Photons1. Why photons?Ask class: most of our information about the universe comes from photons. Whatare the reasons for this? Let’s compare them with other possible messengers, specificallymassive particles, neutrinos, and gravitational waves.• Photons have a small cross section, but not too small. Neutrinos and gravitationalwaves sail through the universe with almost no interactions. That means that if wecould detect them, they would give good directional information about their sources,which combined with energy/frequency resolution could potentially tell us quite a lot.However, they also sail through detectors for the most part, so only exceptionallyenergetic events can carry information via these channels. Massive particles have theopposite problem. Electrons, protons, and nuclei can be accelerated to high energies,but they are curved by the Galactic magnetic field and slam into air molecules (or go allthe way through detectors), so some information is lost. Again, the best observationscan come only from highly energetic sources.• All kinds of objects can emit photons. Heat is all that is needed, but many otherprocesses produce photons as well (this is fundamentally because the electromagneticinteraction is pervasive and relatively strong). In contrast, significant production ofgravitational waves requires fast motion of large masses, and production of high energyparticles needs large potential drops or other acceleration mechanisms. Neutrinos areactually produced pretty commonly (hydrogen fusing into helium generates them), butnot enough to compensate for their extremely low cross section.• Detectors can measure with precision many aspects of photons. These include energy,direction, time of arrival, and polarization. In principle these quantities can also bemeasured for the other messengers, but in practice such measurements are at muchworse precision than is usually available for photons.2. Photons in a vacuumOf course, there are some phenomena that are easiest to characterize using gravitationalwaves, neutrinos, or massive particles, but for the above reasons we will focus first onphotons. We will start by considering photons in a vacuum, then recall interactions withmatter at low energies before considering high-energy interactions specifically.Radiation in vacuum: Consider radiation when there is no matter present. Inparticular, consider a bundle of rays moving through space. Ask class: what can happento those rays in vacuum? They can be bent gravitationally, or redshifted/blueshifted invarious ways (Doppler, gravitational, cosmological). In this circumstance, it is useful torecall Liouville’s theorem, which says that the phase space density, that is, the numberper (distance-momentum)3(e.g., the distribution function), is conserved. For photons, thismeans that if we define the “specific intensity” Iνas energy per everything:Iν=dEdA dt dΩ dν, (1)then the quantity Iν/ν3is conserved in free space. The source of the possible frequencychange could be anything: cosmological expansion, gravitational redshift, Doppler shifts, orwhatever. The integral of the specific intensity over frequency, I =RIνdν, is proportionalto ν4.One application is to the surface brightness. This is defined as flux per solid angle, so ifwe use S for the surface brightness, then S = I. Ask class: how does surface brightnessdepend on distance from the source, if ν is constant? It is independent of distance (can alsoshow this geometrically). However, Ask class: how does the surface brightness of a galaxyat a redshift z compare with that of a similar galaxy nearby, assuming no absorption orscattering along the way? The frequency drops by a factor 1 + z, so the surface brightnessdrops by (1 + z)4. This is why it is so challenging to observe galaxies at high redshift. Notethat in a given waveband, the observed surface brightness also depends on the spectrum,because what you see in a given band will have been emitted in a different band (these arecalled K-corrections).Another application is to gravitational lensing. Suppose you have a distant galaxywhich would have a certain brightness. Gravitational lensing, which does not change thefrequency, splits the image into two images. One of those images has twice the flux of theunlensed galaxy. Assume no absorption or scattering. Ask class: how large would thatimage appear to be compared to the unlensed image? Surface brightness is conserved,meaning that to have twice the flux it must appear twice as large. This is one way thatpeople get more detailed glimpses of distant objects. Lensing magnifies the image, so morestructure can be resolved.This is an extremely powerful way to figure out what is happening to light as it goesevery which way. The specific intensity is all you need to figure out lots of important things,such as the flux or the surface brightness, and in apparently complicated situations you justfollow how the frequency behaves.3. Low-energy photonsNow we need to consider how low-energy (say, UV and longward) photons can interact.Radiative opacity sources: Ask class: what are the ways in which a photon caninteract? Can be done off of free electrons, atoms, molecules, or dust. Specific examplesinclude:• Scattering off of free electrons. At low energy, this process is elastic (the photon energyafter scattering equals the photon energy before scattering), and is called Thomsonscattering. This cross section is useful to remember: σT= 6.65 × 10−25cm2.• Free-free absorption. A photon can be absorbed by a free electron (i.e., one not inan atom) moving past a more massive charge (such as a proton or other nucleus).The inverse process, in which a photon is emitted by an accelerating charge, is calledbremsstrahlung.• Atomic absorption. The two main types are bound-free (in which an electron is kickedcompletely out of an atom by a photon) and bound-bound (in which an electron goesfrom one bound state to another). Free-free and bound-free absorption cross sectionstend to decrease with frequency like ω−3(in the bound-free case this of course appliesonly above the ionization threshold). Bound-bound absorption is peaked stronglyaround the energy difference between the two bound states.• Molecular absorption. The extra degree of freedom associated with multiple atoms in amolecule allows for vibrational and rotational transitions. For relatively simple reasons,there tends to be a strong ordering of energies: