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Cosmology with Supernovae:Lecture 2
Josh Frieman
I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil
July 2010
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Hoje
• V. Recent SN Surveys and Current Constraints on Dark Energy
• VI. Fitting SN Ia Light Curves & Cosmology
• VII. Systematic Errors in SN Ia Distances
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Coming Attractions
• 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
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Lum
inos
ity
Time
m15
15 days
Empirical Correlation: Brighter SNe Ia decline more slowly and are bluerPhillips 1993
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SN Ia Peak LuminosityEmpirically correlatedwith Light-Curve Decline Rate and Color
Brighter Slower, Bluer
Use to reduce Peak Luminosity Dispersion:
Phillips 1993
Pea
k L
umin
osit
y
Rate of declineGarnavich, etal€
M ipeak = c i + f i(Δm15)
in rest - frame passband i
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Type Ia SNPeak Brightnessas calibratedStandard Candle
Peak brightnesscorrelates with decline rate
Variety of algorithms for modeling these correlations: corrected dist. modulus
After correction,~ 0.16 mag(~8% distance error)
Lum
inos
ity
Time
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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
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Low-z Data
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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
€
m − M = 5logv
km/sec
⎛
⎝ ⎜
⎞
⎠ ⎟− 5log h +15
Riess etal 1996
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Acceleration Discovery Data:High-z SN Team
10 of 16 shown; transformed to SN rest-frame
Riess etal
Schmidt etal
V
B+1
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Riess, etal High-z Data (1998)
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High-z Supernova Team data (1998)
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Likelihood Analysis
This assume
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€
−2ln L = χ 2 =(μ i − μmod (zi;Ωm ,ΩΛ,H0)2
σ μ ,i2
i
∑
Since μmod = 5log(H0dL ) − 5log(H0), let ˆ μ ≡ μmod (H0 = 70)
and define Δ i = μ i − ˆ μ . If we fix H0, then we are minimizing
ˆ χ 2 =Δ i
2
σ i2
i
∑
To marginalize over logH0 with flat prior, we instead minimize
χ mar2 = −2ln d(5logH0)exp −χ 2 /2( )∫
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥= ˆ χ 2 −
B2
C+ ln
C
2π
⎛
⎝ ⎜
⎞
⎠ ⎟,
where
B =Δ i
σ i2
i
∑ , C =1
σ i2
i
∑
σ μ ,i2 = σ μ , fit
2 + σ μ ,int2 + σ μ ,vel
2
Goliath etal 2001
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High-z SN Team Supernova Cosmology Project
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1998-2010 SN Ia Synopsis• Substantial increases in both quantity and quality of SN
Ia data: from several tens of relatively poorly sampled light curves to many hundreds of well-sampled, multi-band light curves from rolling surveys
• Extension to previously unexplored redshift ranges: z>1 and 0.1<z<0.3
• Extension to previously underexplored rest-frame wavelengths (Near-infrared)
• Vast increase in spectroscopic data• Identification of SN Ia subpopulations (host galaxies)• Entered the systematic error-dominated regime, but
with pathways to reduce systematic errors
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Supernova Legacy Survey (2003-2008)
Megaprime Mosaic CCD camera
Observed 2 1-sq deg regions every 4 nights
~400+ spectroscopically confirmed SNe Ia to measure w
Used 3.6-meter CFHT/“Megacam”
36 CCDs with good blue response
4 filters griz for good K-corrections and color measurement
Spectroscopic follow-up on 8-10m telescopes
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8 nights/yr:LBL/Caltech
DEIMOS/LRIS for types,
intensive study, cosmology with
SNe II-P
Keck
