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Two useful methods for the supernova cosmologist:. (1) Including CMB constraints by using the CMB shift parameters (2) A model-independent photometric redshift estimator for SNe Ia Yun Wang June 28, 2007, Aspen Workshop on “Supernovae as Cosmological Distance Indicators”.

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two useful methods for the supernova cosmologist

Two useful methods for the supernova cosmologist:

(1) Including CMB constraints by using the CMB shift parameters

(2) A model-independent photometric redshift estimator for SNe Ia

Yun Wang

June 28, 2007, Aspen Workshop on

“Supernovae as Cosmological Distance Indicators”

slide2
Including CMB constraints by using the CMB shift parameters R and la(Y. Wang & P. Mukherjee, astro-ph/0703780)
  • R=[mH02]1/2r(zCMB)

dimensionless distance tozCMB

  • la= r(zCMB) / rs(zCMB)

angular scale of the sound horizon at zCMB

(R, la ) have nearly uncorrelated measured values.

(R, la, bh2) provide an efficient summary of CMB data, independent of the dark energy model.

Yun Wang, 6/28/07

slide5
Gaussian fits:

Normalized correlation matrices:

Yun Wang, 6/28/07

all you have to do is to add this to your 2 tot
All you have to do is toadd this to your 2tot:

2CMB= [pi pidata] Cov-1(pi,pj) [pjpjdata]

with Cov(pi,pj)= σ(pi)σ(pj) Cov(pi,pj)normdata

{pi}={R, la, bh2}

Yun Wang, 6/28/07

slide7
w(z)=w0+wa(1-a)

WMAP3

+182 SNe Ia (Riess et al. 2007, inc SNLS and nearby SNe)

+SDSS BAO

(Wang & Mukherjee 2007)

Yun Wang, 6/28/07

model independent constraints on dark energy as proposed by wang garnavich 2001
Model-independent constraints on dark energy(as proposed by Wang & Garnavich 2001)

Wang & Mukherjee (2007)

Yun Wang, 6/28/07

slide9
Wang & Mukherjee (2007)

[See Wang & Tegmark (2005) for the method to derive uncorrelated estimate of H(z) using SNe.]

Yun Wang, 6/28/07

slide10
(2) A model-independent photometric redshift estimator for SNe Ia(Y. Wang, astro-ph/0609639, ApJ, 654 (2007) L123)

Accurate photo-z’s boost the cosmological impact of large photometric surveys of SNe.

  • Derive a simple photo-z estimator for SNe Ia using imaging observables that reflect the properties of SNe Ia as calibrated standard candles.
  • If SNe Ia were perfect standard candles, the most important observable is peak brightness. Use the maximum flux in the best-sampled band (say, i-band) to represent this. Use the fluxes in other bands at the same epoch to makean effective K-correction.

Yun Wang, 6/28/07

a model independent photo z estimator for sne ia
A model-independent photo-z estimator for SNe Ia

(1) z0phot=c1+c2gf+c3rf+c4if+c5zf+c6if2

gf=2.5 log(fg), rf=2.5 log(fr),

if=2.5 log(fi), zf=2.5 log(fz),

fg,fr,fi,fz : fluxes in griz at the epoch of i max flux

(2) i15=2.5 log(fi15d/fi)

fi15dis the i-band flux at 15 days after the i flux max in the estimated restframe, t15d=15(1+ z0phot)

(3) zphot=z0phot+c7i15

Yun Wang, 6/28/07

a model independent photo z estimator for sne ia1
A model-independent photo-z estimator for SNe Ia
  • The coefficients ci (i=1,2,…,7) are found by using a training set of SNe Ia with both griz light curves and measured spectro z’s
  • Use jackknife technique to estimate bias-corrected mean and covariance matrix of ci

Yun Wang, 6/28/07

jackknife
jackknife
  • Consider a consistent statistic t

tn: value of t calculated from a sample of size n

For a single sample of n points, we extract n subsamples of size n-1 by omitting one element

tn-1,i: omitting i-th element;

tn-1=i=1,ntn-1,i

  • Bias-corrected estimate: tnJ=tn+(n-1)(tn- tn-1)
  • Variance: VJ(tn)=[(n-1)/n]i(tn-1,i-tn-1)2

Yun Wang, 6/28/07

demonstration using snls data
Demonstrationusing SNLS data

Y. Wang (2007)

Yun Wang, 6/28/07

using simulated data with zero a v
Using simulated data with zero AV

Y. Wang, M. Wood-Vasey, G. Narayan, in prep.

Yun Wang, 6/28/07

blind test on simulated data with a v 0
Blind test on simulated data with AV0

(zphot-zspec) versus zspec

(Y. Wang, M. Wood-Vasey, & G. Narayan, in prep.)

Yun Wang, 6/28/07

blind test on simulated data with a v 01
Blind test on simulated data with AV0

(zphot-zspec) versus Av

(Y. Wang, M. Wood-Vasey, & G. Narayan, in prep.)

Yun Wang, 6/28/07

slide18
8.4m (6.5m clear aperture) telescope; FOV: 3.5 deg diameter; 0.3-1mm
  • 106 SNe Ia y-1, z < 0.8, 6 bands, Dt = 7d
  • 20,000 sq deg WL & BAO with photo-z

Yun Wang, 6/28/07

alpaca
ALPACA
  • 8m liquid mirror telescope
  • FOV: 2.5 deg diameter
  • Imaging l=0.3-1mm
  • 50,000 SNe Ia per yr to z=0.8, 5 bands, Dt = 1d
  • 800 sq deg WL & BAO with photo-z

Yun Wang, 6/28/07

conclusions
Conclusions
  • The CMB shift parameters (R and la) provide an efficient summary of the full CMB temperature power spectrum as far as dark energy constraints are concerned. Including R and la is very easy and tightens SN cosmology constraints considerably. (Wang & Mukherjee 2007)
  • The simple model-independent photo-z estimator derived in Wang (2007) works well for current SN Ia data, with [(zphot-zspec)/(1+zspec)]=0.05 for SNe Ia not used in the training set.

Preliminary studies (Wang, Wood-Vasey, & Narayan 2007) indicate that [(zphot-zspec)/(1+zspec)]=0.01-0.02 can be achieved for SN Ia data with much higher S/N. This can boost the cosmological utility of large photometric surveys of SNe.

Yun Wang, 6/28/07