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Chapter 02 Astronomical Measurements Astronomical Measurements 1 3 How do we “see” the Galaxy? Chapter 02 Astronomical Measurements Astronomical Measurements Astronomical Measurements References: CBMB: ch 1 CO: sec 1.3, 24.3 BM: sec 2.1, 2.2, 2.3, 2.5; 3.5, 3.6, 3.7 2 4 How do we “see” the Galaxy? Radiative Mechanisms Astronomical Measurements Astronomical Measurements photons continuum lines thermal synchrotron molecular atomic emission (rotational, relativistic jets (electronic, ro-vibrational, ionization, etc) electronic, jets, fine-structure, molecular blackbody bremsstrahlung hyper fine-structure, ionization, etc) clouds (graybody) (free-free outflows, stars, dust emission) molecular optically thick ionized thermal clouds emissions jets, HII regions 5 7 Equatorial Coordinates Galactic Coordinates Astronomical Measurements Astronomical Measurements (α, δ) = (RA, Dec) (l, b) = (Galactic longitude, Galactic latitude) Declination δ Right ascension α Described by 24 hrs 1 hour = 15 deg Hour circle Local sidereal time: elapsed time since the vernal equinox last traversed the meridian (hour angle of the vernal equinox) Hour angle H Hour circle Carroll & Ostlie Fig. 24.17 Carroll & Ostlie Fig. 1.13 6 8 Precession & Epoch Radial Velocities Astronomical Measurements Astronomical Measurements Precession Frequency observed by an observer First observed by Hipparchus moving at a velocity υr Slow wobble of Earth’s rotation axis due to its non-spherical shape and its ⌫ =(1 β)⌫0 − interactions with the Sun and the Moon β υ /c Slow precession ⌘ r Epoch 1 γ Commonly used: B1950, J2000 ⌘ 1 β2 − Altair, the brightest star in Aquila p (J2000)(19h50m47.0s,+8°52′6.0″) Doppler e↵ect γ 1 ! (B1950)(19h48m22.4s,+8°44′24.8″) ∆λ υr = c λ0 Signs: Carroll & Ostlie Fig. 1.15 Blueshifted: υr < 0, ⌫ > ⌫0 Redshifted: υr > 0, ⌫ < ⌫0 Carroll & Ostlie Fig. 1.1 9 11 Magnitudes Stellar Spectral Types Astronomical Measurements Astronomical Measurements Astronomers measure the brightness of a star with magnitude,which (early) O B A F G K M L T Y (late) is based on human eye response to the light and therefore on a log- Stars (a.k.a. dwarfs): OBAFGKM arithmic scale. In short, 5 magnitude increment corresponds to 100 Brown dwarfs: LTY times dimmer in brightness. Credit: KPNO 0.9-m Telescope, Followed by subclass 0, 1, ..., 9 AURA, NOAO, NSF Apparent magnitudes f m m = k log 1 1 − 2 − f ✓ 2 ◆ f1 0.4(m m ) = 10− 1− 2 f2 Absolute magnitudes m M = 5 log d 5, distance modulus − − D 2 f = F, where D = 10 pc d ✓ ◆ f d m M = 2.5 log = 5 log − − F D ✓ ◆ ✓ ◆ 10 12 Filters and Colors Luminosity Classes Astronomical Measurements Astronomical Measurements U B V R I J H K L M Morgan-Keenan (MK) luminosity class I. supergiants II. bright giants III. normal giants IV. subgiants V. dwarfs = main sequence Credit: Sky & Telescope 13 15 Colors Interpretation of Stellar Spectra Astronomical Measurements Astronomical Measurements With more than one filter bands, we can take the di↵erence in magni- E↵ective temperature Te↵ : tudes measured in two di↵erent bands to form a color, or color index for a selected source. Let X and Y denote two di↵erent filters, a color L 1/4 T . can be obtained with e↵ ⌘ 4⇡ R2σ ✓ SB ◆ X Y m m − ⌘ X − Y Surface gravity: pressure-broadening lines 1 dλ Sλ(X)fλ = const. 2.5 log 0 G − 1 dλ S (Y )f g M. R0 λ λ ⌘ R2 A color can serve as a measure of stellarR temperature when the amount Chemical compositions: metallicity, Z, or iron abundance of extinction is known. Fe n(Fe) n(Fe) log log . H ⌘ n(H) star − n(H) 14 16 Stellar Astronomical Measurements Astronomical Measurements Spectral Types Hertzsprung- Russell Diagram 22000 stars from Hipparcos catalog and 1000 from Gliese catalog of nearby stars Credit: Richard W. Pogge 17 19 Interstellar Interstellar Dust Astronomical Measurements Astronomical Measurements Medium Extinction: measure of absorption Reddening: measure of frequency response, i.e. colors Display of ISM Absorption: dark clouds Scattering: reflection nebulae Emission: emission nebulae Credit: Daniel Verschatse (Antilhue Observatory) Credit: Nick Strobel, Astronomy Notes 18 20 Interstellar Extinction Extinction & Reddening Astronomical Measurements Extinction, AX A m m X ⇥ X − X,0 where mX,0 is the magnitude that would be observed in the absence of dust. Reddening or color excess, E(X Y ) − E(X Y ) [m m ] [m m ] − ⇥ X − Y − X,0 − Y,0 = A A X − Y Measured AX when mX is known m = M + A + 5 log d 5 X X X − 21 23 Standard ISM Extinction Law Color-Color Diagram Astronomical Measurements