AST 301, Lecture 3

James Lattimer

Department of Physics & Astronomy449 ESS Bldg.

Stony Brook University

February 4, 2015

Cosmic Catastrophes (AKA Collisions)james.lattimer@stonybrook.edu

James Lattimer AST 301, Lecture 3

Properties and Types of StarsMost stars are MainSequence (M-S) stars, whichburn H into He in their cores.Other groups are red giants,which have exhausted H fueland “burn” He into C and O,supergiants which areburning even heavierelements, and white dwarfs(dead low-mass stars). M-Sstars can be divided intospectral types O, B, A, F, G,K and M based ontemperature or color. Notethat there are diagonal linesof constant radius.

www.daviddarling.info/encyclopedia/H/HRdiag.html

James Lattimer AST 301, Lecture 3

Spectral Types

Initial M-S M-S M-S M-S # inSpectral Mass Lum. Tsurface Life Radius Galaxy

Type (M�) L�◦ K (years) (R�)

O 60 800,000 50,000 1 · 106 12 5.5 · 104

B 6 800 15,000 1 · 108 3.9 3.6 · 108

A 2 14 8000 2 · 109 1.7 2.4 · 109

F 1.3 3.2 6500 6 · 109 1.3 1.2 · 1010

G 0.9 0.8 5500 1.3 · 1010 0.92 2.8 · 1010

K 0.7 0.2 4000 4 · 1010 0.72 6 · 1010

M 0.2 0.01 3000 2.5 · 1011 0.3 3 · 1011

James Lattimer AST 301, Lecture 3

M-S Properties Related

I A star’s physical properties on the Main Sequence (M-S)are related: Tcenter ∝ M/R ; R ∝ M1/2

I A star radiates like a blackbody, so L ∝ R2T 4

I Approximately Tcenter ∝ Tsurface = T .

I Combining the above, L ∝ M3

I A star’s Main Sequence lifetime can be estimated byconsidering the amount of fuel and dividing by the rate atwhich the fuel is burned:τ ∝ M/L ∝ M/M3 = M−2; τ = M/Lτ�

I Massive stars burn out too quickly for life to form.

I But low-mass stars have a smaller habitable zone, whosevolume V ∝ M4 ∝ L4/3.

James Lattimer AST 301, Lecture 3

Stellar Habitable Zones

Wikipedia

James Lattimer AST 301, Lecture 3

Nuclear Nomenclature

• An atom is composed of a nucleus and 1 or more electrons.

• The nucleus has 1/100,000 the radius of the atom, but nearlyall its mass.

• Nuclei are composed of neutrons and plus-charged protons.

• Elements are distinguished by the atomic (proton) number Z .

• Z (element symbol)A refers toa nucleus or an atom ofatomic number Z and atomicweight A = Z + N .

• Isotopes have the same Z butdifferent neutron numbers Nand are nearly chemicallyidentical.

• Radioactive nuclei are unstableand decay into others.

James Lattimer AST 301, Lecture 3

Bosphorus

James Lattimer AST 301, Lecture 3

Nuclear Energy GenerationI In general, fusion in stars goes from the lightest elements

to heavier ones, because Coulomb repulsion isproportional to Z1Z2

I Fusion of hydrogen nuclei to helium nuclei(proton-proton cycle)

1H1 + 1H

1 → 1H2 + e+ + νe ;

1H2 + 1H

1 → 2He3 + γ;

2He3 + 2He

3 → 2He4 + 1H

1 + 1H1.

νe is the neutrino, a massless nearly invisible particle.I R. Davis (Brookhaven Nat’l Lab) first detected neutrinos

from the Sun using a tank of 100,000 gallons of carbontetrachloride (C2Cl4, cleaning fluid) in the HomestakeGold Mine in Lead, South Dakota in the 1970’s. Theobservation of neutrinos from the Sun proves that energyis generated by the fusion of H into He.

