Stars
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Flux and Luminosity
Brightness of stars and the magnitude scale
Absolute magnitude and luminosity
Distance modulus
Temperature vs heat
Temperature vs color
Colors/spectra of stars
Flux and luminosity
• Luminosity - A star produces light – the total
amount of energy that a star puts out as light
each second is called its Luminosity.
• Flux - If we have a light detector (eye, camera,
telescope) we can measure the light produced
by the star – the total amount of energy
intercepted by the detector divided by the area
of the detector is called the Flux.
Flux and luminosity
• To find the luminosity, we take a shell
which completely encloses the star and
measure all the light passing through the
shell
• To find the flux, we take our detector at
some particular distance from the star and
measure the light passing only through the
detector. How bright a star looks to us is
determined by its flux, not its luminosity.
Brightness = Flux.
Flux and luminosity
• Flux decreases as we get farther from the star
– like 1/distance2
L
F
2
4D
Brightness of stars
• The brightness of a star is a measure of its flux.
• Ptolemy (150 A.D.) grouped stars into 6
`magnitude’ groups according to how bright they
looked to his eye.
• Herschel (1800s) first measured the brightness
of stars quantitatively and matched his
measurements onto Ptolemy’s magnitude
groups and assigned a number for the
magnitude of each star.
Brightness of stars
• In Herschel’s system, if a star is 1/100 as
bright as another then the dimmer star has
a magnitude 5 higher than the brighter one.
• Note that dimmer objects have higher
magnitudes
Little Dipper
(Ursa Minor)
Guide to naked-eye
magnitudes
Apparent Magnitude
Consider two stars, 1 and 2, with apparent magnitudes
m1 and m2 and fluxes F1 and F2. The relation between
apparent magnitude and flux is:
 F1 
m1  m2  2.5 log10  
 F2 
F1
m2  m1  / 2.5
 10
F2
For m2 - m1 = 5, F1/F2 = 100.
Flux, luminosity, and magnitude
L
F
2
4D
 F1 
m2  m1  2.5 log10  
 F2 
 L1 4D22 

m2  m1  2.5 log10 
2
 4D1 L2 
L2
D2
m2  m1  2.5 log10
 5 log10
L1
D1
Distance-Luminosity relation:
Which star appears brighter to the
observer?
Star 1
10L
L
Star 2
d
10d
Flux and luminosity
L2
 10
L1
D2
 10
D1
2
F2
L2 4D
L2  D1 
1





