1 / 42

Observational Cosmology: 4. Cosmological Distance Scale

Observational Cosmology: 4. Cosmological Distance Scale. “ The distance scale path has been a long and tortuous one, but with the imminent launch of HST there seems good reason to believe that the end is finally in sight .” —  Marc Aaronson (1950-1987) 1985 Pierce Prize Lecture).

marvinc
Download Presentation

Observational Cosmology: 4. Cosmological Distance Scale

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Observational Cosmology: 4. Cosmological Distance Scale “The distance scale path has been a long and tortuous one, but with the imminent launch of HST there seems good reason to believe that the end is finally in sight.” — Marc Aaronson (1950-1987) 1985 Pierce Prize Lecture).

  2. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.1: Distance Indicators • Measurement of distance is very important in cosmology • However measurement of distance is very difficult in cosmology • Use a Distance Ladder from our local neighbourhood to cosmological distances Distance Indicators • Primary Distance Indicators direct distance measurement (in our own Galaxy) • Secondary Distance Indicators Rely on primary indicators to measure more distant object.  Rely on Primary Indicators to calibrate secondary indicators!

  3. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.1: Distance Indicators Distance Indicators Primary Distance Indicators • Radar Echo • Parallax  • Moving Cluster Method • Main-Sequence Fitting  • Spectroscopic Parallax • RR-Lyrae stars • Cepheid Variables • Galactic Kinematics • Secondary Distance Indicators • Tully-Fisher Relation • Fundamental Plane • Supernovae • Sunyaev-Zeldovich Effect • HII Regions • Globular Clusters • Brightest Cluster Member • Gravitationally Lensed QSOs • Surface Brightness Fluctuations

  4. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators Primary Distance Indicators Primary Distance Indicators • Radar Echo • Parallax  • Moving Cluster Method • Main-Sequence Fitting  • Spectroscopic Parallax • RR-Lyrae stars • Cepheid Variables • Galactic Kinematics

  5. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators Radar Echo • Within Solar System, distances measured, with great accuracy, by using radar echo • (radio signals bounced off planets). • Only useful out to a distance of ~ 10 AU beyond which, the radio echo is too faint to detect. 1 AU = 149,597,870,691 m

  6. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators • Observe a star six months apart,(opposite sides of Sun) • Nearby stars will shift against background star field • Measure that shift. Define parallax angle as half this shift Trigonometric Parallax

  7. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 p d 1 AU 1 radian = 57.3o = 206265" 4.2: Primary Distance Indicators • Observe a star six months apart,(opposite sides of Sun) • Nearby stars will shift against background star field • Measure that shift. Define parallax angle as half this shift Trigonometric Parallax Define a parsec (pc) which is simply 1 pc = 206265 AU =3.26ly.  A parsec is the distance to a star which has a parallax angle of 1" Nearest star - Proxima Centauri is at 4.3 light years =1.3 pc  parallax 0.8" Smallest parallax angles currently measurable ~ 0.001"  1000 parsecs  parallax is a distance measure for the local solar neighborhood.

  8. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators • The Hipparcos Space Astrometry Mission • Precise measurement of the positions, parallaxes and proper motions of the stars. • Mission Goals • - measure astrometric parameters 120 000 primary programme stars to precision of 0.002” • - measure astrometric and two-colour photometric properties of 400 000 additional stars (Tycho Expt.) • Launched by Ariane, in August 1989, • ~3 year mission terminated August 1993. • Final Hipparcos Catalogue • 120 000 stars • Limiting Magnitude V=12.4mag • complete fro V=7.3-9mag • Astrometry Accuracy 0.001” • Parallax Accuracy 0.002” Trigonometric Parallax

  9. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators • GAIA MISSION (ESA launch 2010 - lifetime ~ 5 years) • Measure positions, distances, space motions, characteristics of one billion stars in our Galaxy. • Provide detailed 3-d distributions & space motions of all stars, complete to V=20 mag to <10-6”. • Create a 3-D map of Galaxy. Trigonometric Parallax

  10. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 The mean distance of the stars is 4.16 for Solar motion in au/yr. 4.2: Primary Distance Indicators • Used to measure distance to stars, assumed to be approximately the same distance from the Earth. • Mean motion of the Solar system is 20 km/s relative to the average of nearby stars • corresponding relative proper motion, dq/dt away from point of sky the Solar System is moving toward. • This point is known as the apex • For anangle q to the apex, the proper motion dq/dt will have a mean component sin(q) (perpendicular tovsun ) • Plot dq/dt - sin(q) slope = m Secular Parallax green stars show a small mean distance red stars show a large mean distance http://www.astro.ucla.edu/~wright/distance.htm Statistical Parallax If stars have measured radial velocities,  scatter in proper motions dq/dt can be used to determine the mean distance.

