ASTROPHYSICS – DEFINITIONS & FACTS

A1.1 Lenses and Optical Telescopes

The principal focus of a lens is the point at which rays parallel to the principle axis converge.

The focal length f, is the distance between the optical centre of the lens and the principle focus.

The power of a lens in dioptres is 1/ f.

A refracting telescope is in normal adjustment when the objective and eyepiece lenses are separated by the sum of their focal lengths: Angular magnification =    angle subtended by the IMAGE at the eye       =  b / a   =  fo / fe

angle subtended by the object at the unaided eye

Cassegrain reflecting telescope has a concave objective and a convex secondary mirror. Chromatic aberration is due to longer (red) wavelengths of light being refracted through smaller angles by a lens than shorter (blue) wavelengths.

Spherical aberration is due to rays further from the axis of a spherical mirror meeting closer to the mirror than rays nearer to the axis.

Rayleigh's Criterion states that 2 objects are just resolved when the bright central maximum, called the Airy Disc, of one object coincides with the first minimum of the other object.

The resolving power of a telescope is the smallest angular separation that can be observed, and is given by  θ = λ / D.

See the diffraction pattern from a circular aperture: A Charge Couple Device (CCD) is a silicon chip divided into picture elements or pixels.

Quantum efficiency = no. of incident photons producing a signal

total no. of incident photons

A1.2 Non Optical Telescopes

• Radio telescopes The resolving power of a radio telescope is given by Rayleigh's Criterion:  q = l / D,

since λ is LARGE, diameter D needs to be LARGE to get a good resolving power.

The dish does not have to be as perfect as a mirror for a light telescope.  As long as the surface is within about 1/20 wavelength, then the focusing will be unaffected by imperfections.  Also the reflector does not have to solid.  Fine wire mesh will do, since radio waves will not pass through a gap less than one wavelength.

• InfraRed telescopes

Water vapour in the atmosphere absorbs IR radiation, so space telescopes are best (eg. Spitzer)
Uses: Study interstellar dust, and star formation, study of Milky Way, extra-solar planets

• UV telescopes

UV is strongly absorbed by the atmosphere so space telescopes are best (eg. SOHO)

Used to determine chemical composition, densities, and temperature of stars and the interstellar medium
• X-Ray telescopes
X-rays are absorbed by Earth’s atmosphere so again space telescopes are best (eg. satellite CXO)
X-rays are expected from sources with very high temperatures: eg.neutron stars, black holes

A 1.3 Classification of Stars

Apparent magnitude m   = brightness as observed from Earth

The lower or more negative, the brighter it is (Sun is -26)

Best (feintest) naked eye visual magnitude = +6 , with long exposure cameras this can be increased considerably.

With a camera and telescope it can be as high as +31 (Hubble) Absolute magnitude M  = brightness we would observe from a distance of 10Pc

m  -  M  = 5 log (d / 10),   where d is the distance in Parsecs from Earth

1 Astronomical Unit (AU)  is the distance between the Earth and the Sun.

A star at a distance of 1 Parsec subtends an angle of 1 arcsecond across 1AU.

1 lightyear (ly) is the distance travelled by light in 1 year.

A black body is a perfect emitter and absorber of electromagnetic radiation. We assume that a star is a black body emitter

Study the intensity / wavelength variation for stars of different temperature: Wien’s Law:   the wavelength at which most radiation is emitted is inversely proportional to the absolute temperature,  λmaxT = constant = 0.0029mK.

Stefan’s Law:  the luminosity (power output) of a star is proportional to its surface area, and to the fourth power of its absolute temperature, P = σAT4.

Stellar spectral classes: O(hottest, blue)  B  A  F  G  K  M(coolest, red): Balmer absorption lines for hydrogen (which occur when hydrogen atoms in the star get excited to the n=2 level) the intensity of the Balmer absorption lines depends on the temperature of the star, so the temperature can be measured.

HR Diagram - classification and evolution of stars: O    B            A             F             G             K             M NB the HR diagram does not indicate time - the Sun actually spends most of its life (13 billion yrs) on the main sequence:

A more massive star will use up its hydrogen much faster and go through the life cycle at a faster rate.

Supernova - a very luminous star explosion, occurs towards the end of a very massive stars life. neutron stars - the remains of a massive star consisting entirely of neutrons- extremely dense, escape velocity close to light speed.

black hole - remains of very massive star, absorbs all light that hits it, escape velocity > than speed of light. The event horizon of a black hole is the boundary beyond which light cannot escape.

The radius of the event horizon is called the Swartzschild radius Rs, given by  Rs = 2GM / c2

A1.4 Cosmology

Doppler Shift    Df is will be + for recession, - for approach: Evidence for the Big Bang theory is the observed red-shift of galaxies, and the cosmic microwave background.

Hubble’s Law:    distance away of galaxy is directly proportional to recessional velocity,   v = Hd,    H = Hubble constant  = 65 ± 10 km s-1 Mpc-1

1/ H = age of the universe.

An open universe will expand for ever, but a closed universe will eventually collapse into a “Big Crunch”. The answer lies in knowing the density of the universe.

Quasars are the most distant, the most luminous and the most red-shifted bodies discovered so far. Many are intense radio sources.

Tony Mead 9.5.10.