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Distance measurements Pierre Hily-Blant Université Grenoble Alpes Université Grenoble Alpes // 2018-19 Contents 1 A current issue: The Hubble constant 2 2 Introduction 3 3 Trigonometric parallax 4 4 Photometric distance 5 4.1 The life cycle of stars....................... 5 5 Cepheids 11 5.1 Period-luminosity curve of δ Cep................ 12 5.2 The instability strip....................... 15 5.3 Other variable stars....................... 17 6 Light echoes 21 6.1 The distance to the LMC.................... 22 6.2 Supernovae light echoes..................... 25 6.3 Calibration of the long-period Cepheids............ 26 7 Cosmological distances 28 7.1 The rst extragalactic object.................. 29 7.2 Hubble's law........................... 30 7.3 Measuring cosmology with Supernovae............. 32 7.4 Distance of galaxies: the Tully-Fisher relation......... 40 1

1 A current issue: The Hubble constant As you know, the Universe is expanding (this expansion is currently accelerating). The Hubble's law says that any two objects move away from each other at a velocity which increases in proportion to the distance between these objects (after removing their peculiar motions). The constant H 0 relates the recession velocity v (through the redshift z) to the distance D: v = cz = H 0 D The value of H 0 is 70 km/s/mpc. But... A crack in the standard cosmological model? 2

ˆ But there is a tension between two most recent measurements: the Planck mission has estimated H 0 based on the Λ CDM: H 0 = 67.7±0.4 km/s/mpc the Cepheid method: H 0 = 73.52±1.62 km/s/mpc ˆ Which is the correct one? A crack in the standard cosmological model? ˆ At the root of the discrepancy, the compelling accuracy of distance determination with Cepheids. We'll see, in this Lecture, how this works... 2 Introduction ˆ Various methods to measure distances from Solar System to cosmological scales ˆ Trigonometic parallax Below 1kpc, the most accurate, simplest, and with least assumptions, method to measure distance, is trigonometric parallax ˆ On scales > 1kpc: Photometric distances: using stars as reference candles Galactic rotation curve Light echoes Supernova Empirical scaling laws (e.g. Tully-Fisher) Hubble's law 3

3 Trigonometric parallax ˆ parallax: angle subtended by 1 au as seen from the star ˆ trigonometric parallax: obtained by measuring the apparent displacement of a target wrt distant objects when observed at two epochs, 6 months apart; apparent motion is an ellipse; semi-major axis is the trig. parallax ˆ half the angular displacement: parallax p usually in arcsec d = 1 au / tan p ˆ 1" = 1rad/206264.806247 1rad/2x10 5 5x10-6 rad ˆ trigonometric parallax: the simplest, most direct, and most assumptionfree 4

4 Photometric distance Some stars are known as standard candles : variable stars (δ Cepheid, RR Lyrae) and type Ia supernovae (SNe Ia) They are the best tools to measure distances on galactic and inter- galactic scales General ideas: Variable stars: stable period-luminosity measure the period, nd the luminosity, hence the distance Supernova: universal light curve ( ux vs time); measure a the magnitude on a portion of the curve, nd the distance Calibration : the key in photometric distance methods is the calibration of the P-L relation for variable stars, and of the light curve for SNe Ia this calibration is not easy: metallicity e ects, reddening 4.1 The life cycle of stars 5

4.1.1 From the main sequence to red giant phase 8

ˆ Plots: evolutionary track for a 5M sun (intermediate mass) star ˆ Main sequence (A to C): core H-burning lasts 80 Myr ˆ C to D: core reaches the Schonberg-Chandrasekhar limit before He-core becomes degenerate (for M>2-2.5 M sun ) core contraction, envelope expansion (R increases) H-burning in a shell surrounding the core when T in the core reaches 10 8 K, core He-burning; core contraction stops new (thermal and hydrostatic) equilibrium: very fast evolution (Kelvin-Helmoltz timescale, 2 Myr) ˆ Reg Giant Branch (RGB) (D to E) extremely fast! ˆ red giant (at point E) Helium burning in the core: red giant phase (path from D to E) close the Hayashi line: deep convective zone strong T-dependence of He-burning: convective core ˆ Similar evolution for M=2.5-10 M sun 9

