1 Introduction

• Observations require position and date measurements
• Evolution of the absolute position accuracy: from 10 mas (Hipparcos) to 10 μas (Gaia)

This Lecture

• Position of celestial bodies: frames
• Measuring time with accuracy
• Definition of distance units

2 The realm of the nebula

2.1 The birth of extragalactic astronomy

The Leviathan of Parsonstown

William Parsons (Lord Rosse), Third Lord of Rosse; 72inch (D=183 cm, f=17m)

The universe in 1922

• Charlier 1922 (Lund Observatory): a map of 11475 nebulae in galactic coordinates
• Note the concentration towards l=90°. This is the Virgo cluster.
• At the time, the extragalactic nature of the 'spiral nebulae' was not established; this was predicted theoretically by Opik (1922) and firmly established by Hubble (1925, 1926) based on observations of a δCepheid in M31.

2.2 The spatial distribution of galaxies

• Nonrandomness of galaxy distribution dates back the 1930s: Shapley, Hubble, Zwicky (1938);
• Shapley-Ames (1932) catalog at Harvard; Virgo cluster, Ursa Major cloud, and two clusters in Fornax
• Ideas that galaxies are organized into clusters and even in superclusters (Shapley 1957)
• Two post-WWII surveys:
  • Lick-20inch Astrographic Survey (near San Francisco); Shane and Wirtanen catalog, covers 70% of the sky, limit magnitude 18.8
  • National Geographic Society-Palomar Observatory Sky Survey (Abell et al, Zwicky et al)
• Is the universe homogeneous and isotropic? Yes on large (>100 Mpc) scales (CMB), no on small scales.

"Tens of thousands of discrete groups and clusters of galaxies are easily identified on the Palomar Sky Survey photographs." (G. Abell's lecture at Caltech)

• Astronomer George Abell (1927-1983) standing next to the 48-inch diameter (1.2 m) Schmidt telescope at Palomar observatory (link; ∼ half way between Los Angeles and San Diego, USA);
• Abell established the first and most extensive catalog of galaxy clusters (Palomar Observatory Sky Survey, or POSS I, which took place from 1949 to 1958);
• Galaxies are not arranged randomly in space: the form groups and clusters, themselves arranged into sheets and filaments surrounding voids.
• Challenges at the time was distance: Abell defined sort of a standard candle assuming that the tenth brightest galaxies in a cluster have the same intrinsic luminosity;

The local group

• The local group: ∼ 60 galaxies, within ∼1Mpc
• The three largest galaxies: MW, M31, M33
• All figures from this site

The nearest groups

• The local group is just one among many others: Sculptor group (#=6, d=1.8 Mpc), M81 group (#=34, d=3.1 Mpc), M101 group (#=9, d=), Maffei group
• Groups tend to lie within a plane called the supergalactic plane;
• These groups are located in the outskirts of the massive Virgo Cluster

Galaxy clusters

• Groups and clusters: groups <50 gal.; clusters 50-10³ gal.; velo. dispersion is ∼1000km/s in a cluster!
• The biggest cluster within 30 Mpc is the Virgo Cluster (@20Mpc) which contains few hundreds of elliptical + spiral galaxies (∼250 large + ∼2000 small)
• The irregular Virgo cluster is itself located at the center of the Virgo supercluster, which contains ∼ 2000 galaxies; centerd on the giant elliptical M84 and M86.

The coma cluster (A1656)

• Diversity of clusters: regular Coma cluster (@100Mpc), ∼ spherical, ∼ 10³, mostly elliptical, galaxies;
• Spiral and irregular extend to outer regions, in contrast with elliptical galaxies.

Galaxy clusters and supercluster

• Clusters form superclusters (few 10 Mpc)

Galaxy clusters and supercluster

• Left: clusters form voids, walls, sheets. Diameter ∼ 7% visible Universe
• Right: Map of major known superclusters within ~1 Gpc; each point, a rich cluster of galaxies (∼ 100 galaxies); Abell catalog of rich clusters

The homogeneous, isotropic universe

• Left: visible
• Middle: radio sources
• Right: far infra-red (IRAS, Strauss+92)

