M.Phys., M.Math.Phys., M.Sc. MTPRadiative Processes in Astrophysics

andHigh-Energy Astrophysics

Professor Garret Cotter

garret.cotter@physics.ox.ac.uk

Office 756 in the DWB & Exeter College

Welcome to M.Phys. & M.Math.Phys. Astrophysics

There have been some recent changes to the course in response to feedback:

• We have re-organised the logical structure, the course now starts with radiative processes and then moves on to more phenomenological topics.

• The size of the lecturing team has been reduced. I will cover the whole of Michaelmas term, giving the lectures on the first two topics, Radiative Processes & High Energy.

There may still be teething troubles, please get in touch with any problems and (constructive!) criticism.

I use a combination of slides and blackboard. Some derivations will be done on the board and some will be on slides. You will need to study these in your own time and consult reference books to gain a good understanding.

I am always happy to answer questions - always feel free to ask at the end of the lecture, or to email if you want to arrange a time have a longer discussion.

Lectures this term are always at 12.00 noon in the Dennis Sciama Lecture Theatre

Radiative Processes in Astrophysics

Week 1 Mon Wed Fri

Week 2 Mon Wed Fri

Week 3 Mon Wed Fri

Week 4 Mon Wed Fri

High-Energy Astrophysics

Week 4 Mon Wed Fri

Week 5 Mon Wed Fri

Week 6 Mon Wed Fri

Week 7 Mon Wed Fri

Week 8 Mon Wed Fri

Synopsis: Radiative Processes

• The EM spectrum in astrophysics; temperature and radiation brightness. • Spectroscopy, forbidden and allowed transitions, cosmic abundances• Two-level atom, A, B and C coefficients and their useful regimes,

thermal populations, IR fine structure, critical density, mass estimates• Recombination and ionization, Stromgren sphere, ionization

balance, effective temperature estimates.• Three-level atom: electron temperature and density.• Absorption lines, equivalent width, curve of growth, column densities.• The interstellar medium. Atomic and ionic absorption lines, abundance

of gas, molecules and dust. Hyperfine transitions: 21cm line of HI• Interstellar extinction, dust, equilibrium and stochastic processes• The sun. Ionization and sources of opacity, radiative transfer, the Gray

atmosphere, limb darkening, absorption line formation.

Synopsis: High-Energy Astrophysics

• Supernova blast waves; shocks.• Acceleration of particles to ultra-relativistic energies.• Synchrotron emission; total power; spectrum; self-absorption;

spectral ageing• Accretion; properties of accretion discs• Eddington luminosity; evidence for black holes.• Relativistic jets; models of jet production; relativistic projection

effects; Doppler boosting.• Cosmic evolution of AGN; high-energy background radiation and

cosmic accretion history of black holes.• Bremsstrahlung; inverse-Compton scattering; clusters of galaxies;

Sunyaev-Zel’dovich effect.• Cosmic rays and very high energy gamma rays; Cherenkov

telescopes.

Books

Radiative Processes

Radiative Processes in Astrophysics by Rybicki, George B., Lightman, Alan P., graduate level text, comprehensive.Physics and Chemistry of the Interstellar Medium by Sun Kwok.Physics of the Interstellar and Intergalactic Medium by Bruce Draine.

High-Energy Astrophysics

High Energy Astrophysics by Malcolm Longair. Very comprehensive, advanced undergrad/graduate level.

The Physics of Extragalactic Radio Sources, David de Young

Accretion Power in Astrophysics, Frank, King & Raine

Philosophy

Many of the physical processes we will study in this course haveexact mathematical descriptions which are either very lengthy, or can only be solved by numerical methods. My aim is to show you asmany interesting advanced physics topics in the time available, andwe will often make approximations—justifiable approximations—toget to a shorter mathematical description of the situation, focussing on the salient features of the physical theory in a variety of situations.

You will learn a lot about how physics is actually done as a part of this process! I will provide you with links to the relevant, fully-detailed research papers where possible.

Observing the whole EM spectrum (and beyond)

Modern astronomical telescopes and detectors span the observational wavelength/photon energy

range from tens of metres in the radio to hundreds of TeV for the highest-energy gamma rays. The

classification of different astronomical wavebands is generally driven by the technology used in the

detectors:

• Radio (from ∼ 10 MHz to ∼ 100 GHz) very highest spatial resolution because coherent detection of

the EM field allows interferometry.

