Dd0 dd0 d

This is the diffraction limit of the telescope, namely 0.05 for d 2.4 m, or 0.013 for d 10 m. Each speckle thus has the small size of the Airy disk expected in the absence of atmospheric turbulence There are thus 500 spatial elements across the two-dimensional image at the focus of our 2.4-m telescope. Only some of these will be bright (constructive interference) other elements will be dark (destructive interference). In general the bright spots (speckles) will be located randomly in the image...

Tip

Where E is the total energy (rest energy + kinetic energy), and mc2 106 MeV is the muon rest energy. What is the kinetic energy Ek of a muon (in GeV) that will just make it to sea level at the end of its (extended) mean life Assume the muon is created at a depth of 1000 kg m2 in the atmosphere, or about 18 km above sea level. You may approximate its speed of travel as about equal to the speed of light c and neglect any energy loss due to ionization during passage through the atmosphere. To what...

Figures

1.4 Brahe, Galileo, Kepler 6 1.9 Globular cluster M10 16 1.10 Andromeda nebula M31 17 2.1 Bands of the electromagnetic spectrum 26 2.2 Atmospheric absorption 30 3.1 Celestial sphere and the earth 36 3.2 Horizon coordinate system 38 3.3 Galaxy bulge, corona, globular clusters, spiral arms 41 3.4 Galactic coordinates 41 3.5 Celestial sphere, equatorial and galactic coordinates 42 3.6 Discrete radio sources, 1420 MHz 43 3.7 Solid angle element 46 4.1 Star motions in horizon coordinate system 61...

Specific intensity

Here we introduce the quantity that takes into account the spread of directions from which the radiation arrives from an extended source. It could be called directional spectral energy flux density, but we will use the simpler, but less informative, name specific intensity. A hypothetical antenna with a narrow beam and narrow bandwidth could survey the entire sky and produce a map of the brightness of the sky. Your eye does this when it surveys the sky and so does the radio antenna that...

Orbiting neutron stars

A neutron star is a possible end state of a star. Its nominal mass is 1.4 MQ and its radius 10 km. This is an extremely compact object a mass comparable to the mass of the sun is contained in an object the size of Manhattan. Neutron stars were first discovered in 1967 as radio pulsars. They spin and send out abeam of radiation that sweeps across the earth once each rotation, as does the searchlight beam in a lighthouse. An astronomer thus detects a pulsing radio source. There are 1500 pulsars...

Astronomy Methods

Astronomy Methods is an introduction to the basic practical tools, methods and phenomena that underlie quantitative astronomy. Taking a technical approach, the author covers a rich diversity of topics across all branches of astronomy, from radio to gamma-ray wavelengths. Topics include the quantitative aspects of the electromagnetic spectrum, atmospheric and interstellar absorption, telescopes in all wavebands, interferometry, adaptive optics, the transport of radiation through matter to form...

Multiple telescope interferometry

Radio astronomers have learned to overcome the limitations of diffraction with interferometry, the use of two or more telescopes viewing the same source at the same time. The instantaneous beam of two telescopes is an interference fringe pattern on the sky. As the earth rotates, the pattern sweeps across a postulated point source yielding a time varying interference signal when the signals from the two telescopes are summed or multiplied. Simple examples show that two telescopes on the rotating...

Early development of astronomy First astronomers

The rhythmic motions of the stars, the planets, and the sun in the sky have fascinated humankind from the earliest of times. The motions were given religious significance Figure 1.1. Stonehenge, an early astronomical observatory used for tracking the sun and moon in their seasonal excursions. (g) Crown copyright, NMR Figure 1.1. Stonehenge, an early astronomical observatory used for tracking the sun and moon in their seasonal excursions. (g) Crown copyright, NMR and were useful agricultural...

Info

A Diffuse objects ranging in size from 5' (Crab) to (Andromeda). a Diffuse objects ranging in size from 5' (Crab) to (Andromeda). as a spinning top precesses about the vertical. Because the equatorial coordinate system is, by definition, locked to the earth's equator and the vernal equinox, the coordinate system slowly slides around the sky as the earth precesses. The coordinates of any given star will therefore change slowly (< 1 per year), and one must assign an epoch or date to any such...

Photonelectron interactions

The interactions wherein an electron disrupts the serene straight-line travel of a photon are usually distinguished by the different energies of the incident photon. Usually, one may think of the electrons as being nearly at rest, but in certain cases, the electron may be very energetic and even relativistic such as in a hot plasma. The electrons may be free or part of an atom. But, in each of the three cases discussed here, Rayleigh, Thomson, and Compton scattering, the interaction is...

