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Cosmology with Supernovae: Lecture 2. Josh Frieman I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil July 2010. 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. - PowerPoint PPT Presentation
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Cosmology with Supernovae:Lecture 2
Josh Frieman
I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil
July 2010
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
2
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
SN Ia Peak LuminosityEmpirically correlatedwith Light-Curve Decline Rate and Color
Brighter Slower, Bluer
Use to reduce Peak Luminosity Dispersion:
Phillips 1993
Peak
Lum
inos
ity
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
7
Published Light Curves for Nearby SupernovaeLow-z SNe:
Anchor Hubble diagram
Train Light-curve fitters
Need well-sampled, well-calibrated, multi-band light curves
Low-z Data
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9
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 = 5log vkm/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 etalSchmidt etal
V
B+1
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 i2
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
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 errors15
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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
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: TorontoIMACS for host
redshifts
MagellanSpectraSN Identification
Redshifts
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 ACSZ=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) pluscompiled ground-based SNe Riess etal 2004
Supernova Cosmology ProjectSN Ia Union Compilation Kowalski et al., ApJ, 2008
Data tables and updates at http://supernova.lbl.gov/Union
26
€
−2ln Pposterior = (μ i − μmod (zi;w,Ωm,ΩDE )2
σ μ ,i2
i∑ + χ BAO
2 + χ CMB2
where latter terms incorporate BAO and CMB priors :
BAO (SDSS LRG, Eisenstein etal 05) :
A(z1;w,Ωm,ΩDE ) =Ωm
E(z1)1/ 3
1z1 Ωk
Sk Ωk1/ 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 Ωk1/ 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
27
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 shown
assuming w = −1
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Only statistical errors shown
assuming flat Univ. and constant w
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
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
Spectroscopic follow-up telescopes
R. Miquel, M. Molla, L. Galbany
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
35
SDSS SN Photometry Holtzman etal (2008)
B. D
ilday
500+ spec confirmed SNe Ia + 87 conf. core collapse plus >1000 photometric Ia’s with host z’s
Spectroscopic Target Selection2 Epochs
SN Ia Fit
SN Ibc Fit
SN II Fit
Sako etal 2008
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
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
Spectroscopic Deconstruction
SN modelHost galaxy modelCombined model
Zheng, et al (2008)
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
€
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 = −2.5log fobs(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)
44
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
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
Carnegie Supernova Project: Low-z
n CSP is a follow-up projectn Goal: optical/NIR light-curves
and spectro-photometry forn > 100 nearby SNIan > 100 SNIIn > 20 SNIbc
n Filter set: BV + u’g’r’i’ + YJHKn Understand SN physicsn Use as standard candles.n Calibrate distant SN Ia
sample
CSP Low-z Light Curves
Folatelli, et al. 2009Contreras, et al. 2009: 35 optical light curves (25 with NIR)
Varying Reddening Law?
Folatelli et al. (2009)
2005A2006X
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
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
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)( )
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
Model Selection Function
Include Selection Function
Monte Carlo Simulations match data distributions
Use recorded observing conditions (local sky, zero-points, PSF, etc)
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57
Show likelihood plots for MLCS
MLCS fit to one of the ESSENCE SNe
58
prior
Marginalized PDFs
μ distribution approximated by Gaussian for cosmology fit
59MLCS Likelihood Contours for this object