Chapter 1 – Astrophysical information

Rytov, S. M., Kravtsov, Yu. A., & Tatarskii, V. I. (1987). Principles of statistical radiophysics, 1–4. Berlin: Springer-Verlag.

Chapter 2 – Photometry

Bessell, M. S. (2005). Standard photometric systems. ARA &A, 43, 293–336.

Bradt, H. (2004). Astronomy methods. Cambridge: Cambridge University Press.

Kitchin, C. R. (2009). Astrophysical techniques, 5th edn. Boca Raton: CRC Press.

Rybicki, G. B. & Lightman, A. P. (1979). Radiative processes in astrophysics. New York: Wiley.

Chapter 5 – Detection systems

McLean, I. S. (2008). Electronic imaging in astronomy: detectors and instrumentation, 2nd edn. Berlin: Springer.

Chapter 7 – Stochastic processes & noise

van Kampen, N. G. (2007). Stochastic processes in physics and chemistry. Amsterdam: Elsevier.

Chapter 8 – Optics

Klein, M. V. & Furtak, T. E. (1986). Optics, 2nd edn. New York: Wiley.

Yoder, P. R., Jr. (1993). Opto-mechanical systems design, 2nd edn. New York: Marcel Decker.

Chapter 9 – Interference

Wolf, E. (2007). Introduction to the theory of coherence and polarization of light. Cambridge: Cambridge University Press.

Chapter 10 – Spectroscopy

Bowen, I. S. & Vaughan, A. H. Jr. (1973). “Nonobjective” gratings. PASP, 85, 174–176.

Mar, D. J., Marsh, J. P., Deen, C. P. et al. (2009). Micromachined silicon grisms for infrared optics. Appl. Opt., 48, 1016–1029.

Traub, W. A. (1990). Constant-dispersion grism spectrometer for channeled spectra. J. Opt. Soc. Am. A, 7, 1779–1791.

Chapter 11 – Ultraviolet, x-ray, and gamma ray astronomy

Atwood,W. B., Abdo, A. A., Ackermann, M. et al. (2009). The large area telescope on the Fermi gamma-ray space telescope mission. ApJ, 697, 1071–1102.

The detection on Earth of ionizing radiation whose strength increased with altitude was the first evidence for the existence of what, today, are known as cosmic rays. In the discussion which follows we will, for the most part, bypass the early history of controversies in this field over whether the radiation consisted of particles or gamma rays and over whether or not the radiation was of extraterrestrial origin. Instead, we will begin with our modern understanding that cosmic rays are indeed of cosmic origin and consist of energetic particles, most of which are charged. The focus thus will be on the measurable properties of such particles and the best ways to make such measurements.

Properties of cosmic rays

The most readily measurable properties of energetic particles are charge, mass, and energy. Charged particle trajectories can also be well determined locally. Such trajectories can be used within a detector to measure a particle charge to mass ratio from the curvature of a track in a magnetic field or to relate multiple secondary particle tracks back to a common point of interaction. However, except possibly for the very highest energy cosmic rays, a primary cosmic ray trajectory does not lead back to the location of the astrophysical source of the cosmic ray.

Observationally, cosmic rays at GeV energies are found to consist mostly of protons, with about a 10% contribution of helium nuclei, 1% of heavier nuclei, and an approximately 1% contribution of electrons and positrons.

This book is based on a required course for graduate students in Astronomy which I taught for a number of years at the University of Illinois. The premise of the course is that both theoretical astronomers and observers should have a basic understanding of the techniques of observational astronomy. The emphasis is on the underlying physics of the methods of detection and analytical tools (statistical and otherwise) that astronomers find useful. The great variety of current instruments and the rapid introduction of new instruments preclude an in-depth treatment of the peculiarities and idiosyncrasies of many instruments. But every instrument has its own idiosyncrasies and its own ways of corrupting the data and deceiving the observer. The topics in this book, I believe, cover the minimum which is required of anyone attempting to understand or interpret observational astronomy data.

Throughout the book equations are given in mks (SI) units so that it is easy to relate the discussion to practical quantities such as volts and watts. This is true even in the chapter on gravitational waves, a subject for which many texts and references use geometrized units (c = 1, G = 1). I prefer to keep c and G around rather than having to figure out where to put them when I need to calculate power. I also like being able to check equations using dimensional analysis. In the text other units are freely worked in.

