Transcript Light from stars part II

Light from Stars cont....
Motion of stars
Three types of spectra:
1) Blackbody – all solids, liquids and
gases radiate EM waves at all
wavelengths with a distribution of
energy over the wavelengths that
depends on temperature T
2) Absorption spectrum: result of
light comprising a continuous spectrum
passing through a cool, low density gas
3) Emission spectrum: result of a low
density gas excited to emit light. The
Light is emitted at specific wavelengths
Three types of spectra:
1) Blackbody – all solids, liquids and
gases radiate EM waves at all
wavelengths with a distribution of
energy over the wavelengths that
depends on temperature T
2) Absorption spectrum: result of
light comprising a continuous spectrum
passing through a cool, low density gas
3) Emission spectrum: result of a low
density gas excited to emit light. The
Light is emitted at specific wavelengths
How do we define ‘Brightness’?
Flux: the total light Energy emitted by one square meter of an
object every second
F (J/m2/s)
1m
1m
How do we define ‘Brightness’?
Luminosity: the total light Energy emitted by the whole surface area of an
object every second
L = Area × F (J/s)
Note: 1 J/s is 1 Watt (W)
e.g. Luminosity of Sun = 4πR2 × Flux
R
How do we define ‘Brightness’?
e.g. 100W light bulb has a surface area of about 0.01 m2
Flux = Luminosity/Area = 100 / 0.01 = 10,000 J/ m2/s
Stefan-Boltzmann law: Flux from a Black Body F = σT4
e.g. If a star were twice as hot as our
Sun, it would radiate 24 = 16 times as
much energy from every square
meter of the surface
Luminosity from a star’s surface L = 4πR2σT4
σ = 5.67 × 10-8 J/m2/s/degree4
Wien’s law: wavelength at which the star radiates most of
its energy is given by
λmax = 3,000,000/T
so long λmax as is measured
in nanometers (nm)
(1nm = 10-9m = 0.000000001m)
Given λmax we can calculate T from T = 3,000,000/ λmax
e.g. λmax = 1000nm gives T = 3,000,000/1000 = 3,000 K
The Photosphere
Hydrogen Spectral Lines
The Chromosphere
Corona/Upper Chromosphere Spectrum
Hydrogen Spectral Lines
Corona/Upper Chromosphere Spectrum
Hydrogen Spectral Lines
The Sun: G2
Million Dollar Question: Are two stars which look to have the same
brightness:
a) Actually the brightness and therefore same distance from our solar
system?
a) Different brightnesses, with the more bright star farther from our
solar system than the less bright star?
Brightness at a distance: the inverse square law
Brightness at a distance: the inverse square law
Increase the size of a sphere
from radius d to radius 2d:
Area increases from 4πd2 to
4π(2d)2 = 16 πd2 i.e. by a factor
of 22 = 4.
Therefore flux (light energy per
second per unit area) decreases
by a factor of 22 = 4.
Fobserver = F/ d2
Apparent Magnitude mv (How bright stars appear)
• First encountered written down in Ptolemy’s Almagest
(150 AD)
• Thought to originate with Hipparchus (120 BC)
• Stars classified by giving a number 1 - 6
• Brightest stars are class 1
• Dimmest stars visible to naked eye are class 6
• Class 1 is twice as bright as class 2, class 2 is twice as
bright as class 3, and so on.
• So class 1 is 26 = 64 times as bright as class 6
Apparent Magnitude mv (How bright stars appear)
• Refined in the 19th Century when instruments became
precise enough to accurately measure brightness
• Modern scale is defined so that 6th magnitude stars are
exactly 100 times brighter than 1st magnitude stars
• This means stars that differ in magnitude by 1 differ by
a factor of 2.512 (e.g. a 3rd magnitude star is 2.512 times
brighter than a 2nd magnitude star).
Absolute Magnitude Mv – How bright stars would appear
If they were all the same distance away
Absolute Magnitude and Luminosity
M1 – M2 = -2.5 log10(L1/L2)
Magnitudes and the Distance Modulus
mv – Mv = -5 + 5 log10(d)
Distance Modulus mv – Mv
0
1
2
3
4
5
6
7
8
9
10
15
20
d (pc)
10
16
25
40
63
100
160
250
400
630
1000
10,000
100,000
d in parsecs
Apparent
30
Absolute
Moon 31.5
Venus 30.14
20
Betelgeuse 0.8
Sirius -1.1
Barnard’s Star 9.5
Polaris 2.5
10
Alpha Centauri -1.1 0
Venus -4.4
-10
Moon -12.5
-20
Sun -26.5
-30
Barnard’s Star 13.24
Sun 4.83
Alpha Centauri 4.38
Sirius 1.4
Polaris -3.63
Betelgeuse -5.6
Motions of the Stars
Space Velocity can be decomposed into two perpendicular components
v
vt
vr
Proper Motion
vt = μ d
d
The Doppler Effect
The Doppler Effect