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 ID: 759867
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Slide1
1
Cosmology with
Supernovae:Lecture 1
Josh FriemanI Jayme Tiomno School of Cosmology, Rio de Janeiro, BrazilJuly 2010
Slide2Hoje
I. Cosmology ReviewII. Observables: Age, DistancesIII. Type Ia Supernovae as Standardizable CandlesIV. Discovery Evidence for Cosmic AccelerationV. Current Constraints on Dark Energy
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Slide3Coming Attractions
VI. Fitting SN Ia Light Curves & Cosmology in detail (MLCS, SALT, rise vs. fall times)VII. Systematic Errors in SN Ia DistancesVIII. Host-galaxy correlationsIX. SN Ia Theoretical ModelingX. SN IIp DistancesXI. Models for Cosmic AccelerationXII. Testing models with Future Surveys: Photometric classification, SN Photo-z’s, & cosmology
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Slide4References
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
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Slide5The only mode which preserves homogeneity and isotropy is overall expansion or contraction:
Cosmic scale factor
Slide66
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
Slide77
Distance between galaxies:
where fixed comoving distanceRecession speed: Hubble’s Law (1929)
Slide8Modern
HubbleDiagram Hubble Space TelescopeKeyProject
Freedman
etal
Hubble parameter
Slide9Recent Measurement of H0
9
HST Distances to 240 Cepheid variable stars in 6 SN
Ia host galaxies
Riess
, etal 2009
Slide10How 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
Slide11Cosmological Dynamics
Friedmann
Equations
Density Pressure
Spatial curvature:
k
=0,+1,-1
Slide12Size of the
Universe
Cosmic Time
Empty
Today
In
these
cases,
decreases with time,
: ,
expansion decelerates
Slide13Cosmological Dynamics
Friedmann
Equations
Slide14Size of the
Universe
Cosmic Time
Empty
Accelerating
Today
p =
(w = 1)
Slide1515
``Supernova Data”
Slide1616
Discovery of Cosmic Acceleration from
High-redshiftSupernovaeType 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
Slide17Cosmic 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?
Slide18Cosmic 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.
Slide1919
Cosmological Constant as Dark Energy
Einstein:
Zel’dovich and Lemaitre:
Slide20Cosmological 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
Slide21Components of the Universe
Dark Matter:
clumps, holds galaxies and clusters togetherDark Energy: smoothly distributed, causes expansion of Universe to speed up
Slide22=Log[a
0
/a(t)]
Equation of State parameter
w
determines Cosmic Evolution
Conservation of Energy-Momentum
Slide2323
Depends on constituents of the Universe:
History of Cosmic Expansion
Slide2424
Cosmological Observables
Friedmann
-
Robertson-Walker
Metric: whereComoving distance:
Slide25Age of the Universe
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Slide2626
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.
Slide27Age of the Universe
(H
0/72)
(flat)
Slide28Luminosity 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:
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 isEnergy flux received by O per unit area is
Slide29Include 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
a
0
=1
Slide3030
Worked Example I
For w=1(cosmological constant ): Luminosity distance:
Slide3131
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
Slide3232
Dark Energy Equation of State
Curves of
constant
d
Lat fixed z
z =
Flat Universe
Slide33Exercise 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.
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Slide3434
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
Slide35Exercise 4
Plot distance modulus vs redshift (z=0-1) for:Flat model withFlat model withOpen model withPlot first linear in z, then log z. Plot the residual of the first two models with respect to the third model
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Slide3636
Discovery of Cosmic Acceleration from
High-redshiftSupernovaeType 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
Slide3737
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
Slide3838
K corrections due to redshift
SN spectrum
Rest-frame B band filterEquivalent restframe i band filter at different redshifts(iobs=7000-8500 A)
Slide3939
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 H0 (for z<<1, dL=cz/H0) If Mi (and H0) unknown but constant, from measurement of mi can infer distance to object at redshift z1 relative to object at distance z2: independent of H0Use low-redshift SNe to vertically `anchor’ the Hubble diagram, i.e., to determine
Slide4040
SN
1994D
Type
Ia
Supernovae as
Standardizable
Candles
Slide4141
Slide4242
SN Spectra
~1 week
after
maximumlightFilippenko 1997
Ia
II
Ic
Ib
Slide43Type Ia Supernovae
Thermonuclear explosions of Carbon-Oxygen White DwarfsWhite 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 secondsIn 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
Slide4444
Type Ia Supernovae
General properties:Homogeneous class* of events, only small (correlated) variationsRise time: ~ 15 – 20 daysDecay time: many monthsBright: MB ~ – 19.5 at peakNo hydrogen in the spectraEarly 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 ellipticalsProgenitor systems must have long lifetimes
*luminosity, color,
spectra at max. light
Slide45SN Ia Spectral Homogeneity(to lowest order)
from SDSS Supernova Survey
Slide4646
Spectral Homogeneity at fixed epoch
Slide4747
SN2004ar z = 0.06 from SDSS galaxy spectrum
Galaxy-subtracted
Spectrum
SN Ia
template
Slide48How similar to one another?Some real variations: absorption-line shapes at maximumConnections to luminosity?Matheson, etal, CfA sample
Slide4949
Hsiao etal
Supernova
Ia
Spectral Evolution
Late times
Early times
Slide5050
Layered
Chemical
Structure
provides
clues to
Explosion
physics
Slide5151
SDSS
Filter Bandpasses
Slide5252
Model
SN
Ia
Light Curves in SDSS filters synthesized from composite template spectral sequenceSNe evolve in time from blue to red;K-corrections are time-dependent
Slide5353
SN1998bu Type Ia
Multi-band Light curve
Extremely
few light-curves are this well sampled
Suntzeff, etal
Jha, etal
Hernandez, etal
Slide54Luminosity
Time
m
15
15 days
Empirical Correlation: Brighter
SNe
Ia
decline more
slowly
and are bluer
Phillips 1993
Slide55SN
Ia Peak LuminosityEmpirically correlatedwith Light-Curve Decline RateBrighter SlowerUse to reduce Peak Luminosity DispersionPhillips 1993
Peak Luminosity
Rate of decline
Garnavich, etal
Slide5656
Type
Ia SNPeak Brightnessas calibratedStandard CandlePeak brightnesscorrelates with decline rateVariety of algorithms for modeling these correlations: corrected dist. modulusAfter correction,~ 0.16 mag(~8% distance error)
Luminosity
Time
Slide5757
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
Slide5858
Carnegie
Supernova
Project
Nearby
Optical+
NIR LCs
Slide5959
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
Slide6060
Acceleration Discovery Data:High-z SN Team
10 of 16 shown; transformed to SN rest-frameRiess etalSchmidt etal
V
B+1
Slide6161
Discovery of Cosmic Acceleration from
High-redshiftSupernovaeApply same brightness-decline relation at high zType 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
Slide62Likelihood Analysis
This assumes errors in distance modulus estimates are Gaussian. More details on this next time.
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Data Model
Slide6363
Slide64Exercise 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 H0 with a flat prior.
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Slide65Riess, etal High-z Data (1998)
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Slide66Low-z Data
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