is true for any stable object that is held together by gravity.
mv2
r=
GMm
r2
KE =1
2mv2 =
GMm
2rPE = �GMm
r
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VT and Stars• In a star, the kinetic energy is thermal (possibly
combined with convection and turbulence, which we ignore here).
• The gravitational potential energy is (uniform density):
• The thermal energy is (uniform temperature):
• Using the VT we can solve for temperature:
PE = �3GM2
5R
KE = N
⌧1
2mv2
�=
3
2
M
mkT
T =1
5
GMm
kR
k = Boltzmann’s constantm = particle mass (e.g. mass of a proton)M = Mass of star; R = its radius.
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Internal Temperatures of Stars
• Use
to estimate T ~ 4.6 x 106 K for the Sun.
• This is an average temperature but is comparable to what is needed to drive nuclear reactions.
T =1
5
GMm
kR
G = 6.67 x 10-8 cgsM¤ = 2 x 1033 gR = 7 x 1010 cmm = mH = 1.67 x 10-24
k = 1.38 x 10-16 cgs
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Kelvin-Helmholtz Contraction Time
• The VT says that KE and PE are balanced. In order for a star like the Sun to contract, it must lose energy. The VT further implies that while ½ of the PE goes into an increase in KE, the other half must be radiated away.
• The measured luminosity of the Sun is L ~ 4 x 1033 erg s-1. If this luminosity were solely due to radiation of GPE, the lifetime of the Sun would be only about 3x1014 s, or ~ 10 Myr (the K-H contraction time).
• What gives? Either the solar system is very young or there is another source of energy, i.e. nuclear reactions.
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Solar Interior
• Radiative zone:– Energy is
transported by electromagnetic radiation.
• Convection zone:– Energy carried by
convection.
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The Core of the Sun
• The core of the sun is the place where nuclear fusion reactions power the sun.
• Approximate T ~ 15´106 K. • The sun has been “burning” for 5 billion years
and theoretically should continue burning for another 4 to 5 billion years.
• Should the core stop burning, the star’s luminous life would be at an end.
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The Proton-Proton Chain Reaction
• Three steps complete this fusion reaction:
• Net effect reaction: 4p è 4He + energy
• The release of energy is about 0.007 times the rest mass of the input hydrogen.
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The CNO Cycle
• Six steps complete this fusion reaction:
The CNO cycle requires higher temperatures than the proton-proton chain because C and N nuclei have larger positive charge that the proton needs to push against.
This requires higher thermal velocities for the protons.
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Mass-Luminosity RelationMain Sequence Stars
• Nuclear reactions in hotter stars are faster, and T = T(M), so luminosities scale strongly with mass.
• A simple approach gives L ~ M3. More detailed analysis - get scaling laws:
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The Milky Way
0
25
50
75
100
O-M F-M O B A F G K M B-F
Supergiant(I & II)
Red Giant(III)
Main Sequence (V) WhiteDwarf
Luminosity Class and Spectral Type
Percentage of Galactic LuminosityPercentage in Number Percentage of Galactic Stellar Mass
75% of the Milky Way’s luminosity
arise from the rarest stars.
K & M stars account for ¾’s of the stars in the
galaxy but contribute less than 5% of its luminosity.