Two useful methods for Two useful methods for the supernova the supernova cosmologist:cosmologist:

(1) Including CMB constraints by (1) Including CMB constraints by using the CMB shift parametersusing the CMB shift parameters(2) A model-independent photometric (2) A model-independent photometric

redshift estimator for SNe Iaredshift estimator for SNe Ia

Yun WangYun WangJune 28, 2007, Aspen Workshop on June 28, 2007, Aspen Workshop on

““Supernovae as Cosmological Distance Indicators”Supernovae as Cosmological Distance Indicators”

Yun Wang, 6/28/07

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

and and llaa

((Y. Wang & P. Mukherjee, astro-ph/0703780)Y. Wang & P. Mukherjee, astro-ph/0703780)• R=[mH0

2]1/2 r(zCMB) dimensionless distance to zCMB

• 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

Yun Wang, 6/28/07

Yun Wang, 6/28/07

Gaussian fits:

Normalized correlation matrices:k=0 R la bh2

R 1.0 .09047 .0197

la .09047 1.0 .6283

bh2 .0197 .6283 1.0

k0 k=0

R 1.710.03 1.700.03la 302.5 1.2 302.2 1.2

bh2 .02173 .00082 .022 .00082

k0 R la bh2

R 1.0 .1237 .06627

la .1237 1.0 .6722

bh2 .06627 .6722 1.0

Yun Wang, 6/28/07

All you have to do is toAll you have to do is toadd this to your add this to your 22

tottot::

2CMB= [pi pi

data] 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

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-Model-independent independent constraints constraints

on dark on dark energyenergy(as proposed by (as proposed by

Wang & Garnavich 2001)Wang & Garnavich 2001)

Wang & Mukherjee (2007)

Yun Wang, 6/28/07

Wang & Mukherjee (2007)[See Wang & Tegmark (2005) for the method to derive uncorrelated estimate of H(z) using SNe.]

Yun Wang, 6/28/07

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

(Y. Wang, astro-ph/0609639, ApJ, 654 (2007) L123(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 make an effective K-correction.

Yun Wang, 6/28/07

A model-independent photo-A model-independent photo-z estimator for SNe Iaz estimator for SNe Ia

(1) z0phot=c1+c2gf+c3rf+c4if+c5zf+c6if

2

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)

fi15d is the i-band flux at 15 days after the i flux max

in the estimated restframe, t15d=15(1+ z0phot)

(3) zphot=z0phot+c7i15

Yun Wang, 6/28/07

A model-independent photo-A model-independent photo-z estimator for SNe Iaz 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 elementtn-1,i: omitting i-th element;

tn-1=i=1,n tn-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

DemonstratioDemonstrationn

using SNLS using SNLS datadata

Y. Wang (2007)

Yun Wang, 6/28/07

Using Using simulated simulated

data with zero data with zero AAVV

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

Yun Wang, 6/28/07

Blind test on simulated data with Blind test on simulated data with AAVV00

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

Yun Wang, 6/28/07

Blind test on simulated data with Blind test on simulated data with AAVV00

(zphot-zspec) versus Av(Y. Wang, M. Wood-Vasey, & G. Narayan, in prep.)

Yun Wang, 6/28/07

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

Yun Wang, 6/28/07

ALPACAALPACA• 8m liquid mirror

telescope • FOV: 2.5 deg

diameter• Imaging=0.3-1m• 50,000 SNe Ia per yr

to z=0.8, 5 bands, t = 1d

• 800 sq deg WL & BAO with photo-z

Yun Wang, 6/28/07

ConclusionsConclusions• 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.