Cosmology with Supernovae Lecture 1 Josh Frieman I

Cosmology with Supernovae: Lecture 1 Josh Frieman I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil July 2010 1

Hoje • I. Cosmology Review • II. Observables: Age, Distances • III. Type Ia Supernovae as Standardizable Candles • IV. Discovery Evidence for Cosmic Acceleration • V. Current Constraints on Dark Energy 2

Coming Attractions • VI. Fitting SN Ia Light Curves & Cosmology in detail (MLCS, SALT, rise vs. fall times) • VII. Systematic Errors in SN Ia Distances • VIII. Host-galaxy correlations • IX. SN Ia Theoretical Modeling • X. SN IIp Distances • XI. Models for Cosmic Acceleration • XII. Testing models with Future Surveys: Photometric classification, SN Photo-z’s, & cosmology 3

References • Reviews: Frieman, Turner, Huterer, Ann. Rev. of Astron. Astrophys. , 46, 385 (2008) Copeland, Sami, Tsujikawa, Int. Jour. Mod. Phys. , D 15, 1753 (2006) Caldwell & Kamionkowski, Ann. Rev. Nucl. Part. Phys. (2009) Silvestri & Trodden, Rep. Prog. Phys. 72: 096901 (2009) Kirshner, astro-ph/0910. 0257 4

The only mode which preserves homogeneity and isotropy is overall expansion or contraction: Cosmic scale factor

On average, galaxies are at rest in these expanding (comoving) coordinates, and they are not expanding --they are gravitationally bound. Wavelength of radiation scales with scale factor: Redshift of light: emitted at t 1, observed at t 2 6

Distance between galaxies: where fixed comoving distance Recession speed: Hubble’s Law (1929) 7

Modern Hubble Diagram Hubble Space Telescope Key Project Hubble parameter Freedman etal

Recent Measurement of H 0 Riess, etal 2009 HST Distances to 240 Cepheid variable stars in 6 SN Ia host galaxies 9

How does the expansion of the Universe change over time? Gravity: everything in the Universe attracts everything else expect the expansion of the Universe should slow down over time

Cosmological Dynamics Spatial curvature: k=0, +1, -1 Friedmann Equations Density Pressure

Empty Size of the Universe In these cases, decreases with time, : , expansion decelerates Today Cosmic Time

Cosmological Dynamics Friedmann Equations

p = (w = 1) Accelerating Size of the Universe Empty Today Cosmic Time

``Supernova Data” 15

Log(distance) Discovery of Cosmic Acceleration from High-redshift Supernovae Accelerating Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Not accelerating = 0. 7 = 0. m = 1. redshift 16

Cosmic Acceleration This implies that increases with time: if we could watch the same galaxy over cosmic time, we would see its recession speed increase. Exercise 1: A. Show that above statement is true. B. For a galaxy at d=100 Mpc, if H 0=70 km/sec/Mpc =constant, what is the increase in its recession speed over a 10 -year period? How feasible is it to measure that change?

Cosmic Acceleration What can make the cosmic expansion speed up? 1. The Universe is filled with weird stuff that gives rise to `gravitational repulsion’. We call this Dark Energy 2. Einstein’s theory of General Relativity is wrong on cosmic distance scales. 3. We must drop the assumption of homogeneity/isotropy.

Cosmological Constant as Dark Energy Einstein: Zel’dovich and Lemaitre: 19

Cosmological Constant as Dark Energy Quantum zero-point fluctuations: virtual particles continuously fluctuate into and out of the vacuum (via the Uncertainty principle). Vacuum energy density in Quantum Field Theory: Pauli Theory: Data: Cosmological Constant Problem

Components of the Universe Dark Matter: clumps, holds galaxies and clusters together Dark Energy: smoothly distributed, causes expansion of Universe to speed up

Equation of State parameter w determines Cosmic Evolution Conservation of Energy-Momentum =Log[a 0/a(t)]

History of Cosmic Expansion • Depends on constituents of the Universe: 23

Cosmological Observables Friedmann. Robertson-Walker Metric: where Comoving distance: 24

Age of the Universe 25

Exercise 2: A. For w= 1(cosmological constant ) and k=0: Derive an analytic expression for H 0 t 0 in terms of Plot B. Do the same, but for C. Suppose H 0=70 km/sec/Mpc and t 0=13. 7 Gyr. Determine in the 2 cases above. D. Repeat part C but with H 0=72. 26

(H 0/72) Age of the Universe (flat)

Luminosity Distance • Source S at origin emits light at time t 1 into solid angle d , received by observer O at coordinate distance r at time t 0, with detector of area A: Proper area of detector given by the metric: A S r Unit area detector at O subtends solid angle at S. Power emitted into d is Energy flux received by O per unit area is

Include Expansion • Expansion reduces received flux due to 2 effects: 1. Photon energy redshifts: 2. Photons emitted at time intervals t 1 arrive at time intervals t 0: Convention: choose a 0=1 Luminosity Distance

Worked Example I For w= 1(cosmological constant ): Luminosity distance: 30

Worked Example II For a flat Universe (k=0) and constant Dark Energy equation of state w: Luminosity distance: Note: H 0 d. L is independent of H 0 31

Dark Energy Equation of State Curves of constant d. L at fixed z Flat Universe z= 32

Exercise 3 • Make the same plot for Worked Example I: plot curves of constant luminosity distance (for several choices of redshift between 0. 1 and 1. 0) in the plane of , choosing the distance for the model with as the fiducial. • In the same plane, plot the boundary of the region between present acceleration and deceleration. • Extra credit: in the same plane, plot the boundary of the region that expands forever vs. recollapses. 33

