Preface to the First Edition

The study of Solar System objects was the dominant branch of Astronomy from antiquity until the nineteenth century. Analysis of planetary motion by Isaac Newton and others helped reveal the workings of the Universe. While the first astronomical uses of the telescope were primarily to study planetary bodies, improvements in telescope and detector technology in the nineteenth and early twentieth centuries brought the greatest advances in stellar and galactic astrophysics. Our understanding of the Earth and its relationship to the other planets advanced greatly during this period. The advent of the Space Age, with lunar missions and interplanetary probes, has revolutionized our understanding of our Solar System over the past forty years. Dozens of planets in orbit about stars other than our Sun have been discovered since 1995; these massive extrasolar planets have orbits quite different from the giant planets in our Solar System, and their discovery is fueling research into the process of planetary formation.

Planetary Science is now a major interdisciplinary field, combining aspects of Astronomy/Astrophysics with Geology/Geophysics, Meteorology/Atmospheric Sciences and Space Science/Plasma Physics. We are aware of more than ten thousand small bodies in orbit about the Sun and the giant planets. Many objects have been studied as individual worlds rather than merely as points of light. We now realize that the Solar System contains a more dynamic and rapidly evolving group of objects than previously imagined.

Planetary sciences is an active research field, and our knowledge of the planets and smaller bodies in the Solar System is increasing very rapidly. Thus, no compendium on this subject can be completely up to date. To give the student a flavor of this progress, we include in this appendix a selection of some of the most spectacular images sent back by NASA spacecraft that were released to the public during 2009 and early 2010. The images in this appendix are arranged by planet in order of increasing heliocentric distance; the majority of images are from Mars and the Saturn system, which are under intensive close-up study.

We close with some additional topics of interest both to general relativity, and to the program of “advanced classical mechanics”. First, because it is of the most immediate astrophysical interest, we discuss qualitatively the Kerr solution for the exterior of a spinning, spherically symmetric mass. The Kerr metric is stated, and its linearization compared to the closest electromagnetic analogue: a spinning sphere of charge. Using this comparison, we can interpret the two parameters found in the Kerr metric (when written in Boyer–Lindquist coordinates) as the mass and angular momentum (per unit mass) of the source.

The Kerr metric is nontrivial to derive using our Weyl method, so we are content to verify that it is a solution to Einstein's equation in vacuum. Some of the physical implications of the Kerr solution are available in linearized form, but the more interesting and exotic particle motions associated with the geodesics are easier to explore numerically (see for an exhaustive analytical treatment). For this reason, we include a brief discussion of numerical solutions to the geodesic ODEs that arise in the context of the Kerr space-time. In some ways, a hands-on approach to these trajectories can provide physical insight, or at the very least, predictions of observations that are interesting and accessible.

Finally, given the work we have done on variational methods and geometry, we are in good position to understand extremization in the context of physical area minimization.

Introduction

GRIPS, Gamma-Ray Burst Investigation via Polarimetry and Spectroscopy, had been proposed in 2007 in response to the ESA Cosmic Vision call as a new-generation Compton-and-pair telescope. Though it was not selected for further study, a variety of investigations are being performed to improve the concept and to verify the performance.

With the Compton scattering being dependent on the polarization of the incoming photons, any Compton telescope is, per se, a decent polarimeter. Beyond this, such detectors can be tailored to have a particularly high polarization sensitivity by obeying some simple design principles.

Polarization is the last property of high-energy electromagnetic radiation which has not been utilized to its full extent, and promises to uniquely determine the emission processes of a variety of astrophysical sources, among them pulsars, anomalous X-ray pulsars (AXP) and soft-gamma repeaters (SGR), or gamma-ray bursts (GRB).

GRIPS would carry two major telescopes: the gamma-ray monitor (GRM) and the X-ray monitor. The GRM is a combined Compton-scattering and pair-creation telescope for the energy range 0.2–50 MeV. It will thus follow the successful concepts of imaging high-energy photons used in COMPTEL (0.7–30 MeV) as well as EGRET (>30 MeV) and Fermi (>100 MeV) but combines them into one instrument. The following deals exclusively with the GRM concept, and its capability to measure polarization at unprecedented sensitivity.

Introduction

The Polarized Gamma-ray Observer (PoGOLite) is a balloon-borne, Compton-based polarimeter, with an energy range of 25–80 keV. In the pathfinder instrument to be flown in August 2010, the detector system will employ 61 phoswich detector cells (PDC) and 30 side anticoincidence shield (SAS) detectors situated in an unbroken ring around the PDCs. The full size PoGOLite instrument will contain 217 PDCs. The previous tests and simulations of the detector system are explored in more detail in.

