Flashcards · 7408 · Topic 9

Astrophysics flashcards

20 cards on Topic 9, subtopics 3.9.1 to 3.9.3. Pick a subtopic or study them all.

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Refracting telescope in normal adjustment: angular magnification and length: M = β/α = fₒ/fₑ. The lenses are fₒ + fₑ apart, the principal foci coincide, and the final image is at infinity.
Cassegrain telescope: Parabolic concave primary mirror and convex secondary mirror; light returns through a hole in the primary to the eyepiece.
Spherical aberration: Edge and central rays focus at different points (spherical surfaces). Cured by using a parabolic mirror.
Chromatic aberration: Lenses focus different colours at different points. Mirrors do not have it.
Resolving power vs collecting power: Resolving power: θ ≈ λ/D (Rayleigh criterion, θ in radians), the detail seen. Collecting power ∝ D², which sets how faint an object can be seen.
CCD vs the eye: A CCD has much higher quantum efficiency, resolution set by pixel spacing, long exposures and digital storage. The eye is real-time and needs no equipment.

Apparent magnitude m: The Hipparcos scale: the dimmest visible stars are m = 6; a lower number means brighter. A difference of 1 magnitude is a brightness ratio of 2.51; 5 magnitudes is about 100.
Absolute magnitude M, and the distance modulus: M is the apparent magnitude the star would have at 10 pc. m − M = 5 log₁₀(d/10), with d in parsecs.
A star has m − M = 5. How far away is it?: 5 log₁₀(d/10) = 5, so d/10 = 10 and d = 100 pc.
Wien's law and Stefan's law: Wien: λₘₐₓT = 2.9 × 10⁻³ m K. Stefan: P = σAT⁴, with A = 4πr² for a star.
In which stars are the hydrogen Balmer lines strongest, and why?: In A stars. The lines need hydrogen atoms in the n = 2 level: cooler stars have too few excited atoms, and in the hottest stars the hydrogen is mostly ionised.
HR diagram axes and regions: Absolute magnitude from +15 (bottom) to −10 (top); temperature from 50 000 K (left) to 2 500 K (right). Main sequence diagonal; giants top right; white dwarfs bottom left.
Evolution of a Sun-like star: Protostar → main sequence → red giant (moving up and right on the HR diagram) → white dwarf (moving left and down).
Type 1a supernova: Always the same peak absolute magnitude, so it is a standard candle; quick rise, slow fall. Faint distant ones suggest the Universe's expansion is accelerating (dark energy, controversial).

Red shift and recession speed: z = Δλ/λ = −v/c for v ≪ c, with v positive for approach. A receding source has negative v, so λ increases (red shift), z is positive and the recession speed is zc. Applies to optical and radio frequencies.
Hubble's law and the age of the Universe: v = Hd. The Universe is expanding; if H has been constant, its age ≈ 1/H (H in s⁻¹).
H = 70 km s⁻¹ Mpc⁻¹ (1 Mpc = 3.08 × 10²² m). Estimate the age of the Universe.: H = 70 × 10³ ÷ 3.08 × 10²² = 2.27 × 10⁻¹⁸ s⁻¹. 1/H = 4.4 × 10¹⁷ s ≈ 1.4 × 10¹⁰ years.
Two pieces of evidence for the Big Bang (besides Hubble's law): The cosmic microwave background (about 2.7 K, nearly uniform in all directions), and the relative abundance of hydrogen and helium (about 3 : 1 by mass).
Quasars: The most distant measurable objects; discovered as bright radio sources; large optical red shifts; huge power output; thought to be active supermassive black holes.
Detecting exoplanets: radial velocity vs transit method: Radial velocity: a periodic Doppler shift in the star's light. Transit: a periodic dip in the star's intensity, dip ≈ (r_planet/r_star)².