• Millimetre, sub-millimetre and far-infrared (∼ 0.3 mm to ∼ 10 µm). Bolometers onboard satellites

and high-altitude terrestrial sites.

• Infrared (10 µm to 1 µm) and optical (1 µm to 0.3 µm). Almost all of “traditional” astronomy.

Most stars put out most of their energy in this range. Unsurprisingly the human eye is adapted

to use these wavelengths!

• Ultraviolet (0.3 µm to ∼ 3 nm). Satellite-borne instruments are needed because the

atmosphere is opaque now; but we can still use essentially “ordinary” telescopes.• X-rays (3 nm to ∼ 3×10−12 m; 0.4 keV to ∼ 100 keV). Satellite- and rocket-borne instruments are

needed. Special grating-incidence mirrors are used to focus X-rays.

• Gamma-rays (∼ 100 keV and above). At the lower energies, telescopes are satellite-borne and

similar detectors to particle physics experiments. Very high-energy photons and particles

entering the Earth’s atmosphere produce Cherenkov radiation. This is detected by very large

telescopes with very high-speed cameras (nanosecond imaging)

• Beyond the EM spectrum: gravitational waves, neutrinos

W.M. Keck observatory, Mauna Kea, Hawai’i.

Keck telescope 10-m segmented mirror.

European Southern Observatory, Cerro La Silla, Atacama Desert, Chile August 2011

Average optical/UV spectra of quasars

Note non-blackbody spectrum with prominent emission lines.

Very Large Array in New Mexico. Radio interferometer, 73 MHz—43 GHz. 27 antennae, baselines up to 36 km.

The sky as it would appear if we could see at 1.4 GHz. Almost all the

sources lie far beyond the Milky Way. (Credit: NRAO / AUI / NSF)

Radio spectra of some sources from the 3C survey

Frequency / MHz

ROSAT (Rontgensatellit) X-ray observatory 1990—2011

ROSAT all-sky survey. Note the fairly uniform background which is caused by unresolved extragalactic point sources

X-ray “zoom-in” from the high-resolution Chandra satellite.

We can now see the individual X-ray sources.

X-ray spectrum of intracluster plasma in the Coma cluster of galaxies

Again note non-blackbody and emission lines.

Fermi Gamma-Ray Space Telescope, launched June 11 2008.

CTA - proposed array telescope for observing high-energy Cherenkov showers.

Primary !-ray

~ 10 km

ParticleShower

» Air-shower...

~ 100 m

Cherenkov technique (figure from Prof J. Hinton, CTA collaboration).

Active galaxies: broad-band spectra

Observed spectrum of high-energy particles hitting the atmosphere.

Gravitational waves

Surface brightness/specific intensity

Traditionally in astronomy the observed flux of stars is given in magnitudes:

so, a star 100 times fainter than Vega through a V-band filter has V = 5.

However this does not express the flux as a physical quantity. One of the mostcommonly-used physical units is the Jansky (Jy, named after the discoverer of radio waves from the Milky Way):

1 Jy = 10−26 W Hz−1 m −2

i.e. the units are power collected per square metre of telescope collecting area per unit bandwidth of the receiving device. As a yardstick, Vega has a flux density of about 3600 Jy at 500 nm.

(For fun: The faintest stars the human eye can see at a dark site are about magnitude 6. Howmuch power does the eye receive from them? How many photons does it take to trigger a light-sensitive cell in the eye? Take the integration time to be ∼ 20 ms and the starlight to be spread over ∼ 10 cells in the eye.)

Surface brightness

Optical astronomers describe the observed flux of stars in magnitudes:

mstar = �2.5 log10

✓fluxVega

fluxstar

◆

so, e.g., a star 100 times fainter than Vega through a V -band filter has V = 5.

At radio, far-infrared, X-ray etc. wavelengths it is more common to use physicalunits. One of the most used is the unit of flux density, the Jansky (Jy, named afterthe discoverer of radio waves from the Milky Way):

1Jy = 10�26

WHz�1

m�2

i.e. the units are power collected per square metre of telescope collecting areaper unit bandwidth of the receiving device. As a yardstick, Vega has a flux densityof about 3600 Jy at 500 nm.