120 hr/yr: France/UK FORS 1&2 for types,
redshifts
VLT
120 hr/yr: Canada/US/UK
GMOS for types, redshifts
Gemini 3 nights/yr: Toronto
IMACS for host redshifts
Magellan
Spectra
SN Identification
Redshifts
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Power of a Rolling Search
SNLS Light curves
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First-Year SNLS Hubble Diagram
SNLS 1st Year Results
Astier et al. 2006
Using 72 SNefrom SNLS+40 Low-z
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Wood-Vasey, etal (2007), Miknaitis, etal (2007): results from ~60 ESSENCE SNe (+Low-z)
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60 ESSENCE SNe72 SNLS SNe
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Higher-z SNe Ia from ACS
Z=1.39 Z=1.23Z=0.46 Z=0.52 Z=1.03
50 SNe Ia, 25 at z>1 Riess, etal
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(m
-M)
HST GOODS Survey (z > 1) plus
compiled ground-based SNe Riess etal 2004
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Supernova Cosmology ProjectSN Ia Union Compilation Kowalski et al., ApJ, 2008
Data tables and updates at http://supernova.lbl.gov/Union
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€
−2ln Pposterior =(μ i − μmod (zi;w,Ωm,ΩDE )2
σ μ ,i2
i
∑ + χ BAO2 + χ CMB
2
where latter terms incorporate BAO and CMB priors :
BAO (SDSS LRG, Eisenstein etal 05) :
A(z1;w,Ωm,ΩDE ) =Ωm
E(z1)1/ 3
1
z1 Ωk
Sk Ωk
1/ 2 dz
E(z)0
z1
∫ ⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
2 / 3
with
χ BAO2 = [(A(z1;w,Ωm,ΩDE ) − 0.469) /0.017]2 for z1 = 0.35
CMB (WMAP5, Komatsu etal 08) :
R(zCMB ;w,Ωm ,ΩDE ) =Ωm
Ωk
Sk Ωk
1/ 2 dz
E(z)0
zCMB
∫ ⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
with
χ CMB2 = [(R(zCMB ;w,Ωm ,ΩDE ) −1.710) /0.019]2 for zCMB =1090
Likelihood Analysis with BAO and CMB Priors
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Recent Dark Energy Constraints
Improved SN constraints
Inclusion of constraints from WMAP Cosmic Microwave Background Anisotropy (Joana) and SDSS Large-scale Structure (Baryon Acoustic Oscillations; Bruce, Daniel)
Only statistical errors shownassuming w = −1
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Only statistical errors shown
assuming flat Univ. and constant w
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SNLS Preliminary 3rd year Hubble Diagram
Conley et al, Guy etal (2010): results with ~252 SNLS SNe
Independent analyses with 2 light-curve fitters: SALT2, SiFTO
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Results published from 2005 season
Frieman, et al (2008); Sako, et al (2008)
Kessler, et al 09; Lampeitl et al 09; Sollerman et al 09
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SDSS II Supernova Survey Goals• Obtain few hundred high-quality* SNe Ia light curves in the
`redshift desert’ z~0.05-0.4 for continuous Hubble diagram• Probe Dark Energy in z regime complementary to other
surveys• Well-observed sample to anchor Hubble diagram, train
light-curve fitters, and explore systematics of SN Ia distances
• Rolling search: determine SN/SF rates/properties vs. z, environment
• Rest-frame u-band templates for z >1 surveys • Large survey volume: rare & peculiar SNe, probe outliers of
population
*high-cadence, multi-band, well-calibrated
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Spectroscopic follow-up telescopes
R. Miquel, M. Molla, L. Galbany
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Search Template Difference
g
r
i
Searching For Supernovae• 2005
– 190,020 objects scanned– 11,385 unique
candidates– 130 confirmed Ia
• 2006– 14,441 scanned– 3,694 candidates– 193 confirmed Ia
• 2007 – 175 confirmed Ia
• Positional match to remove movers• Insert fake SNe to monitor efficiency
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SDSS SN PhotometryHoltzman etal (2008)
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B.
