Energy Losses and Gravitational RadiationEnergy loss processesNow, we need to consider energy loss processes. Ask class: what are ways in whichhigh-energy particles can lose energy? Generically, can lose energy by interacting withphotons or other particles, or by interacting with a field and radiating. Let’s break it down.First, interaction with photons (inverse Compton scattering). Ask class: would they expectprotons or electrons to lose more energy by scattering with photons? Electrons have a muchlarger cross section, so they do. Now, interaction with particles. Electrons can interactwith other electrons or with protons, but at ultrarelativistic energies these cross sectionsare relatively small. For protons, as we saw in the last lecture they can scatter off of otherprotons or nuclei. In such interactions the strong force is involved, and the cross sectionis something like ∼ 10−26cm2. Ask class: what does the column depth have to be foroptical depth unity? The reciprocal of this, or about 1026cm−2. That’s a lot! So, in adense environment, collisions with particles can sap energy from high-energy particles. Butwhat if the environment is low-density? Then, as we’ve argued, acceleration of particlesto ultrarelativistic energies means that magnetic fields are present. In fact, the fields needto be strong enough to confine the particles as well (otherwise they escape without furthergain of energy). Therefore, interaction of the particles with the field can produce radiation,diminishing the particle energy.Curvature radiation.—First, suppose that the particle is forced to move along magneticfield lines with curvature radius R. As we found in the last lecture, the power radiated bya particle moving at a Lorentz factor γ À 1 is P ≈ (2e2c/3R2)γ4. A relativistic particle ofcharge e moving along an electric field E receives a power eEc from the field. Equating thepower gain and power loss, the limiting Lorentz factor isγ < 2 × 107R1/28E1/44, (1)where R = 108R8cm and E = 104E4sV cm−1. For a supermassive black hole with R =1014cm, γ might get up to 2 × 1010(note the weak dependence on E ; also, the requiredmagnetic field for E4À 1 would be unrealistically high for a supermassive black hole). Thiswould give a proton an energy of 2 × 1019eV, which sounds high but is a factor of 10 short ofthe highest observed energies. For a neutron star with R = 106cm and E = 1012, γ < 2×108.So it sounds bad. Ask class: but is curvature radiation always relevant? What if you havea very high-energy particle? Then, the particle doesn’t follow the field lines. Remember thatcurvature radiation and synchrotron radiation are both just types of acceleration radiation.If a particle is moving in a straight line, it radiates very little. So, the question is whethersynchrotron radiation keeps the particle along the field lines.– 2 –Synchrotron radiation.—From the last lecture, proton synchrotron radiation causes anenergy decay at a rate˙E/E ≈ 3 × 105γB212s−1if the highly relativistic protons moveperpendicular to field lines. If E/˙E is short compared to the time needed to travel acrossthe acceleration region, the proton will follow field lines. Near a strongly magnetic neutronstar, with B = 1012G, there’s no chance of highly relativistic protons moving across fieldlines. Even for a supermassive black hole, where B ∼ 105G, a proton with γ = 1011asrequired will be forced to follow the field lines in a time much less than the crossing time ofthe region, so in both cases it is likely that protons will be forced to follow field lines.This is a problem. My best guess is that there are AGN with field geometries such thatthe curvature radius is much greater (factor of >100!) than the distance from the hole. Thatwould just barely allow the observed energies. If future detectors (such as the Pierre AugerArray) see cosmic rays of energies much greater than the current record holders, this wouldbe a real problem. We’ll get into other issues with the highest energy cosmic rays near theend of the course.Gravitational radiationAs direct detection of gravitational radiation draws nearer, it is useful to consider whatsuch detections will teach us about the universe. The first such detection, of course, will beof immediate significance because it will be a direct confirmation of a dramatic prediction ofgeneral relativity: to paraphrase John Wheeler, that spacetime tells sources how to move,and moving sources tell spacetime how to ripple.Beyond this first detection, gravitational wave detections will pass into the realm ofastronomy, allowing new observational windows onto some of the most dynamic phenomenain the universe. These include merging neutron stars and black holes, supernova explosions,and possibly echoes from the very early history of the universe as a whole. They are alsoanticipated to provide the cleanest tests of predictions of general relativity in the realm ofstrong gravity.However, there are important differences from standard astronomy. In electromagneticobservations, in every waveband there are sources so strong that they can be detected withoutknowing anything about the source. You don’t need to understand nuclear fusion in orderto see the Sun! In contrast, as we will see, most of the expected sources of gravitationalradiation are so weak that sophisticated statistical techniques are required to detect themat all. These techniques involve matching templates of expected waveforms against theobserved data stream. Maximum sensitivity therefore requires a certain understanding ofwhat the sources look like, hence of the characteristics of those sources. In addition, whendetections occur, it will be important to put them into an astrophysical context so that the– 3 –implications of the discoveries are evident.Before discussing types of sources, though, we need to have some general perspective onhow gravitational radiation is generated and how strong it is. We will begin by discussingradiation in a general context.By definition, a radiation field must be able to carry energy to infinity. If the amplitudeof the field a distance r from the source in the direction (θ, φ) is A(r, θ, φ), the flux through aspherical surface at r is F (r, θ, φ) ∝ A2(r, θ, φ). If for simplicity we assume that the radiationis spherically symmetric, A(r, θ, φ) = A(r), this means that the luminosity at a distance ris L(r) ∝ A2(r)4πr2. Note, though, that when one expands the