3 Time

Chronology

• First atomic timescale (1949, NIST): ammonia cavity (23870 MHz)
• 1952: first atomic clock using Cs atoms
• 1955: first primary calibration source (National Physical Laboratory in England, using a Cs clock;
• 1970: definition of a second; "The duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom."
• This definition becomes independent of astronomical events (e.g. 1/86400 of the mean solar day, 1.31556925.9747 of the 1900.0 tropical year)
• Today: Cs133 clock (10^-12 relative accuracy)
  • A cavity is used to tune a frequency to 9 192 631 770 Hz, the frequency of the F=4-3 hyperfine transition of Cs133.
  • The second is thus defined to be exactly 9 192 631 770 oscillations; an electronic device is used to count the number of oscillations.
• Cooled CS and Ru fountains: 10^-16 relative accuracy

The second

• One of the 7 fundamental units of the SI, noted s
• Fundamental system of time: Temps Atomique International (TAI)
  • Based on worldwide network of ∼500 Cs133 atomic clocks in ∼70 laboratories
• Today: everything is defined wrt the second of time, and therefore do not depend on the motion of celestial bodies (the device used to accumulate seconds is called a clock):
  • 1 d = 86400 s
  • 1 Julian year = 365.25 d
  • one Julian century = 36525 d

3.1 Sideral time

• Difference between solar time and stellar time: more than 360° rotation is needed to bring the Sun on the meridian;
• Solar day is 24h; mean sidereal day is 23h56m04s of solar time; sidereal time = 0.99726851 solar time;

4 Positioning celestial bodies

Astronomical reference frames

• Purpose: record observations in catalogs in a time-independent way to allow for later observations
• Celestial coordinate system:
  • Celestial sphere: spherical coordinates, with arbitrary radius ⇒ two angular coordinates
  • Spatial frame
    • a triad: an origin O and three, usually right-handed, fundamental directions, e₁, e₂, e₃=e₁ x e₂
    • usually, a triad is built by defining reference direction (e.g. e₃) and the plane perpendicular to it, containing e₁ and e₂
  • Celestial coordinate system: for a given spatial frame, choice of coordinates is arbitrary
  • Usual reference frames: horizontal, equatorial, galactic, ecliptic

4.1 Motions on the celestial sphere

• Top: Motions (on the celestial sphere) of stars at a latitude Φ=45^o
• Bottom: the same, but at a latitude Φ=10^o

Latitude and Longitude

• In the following, and by convention, the latitude and longitude of the observer are noted Φ and λ; Φ is counted positively north, and longitude is measured east from the Greewich meridian
• Grenoble is at +5.7°, while Paranal is at 70°24'W or λ=-70°24'.

• Note that the elevation of the celestial pole is equal to the latitude Φ of the observer;

  

4.2 The Horizontal frame

• Triad: Origin = observer
  • e₃ = Local vertical: reference for the Elevation; zenith and nadir
  • e₁ e₂ = horizon; reference for the height h
  • Local meridian plane = plane containing vertical + celestial pole: reference for the Azimuth angle A (longitude); related notion: Astronomical meridian
• Observatory and time dependent (no unique choice for the reference longitude)
• Coordinates: Azimuth (Az) and Elevation (El, or height h); Astronomical convention: Az increases with body motion in the northern hemisphere

Airmass

• Useful to compute the airmass X=sec(z)=1/cos(z), z=zenith angle=90-El
• Atmospheric opacity increases with airmass: τ(z)=τ(0) X(z) (plane-parallel atmosphere approximation)

set angle degree
set xlabel "Elevation (deg)"
set ylabel "Airmass"
plot [10:90] 1/cos(90-x) t "Airmass"

4.3 The Equatorial frame

• Independent of the observer
• Celestial pole: e₃
• e₁, e₂: Celestial equator: projection of Earth's equator on the celestial sphere; Inclined by ε wrt Ecliptic = Earth orbit; this angle is called ecliptic obliquity, noted ε; its value is ε=23°26'21" in J2000.0; gives rise to seasons.

• Coordinates:
  • Right Ascension α [0:24h]; Origin of α: vernal point or spring equinox, noted ϒ (Sun on March 21st of a given year)
  • Declination δ [-90° : 90°]; origin = equatorial plane

Circumpolar stars

• Stars describe circles centered on the celestial pole;
• Some stars are said 'circumpolar' when they are always above the horizon; what is the declination of such stars? [Ans: δ > π/2-Φ]
• Show that stars with δ < -(90-Φ) never rise above the horizon

Maximum elevation

• Show that the maximum elevation is given by

  h_max = 90 - |Φ-δ|

• Similarly, h_min = -90 + |Φ+δ|
• Az-El telescopes can not observe sources that culminate too high in the sky; do you understand why?