  11. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 vC vt q vr q d m (“/yr) Tangential Velocity (km/s) 4.2: Primary Distance Indicators Moving Cluster Method Observe cluster some years apart  proper motion m Radial Velocity (km/s) vR from spectral lines Stars in cluster move on parallel paths  perceptively appear to move towards common convergence point (Imagine train tracks or telegraph poles disappearing into the distance) Distance to convergence point is given by q Main method for measuring distance to Hyades Cluster ~ 200 Stars (Moving Cluster Method  45.7 pc). One of the first “rungs” on the Cosmological Distance Ladder c.1920: 40 pc (130 ly) c.1960: 46 pc (150 ly) (due to inconsistency with nearby star HRD) Hipparcos parallax measurement 46.3pc (151ly) for the Hyades distance.

  12. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators Ursa Major Moving Cluster: ~60 stars 23.9pc (78ly) Scorpius-Centaurus cluster: ~100 stars 172pc (560ly) Pleiades: ~ by Van Leeuwen at 126 pc, 410 ly) Moving Cluster Method • Hipparcos 3D structure of the Hyades as seen from the Sun in Galactic coordinates. • X-Y diagram = looking down the X-axis towards the centre of the Hyades. • Note; Larger spheres = closer stars • Hyades rotates around the Galactic Z-axis. • Circle is the tidal radius of 10 pc • Yellow stars are members of Eggen's moving group (not members of Hyades). • Time steps are 50.000 years. (Perryman et al. )

  13. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 • can calculate • Flux (S) from luminosity, (L) • Calculate distance (DL) • Measuring redshift (z) •  Cosmological parameters Ho, Wm,o, WL,o DISTANCEMODULUS 4.2: Primary Distance Indicators Standard Rulers and Candles • To measure greater distances (>10-20kpc - cosmological distances) •  Require some standard population of objects • e.g., objects of • the same size (standard ruler) • or • the same luminosity (standard candle) • and • high luminosity

  14. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 AGB Red Giant Branch Get Distance from the distance modulus Turn off near stars Magnitude (more -ve) Main sequence WHITE DWARF m-M far stars  temperature 4.2: Primary Distance Indicators Einar Hertzsprung & Henry Norris Russell: Plot stars as function of luminosity & temperature  H-R diagram Normal stars fall on a single track  Main Sequence Main sequence Fitting Observe distant cluster of stars, Apparent magnitudes, m, of the stars form a track parallel to Main Sequence  correctly choosing the distance, convert to absolute magnitudes, M, that fall on standard Main Sequence. • Useful out to ~few 10s kpc (main sequence stars become too dim) • used to calibrate clusters with Hyades

  15. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators Spectroscopic Parallax Information from Stellar Spectra • Spectral Type  Surface Temperature - OBAFGKM RNS • O stars - HeI, HeII • B Stars - He • A Stars - H • F-G Stars - Metals • K-M Stars - Molecular Lines • Surface Gravity  Higher pressure in atmosphere  line broadening, less ionization - Class I(low) -VI (high) • Class I - Supergiants • Class III - Giants • Class V - Dwarfs • Class VI - white Dwarfs Temperature from spectral type, surface gravity from luminosity class  mass and luminosity. Measure flux  Distance from inverse square Law

  16. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators Cepheid variable stars - very luminous yellow giant or supergiant stars. Regular pulsation - varying in brightness with periods ranging from 1 to 70 days. Star in late evolutionary stage, imbalance between gravitation and outward pressure pulsation Radius and Temperature change by 10% and 20%. Spectral type from F-G Cepheid Variables • Henrietta S. Leavitt (1868 - 1921) - study of 1777 variable stars in the Magellanic Clouds. • c.1912 - determined periods 25 Cepheid variables in the SMC  Period-Luminosity relation • Brighter Cepheid Stars = Longer Pulsation Periods • Found in open clusters (distances known by comparison with nearby clusters).  Can independently calibrate these Cepheids

