Radiative Processes Ask class most of our information about the universe comes from photons What are the reasons for this Let s compare them with other possible messengers specifically massive particles neutrinos and gravitational waves Photons have a small cross section but not too small Neutrinos and gravitational waves sail through the universe with almost no interactions That means that if we could 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 exceptionally energetic events can carry information via these channels Massive particles have the opposite 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 all the way through detectors so some information is lost Again the best observations can come only from highly energetic sources All kinds of objects can emit photons Heat is all that is needed but many other processes produce photons as well this is fundamentally because the electromagnetic interaction is pervasive and relatively strong In contrast significant production of gravitational waves requires fast motion of large masses and production of high energy particles needs large potential drops or other acceleration mechanisms Neutrinos are actually produced pretty commonly hydrogen fusing into helium generates them but not 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 be measured for the other messengers but in practice such measurements are at much worse precision than is usually available for photons 1 Photons in a vacuum Of course there are some phenomena that are easiest to characterize using gravitational waves neutrinos or massive particles but for the above reasons we will focus first on photons We will start by considering photons in a vacuum then recall interactions with matter at low energies before considering high energy interactions specifically Radiation in vacuum Consider radiation when there is no matter present In particular consider a bundle of rays moving through space Ask class what can happen to those rays in vacuum They can be bent gravitationally or redshifted blueshifted in various ways Doppler gravitational cosmological In this circumstance it is useful to recall Liouville s theorem which says that the phase space density that is the number per distance momentum 3 e g the distribution function is conserved For photons this means that if we define the specific intensity I as energy per everything I dE dA dt d d 1 then the quantity I 3 is conserved in free space The source of the possible frequency change could be anything cosmological expansion gravitational redshift Doppler shifts or R whatever The integral of the specific intensity over frequency I I d is proportional to 4 One application is to the surface brightness This is defined as flux per solid angle so if we use S for the surface brightness then S I Ask class how does surface brightness depend on distance from the source if is constant It is independent of distance can also show this geometrically However Ask class how does the surface brightness of a galaxy at a redshift z compare with that of a similar galaxy nearby assuming no absorption or scattering along the way The frequency drops by a factor 1 z so the surface brightness drops by 1 z 4 This is why it is so challenging to observe galaxies at high redshift Note that 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 are called K corrections Another application is to gravitational lensing Suppose you have a distant galaxy which would have a certain brightness Gravitational lensing which does not change the frequency splits the image into two images One of those images has twice the flux of the unlensed galaxy Assume no absorption or scattering Ask class how large would that image 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 that people get more detailed glimpses of distant objects Lensing magnifies the image so more structure can be resolved This is an extremely powerful way to figure out what is happening to light as it goes every 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 just follow how the frequency behaves 2 Low energy photons Now 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 can interact Can be done off of free electrons atoms molecules or dust Specific examples include Scattering off of free electrons At low energy this process is elastic the photon energy after scattering equals the photon energy before scattering and is called Thomson scattering This cross section is useful to remember T 6 65 10 25 cm2 Free free absorption A photon can be absorbed by a free electron i e one not in an 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 called bremsstrahlung Atomic absorption The two main types are bound free in which an electron is kicked completely out of an atom by a photon and bound bound in which an electron goes from one bound state to another Free free and bound free absorption cross sections tend to decrease with frequency like 3 in the bound free case this of course applies only above the ionization threshold Bound bound absorption is peaked strongly around the energy difference between the two bound states Molecular absorption The extra degree of freedom associated with multiple atoms in a molecule allows for vibrational and rotational transitions For relatively simple reasons there tends to be a strong ordering of energies atomic vibrational rotational Ask class why haven t we talked about interactions of photons with protons or other nuclei Because protons are much tougher to affect with the oscillating