4.1.2... to pulsating variable stars ˆ giants, narrow strip parallel to Hayashi line in the HR diagram ˆ only for M>5M sun can we observe passage in the instability strip ˆ Instability strip in the H-R diagram: 10

Maeder 2009 Cepheids (giants to supergiants) RR Lyrae stars (subgiants to giants) and other stars: δ Scuti stars (main sequence stars) and the ZZ Cet white dwarfs (now shown here) 5 Cepheids 25 variable stars in the SMC, Leavitt & Pickering 1912 11

5.1 Period-luminosity curve of δ Cep δ Cephei, a 4th magnitude F5 supergiant; P=5.37 d The Cepheid periodluminosity relation ˆ Period-Luminosity relation discovered by Henrietta Levitt early 20th century ˆ Cepheids: P=1-100 d 12

ˆ Measure P and m; check the P-L or P-M relation and nd distance modulus DM=5log(d)-5 ˆ Calibration of the P-L relation: trigonometric parallax 5.1.1 Period-Luminosity-Color relation ˆ P = Q ( ρ / ρ ) 1/2 Q = 0.035-0.050 days for Cepheids Physical origin: * P sound crossing-time = R/c s R/T 1/2 * virial equilibrium: E pot = 2E kin or kt=gmm p /R P ρ -1/2 ˆ Period-Luminosity-Color (PLC) relation using the mass-luminosity relation L M α, and L R 2 T 4 eff, we nd log P = (3/4-1/2α)log(L/L sun ) - 3log T e + log Q + cst adopting α=3.3 for Cepheids, this gives: log (L/L sun ) = 1.67 log P + 5 log T e - 1.67 log Q + cst' translated in terms of absolute magnitude M = M 0-2.5log L = M 0-4.2 log 10 P + 12.5 log T e 13

5.1.2 Observed Magnitude-Period relation for Cepheids ˆ Classical Cepheids (prototype δ Cephei): 14

ˆ giants to supergiants, young intermediate-mass stars, found in the disk population and in young clusters; ˆ period 1 to 100 d ˆ disk midplane implies that reddening is important: observe at longer wavelength ˆ note that at longer wavelength, M-P relation is steeper hence more accurate Tammann et al A&A 2003 5.2 The instability strip ˆ Evolution after core He-burning started: so-called blue loops moving down, and left to F moving right again to G timescales ( 15-20 Myr) are large enough that these stars can be observed ˆ Blue loops cross the instability strip: a narrow band in the HRD, which is crossed by stars with M=3 to 12 M sun ; Why pulsations? Why in a narrow range of T e? 15

5.2.1 The physics of the instability strip ˆ From the point of view of the evolution of pulsations (stable/unstable), stellar enveloppe = three zones: inner, intermediate, and outer zones depending on their heat content and the coupling between energy exchange and dynamics; * outer zone: large R, small mass and heat; energy exchange are small, heat constant; small coupling; * intermediate zone: non-adiabatic and signicant mass and heat contents; strong coupling; can drive or damp the pulsations; * inner zone: very large heat content so unperturbed by heat exchange due to pulsations; Instability strip = location of the intermediate zone ˆ To understand how the instability sets in, we need to look at the opacity and its variations upon compression; the opacity depends on the ionization state of the main constituents, H and He; in fully ionized regions, the opacity is given by the Kramers formula, κ ρ T -7/2 ; κ decreases upon compression, heat can be radiated away stable in partially ionized regions where where He + He ++ (T 2-4 10 4 K), κ increases with T; compression of these layers increases the opacity, hence temperature increases making these layers even more opaque: unstable ˆ as a star evolves after the ignition of core-he burning, T e increases and decreases (loops): let us follow a star on its way from the left to the right of the HRD; initially, the partial ionization region is in the outer zone: stable; when T e decreases, the partial ionization region goes down into the intermediate zone and the star becomes unstable at even lower T e, the He + /He ++ region goes into the inner adiabatic zone where the destabilizing dependence of ρ has no inuence; ˆ It can be shown that when the star is in the instability strip: R T -12 e and L5/3 T -20 e 16

