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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”.

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Two useful methods for the supernova cosmologist:

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  1. 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”

  2. 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

  3. Yun Wang, 6/28/07

  4. Yun Wang, 6/28/07

  5. Gaussian fits: Normalized correlation matrices: Yun Wang, 6/28/07

  6. 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

  7. 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

  8. Model-independent constraints on dark energy(as proposed by Wang & Garnavich 2001) Wang & Mukherjee (2007) Yun Wang, 6/28/07

  9. Wang & Mukherjee (2007) [See Wang & Tegmark (2005) for the method to derive uncorrelated estimate of H(z) using SNe.] Yun Wang, 6/28/07

  10. (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

  11. 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

  12. 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

  13. 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

  14. Demonstrationusing SNLS data Y. Wang (2007) Yun Wang, 6/28/07

  15. Using simulated data with zero AV Y. Wang, M. Wood-Vasey, G. Narayan, in prep. Yun Wang, 6/28/07

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

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