Astronomy 114 Lecture 15: Properties of Stars Martin D. Weinberg [email protected] UMass/Astronomy Department A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—1/18 Announcements PS #4 posted; due next Friday (before Spring break) A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—2/18 Announcements PS #4 posted; due next Friday (before Spring break) Quiz #1 redux due next Wednesday A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—2/18 Announcements PS #4 posted; due next Friday (before Spring break) Quiz #1 redux due next Wednesday Today: Properties of Stars The Nature of Stars, Chap. 19 The Birth of Stars, Chap. 20 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—2/18 Quiz #1 Redo exam questions that you missed Separate sheets of paper Turn in on Wednesday before Spring Break Average of original and new scores A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—3/18 Distances to stars D = dα = D d α A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—4/18 Distances to stars D = dα = D d α A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—4/18 Distances to stars D = dα = D d α If α = 1 arc sec and D =1AU then d = 206, 265AU. This is a PARSEC Therefore: d(pc) = 1/p(arc sec) A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—4/18 Parallax Parallax is the first step in the cosmic distance ladder Fundamental distances, by direct measurement Hipparcos satellite: measured distances 120,000 stars to high accuracy Parallax angles of 0.001 arc sec 1 1 d = pc = pc = 1000 pc =1 kpc p 0.001 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—5/18 Parallax Parallax is the first step in the cosmic distance ladder Fundamental distances, by direct measurement Hipparcos satellite: measured distances 120,000 stars to high accuracy Parallax angles of 0.001 arc sec 1 1 d = pc = pc = 1000 pc =1 kpc p 0.001 Example: Proxima Centauri p =0.772 arc sec 1 1 3.26 ly d = pc = pc =1.3 pc =1.3 pc × = p 0.772 1 pc 4.2 ly A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—5/18 Distance to stars using brightness (1/4) Stars have different luminosities Use parallax to determine distance Brightness of star depends on distance A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—6/18 Distance to stars using brightness (1/4) Stars have different luminosities Use parallax to determine distance Brightness of star depends on distance Brightness or flux is the luminosity per area Luminosity divided by the area of a sphere: 4πd2 L b = 4πd2 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—6/18 Distance to stars using brightness (2/4) Example: flux from Sun on Earth 26 3.827 × 10 W 2 b⊙ = = 1353 W/m 4π(1.50 × 1011m)2 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—7/18 Distance to stars using brightness (2/4) Example: flux from Sun on Earth 26 3.827 × 10 W 2 b⊙ = = 1353 W/m 4π(1.50 × 1011m)2 Can get star’s luminosity from apparent brightness! L =4πd2b 2 L d b = L⊙ d⊙ ! b⊙ A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—7/18 Distance to stars using brightness (3/4) Star #1 has twice the brightness of Star #2; Star #1 is at half the distance of Star #2 2 L1 d1 b1 2 = = (0.5) ×2=0.25×2=0.5 L2 d2 ! b2 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—8/18 Distance to stars using brightness (3/4) Star #1 has twice the brightness of Star #2; Star #1 is at half the distance of Star #2 2 L1 d1 b1 2 = = (0.5) ×2=0.25×2=0.5 L2 d2 ! b2 Star Q has the same luminosity as Proxima Centauri but has only 1/9 the brightness. How far is Star Q? 2 d1 (L1/L2) = d2 ! (b1/b2) d1 (L1/L2) 1 = v = =3 d2 u (b1/b2) s1/9 u t A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—8/18 Distance to stars using brightness (4/4) Stellar Luminosity Func- tion Take p larger than p∗ Observe apparent brightness of stars Compute number within volume of the sphere with radius d =1/p∗ A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—9/18 Magnitude scale Greek astronomer Hipparchus divided stars into six classes or magnitudes (2nd century BC) 1st magnitude is brightest, 6th magnitude is faintest A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—10/18 Magnitude scale Greek astronomer Hipparchus divided stars into six classes or magnitudes (2nd century BC) 1st magnitude is brightest, 6th magnitude is faintest Sensitivity of human eye is logarithmic Magnitude difference of 1 corresponds log(1000) 3 − to 2.5 log(F1/F2) log(100) 2 log(10) 1 log(1) 0 log(0.1) -1 log(0.01) -2 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—10/18 Magnitude scale Greek astronomer Hipparchus divided stars into six classes or magnitudes (2nd century BC) 1st magnitude is brightest, 6th magnitude is faintest Sensitivity of human eye is logarithmic Magnitude difference of 1 corresponds log(1000) 3 − to 2.5 log(F1/F2) log(100) 2 1 magnitude is factor 1001/5 =2.512 in log(10) 1 brightness log(1) 0 2 magnitudes is 2.512 × 2.512 log(0.1) -1 5 magnitudes is 100 log(0.01) -2 10 magnitudes is 100 × 100 = 10000 A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—10/18 Measuring colors of stars (1/3) Our perception of the color of star is telling us about the ratio of energy at different wavelengths Can get surface temperature of a star from its color A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—11/18 Measuring colors of stars (1/3) Our perception of the color of star is telling us about the ratio of energy at different wavelengths Can get surface temperature of a star from its color A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—11/18 Measuring colors of stars (1/3) Our perception of the color of star is telling us about the ratio of energy at different wavelengths Can get surface temperature of a star from its color A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—11/18 Measuring colors of stars (2/3) Astronomers use filters to measure brightness in specific ranges of wavelengths A typical scheme is three filters (UBV): 1. Ultraviolet 2. Blue 3. Visible A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—12/18 Measuring colors of stars (3/3) A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—13/18 Spectra of stars reveal temperature (1/2) Overall, stars have blackbody (thermal) spectra Relative strength of absorption lines is a sensitive probe of temperature A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—14/18 Spectra of stars reveal temperature (2/2) Overall, stars have blackbody (thermal) spectra Relative strength of absorption lines is a sensitive probe of temperature A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—15/18 Spectral classes A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—16/18 Inferring the size of stars (1/2) Use UBV photometry or spectral class to estimate temperature Recall: L =4πR2σT 4 2 4 For Sun:L⊙ =4πR⊙σT⊙ Ratio: 2 4 L R T = L⊙ ! R⊙ ! T⊙ ! Solve for radius: −2 R T L = R⊙ T⊙ ! sL⊙ A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—17/18 Inferring the size of stars (2/2) Example: Betelgeuse 4 L = 60, 000 (L⊙ =6 × 10 L⊙) T = 3500K (T⊙ = 5800K) Ratio of radii: −2 R 3500 2 = 6 × 104 =6.7 × 10 = 670 R⊙ 5800 q A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—18/18 Inferring the size of stars (2/2) Example: Betelgeuse 4 L = 60, 000 (L⊙ =6 × 10 L⊙) T = 3500K (T⊙ = 5800K) Ratio of radii: −2 R 3500 2 = 6 × 104 =6.7 × 10 = 670 R⊙ 5800 q 5 R⊙ =6.96 × 10 km 1AU =1.5 × 108km R = 670 × 6.96 × 105km =4.7 × 108km =3.1AU A114: Lecture 15—09 Mar 2007 Read: Ch. 19,20 Astronomy 114—18/18.