Distance measurements Pierre Hily-Blant 2018-19 Contents 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... 1
A crack in the standard cosmological model? 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 2
determination with Cepheids. works... We'll see, in this Lecture, how this 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 Trigonometric parallax 3
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 Photometric distance ˆ Some stars are known as standard candles: variable stars (δ Cepheid, RR Lyrae) and type Ia supernovae (SNe Ia) ˆ They are the best tools to measure distances on galactic and intergalactic scales ˆ 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 ˆ 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 eects, reddening 4
The life cycle of stars 5
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From the main sequence to red giant phase 7
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 8
... 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: 9
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) Cepheids 25 variable stars in the SMC, Leavitt & Pickering 1912 10
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 11
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 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 The instability strip 12
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? 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: compressing a layer increases ρ and T: normally, opacity κ ρ T -7/2, so that κ decreases in the process: heat can be radiated away stable but in RG stars, outer layer where He + He ++ (T 2-4 10 4 K), opacity increases with T compression of these layers increase the opacity, hence temperature increases making these layers to mechanism: κ-mechanism 13
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 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 15
The variable stars zoo 16
Gaia DR2 Pulsating stars, Catelan & Smith 2015 17
The Gaia view of variable stars 18
Gaia DR2 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) 19
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) Calibration of the long-period Cepheids Figure 1: Kervella et al 2008 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 ˆ ˆ observations with 3.6 m ESO New Technology Telescope (NTT), La Silla Observatory (Chile) 20
ˆ ESO Multi-Mode Instrument (EMMI): multipurpose imager and spectrograph the distance to the LMC 21
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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 23
Supernovae light echoes Yang et al ApJ 2017 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 24
The rst extragalactic object 25
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 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 26
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 27
The distance ladder Distance of galaxies: the Tully-Fisher relation 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 28
type II provide distance accuracy 10% ˆ acceleration of universe expansion ˆ Nobel Prize 2011: Perlmutter, Riess, and Schmidt SN Ia light curve 29
ˆ Decay rate of luminosity correlates with absolute magnitude ˆ Applies to Branch Normal SNIa and also to peculiar type Ia 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 30
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) 31
ˆ K-correction for distant SN Ia: photometric bands must be redshifted *Discovery of 32
Results from the SCP (Perlmutter et al 1999) and HZSNSS programs (Riess et al 1998) The Planck 2018 results 33