Univ. Frankfurt – Jan 2014 Univ. Frankfurt – Jan 2014 Measuring Perturbations Measuring Perturbations with Weak Lensing of SNe with Weak Lensing of SNe In collaboration with: Luca Amendola, Tiago de Castro & Valerio Marra Miguel Quartin Miguel Quartin Instituto de Física Instituto de Física 1 1 Univ. Federal do Rio de Janeiro Univ. Federal do Rio de Janeiro
The Hubble's Law The Hubble's Law Lemaître (and later Hubble)* found out that galaxies are, Lemaître (and later Hubble)* found out that galaxies are, in average, receding from us; in average, receding from us; The redshift The redshift z z is linear with distance is linear with distance The velocity is approx. also linear with distance The velocity is approx. also linear with distance * Stigler's law of eponymy: "No scientific discovery is * Stigler's law of eponymy: "No scientific discovery is named after its named after its original discoverer." original discoverer." 2 2
10 9 light-years 2 .10 9 light-years 3 3
Distances in Cosmology Distances in Cosmology → → Inside the solar system Inside the solar system Laser Ranging Laser Ranging Shoot a strong laser at a planet and measure the time it Shoot a strong laser at a planet and measure the time it takes to be reflected back to us takes to be reflected back to us → → Inside the galaxy Inside the galaxy stellar parallax stellar parallax Requires precise astrometry Requires precise astrometry Maximum distance measured: 500 pc (1600 ly), by the Maximum distance measured: 500 pc (1600 ly), by the Hipparcos satellite (1989–1993) Hipparcos satellite (1989–1993) → → → → Dec. 2013 Dec. 2013 Gaia satellite launched (2013 – 2019) Gaia satellite launched (2013 – 2019) parallax up to ~50 kpc parallax up to ~50 kpc Compare with: Compare with: → → Milky Way Milky Way ~15 kpc radius ~15 kpc radius → → Andromeda 4 4 Andromeda ~1 Mpc ~1 Mpc
Standard Candles Standard Candles A plot of distance vs. z is called a A plot of distance vs. z is called a Hubble Diagram Hubble Diagram To measure distances at To measure distances at z >~ 0.0001 z >~ 0.0001 (~0.4 Mpc) we need (~0.4 Mpc) we need good standard candles (known intrinsic luminosity) good standard candles (known intrinsic luminosity) There are 2 classic standard (rigorously, There are 2 classic standard (rigorously, standardizible standardizible ) ) candles in cosmology: candles in cosmology: Cepheid variable stars ( * Jones et al., 1304.0768 Cepheid variable stars (0 < z < 0.05 0 < z < 0.05) ) Type Ia Supernovae ( Type Ia Supernovae (0 < z < 1.91* 0 < z < 1.91*) ) Both classes have Both classes have intrinsic variability intrinsic variability, but there are , but there are empirical relations that allow us to calibrate and empirical relations that allow us to calibrate and standardize them them standardize 5 5
Type Ia Supernovae Supernovae Type Ia Supernovae Supernovae 6 6
Type Ia Supernovae (2) Type Ia Supernovae (2) Standardizable candles Standardizable candles 100 25 7 7
Type Ia Supernovae (3) Type Ia Supernovae (3) Supernovae (SNe) are Supernovae (SNe) are very bright very bright explosions of stars explosions of stars There are 2 major kinds of SNe There are 2 major kinds of SNe Core-collapse (massive stars which run out of H and He) Core-collapse (massive stars which run out of H and He) Collapse by mass accretion in binary systems ( Collapse by mass accretion in binary systems (type Ia type Ia) ) White dwarf + red giant companion (single degenerate) White dwarf + red giant companion (single degenerate) White dwarf + White dwarf (double degenerate) White dwarf + White dwarf (double degenerate) → → Type Ia SNe explosion Type Ia SNe explosion ~ standard energy release ~ standard energy release Chandrasekar limit on white dwarf mass: M Chandrasekar limit on white dwarf mass: M max = 1.44 M sun max = 1.44 M sun → → → → Beyond this Beyond this instability explosion instability explosion → → SNe Ia SNe Ia less intrinsic scatter + strong correlation between less intrinsic scatter + strong correlation between brightness & duration brightness & duration 8 8
