Radius density 0.01R 400 R 10 -6 g/cm 3 10 6 g/cm 3 mass 100 M 0.07M

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radius density 0.01R 400 R 10 -6 g/cm 3 10 6 g/cm 3 mass 100 M 0.07M
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Transcript of Radius density 0.01R 400 R 10 -6 g/cm 3 10 6 g/cm 3 mass 100 M 0.07M

Page 1: Radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M

radius

density

0.01R

400 R

10-6 g/cm3

106 g/cm3

mass

100 M

0.07M

Page 2: Radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M
Page 3: Radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M

uses ~20,000 stars

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Mass - Luminosity Relation

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Stellar Evolution

Models ObservationsRadius

Mass

L

T

Pressure

Density

Composition

H-R Diagram

[B-V, Mv]

Evolution always faster for larger mass

Stars pile up where times are long

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Basic Stellar Structure Equations:

1) Eqtn of State: PT P1/V~ PT so P=(k/H)T where 1/ = 2X + (3/4)Y + (1/2)Z with radiative P: P = (k/H)T + (a/3)T4

2) Hydrostatic Equilibrium: P(r)/r = -GM(r)(r)/r2

3) Mass continuity: M(r)/r = 4r2(r)

4) Luminosity gradient (in thermal equilibrium): L(r)/r = 4r2(r)(,T, comp) where T

5) T gradient: T(r)/r = -3(r)L(r)/16acr2T(r)3 where T-3.5 (opacity is bound-free, free-free, e- scattering)

R

T=6000K

=3x10-8 g/cm3

0.5R

T=3x106

=10.1R

T=15x106

=100g/cm3

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Stellar Life Cycle

1. Birth [Molecular Clouds, T Tauri stars]

2. Middle Age [Main sequence, H>He fusion]

3. Giant-Supergiant [Shell burning, high z fusion]

4. Death [low mass-planetary nebula>white dwarf]

[high mass- Supernova>pulsar, black hole]

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Theory ObservationGiant Molecular Clouds

10-100pc, 100,000M

T<100K

Radio

Collapse trigger:

SNcloud-cloud collisionsdensity wave

O and B stars form

winds

smaller mass stars

IR

Herbig-Haro,

T Tauri

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Star Cluster NGC 2264

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Minimum mass for collapse (Jean’s Mass)

MJ ~ (5kT/GmH)3/2 (3/4o)1/2

or MJ ~ 3kTR/GmH

Minimum radius:

RJ ~ (15kT/4GmH o)1/2

or RJ ~ GmHM/3kT

Cloud fragments & collapses if M>MJ, R>RJ

Free-fall time = (3/32Go)1/2

for T~150K, n~108/cm3, ~2x10-16 g/cm3 tff ~ 4700 yr

Dense, cold regions can support only small masses (so collapse), while warm, diffuse regions can support larger masses (stable)

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Unfortunately, no good quantitative theory to predict star formation rate or stellar mass distribution !

IMF = Initial Mass Function

Big question: Is it universal?

(log m) = dN/d log m m-

N is number of stars in logarithmic mass range log m + d log m

= 1.35 Salpeter slope (logarithmic)

in linear units (m)= dN/dm m-

where = + 1 (= 2.35 Salpeter)

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Birth Sequence• trigger [SN, cloud-cloud, density wave]

• cloud fragments and collapses [Jeans mass and radius]

• early collapse isothermal - E radiated away

• interior becomes adiabatic[no heat transfer] - E trapped so T rises

• protostellar core forms [~ 5 AU] with free-falling gas above

• dust vaporizes as T increases

• convective period

• radiative period

• nuclear fusion begins [starts zero-age main sequence]

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Pre–Main-Sequence Evolutionary Tracks

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Hiyashi tracks

convective

radiative

105 yrs

107 yrs

106 yrs

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Main sequence [stage of hydrostatic equilibrium]

• Mass >1.5 Msun [CNO cycle, convective core, radiative envelope]

• Mass = 0. 4 - 1.5Msun[p-p cycle, radiative core, convective envelope]

• Mass = 0. 08 - 0. 4Msun[p-p cycle, all convective interior]

• Mass = 10 - 80 MJup [0. 01 - 0. 08Msun][brown dwarf]

• Mass < 10MJup[< 0.01Msun][planets]

Lifetime on Main Sequence = 1010 M/L

Gravity balance pressure

Middle Age - stable stars

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Energy in sun (stars)

L = 4 x 1033 ergs/s solar constant

Age = 4.6 billion yrs (1.4 x 1017 secs

Total E = 6 x 1050 ergs

fusion is only source capable of this energy

mass with T > 10 million E=1. 3 x 1051 ergs

lifetime = E available = 1. 3 x 1051 ergs ~ 3 x 1017s ~ 10 billion yrsE loss rate 4 x 1033 ergs/s

test with neutrinos37Cl + 37Ar + e- for E > 0.81 MeV71Ga + 71Ge + e- for E > 0.23 MeV