Few physicists today doubt the reality of gravitational radiation. The existence of gravitational waves is a firm prediction of the theory of general relativity, and gravitational radiation is observed indirectly through the energy loss and decreasing orbital period of the Hulse–Taylor binary pulsar system PSR J1915+1606 (Hulse & Taylor, 1975). Observing gravitational radiation directly would certainly be a further confirmation of general relativity. But more importantly, observations of gravitational radiation will enable us to determine properties of regions and of times for which we otherwise have little information.

The pioneering work of Joseph Weber using resonant bar detectors (Weber, 1966) is of great importance in this field and has inspired much of the observational work that followed. Most books and reviews on gravitational wave detection begin with a discussion of Weber bars. In this chapter we concentrate on interferometric detectors, which seem at this time to hold the greatest promise for detecting gravitational waves.

Characteristics of gravitational radiation

Gravitation is described in the field equations of general relativity as curvature of space-time. In quantum field theory the mediator of the gravitational interaction is thought to be the massless, spin-2 graviton. In the classical limit these formulations are equivalent. Both predict the existence of gravitational radiation which is quadrupolar in nature.

In a linearized theory, gravitational waves in free space are described as small perturbations hμν on the Minkowski flat space-time metric.

Interaction of radiation and matter

In order to study electromagnetic radiation, it is necessary for the radiation to interact in some fashion with some physical “detector.” If we think of the radiation in terms of photons, there are three types of interactions available to us: the photoelectric effect, Compton scattering, and pair production. Variations on these effects form the basis of photon detectors. Electromagnetic radiation can also be thought of in terms of waves, and in some situations the wave picture is more appropriate for understanding the detection process. Wave detectors could either measure the electromagnetic field directly or measure the power transfer from electromagnetic energy into thermal energy. There is no strict dividing line between these views since electromagnetic radiation always retains both particle and wave characteristics. But roughly speaking, the particle viewpoint is more useful at high frequencies, where the photons are energetic, and the wave viewpoint is more useful at lower frequencies. One characteristic which helps determine which viewpoint may be more useful is 〈n〉, the average photon occupation number of the modes of the radiation field.

Photoelectric effect

For an isolated atom, there is a threshold energy for removing a bound electron, the ionization potential, which varies depending on what shell the electron occupies. The shells are designated K, L, M…, depending on the principal quantum number (n = 1, 2, 3, …). For hydrogen, the ionization potential from n = 1 corresponds to an ultraviolet photon (the Lyman limit at 91.2 nm or 13.6 eV).

In observational astronomy we study the processes by which Earth-bound astronomers obtain and interpret information about distant parts of the universe. Theoretical descriptions of the natural world and observational/experimental data are complementary, and their interplay is a fundamental feature of scientific inquiry. For progress in astronomy we need extensive, sensitive, and accurate observations. But such data do not come for free. They are not just lying around for anybody to pick up. Work is required. An observer who simply accepts data at face value is likely to encounter problems.

In studying the observational process it will be helpful to adopt the following point of view. There is something we will call information which is present in an astronomical source. This information leaves the source, perhaps in the form of electromagnetic radiation. As it travels from the source to the observer it passes through intervening regions, often being modified in the process. The information then reaches the detection system. This final stage inevitably involves significant modification of the information. Noise is added, much information is lost, and other changes occur. From this final state the astronomer attempts to infer characteristics of the original source.

Electromagnetic radiation

The most important carrier of astronomical information is electromagnetic radiation. The electromagnetic spectrum is commonly broken down into various wavelength bands, as indicated in Table 1.1. Each band may be roughly described by both a characteristic photon energy hν and a characteristic temperature hν/k.

We begin our treatment of optics by first considering geometrical optics. In the limit of small wavelengths, geometrical optics describes the direction in which light travels through space as it encounters materials with different indices of refraction. Initially the refractive index will simply be assumed to be a property of a material which describes the speed at which light propagates in that material. That will be sufficient to allow us to treat the theory of aberrations and to look into some basic aspects of telescope design. Next we will look at the physical origins of the refractive index and at the Fresnel coefficients, which are important in a number of contexts including the design of various spectroscopic devices. Then we will consider physical optics, the behavior of light in the regime of finite wavelengths where diffractive effects become important. This will include a look at the Airy pattern. Finally we will introduce the concepts of the point spread function and the modulation transfer function and use them to consider some general properties of imaging.