The 61 PDC and 30 SAS detectors must be arranged in a way which optimizes the detection efficiency of valid events, while also allowing for the virtually complete rejection of background. For this purpose, the light yield of each component of each PDC and SAS unit was measured, using radioactive sources with particles and energies to which the detector materials are most sensitive. The light yield of a detector indicates its efficiency and is given by the peak channel number in the spectrum.

The ultimate goal of the next two chapters is to connect Einstein's equation to relativistic field theory. The original motivation for this shift away from geometry, and toward the machinery of field theory, was (arguably) the difficulty of unifying the four forces of nature when one of these is not a force. There was a language for relativistic fields, and a way to think about quantization in the context of that language. If gravity was to be quantized in a manner similar to E&M, it needed a formulation more like E&M's.

We will begin by developing the Lagrangian description for simple scalar fields, this is a “continuum”-ization of Newton's second law, and leads immediately to the wave equation. Once we have the wave equation, appropriate to, for example, longitudinal density perturbations in a material, we can generalize to the wave equation of empty space, which, like materials, has a natural speed. This gives us the massless Klein–Gordon scalar field theory. We will explore some of the Lagrangian and Hamiltonian ideas applied to fields, and make the connection between these and natural continuum forms of familiar (point) classical mechanics. In the next chapter, we will extend to vector fields, discuss electricity and magnetism, and move on to develop the simplest second-rank symmetric tensor field theory. This is, almost uniquely, Einstein's general relativity, and the field of interest is the metric of a (pseudo-)Riemannian space-time.

Introduction

Polarization of light originating from different regions of a black hole accretion disc and detected by a distant observer is influenced by strong gravitational field near a central black hole.

Introduction

The presence of a ‘soft excess’, i.e. soft X-ray emission above the extrapolation of the absorbed nuclear emission, is very common in low-resolution spectra of nearby X-ray obscured active galactic nuclei (AGN). It is generally very difficult to discriminate between thermal emission, as expected by gas heated by shocks induced by AGN outflows or episodes of intense star formation, and emission from a gas photoionized by the AGN primary emission. However, the high energy and spatial resolution of XMM-Newton and Chandra have allowed us to make important progress in the last few years.

The photoionization signatures

The high-resolution spectra of the brightest obscured AGN, made available by the gratings aboard Chandra and XMM-Newton, revealed that the ‘soft excess’ observed in CCD spectra was due to the blending of strong emission lines, mainly from He- and H-like transitions of light metals and L transitions of Fe (see Figure 19.1, e.g).

Introduction

Despite the wealth of sources accessible to polarization measurements and the importance of these measurements, there has been a paucity of missions with dedicated instrumentation. The most recent was a measurement of the Crab at 2.6 keV and 5.2 keV by an experiment on the OSO-8 satellite in 1976. Measurements using instruments on-board the INTEGRAL satellite have reinvigorated the field of late. At soft gamma-ray energies, nonthermal processes are likely to produce high degrees of polarization.

Introduction

A recent flurry of new mission proposals has renewed interest in X-ray polarization from a variety of astrophysical sources, hopefully marking the “coming of age of X-ray polarimetry” in the very near future. The Gravity and Extreme Magnetism SMEX (GEMS) mission, for example, should be able to detect a degree of polarization δ < 1% for a flux of a few mCrab (e.g. and these proceedings). A similar detector for the International X-ray Observatory (IXO) could achieve sensitivity roughly 10× greater (δ <0.1%, Alessandro Brez in these proceedings). In this talk, based on our recent paper, we focus on the polarization signal from accreting stellar-mass black holes (BHs) in the thermal state, which are characterized by a broad-band spectrum peaking around 1 keV.

Introduction

We are discussing the state of the art of X-ray polarization detection techniques in this conference, so that it is important to remind ourselves of the expected X-ray polarization properties of various astrophysical objects. In this paper, we give a brief overview of the expected X-ray polarization signatures of magnetic neutron stars found in diverse situations, e.g. in accretion-powered pulsars, low-mass X-ray binaries (LMXBs), recycled pulsars, isolated neutron stars and finally the fascinating magnetars. We concentrate here only on some aspects of the basic physics of radiation propagation around magnetized neutron stars which lead to some basic, expected polarization features in the X-rays which we consider relatively robust. Accordingly, our discussion here is qualitative. Quantitative aspects of a few of these features have been described by other participants of the conference, and detailed calculations on some other aspects will be reported elsewhere.

