Stellar Evolution

Consider a cloud of cold (50 deg K) atomic hydrogengas. If an electron of one atom flips its spin state andthe electron then has a slightly lower energy state, the photon that is emitted is a.An ultraviolet photon of wavelength 1216 Angstromsb.An optical photon of wavelength 6563 Angstromsc.An infrared photon of wavelength 4.05 micronsd.A radio photon of wavelength 21 cm

Consider two stars, one with a photospheric temperatureof 4000 deg K, the other with a photospheric temp of8000 deg K. How much more total energy does thehotter star give off?a.twice as muchb.4 times as muchc.8 times as muchd.16 times as much

Stages of the Sun's life:

1) initial collapse from interstellar gas (5 million yrs)2) onset of nuclear reactions to start of main sequence phase (30 million yrs)3) main sequence (10 billion years)4) red giant phase (roughly 1 billion years)5) production of planetary nebula (50,000 yrs)6) white dwarf phase (will last for billions and billions of years, as the only the thing the Sun can do is to cool down; Sun's mass will be about 0.6 of its present mass)

The mass-luminosity relation revisited

total energy produced converting H to He =

luminosity (in Joules/sec) X number of seconds in MS lifetime =

Etot

(Joules) = m c2 =

[mass of star X fraction converted to energy] X c2

So L * TMS

proportional to M, or

TMS

proportional to M/L

From measures of the masses of binary stars, we findthat for a great range of masses,

L ~ M3.5

Combining the last two proportionalities,

TMS

~ M/L ~ M/M3.5 ~ M-2.5

The bottom line is that massive stars evolve veryquickly, and low mass stars evolve very slowly.

mass of Sun = 2 X 1030 kg

0.007 of mass of hydrogen is converted into energy

0.1 of mass of Sun (the core) is converted in He

Total energy liberated by Sun during main sequencephase is (2 X 1030) X 0.007 X 0.1 X c2 = 1.26 X 1044 J.

Luminosity of Sun = 3.8 X 1026 Joules/sec

main sequence lifetime = 1.26 X 1044 / 3.8 X 1026 =3.32 X 1017 sec = 10.5 billion years

How long will a 10 solar mass star last on the mainsequence?a.10 billion yearsb.300 million years c.30 million yearsd.3 million years

More massive main sequence stars have hotter coresbecause the weight of all the layers presses down on the core more than the layers in less massive stars.

The hotter the core, the faster the nuclear reactionsrun.

The faster the nuclear reactions run, the more luminositythe star has. This explains why more massive stars havegreater luminosity, and why more massive stars use uptheir core hydrogen at a much faster rate.

Most stars on the main sequence are stable.

However, very massive stars generate very strongstellar winds. A 60 solar mass star can lose halfof its mass due to such wind in a million years.

If a protostar, mainsequence star, orpost-main sequencestar is in the instabilitystrip (purple) it willpulsate.

When a star runsout of H in its core,it ignites a hydrogenburning shell. Thehelium core contractsand heats up. Theenvelope expands and cools.

Massive starsbecome supergiants.

Not so massive stars become redgiants.

As the hydrogen in the core of a star is transformed into helium, the matter in the core becomes degenerate.In a low density gas many possible energy levels of theelectrons are open, but as the gas become denser allthe lower energy levels are filled.

The Pauli exclusionprinciple states thateach energy level canonly contain one spin up electron andone spin down electron.

Stars in between 0.4and 3 solar massesbegin helium burningwith a flash. For afew minutes these starsproduce 1014 timesmore energy than the Sun – more energy thanan entire galaxy!

As hydrogen in thecore is used up, itis burned in a shell.The star swells upto be a cool giant.As helium startsbeing transformedinto carbon in thecore, the star contractsand heats up slightly.When He shell burningoccurs, the star swellsup again.

Massive starscan fuse elementsup to 56Fe (iron 56).

Eventual structure of a star with more than 8 solar masses.

Once an ironcore developsin a massivestar, the nuclearreactions canno longer pushup on the upperlayers and keepthem there. Theouter layerssqueeze downon the star, andit explodes.

Eventually, the core of the Sun will be made of carbonand oxygen. Once the outer layers are exhaled as a planetarynebula, the remant of the Sun will be a C-O white dwarf star.

Though the time scale for evolution of stars istypically much, much longer than a human lifetime,during some stages of a star's life we can measurechanges in its structure. Stars that pulsate may changetheir pulsational periods, indicating that the star isgetting cooler or hotter.

When theevolutionarytrack of a starplaces it inthe instabilitystrip, it willpulsate.

If a Cepheid variable star with a period of 30 days were at a distance of 10 parsecs what would its apparent brightness be?A.as bright as the SunB.a bit brighter than the planet VenusC.just barely visible to the unaided eyeD.only visible in a medium size telescope

A Cepheid with a period of 30 days is 10,000 timesmore luminous than the Sun. The Sun at d = 10 pc wouldbe just visible to the unaided eye. A 30 day Cepheid wouldbe 10 magnitudes brighter, or a bit brighter than Venus.

Betelgeuse is ared supergiantthat pulsates withmore than oneperiod. Here is itslight curve fromOctober, 1979,through November,1996. It varied fromV = 1.0 to 0.3.

Period changes in a star, which are measurable on timesscales of decades, are evidence for changes in stars onhuman time scales.

The strange case of FG Sagittae

Year Spectral Type Temperature (K)

1955 B4Ia 20,0001967 A5Ia 9,0001972 F6Ia 7,000 now K2Ib 4,500

apparent magnitude ~ 13in 1900, but brightened to9th mag by 1960

FG Sge fromJuly 1, 1992,to December,1998.

The canonical wisdom is that FG Sge is going throughits helium flash stage.