# Section 2 (Stars) Review

Following are what I consider the most important topics covered in this section.

• The Sun

• Parts of the Sun:

• photosphere, from which almost all light we see arises

• sunspots, active regions that are dark because of relatively lower temperature than surrounding regions

• granules, boiling (convective) flows below the photosphere.

• corona, typically seen only during a full solar eclipse and hotter than the photosphere. The corona is believed to be heated by solar magnetic fields.

• flares and prominences, bursts of magnetic field above the photosphere.

• Properties:

• surface temperature: 6000K --> peak wavelength of black body: 500 nm

• rotates once/25 days at equator; longer at poles (differential rotation)

• --> no solid surface; gaseous

• 75% hydrogen, 23% helium, 2% trace elements

• 11-year sunspot cycle; 22-year magnetic cycle

• magnetic field -- due to differential rotation

• Measurements of Stars

• Distances to stars by parallax

• Use Earth's orbit as large baseline, look for annual "wiggle" in apparent position of nearby stars

• 1 pc = 1 parsec = 1 parallax second = 3.26 light years: a star at distance 1 pc from Earth wiggles back and forth 1 arcseconds each year as Earth moves in orbit with radius 1 A.U.

• distance (pc) = 1 (A.U.)/parallax (arcsecond) or

parallax (arcsecond) = 1 (A.U.)/distance (pc).

If a star has a parallax of 0.05 seconds of arc, what is its distance?

Would the parallax of a star be larger if Earth's orbit were larger?

• Parallax is most secure method of distance measurement, but is good only for nearest stars (in solar neighborhood) -- out to < 100 pc or so.

• Nearest star: Proxima Centauri, 1.3 parsecs. What is its parallax?

• Intrinsic vs. apparent brightness

• Inverse square law of light --> apparent brightness depends on both intrinsic brightness (luminosity) and distance

• So from the measured apparent brightness (light intensity) and distance of a star, one can infer its luminosity.

• Temperature and radius

• Temperature of a gas is a measure of the average speed of the particles in the gas.

• Spectral type (spectral shape or lines)  of a star -->  its surface  temperature.

• Since luminosity is proportional to R2T4, one can infer the size (radius) of the star.

If a star is half as hot as our Sun, but has the same luminosity, how large is its radius compared to the Sun?

• Binary stars allow for estimating the mass of stars

• Classification of stars: The Hertzprung-Russell (H-R) Diagram

• One of the most important diagrams in astronomy

• Plots color (or temperature) on the horizontal axis -- blue=hot=left, red=cool=right -- and luminosity (or magnitude) on the vertical axis -- bright=up, faint=down.

• Spectral Types of Stars

• OBAFGKM: O=hottest, M=coolest.

• spectral type carries almost same info as color or temperature

• Most (about 90%) stars -- including the Sun -- appear to lie on the main sequence. Others are in red giant and white dwarf regions.

• Temperature can explain MS (hotter --> bright and blue)

• High-mass stars on bright blue MS, low-mass stars on faint red MS. Mass determines location of star on Main Sequence!

• Upper main sequence (massive stars) is much brighter than Sun -- up to 1,000,000 times brighter. L M3.5 -- Luminosity depends very strongly on mass. Star with mass 10 MSun is 3,100 times more luminous than Sun.

• Large size (radius) makes star brighter too --> Red Giants are bright because they're big, even though cool. WD's are faint because they're tiny, even though hot.

• Power Sources: How do Stars Shine?

• Hydrostatic pressure: balance of gravity pushing in, pressure pushing out

• Temperature at core of Sun: T~10,000,000 K

• Hot enough to overcome the Coulomb barrier to undergo nuclear fusion

• Fusion converts small amount of mass into energy (E=mc2) in form of photons (light) and neutrinos

• Three ways to transport heat: conduction, radiation, and convection

• The Life of a Star

• Birth

• Collapses gravitationally out of huge cloud of gas (H, He...)

• As soon as enough mass assembled, gravitational force compresses --> core heats up --> fusion begins --> it's a star!

• Middle Age

• All stars fusing H into He in their cores live on the main sequence (MS) in the H-R diagram.

• Mass of star determines location on the MS: Sun in lower middle; low-mass (=red dwarfs) on lower (right) end of the MS; massive stars on upper (left) end of the MS.

• Mass also determines lifetime of star: more mass --> more fuel, but much more luminous --> uses up fuel more quickly. Main sequence star with mass M=5 MSun has a MS lifetime of only 180 million years, while star with mass 0.5 MSun has a MS lifetime of 56 billion years -- much older than age of Universe so far.

• Death

When H in core is depleted, gravity wins over pressure and core collapses.

• Low-mass stars become He white dwarfs (WD)

• Medium-mass stars (Sun)

• Core heats up until H in shell around core begins fusion

• Atmosphere inflates like a balloon and cools --> star become red giant, larger than orbit of Earth

• He core keeps contracting, heating up until He can fuse to C and O (T~100,000,000 K). But the core never get hot enough to ignite carbon.

• Red giant has WD buried deep inside it

• Eventually, He will run out, core contracts more, and atmosphere blows away --> planetary nebula --> blows away more --> C-O WD left in middle.

• Massive stars: M> 7 MSun

• When H used up, core collapses, fuses He to C and O

• Core can't withstand gravity, keeps collapsing, fusing C and O to Ne, Mg, Si, S, and finally Fe (iron)

• Fe has highest binding energy so can't extract energy

• Gravity wins! Whole star collapses, rebounds in supernova (mostly type II) ; can outshine whole galaxy; ejects chemically-enriched material at tens of thousands of kilometers per second, and spreads material throughout interstellar space.

Without supernovae, we would not exist!

• Some dense material remains at core as a neutron star or a black hole

• The mass of a star is the most important characteristic for determine its lifetime.

• More low mass stars are typically formed than massive ones. Also low mass stars live longer. Thus the most common stars are low-mass MS stars.

• Stellar remnants:

• White dwarf - a compact star supported by electron degeneracy pressure. Maximum mass allowed for WD is 1.4 MSun = Chandresekhar limit; more massive WD will collapse further. The accretion of a WD from its companion in a binary may result in a type-I supernova, the detonation of remaining nuclear fuels.

• Neutron star - a compact star supported by neutron degeneracy pressure; The maximum mass is 2-3 Msun.

The angular momentum conservation leads to the rapid spinning of a neutron star, which may be seen as a pulsar.

• Black Hole - a dense object from which even light cannot escape (i.e., the escape velocity exceeds the speed of light). But the gravitational effects of a black hole (e.g., stellar motion and X-ray emission) may be used to trace its presence.

• Origin of elements

• H and He are the most abundant elements in the Universe, and almost of them were produced during the Big Bang.

• Elements heavier than He (up to Fe) are synthesized  in stars.

• Elements heavier than Fe can be synthesized in supernovae and during mergers between two neutron stars

• Four basic forces

• Gravitational force - mutual attractions between all matters in the Universe;

• Electromagnetic force between charged particles (e.g., protons and electrons in atoms);

• Strong force that binds nuclear particles (protons and neutrons);

• Weak force that controls the radioactive decay of certain kinds of nuclear particles (e.g., neutrons).