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AST 248, Lecture 4

James Lattimer

Department of Physics & Astronomy449 ESS Bldg.

Stony Brook University

February 10, 2020

The Search for Intelligent Life in the [email protected]

James Lattimer AST 248, Lecture 4

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


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


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.


Stellar Habitable Zones

Wikipedia


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.


Bosphorus


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.


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 atomic weight 5 or 8.

I Therefore, the reactions 2He4 + 1H

1 or 2He4 + 2He

4

involving the most abundant isotopes do not proceed.

I Extremely rare three-body collisions 2He4 + 2He

4 + 2He4

are required to generate heavy elements.

I Nuclei heavier than helium cannot be produced during theBig Bang because the universe expands and cools toorapidly for three-body collisions to occur.

I As a result, heavy elements can only be produced by stars.


Advanced Evolution of Low-Mass Stars

Low-mass stars < 8M� evolve into a red giant phase in whichtheir surfaces greatly expand and cool, but their interiors shrink

and heat when theH fuel in the star’score is depleted. Ared giant burns Heinto C and O.When He is eventu-ally exhausted, theouter parts of thestar escape to formplanetary nebula,and the core coolsand dies as a whitedwarf.


What Happens When Nuclear Fuel Runs Out?

I Normal stars are supported by gaseous thermal pressure,with P ∝ ρT .

I When nuclear fuel is exhausted, the temperature andpressure can only be maintained by compressing the core.

I But as its density increases, another kind of pressure dueto the quantum mechanical Pauli Exclusion Principletakes over. Matter resists squeezing electrons intotoo-small a volume.

I This additional source of pressure, called degeneracypressure, exists even at zero temperature.

I Ordinary solid matter at low temperatures, like rock, isalso difficult to compress.

I As a stellar core dies, it finally stops compressing butcontinues to radiate energy. It eventually freezes as itsnuclei form a rock-like crystal lattice.


White Dwarfs

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.Chandrasekhar showed that the upper limit to the whitedwarf mass, now called the Chandrasekhar mass, is about1.4 M�. Larger masses must collapse and becomeneutron stars.

I Typical white dwarfs have masses between 0.1M� and1.2M� and radii about equal to R⊕ ' 0.01 R�.

I The density in a white dwarf is about 106 g cm−3, amillion times higher than water (a teaspoonful on theEarth would weigh as much as an elephant).


The Sun’s Evolution in the H-R Diagram


Proof of Evolution

ClusterMain

Sequence

WD→

Blue Stragglers

Horizontal Branch

Red

Giant

Branch

AsymptoticGiant Branch

M55

M4


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 converts toFe (iron), the most boundelement, nuclear burningno longer releases energy.Its core collapses to forma neutron star or blackhole, a violent eventaccompanied by asupernova explosion (aso-called Type II) thatexpels the rest of the star.

SN 1987aJames Lattimer AST 248, Lecture 4

I Supernovae within a few thousand light-years would belethal to Earth life.

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

I Until supernovaeoccur, gas fromwhich stars andplanets are madecontain virtually noelements heavier thanHe.

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

Crab Nebula, SN 1054


Advanced Evolution in BinariesI Stars in close binaries may evolve

in a significantly different way thansingle stars since mass can beexchanged when one star becomesa red giant or supergiant.

I White dwarfs in close binaries mayalso accrete (gain) matter fromtheir normal companion. If theygrow beyond the Chandrasekharmass limit (' 1.4 M�), they beginto collapse. However, white dwarfsconsist of nuclear fuel (e.g., C, O),so this triggers thermonuclearfusion, converting these elementsinto iron, and causing a Type Isupernova explosion.

NASA

Tycho’s Supernova RemnantSN 1572


Types of Supernovae

We conveniently subdivided supernovae into two types, Type I(thermonuclear) and Type II (gravitational collapse).

They have approximately equal luminosities in visible radiationand kinetic energies of their expanding gaseous remnants.

They both produce and eject heavy elements (like carbon,nitrogen, oxygen and iron) into the interstellar medium, wherethese elements can then be used in the formation of newerstars and their planets.

They are thus both essential for the origin of life, but can alsocause its catastrophic demise if too near.

But there are significant differences between these two typesof supernovae:


I Type I supernovae: from white dwarfs evolved fromlow-mass stars (M <∼ 5M�) in binary systems.

I These have no H observed in their spectra.I They do not emit many neutrinos, and are intrinsically

less powerful than Type II supernovae.I Their energy source is thermonuclear (the conversion of

carbon and oxygen into iron).I The explosion occurs when mass from a companion star

accumulates (or accretes) onto the white dwarf, pushingits mass above the Chandrasekhar limit (1.4M�).

I They leave behind only an expanding gaseous remnant.I They are relatively similar to each other they can be used

as standard candles to measure cosmological distances.This realization led to the discovery of dark energy.


I Type II supernovae are explosions of massive stars(M >∼ 5M�) at the ends of their lives.

I These sometimes have H observed in their spectra.I These emit copious neutrinos, and are 100 times more

powerful than Type I supernovae.I But 99% of the released energy appears as neutrinos, so

their light output and kinetic energies are similar to TypeI supernovae.

I Their energy source is gravitational potential energy(also called binding energy) released when massivestellar cores contract into a neutron star or black hole.

I The explosion occurs when the iron core of a massivestar grows larger than the Chandrasekhar limit (1.4M�).

I They leave behind both an expanding gaseous remantand a collapsed remnant, either a neutron star or a blackhole.


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

neutrinos than converted to useful thermal support.Neutrinos readily escape from inside the star.

I Neutrino interactions with matter are so weak, that tohave a 50% chance of stopping a solar neutrino, a watershield would have to be a light-year thick.

I The release of neutrinos increases as massive stars evolve,culminating during the gravitational collapse leading to aType II supernova. For a few seconds, the power outputexceeds that of all stars in all galaxies of the visibleuniverse! The total supernova neutrino energy is morethan 300 times the solar output during 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.


• 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.

• In late 2019, an hotdust blob was foundthat appears to hidethe neutron star thatwas formed.

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

Super-K detector in Kamioka, Japan


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


• 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 stellar

winds 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 of

heavier elements (called r-process or rapid neutron captureprocess) can be created only in rare explosive events.• It has long been thought the source of r-process elements

(includes gold, platinum, and uranium) are Type II supernovae.• However, the binary neutron star merger GW170817 observed

in gravitational waves, as a gamma-ray burst, and as akilonova (powered by radioactive decay of extremelyneutron-rich nuclei), indicates that the primary source ofr-process elements are binary neutron star or blackhole-neutron star mergers.


Neutron Stars• If matter is forced to higher than white dwarf densities (106

times water), it collapses to form a neutron star, stabilizedwith aid of additional pressure from the strong nuclear force.

• Observed neutron stars have anaverage mass 1.4 M� and radiusabout 12 km, only 3–4 times largerthan the same mass black hole.

• The most massive known neutronstar is about 2M�. The upper masslimit is uncertain but believed to beless than about Mmax = 2.3M�.

• Further addition of mass causescollapse to a black hole.


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

ce.cartoonsplus.co

m


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