E5 Fusion and Stars

nuclear fusion

• two or more smaller, lighter nuclei combine to form a heavier, stable nuclei

• releases energy because BE product > BE of reactants (same as fission, since higher BE means more stable)→ released as KE through fusion products

• mass of reactants > mass of product (opp to fission)

• usually need high temp high pressure to overcome coulomb repulsion, even though it releases energy

nuclear fusion in stars

• nuclear fusion happens at the core

  • hydrogen fuse into helium

  • overcome coulomb repulsion between positively-charged nuclei → undergo fusion, release energy

• stability of stars relies on equilibrium between outward radiation pressure and inward gravitational force

fusion vs fission

• fusion products are safer than fission’s radioactive waste

• fusion mass of product > reactants but fission mass of reactant > products

  • but both BE of products > reactants because more stable

lightyear

• distance light travels in one year

AU

• astronomical unit. average distance of earth to sun.

• extension: how long does light take to travel from earth to sun?

  • time = distance/speed = 1AU/3×10⁸

pc

• parsec. distance at which 1 AU subtends an angle of 1 arcsec

  • 1 degree = 60 arc mins = 3600 arc secs

• distance in parsec = 1 AU / angle in arcsec

stellar parallax

• difference in apparent position of an object viewed from two different lines of sight

• used to measure distance of stars and planets

• to be accurate, measure biggest possible angle → 6 months apart so that diff in position is max

• limitations

  • only for nearby stars

  • very distant stars have unmeasurably small parallax

  • earth’s orbit provides limited baseline

brightness

• brightness is measured from earth. depends on 1) power emitted from star; 2) distance of star from earth

  • physical quantity is intensity, units W m^-2

• apparent magnitude: scale for brightness of stars (1 is brightest, but can be even brighter ie negative numbers → sun is magnitude 26)

• b = L/4pid² because assume energy spreads out in spherical shape

luminosity

• total power emitted by star (units: W)

  • aka energy emitted per unit time

  • independent of distance from earth (unlike brightness)

black body radiation

• theoretical model for perfect emitter/absorber of radiation

  • assumes radiation does not depend on nature of emitting surface, only its temperature

stefan-boltzmann law

• total power radiated by black body is directly proportional to T⁴

stellar spectra

• at any temp, there is a range of wavelengths of radiation emitted

  • in order of increasing temp: infrared → red → yellow → white

• stellar spectrum

  • spectral intensity distribution (wavelengths) against intensity → usually multiple graphs at different temperatures

  • when temp increase, peak of curve shifts towards shorter wavelength (ie higher freq)

  • area under graph gives total power radiated

  • absorption lines: radiation emitted from core is continuous spectrum, but some is absorbed by different gases as it passes through outer layers of stars → produces gaps in spectrum which are unique to each element. → can determine chemical composition of gases.

• wien’s displacement law: wavelength at which intensity is maximum is related to temperature of black body by λ_maxT = constant

  • assumes black body

HR diagram

• used to

  • classify stars

  • predict stellar evolution

  • estimate distance to stars

  • study stellar populations in galaxies

• luminosity against surface temperature

  • luminosity in log scale due to large range → limitation: not precise

  • surface temperature increases from right to left

• cool stars appear red, hot stars appear blue

stellar evolution for main seq stars

• stellar nebula → protostars → main seq stars → red giant → planetary nebula → white dwarf

stellar evolution for massive stars

• stellar nebula → protostars → massive stars → red supergiant → supernova → neutron star/black hole

stellar nebula → protostar

• giant molecular clouds of gas and dust, mainly H and He

• gravity causes cloud to collapse over millions of years

• nebula gets denser, forms protostar

protostar → main sequence star

• gravity continues to cause protostar to collapse, core gets hotter → causes H in the core to undergo nuclear fusion to form He → produces outward pressure that balances out inward gravitational force

• massive: luminosity constant, surface area smaller but temperature increase (luminosity constant, temperature increase)

• average (sun): will get smaller so luminosity decrease, outer layers stay cool UNTIL core gets hotter and heats up the outer layers (luminosity decrease first, then temperature increase)

• small: core will not get hotter, luminosity will decrease as it becomes smaller (luminosity decrease, temperature constant)

main sequence

• most stable, 90% of stars are main sequence stars, stars stay here for most of their lifespan

• top left: large hot blue stars, bottom right: small cool red stars (based on stefan-boltzmann)

• at core: H undergoes nuclear fusion to become He, until core runs out of H

• hydrostatic equilibrium at core → allows for fixed radius + most stable

  • gravitational force pulls atoms inward

  • nuclear fusion creates outward pressure

• when run out of H,

  • heavier He nuclei sink to centre of core

  • H continues fusion outside the core

  • rate of H fusion decrease → outward pressure decrease → core collapses → core temp increase → heats up outer layers, which expand → radius increase, temp decrease for same luminosity (which is why red giants have low temp)

main sequence → red giants

• core runs out of hydrogen, no more fusion to produce outward pressure → collapses

• core becomes dense and higher temperature, He undergoes nuclear fusion (helium flash) → outward pressure > gravitational force, outer layer expands

• red giants: top right of HR diagram. large, cool, red, high luminosity.

red giant → planetary nebula → white dwarf

• runs out of helium

• final bursts of energy eject outer layers, which drift into space and form planetary nebula

• core remains as a hot, dense object which contracts to form white dwarf

• white dwarf cools down to become black dwarf

white dwarfs

• lower left. small, high temperature, low luminosity.

• no more fusion in core → no outward radiation pressure

• prevented from further collapse because of electron degeneracy pressure/pauli exclusion principle (out of syllabus)

massive stars → red supergiants

• massive stars (mass > 4M_☉) have higher luminosity and temperature (therefore appear blue)

• run out of H faster

• can fuse heavier elements in cores

• as fusion progresses, develops layered structure. each layer has fusion of different element.

• H → He → C → O → Ne → Si → Fe (recall iron is the most stable because highest BE per nucleon)

• iron core limit: fusion is energetically favourable up to iron, anything beyond would need energy input

red supergiants

• top right, above red giants

• very large, high luminosity, low temperature

red supergiant → supernova

• iron core limit: core full of iron, no more fusion so no more outward radiation

• star collapses quickly → triggers explosion (supernova)

• outer layers ejected into space, high energy of supernova allows for nucleosynthesis → produces elements heavier than iron, which are ejected into space.

  • absorb energy in order for stable iron to undergo nuclear fusion to give unstable product (opposite of usual fusion where energy is released)

supernova → neutron stars

• only if core is 1.4 to 3M_☉

• electrons forced into protons, forms neutrons

• high density, small size

supernova → black hole

• only if core is more than 3M_☉

• gravity is extremely strong, not even light can escape. mass compressed into point of infinite density.

marked ws Q3: natural uranium in earth was formed from nuclear fusion of iron nuclei in some ancient stars. which statement about the nuclear fusion is correct?

• cooled star

• heated star

• could’ve done either

• impossible to determine

• cooled star

• usually, release E

• but Fe already stable. to become unstable, need absorb E from surroundings → therefore cools the star (nucleosynthesis in supernova)