(For fun: The faintest stars the human eye can see at a dark site are about magnitude 6. How

much power does the eye receive from them? How many photons does it take to trigger a light-

sensitive cell in the eye? Take the integration time to be ⇠ 20 ms and the starlight to be spread

over ⇠ 10 cells in the eye.)

In virtually all of optical astronomy stars are effectively point sources (their angular size ismuch smaller than the ∼ 1 arcsec limit imposed by atmospheric turbulence). Howeverwhen we look at the diffuse interstellar medium, or at extragalactic sources, often we dealwith objects whose angular extent can be resolved, and this leads us to a perhaps morefundamental quantity, the surface brightness or specific intensity. This is the flux densityper solid angle, and has SI units of

W Hz-1 m-2 Sr-1

• Power developed in the detector,

• per unit bandwidth of the detector,

• per square metre of telescope collecting area,

• per unit solid angle of sky from which the telescope is collecting energy.

This is also sometimes called simply “brightness” and the term in the SI system is “spectral radiance”. Notation is usually Iν. You will often also see it in units such as Jansky per square arcsec, or Jansky per square arcminute.

Hand-held infrared thermometer measures temperature via σT 4.

“Thermocouples were the traditional devices used for this purpose, but they are unsuitable for continuous measurement because they rapidly dissolve.”

Antenna area A

Beam solid angle OmegaReceiver bandwidth Delta nu

Power received by system

Brightness and temperatureThought experiment: take two cavities of different size and shape, but bothfilled with black-body radiation at the same temperature T. Suppose there isan aper- ture between the cavities and that in this aperture there is a filterwhich transmits only through some narrow range of frequencies.

TT

Filter

We know from the Zeroth Law that there is no heat transfer between box 1and box 2 so Iν,1 = Iν,2 i.e. for black-body radiation Iν can only be a functionof T and ν.

So brightness and temperature are intimately linked. The brightness of ablack- body as a function of frequency is given by the Planck function.

This you will be familiar with – the Bν here is the same thing, for a blackbody, as the Iν we just defined.

It gives the flux per unit frequency through an element of area from an elementof solid angle. So if we know Iν for an astronomical object from observation, wecan calculate the temperature of a blackbody that would have the samebrightness at that frequency: the “brightness temperature”.

Jargon alert: Pedantically, one should use Bν when referring to the brightness of ablack-body and Iν when referring to the brightness of an object with an arbitrary spectrum. But don’t be surprised if you sometimes see them interchanged. That’s astronomers for you.

“I learned very early the difference between knowing the name of something and knowing something.” - Feynman

Brightness and temperatureThought experiment: take two cavities of different size and shape, but both filledwith black-body radiation at the same temperature T . Suppose there is an aper-ture between the cavities and that in this aperture there is a filter which transmitsonly through some narrow range of frequencies.

TT

Filter

We know from the Zeroth Law that there is no heat transfer between box 1 andbox 2 so I⌫,1 = I⌫,2 i.e. for black-body radiation I⌫ can only be a function of Tand ⌫.

So brightness and temperature are intimately linked. The brightness of a black-body as a function of frequency is given by the Planck function:

B⌫ =2h⌫3

c2

⇢exp

✓h⌫

kBT

◆� 1

��1

Extremes of brightness

Most stars radiate approximately as black-bodies, ranging from ≈ 3000 K for M- typered dwarfs to ≈ 50 000 K for O-type supergiants. We will spend a lot of time in the next few weeks discussing the wealth of physics can can be derived from the emission and absorptions features where stellar spectra deviate from the black-body.

But when we go to both long (radio) and short (X-ray) wavelengths, we find objects which have brightnesses far in excess of those achieved by blackbody processes in stars.

Broadly speaking, when we move on to high-energy astrophysics in the second half of term, we will encompasses physical process and objects where the energies andtemperatures involved are far in excess of those observed in normal stellar systems(often implying that the energy source is not nuclear fusion). And we often findcases where the temperatures and densities of the material involved lendthemselves to spectral energy distributions that are greatly different from a black-body.

(See problem sheet)