10

0
.
1


2
F1 4D2 L1
L1  D2 
 10 
2
1
2
Star 2 is dimmer and has a higher magnitude.
Flux and luminosity
L2
 10
L1
D2
 10
D1
L2
D2
m2  m1  2.5 log10
 5 log10
L1
D1
m2  m1  2.5 log10 10  5 log10 10
m2  m1  2.5  5  2.5
Star 2 is dimmer and has a higher magnitude.
Absolute magnitude
• The magnitude of a star gives it brightness
or flux when observed from Earth.
• To talk about the properties of star,
independent of how far they happen to be
from Earth, we use “absolute magnitude”.
• Absolute magnitude is the magnitude that a
star would have viewed from a distance of
10 parsecs.
• Absolute magnitude is directly related to
the luminosity of the star.
Absolute Magnitude and
Luminosity
The absolute magnitude of the Sun is M = 4.83.
The luminosity of the Sun is L = 3.861026 W.
4.83 M  / 2.5
L  L 10
 L 
M  4.83  2.5  log10  
 L 
Note the M includes only light in the visible band, so this is
accurate only for stars with the same spectrum as the Sun.
Absolute Magnitude
Absolute magnitude, M, is defined as
M  m  5 log10 D  5
where D is the distance to the star measured in parsecs.
For a star at D = 10 parsecs, 5log10 = 5, so M = m.
If we can figure out the absolute magnitude of a star, then
we can determine its distance using the apparent
magnitude. The “distance modulus is defined as
m  M  5 log10 ( D / 10 pc)
Is Sirius brighter or fainter than Spica:
(a) as observed from Earth [apparent magnitude]
(b) Intrinsically [luminosity]?
Sun
Which star would have the highest
magnitude?
1.
2.
3.
4.
Star A - 10 pc away, 1 solar luminosity
Star B - 30 pc away, 3 solar luminosities
Star C - 5 pc away, 0.5 solar luminosities
Star D - Jennifer Lawrence
Stars: Temperature and Color
• Temperature vs heat
• Temperature vs color
• Colors/spectra of stars
Temperature
lower T
higher T
• Temperature is proportional to the average kinetic
energy per molecule
1 2 3
K  mv  kT
2
2
k = Boltzmann constant =
1.3810-23 J/K = 8.6210-5 eV/K
Temperature vs. Heat
lower T
higher T
• Temperature is proportional
to the average kinetic
energy per molecule
• Heat (thermal energy) is
proportional to the total
kinetic energy in box
less heat
same T
more heat
Wien’s law
• Cooler objects produce radiation which peaks
at lower energies = longer wavelengths =
redder colors.
• Hotter objects produce radiation which peaks
at higher energies = shorter wavelengths =
bluer colors.
• Wavelength of peak radiation:
Wien Law max = 2.9 x 106 / T(K) [nm]
A object’s color depends on its
surface temperature
• Wavelength of peak radiation:
Wien Law max = 2.9 x 106 / T(K) [nm]
What can we learn from a
star’s color?
The color indicates the temperature of the
surface of the star.
Observationally, we measure colors by
comparing the brightness of the star in two
(or more) wavelength bands.
U
B
V
This is the same way your eye determines color, but
the bands are different.
Use UVRI filters to
determine apparent
magnitude at each color
The ratio of fluxes in two bands translates to the difference
in magnitudes, or a color, e.g. B – V = mB – mV.
Stellar temperature follow an approximate, empirical
relation: T ~ 9000 K/[(B-V) + 0.93]
The spectrum of a star is
primarily determined by
1.
2.
3.
4.
The temperature of the star’s surface
The star’s distance from Earth
The density of the star’s core
The luminosity of the star
Stars are assigned a `spectral
type’ based on their spectra
• The spectral classification essentially
sorts stars according to their surface
temperature.
• The spectral classification can also use
spectral lines.
Spectral type
• Sequence is: O B A F G K M
• O type is hottest (~25,000K), M type is coolest
(~2500K)
• Star Colors: O blue to M red
• Sequence subdivided by attaching one numerical
digit, for example: F0, F1, F2, F3 … F9 where F1
is hotter than F3 . Sequence is O … O9, B0, B1,
…, B9, A0, A1, … A9, F0, …
• Useful mnemonics to remember OBAFGKM:
– Our Best Astronomers Feel Good Knowing More
– Oh Boy, An F Grade Kills Me
– (Traditional) Oh, Be a Fine Girl (or Guy), Kiss Me
Question
• Which is cooler, a star with spectral type G2
or a star with spectral type A6?
Classifying stars
• We now have two properties of stars
that we can measure:
– Luminosity
– Color/surface temperature
• Using these two characteristics has
proved extraordinarily effective in
understanding the properties of stars –
the Hertzsprung-Russell (HR) diagram
HR diagram
Absolute Bolometric Magnitude
and Luminosity
The bolometric magnitude includes radiation at all
wavelengths.
The absolute bolometric magnitude of the Sun is
Mbol = +4.74.
M bol
 L 
 4.74  2.5  log10  
 L 
Bolometric Correction
It is difficult to measure the radiation from a star at all
wavelengths. However, if one knows the temperature and
the magnitude in one band, then one can integrate the
blackbody spectrum over all wavelengths.
We typically estimate the bolometric magnitude using the
V-band magnitude and a color to estimate the temperature.
“Bolometric correction” = BC = Mbol - MV.