Transcript Blackbody Radiation

3671 MWA Lecture 2
• In this lecture we will review:
– Attenuation of radiation by matter
– Optical Depth tl
– Mean free path
– Blackbody radiation
– Wien displacement law
• (how to measure the wavelength a BB emits
most of its energy at)
– Stefan-Boltzmann Law
• Flux is proportional to T4
Dr. Matt Burleigh
Optical Depth tl
• Il = Il0 e-tl
• E.G. a ray travelling through a star’s
atmosphere
• If ray starts at an optical depth tl=1 then
its intensity will decline by a factor e-1
before escaping the star
• Usually we choose tl = 0 to represent
the top of a star’s atmosphere
Dr. Matt Burleigh
Optical Depth tl
• Optical depth can be thought of as the number of
mean free paths from a particle’s original position,
measured along its path
• If tl>>1, then cylinder of gas or dust is considered
optically thick
• If tl<<1, then cylinder of gas or dust is considered
optically thin
• Since tl is wavelength-dependent, the dust or gas
may be optically thick at one wavelength and thin at
another
– Dust blocks optical light but we can see through some of it in
the infra-red
– Earth’s atmosphere is optically thin in the visible (we see
stars) but optically thick at X-rays (we detect none from the
ground)
Dr. Matt Burleigh
Blackbody Radiation
• A blackbody is an ideal emitter – an object that absorbs all
light energy incident upon it & re-radiates it with a
characteristic spectrum
• This radiation is called Blackbody radiation
• Stars & planets are blackbodies, to a rough approximation
• A blackbody of temperature T emits a continuous spectrum
which peaks at lmax
• lmax moves to shorter l with increasing T
• See Carroll & Ostlie Ch3.4 P.75 “Blackbody Radiation”
Dr. Matt Burleigh
Wien Displacement Law
lmaxT = 2.9x106nm.K
Example
Coronae
O star
G star
(sun)
M star
Hot dust
Earth
Dr. Matt Burleigh
Temp(K)
106
30,000
6,000
lmax
1keV
1000A
5000A
Regime
X-ray
UV
Optical
3,000
1,500
300
1mm
2mm
10mm
Near-IR
Near-IR
Mid-IR
Other emission processes
• BB radiation is a thermal process
– In thermodynamic equilibrium with surroundings
• Brehmstrahlung – thermal
– “braking radiation”
– Free electron experiences a deceleration when it collides with a
positive ion, and radiates energy
• Synchrotron – non-thermal
– Electron spinning in a magnetic field
– Seen in e.g. Crab Nebula (pulsar has large B field)
• Electron/photon scattering – non-thermal
• Inverse Compton scattering – non-thermal
– Collision of relativistic electron with a photon
– Photon energy changes
• To learn more about emission processes, attend Graham
Wynn’s “Interaction of radiation with matter” course
Dr. Matt Burleigh
Summary of lecture 2
• From today’s lecture you will need to
– Understand concept of Optical Depth (and
derive I=I0e-t)
– Understand Blackbody radiation
– Remember Wien Law and how to use it
 lmaxT = 2.9x106 nm.K
– Remember Stefan-Boltzmann Law
• F = sT4 and L=4pR2sT4
– No need to derive Wien or SB Laws, just remember,
understand and know how/when to use!
Dr. Matt Burleigh