Lunar and planet motions eclipses

The bodies in the solar system are quite close to us compared to the stars thus they have substantial angular velocities relative to the earth. Their apparent positions on the celestial sphere change radically on an annual scale and by significant amounts day by day. The celestial motions of these bright objects have long fascinated humankind. The motions of the sun and moon on the celestial sphere lead to solar and lunar eclipses. The former occurs when the moon comes between the earth and sun...

Isophase patches and speckles

In the ideal case of no atmosphere, the electromagnetic signal would be a plane wave upon its arrival at the telescope (Fig. 8a). Its image in the focal plane would be an Airy disk of angular size X d where d (aj Plane wavetronl (b) Isoph& se patches (aj Plane wavetronl (b) Isoph& se patches (c) Instantaneously -- . - (c) Instantaneously -- . - Figure 5.8. Isophase patches arriving at lenses and mirrors. (a) Plane-parallel wavefronts yield a small...

Primary and secondary fluxes

Extensive Air Shower

The general picture that emerged from subsequent research is that charged particles (protons with an admixture of heavier atomic nuclei), are accelerated to high energies by processes not yet well determined, but probably in part in supernovae and the shock waves of their aftermath. They then travel through the Galaxy, trapped (stored) therein by the galactic magnetic fields about which they spiral under the influence of the v x B force. Some cosmic rays are so energetic they could not have...

Crosscorrelation or shading method

If there are multiple sources in the field of view, the observed response R'(t) would include the contributions of the several sources. (Here we choose the response function R' that is always positive, Fig. 2d). In the case of a rotating fringe pattern (Fig. 3), the responses of the different sources cancel or reinforce each other depending on the rotation angle of the earth. The modulation would go to zero if two sources (of equal intensities) were perchance modulating exactly out of phase...

Photographs and charts

Palomar, SRC, and ESO sky surveys The true comprehensive charts of the faint stars in the sky at optical wavelengths are actually deep (i.e., sensitive) photographs of the sky. The first and most famous of these is the Palomar Observatory Sky Survey (POSS-I) carried out in the early 1950s. It consists of 936 pairs of large glass plates (350 mm x 350 mm) taken with the large Schmidt telescope at Palomar Mountain in California. The plates cover declinations +90 to -30. At each position, a...

Horizon coordinate system

An observer on the earth's surface at low latitudes notes that the sun rises in the east and sets in the west. During the night, the same observer would note that the stars and planets also rise in the east, move across the sky, and set in the west. These motions are simply an effect of the earth's daily rotation about its axis. For an observer at the earth's north pole, the north celestial pole (NCP) of the celestial sphere is directly overhead (at the zenith). For this same observer, the...

Interplay of observation and theory

The objective of astronomical studies is to learn about the nature of the celestial objects, including their sizes, masses, constituents, and the basic physical processes that take place within or near them. Progress is made through an interplay of observational data and theoretical insight. Observations guide the theorist and theories suggest observations. The pace of this interplay greatly accelerated in the late nineteenth and twentieth centuries due to the rapid increase in technical...

Distances and sizes Distance ladder

The relative sizes of some astrophysical objects and the distances to them are listed in Table 2 and illustrated on logarithmic scales in Fig. 2. The large ranges mentioned above are very evident here. For example, the ratio of the size of the observable 266 9 Properties and distances of celestial objects Table 9.2. Size (radius) and distance examples Solar system Nearest star (Prox. Cen) Crab nebula Center of the Galaxy Galaxy (Milky Way) Andromeda galaxy, M31 Virgo cluster of galaxies 3C273...

Problems

8.2 Unresolved point-like sources Problem 8.21. (a) What is the (partial) luminosity within a narrow 104 Hz bandwidth at frequency v of a radio source radiating isotropically if it is detected at distance 3000 LY with a spectral flux density S 1.0 Jy in this band Repeat for the broad band 50 to 200 MHz if S(v) is constant at 1.0 Jy over this frequency range (b) Another source at the same distance has a spectral flux density S (W m-2 Hz-1) that varies as S kv-2 where k is a constant. The...

Pinhole Telescope

Spherical Pinhole Telescope

Optical light may be collected and focused by means of a transmitting lens that refracts the rays as shown in Figs. 1a and 2a. The disadvantage of a lens in astronomy is that the light must traverse the glass which can lead to imperfect focusing due for example to color dependence of the index of refraction (chromatic aberration). Also, the lenses become very heavy as they become larger. This makes difficult the precision positioning and support of the lens in a movable telescope structure as...

