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Lecture 9

Energy Sources in Stars •  Most stars generate their energy via

nuclear fusion –  Fusing 4 protons (Hydrogen nuclei)

into one helium nucleus

–  The mass of the He nucleus is 0.007 = 0.7% smaller than the sum of the 4 Hydrogen nuclei that formed it.

–  The mass difference that “disappears” is the source of the energy via Einstein’s:

E=mc2

Stars live most of their lives in a balance, between two powerful forces -- outward pressure from their heat and the inward pull of gravity.

- Stars spend most of their lives in this equilibrium state, on the main sequence. - During this time, there is a tight relationship between a star’s temperature and its luminosity

-10 billiion yrs: the Sun runs out of hydrogen fuel in its core. - Core is pure helium, shrinks. - Hydrogen farther out in the star gets hot enough to fuse “hydrogen shell burning” - Overall luminosity of star goes up and becomes a red giant.

- 300million yrs later: Core gets hot enough to fuse helium. -  Helium Flash! Burns helium for about another billion years. (back on main sequence - Eventually the core contains only inert carbon, and a shell around the core starts burning helium. This time the star may become a Red Supergiant, - Carbon core doesn’t get hot enough to fuse (600 million K!) - Instead, the outer layers of the star are ejected into space in a planetary nebula.

Death of the Sun (low mass star)

See: http://web.njit.edu/~gary/202/Lecture18.html

What is left? A White Dwarf star!

- A carbon core, with the mass of the sun but as small as the Earth!

Hot at first and then cools.

Stars that are not on the main sequence.

Red giants: stars smaller than 8 times the sun’s mass become much larger and slightly cooler when fusion exhausts the hydrogen in their centers.

Pressure goes down in the center, matter falls in, and fusion again “turns on” but now in a shell around the core.

The new energy causes the star to swell. (e.g., we expect the Sun to swell to 60 times its current diameter, ~30% the radius of the earth).

Stars not on the main sequence. supergiants: stars > 10 times the sun’s mass use up hydrogen >1000 times faster than the sun.

Outer layers expand as helium core contracts… Helium fuses to form carbon, carbon fuses with helum to make oxygen, and heavier and heavier nuclei get built until Iron (Fe) is made.

Betelgeuse - shoulder of constelation Orion

Stars not on the main sequence. The last days of massive stars:

Outer layers expand as helium core contracts… Helium fuses to form carbon, carbon fuses with helum to make oxygen, and heavier and heavier nuclei get built until Iron (Fe) is made.

Iron does not fuse (because it takes energy to fuse Fe to heavier elements).

Whole thing stops…

Equilibrium breaks down and something bad is about to happen

Last Days of a Massive Star

Star burns through a succession of nuclear fusion fuels: Hydrogen burning: 10 Myr Helium burning: 1 Myr Carbon burning: 1000 years Neon burning: ~10 years Oxygen burning: ~1 year Silicon burning: ~1 day Finally builds up an inert Iron core in the center.e in the center.���������������������

http://www.astronomy.ohio-state.edu/~pogge/Ast162/

Iron Core Collapse

Iron core grows until its mas is about 1.2-1.4 Msun, and then pressure and temperatures cause the core to shrink and disintegrate in less than 1 second.

At the start of Iron Core collapse, the core properties are: ･Radius ~ 6000 km (~Rearth)･ Density ~ 108 g/cc

A second later, the properties are: ･Radius ~50 km･ Density ~1014 g/cc･

Supernova

•  Core collapses until its density hits ~2.4x1014 g/cc, which is about density of an atomic nucleus!

•  Infall in the center stops, and bounces back.

•  BOOM!

Supernovae As bright as An entire galaxy Of 10 billion stars.

“Crab Nebula” remnant of Supernova noted by Chinese, Japanese, and Korean astrologers in 1054

Remnant of Supernova noted by Kepler in 1604. (Chandra x-ray image)

Massive stars die and turn into black holes.

•  After some massive stars (> 10 suns) explode as supernovae, they will retain a mass of 2 to 3 solar masses in their cores.

•  Nothing in the universe is strong enough to hold up the remaining mass against the force of gravity, so it collapses into a black hole.

•  Matter that falls into a black hole disappears from contact with the rest of the Universe. Not even light can escape the gravitational pull of a black hole.

•  The “escape velocity” exceeds the speed of light. •  Black holes are a consequence of Einstein’s theory of gravity

which is called General Relativity.

Fission: Big nucleus is more massive than the sum of its parts. Can gain energy by splitting nuclei apart.

Fusion: Big nucleus is less massive than the sum of its parts. Can gain energy by building heavier nuclei.

()

Fusion vs. Fission

Also used in modern

“thermonuclear” bombs

Used in power plants

Fusion Fission

Fission reactors Under 1% of the uranium found in nature is the easily fissionable U-235 isotope. The uranium must be enriched to about 4% U-235, usually by means of gaseous diffusion or gas centrifuge. "

The U-235 absorbs a neutron, and then becomes an unstable U-236 isotope and then splits into two or more lighter nuclei along with neutrons that go on to produce more fissions."

The process generates entergy (in the form of heat) and this is used to turn a steam turbine (and is one million times more efficient than coal per unit mass)."

Fission reactors Under 1% of the uranium found in nature is the easily fissionable U-235 isotope. The uranium must be enriched to about 4% U-235, usually by means of gaseous diffusion or gas centrifuge. "

The U-235 absorbs a neutron, and then becomes an unstable U-236 isotope and then splits into two or more lighter nuclei along with neutrons that go on to produce more fissions."

The process generates entery (in the form of heat) and this is used to turn a steam turbine (and is one million times more efficient than coal per unit mass)."

