Observed Properties of Stars - 2 ASTR 2120 Sarazin

Observed Properties of Stars - 2 ASTR 2120 Sarazin

Properties Location Distance Speed Radial velocity Proper motion Luminosity, Flux Magnitudes

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

Stellar Colors Star 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 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,

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) (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

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

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)

Binary Stars ASTR 2120 Sarazin Albereo (β Cygni) Binary Star System

Types of Binary Stars Many types, here concentrate on main ones Visual Binaries: See the stars orbit, separate stars far apart, binary close to Earth Spectroscopic Binaries: See moving spectra lines from one or both stars (Doppler effect) stars close together, any distance from Earth Eclipsing Binaries: Periodic changes in brightness, stars block one another stars close together, seen along orbital plane

Visual Binaries See stars orbit one another

Determining Masses Kepler s 3 rd M P yr2 = a AU3 / ( M tot / ) M [( M 1 + M 2 ) / ] = a AU3 P yr 2 a 1 / a 2 = a 1 / a 2 = M 2 / M 1

Determining Masses Example: a 1 = 1, a 2 = 4, π = 0.1, P = 100 yr, i = 0 o Masses? a = 5, a AU = a / π = 5 / 0.1 = 50 AU (M 1 + M 2 ) = a AU3 / P yr2 = (50) 3 / (100) 2 = 12.5 M 1 /M 2 = a 2 / a 1 = 4 / 1 = 4 M 1 = 10 primary, M 2 = 2.5 secondary M M M

Stellar Masses Narrower range than luminosity Roughly, 0.1 M < M < 100 M Lower masses: brown dwarfs, planets

Mass Luminosity Relation Main Sequence Stars: (Normal stars) (L / ) ~ (M / ) 3 Also L (R / ) ~ (M / ) 0.75 R (T eff /6000 K) M M M ~ (M / ) 0.4 Doesn t work for giants, supergiants, white dwarfs WDs Giants

Masses in Astronomy Mass = total amount of matter in an object Really, really want to know Mass è Gravity è motions of nearby things Method to determine mass in Astronomy Planets, Sun, moons, Stars Star clusters Galaxies Clusters of Galaxies The Universe

Visual Binaries: Types of Binary Stars Spectroscopic Binaries: See moving spectra lines from one or both stars (Doppler effect) Eclipsing Binaries:

Spectroscopic Binaries

Spectroscopic Binaries See moving spectra lines (Doppler effect) Single-lined or Double-lined Velocity Curve: Assume v << c z = Δλ / λ = v r (t)/c v r (t) = velocity curve (usually in km/s)

i y x W

Spectroscopic Binaries See moving spectra lines (Doppler effect) Single-lined or Double-lined Velocity Curve: Assume v << c Δλ / λ = v r (t)/c v r (t) = velocity curve (usually in km/s) v r (t) = v x (t) sin i

Spectroscopic Binaries v r (t) = v x (t) sin i Example: i = 90 o (edge-on), circular orbit v r (t) = v orb sin(2πt / P) sinusoidal velocity curve v orb = 2 π a / P

i y x W

Spectroscopic Binaries General case: i 90 o, e 0, Ω e, Ω è change shape of velocity curve, not sinusoidal v r time

Spectroscopic Binaries General case: i 90 o, e 0, Ω e, Ω è change shape of velocity curve, not sinusoidal Determine e, Ω from shape of velocity curve Inclination i? v r (t) = v x (t) sin i Just change all velocities by a constant factor Cannot be determined from observations!!