  17. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 2 types of Classical Cepheids Distance Modulus 4.2: Primary Distance Indicators Cepheid Variables Prior to HST, Cepheids only visible out to ~ 5Mpc

  18. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.2: Primary Distance Indicators Stellar pulsation  transient phenomenon Pulsating stars occupy instability strip ~ vertical strip on H-R diagram.  Evolving stars begin to pulsate  enter instability strip. Leave instability strip  cease oscillations upon leaving.   RR Lyrae Variables • RR-Lyrae stars • Old population II stars that have used up their main supply of hydrogen fuel • Relationship between absolute magnitude and metallicity (Van de Bergh 1995) • Mv = (0.15 ±0.01) [Fe/H] ±1.01 • Common in globular clusters major  rung up in the distance ladder • Low luminosities,  only measure distance to ~ M31

  19. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.3: Secondary Distance Indicators Secondary Distance Indicators Secondary Distance Indicators • Tully-Fisher Relation • Fundamental Plane • Supernovae • Sunyaev-Zeldovich Effect • HII Regions • Globular Clusters • Brightest Cluster Member • Gravitationally Lensed QSOs • Surface Brightness Fluctuations

  20. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Globular Cluster Luminosity Function (GCLF) (similarly for PN) Use Number density of globular clusters as function of magnitude M Peak in luminosity function occurs at same luminosity (magnitude) Number density of globular clusters as function of magnitude M for Virgo giant ellipticals 4.3: Secondary Distance Indicators Globular Clusters • Main Sequence Fitting • H-R diagram for Globular clusters is different to open Clusters (PII objects!) • Cannot use M-S fitting for observed Main Sequence Stars • Use Theoretical HR isochrones to predict Main Sequence  distance • Alternatively use horizontal branch fitting • Angular Size • Make assumption that all globular clusters ~ same diameter ~ D • Distance to cluster, d, is given by angualr size q=D/d Distance range of GCLF method is limited by distance at which peak Mo is detectable, ~ 50 Mpc

  21. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Centrifugal Gravitational Redshift Assume same mass/light ratio for all spirals Assume same surface brightness for all spirals Flux In Magnitudes Dn More practically Blueshift Wo = spread in velocities i = inclination to line of sight of galaxy 4.3: Secondary Distance Indicators Tully Fisher Relationship

  22. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 DISTANCEMODULUS Tully-Fisher Fornax & Virgo Members Bureau et al. 1996 • TF Depends on Galaxy Type Mbol = -9.95 lgVR + 3.15     (Sa) Mbol = -10.2 lgVR + 2.71     (Sb) Mbol = -11.0 lgVR + 3.31     (Sc) 4.3: Secondary Distance Indicators Tully Fisher Relationship Tully and Fischer (1977): Observations with I  45o a = 6.25±0.3 b = 3.5 ± 0.3, Knowing M   Problems with Tully-Fisher Relation • TF depends on waveband • Relation is steeper by a factor of two in the IR band than the blue band. (Correction requires more accurate measure of M/L ratio for disk galaxies)

  23. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 M32 (companion to M31) Ellipticals Lenticulars Intensity profile (surface brightness) (r1/4 De Vaucouleurs Law) http://burro.astr.cwru.edu/Academics/Astr222/Galaxies/Elliptical/kinematics.html Virial Theorem Mass/Light ratio Fundamental Plane (Dressler et al. 1987) 4.3: Secondary Distance Indicators • Elliptical Galaxies  Cannot use Tully Fisher Relation • Little rotation • little Hydrogen (no 21cm) D-s Relationship Faber-Jackson (1976): Elliptical GalaxiesLs4 L = Luminosity s= central velocity dispersion Large Scatter  constrain with extra parameters Define a plane in parameter space Faber-Jackson Law

