Light and Stars
ASTR 2110


Sarazin


Doppler Effect Frequency and wavelength of light

changes if source or observer move

Doppler Effect

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vr ≡drdt≡ radial velocity

> 0 moving apart < 0 moving toward

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

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

Redshift

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z ≡ λobs −λemλem

redshift

z ≈ vr /c for v 0 moving apart (redshift) < 0 moving toward (blueshift)

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

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

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

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

Parallax

π

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

sinπ (rad) = AUd

, π (rad)

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

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

Extrinsic Properties Location Motion

Separate into two components vr = radial velocity

changes distance vt = tangential velocity

changes angle

vr

v vt

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

Tangential Velocity
Proper Motion

vt è RA, Dec (angles) change

tanΔθ = s / d = vt Δtd

d

s = vt Δt Δθ

Tangential Velocity:
Proper Motion

tanΔθ = s / d = vt Δtd

, Δθ

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

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

Intrinsic Properties of Stars

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

Magnitudes

Hipparchus 1)  Classified stars by

brightness, brighter = 1st magnitude, … 6th magnitude

2)  Used eyes, human senses logarithmic

Magnitudes è go backwards, logarithmic

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 )

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

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

Magnitudes

Stellar Colors

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: FU, FB, FV, … Magnitudes: mU = U, mB = B, mV = V, …

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

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

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

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

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

mbol

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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m−M = −2.5log 10dpc

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--= −5log 10 / dpc( )

m−M = 5logdpc − 5≡ distance modulus

Luminosity &
Absolute Magnitude

m−M = 5logdpc − 5≡ distance modulusM =m− 5logdpc + 5

=m+ 5log ##π + 5

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

Stellar Luminosities

Very wide range 10-4 L ≤ L ≤ 106 L

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Basic Numbers of Astronomy

Memorize

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

Stellar Radii Measure flux F, distance d è L Measure color èTeff (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(Earth)

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