The X-ray emission we are concerned with here is basically thermal emission from the surface of the neutron star, powered by accretion or otherwise. This radiation propagates through the neutron-star atmosphere, then through the accretion columns over the magnetic poles of the neutron star if it is an accreting one, and finally through the neutron-star magnetosphere.

We have, so far, studied classical mechanics from a variety of different points of view. In particular, the notion of length extremization, and its mathematical formulation as the extremum of a particular action, were extensible to define the dynamics of special relativity. As we went along, we developed notation sufficient to discuss the generalized motion of particles in an arbitrary metric setting. Most of our work on dynamics has been done in an explicitly “flat” space, or in the case of special relativity, space-time. But, we have pushed the geometry as far as we can without any fundamentally new ideas. Now it is time to turn our attention to the characterization of geometry that will allow us to define “flat” versus “curved” space-times. In order to do this, we need less familiar machinery, and will develop that machinery as we push on toward the ultimate goal: to find equations governing the generation of curvature from a mass distribution that mimic, in some limit, the Newtonian force of gravity.

Remember that it is gravity that is the target here. We have seen that the classical gravitational force violates special relativity, and that a modified theory that shares some common traits with electricity and magnetism would fix this flaw. For reasons that should become apparent as we forge ahead, such a modified theory cannot capture all of the observed gravitational phenomena, and, as it turns out, a much larger shift in thinking is necessary.

Advances in X-ray astronomy over the almost five decades since the first rockets were launched have been impressive in the domains of imaging, spectroscopy and timing. On the contrary, polarimetry has not progressed much since the historic results of the Columbia team headed by Bob Novick with rockets and with the OSO-8 satellite. The introduction, since Einstein, of X-ray telescopes and imaging detectors produced a dramatic jump in the sensitivity of X-ray missions. Polarimetry based on the conventional techniques of Bragg diffraction and Compton scattering has suffered from the increased mismatching in terms of sensitivity which resulted in the preclusion of the whole extragalactic sky. Moreover the shift from satellites stabilized on one axis to those stabilized on three axes made cumbersome the hosting of polarimeters, which needed the rotation of the whole instrument, in the focal plane of telescopes. As a consequence no polarimeter was included in the final design of Einstein, Chandra and XMM-Newton.

The advent of a new generation of detectors, to be combined with large area X-ray telescopes, has renewed interest in X-ray polarimetry, as demonstrated by the several polarimetric missions recently proposed. One of them, GEMS, has been recently selected by NASA within the SMEX program, with a launch due in 2014. There are discussions in Italy about the possibility of a national X-ray mission including polarimetry, to be launched in the same time frame.

Introduction

Observations in the γ-ray regime allow us to scrutinize some of the most energetic emission processes associated with cosmic sources. Unlike other wave bands that mainly show emission due to thermal reprocessing within hot gases, the majority of γ-ray emission is decidedly non-thermal in nature and is generally produced directly by electrons and other elementary particles in magnetic fields. The electrons which produce the γ-rays are extremely energetic and often at the upper limit of the capability of the accelerator that produces them.

Introduction

Magnetic cataclysmic variables (mCVs) and Ultra-compact double degenerate binaries (UCDs) are potential X-ray polarization sources. The mCVs contain a magnetic white dwarf accreting material from a low-mass, Roche-lobe filling companion star. There are two major types: (i) the AM Herculis binaries (AM Hers, also known as polars) and (ii) the intermediate polars (IPs) (see). In AM Hers, the white-dwarf magnetic field (B ∼ 107 −108 G) is strong enough to lock the whole system into synchronous rotation. It also prohibits the formation of an accretion disk, and the accretion flow is channelled by the magnetic field into the magnetic polar regions of the white dwarf.

Introduction

Polarimetry is a powerful diagnostic tool to study spatially unresolved sources at cosmological distances, such as gamma-ray burst (GRB) afterglows. Radiation mechanisms that produce similar spectra can be disentangled by means of their polarization signatures. Also, polarization provides unique insights into the geometry of the source, which remains hidden in the integrated light.

Historically, essentially all interpretative studies about GRB afterglow polarimetry have been based on the cosmological fireball model, which we will also use as a reference for our discussion. Afterglow polarization studies have indeed the advantage that different models are often almost indistinguishable in terms of radiation output in the optical, but produce markedly distinct predictions about polarization.

In this proceeding, we will briefly review in Section 32.2 what we have derived by optical afterglow polarimetric observations and discuss the most recent development in the field in Section 32.3.