Antenna beams

The concept of an antenna beam is intrinsic to all astronomy. The beam is simply the portion of the sky observed by the detector at a given time (Fig. 5). For example, in a non-focusing detection system, mechanical collimators might restrict the field-of-view to a circular region on the sky of 0.7 radius. The detector would be said to have a 0.7 beam (half width) or 1.4 (full width) that views (0.7)2 1.5 deg2 of the sky. A parabolic radio antenna is a classic example of a focusing system. If...

Thermal and nonthermal radiation

Temperature is one of the most basic quantities in physics and astrophysics. At its simplest, according to the approximation hv kT (2.15), the frequencies of detected photons may be an indicator of the temperature of the originating bodies. For example, photons from the sun at optical frequencies tell us that the surface layers of the sun have temperature of 6000 K (kelvin). The infrared emission from a human being indicates a temperature of about 300 K. A pervasive radio radiation from the sky...

Celestial Sphere Problems

Problem 11.21. (a) The spectral flux density in wavelength units of some source varies as the inverse fourth power of the wavelength, Sx K4, where K is a constant. What is Sv, expressed as a function of v See if you can do this from first principles without reference to the text. Give the units of S in both forms. (b) Develop an expression for the specific intensity in wavelength units, x (k,T), for blackbody radiation. Start with the blackbody spectrum (23). Give the units of h. Problem 11.22....

Blackbody radiation

An emitting body can be optically thick. The conditions are such that the photons scatter, or are absorbed and re-emitted, many times prior to being emitted from the surface. In this case one obtains a spectral shape known as the blackbody spectrum. The spectrum depends upon the temperature of the emitting body. Many ordinary objects emit radiation that approximates a blackbody spectrum. Objects at room temperature (T 300 K) emit photons with a spectrum characteristic of T 300 K (infrared...

Spectral flux density

The flux from an unresolved (point-like) object may be considered to be a parallel beam of light or a plane wave originating at infinity. It impinges on the telescope with a given amount of energy deposited per second, per square meter, and per unit frequency interval at frequency v (e.g., in the interval v - 0.5 Hz to v + 0.5 Hz). This is known as the spectral flux density, S(v) Spectral flux density (W m-2 Hz-1) (8.1) but it could be more properly called the spectral energy flux density to...

Radiative transfer equation RTE

Specific Intensity

The differential equation that governs the absorption and emission in a layer of gas follows from the geometry of Fig. 17. A uniform cloud (source) of temperature Ts, depth A, and optical depth ta lies between the observer and a background source at some other temperature T0. Figure 11.17. Geometry for the radiative transfer equation. The background surface emits with specific intensity I0 and the intervening gas cloud emits thermal radiation with specific intensity Is when it is optically...

Spectral lines

Spectral lines provide powerful diagnostics of the conditions in the emitting region of a celestial source. Normal stars exhibit absorption lines due to decreasing temperature (with altitude) in the photosphere (Fig. 10a) while ejected gas near a star or an active corona can result in emission lines (Fig. 10b). Here we discuss the several types of spectral lines and their measurable characteristics. In the following section, we present the physics of radiation propagation that creates the...

Image formation

Focal Range Ray

Telescopes and antennas are the light collectors of astronomy. They come in varying shapes and sizes that depend in part on the frequency of radiation they are designed to detect. Most systems concentrate the incoming radiation by means of focusing. Optical telescopes gather light with a lens or a reflecting surface (a mirror). Radio telescopes make use of reflecting metal surfaces. X-ray telescopes make use of the reflecting character of a smooth metal surface for x rays impinging on it at a...

Solid angle on the celestial sphere

Solid Angle

The concept of solid angle Q is fundamental to all of astronomy. It is simply an angular area on the sky, or equivalently, on the celestial sphere. This area can be expressed as square degrees or square radians the latter unit is called the The solid angle is expressed in terms of two angular displacements, e.g., d9 and d0 in Fig. 7. The beam of an antenna, e.g., 1 x 1 , or 1x 2, or a fan beam of 1 x 100 can be characterized by its solid angle, approximately 1 deg2, 2 arcsec2, and 100 deg2 for...

Epochs for coordinate systems

The equatorial coordinate system used for celestial measurements depends on the orientation of the earth, and this is a continuously changing function of time (Section 3.2). The time chosen during some period (usually decades) for the specification of celestial coordinates in catalogs and communications between astronomers is called the standard epoch, traditionally expressed in years. The standard epochs in use in the last century, B1900.0 and B1950.0 were based on the Besselian year which...