Astronomical Measurements E(X V ) AX Band X − E(B V ) A − V Reddening vector U 1.64 1.531 B 1 1.324 V 0 1 1989ApJ...345..245C R -0.78 0.748 I -1.6 0.482 J -2.22 0.282 H -2.55 0.175 K -2.74 0.112 L -2.91 0.058 M -3.02 0.023 N -2.93 0.052 Carroll & Ostlie Fig. 3.11 22 24 Extinction Curve Reddening-Free Indices stronomical Measurements A Astronomical Measurements Reddening-free indices: a photometric parameter that depends only on the AV spectral type of a star and is independent of the amount of reddening. : slope of extinction curve AJ RV near the V band E(U B) Q (U B) − (B V ) ⌘ − − E(B V ) − A A R V = V − V ⌘ A A E(B V ) (U B) 0.72(B V ). B − V − ' − − − 3.1 ' For early-type stars of spectral types O through A0, Q determines uniquely a star’s intrinsic color from photometric data alone without the need for their Gas-to-dust ratio spectra. One finds that NH 21 2 1 (B V )0 =0.332Q. =5.8 10 cm− mag− , − E(B V ) ⇥ − Spectral Type Q Spectral Type Q equivalent to a mass ratio of 100. O5 -0.93 B3 -0.57 One may infer the column density O8 -0.93 B5 -0.44 2 NH (cm− ) by measuring the color ex- O9 -0.9 B6 -0.37 cess E(B V ) (mag). B0 -0.9 B7 -0.32 − B0.5 -0.85 B8 -0.27 Cardelli, Clayton, & Mathis, 1989, ApJ, 345, 245 Mathis 1990, ARA&A, 28, 37 B1 -0.78 B9 -0.13 B2 -0.7 A0 0 25 27 Distances for Nearby Stars Moving Cluster Method I Astronomical Measurements Astronomical Measurements Photometric parallax d = 10 (m-M+5)/5 Trigonometric parallax Moving-cluster method Secular parallax Statistical parallax Proper motions of Hyades members Carroll & Ostlie Fig. 24.29 26 28 Trigonometric Parallax Moving Cluster Method II Astronomical Measurements Astronomical Measurements Require stationary background references Determine the distance of a star cluster with identified members and the con- Hipparcos: accuracy of ~ 2 mas vergent point 1 d tan φ υ µ − parsec (parallax-second; pc) = r . pc 4.74 km s 1 mas yr 1 − ✓ − ◆ = 3.09 × 1018 cm ⇣ ⌘ = 3.26 light years υt = υr tan φ = 206264.8 AU = µd d 1 = pc p Carroll & Ostlie Fig. 24.30 29 31 Secular Parallax I Secular Parallax III Astronomical Measurements Astronomical Measurements Utilize solar peculiar motion to extend the baseline for trigonometric parallaxes (xˆi υˆ ) ((υi xˆi)+(xˆi υ )) µ i = ⇥ · ⇥ ⇥ -1 -1 k x sin φ Solar motion = 13.4 km s = 2.8 AU yr i i 2 υ xˆi υˆ (xˆi υˆ ) (xˆi υi) Select stars of same spectral type, same distance (apparent xi = | ⇥ | ⇥ · ⇥ ) µ i sin φi − µ i sin φi magnitude) k k 2 sin φi (xˆi υˆ ) (xˆi υi) = υ ⇥ · ⇥ . µ i sin φi − µ i sin φi k k =0 ⇥ d = Taking average over all N stars, we| find that{z the second} term vanishes µ d ⇥ µ since i υi = 0 by our choice of reference frame. Given p 1/xi,we obtain h i⌘ P µ i sin φi k p = h 2 i h i υ sin φi h i υr = υ ± 30 32 Secular Parallax II Statistical Parallax Astronomical Measurements Astronomical Measurements Statistical parallaxes are similar to secular parallaxes but use the per- pendicular component of the proper motions. An additional assumption Choose a frame in which the µ i mean velocity of the stars of ⊥ µi µi ⇥ˆ is introduced that the velocities vi are isotropically distributed. the · observed radial velocity of the ith star is µ µ i the chosen group is zero, i.e. i xˆ uri = xˆi (υi υ ) i υi = 0. The heliocentric ve- i · − locity of the ith star is φi xˆi = xˆi υi υ cos φi. υ · − P φi The component of vi perpendicular to the plane congaing the Sun, the ui υi υ ⌘ − star, and v is xiµ i, and by the hypothesis that the mean magnitude ? of any component of vi is the same, we have Given the vector identity (a b) c =(b c) a, one can prove that ⇥ · ⇥ · xˆi υi = xiµ i . h| · |i h| ? |i (ui xˆi) xˆi ((υi υ ) xˆi) xˆi Therefore, the statistical parallax is µi = ⇥ ⇥ = − ⇥ ⇥ . xi xi µ i p = h| ? |i µi υˆ (((υi υ ) xˆi) xˆi) υˆ h i uri + υ cos φi µ i = · = − ⇥ ⇥ · h i k sin φi xi sin φi Note that isotropic assumption is not always valid. A more sophisticated (xˆi υˆ ) ((υi υ ) xˆi) = ⇥ · − ⇥ . analysis involves the ellipsoidal shape of the random velocity distribution x sin φ i i is also available. 33 35 Summary of Methods Biases in Counting Astronomical Measurements Astronomical Measurements Supergiants Occurs in a survey of fixed solid angle, in which the volume studied increases with distance clusters Malmquist bias (Malmquist 1922, 1936) O-A stars The mean absolute magnitude of observed sample is brighter than clusters, secular and statistical parallaxes the mean absolute magnitude of the population F-M dwarfs Caused by magnitude-limited survey, i.e.
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