PHY688, IntroductionPHY688, Introduction James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University January 24, 2017 Nuclear Astrophysics [email protected]

PHY688, Introduction

James Lattimer

Department of Physics & Astronomy449 ESS Bldg.

Stony Brook University

January 24, 2017

Nuclear Astrophysics [email protected]

James Lattimer PHY688, Introduction

Course Components

I Office: ESS 449; Hours: MWF 2 – 3I URL: www.astro.sunysb.edu/lattimer/PHY688I Text: None requiredI Useful References:

I Shapiro & Teukolsky ”Black Holes, White Dwarfs and Neutron Stars”I Rolfs & Rodney “Cauldrons in the Cosmos”I Haensel, Potekhin and Yakovlev ”Neutron Stars 1: Equation of State

and Structure”I Iliadis “Nuclear Physics of Stars, 2nd edition” (heavily nuclear

experimental techniques)I Jose “Stellar Explosions: Hydrodynamics and Nucleosynthesis”

(heavily radiation hydrodynamical and nuclear network techniques)I Camenzind “Compact Objects in Astrophysics: White Dwarfs,

Neutron Stars and Black Holes” (heavily mathematical and GR).I Exams: No examsI Homeworks: About 10, count 40% of total, 1 per week (except first

week). Consist of short computer or analytical exercises; submitsummary of results, code, tables and figures to Blackboard as aunified pdf document. Homeworks will be posted on the coursewebsite the week before their due date. Late penalties apply.


Course Components, cont.

I Term Reports: Two term reports, counting 60% total. Due datesare 9 March and 20 April, submitted as pdf files to Blackboard. Latepenalties apply. Suggested topics are on course website, andalternate topics that are highly relevant to the course are OK.

I Class Presentation: We want to discuss reports in class, so beprepared to give a brief oral presentation (15-20 minutes). This canbe blackboard or computer-based; if you don’t have a pdf file bringyour own laptop and Apple video convertor.Grade is primarily, but not exclusively, determined by written report.

I Be forewarned about the consequences of plagiarism.


Outstanding Problems We Will Examine

I The dense matter equation of state

I White dwarfs

I Pulsars

I Neutron stars

I Quark matter and quark stars

I Supernovae

I Neutrino astrophysics

I Proto-neutron stars

I X-ray bursts and magnetar flares

I Neutron star thermal evolution

I Black holes

I Gamma-ray bursts

I Gravitational radiation sources and signals

I Mergers involving neutron stars and black holes

I Nucleosynthesis of the heavy elements


Luminosity, Flux and Magnitude

Fλ is amount of energy at wavelength λ traversing a unit area and time.

L = 4πR2

∫ ∞0

Fλdλ.

fλ = Fλ (R/r)2 is the incident energy flux in the absence of absorption.

b is the apparent brightness, Aλ is the specific atmospheric transmissivity,Eλ is telescope’s specific efficiency, a is telescope’s aperture.

b = πa2

∫ ∞0

fλAλEλdλ = B(10 pc/r)2.

b1/b2 = 100(m2−m1)/5 = 10.4(m2−m1) = 2.512m2−m1 .

m is the apparent magnitude, M (Mb) is the absolute (bolometric)magnitude, B is the absolute brightness, BC is the bolometric correction.

M = m + 5− 5 log(r/pc)

BC = 2.5 log

[incident energy fluxrecorded energy flux

], Mb = −2.5 log

(L

L

)+4.72.

L ' 3.9× 1033 erg s−1


Distances and Masses

I R ' 7× 1010 cm

I 1 AU = 1.5× 1013 cm

I 1 lt. yr. = 9.3× 1017 cm

I 1 pc = 3.1× 1018 cm = 3.26 lt. yr. = 1 AU/tan 1′′

Distances are most accurately measured by parallax.

Masses are most accurately measured using gravity (Kepler’s 1-2-3 Law).

