Midterm ReviewAST443Stanimir Metchev2Administrative• Homework 2:– problems 4.4, 5.1, 5.3, 5.4 of W&J– due date extended until Friday, Oct 23• drop off in my office before 6pm• Midterm: Monday, Oct 26– 8:20–9:20pm in ESS 450– closed book– no cheat sheet– no need to memorize obscure constants or formulae3Midterm Review• Coordinates and time• Detection of light:– telescopes, detectors• Radiation:– specific intensity, flux density, etc– optical depth, extinction, reddening– differential refraction• Magnitudes and photometry:– apparent, absolute; distance modulus– CMDs and CCDs– photometry, PSF fitting• Statistics– testing correlations and hypotheses– non-parametric vs. parametric tests– one-tailed vs. two-tailed tests– one-sample, two-sample tests4Celestial Coordinates• horizoncoordinates– altitude/elevation (a),azimuth (A)– zenith, zenith angle(z)• observer’s latitude– angle PZ5Celestial Coordinates• equatorialcoordinates– right ascension• R.A., α– declination• DEC, δ• cf., Earth’s longitude,latitude• meridian, hour angle(HA)6Celestial Coordinates• ecliptic coordinates– ecliptic longitude (λ)– ecliptic latitude (β)• vernal equinox (ϒ)– Earth passes through eclipticon Mar 20/21– origin of equatorial andecliptic longitude• Earth’s axial tilt:–ε = 23.439281º– a.k.a., “obliquity of theecliptic”7Celestial Coordinates• galactic coordinates– galactic longitude (l; letter“ell”)• l = 0 approx. toward galacticcenter (GC)• definitionlNCP = 123º (B1950.0)– galactic latitude (b)• NGP definition (B1950.0)α = 12h 49mδ = 27.4º– Sagittarius Al = 359º 56′ 39.5″b = –0º 2′ 46.3″8Coordinate Transformations• equatorial ↔ ecliptic• equatorial ↔ horizontal! cos"cos#= cos$cos%cos"sin#= cos$sin%cos&' sin$sin&sin"= cos$sin%sin&+ sin$cos&cos$sin%= cos"sin#cos&+ sin"sin&sin$= sin"cos&' cos"sin#sin&! cos asin A = "cos#sin HAcos acos A = sin#cos$" cos#cos HA sin$sin a = sin#sin$+ cos#cos HA cos$cos#sin HA = "cos asin Asin#= sin a sin$+ cos a cos A cos$φ ≡ observer’s latitude9Equatorial CoordinateSystems• FK4– precise positions and motions of 3522 stars– adopted in 1976– B1950.0• FK5– more accurate positions– fainter stars– J2000.0• ICRS (International Celestial Reference System)– extremely accurate (± 0.5 milli-arcsec)– 250 extragalactic radio sources• negligible proper motions– J2000.010Astronomical Time• sidereal time– determined w.r.t. stars– local sidereal time (LST)• R.A. of meridian• HA of vernal equinox– sidereal day: 23h 56m 4.1s• object’s hour angleHA = LST – α11Astronomical Time• sidereal time– determined w.r.t. stars– local sidereal time (LST)• R.A. of meridian• HA of vernal equinox– sidereal day: 23h 56m 4.1s• object’s hour angleHA = LST – α• solar time– solar day is 3 min 56 seclonger than sidereal day12Astronomical Time• universal time– UT0: determined from celestial objects• corrected to duration of mean solar day• HA of the mean Sun at Greenwich (a.k.a., GMT)– UT1: corrected from UT0 for Earth’s polar motion• 1 day = 86400 s, but duration of 1 s is variable– UTC: atomic timescale that approximates UT1• kept within 0.9 sec of UT1 with leap seconds• international standard for civil time• set to agree with UT1 in 1958.013Astronomical Time• tropical year– measured between successive passages of the Sun through the vernalequinox– 1 yr = 365.2422 mean solar days• mean sidereal year– Earth: 50.3″/yr precession in direction opposite of solar motion– 365.2564 days• Julian calendar– leap days every 4th year; 1 yr = 365.25 days– t0 = noon on Jan 1st, 4713 BC• Gregorian calendar– no leap day in century years not divisible by 400 (e.g., 1900)– 1 yr = 365.2425 days14Coordinate Epochs• Coordinates are given at B1950.0 or J2000.0 epochs– Besselian years (on Gregorian calendar; tropical years)– Julian years (Julian calendar)• Gregorian calendar is irregular– complex for precise measurements over long time periods• Julian epoch:– Julian date: JD = 0 at noon on Jan 1, 4713 BC– J = 2000.0 + (JD – 2451545.0) / 365.25– J2000.0 defined at• JD 2451545.0• January 1, 2000, noon15Focusing• focal length (fL), focal plane• object size (α, s) in the focal planes = fL tan α ≈ fLα• plate/pixel scaleP = α/s = 1/fL– Lick observatory 3m• fL = 15.2m, P = 14″/mm16Energy and Focal Ratio• Specific intensity:– Planck law– [erg s–1 cm–2 Hz–1 sterad–1] or [Jy sterad–1]• Integrated apparent brightnessEp ∝ (d / fL)2 : energy per unit detector area• focal ratio: ℜ ≡ fL / d– “fast” (< f/3) vs. “slow” optics (>f/10)– fast data collection vs. larger magnificationmagnification = fL / fcamera! I(",T) =2h"3c21eh"kT#117Optical Telescope ArchitecturesAlso:• Schmidt-Cassegrain• spherical primary (sph. aberration), corrector plate; cheap for large FOV• no coma or astigmatism; severe field distortion• Ritchey-Chrétien• modified Cassegrain with hyperbolic primary and hyperbolic convex secondary• no coma; but astigmatism, some field distortion18Imaging through a TurbulentAtmosphere: Seeing• FWHM of seeing disk–θseeing <1.0″ at a good site• r0: Fried parameter–θseeing = 1.2 λ/r0– r0 ∝ λ6/5 (cos z)3/5–θseeing ∝ λ–1/5• t0: coherence time– t0 = r0 / vwind– vwind ~ several m/s– t0 is tens of milli-sec19Basic Concept of aSemi-Conductor Detector• electron-hole pair generation• doping:– n-type (electrons)– p-type (holes)– creates additional energy levelswithin band gap– increases conductivity• silicon (Si)– band gap: Eg = 1.12 eV• cut-off wavelength λc = 1.13µm– free-electron energy: 4 eV (3000Å)– 1 photon -> 1 electron! "c=hcEg=1.24µmEg(eV)20Basic Concept of a CCD Pixel:A P-N Photo Diode• depleted region– low conductivity– can support an E field• net positive charge (higher charge density near top)• additional E-field applied• subsequently generated electrons get trapped in potential well near top21Charge Transfer22Front- vs. Back-Illumination23Read Noise• electrons / pix / read• sources– A/D conversion not perfectly repeatable– spurious electrons from electronics (e.g.,from amplifier heating)• alleviated through cooling• nowadays: <3–10 electrons24Dark Current• electrons / pixel / second• source– thermal