Type Ia Supernovae (4) Type Ia Supernovae (4) SNe Ia are so far the only SNe Ia are so far the only proven proven standard(izible) candles standard(izible) candles for cosmology for cosmology → → With good measurements With good measurements scatter < 0.15 mag in the in the scatter < 0.15 mag Hubble diagram Hubble diagram But arguably they are subject to more systematic effects But arguably they are subject to more systematic effects than BAO (baryon acoustic oscillations) & CMB than BAO (baryon acoustic oscillations) & CMB Systematic errors already the dominant part (N Systematic errors already the dominant part (N SNe ~ 1000) SNe ~ 1000) → → In the next ~10 years In the next ~10 years statistics will increase by 100x statistics will increase by 100x Huge effort to improve understanding of systematics Huge effort to improve understanding of systematics Howell, 1011.0441 (review of SNe) 9 9
SNe Systematics SNe Systematics 10 10
Hubble diagram Hubble diagram d d L (z) L (z) 11 11
Supernova Lensing Supernova Lensing → → Standard SNe analysis Standard SNe analysis geodesics in FLRW geodesics in FLRW → → → → Real universe Real universe structure (filaments & voids) weak- structure (filaments & voids) weak- → very skewed PDF → lensing (WL) very skewed PDF (Probab. Distr. Function)! (Probab. Distr. Function)! lensing (WL) → → Most SNe Most SNe demagnified a little (light-path in voids) demagnified a little (light-path in voids) → → A few A few magnified “a lot” (path near large structures) magnified “a lot” (path near large structures) The lensing PDF is the The lensing PDF is the key quantity key quantity → → Hard to measure Hard to measure need many more SNe need many more SNe Can be computed: ray-tracing in N-body simulations Can be computed: ray-tracing in N-body simulations See: Takahashi et al. 1106.3823 See: Hilbert et al. astro-ph/0703803 → → → → N-body N-body too expensive to do likelihoods many too expensive to do likelihoods many parameter values (many Ω Ω m0 , σ σ 8 , w DE , etc.) parameter values (many , , w DE , etc.) 12 12 m0 8
Supernova Lensing (2) Supernova Lensing (2) Supernova light travels huge distances Supernova light travels huge distances → on average → → → Lensing Lensing on average no magnification (photon # conser.) no magnification (photon # conser.) → → Important quantity Important quantity magnification PDF magnification PDF Zero mean; very skewed (most objects de-magnified) Zero mean; very skewed (most objects de-magnified) Adds Adds non-gaussian dispersion non-gaussian dispersion to the Hubble diagram to the Hubble diagram Function of three d A (z) 13 13
Supernova Lensing (3) Supernova Lensing (3) Note that the N-body approach might not be appropriate Note that the N-body approach might not be appropriate Supernovae light bundles form a very thin (< 1 AU) pencil Supernovae light bundles form a very thin (< 1 AU) pencil N-body simulations coarse grained in scales >>> 1 AU N-body simulations coarse grained in scales >>> 1 AU Relativistic effects (e.g. Ricci + Weyl focusing) might be Relativistic effects (e.g. Ricci + Weyl focusing) might be important important Clarkson, Ellis, Faltenbacher, Maartens, Umeh, Uzan (1109.2484, MNRAS) There are also corrections due to a neglected Doppler term There are also corrections due to a neglected Doppler term Bolejko, Clarkson, Maartens, Bacon, Meures, Beynon (1209.3142, PRL) We neglect these corrections here We neglect these corrections here 14 14
The Lensing PDF The Lensing PDF de-magnif. magnification 15 15
Finite Finite sources sources 16 16 Takahashi et al. 1106.3823
A New Method A New Method → stochastic GL analysis (sGL) → We need something faster We need something faster stochastic GL analysis (sGL) → → Populate the universe with NFW halos Populate the universe with NFW halos Halo Model Halo Model need prescriptions for mass fun. & concentration param. need prescriptions for mass fun. & concentration param. In a given direction, draw nearby distribution of halos In a given direction, draw nearby distribution of halos Bin Bin in distance & impact parameter in distance & impact parameter compute the compute the convergence ( convergence (fast fast) ) K. Kainulainen & V. Marra 0906.3871 (PRD) 0909.0822 (PRD) 17 17
A New Method (2) A New Method (2) 18 18
NFW NFW Profile Profile 19 19
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