M1 + M2

M=( a

AU

)2 (yearP

)3

Period P and component velocities vi along line-of-sight are determinedfrom spectral Doppler shifts; ai are semi-major axes.

vi sin i = ai/P, a1 + a2 = a, a1/a2 = M1/M2

Inclination i can be estimated from eclipses (or lack thereof), or fromGR effects.

I M ' 1.99× 1033 g


Effective Temperature

Teff is the effective temperature

L = 4πR2σT 4eff .

σ is the radiation constant, Iλ = πBλ is the specific intensity.

σ ≡ T−4

∫Iλdλ =

2π4k4B

15c2h3= 5.67× 10−5erg cm−2s−1deg−4.

Bλ is the Planck function (Boson distribution).

Bλ =2c2h

λ5

1

ech/λkB T − 1

Iν =2πhν3

c2

1

ehν/kB T − 1= πBν .

The energy density of radiation in thermodynamic equilibrium is

u = 4π

∫Bνdν = 4π

∫Bλdλ = aT 4,

a =4σ

c=

8π5k4B

15c3h3= 7.565× 10−15erg cm−3deg−4.


Color Temperature

Blackbody:

λmax =hc

5kB Tmax=

0.29 cm KTmax

.

Matching this to Tmax at the peak of the observed spectrum is oneestimate of the color temperature Tc . Another barometer of colortemperature comes from broadband magnitudes like U (ultraviolet), B(blue) and V (visual). The color index is B − V .

The excitation temperature can be determined from level densities inthermal equilibrium:

ni

nj=

gi

gje(Ei−Ej )/kB T .

The statistical weight factor gi = 2Ji + 1; J is the angular momentum.For hydrogen, En = −13.6 eV/n2 and gn = 2n2.

The ionization temperature is similar, using ionization potential χi :

ni+1ne

ni=

Gi+1ge

Gi

(2πmekB T )3/2

h3e−χi/kB T .

Gi = gi,0 + gi,1e−Ei,1/kB T + gi,2e−Ei,2/kB T + . . .


Spectral Types

I Class O (T > 25, 000 K), ionized He dominates, other atoms withhigh ionization potential.

I Class B (11, 000 K < T < 25, 000 K, Balmer H and neutral Hedominate, ionized C, O.

I Class A (7500 K < T < 11, 000 K, H and ionized Mg dominate, butionized Fe, Ti, Ca, &c become more important at lowertemperatures.

I Class F (6000 K < T < 7500 K, ionized metals

I Class G (5000 K < T < 6000 K, neutral metals, molecular CN, CH(Sun is G2)

I Class K (3500 K < T < 5000 K, molecular bands, neutral metals

I Class M (2200 K < T < 3500 K, complex molecular oxide bands,TiO

Oh, be a fine girl, kiss me


Hertzsprung-Russell Diagram


H-R Diagram


Hydrostatic Equilibrium

dP

dr= −Gm(r)ρ(r)

r2,

dm

dr= 4πρr2

Perfect gas law, mean molecular weight µ

P = ρN0kB T/µ

Example:ρ = ρc [1− (r/R)2] ≡ ρc (1− x2), µ = constant

m =4π

3ρc R3x3

(1− 3

5x2

)P = Pc −

2πGρ2c

3R2x2

(1− 4

5x2 +

1

5x4

)= Pc (1− x2)2

(1− 1

2x2

)T = Tc (1− x2)

(1− 1

2x2

)Pc =

15G

16π

M2

R4= 3.18×1015 erg cm−3, Tc =

Gµ

2kB N0

M

R= 1.0×107 K

ρc =15M

8πR3= 3.5 g cm−3


Radiative Transport

κ(ρ, µ,T ) is the radiative opacity, or resistance to radiation flow (cm2/g).

L(r) =16πacr2T (r)3

3κ(r)ρ(r)

dT (r)

dr

The mean free path of a photon is ` = 1/(κρ).