  24. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 I I 4.3: Secondary Distance Indicators Any 2 parameters  scatter (induced by 3rd parameter) D-s Relationship • Combine parameters • Constrain scatter • Fundamental Plane Instead of Io, ro: Use Diameter of aperture, Dn, Dn - aperture size required to reach surface Brightness ~ B=20.75mag arcsec2 • Advantages • Elliptical Galaxies - bright  measure large distances • Strongly Clustered large ensembles • Old stellar populations  low dust extinction • Disadvantages • Sensitive to residual star formation • Distribution of intrinsic shapes, rotation, presence of disks • No local bright examples for calibration • Usually used for RELATIVE DISTANCES and calibrate using other methods

  25. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Consider 2 images taken by CCD to illustrate the SBF effect; Represent 2 galaxies with one twice further away as the other measure the mean flux per pixel (surface brightness) rms variation in flux between pixels. Compare nearby dwarf galaxy, nearby giant galaxy, far giant galaxy Choose distance such that flux is identical to nearby dwarf. The distant giant galaxy has a much smoother image than nearby dwarf.’ 4.3: Secondary Distance Indicators SBF method Measure fluctuation in brightness across the face of elliptical galaxies Fluctuations - due to counting statistics of individual stars in each resolution element (Tonry & Schneider 1988) Surface Brightness Fluctuations Can use out to 70 Mpc with HST

  26. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.3: Secondary Distance Indicators • Assume: • Galaxy clusters are similar • Brightest cluster members ~ similar brightness ~ cD galaxies Brightest Cluster Members • Calibration: • Close clusters • 10 close galaxy clusters: • brightest cluster member MV = 22.820.61 • Advantage: • Can be used to probe large distances • Disadvantage: • Evolution ~ galaxy cannibalism • Large scatter in brightest galaxy • Use 2nd, 3rd brightest • Use N average brightest N galaxies.

  27. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Type Ib,c (H poor massive Star M>8Mo) Stellar wind or stolen by companion Type II (Hydrogen Lines) Type Ia (M~1.4Mo White Dwarf + companion) Type I (no Hydrogen lines) Supernova ! Massive star M>8Mo White dwarf pushed over Chandrasekhar limit by accretion begins to collapse against the weight of gravity, but rather than collapsing , material is ignited consuming the star in an an explosion 10-100 times brighter than a Type II supernova 4.3: Secondary Distance Indicators (similarly applied to novae) Supernova Ia Measurements SN1994D in NGC4526

  28. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 SN1994D in NGC4526 in Virgo Cluster (15Mpc) 4.3: Secondary Distance Indicators • Supernova Ia: • Found in Ellipticals and Spirals (SNII only spirals) • Progenitor star identical • Characteristic light curve fast rise, rapid fall, • Exponential decay with half-Life of 60 d. • (from radioactive decay Ni56 Co56 Fe56) • Maximum Light is the same for all SNIa !! Supernova Ia Measurements Supernovae: luminosities  entire galaxy~1010Lo (1012Lo in neutrinos)

  29. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Gibson et al. 2000 - Calibration of SNIa via Cepheids Distance derived from Supernovae depends on extinction 4.3: Secondary Distance Indicators Supernova Ia Measurements Lightcurves of 18 SN Ia z < 0:1 (Hamuy et al ) Supernovae distances good out to > 1000Mpc  Probe the visible Universe ! after correction of systematic effects and time dilatation (Kim et al., 1997).

  30. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 q f http://spiff.rit.edu/classes/phys240/lectures/lens_results/lens_results.html 4.3: Secondary Distance Indicators Gravitational Lens Time Delays • Light from lensed QSO at distance D, travel different distances given by D=[Dcos(q) - Dcos(f)] • Measure path length difference by looking for time-shifted correlated variability in the multiple images source - lens - observer is perfectly aligned  Einstein Ring source is offset  various multiple images Can be used to great distances • Uncertainties • Time delay (can be > 1 year!) and seperation of the images • Geometry of the lens and its mass • Relative distances of lens and background sources

