The extragalactic Universe • The distance scale • Gravitational mirages • Dark matter

The distance scale Measurement of distances: One of the most difficult problems in modern astrophysics! → proceed by steps From nearest objects… … to most distant ones → cosmological distance scale Danger: propagation of errors Georgia O’Keeffe « Ladder to the Moon »

The distance scale - 2 The astronomical unit The mean distance from Earth to Sun can be determined from the distance of any planet in the solar system 1671: First  `modern´ estimate Cassini (from Paris) and Richer (from Guyana) simultaneously measure the position of Mars with respect to stars (↔ a parallax) → obtain 1 AU = 140 million km 1815: Duration of Venus transit in front of the Sun Encke obtains 1 AU = 153 million km Modern value, obtained by RADAR measurements 1 AU = 149.5 million km

The distance scale - 3 The parallax The distance to relatively nearby stars can be obtained by measuring their annual parallax The most accurate parallaxes have been measured by the Hipparcos satellite (HIgh Precision PARallax COllecting Satellite) of ESA, launched in 1989 The accuracy is ~0.001 arcseconds → distances to stars at 100 pc are known with a ~10% accuracy NB: 1 pc = 206265 AU = 3.26 LY The Hipparcos satellite

The distance scale - 4 Cepheids 1912: Henrietta Leavitt finds that the period of Cepheids is a function (~proportional) of their luminosity These stars are luminous → observable at rather large distances → very useful distance standards (standard candles) Difficulties: • The distance to some Cepheids must be known to calibrate the relation • The period – luminosity relation depends on the star’s chemical composition

Calibration of Cepheids The distance scale - 5 Calibration of Cepheids vrad (spectro) → ΔR + Δθ (interfe-rometry) → d

Calibration of Cepheids The distance scale - 6 Calibration of Cepheids δ Cep: parallax measured by HST L Car: calibrated par interferometry (+ others…) → accurate calibration of the relation for a given metallicity (≈ Milky Way)

The distance scale - 7 Type Ia Supernovae To go further away than Cepheids: we need more luminous objects • Transfer of matter on a white dwarf in a binary system → Nova eruptions • If M > 1.4 M → explosion of the star → Lmax ≈ constant (more precisely, it can be determined from the shape of the light curve) Uncertainties: – effect of metallicity – absorption by dust – filter(z),…

Other distance indicators The distance scale - 8 Other distance indicators • Luminosity function of globular clusters: one assumes a `universal´ law for N(MB) • Luminosity function of planetary nebulae • Tully-Fisher relation / fundamental plane (relations between velocities of stars and luminosity of the galaxy) • Brightness fluctuations of elliptical galaxies (apparent granularity)

The distance scale - 9 The Hubble law 1929: Hubble finds that sufficiently distant galaxies move away from us with a speed proportional to their distance: • d: measured by distance indicators • v: measured by Doppler effect: • z = redshift • H0 = Hubble constant (in km/s/Mpc) Edwin Hubble

The distance scale - 10 The Hubble law Hubble obtained H0 ≈ 500 km/s/Mpc, which is larger by a factor 7 to 8 than the modern value • He estimated distances from (1) Cepheids and (2) the most luminous stars (1) He mixed two different Cepheid types (2) Unresolved clusters were mistaken as stars → underestimate of distances Original Hubble diagramme

The distance scale - 11 The Hubble constant From the 1960s on, measurements of the Hubble constant gave values close to 50 or 100 km/s/Mpc → quarells of experts Measurements of the Hubble constant since 1920

The distance scale - 12 The Hubble constant More recent measurements generally give values between 58 and 72 km/s/Mpc → uncertainty ~ 20% Still 2 sides: HST key project / Sandage &Tammann Measurements of the Hubble constant since 1970

Gravitational mirages Atmospheric mirages Our brain assumes light rays propagate on straight lines If refraction index varies → light rays are bended → we see the object in another direction → sometimes several images – possibly • deformed • reversed

Gravitational mirages - 2 General relativity → space-time curvature → light rays are deflected in the vicinity of massive objects → sometimes several images – possibly • deformed • magnified → gravitational mirage by analogy with atmospheric mirage • the deflecting object is called a gravitational lens • effect predicted by Einstein who thought it would be unobservable as stars were the only lens candidates • predicted by Zwicky in the 1930s with galaxies as lenses

Gravitational mirages - 3 The first gravitational mirage 1979: Walsh, Carswell and Weymann were studying quasar spectra They realised that 2 quasars 6″ apart had the same spectrum → hypothesis: these are two images of the same quasar – confirmed by the detection of the lens galaxy, close to an image Quasars are good candidates since very luminous → observable far away → higher probability to have a galaxy in front The 2 images of quasar Q0957+561

