Astronomy 113 Dr. Joseph E. Pesce, Ph.D. The Nature of Stars For nearby stars - measure distances with parallax 1 AU d p 8-2 Parallax A January ³ d = 1/p (arcsec) [pc] ³ 1pc when p=1arcsec; 1pc=206,265AU=3 x 10 13 km ³ P = VERY small!! (<<1 ) ³ Using satellites, can measure start to d~1,000pc away A A July Apparent Magnitude (log scale - the eye s response) 8-3 Brightness +1 +6 (naked-eye limit) Bright Faint 1 magnitude = 2.5 times real brightness (so 1 to 6 is 100 times difference: 2.5 5 = 100) Magnitudes can be negative too. So, Sun = -25 Moon = -12 Sirius = 0 Faintest objects = +30 (with HST, for example) 8-4 Magnitudes ³ Apparent magnitude (m) is not real brightness ³ Apparent brightness decreases inversely with square of distance - the inverse square law : Double distance apparent brightness decreases (1/2) 2 =1/4 Triple distance (1/3) 2 =1/9 8-5 Inverse-square Law Need to be able to compare real brightness, so correct for distance Absolute magnitude (M) = apparent magnitude an object would have if it were at 10 pc Sun = +4.8 (range for stars: -10 to +17) Measure m and d, then: M = m - 5log(d/10) 1
8-6 Luminosity ³ Absolute magnitude is related to Luminosity (the physical brightness of an object) ³ Solar luminosity = 3.9 x 10 26 Watts ³ Call this 1 L Stars with: M = -10 have 10 6 L M = +17 have 10-5 L 8-7 Stellar Temperatures ³ Remember Wien s law? (λ max = 1/T; color related to surface tempature) Intensity U B V Wavelength Use a photometer to measure light intensity and filters to measure intensity at different bands : U (UV), B (blue), V (visual) That is, 3 apparent magnitudes which tell us where most energy in spectrum is (B-V = color index; if small, object is blue, if large, it is red) From blackbody curves, get T vs. B-V, and thus a surface temperature At different temperatures, different elements produce different emission lines - can measure temperature this way too 8-8 Spectral Types 8-9 Spectral Types ³ A star s surface temperature determined from color index or spectral line strengths ³ In the 1920s, Cecilia Payne classified stars based on spectral features visible (and ordered them by surface temperature) ³ Spectral types: O B A F G K M Hottest T~35,000 K HeII (singly ionized) SiIV (triply ionized) Sun = G2 Coolest T~3,000 K Molecules (TiO) Further subdivided: B0 - B9 Hottest Coolest 9-2 The Hertzsprung-Russell Diagram Hot 40,000K Cool 2,500K Supergiants Bright 100 1000-10 Giants Types of Stars Luminosity Absolute Magnitude -5 0 +5 +10 1 0.01 10 Sun Main Sequence Faint +15 0.001 O0 B0 A0 F0 G0 K0 M0 White Dwarfs Surface Temperature 2
9-3 The Hertzsprung-Russell Diagram 9-4 The Hertzsprung-Russell Diagram ³ Pattern when color-index is plotted against absolute magnitude ² Also called Color-Magnitude diagram Surface Temperature and Absolute Magnitude are Related! ³ Main Sequence: 90% of stars in Solar neighborhood are on Main Sequence (called dwarf stars) ² M-type stars most common ² O-type stars rarest ² Most M.S. stars are like the Sun ³ From Stefan-Boltzmann Law: E = T 4 9-5 Giants ³ Cool objects radiate less E than hot (per unit surface area) ³ So, for Giants to be so bright, they must be huge! T ~ 3,000-6,000K R ~ 10-100x Solar Radius Red Example: Arcturus ³ Even bigger and brighter than Giants ³ Example: Betelgeuse ³ 1% of all stars in Solar neighborhood 9% of stars in Solar neighborhood are white dwarfs - more later 9-6 Supergiants 9-7 Binary Stars ³ Two stars gravitationally bound ³ Orbital motion of binaries shifts spectral lines (Doppler Shift) ³ We see stars along their orbital plane ³ Causes effects in light curve: 9-8 Eclipsing Binaries Approaching Radial Velocity Curve Intensity Radial Velocity 0 Time Time to cross disk Time Receding ³ Total eclipses allow us to measure radii of stars Mass 3