  31. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 lens equation (relation between the angles b, h, a) Where e is the Einstein Radius Lens equation - 2 different solutions corresponding to 2 images of the source: 4.3: Secondary Distance Indicators • Light from the sourceS is deflected by the angleawhen it arrives at the plane of the lensL, finally reaches an observer's telescope O. • Observer sees an image of the source at the angular distancehfrom the optical axis • Without the lens, she would see the source at the angular distancebfrom the optical axis. • The distances between the observer and the source, the observer and the source, and the lens and the source areD1,D2, andD3, respectively. Gravitational Lens Time Delays http://leo.astronomy.cz/grlens/grl0.html Small angles approximation Assume angles b, h, and deflection angle a are <<1  tanq~q Weak field approximation Assume light passes through a weak field with the absolute value of the perculiar velocities of components and G<<c2 For perfectly aligned lens and source (b=0) - two images at same distance from lens h1 = h2 = e

  32. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.4: The Distance Ladder The Distance Ladder The Distance Ladder

  33. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.4: The Distance Ladder The Distance Ladder Comparison eight main methods used to find the distance to the Virgo cluster. Jacoby etal 1992, PASP, 104, 599 HST Measures distance to Virgo (Nature 2002) D=17.1 ± 1.8Mpc

  34. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.4: The Distance Ladder The Distance Ladder Supernova (1-1000Mpc) Hubble Sphere (~3000Mpc) 1000Mpc Tully Fisher (0.5-00Mpc) Coma (~100Mpc) 100Mpc 10Mpc Virgo (~10Mpc) Cepheid Variables (1kpc-30Mpc) 1Mpc M31 (~0.5Mpc) RR Lyrae (5-10kpc) 100kpc LMC (~100kpc) Spectroscopic Parallax (0.05-10kpc) 10kpc Galactic Centre (~10kpc) Parallax (0.002-0.5kpc) 1kpc RADAR Reflection (0-10AU) Pleides Cluster (~100pc) Proxima Centauri (~1pc)

  35. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.5: The Hubble Key Project The Hubble Key Project The Hubble Key Project

  36. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.5: The Hubble Key Project To the Hubble Flow • The Hubble Constant • Probably the most important parameter in astronomy • The Holy Grail of cosmology • Sets the fundamental scale for all cosmological distances

  37. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Must correct for local motions / contaminations vo = radial velocity of observer vG = radial velocity of galaxy vo - Measured from CMB Dipole ~ 220kms-1 (Observational Cosmology 2.3) vG - Contributions include Virgocentric infall, Great attractor etc… Decompostion of velocity field (Mould et al. 2000, Tonry et al. 2000) 4.5: The Hubble Key Project To the Hubble Flow • To measure Ho require • Distance • Redshift Cosmological Redshift - The Hubble Flow - due to expansion of the Universe

  38. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.5: The Hubble Key Project Hubble Key Project • Observations with HST to determine the value of the Hubble Constant to high accuracy • Use Cepheids as primary distance calibrator • Calibrate secondary indicators • Tully Fisher • Type Ia Supernovae • Surface Brightness Fluctuations • Faber - Jackson Dn-s relation • Comparison of Systematic errors • Hubble Constant to an accuracy of 10% • Cepheids in nearby galaxies within 12 million light-years. • Not yet reached the Hubble flow • Need Cepheids in galaxies at least 30 million light-years away • Hubble Space Telescope observations of Cepheids in M100. • Calibrate the distance scale

  39. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.5: The Hubble Key Project Hubble Key Project H0 = 75 10 km=s=Mpc

  40. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Mould et al. 2000; Freedman et al. 2000 H0 = 716 km s-1 Mpc-1 t0 = 1.3  1010 yr 4.5: The Hubble Key Project Combination of Secondary Methods • Biggest Uncertainty • zero point of Cepheid Scale (distance to LMC)

  41. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 H0 = 716 km s-1 Mpc-1 t0 = 1.3  1010 yr 4.6: Summary Summary • There are many many different distance indicators • Primary Distance Indicators  direct distance measurement (in our own Galaxy) • Secondary Distance Indicators  Rely on primary indicators to measure more distant object.  • Rely on Primary Indicators to calibrate secondary indicators • Create a Distance Ladder where each step is calibrated by the steps before them • Systematic Errors Propagate! • Hubble Key Project - Many different methods (calibrated by Cepheids) • Accurate determination of Hubble Constant to 10% Is the Ho controversy over ?

  42. Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4.6: Summary Summary 終 Observational Cosmology 4. Cosmological Distance Scale Observational Cosmology 5. Observational Tools 次：

More Related