Transcript 02blackbodiesx

Magnitudes and Filters

Astronomical magnitude system dates back ~2100 y ago to
Hipparchus

Defined their flux in terms of apparent magnitudes (m), where the
brightest stars were first magnitude (m=1) and the faintest stars visible
to the naked eye were sixth magnitude (m=6).

numerically, smaller magnitudes are brighter!

The magnitude scale was originally defined by eye, but the eye is a
notoriously non-linear detector, especially at low light levels. So a star
that is two magnitudes fainter than another is not twice as faint, but
actually about 6 times fainter (6.31 to be exact).

magnitude is a logarithmic scale!
Modern definitions

A difference of 5 magnitudes is
equivalent to a factor of 100 in flux.
M1 – M2 = 2.5 log (F2 / F1)

A star will have the same apparent
magnitude (m) and absolute
magnitude (M) if it is located 10 pc
away.
m – M = 5 log dpc - 5
Blackbody Radiation

A blackbody is something that absorbs all radiation that
shines on it

Are all blackbodies black?
-
-
no!!
imagine a box full of lava
A constant temperature
blackbody
(a.k.a. a very precise oven)
Order your own
blackbody online
Blackbodies and Astronomy

Stars are very similar to blackbodies


emit a continuous spectrum of radiation
Why aren’t they black?


Blackbodies emit light at all wavelengths
Cooler blackbodies emit more red than blue light.
2 h
I (T ) d  2 h / kT
d
c e
1
3
2hc / 
I  (T ) d 
d
exp(hc / kT )  1
2
5
Planck
Function
Iν(T) is the specific intensity, depends on T and ν
T is temp in Kelvin (Kelvin = Celsius + 273.2)
h is Planck’s constant: 6.636 x 10-34 J s
k is Boltzmann’s constant 1.38 × 10-23 m2 kg s-2 K-1
c is the speed of light
Rayleigh Jeans Limit

At low frequencies, hν << kT so the
Planck function can be approximated as
2kT 2
I (T ) d 
d
2
c
I  (T ) d 
2ckT

4
d
Properties of the Planck Law
• Wien Displacement Law: m T = b, where m is
the wavelength at which I peaks, and b
(=0.0029 m K) is a constant.
Alternatively, νm / T = 5.88 x 10
frequency at which Iν peaks.
Note that
m m  c
10
Hz K-1, where νm is the

The peak wavelength of a blackbody spectrum
is inversely proportional to temperature:
Wien’s
Law
Temperatures of
stars and
planets are
measured using
Wien’s law.
Properties of the Planck Law

Stefan-Boltzmann law: F = sT ,
where F is the total radiated power
per unit area (W per square m) and
s is the Stefan-Boltzmann constant:
5.67 x 10-8 W m-2 K-4.
4
Stefan-Boltzmann Law:

Hotter blackbodies emit more total energy

notice the area under the blackbody curve:
5000 K
4000 K


A perfect blackbody produces a continuous spectrum:
Dark lines in solar spectrum are from absorption by Sun’s
outer atmosphere
Emission Line Spectra

Take a thin cloud of gas composed of a pure element
(e.g. hydrogen) and heat it to high temperature


It does not emit a continuous spectrum.
It emits light at specific wavelengths:

the exact same ones at which it absorbs
The role of density

If thin gases produce only emission
lines, and the Sun is made of gas, why
does the Sun’s spectrum look
continuous (like a rainbow?)
Solar spectrum
http://astro.unl.edu/animationsLinks.html
Low-density
A high-density gas cloud produces a continuous spectrum
Spectrum (Fλ) of the Star Vega
Spectrum (Fλ) of the Star Vega
Color Index
Taking the
difference in
magnitudes
(e.g., mB –
mV) using two
different
filters gives a
crude
measure of a
star’s
temperature
http://astro.unl.edu/classaction/animations/light/bbexplorer.html