Page 20: Radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M

1) p + p np + e+ +

2) np + p npp +

3) npp + npp npnp + p + p

4H 1 He + energy4.0132 4.0026 (m=0.05 x 10-24g

E = mc2 = 0.05 x 10-24g (9 x 1020cm2/s2) = 4 x 10-5 ergs

Page 21: Radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M

1H + 1H 2H + e+ + 1H + 1H 2H + e+ +

2H + 1H 3He +

3He + 3He 4He + 2 1H

3He + 3He 7Be +

7Be + e- 7Li + 7Be + 1H 8B +

7Li + 1H 4He + 4He 8B 8Be + e+ +

8Be 4He + 4He

99.8% 0.25%

91%

9%ppI

ppII

ppIII

0.43 MeV 1.44 MeV

0.1%

Page 22: Radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M

High vs Low mass stars have different fusion reactions and different physical structure

M > 1.5 M CNO cycle; convective core and radiative envelope

M < 1.5 M p-p cycle; radiative core and convective envelope

M < 0.4 M p-p cycle; entire star is convective

M < 0.7 M H fusion never begins

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Giant-Supergiant Stage• H fusion stops - core contracts and heats up

• H shell burning starts - outer layers expand

• core T reaches 100 million K - He flash, He fusion starts

• high mass - multiple shell and fusion stages

• C to O, O to Ne, Ne to Si, Si to Fe

• Fusion stops at Fe

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Post–Main-Sequence Evolution

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He-C fusion : Triple Alpha

4He + 4He 8Be + 8Be + 4He 12C +

3He 1C

energy = 1.17 x 10-5 ergs

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H-R Diagram of a Globular Cluster

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Clusters of Different Ages

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Main-sequence fitting for cluster distances

1. Use CCD to get b, v images of cluster stars

2. Plot color-mag diagram of v vs b-v

3. Find main sequence turnoff & lower MS stars

4. For the SAME B-V on lower MS, read mv from cluster and Mv from H-R diagram

5. Use distance modulus m-M to calculate d

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Stellar Death

Low massHe or C,O corePlanetary nebulaRemnant < 1.4 Msun

White Dwarf

High massFe coreSupernovaRemant < 3Msun > 3Msun

Neutron star Black Hole

Size ~ Earth ~15 km 0

Density(g/cm3) 106 1014 infinity

MagField(G) 104-108 1012 ?

Rotation minutes <sec <<sec

Pressure e- degeneracy neutron degeneracy none

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Low Mass Death - a White Dwarf

degeneracyPauli exclusion principle: no 2 electrons can be in the same state (position & momentum)

as T increases, more states available P T

at high density, collisions restricted P

if all states full, gas is degenerate

as star contracts, increases so becomes degenerate

as T increases, degeneracy is liftedwhen He - C fusion starts, core is degenerate

He flash removes degeneracy

WDs are totally degenerate

up to 1. 4 M degeneracy pressure stops the collapse

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White Dwarf M-R Relation

P 5/3

hydro-equil

P M2/R4

M/R3

M2/R4 M5/3/ R5

M1/3 1/R

R 1/M1/3

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1175 WDs from SDSS

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WDs from SDSS

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massive single stars

a (WD binary, b,c massive single stars)

Type I - no H, found in all galaxies

Type II - H, only in spiral arms (massive stars)

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Famous Supernovae

Naked eye in Milky Way:

1054 Crab

1572 Tycho

1604 Kepler

In LMC

SN 1987a Feb 1987 neutrino burst seen

We are overdue ~ 1/20 yrs/galaxy

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Neutron stars=pulsars

density=1014g/cm3

mass < 3M

R ~ 10 km

B ~ 1012G

pulse 1-1000/sec

found in radio 1967

LGM

pulsting neutron star

rotating neutron star

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Black Body = thermal (Planck Function)

Synchrotron = non-thermal (relativistic)

c = eB/2me

Wavelength

Flux

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Black Holes (R=0, = )

escape velocity = (2GM/R)1/2

for light, v = c

c= (2GM/R)1/2

c2 = 2GM/R

for object in orbit around mass M at distance R:

Rs = 2GM/c2 Schwarzschild radius

Rs is event horizon

1M Rs = 3km, 10M Rs = 30km, 150kg Rs = 10-23cm

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Earth has Newtonian Physics; BHs have Relativistic Physics

if you ride into a BH you go in

if you watch someone ride in they stay at Rs

Proof of Black Hole:

1) Single-lined spectroscopic binary

2) strong X-ray emission

Kepler’s Law M1+M2=P(K1+K2) 3/4Gsin3i ~ 20M

spectral type M1 shows M1 ~ 10M

M2 ~ 10M but invisible

1036-38 ergs/s