Radiative Processes

LecturerAlessandro Patruno

Lecturer

patruno@strw.leidenuniv.nl

Office #468

High Energy Astrophysics, Black Holes, Neutron Stars

Yvette Welling Valeriya Korol

Teaching Assistant Teaching Assistantwelling@strw.leidenuniv.nl korol@strw.leidenuniv.nl

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