If the opacity were constant, dimensional analysis implies

L ∝ R2T 4eff ∝ R4T 4

c /M ∝ M3

Teff ∝ Tc R1/2/M1/4 ∝ M3/4/R1/2 ∝ R1/4T 3/4c

The energy generation rate for H-burning roughly varies as ρ2T 5, giving

L ∼∫ R

0

ρ2T 5dr3 ∼ ρ2c T 5

c R3 ∼ M7R−8.

These relations combined imply that R ∼ M1/2.


Stellar Energetics

Gravitational binding energy

Ω = −GM2/R = −4× 1048 erg.

τK−H, = −Ω/L ≈ 1015 s = 3× 107 yr.

Rest-mass energyMc2 ' 2× 1054 erg

τE , =Mc2

L≈ 5× 1020 s = 1.6× 1012 yr.

Thermal energy near the Sun’s center is

kB Tc = 8.62× 10−8Tc keV/K ' 1 keV.

But the Coulomb barrier between two positively charged protons is

V =e2

r=

1.44 MeV − fmr

.


Nuclear Fusion Reactions in Stars

Main Sequence: 4H → HePP cycle or CNO cycle

Red Giant: 3He → C ; C + He → O

Later Stages: C ,O + nHe → Na,Ne,Mg ,S ,Si ,Ca,Ti ,Cr ,Ni


Low-Mass Stellar Evolution in the H-R Diagram


H-R Diagram of M55


Stellar Evolution in the Hertzsprung-Russell Diagram


Supernovae

I Thermonuclear involves the explosion of a white dwarf in binary ormultiple systems; the energy release is from a solar mass of C,Onuclei fusing to Fe. The binding energy of C is about 7.8 MeV perbaryon, the binding energy of Fe is about 8.8 MeV per baryon.

1MN0 × (1MeV /b) = 1.9× 1051 erg

The energy primarily goes to the kinetic energy of expansion at 1%light speed (99%), secondarily to producing a light curve.

There are multiple models for these events, and observationalsupport in terms of amount of iron produced, but little observationalsupport for progenitors other than they occur in very old populations.


I Gravitational collapse involves the iron core collapse of a massivestar at the end of its life to a proto-neutron star. This ultimatelyproduces a neutron star or a black hole.

GM2

R= 3× 1053 erg

The energy primarily is emitted as neutrinos (99%), secondarily askinetic energy of expansion (1%), and the light curve (0.01%).

This model has abundant observational support: progenitorsidentified, neutrino signal observed from SN 1987A, nucleosynthesisas evidenced by radioactive-powered late-time light curves andremnant heavy-element abundances.

There are multiple sub-types characterized by spectral differences:H-abundant eject, H-poor ejecta, H+He-poor ejecta, probablyreflecting progenitor masses and relative amounts of mass lost dueto winds and accretion onto companions.


I Stranger types involvingI super-luminous events (hypernovae), possibly resulting from

highly-magnetized proto-neutron star remnants and leading to longgamma-ray bursts,

I pair-instability supernovae, orI sub-luminous events possibly due to stellar mergers.


Neutron Stars

Neutron stars are the ultimate probe of high-density matter. Whilematter in atomic nuclei has a maximum density of about 3× 1014 gcm−3, and approximately equal numbers of neutrons and protons, matterat the center of neutron stars can be 5–8 times denser and have only afew percent protons. Thus, extrapolations in terms of both density andneutron excess have to be explored.

Most neutron stars are observed as pulsars; the rest as thermally-coolingobjects.

Due to General Relativity, neutron stars have a finite maximum mass. It’svalue is uncertain, but must be greater than the largest observed pulsarmass, 2M, and less than the causal limiting value of about 3M. Manyneutron stars have masses precisely measured from pulsar timing inbinaries. Masses range from 1.2M to 2M with an average of 1.4M.

In theory, neutron star radii could range from 8 to 15 km. However, fromcausality, the lower limit to the neutron star maximum mass, and nuclearexperiments, it is likely that 1.4M stars have radii between 10 and 13km. Observations are not yet precise enough to restrict this range further.


Documents

PHY688, IntroductionPHY688, Introduction James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University January 24, 2017 Nuclear Astrophysics [email protected]