Rectangular Offsets in Projected Maps

How to convert rectangular offsets from/to RA-DEC?

• Consider a region of the sky centered on (α₀, δ₀). What are the (α,δ) coordinates of a point at offsets (Δx,Δy)?
• Show that:
  • Δx = cos(δ₀) Δα
  • Δy = Δδ
• Warning RA increase towards the East; furthermore, West is represented towards the right, East towards the left; watch out!

4.4 Local sideral time (LST)

• Local frame: the meridian is rotating, and the location of the vernal point thus changes with time (contrary to its value in the Equatorial frame which is, by definition, fixed); this angle is called Local Sideral Time (LST).

• LST increases with time and with the longitude λ of the observatory

  LST = UTC + λ + date shift

  • λ is positive towards the East: example, Paranal longitude is λ=70°24' W or -70.4deg East or -4.7h (15°=1h);
• LST is zero when Vernal Equinox is on the local meridian; stars with RA=0h are culminating.
• By definition, LST=UTC+12 on March 21st, or LST=UTC on Sept 21st;
• LST increases by 2h per month:
  • March 21st: LST=UTC+12,
  • April 21st: LST=UTC+14

  • Show that we may write:

    LST ≈ UTC + 4.67 + 2× m + λ/15

    with m=1.5 for 15-jan, etc

• LST is very useful: a source of Right Ascension α culminates (reaches its highest elevation) when LST=α.
• Grenoble: lat=45.19deg, long=5.72deg; LST @Greenwich on March 21st is equal to UTC (UTC is Greenwich time); then a positive shift of 2h per month (24h in one year);
• Question: when would be the best moment to observe a source of Right Ascension α for a telescope located at Paranal?

4.5 The Galactic frame

• North Galactic Pole (NGP): IAU definition, in B1950.0 EQ coordinates system:

  α=12h49min = 192.25^o,

  β=27^o 24'= +27.4^o

• The Abell catalog in Galactic (left) and Equatorial (right) coordinates.

4.6 Summary

Change of frame

• Useful coordinate converter

4.7 Perturbations of the coordinates

Precession and nutation

• Precession
  • Secular periodic motion of the Earth rotation axis due to the flattening of the Earth
  • Period 25770 yr (50.26"/yr); leads to precession of the equinox;
  • The Polaris star is currently within 1° from the CP; in 13000yr, it will be 47° off, poiting towards Vega
  • Hipparque de Nicée (Hipparcos, 127 BC) measured 46"/yr ! Theoretical explanation from Newton (Principia mathematica, 1687)
• Nutation due to the precession of the Moon
  • Fast periodic motion of small amplitude (period of 18.6 yr)
  • Motion of the celestial pole (up to 20" per year introducing changes of up to 50" of the coordinates)
• Consequence for catalogues in the Eq Sys: an equinox and an epoch (e.g. the median date of the observations)
  • B1950.0 (B≡ Besselian year)
  • J2000.0 (J≡ Julian year – nothing to do with Julian calendar); J2000 refers to 12h in Greenwich on 2000 January 1st

Aberration

• Because of fine light speed, relative motion of the observer wrt target shifts the apparent direction
• Detection at t=0 was emitted at -t by an object at position θ₀; apparent position shifted at most by v/c
• v≈ 30 km/s => v/c≈ 10^-4 rad = 20"

4.8 Reference Catalogs

• How to locate objects in the sky in a time-independent fashion ?
• Basic idea: locate them with respect to reference objects ⇒ reference catalogs
• Reference catalogues or reference frames
  • set of objects with high astrometrical accuracy
  • contain a small number of stars
• Usual reference catalogs (inertial by convention):
  • FK1 (1879), …, FK5 (1984)
  • Hipparcos Celestial Reference Frame (HCRF)
  • Tycho-2 (from the name of the Danish astronomer Tycho Brahe)
  • Coordinates in equatorial coordinates at a given epoch; e.g. Hipparcos catalogue gives coordinates in J1991.25; then need to precess to J2000.0 to use at observatories
• Useful tools
  • the vizier portal from the CDS (Centre de Données astronomiques de Strasbourg)
  • coordinate converter