Nuclear power produces this “spent fuel”, a unique solid waste problem. In volume spent fuels from nuclear power plants are roughly a million times smaller than fossil fuel solid wastes. However, because spent nuclear fuels are radioactive, they are pound for pound a more substantial problem. "

Fusion is a lot harder to achieve than fission, because like charges repel. If you try to shove two hydrogen nuclei together--each consisting of a single positively charged proton--they're not going to like it.

The sun overcomes this by cramming everything together to a density 100 times that of water, then heating it up to 15 or 20 million degrees. Even in the centre of the sun, it's estimated that a proton will exist on the average for 10 billion years before it's finally fused with another. Slow!

Why a Fusion reactor on earth is hard: In order to create the high temperatures required for fusion, physicists must turn the deuterium and tritium into a plasma. Trouble is, this plasma is at a temperature of 100 million degrees Kelvin. Obviously you can't let this touch the walls of the container you're trying to keep it in.

Fusion

The promise of a fusion reactor The half-lives of the radioactive material produced by fusion tend to be shorter than those from fission. They also tend to be less biologically dangerous."

Unlike fission reactors, whose waste remains dangerous for thousands of years, most of the radioactive material in a fusion reactor would would be dangerous for about 50 years. By 300 years the material would have the same radioactivity coal ash. "

⇒ many benefits (e.g. no greenhouse gases, virtually infinite supply)"

⇒  Much less dangerous than fusion waste."

Luminosity and Brightness of Stars

Luminosity is the same as Power

Power = Energy per unit time

Unit of Energy: Joules

Your energy bill: typically charged per kiloWatt * hr (kWhr) -- that’s 1000 Watts * hr = 1000 (Joules/s) *(3600 s)

= 3,600,000 Joules = 3.6 Million Joules

A typical household in California uses about 8,000 kWhr per year or ~ 25 million joules per year.

Unit of Power: Watt= Joules/s Light bulb: 100 watts (uses 100 Joules/s of energy) If you leave a 100W light bulb on for 100 seconds you use 100*100 = 10,000 Joules of energy.

Luminosity: •  Luminosity = Energy given off per time = power •  The sun:

Think of a 100 watt light bulb…

Luminosity: How “bright” are stars? •  Luminosity = Energy given off per time = power •  The sun:

You can figure out how far away a star is by comparing how bright it looks with its intrinsic luminosity.

This is like knowing that one light bulb is further away than another one based on how bright it looks to your eye.

Inverse square law: dimming with distance

•  A star’s apparent brightness depends on its distance

•  The light spreads out uniformly in all directions over a sphere whose radius is the distance.

•  Surface area of a sphere = 4 π R2 •  The star’s apparent brightness will

depend on intrinsic luminosity L, and distance from the star R, as:

Distance between lights in the sky…

•  If two stars have the same luminosity but one appears 100 times dimmer to the eye, how much farther away is the dim star?

•  You are 1m away from a candle and 5m away from a 100 watt light bulb, but both the candle and the bulb look to be the same brightness to you. How many watts of luminosity (or power) is the candle producing?

Distance between lights in the sky…

•  If two stars have the same luminosity but one appears 100 times dimmer to the eye, how much farther away is the dim star? A: 10 times farther away.

•  You are 1m away from a candle and 5m away from a 100 watt light bulb, but both the candle and the bulb look to be the same brightness to you. How many watts of luminosity (or power) is the candle producing? A: 4 watts.

The Luminosity - Temperature relation for stars

Normal stars on the longest-lasting phase of their lifetime sit in this band.

How do we know the overall luminosities of stars?

Temperature Hottest stars cool stars Hotter stars

More massive stars are also hotter.

90% of sun’s life will be “spent” here.

Lum

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ity

The Luminosity - Temperature relation for stars •  Recall that we can determine a

star’s temperature by measuring the wavelength of its peak brightness.

•  Astronomers can also determine the distance to the nearest stars using the method of “parallax”.

Wien’s law:

•  Distance + Apparent brightness

Allows us to determine the underlying luminosity of a star!

Apparent Brightness

Problem: A typical household needs about 1000 watts of power continuously averaged over a year to operate its lights, heating, cooling etc.

How big of a solar panel would you need to power your house if the solar panel could convert 100% of the sun’s energy into usable energy?

•  The sun has an apparent brightness of

•  b = 1370 Joules/s/m2 = 1370 watts/m2.

•  That is, if you had a perfectly efficient solar panel one meter on a side, if you held it perpendicular to the Sun's rays, it would generate 1370 watts of electricity

Apparent Brightness •  bsun = 1370 watts/m2. •  => If you had a perfectly efficient solar panel one

meter on a side, if you held it perpendicular to the Sun's rays, it would generate 1370 watts of electricity

Assume it’s dark half of the time. If you had a 2m2 perfect solar panel, you could collect ~2x1370 = 2740 Watts of power during the day, and store half of it to use at night!

Problem: solar panels are far from perfect! But you can see that the potential is awesome.

Apparent Brightness

Problem: What is the apparent brightness of a nearby star with the same intrinsic luminosity L, of the sun, but which is 3 lt yrs away?

•  The sun has an apparent brightness of

•  b = 1370 Joules/s/m2 = 1370 watts/m2.

•  That is, if you had a perfectly efficient solar panel one meter on a side, if you held it perpendicular to the Sun's rays, it would generate 1370 watts of electricity

Use: dsun = 1.5 x 1011 m 1 lt yr = 9.5 x 1015 m (1.5/(3*9.5))^2 =2.77x10-3

Show: bstar = 3.8 x 10-8 watts/m2