light and stars astr 2110 sarazin - university of...
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Light and Stars ASTR 2110
Sarazin
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Doppler Effect Frequency and wavelength of light
changes if source or observer move
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Doppler Effect
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vr ≡drdt≡ radial velocity
> 0 moving apart < 0 moving toward
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Doppler Effect
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λobs = λem + s = λem + vrPemPem =1/νem =1/(c /λem ) = λem /cRecall ν = c /λλobs ≈ λem 1+ vr /c( )νobs ≈ νem / 1+ vr /c( ) ≈ νem 1− vr /c( )approximate, assuming : v
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Doppler Effect (Cont.)
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Time Dilation
Δtobs = Δtem 1− v2 /c2
for radial motion v = vr# of waves emitted = νΔtνobsΔtobs = νemΔtem
νobs = νem 1− vr2 /c2 /(1+ vr /c)
νobs = νem1− vr /c1+ vr /c
λobs = λem1+ vr /c1− vr /c
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Redshift
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z ≡ λobs −λemλem
redshift
z ≈ vr /c for v 0 moving apart (redshift) < 0 moving toward (blueshift)
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Doppler Effect - Summary
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vr ≡drdt≡ radial velocity
for radial motion
νobs = νem1− vr /c1+ vr /c
λobs = λem1+ vr /c1− vr /c
for v
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Observed Properties of Stars ASTR 2110
Sarazin
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Extrinsic Properties
Location Motion
“kinematics”
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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
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Extrinsic Properties Location
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
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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
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Distances - Parallax Earth travels around Sun è we view stars
from different angles The stars will appear to shift back and
forth every year
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Parallax
π
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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
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sinπ (rad) = AUd
, π (rad)
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Parsec
Basic unit of distance in astronomy parsec = 2.06 x 105 AU = 3.09 x 1018 cm = 3.26 light years AU = 1.50 x 1013 cm
Memorize
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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
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Extrinsic Properties Location Motion
Separate into two components vr = radial velocity
changes distance vt = tangential velocity
changes angle
vr
v vt
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Radial Velocity, Doppler Shift vr > 0 è distance increases Measured by Doppler Shift z ≡λobs −λemλem
redshift or Doppler shift
z > 0→moving awayfor v
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Tangential Velocity Proper Motion
vt è RA, Dec (angles) change
tanΔθ = s / d = vt Δtd
d
s = vt Δt Δθ
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Tangential Velocity: Proper Motion
tanΔθ = s / d = vt Δtd
, Δθ
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Parallax + Proper Motion vorb (Earth) = 30 km/s v (nearby stars) ~
20 km/s Proper motion (1 year)
~ parallax Parallax, periodic 1
year, east-west Proper motion
continuous
μ
π
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Distance Dependence
Doppler shift: z = vr / c Independent of distance!! Can do across whole Universe
Proper motion, parallax π = 1 / dpc , μ = vt / d, both ~ 1 / d
Can only easily detect for nearby stars, < 100 pc, from Earth
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Intrinsic Properties of Stars
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Luminosity and Flux L = luminosity = energy / time from star
(erg/s) “Brightness” = flux F = energy / area / time
at Earth (erg/cm2/s)
“inverse square law”
F = L4πd 2
L = 4πd 2F
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Magnitudes
Hipparchus 1) Classified stars by
brightness, brighter = 1st magnitude, … 6th magnitude
2) Used eyes, human senses logarithmic
Magnitudes è go backwards, logarithmic
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Magnitudes
Write as 1 .m
3 or 1.3 mag5 mag = factor of 100 fainter2.5 mag = factor of 10 fainter (1 order of magnitude)Two stars, fluxes F1, F2F1 / F2 =10
−(m1−m2 )/2.5 =10−0.4(m1−m2 )
m1 −m2 = −2.5log(F1 / F2 )(log ≡ log10 , ln ≡ loge )
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Examples - 1 Two stars, a is twice as bright as bmb =10 mag. What is ma ?Fa / Fb = 2ma −mb = −2.5log(Fa / Fb ) = −2.5log(2)
= −2.5•0.3= −0.75ma =mb − 0.75=10− 0.75= 9.25 mag
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Examples - 2
Sirius is -1.5 mag, Castor is 1.6 mag. Which isbrighter, and by what factor?Brighter → smaller mag → SiriusΔm = −3.1FS / FC =10
−0.4•Δm =10−0.4•(−3.1) =101.24 =17
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Magnitudes
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Stellar Colors
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Stellar Colors
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Stellar Colors
Stars vary in color: Betalgeuse red, Sun yellow, Vega blue-white
Use filters to get flux in one color, compare
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Color Filters for Observing
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Stellar Colors
Stars vary in color: Use filters to get flux in one color,
compare Fluxes: FU, FB, FV, … Magnitudes: mU = U, mB = B, mV = V, …
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Stellar Colors
Color index, or just “color” CI = B – V, …
Note: Given B – V è fixed FB / FV Just measures shape of spectrum, not
total flux Independent of distance
Just gives color
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Temperature & Color
Color mainly determined by temperature of stellar surface
Stellar spectra ~ black body λmax ≈ 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
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Temperature & Color
Color mainly determined by temperature of stellar surface
Stellar spectra ~ black body λmax ≈ 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
Solar spectrum vs. BB
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Temperature & Color
Color mainly determined by temperature of stellar surface
Stellar spectra ~ black body λmax ≈ 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
Solar spectrum vs. BB
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Stellar Temperatures
Range from T ≈ 3000 K to 100,000 K (brown dwarfs, planets cooler; some
stellar corpses hotter)
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Stellar Temperatures
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Bolometric Magnitude
Hard to measure all light from star, but
Bolometric magnitude è magnitude based on total flux
mbol
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Luminosity & Absolute Magnitude
Absolute magnitude M = magnitude if star moved to d = 10 pc
F = L4πd 2
L = 4πd 2F
F = L4πd 2
FF10
=10dpc
!
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Luminosity & Absolute Magnitude
F = L4πd 2
FF10
=10dpc
!
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2
m−M = −2.5log 10dpc
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+
,
--= −5log 10 / dpc( )
m−M = 5logdpc − 5≡ distance modulus
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Luminosity & Absolute Magnitude
m−M = 5logdpc − 5≡ distance modulusM =m− 5logdpc + 5
=m+ 5log ##π + 5
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Luminosity & Absolute Magnitude
From distance to Sun (AU) and flux Mbol(¤) = +4.74 L = 3.845 x 1033 erg/s = 3.845 x 1026 J/s = W Mbol = 4.74 − 2.5 log(L/L ) Note: ¤= astronomical symbol for Sun
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Memorize
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Stellar Luminosities
Very wide range 10-4 L ≤ L ≤ 106 L
¤ ¤
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Basic Numbers of Astronomy
Memorize
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Stellar Radii For BB, L = (area) σ T4 = 4π R2 σ T4 σ = 5.67 x 10-5 erg/cm2/s/K4 Stefan-Boltzmann constant
Define effective temperature Teff such that L = 4π R2 σ Teff4
If BB, then T = Teff
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Stellar Radii Measure flux F, distance d è L Measure color èTeff (estimate) Solve for radius R
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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(Earth)
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