James Lattimer AST 301, Lecture 3

I In the red giant phase, helium is converted into heavierelements by

3(2He4) → 6C

12

6C12 + 2He

4 → 8O16

I There are no stable elements of mass 5 or 8.

I Therefore the reactions involving the most abundantisotopes 2He

4 + 1H1 or 2He

4 + 2He4 are not allowed.

I A very-rare three-body collision is required to generateheavy elements.

I The Big Bang can’t produce many nuclei heavier thanhelium, because it is expanding and cooling too rapidly.

I Heavy elements can only be produced by stars.

James Lattimer AST 301, Lecture 3

Advanced Evolution of Low-Mass StarsLow-mass stars < 8M�evolve into a red giantphase in which theirsurfaces greatly expandand cool, but theirinteriors shrink and heat.This occurs when the Hfuel in the star’s core isdepleted. A red giantburns He into C and O.When He is eventuallyexhausted, the outerstellar portions expandaway (planetary nebula)and core cools and diesas a white dwarf.

James Lattimer AST 301, Lecture 3

White Dwarfs

I Normal stars are composed of gas supported by thermalpressure, where P ∝ ρT .

I Ordinary solid matter at room temperature, like rock, hasessentially zero pressure.

I As the temperature is lowered, gas pressure tends to zero.So when a star dies and subsequently cools off, littlepressure exists to support it against gravity even if itcrystallizes (freezes).

I However, quantum mechanics predicts, because of thePauli Exclusion Principle, that it is difficult to squeezeelectrons or nucleons into too small a volume. Thisadditional source of pressure, which exists even at zerotemperature, is called degeneracy pressure.

James Lattimer AST 301, Lecture 3

I A star, as it cools off, eventually replaces thermal pressurewith degeneracy pressure and becomes a white dwarf.

I Degeneracy pressure is large, but not infinite. S.Chandrasekhar showed that an upper limit to the whitedwarf mass is about 1.4 M� (called the Chandrasekharlimit). Larger masses would collapse and become neutronstars.

I Typical white dwarfs have masses within 0.1 – 1.2 M�,and radii 3 R⊕ ' 0.01 R�.

I The density in a white dwarf is about 106 g cm−3, amillion times that of water (a teaspoon of a white dwarfwould weigh as much as an elephant on the Earth).

James Lattimer AST 301, Lecture 3

The Sun’s Evolution in the H-R Diagram

James Lattimer AST 301, Lecture 3

Proof of Evolution

ClusterMain

Sequence

WD→

Blue Stragglers

Horizontal Branch

Red

Giant

Branch

AsymptoticGiant Branch

M55

M4

James Lattimer AST 301, Lecture 3

Advanced Evolution of High-Mass Stars

I High-mass stars (M > 8M�) evolve into both red andblue giants and supergiants as their cores burn heavierelements: C,O → Ne → Mg, Si → S, Ca → Fe, Ni

I After the core isconverted into Fe (iron),the most boundelement, nuclear burningceases to produce energyand the star collapses toform a neutron star orblack hole, a violentevent accompanied by asupernova explosion(called Type II).

SN 1987aJames Lattimer AST 301, Lecture 3

James Lattimer AST 301, Lecture 3

I Supernovae within a few thousand lt.-yrs. would be lethalto Earth life.

I Yet life could notexist withoutsupernovae, becausesupernovae ejectnearly all heavyelements into space.

I Until supernovaeoccurred, gas fromwhich stars andplanets were madecontained virtually noelements heavier thanhelium.

www.mpa-garching.mpg.de/ thj/popular

James Lattimer AST 301, Lecture 3

Advanced Evolution in BinariesI Stars in binaries may evolve

significantly different than singlestars if mass can be transferedwhen a star becomes a red giant orsupergiant.

I White dwarfs in close binaries mayaccrete matter from a normalstellar companion. If they grow toexceed the Chandrasekhar masslimit ' 1.4 M�), they begin tocollapse. However, white dwarfsconsist of nuclear fuel (e.g., C, O),so collapse leads to athermonuclear explosion,converting these elements intoiron, in a Type I supernova.

