1. 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 2

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 3

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 4

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

6. 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 t 1, observed at t 2

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

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

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

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

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

13. Cosmological Dynamics Friedmann Equations

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

15. 15 ``Supernova Data”

16. 16 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   = 0.7   = 0.  m = 1. Log(distance) redshift Accelerating Not accelerating

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 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?

18. 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.

19. 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 together Dark Energy: smoothly distributed, causes expansion of Universe to speed up

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

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

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

25. Age of the Universe 25

26. 26 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.

27. Age of the Universe  (H 0 /72) (flat)

28. 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: S A r  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

29. 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 : Luminosity Distance Convention: choose a 0 =1

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

31. 31 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

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

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. 33

34. 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 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

36. 36 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   = 0.7   = 0.  m = 1. Log(distance) redshift Accelerating Not accelerating

37. 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. 38 K corrections due to redshift SN spectrum Rest-frame B band filter Equivalent restframe i band filter at different redshifts (i obs =7000-8500 A)

39. 39 Absolute vs. Relative Distances Recall logarithmic measures of luminosity and flux: If M i is known, from measurement of m i can infer absolute distance to an object at redshift z, and thereby determine H 0 (for z<<1, d L =cz/H 0 ) If M i (and H 0 ) unknown but constant, from measurement of m i 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

40. 40 SN 1994D Type Ia Supernovae as Standardizable Candles

41. 41

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

43. 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~1.4M sun (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

44. 44 Type Ia Supernovae General properties: Homogeneous class* of events, only small (correlated) variations Rise time: ~ 15 – 20 days Decay time: many months Bright: M B ~ – 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

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

46. 46 Spectral Homogeneity at fixed epoch

47. 47 SN2004ar z = 0.06 from SDSS galaxy spectrum Galaxy-subtracted Spectrum SN Ia template

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

49. 49 Hsiao etal Supernova Ia Spectral Evolution Late times Early times

50. 50 Layered Chemical Structure provides clues to Explosion physics

51. 51 SDSS Filter Bandpasses

52. 52 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 time- dependent

53. 53 SN1998bu Type Ia Multi-band Light curve Extremely few light-curves are this well sampled Suntzeff, etal Jha, etal Hernandez, etal

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

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

56. 56 Type Ia SN Peak Brightness as calibrated Standard Candle 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 Time

57. 57 Published Light Curves for Nearby Supernovae Low-z SNe: Anchor Hubble diagram Train Light- curve fitters Need well- sampled, well- calibrated, multi-band light curves

58. 58 Carnegie Supernova Project Nearby Optical+ NIR LCs

59. 59 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

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

61. 61 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   = 0.7   = 0.  m = 1. Log(distance) redshift Accelerating Not accelerating HZT SCP

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

63. 63

64. 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

65. Riess, etal High-z Data (1998) 65

66. Low-z Data 66