Note: the strip is almost vertical in the HRD this leads to log T e = -0.05 log L/L sun + cst This is in very good agreement with results based on numerical simulations (e.g. Eq. 37 of Tammann et al A&A 2003): log T e = -0.048 log L/L sun + 3.901 5.3 Other variable stars ˆ RR Lyrae stars (subgiants to giants) lower mass than Cepheids; population II, metal-poor, stars, found in the halo (globular clusters) and in the bulge; extremely useful because have an constant absolute magnitude (M V 0.6) period 0.2 to 1 d ˆ δ Scuti stars (or dwarf Cepheids; spectral type A-F) are main sequence variable stars with period <0.3 d ˆ can be seen with HST in host galaxies of SNe Ia at d up to 50 Mpc ˆ but only long-period (P>10 d) are bright enough ˆ in the MW, all long-period Cepheids live at d>1 kpc parallax precision better than 100µas 17

5.3.1 The variable stars zoo 18

Gaia DR2 Pulsating stars, Catelan & Smith 2015 19

5.3.2 The Gaia view of variable stars 20

Gaia DR2 6 Light echoes ˆ light echoes: interaction of light with ambient material light of a transient event scattered by a dust cloud in the vicinity of a mass loss star (e.g. RS Pup) 21

SN explosions ˆ Measurement: a time series showing dierent parts shining progressively dierence in time gives the distance (assumptions on the geometry, light emission mechanism) 6.1 The distance to the LMC 22

ˆ Interaction of light emitted by the explosion reaches a ring of gas (left by the star before the explosion; why a ring and not a sphere is not known) ˆ light curves from atoms ionized by photons from the explosion: nite speed of light: dierent arrival times from dierent parts of the ring no light until t 0 ; then, closest part shines rst; max. intensity at t max, when entire ring is illuminated ˆ recover the ring inclination, t 0, and t max : actual size of the ring ˆ actual size / angular size = distance ˆ distance to the LMC: 52±3 kpc 24

6.2 Supernovae light echoes Yang et al ApJ 2017 25

6.3 Calibration of the long-period Cepheids Kervella et al 2008 ˆ observations with 3.6 m ESO New Technology Telescope (NTT), La 26

Silla; ESO Multi-Mode Instrument (EMMI): multipurpose imager and spectrograph ˆ long-period Cepheids (the brightest) are used to measure extragalactic distances ˆ RS Pup: a 41.4 d period Cepheid is located 2 kpc; trigonometric parallax is uncertain 6.3.1 Light echo from a Cepheid 27

ˆ idea: see the modulation of the reection nebula by the Cepheid light curve ˆ Method: positions studied (left) and their reected light curves (right) ˆ phase shift: propagation time due to light speed: projected distance hence distance to 1.4% accuracy (1992±28 pc) 7 Cosmological distances ˆ Studies of external galaxies (star formation history, etc) ˆ Study of the large scale structures (galaxy clusters, Big Wall, etc) ˆ Models of the Universe 28

7.1 The rst extragalactic object 29

Using a Cepheid, E. Hubble (1927) was able to compute the distance to the Andromeda Galaxy (M31) His value, 300 kpc (actually a factor two lower than the modern deter- mination) implies that M31 is outside the M-W. This was the rst proof for the existence of structures outside the MW 7.2 Hubble's law Cosmic expansion: v = cz = H0 D Redshift z is easily measured H0 70 km/s/mpc (Planck 2018 value: 67.7±0.4 km/s/mpc) However: peculiar motions (galaxy velocities in clusters, etc) cz for the redshift to be dominated by cosmic expansion, large distances 30

7.2.1 Our peculiar motion ˆ Our galaxy is moving the MW is part of the Virgo Cluster gravitational attraction caused by the cluster mass ˆ CMB dipole anisotropy CMB is isotropic but appears anisotropic due to the motion of the Solar System: v Sun/CMB = 369.82±0.11 km/s towards (l,b)=(264 o,48o ) The amplitude of the dipole is 3362.08±0.99 µ K CMB. Can you recover the value of v Sun/CMB? ˆ Local Group wrt CMB: v LG =620±15 km/s 31

7.3 Measuring cosmology with Supernovae ˆ Supernovae are the brightest events: how to use them as distance indicators? ˆ Supernovae: based on their optical spectra, four types Type Ia: a white dwarf (degenerate electron core) in a binary system is brought above the Chandrasekhar limit (M ch 1.44 M sun ) by accretion from a giant companion; collapse and rebound, leaving only a degenerate gas of neutrons (neutron stars, pulsars); one example is the Crab Nebula (explosed in 1054); SNIa are the most luminous and homogeneous; Type Ib,c: massive star undergoing core collapse Type II: mass > 8 M sun ; no degenerate core; complete explosion; used to measure distance with the expanding photosphere method; ˆ Supernovae: intrinsic brightness (observable in the distant Universe) ubiquity (both nearby and distant Universe) type Ia provide accurate (8%) distance measurements type II provide distance accuracy 10% ˆ acceleration of universe expansion 32

