Radiative Processes - WordPress.com · Textbook: “Radiative Processes in Astrophysics” ......
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Radiative Processes
LecturerAlessandro Patruno
Lecturer
Office #468
High Energy Astrophysics, Black Holes, Neutron Stars
Yvette Welling Valeriya Korol
Teaching Assistant Teaching [email protected] [email protected]
Cosmology Gravitational waves and binary mergers
Teaching Assistants
Website and Course Material
https://apatruno.wordpress.com/teaching/rp-2016/
Textbook: “Radiative Processes in Astrophysics” (Rybicki & Lightman)
Other books and interesting material:
- “Radiative Processes in High Energy Astrophysics” (2nd edition) (Free book)( http://www.brera.inaf.it/utenti/gabriele/total.pdf )
- “Essential Radio Astronomy”, J. J. Condon and S. M. Ransom http://www.cv.nrao.edu/course/astr534/ERA.shtml
- “Topics in High-Energy Astrophysics”, Jeremy Goodman, Princeton University Observatorywww.astro.princeton.edu/~jeremy/heap.pdf
Lectures and Exercises
Tests: open questions and multiple choice. The maximum time for this open test is 15 minutes. The test is a “closed book” test, i.e., lecture notes and books are NOT allowed
Lectures: every Monday 11:15-13:00Last lecture: December 5Last werkcollege: November 30Vragenuur: December 7Exam: December 16, 14:00-17:00
Werkcollege: Wednesday 9:00 – 10:45 The tests are done at the beginning of each werkcollege.
Check the lecture/werkcollege scheule: http://www.physics.leidenuniv.nl/images/institute/education/bachelor/2016-2017/Bachelorrooster_jaar3NA2016-2017.pdf
Rules● Each Monday there is a lecture and each Wed. there is a werkcollege. ● At the beginning of each werkcollege there is a test (15 minutes in total) where
you will be asked about the material covered in the lecture of the Monday of the same week.
● The tests are graded. The grade you obtain counts for 30% of the total final score (30% tests and 70% final exam). If in the final exam you get a better score than in the test, then you get 100% of the grade from the final exam.
● You can skip only 1 test. If you skip more than 1 test all the other skipped tests will count as if you scored 0. (So, if you skip two tests you will get one zero, if you skip three tests you will get two zeros, etc...).
● If you skip NO test, then we will calculate the average of your best 10 scores out of 11.
● You're not obliged to take the tests, but you're strongly encouraged to do so. ● The final written exam is based on material covered in the werkcollege, so you
are strongly encouraged to do the homeworks.
● Re-take: The same identical rules of the final exam apply for the retake.
● IMPORTANT: THERE IS NO CAVEAT to the above rules.
Course Topic 2015
Radiative processes are those physical processes that involve emission, absorption, and/or scattering of electromagnetic radiation.
Course Topic 2016
Radiative processes are those physical processes that involve emission, absorption, and/or scattering of electromagnetic and gravitational radiation.
Thermal and Blackbody Radiation
0
50
100
150
200
250
300
350
400
2 4 6 8 10 12 14 16 18 20 22
Inte
nsity
[MJy
/sr]
Frequency [1/cm]
Cosmic Microwave Background Spectrum from COBE
COBE DataBlack Body Spectrum
ALMA is an array of microwave telescopes in Chile. It has an unprecedented sensitivity in this area of the electromagnetic spectrum.
HL Tauri is a T-Tauri star(pre-main sequence stars)with a huge protoplanetarydisk 25 light-hours across.
This image (in the microwaveband) shows with unprecedenteddetail the protoplanetary disk. Gaps (black bands) are seen throughout the disk, which mightindicate the presence of planets.
The age of the system is <1Myr. The radiation you see is thermal(specifically blackbody).
