The Sun A typical Star The only star

The Sun – A typical Star • • The only star in the solar system Diameter: 100 that of Earth Mass: 300, 000 that of Earth Density: 0. 3 that of Earth (comparable to the Jovians) • Rotation period = 24. 9 days (equator), 29. 8 days (poles) • Temperature of visible surface = 5800 K (about 10, 000º F) • Composition: Mostly hydrogen, 9% helium, traces of other elements Solar Dynamics Observatory Video

How do we know the Sun’s Diameter? • Trickier than you might think • We know only how big it appears – It appears as big as the Moon • Need to measure how far it is away – Kepler’s laws don’t help (only relative distances) • Use two observations of Venus transit in front of Sun – Modern way: bounce radio signal off of Venus

How do we know the Sun’s Mass? • Fairly easy calculation using Newton law of universal gravity • Need to know distance Earth-Sun • General idea: the faster the Earth goes around the Sun, the more gravitational pull the more massive the Sun • Earth takes 1 year to travel 2π (93 million miles) Sun’s Mass = 300, 000 that of Earth

How do we know the Sun’s Density? • Divide the Sun’s mass by its Volume • Volume = 4π × (radius)3 • Conclusion: Since the Sun’s density is so low, it must consist of very light materials

How do we know the Sun’s Temperature? • Use the fact that the Sun is a “blackbody” radiator • It puts out its peak energy in visible light, hence it must be about 6000 K at its surface

Black Body Spectrum • Objects emit radiation of all frequencies, but with different intensities Ipeak Higher Temp. Ipeak Lower Temp. fpeak<fpeak

How do we know the Sun’s composition? • Take a spectrum of the Sun, i. e. let sunlight fall unto a prism • Map out the dark (Fraunhofer) lines in the spectrum • Compare with known lines (“fingerprints”) of the chemical elements • The more pronounced the lines, the more abundant the element

Spectral Lines – Fingerprints of the Elements • Can use spectra to identify elements on distant objects! • Different elements yield different emission spectra

Sun Compare Sun’s spectrum (above) to the fingerprints of the “usual suspects” (right) Hydrogen: B, F Helium: C Sodium: D

“Sun spectrum” is the sum of many elements – some Earth-based!

The Sun’s Spectrum • The Balmer line is very thick lots of Hydrogen on the Sun • How did Helium get its name?

How do we know the Sun’s rotation period? • Crude method: observe sunspots as they travel around the Sun’s globe • More accurate: measure Doppler shift of spectral lines (blueshifted when coming towards us, redshifted when receding). – THE BIGGER THE SHIFT, THE HIGHER THE VELOCITY

Actual Data: Spectra of East and West Limb of the Sun • Note unshifted lines due to Earth’s atmosphere

How do we know how much energy the Sun produces each second? • The Sun’s energy spreads out in all directions • We can measure how much energy we receive on Earth • At a distance of 1 A. U. , each square meter receives 1400 Watts of power (the solar constant) • Multiply by surface of sphere of radius 149. 6 bill. meter (=1 A. U. ) to obtain total power output of the Sun

Energy Output of the Sun • Total power output: 4 1026 Watts • The same as – 100 billion 1 megaton nuclear bombs per second – 4 trillion 100 W light bulbs – $10 quintillion (10 billion) worth of energy per second @ 9¢/k. Wh • The source of virtually all our energy (fossil fuels, wind, waterfalls, …) – Exceptions: nuclear power, geothermal

What process can produce so much power? • For the longest time we did not know • Only in the 1930’s had science advanced to the point where we could answer this question • Needed to develop very advanced physics: quantum mechanics and nuclear physics • Virtually the only process that can do it is nuclear fusion

Nuclear Fusion • Atoms: electrons orbiting nuclei • Chemistry deals only with electron orbits (electron exchange glues atoms together to from molecules) • Nuclear power comes from the nucleus • Nuclei are very small – If electrons would orbit the statehouse on I-270, the nucleus would be a soccer ball in Gov. Kasich’s office – Nuclei: made out of protons (el. positive) and neutrons (neutral)

Nuclear fusion reaction – In essence, 4 hydrogen nuclei combine (fuse) to form a helium nucleus, plus some byproducts (actually, a total of 6 nuclei are involved) – Mass of products is less than the original mass – The missing mass is emitted in the form of energy, according to Einstein’s famous formulas: E= 2 mc (the speed of light is very large, so there is a lot of energy in even a tiny mass)

Hydrogen fuses to Helium Start: 4 + 2 protons End: Helium nucleus + neutrinos Hydrogen fuses to Helium

The Standard Solar Model (SSM) • Sun is a gas ball of hydrogen & helium • Density and temperature increase towards center • Very hot & dense core produces all the energy by hydrogen nuclear fusion • Energy is released in the form of EM radiation and particles (neutrinos) • Energy transport well understood in physics

Standard Solar Model

Hydrostatic Equilibrium • Two forces compete: gravity (inward) and energy pressure due to heat generated (outward) • Stars neither shrink nor expand, they are in hydrostatic equilibrium, i. e. the forces are equally strong Gravity Heat Gravity

More Mass means more Energy • More mass means more gravitational pressure • More pressure means higher density, temperature • Higher density, temp. means faster reactions & more reactions per time • This means more energy is produced

How do we know what happens in the Sun? • We can’t “look” into the Sun • But: come up with theory that explains all the features of the Sun and predicts new things • Do more experiments to test predictions • This lends plausibility to theory

Understanding Stars • “Understanding” in the scientific sense means coming up with a model that describes how they “work”: – Collecting data (Identify the stars) – Analyzing data (Classify the stars) – Building a theory (Explain the classes and their differences) – Making predictions – Testing predictions by more observations

Identifying Stars - Star Names • Some have names that go back to ancient times (e. g. Castor and Pollux, Greek mythology) • Some were named by Arab astronomers (e. g. Aldebaran, Algol, etc. ) • Since the 17 th century we use a scheme that lists stars by constellation – in order of their apparent brightness – labeled alphabetically in Greek alphabet – Alpha Centauri is the brightest star in constellation Centaurus • Some dim stars have names according to their place in a catalogue (e. g. Ross 154)

Classification by Star Properties • What properties can we measure? – distance – velocity – temperature – size – luminosity – chemical composition – mass

Classification of the Stars: Temperature Class O B A F G K M Temperature 30, 000 K 20, 000 K 10, 000 K 8, 000 K 6, 000 K 4, 000 K 3, 000 K Color blue bluish white yellow orange red Examples Rigel Vega, Sirius Canopus Sun, Centauri Arcturus Betelgeuse Mnemotechnique: Oh, Be A Fine Girl/Guy, Kiss Me

The Key Tool to understanding Stars: the Hertzsprung-Russell diagram • Hertzsprung-Russell diagram is luminosity vs. spectral type (or temperature) • To obtain a HR diagram: – get the luminosity. This is your y-coordinate. – Then take the spectral type as your x-coordinate, e. g. K 5 for Aldebaran. First letter is the spectral type: K (one of OBAFGKM), the arab number (5) is like a second digit to the spectral type, so K 0 is very close to G, K 9 is very close to M.

Constructing a HR-Diagram • Example: Aldebaran, spectral type K 5 III, luminosity = 160 times that of the Sun L 1000 160 100 Aldebaran 10 1 Sun (G 2 V) O B A F G K M Type … 0123456789 012345…

The Hertzprung -Russell Diagram • A plot of absolute luminosity (vertical scale) against spectral type or temperature (horizontal scale) • Most stars (90%) lie in a band known as the Main Sequence

Hertzsprung-Russell diagrams … of the closest stars …of the brightest stars