Neutrinos and Gravitational RadiationInitial question: What can neutrinos and gravitational waves tell us about theuniverse that is not accessible via observations with photons?Throughout this course we’ve focused almost exclusively on photons. This is reasonablefor a radiative processes class, especially because virtually all information we have aboutastronomy comes from detections of photons in one way or another. For this final lecture,however, we’ll take steps in other directions. More and more experiments are aimed atdetecting qualitatively different types of radiation, and in particular we’ll look at neutrinosand gravitational radiation.Let’s start with neutrinos. Neutrinos are produced when the weak force is involvedin an interaction. Ask class: can they think of examples? Conversion of a proton to aneutron (or vice versa) involves neutrinos, so nuclear processes in the center of the Sunare an example, particularly hydrogen fusion, which requires eventual conversion of fourprotons into a helium nucleus of two protons and two neutrons. Another example is theneutronization that occurs during core collapse of a massive star. The conversion of aproton plus electron into a neutron is fundamentally driven by the rising Fermi energyof the electron, but in order to conserve various quantities, a neutrino must be involved.Let’s examine this: in addition to energy, linear momentum, and angular momentum beingconserved, we know that electric charge, baryon number, and lepton number must beconserved. Therefore, if we want to convert a proton into a neutron:p → n (1)we have to add things to either side. Baryon number is already conserved, so we have toworry about lepton number and charge. The proton is positively charged and the neutronis uncharged, so either a negative charge (e.g., an electron) must be added to the left sideor a positive charge (e.g., a positron) must be added to the right. If this happens, though,then a compensating lepton with no charge must be added to the proper side, and this iswhere a neutrino comes in:n → p + e + ¯νeorp + e → n + νe(2)are typical. Neutrinos are thought to carry most of the energy in a typical supernova andare primary indicators of nuclear fusion, so it would be wonderful to observe them.Unfortunately, neutrinos interact very weakly. Typically, a neutrino of energy Eνhasan electron scattering cross section ofσν≈ 10−44µEνmec2¶2cm2. (3)This is what is technically known as an itsy bitsy cross section. Now, particle physicistshave a lot of time and a fondness for alcohol, leading to interesting terminology and namesfor units. In this case, they’ve dubbed 10−24cm2a “barn” and 10−48cm2a “shed”, so atypical neutrino cross section is some ten thousand sheds! This compares with the Thomsoncross section, which is close to one barn; indeed, hitting an electron with a photon is likehitting the broad side of a barn compared to hitting an electron with a neutrino. For peoplewithout a sense of humor, 10−44cm2=10−48m2is one square yoctometer. Pretty small, nomatter how you slice it.Let’s figure out the fraction of neutrinos interacting in certain circumstances. First, theSun. Ask class: to order of magnitude, what is the density of the Sun? About 1 g cm−3.That means that the number density is about 1024cm−3. Ask class: so, what is the meanfree path of ∼ 1 MeV neutrinos? About 1020cm. The Sun is about 1011cm in radius, soonly a fraction ∼ 10−9of the neutrinos interact.Now let’s think about the dense core in the center of a star just prior to a supernova.Ask class: if you crush the Sun down to a radius 1000 times less than it actually has,what happens to the optical depth to neutrinos? Density is 10003= 109times greater, butthe length traveled is 1000 times less, so optical depth is 106times greater. That suggestsan optical depth of about 10−3. The neutrinos in supernova are actually somewhat moreenergetic as well, about 3–5 MeV, so a fraction ∼ 10−2of the energy is absorbed. Thisseems to be enough to be the crucial driver of the supernova, since a good 1053erg isreleased in neutrinos.Sadly, this tiny cross section makes neutrinos really tough to detect! Ask class:what detection strategies could be used? The basic issue is that, since the probability ofinteraction is tiny, there have to be an enormous number of things with which the neutrinoscan interact.The first approach used (by Raymond Davis, co-winner of the 2002 Nobel Prize inPhysics) was radiochemical. That is, he put 4 × 108cm3of cleaning fluid (!) in theHomestake gold mine in South Dakota. The point is that cleaning fluid contains a lot ofchlorine, and neutrinos can cause the reaction νe+37Cl→e−+37Ar, with a threshold energyof Eth=0.814 MeV. The Argon was chemically separated every month or so, and detectedfrom37Ar decay. The point was to observe the neutrinos from fusion in the Sun and getdirect information about those processes. Ask class: what drawbacks might there be tothis approach? There is no information about time, direction, or spectrum of the neutrinos.It just gives a total number. This number, however is substantially less than predicted ina standard solar model with standard particle physics, and this has turned out to be arather profound issue. As Elim mentioned in class, vacuum oscillations of neutrino flavors(which dominate below 5 MeV) and the density-dependent MSW oscillation mechanism(which dominates above 5 MeV), mean that there is a deficit in the electron neutrinos wecan detect. More specifically, since only electron neutrinos are produced initially and aredetected by this method, there’s a deficit. More recent radiochemical methods use gallium:νe+71Ga→e−+71Ge, with a threshold energy of Eth=0.2332 MeV.A second method uses scattering directly. If a neutrino with high enough energy scattersoff an electron in some medium, then Cerenkov light will be emitted if the electron hasenough kinetic energy. Again, you need tremendous volume to do this. The largest-scalewater tank of this type is the super-Kamiokande detector in Japan. The advantage of thismethod is that when the Cerenkov light is observed, it gives the direction and time of aninteraction as well as the spectrum of the neutrinos. The disadvantage is that a neutrinowith E > 5 − 8 MeV is needed, so the signal is weak.A new generation of detectors looks for ultrahigh energy neutrinos, such as might comefrom gamma-ray bursts or some categories of