Resolution: 35 micro-arcsec (a coin at ~100 km distance)
Bremsstrahlung(“braking radiation”)
Coma Cluster
X-Rays
Coma Cluster
Optical
Hot intracluster gas
Relativistic Phenomena in Radiative Processes
Relativistic Doppler shift Aberration of light
(Apparent) Superluminal Motion of Jets
Synchrotron
Crab Nebula
Black Hole Jets
Crab Pulsar
Compton ScatteringGamma Ray Burst
5
Emission Lines
Cat's Eye
FIR (~60 μm) shows the presence of stellar dust formed during the last phases of the progenitor star's life. It absorbs light from the central star and re-radiates it at infrared wavelengths. IR emission shows also molecular hydrogen (H2) and argon.
Planetary Nebua
White Dwarf
Orion Nebula
Closest region of star formation to Earth. CO2, H2O, HCN (etc...) glow at microwave radio frequencies and are used as "tracers"for the otherwise invisible H2 molecule.
Galactic Center
Large Molecule Heimat
amino acid, glycine (NH2CH2COOH)
Absorption Lines
Pillars of Creation
Cool molecular hydrogen (H2) and dust that form the cocoons of new stars. The
dust/H2 is being eroded by the UV light of relatively close and
hot stars.
Gravitational Waves
Tentative Schedule1st class: Introduction & Transfer Theory
2nd class: Transfer Theory
3rd class: Thermal Radiation, Black Body
4th class: Bremsstrahlung
5th class: Reminder of Special Relativity
6th class: Synchrotron I
7th class: Synchrotron II
8th class: Thomson & Compton Scattering
9th class: Inverse Compton and Cosmic Rays
10th class: Inverse Compton and Thermal Comptonization
11th class: Absorption and Emission Lines
12th class: Gravitational Waves
λ=cν
E=hν=ℏω
Radio .>1mm
1eV →11,000 K (E=k BT )
IR
Optical
UV
X-Rays
Gamma
700nm−1mm
400−700nm
100−400nm
0.1−1000keV
.>1MeV
Energy Flux (or Flux)
Assumption: the scale of a system greatly exceeds the wavelength of radiation. In other words dA >> wavelength^2
In this case you can assume that light travels in straight lines → Transfer Theory
Energy flux: consider an element of area dA exposed to radiation for a time dt. The amount of energy passing through the element should be proportional to dA dt, and we write it as dE = F dA dt
Flux is an energy per unit area per unit time (c.g.s. Units: erg/s/cm2 )
If you consider monochromatic light then of course you need to add the frequency dependence:
dE=F νdAdt→[erg cm−2 s−1 Hz−1]
Energy Flux (or Flux)
A source of radiation is called isotropic if it emits energy equally in all directions
r1
S1
Energy Flux (or Flux)
r1
S1
A source of radiation is called isotropic if it emits energy equally in all directions
Energy Flux (or Flux)
r1
S1
r
S
F (r 1)4π r 12=F (r)4 π r 2→F (r)=F (r1)
r12
r 2
If r1 is fixed then:
F (r )=constant
r 2
A source of radiation is called isotropic if it emits energy equally in all directions
Specific Intensity (Brightness)The flux is a measure of the energy carried by all rays passing through agiven area.
What if we want to follow each ray instead? Note: in transfer theory (which is the one we're using here) a single ray carries no energy, so we need to consider an infinitesimal amount of energy carried by a set of rays which differ infinitesimally from the given ray.
dE=I νdAdΩdt d ν
Specific Intensity: energy passing through an area dA normal to the
direction of the given ray and consider all rays
passing through dA whose direction is within an infinitesimal solid angle
of the given ray
Momentum FluxSuppose now that we have a radiation field (rays in all directions) and construct a small element of area dA at some arbitrary orientation n.
