Light and Stars ASTR 2110 Sarazin

Doppler Effect Frequency and wavelength of light changes if source or observer move

Doppler Effect v r dr radial velocity dt > 0 moving apart < 0 moving toward

Doppler Effect s λ em v r em obs λ obs = λ em + s = λ em + v r P em P em =1/ν em =1/(c /λ em ) = λ em /c Recall ν = c /λ λ obs λ em 1+ v r /c ν obs ν em / 1+ v r /c ( ) ( ) ν em ( 1 v r /c) approximate, assuming : v << c

Doppler Effect (Cont.) Time Dilation Δt obs = Δt em 1 v 2 /c 2 for radial motion v = v r # of waves emitted = νδt ν obs Δt obs = ν em Δt em ν obs = ν em 1 v r 2 /c 2 /(1+ v r /c) ν obs = ν em 1 v r /c 1+ v r /c λ obs = λ em 1+ v r /c 1 v r /c

Redshift z λ obs λ em redshift λ em z v r /c for v << c > 0 moving apart (redshift) < 0 moving toward (blueshift)

Doppler Effect - Summary v r dr radial velocity dt for radial motion ν obs = ν em 1 v r /c 1+ v r /c λ obs = λ em 1+ v r /c 1 v r /c for v << c, only depends on v r ( ) ( ) ν obs ν em 1 v r /c λ obs = λ em 1+ v r /c

Observed Properties of Stars ASTR 2110 Sarazin

Extrinsic Properties Location Motion kinematics

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

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

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

Distances - Parallax Earth travels around Sun è we view stars from different angles The stars will appear to shift back and forth every year

π Parallax

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

Parallax sinπ (rad) = AU d, π (rad)<<1 π (rad) = AU d 1 rad = 206,265!! (arcsec) π!! = 206265 AU d Define 1 pc 206265 AU = 3.09 10 18 cm = parsec π!! = 1, d pc = 1 d pc π!! AU d π

Parsec Basic unit of distance in astronomy parsec = 2.06 x 10 5 AU = 3.09 x 10 18 cm = 3.26 light years AU = 1.50 x 10 13 cm Memorize

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

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

Radial Velocity, Doppler Shift v r > 0 è distance increases Measured by Doppler Shift z λ obs λ 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

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

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

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

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 t / d, both ~ 1 / d Can only easily detect for nearby stars, < 100 pc, from Earth

Intrinsic Properties of Stars

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

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

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 )

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 = 2.5 0.3 = 0.75 m = m 0.75 =10 0.75 = 9.25 mag a b

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 =10 0.4 Δm =10 0.4 ( 3.1) =10 1.24 =17 S C

Magnitudes

Stellar Colors

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

Color Filters for Observing

Stellar Colors Stars 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,

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

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

Stellar Temperatures Range from T 3000 K to 100,000 K (brown dwarfs, planets cooler; some stellar corpses hotter)

Stellar Temperatures

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

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

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

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

Luminosity & Absolute Magnitude From distance to Sun (AU) and flux M bol ( ) = +4.74 L = 3.845 x 10 33 erg/s = 3.845 x 10 26 J/s = W M bol = 4.74 2.5 log(l/l ) Memorize Note: = astronomical symbol for Sun

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

Basic Numbers of Astronomy Memorize

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

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

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)