Bolometric Distance Modulus • Logarithmic measures of luminosity and flux: • Define distance modulus: flux measure redshift from spectra • For a population of standard candles (fixed M), measurements of vs. z, the Hubble diagram, constrain cosmological parameters. 34

Exercise 4 • Plot distance modulus vs redshift (z=0 -1) for: • Flat model with • Open model with – Plot first linear in z, then log z. • Plot the residual of the first two models with respect to the third model 35

Log(distance) Discovery of Cosmic Acceleration from High-redshift Supernovae Accelerating Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Not accelerating redshift = 0. 7 = 0. m = 1. 36

Distance Modulus • Recall logarithmic measures of luminosity and flux: • Define distance modulus: denotes passband • For a population of standard candles (fixed M) with known spectra (K) and known extinction (A), measurements of vs. z, the Hubble diagram, constrain cosmological parameters. 37

K corrections due to redshift SN spectrum Rest-frame B band filter Equivalent restframe i band filter at different redshifts (iobs=7000 -8500 A) 38

Absolute vs. Relative Distances • Recall logarithmic measures of luminosity and flux: • If Mi is known, from measurement of mi can infer absolute distance to an object at redshift z, and thereby determine H 0 (for z<<1, d. L=cz/H 0) • If Mi (and H 0) unknown but constant, from measurement of mi can infer distance to object at redshift z 1 relative to object at distance z 2: independent of H 0 • Use low-redshift SNe to vertically `anchor’ the Hubble diagram, i. e. , to determine 39

Type Ia Supernovae as Standardizable Candles SN 1994 D 40

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Ia SN Spectra ~1 week after maximum light II Ic Ib Filippenko 1997 42

Type Ia Supernovae Thermonuclear explosions of Carbon-Oxygen White Dwarfs White Dwarf accretes mass from or merges with a companion star, growing to a critical mass~1. 4 Msun (Chandrasekhar) After ~1000 years of slow cooking, a violent explosion is triggered at or near the center, and the star is completely incinerated within seconds In the core of the star, light elements are burned in fusion reactions to form Nickel. The radioactive decay of Nickel and Cobalt makes it shine for a couple of months

Type Ia Supernovae General properties: Homogeneous class* of events, only small (correlated) variations • Rise time: ~ 15 – 20 days • Decay time: many months • Bright: MB ~ – 19. 5 at peak • No hydrogen in the spectra • Early spectra: Si, Ca, Mg, . . . (absorption) • Late spectra: Fe, Ni, …(emission) • Very high velocities (~10, 000 km/s) SN Ia found in all types of galaxies, including ellipticals • Progenitor systems must have long lifetimes *luminosity, color, spectra at max. light 44

SN Ia Spectral Homogeneity (to lowest order) from SDSS Supernova Survey

Spectral Homogeneity at fixed epoch 46

SN 2004 ar z = 0. 06 from SDSS galaxy spectrum Galaxy-subtracted Spectrum SN Ia template 47

How similar to one another? Some real variations: absorption-line shapes at maximum Connections to luminosity? Matheson, etal, Cf. A sample

Supernova Ia Spectral Evolution Late times Early times Hsiao etal 49

Layered Chemical Structure provides clues to Explosion physics 50

SDSS Filter Bandpasses 51

Model SN Ia Light Curves in SDSS filters synthesized from composite template spectral sequence SNe evolve in time from blue to red; K-corrections are timedependent 52

SN 1998 bu Type Ia Multi-band Light curve Extremely few light-curves are this well sampled Suntzeff, etal Jha, etal Hernandez, etal 53

Luminosity m 15 15 days Time Empirical Correlation: Brighter SNe Ia decline more slowly and are bluer Phillips 1993

Brighter Slower Use to reduce Peak Luminosity Dispersion Peak Luminosity SN Ia Peak Luminosity Empirically correlated with Light-Curve Decline Rate Phillips 1993 Garnavich, etal Rate of decline

Peak brightness correlates with decline rate Variety of algorithms for modeling these correlations: corrected dist. modulus After correction, ~ 0. 16 mag (~8% distance error) Luminosity Type Ia SN Peak Brightness as calibrated Standard Candle Time 56

Published Light Curves for Nearby Supernovae Low-z SNe: Anchor Hubble diagram Train Lightcurve fitters Need wellsampled, wellcalibrated, multi -band light curves 57

Carnegie Supernova Project Nearby Optical+ NIR LCs 58

Correction for Brightness-Decline relation reduces scatter in nearby SN Ia Hubble Diagram Distance modulus for z<<1: Corrected distance modulus is not a direct observable: estimated from a model for light -curve shape Riess etal 1996 59

Acceleration Discovery Data: High-z SN Team 10 of 16 shown; transformed to SN rest -frame V B+1 Riess etal Schmidt etal 60

Discovery of Cosmic Acceleration from High-redshift Supernovae Apply same brightness-decline relation at high z Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Log(distance) HZT SCP Accelerating Not accelerating redshift = 0. 7 = 0. m = 1. 61

Likelihood Analysis Data Model This assumes errors in distance modulus estimates are Gaussian. More details on this next time. 62

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Exercise 5 • Carry out a likelihood analysis of using the High-Z Supernova Data of Riess, etal 1998: see following tables. Assume a fixed Hubble parameter for this exercise. • Extra credit: marginalize over H 0 with a flat prior. 64

Riess, etal High-z Data (1998) 65

Low-z Data 66