The net flux in the direction n, is obtained by integrating dF over
all solid angles
dF ν= I ν cosθdΩ→dF ν
c=momentum flux
dA'=dAcosθ
F ν=∫ΩI ν cosθ dΩ
Momentum Flux
Remember now that a photon has momentum E/c
Therefore the magnitude of momentum passing through the surface in the same direction is
However, momentum is a vector quantity. The componentof momentum flux normal to the surface dA is:
d pν=dE ν
c=
I ν
ccosθd ν dAdt dΩ
dpν cosθ=I ν
ccos2θd ν dAdt dΩ
Radiation Pressure
pν=1c∫ I ν cos2
θdΩ→[dynes cm−2 Hz−1]
p=∫ pνd ν
RADIATION PRESSURE (dyne/cm2)
IKAROS mission
Radiative Energy Density
The specific energy density is defined as the energy per unit volume per unit frequency range. To determine this it is convenient to consider first the energy density per unit solid angle via:
uν
uν(Ω)
dE=uν(Ω)dV dΩd ν=uν(Ω)dAc dt dΩd ν
Remember what we said before:
dE=I νdAdΩdt d ν
uν(Ω)=I ν
c
Equating the two:
Radiative Energy Density
uν(Ω)=I ν
c→uν=∫uν(Ω)dΩ=
1c∫ I νdΩ=
4πc
J ν
Integrate now over the solid angle:
where we have defined the mean intensity as:
J ν=1
4 π∫ I νdΩ
Radiative Energy Density
The total energy density u is therefore:
u=∫ uνd ν=4π
c∫ J νd ν
Radiation PressureConsider a reflecting enclosure containing an isotropic radiation field.Each photon transfers twice its normal component of momentum onreflection.
It is an easy exercise to show that the radiation pressure of such field is one third the energy density:
p=u3
Constancy of Brightness in Free Space
Consider the energy flux through an elementary surface dA1 within solid angle Consider all of the photons which pass through dA1 in this direction which then passthrough dA2 . We take the solid angle of these photons to be
Consider any ray and any two points along the ray
dΩ1
dΩ2
Constancy of Brightness in Free Space
We use now energy conservation:
dE=I ν1dA1dΩ1 dt d ν1=I ν 2 dA2dΩ2dt d ν2
Remember the definition of solid angle:
dΩ1=dA2/R2 dΩ2=dA1/R
2
Since the frequency of the ray is the same ( ) we have:d ν2=d ν1
I ν1= I ν 2=constant
Brightness does NOT depend on distance
Inverse Square Law
Is the fact that specific intensity (brightness) is conserved along a ray compatible with the inverse square law?
Consider a uniformly bright sphere (i.e., an isotropic emitter where brightness is the same for each ray leaving the surface). Let's call this constant brightness as B.
At P the observer measures the brightness which is either B (if the ray intersects the sphere) or zero if otherwise.
Inverse Square Law
We saw how to calculate the total flux from specific intensity:
F=∫ΩI cosθdΩ=B∫0
2π
d ϕ∫0
θc
sinθcosθ d θ
Here is the angle at which
a ray from P Is tangent to the sphere
θc=sin−1(Rr)
Inverse Square Law
The integration gives:
F=π B(1−cos2θc)=π Bsin2θc
But we know that and therefore:θc=sin−1(Rr) F=π B(
Rr
)2
Inverse Square Law
● Thus the specific intensity is constant, but the solid angle subtended by the given object decreases in such a way that the inverse square law is recovered.
Question: take a telescope that is collecting light from an astronomical source. Does it measure flux or Intensity?
Do we measure Flux or Brightness?Answer: it depends on the object!!
If the telescope cannot resolve the object then we measure flux.If the telescope can resolve the object, then we measure intensity.
Why? Consider the case when the source is unresolved. Now imagine pushing the source to farther distance. As the distance increases, the number of photons falls as r^2 . The flux is measured.
If instead the the source is resolved, then as the source is pushed farther away, more area of the source would be included with the solid angle, which compensates for the the increased distance and the collected number of photons remain the same.
Do we measure Flux or Brightness?Answer: it depends on the object!!
If the telescope cannot resolve the object then we measure flux.If the telescope can resolve the object, then we measure intensity.
Why? Consider the case when the source is unresolved. Now imagine pushing the source to farther distance. As the distance increases, the number of photons falls as r^2 . The flux is measured.
If instead the the source is resolved, then as the source is pushed farther away, more area of the source would be included with the solid angle, which compensates for the the increased distance and the collected number of photons remain the same.
Do we measure Flux or Brightness?
Earth Mars