Observed Properties of Stars ASTR 2120 Sarazin

Transcription

1 Observed Properties of Stars ASTR 2120 Sarazin

2 Extrinsic Properties Location Motion kinematics

3 Extrinsic Properties Location Use spherical coordinate system centered on Solar System Two angles (θ,φ) Right Ascension (α = RA) Declination (δ = Dec) (review in Chapt. 1) easy to measure accurately

4

5 Location Extrinsic Properties Use spherical coordinate system (r,θ,φ) centered on Solar System Two angles (θ,φ) Right Ascension (α = RA) Declination (δ = Dec) Radius r = distance d Very hard to measure

6 Distances Key Measurement Problem Celestial Sphere Astronomical objects are so far away, we have no ability to judge depth Stars which appear close on the sky can be very far apart

7 Distances - Parallax Earth travels around Sun è we view stars from different angles The stars will appear to shift back and forth every year (Review: Secs. 2.2, 2.6.2)

8 π Parallax

9 Parallax Earth travels around Sun è we view stars from different angles The stars will appear to shift back and forth every year Effect decreases with increasing distance

10 Parallax sinπ (rad) = AU d, π (rad)<<1 π (rad) = AU d 1 rad = 206,265!! (arcsec) π!! = AU d Define 1 pc AU = cm = parsec π!! = 1, d pc = 1 d pc π!! AU d π

11 Parsec Basic unit of distance in astronomy parsec = 2.06 x 10 5 AU = 3.09 x cm = 3.26 light years AU = 1.50 x cm Memorize

12 Parallax Example: Nearest star Proxima Centauri d = 1.3 pc è π = 0.77 arcsec Spatial resolution of telescopes, seeing 1 arcsec So, very hard to center images < 0.01 Can only determine parallax, distance for relatively nearby stars, d << 100 pc

13 Extrinsic Properties Location Motion Separate into two components v r v r = radial velocity changes distance v t = tangential velocity changes angle v t v

14 Radial Velocity, Doppler Shift v r > 0 è distance increases Measured by Doppler Shift z λ λ obs em redshift or Doppler shift λ em z > 0 moving away for v << c, (true of all Milky Way stars) z v r / c v r = zc review?

15 Tangential Velocity Proper Motion v t è RA, Dec (angles) change Δθ d s = v t Δt tanδθ = s / d = v t Δt d

16 Tangential Velocity: Proper Motion tanδθ = s / d = v t Δt d Δθ = s / d = v Δt t d, Δθ <<1 radian, tanδθ Δθ Define "proper motion" µ dθ dt Δθ Δt µ = v t d measured in "/yr

17 Parallax + Proper Motion v orb (Earth) = 30 km/s v (nearby stars) ~ 20 km/s Proper motion (1 year) ~ parallax Parallax, periodic 1 year, east-west Proper motion continuous π μ

18 Distance Dependence Doppler shift: z = v r / c Independent of distance!! Can do across whole Universe Proper motion, parallax π = 1 / d pc, μ = v r / d, both ~ 1 / d Can only detect for nearby stars, < 100 pc

19 Parallax and Proper Motion Tough measurements from Earth due to seeing Adaptive Optics Observe from Space: Small field of view Hubble Space Telescope GAIA 1 billion stars observed 70x each in 5 years Positions accurate to 24 micro-arcsec Radial velocities for 150 million stars

20 GAIA

21 Intrinsic Properties of Stars

22 Luminosity and Flux L = luminosity = energy / time from star (erg/s) Brightness = flux F = energy / area / time at Earth (erg/cm 2 /s) F = L 4πd 2 inverse square law L = 4πd 2 F

23 Magnitudes Hipparchus 1) Classified stars by brightness, brighter = 1 st magnitude, 6 th magnitude 2) Used eyes, human senses logarithmic Magnitudes è go backwards, logarithmic

24 Magnitudes Write as 1 ṃ 3 or 1.3 mag 5 mag = factor of 100 fainter 2.5 mag = factor of 10 fainter (1 order of magnitude) Two stars, fluxes F 1, F 2 F 1 / F 2 =10 (m 1 m )/2.5 2 =10 0.4(m 1 m 2 ) m 1 m 2 = 2.5log(F 1 / F 2 ) (log log 10, ln log e )

25 Examples - 1 Two stars, a is twice as bright as b m =10 mag. What is m? b a F / F = 2 a b m m = 2.5log(F / F ) = 2.5log(2) a b a b = = 0.75 m = m 0.75 = = 9.25 mag a b

26 Examples - 2 Sirius is -1.5 mag, Castor is 1.6 mag. Which is brighter, and by what factor? Brighter smaller mag Sirius Δm = 3.1 F / F = Δm = ( 3.1) = =17 S C

27 Magnitudes

28 Stellar Colors

29 Stellar Colors

30 Stellar Colors Star vary in color: Betalgeuse red, Sun yellow, Vega blue-white Use filters to get flux in one color, compare

31 Color Filters for Observing

32 Stellar Colors Star vary in color: Use filters to get flux in one color, compare Fluxes: F U, F B, F V, Magnitudes: m U = U, m B = B, m V = V,

33 Stellar Colors Color index, or just color CI = B V, Note: Given B V è fixed F B / F V Just measures shape of spectrum, not total flux Independent of distance Just gives color

34 Temperature & Color Color mainly determined by temperature of stellar surface Stellar spectra ~ black body λ max 0.3 cm / T (Wiens Law) (Review: Sec. 5.7) Higher T è shorter λ è bluer light Hot stars blue, B V negative Cool stars red, B V positive Solar spectrum vs. BB

35 Stellar Temperatures Range from T 3000 K to 50,000 K (brown dwarfs, planets cooler, some stellar corpses hotter)

36 Stellar Temperatures

37 Bolometric Magnitude Hard to measure all light from star, but Bolometric magnitude è magnitude based on total flux m bol

38 Luminosity & Absolute Magnitude F = L 4πd 2 L = 4πd 2 F Absolute magnitude M = magnitude if star moved to d = 10 pc F = L 4πd 2 F! = 10 # F d 10 " pc $ & % 2

39 Luminosity & Absolute Magnitude F = L 4πd 2 F! = 10 # F d 10 " pc (! m M = 2.5log* 10 *# " d ) pc $ & % 2 +, $ & % = 5log ( 10 / d ) pc m M = 5logd pc 5 distance modulus

40 Luminosity & Absolute Magnitude m M = 5logd pc 5 distance modulus M = m 5logd pc + 5 = m + 5log ## π + 5

41 Luminosity & Absolute Magnitude From distance to Sun (AU) and flux M bol ( ) = L = x erg/s = x J/s = W M bol = log(l/l ) Memorize

42 Stellar Luminosities Very wide range 10-4 L L 10 6 L

43 Basic Numbers of Astronomy Memorize

44 For BB, Stellar Radii L = (area) σ T 4 = 4π R 2 σ T 4 σ = 5.67 x 10-5 erg/cm 2 /s/k 4 Stefan-Boltzmann constant Define effective temperature T eff such that L = 4π R 2 σ T eff 4 If BB, then T = T eff

45 Stellar Radii Measure flux F, distance d è L Measure color èt eff (estimate) Solve for radius R

46 Stellar Radii Find mainly three sets of radii Normal Stars: main sequence, dwarfs 0.1 R < R < 20 R sequence: small, cool, faint è big, hot, bright Giants: R > 100 R ~ AU cool, T ~ 3000 K White Dwarfs: R 0.01 R ~ R(Earth)