Gravitational mirages - 4 Properties of gravitational mirages As a function of: • the mass distribution in the lens • the alignment source – lens – observer Several possible image configurations: • doubles • quadruples • arcs • ring (only extended sources give rise to arcs or rings)

Gravitational mirages - 5 Some gravitational mirages If source – lens – observer aligned + symmetric lens → ring-like image = Einstein ring of angular radius: dLS = distance (lens – source) dOS = distance (observer – source) dOL = distance (observer – lens) SDSS J162746.44-005357.5 (HST)

Gravitational mirages - 6 Some gravitational mirages If slight misalignment → 4 nearly symmetrical images HE0435–1223 (HST) H1413+117 (HST)

Gravitational mirages - 7 Some gravitational mirages If misalignment more important → 4 less symmetrical images WFI2033–4723 (HST) RXJ0911+1551 (HST)

Gravitational mirages - 8 Some gravitational mirages If misalignment even more important → 2 images HE2149–2745 (HST)

Gravitational mirages - 9 Giant arcs If lens = concentrated galaxy cluster → mass of the lens much higher → image separations much larger (arc minutes) If source = background galaxy (extended object) → images = arcs (sometimes very large) → magnified image of the source → `gravitational telescope´ Cl2244–02 (ESO)

Gravitational mirages - 10 Gravitational telescope Example: • multiple • magnified • deformed images of a single background galaxy by a compact cluster Cl00244+1654 (HST)

Gravitational mirages - 11 Mirages and distances Differents optical paths have different lengths + gravitational time dilation → time delay between the detection of an event in the different images If quasar varies, one can measure this delay If the mass distribution is known: → one gets a distance Δd = c Δt → cosmological distance

Gravitational mirages - 12 Mirages and Hubble constant Time delays tend to give rather low values for H0 (similar to Sandage and Tammann’s value) → conclusion? • either Sandage and Tammann are right against the majority • or the mass distribution in the lenses is not modelled correctly Main uncertainty: distribution of dark matter Hubble constant deduced from time delays

Rotation curves of spiral galaxies Dark matter Rotation curves of spiral galaxies If circular orbits in the disk (and spherical total mass distribution) Where M(r) = total mass inside the orbit In outer regions: M(r) ≈ Ct → v ~ r –1/2 However, in our Galaxy and other spirals, one measures v ~ Ct in outer regions → one assumes that mass continues to increase despite nothing being seen

Dark matter - 2 Dark matter halo → one assumes the existence of a spherical halo of invisible matter Rotation curve: Mass conservation: → in outer regions: To avoid the central singularity, one assumes: (must also be truncated at large distance to avoid infinite mass)

Dark matter - 3 Dark matter halo Other analytical formulae have been proposed for the dark matter distribution From numerical simulations, Navarro, Frank and White (1996) propose the formula: Dark matter is estimated to account for 80 to 95% of our Galaxy’s mass … and similar values for other spiral galaxies

Dark matter in galaxy clusters 1933: Zwicky measures velocities of a few galaxies in the Coma cluster He gets a dispersion σ(vrad) = 977 km/s At such velocities, in order for the galaxies to stay gravitationally bound in the cluster, one needs a total mass Mtot ~ 3 1015 M This is muuch higher than the visible mass: Mvis ~ 1013 M Dark matter galactic halos are not massive enough to explain the difference → there must be additional dark matter, scattered in between the galaxies Fritz Zwicky

Hot gas in clusters Observations in X-rays Dark matter - 5 Hot gas in clusters Observations in X-rays → discovery of very hot gas (~ 108 K) in galaxy clusters Mgas (Coma) ~ 3 1013 M → this hot gas + `orphan´ stars are not massive enough to explain the missing mass → dark matter also in clusters Chandra and HST images of 2 clusters

Detection of dark matter (galaxies) Gravitational mirages of quasars lensed by a galaxy: Deflection of light rays: depends on the total mass (luminous + dark), whatever its nature If H0 is known: → the time delays give constraints on the mass distribution → on the distribution of dark matter in the lens up to angular distances probed by the light rays Radio image of a mirage (Merlin)

Detection of dark matter (clusters) Gravitational lensing of galaxies by clusters: No time delay (sources not variable) but the numerous arcs allow to reconstruct the mass distribution Two clusters in collision in visible light (HST) + X-rays (pink, shock) + total mass (lensing, blue) Separation of the hot gas from the total mass (≈ dark matter) → evidence in favour of the existence of dark matter? The `bullet´ cluster

Detection of dark matter (clusters) The cluster dark matter supporters avoid to show: Abell 520 Another collision of clusters in visible light (HST, smoothed version in orange) + X-rays (green) + total mass (lensing, blue) → behaves differently from the bullet cluster → ? The `train wreck´ cluster Abell 520