4.8.1 Inertial astronomical frames

• Reference frames must be inertial (laws of physics the same)
  • No relative motions between these objects
  • No global rotation
• Inertial frames: use distant QSO referred to the barycenter of the Solar System chosen as the center of the frame (IAU 1991); axes are fixed with respect to distant extragalactic objects

The International Celestial Reference Frame (ICRF)

• One realization of the International Celestial Reference System (ICRS)
• Based on radio observations (VLBI) of quasars: objects in the visible are weak; Hipparcos frame (1990s): 120 000 stars with 1mas accuracy but limited to V<13 ⇒ intersection with ICRF = 1 source !
• ICRF1 (IAU 1998): 212 defining sources, replacing FK5; 250μas
• ICRF2 (IAU 2009): 295 defining sources; 40μas
• ICRF3 (IAU Vienne 2018): >4000 sources with 10μas astrometry

4.8.2 The Gaia Celestial Reference Frame

• Requirement: consistency across the e-m spectrum: the axes must coincide with the ICRF3
• 560000 QSO with 0.4mas accuracy; agreement with ICRF3 20-30μas
• The first optical reference frame built only on extragalactic sources
• proposed to be a new Reference Frame
• Reference article and useful webpage for the Gaia DR1

5 Distances

• Measuring distances: the most fundamental task with measurement of time
• Various methods to measure distances from Solar System to cosmological scales
  • Distance ladder concept
• Trigonometic parallax: below ∼ 1kpc
  • distances to galactic sources (essentially stars)
  • the most accurate, simplest, and with least assumptions, method to measure distance
• On scales > 1kpc:
  • Standard candle concept
  • Photometric distances: using stars as reference candles
  • Galactic rotation curve
  • Light echoes
  • Supernova
  • Empirical scaling laws (e.g. Tully-Fisher)
  • Hubble's law
  • etc
• In this lecture: trigonometric parallax method; other methods will be discussed in the next lecture

5.1 The astronomical unit (au)

• Current method: distance Earth-Venus with radar techniques (1 km, 0.01 ppm): power received ∝ d^-4
  • closest approach \(a\) and most distant separation \(b\)
  • orbits of Venus and Earth (diameters, eccentricities)
  • astronomical unit = (a+b)/2
• The value of the au is exactly 149 597 870 700 m ≈ 1.5x10¹¹ m (see the IAU webpage);
• Previous techniques: Venus transits (only 7 transits have been observed: 1639, 1761-69, 1874-82 and 2004-12)
• References: technical and historical (here, here and here)

5.2 The parsec

Trigonometric parallax

• parallax: angle subtended by 1 au as seen from the star

• trigonometric parallax: obtained by measuring the apparent displacement of a target with respect to distant objects, when observed at two epochs, e.g. 6 months apart; apparent motion is an ellipse; semi-major axis is the trigonometric parallax p

  d = 1 au / tan p

• Trigonometric parallax: the simplest, most direct, and most assumption-free
• ESA/Hipparcos satellite: 10⁵ stars, parallaxes to 1mas accuracy; ESA/Gaia: ∼10⁹ stars, ∼20μas

The parsec

• parsec, pc: 1 au at 1 parsec = 1"

  1 pc = 1 au / 1" = 3.086x10¹⁶ m ≈ 2x10⁵ au

• From what preceeds:

  d = 1 au / tan p

• With d in pc and the parallax p in arcsec:

  d[pc] = 1/p[arcsec]

• 1" = 1rad/206264.806247 ≈ 1rad/2x10⁵ ≈ 5x10^-6 rad

• Comparable scale: light-year (distance traveled by light in vacuum during one Julian year, 365.25 d or 3.15576x10⁷ seconds)

  1 ly = 9.461 x 10¹⁵ m

  1 pc = 3.26 ly

5.3 Examples

• From Gaia/dr2, parallax of Sirius (α CMa): p=376.6801mas ± 0.4526mas: give the distance to Sirius in ly and in pc, with 1σ uncertainties
• Rigel (β Ori): p=2.92±0.08 mas; d=?
• Query the Gaia/DR2 catalog using the CDS/Vizier platform to find the distance of Proxima Centauri (α Cen C)
• Compute the angular diameter of the Moon (or the Sun)
• See 5.2