ˆ Nobel Prize 2011: Perlmutter, Riess, and Schmidt SN Ia light curve ˆ Decay rate of luminosity correlates with absolute magnitude ˆ Applies to Branch Normal SNIa and also to peculiar type Ia 33

Phillips ApJ 1993 SN Ia light curve ˆ Decay rate of luminosity correlates with absolute magnitude ˆ Universal light curve in each band; and also for color index ˆ Light curve is strongly wavelength dependent ˆ However, time of maximum magnitude depends on photometric band (reddenning): taking B max. as reference, U-max is reached 2.8 days before, while V-max is reached 2.5 after. ˆ Correct for interstellar reddenning (multi-λ) The B band light curve of 22 SNe Ia Type Ia SNe can be used as standardized candles Distinguishing cosmological models 34

ˆ Need to nd high-z SN Ia ˆ Problem: occurence rate of SN Ia is weak; few times per Myr in MWtype galaxy ˆ 4m-class telescopes: 1/3 degree 2 down to R=24 mag in less than 10min 10 6 galaxies to z<0.5 in one night ˆ It takes 20 days to reach maximum luminosity 14 rest frame days at z=0.5 observe the same elds three weeks apart (before and after full moon) 35

ˆ K-correction for distant SN Ia: photometric bands must be redshifted 36

Results from the SCP (Perlmutter et al 1999) and HZSNSS programs (Riess et al 1998) The Planck 2018 results 37

7.3.1 A Hubble diagram for z<0.4 Riess et al 2016 7.3.2 The distance ladder ˆ use various distance tools from local to distant Universe ˆ use one tool to calibrate another to be used at a larger distance, etc ˆ Example: The Cepheid-SNIa distance ladder (Riess et al 2016) 38

7.4 Distance of galaxies: the Tully-Fisher relation ˆ The Tully-Fisher (1977) relation links the maximum rotation speed of a disk galaxy with its luminosity, that is, the stellar mass L v α max, α 4 ˆ v max is a distance-independent quantity, while the stellar (or baryonic) mass does depend on the distance ˆ Proper calibration of the Tully-Fisher relation thus provides a distance measurement tool, in the local universe; ˆ TF relation applies to spiral galaxies (similar relation for elliptical is the Faber-Jackson relation) ˆ Explaining the TF scaling is a challenge because the rotation speed not only depends on the baryonic mass and size, but also on the radial 40

distribution of the dark mass which itself depends on the dark matter halo on larger scales; ˆ TF relation may be fundamentally linked to the baryonic mass however (McGaugh et al 2000) ˆ Although simple arguments can be used to understand why the rotation speed may scale with the stellar mass, the TF (or FJ) relation are not entirely understood. The Tully-Fisher method 41

Calibrated TF relation for galaxies from various groups (Local, Sculptor, M81); absolute magnitude agains H21cm linewidth; distances obtained from Cepheids; (Pierce & Tully 1992) Determination of v max from H21 cm (Macri et al 2000) 43

ˆ Taken from Aaronson et al 1982 ˆ Absolute H-band magnitude M H against H21cm velocity widths ˆ Dashed-line has a slope 10 (hence L v 4 ) The Tully-Fisher relation ˆ Less scatter in red bands (less extinction) ˆ Steeper (hence more accurate) in H band ˆ Uncertainties: cosmic scatter, photometric (extinction correction) and velocity width measurements (inclination), distance assignments Physical arguments ˆ We can show that M v 4 max 44

ˆ Observations show that M/L H (H-band luminosity) is constant for all spirals ˆ Therefore L v 4 max ˆ How to show that M v 4 max? Virialized baryonic mass distribution: 2T+Ω=0 gives Mv 2 max M 2 /R max or M R max v 2 max Observationnaly, mean surface brightness <I> L/R 2 max is cst Also, M/L H cst for all spirals cst Thus: L H M and R max L 1/2 H hence L H L 1/2 H v2 max which leads to L H v 4 max 45