³ How do you measure mass? ³ Newton s adaption of Kepler s Law: 9-9 Stellar Masses M 1 + M 2 = a 3 / p 2 (both measured in binaries) Mass-Luminosity Relationship: On the Main Sequence, the more massive a star, the more luminous ³ Roche Lobe - Sphere of gravitational influence Detached Binaries Semi-detached Binaries 9-10 Contact Binaries 10 6 10 4 10 2 L/L 1 10-2 10-4 Contact Binaries 50 Mass 0.1 10-2 ³ The nearest star - easiest to study - use as a model ³ The Atmosphere 1. Photosphere - the visible layer (about 400km thick) q Low density (0.01% of our atmosphere at sea level) q Perfect blackbody at 5800 K q Can t see below q Features: Granulation Limb Darkening Proof that Sun is made of gas (not solid) ³ 10-3 The Atmosphere 2. Chromosphere - layer of less dense gas above the photosphere (about 500km thick) q T ~ 4000 K q Features: Spicules - spikes or jets of gas ³ 10-4 The Atmosphere 3. Corona - upper most layer of atmostphere; extends to millions of km q Very low density q Can be seen during eclipses q T ~ 2 x 10 6 K q Heated by magnetic fields q So hot particles have high velocities and escape as solar wind (p & e - ): 1 million tons per second!! corona spicule chromosphere photosphere interior 4
1/31/14 10-5 ³ The Atmosphere Sunspots - cooler regions on surface (where magnetic fields exit and enter Sun) Follow an 11-year cycle 10,000s km (Earth-sized) Last days - month Can determine Sun s rotation rate Differential Rotation - Equator rotates more rapidly than poles (25day - 35 day) Further proof Sun is gaseous Solar Flares - eruptions of charged particles and radiation 2007-2011 Joseph E. Pesce, Ph.D. 10-8 2007-2011 Joseph E. Pesce, Ph.D. 10-9 10-10 The Solar Interior The Energy source - (18th cent. View - coal, etc) ³ Thermonuclear Reactions E = mc2 c is so large that E is big even for small m! ³ Fusion in core Because P (3 x 1011 atm) and T (2 x 107 K) are so high, protons stick (H = 1p 1n & He = 2p 2n), so: 4H 1 He + energy + neutrinos For this reaction: E = 4 x 10-12 J (enough to light a 10W light bulb for -12 5 x 10 seconds!) But the Sun s luminosity is ~ 4 x 1026 W/sec!! 600 million metric tons/sec of Hydrogen is being converted into He!!! We use models to understand what s happening in the interior 5
In the sun: (600million tons of Hydrogen/sec = 170,000 yrs to consume mass of earth; in 10 billion years. p + p + p + p + e - e - 4 protons: (Hydrogen) + 2 electrons n n Fusion p + p + 1 helium nucleus More mass before than after - mass conserved, so extra becomes energy (E=mc 2 ) in the form of a photon, the γ-ray. + γ-ray & neutrino Neutrinos Nearly massless subatomic particles Produced in huge quantities during fusion and supernovae. Important for cosmological reasons and understanding of nuclear fusion Billions of them pass through every square centimeter all the time - yes, even now! Weakly interacting: can pass through 1 light year of lead without interacting with a lead atom!! (Luckily for us) Can be detected 1 light year of lead 2007-2011 Joseph E. Pesce, Ph.D. 10-13 The Solar Interior ³ Hydrostatic Equilibrium ² Balance of force of gravity, which tries to squeeze Sun, and radiative pressure from fusion, which tries to blow apart Sun ³ Radiative transport ² Energy transported outward by photons High P, High T create High E photons (γ-rays) But High P keeps them in, leading to a Random Walk - photons collide, lose E, eventually fly free (after 10 6 yrs) from photosphere as visible photons Transport of energy Radiative (= photons) + Convection Interior of Sun Random walk : γ-ray to visible (Infrared) 1 million yrs 10-15 3 The Solar Interior Thank You! 6