NASA

James Lattimer AST 301, Lecture 3

Neutrinos and SupernovaeI Beyond C, O burning, more energy is wasted as neutrinos

than as useful thermal support. Neutrinos escape ratherthan giving up their energy inside the star.

I Neutrino interactions with matter are so weak, that tohave a 50% chance of stopping a solar neutrino, a leadshield would have to be 100 lt.-yrs. thick.

I The production of neutrinos increases in the gravitationalcollapse leading to a Type II supernova, reaching, for afew seconds, the power output of all the stars in all thegalaxies of the visible universe! The total supernovaneutrino energy is more than 300 times the solar outputduring its entire life!

I The production of neutrinos and the nucleosynthesis andejection of heavy nuclei in Type II supernovae wasconfirmed by SN 1987a in the Large Magellenic Cloud, anearby galaxy, on February 23, 1987.

James Lattimer AST 301, Lecture 3

• Neutrino detectors inOhio and Japansimultaneouslydetected a total ofabout 20 neutrinoseven though thissupernova was 180,000lt.-yrs. from the Earth.

• Radioactive Ni, Co andTi nuclei were alsoobserved in the ejecta.

• To date, no neutronstar is visible within theremnant, suggestingthat a black hole mighthave later formed.

http://www.geek.com/wp-content/uploads/2013/11

James Lattimer AST 301, Lecture 3

Nucleosynthesis• After the Big Bang, matter in

the universe consisted almostentirely of only H and He.

• Heavy elements aresynthesized only in stars.

• Because of Coulombrepulsion, the abundance ofelements decreases with Z .

• Elements made of multiplesof α−particles (He nuclei)are more abundant thanaverage.

• Elements with even numbersof protons are more abundantthan odd Z elements.

www.greenspirit.org.uk/Resources/ElementAbundance.htm

James Lattimer AST 301, Lecture 3

• Most of the lighter heavy elements (i.e., up to iron) and halfof heavier elements (called s-process or slow neutron captureprocess) are synthesized in stars and are mostly dispersedthrough supernova explosions, of both Type I and Type II.

• Some C, N, O and Ne are also ejected from stars in stellarwinds and in novae (when H is accreted, burned, and ejectedfrom the surface of a white dwarf in a close binary).

• Fe and Ni are the most bound elements, so the other half ofheavier elements (called r-process or rapid neutron captureprocess) can be created only in rare explosive events.

• It has long been favored that the source of r-process elements(which includes gold, platinum, and uranium) is supernovae ofType II.

• However, models show that matter ejected from supernovae isnot rich enough in neutrons and an alternative site, compactbinary mergers of neutron stars with neutron stars or blackholes, is now beginning to be favored.

James Lattimer AST 301, Lecture 3

Neutron Stars• If matter is forced to even higher densities than in a white

dwarf, 106 times that of water, it collapses but could stabilizeto form a neutron star with aid of additional pressure fromnucleon degeneracy and thestrong nuclear force.

• Observed neutron stars havemasses 1.2–2.0 M� and radiiof about 12 km, only 3–4times the radius of the samemass black hole.

• The upper mass limit to aneutron star is not wellknown, but has to be lessthan about 3 M�.

James Lattimer AST 301, Lecture 3

Black Holes

• Without degeneracy pressure, a cold star would eventuallycollapse into a black hole, first predicted by John Michell in1783, but termed corps obscura by Laplace in 1795.• A black hole occurs when the size of the object becomes small

enough that the escape velocity becomes equal to c .

vescape =√

2GM/R ,⇒ R = 2GM/c2 ' 3(M/M�) km

• Cold objects of larger mass than themaximum neutron star mass must beblack holes. Many black holes are knownto exist, with masses ranging from about 6M� to millions of solar masses.

• Masses of white dwarfs, neutron stars andblack holes have been precisely measuredin binary systems using Kepler’s Laws withgeneral relativistic refinements.

S.Harris,

www.scien

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James Lattimer AST 301, Lecture 3