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Cosmology with Supernovae: Lecture 1

Cosmology with Supernovae: Lecture 1. Josh Frieman I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil July 2010. Hoje. I. Cosmology Review II. Observables: Age, Distances III. Type Ia Supernovae as Standardizable Candles IV. Discovery Evidence for Cosmic Acceleration

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Cosmology with Supernovae: Lecture 1

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

  2. 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

  3. 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

  4. References • Reviews: Frieman, Turner, Huterer, Ann. Rev. of Astron. Astrophys., 46, 385 (2008) Copeland, Sami, Tsujikawa, Int. Jour. Mod. Phys., D15, 1753 (2006) Caldwell & Kamionkowski, Ann. Rev. Nucl. Part. Phys. (2009) Silvestri & Trodden, Rep. Prog. Phys. 72:096901 (2009) Kirshner, astro-ph/0910.0257

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

  6. 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 t1, observed at t2

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

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

  9. Recent Measurement of H0 Riess, etal 2009 HST Distances to 240 Cepheid variable stars in 6 SN Ia host galaxies

  10. 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

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

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

  13. Cosmological Dynamics Friedmann Equations

  14. p =  (w = 1) Accelerating Empty Size of the Universe Today Cosmic Time

  15. ``Supernova Data”

  16. Log(distance) Discovery of Cosmic Acceleration from High-redshift Supernovae Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Accelerating = 0.7 = 0. m= 1. Not accelerating redshift

  17. 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 H0=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?

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

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

  20. 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: Theory: Data: Pauli Cosmological Constant Problem

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

  22. Equation of State parameter w determines Cosmic Evolution Conservation of Energy-Momentum =Log[a0/a(t)]

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

  24. Cosmological Observables Friedmann- Robertson-Walker Metric: where Comovingdistance:

  25. Age of the Universe

  26. Exercise 2: A. For w=1(cosmological constant ) and k=0: Derive an analytic expression for H0t0 in terms of Plot B. Do the same, but for C. Suppose H0=70 km/sec/Mpc and t0=13.7 Gyr. Determine in the 2 cases above. D. Repeat part C but with H0=72.

  27. Age of the Universe (H0/72) (flat)

  28. Luminosity Distance • Source S at origin emits light at time t1 into solid angle d, received by observer O at coordinate distance r at time t0, with detector of area A: Proper area of detector given by the metric: Unit area detector at O subtends solid angle at S. Power emitted into d is Energy flux received by O per unit area is S A  r

  29. Include Expansion • Expansion reduces received flux due to 2 effects: 1. Photon energy redshifts: 2. Photons emitted at time intervals t1 arrive at time intervals t0: Luminosity Distance Convention: choose a0=1

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

  31. Worked Example II For a flat Universe (k=0) and constant Dark Energy equation of state w: Luminosity distance: Note: H0dL is independent of H0

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

  33. 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.

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

  35. Exercise 4 • Plot distance modulus vsredshift (z=0-1) for: • Flat model with • 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

  36. Log(distance) Discovery of Cosmic Acceleration from High-redshift Supernovae Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Accelerating = 0.7 = 0. m= 1. Not accelerating redshift

  37. Distance Modulus • Recall logarithmic measures of luminosity and flux: • Define distance modulus: • 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. denotes passband

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

  39. 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 redshiftz, and thereby determine H0 (for z<<1, dL=cz/H0) • If Mi (and H0) unknown but constant, from measurement of mi can infer distance to object at redshiftz1 relative to object at distance z2: independent of H0 • Use low-redshiftSNe to vertically `anchor’ the Hubble diagram, i.e., to determine

  40. Type Ia Supernovae as Standardizable Candles SN 1994D

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

  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~1.4Msun (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

  43. 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 Type Ia Supernovae *luminosity, color, spectra at max. light

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

  45. Spectral Homogeneity at fixed epoch

  46. SN2004ar 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 maximumConnections to luminosity?Matheson, etal, CfA sample

  48. Supernova IaSpectral Evolution Late times Early times Hsiao etal

  49. Layered Chemical Structure provides clues to Explosion physics

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