Dild
ay
500+ spec confirmed SNe Ia + 87 conf. core collapse plus >1000 photometric Ia’s with host z’s
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Spectroscopic Target Selection2 Epochs
SN Ia Fit
SN Ibc Fit
SN II Fit
Sako etal 2008
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Spectroscopic Target Selection2 Epochs
SN Ia Fit
SN Ibc Fit
SN II Fit
31 Epochs
SN Ia Fit
SN Ibc Fit
SN II Fit
Fit with template library
Classification>90%accurate after 2-3 epochs
Redshifts 5-10% accurate
Sako etal 2008
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SN and Host Spectroscopy
MDM 2.4mNOT 2.6mAPO 3.5mNTT 3.6mKPNO 4mWHT 4.2mSubaru 8.2mHET 9.2mKeck 10mMagellan 6.5mTNG 3.5mSALT 10m SDSS 2.5m
2005+2006Determine SN Type and Redshift
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Spectroscopic Deconstruction
SN modelHost galaxy modelCombined model
Zheng, et al (2008)
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Fitting SN Ia Light Curves
• Multi-color Light Curve Shape (MLCS2k2)
Riess, etal 96, 98; Jha, etal 2007
• SALT-II
Guy, etal 05,08
41
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€
mmodi (t − t0) = μ + M j (t − t0) + P j (t − t0)Δ + Q j (t − t0)Δ2
+ K ij (t − t0) + Xhostj (t − t0) + XMW
i (t − t0)
fit parameters
Time of maximum distance modulus host gal extinction stretch/decline rate
time-dependent model “vectors”
trained on Low-z SNe
∆ <0: bright, broad∆ >0: faint, narrow, redder
MLCS2k2 Light-curve Templatesin rest-frame j=UBVRI;built from ~100 well-observed, nearby SNe Ia
observedpassband
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Host Galaxy Dust Extinction
€
Aλ = −2.5logfobs(λ )
f true (λ )
⎛
⎝ ⎜
⎞
⎠ ⎟
€
Aλ
AV
= a(λ ) +b(λ )
RV
• Extinction:
• Empirical Model for wavelength dependence:
• MLCS: AV is a fit parameter, but RV is usually fixed to a global value (sharp prior) since it’s usually not well
determined SN by SN
Cardelli etal 89 (CCM)
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Host Galaxy Dust Extinction
Jha
Milky Way avg.
Historically, MLCS used Milky Way average of RV=3.1
Growing evidence that this doesn’t represent SN host galaxy population well
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Extract RV by matching colors of SDSS SNe to MLCS simulations
• Use nearly complete (spectroscopic + photometric) sample
• MLCS previously used Milky Way avg RV=3.1
• Lower RV more consistent with SALT color law and other recent SN RV estimates
D. Cinabro
€
RV =AV
E(B −V )≈ 2
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Carnegie Supernova Project: Low-z
n CSP is a follow-up project
n Goal: optical/NIR light-curves and spectro-photometry for
n > 100 nearby SNIa
n > 100 SNII
n > 20 SNIbc
n Filter set: BV + u’g’r’i’ + YJHK
n Understand SN physics
n Use as standard candles.
n Calibrate distant SN Ia sample
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CSP Low-z Light Curves
Folatelli, et al. 2009Contreras, et al. 2009: 35 optical light curves (25 with NIR)
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Varying Reddening Law?
Folatelli et al. (2009)
2005A2006X
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Local Dust?
Goobar (2008): higher density of dust grains in a shell surrounding the SN: multiple scattering steepens effective dust law(also Wang)
Folatelli et al. (2009)
Two Highly Reddened SNe
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Priors & Efficiencies
€
χMLCS2 =
Fidata − Fi
mod (t0,Δ,AV ,μ)[ ]2
σ i2
i
∑ − 2ln P(AV )P(Δ)ε(z,AV ,Δ)( )
Determine priors and efficiencies from data and Monte Carlo simulations
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Priors & Efficiencies
Determine priors and efficiencies from data and Monte Carlo simulations
Inferred P(AV) Inferred P()
€
χMLCS2 =
Fidata − Fi
mod (t0,Δ,AV ,μ)[ ]2
σ i,phot2 + σ i,mod
2i
∑ − 2ln P(AV )P(Δ)ε(z,AV ,Δ)( )
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Model Spectroscopic & Photometric Efficiency
Redshift distribution for all SNe passing photometric selection cuts (spectroscopically complete sample)
Data
Need to model biases due to what’s missing
Difficult to model spectroscopic selection
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Model Selection Function
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Include Selection Function
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Monte Carlo Simulations match data distributions
Use recorded observing conditions (local sky, zero-points, PSF, etc)
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Show likelihood plots for MLCS
MLCS fit to one of the ESSENCE SNe
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prior
Marginalized PDFs
μ distribution approximated by Gaussian for cosmology fit
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59MLCS Likelihood Contours for this object