Geometrical optics

The properties of light propagation can often usefully be described by geometrical optics, an approximation which is valid in the limit of small wavelengths. The wavelength λ is assumed to be small compared with all relevant length scales, including the dimensions of any physical objects present. The media of propagation are described by various values of the refractive index n, which in general is wavelength dependent.

Sources of polarized radiation

Synchrotron radiation

Polarization of electromagnetic radiation may occur in a variety of astrophysical circumstances. In some cases the polarization may be considered to be intrinsic to the source (arising simultaneously with the radiation). One example is synchrotron radiation, in which the radiation arises from energetic electrons spiraling along magnetic field lines. The polarization of synchrotron radiation will be in general elliptical and will depend on the angle between the line of sight and the magnetic field. See Figure 17.1 for geometries giving rise to linear, elliptical, and circular polarization. For relativistic electrons, radiation is beamed in the forward direction, making linear polarization more likely to be seen than circular polarization. Linear polarizations approaching 50% are common at centimeter wavelengths in extragalactic radio jets. For a synchrotron spectral index of -1 (I(ν) ∝ ν-1), linear polarization up to 75% is possible (Saikia & Salter, 1988).

Zeeman effect

The Zeeman effect also produces polarized radiation. For a magnetic quantum numberM, magnetic fields split energy levels into 2M+1 magnetic sublevels. Radiation will then be linearly or circularly polarized depending on the direction of radiation with respect to the magnetic field and the change in the projected magnetic quantum number, as indicated in Figure 17.2. Relevant magnetic fields vary from 10-6 gauss for the interstellar medium, to 10 000 gauss for magnetic stars. Compact objects such as white dwarfs can have even higher fields.

Tables A4.1, A4.2, and A4.3 list major X-ray satellites in order of their launch date along with some basic parameters about each. Table A4.1 includes all missions completed by 1980, and provides basic information about each including the detectors, energy bandpass, peak effective area, and FOV. None of these missions used focusing X-ray optics, relying instead upon collimators to select sources in a limited FOV.

Table A4.2 lists missions launched between 1980 and 1996 which are no longer operating, while Table A4.3 gives parameters for missions launched since 1996, which are still returning data as of 2010. Many of the missions in Tables A4.2 and A4.3 used X-ray optics and so more information is provided including the PSF and detector spectral resolution.

Our primary source for this information, especially for the Uhuru, ANS, Ariel-V, SAS-3, OSO-8, HEAO-1, the Einstein Observatory, EXOSAT, ASCA, RXTE, Swift, and Suzaku missions, was the HEASARC list of observatories. In addition, the National Space Science Data Center spacecraft website was invaluable. Both sites contain a large number of original source references. Information was also taken from the HEASARC calibration database CALDB in order to determine the peak effective area and spectral resolution. For the ROSAT HRI, some information also came from the SAO ROSAT site. Specifications for Chandra, XMM–Newton and MAXI came from their websites. Other sources are given in footnotes to the tables.

The next five chapters cover the practical details of data analysis in X-ray astronomy. In this chapter we will consider what it takes to get the data to the stage of performing scientific analysis, which will itself be described in the following chapter. We will then survey the archives, catalogs, and software available, follow that with a short discussion of statistical issues peculiar to X-ray astronomy, and finish with the special considerations required when analyzing observations of sources which occupy the entire field-of-view (FOV).

We start with a description of the standard files, their contents, and the processing pipeline which produces them, as well as the initial data-reduction steps typically performed by the individual scientist.

The event file

All X-ray detectors measure individual photons. This is in contrast to many instruments for longer wavelengths, which measure integrated flux. The reason for this difference is that X-ray photons have relatively large energies, so single ones can be easily detected, but have relatively low fluxes, so they are easy to count. The basic data structure is thus a list of detected events, each of which has a set of attributes. Current X-ray instrumentation typically measures the position the X-ray arrived on the detector, the time of arrival, and some attribute which relates to the energy of the photon. Polarization is harder to determine and the first sensitive X-ray polarimeter is due to be launched on the GEMS satellite in 2014.