Stars. … how I wonder what you are. Goals. Stars are Suns. Are they: Near? Far? Brighter? Dimmer? Hotter? Cooler? Heavier? Lighter? Larger? Smaller? What categories can we place them in?. Linear size = how big something really is Meters, inches, light years, feet
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Stars … how I wonder what you are.
Goals • Stars are Suns. • Are they: • Near? Far? • Brighter? Dimmer? • Hotter? Cooler? • Heavier? Lighter? • Larger? Smaller? • What categories can we place them in?
Linear size = how big something really is Meters, inches, light years, feet Angular size = how big something looks Degrees, arcminutes, arcseconds, milliarcseconds Circle = 360 degrees 1 degree = 60 arcmin 1 arcmin = 60 arcsec 1 arcsec = 1000 mas Angular Size
Distance • One proof of a heliocentric Universe is stellar parallax. • Tycho Brahe saw no parallax. • Copernicus: stars too far away. • Nearest star: Proxima Centauri Parallax angle = 0.76 arcsec • Tycho’s precision = 1 arcmin
What is the distance of an object with a parallax angle of 1 arcsec? Distance = 206,265 AU This distance is 1 parsec (pc) 1 pc = 206,265 AU = 3.3 ly 1 lightyear = distance light travels in one year. The Parsec
Concept Test • If Star A has a parallax of 2 arcseconds, and Star B has a parallax of 0.25 arcseconds: • Star A is closer to us than Star B. Both are farther from us than 1 pc. • Star A is closer to us than Star B. Both are closer to us than 1 pc. • Star A is closer to us than 1 pc. Star B is farther than 1 pc. • Star B is closer to us than 1 pc. Star A is farther than 1 pc. • Star B is closer to us than Star A. Both are farther away than 1 pc.
Distances • Closest star: Proxima Centauri parallax = 0.76 arcsec Distance = 1.3 pc or 4.3 lightyears
Terms • Brightness = How intense is the light I see from where I am. • Magnitude is numerical term for this. • Luminosity = how much light is the thing really giving off.
Magnitude Scale • The SMALLER the number the BRIGHTER the star! • Every difference of 1 magnitude = 2.5x brighter or dimmer. • Difference of 2 magnitudes = 2.5x2.5 = 6.3x brighter or dimmer
Star light, star bright • Sirius is magnitude -1.5 Polaris is magnitude 2.5 • Is Sirius really more luminous than Polaris? • No, Sirius is just closer.
Apparent and Absolute • Apparent Magnitude = brightness (magnitude) of a star as seen from Earth. m • Depends on star’s total energy radiated (Luminosity) and distance • Absolute Magnitude = brightness (magnitude) of a star as seen from a distance of 10 pc. M • Only depends on a star’s luminosity
Concept Test • Polaris has a an apparent magnitude of 2.5. It’s absolute magnitude is 3.1. Polaris is: • Closer to us than 10pc. • Farther from us than 10 pc. • Exactly 10 pc away. • Can’t know without the parallax angle. • None of these is correct.
Concept Test • Polaris has a parallax angle of 0.01 arcsconds. Polaris is therefore: • Closer to us than 1pc. • Farther from us than 1pc. • Exactly 1pc away.
Concept Test • Polaris has a parallax angle of 0.01 arcsconds. Polaris is therefore: • 1pc. • 10pc. • 100pc. • 1000pc. • None of the above.
example • Our Sun: • m = -26.8, • distance = 4.8 x 10-6 pc So: M = 4.8 • Polaris: • m = 2.5, • distance = ~100pc So: M = -3.1 • Polaris is 1500 times more luminous than the Sun!
Concept Test • The most likely absolute magnitudes (M) for each is: • A = 2.5, B = -2.5, C = 2.5 • A = 2.5, B = 2.5, C = -2.5 • A = -2.5, B = 2.5, C = 2.5 • A = 2.5, B = 2.5, C = 2.5 • None of the above.
Emission lines Absorption lines Continuum A Spectrum • A spectrum = the amount of light given off by an object at a range of wavelengths.
Three Reasons All objects do one or more: • Reflect light because of color or smoothness (same as scatter) • Emit light because of their temperature (thermal radiation) • Emit or absorb light because of their composition (spectral lines) A person, house, or the Moon: reflects visible light, and because each is warm, emits infrared light.
Temperature and Light • Warm objects emit light. • Thermal radiation
Hot Stellar Spectra Cool Stellar Temperatures How hot are stars? • Thermal radiation and temperature. • Different stars have different colors, different stars are temperatures. • Different temp, different trace compositions
Stellar Masses How massive are stars? • Kepler’s Laws – devised for the planets. • Apply to any object that orbits another object. • Kepler’s Third Law relates: • Period: “how long it takes to orbit something” • Semimajor axis: “how far you are away from that something” • Mass: “how much gravity is pulling you around in orbit” • Where M is the Total Mass. • Can calculate the mass of stars this way.
Binary Stars • Most stars in the sky are in multiple systems. • Binaries, triplets, quadruplets, etc…. • Sirius • Alcor and Mizar • Tatooine • The Sun is in the minority by being single.
Stellar Masses How massive are stars? • Most stars have masses calculated this way. • Find: • The more massive the star, the more luminous it is. • The more massive the star, the hotter it is.
50 mas Stellar Radii How big are stars? • We see stars have different luminosities and different temperatures. • Stars have different sizes. • If you know: • Distance • Angular size • Learn real size.
Betelgeuse • Angular size = 50 mas • Parallax = 7.6 mas = 0.0076 arcsec • Apparent mag = 0.6 • Distance = 1/parallax = 132 pc • True size = distance * angular size = 1400 Rsol • Model solar system: 97 yards in radius. • Absolute Mag = m – 5log(d/10pc) = -5 • Our sun M ~5, Betelgeuse = 10,000x luminosity
Angular versus Linear Supergiants, Giants and Dwarfs
H-R Diagram • Can order the stars by: • Temperature (or spectral type) • Luminosity (or absolute magnitude). • And see where other qualities fall: • Mass • Radius
Luminosity Class • The roman numerals. • Stars at same temp can have different luminosities. • Corresponds to different classes: MS, giant, supergiant. I V III
Concept Test Which star is: • Hottest? • Coolest? • Faintest as seen from Earth? • Most luminous? Of Main Seq. Stars? • Most massive? • Most like the Sun?
The Main Sequence • Stars characterized by what holds them up. • 90% held up by heat of Hydrogen fusion? 4H He + Energy