Global Integrated Sachs-Wolfe Significance:An Exercise in Method & HubrisRyan Scranton28 September 2006
Global ISW 1It Seemed Like a Good Idea at the Time...Date: Fri, 5 May 2006 17:54:32 -0400 (EDT)From: Ryan Scranton To: Albert Stebbins Hey Albert...As for the conference, I’m not entirely certain what I’m going totalk about. I’m toying with the idea of doing a globalmeasurement of the ISW using 2MASS, SDSS, and FIRST/NVSS usingthe Teragrid. Given the fact that I was able to do the LRG stuffin less than 24 hours, I think I can do it all by the end of nextweek.-Ryan
Global ISW 2ISW in 2 Minutes• After matter-radiation equality,dark matter falls into potentialwells set up during inflation. ForΛCDM, universe expands fasterthan potentials grow• CMB photons passing throughpotentials see net blue-shift inenergy ⇒ IntegratedSachs-Wolfe EffectPhysicsWeb• Increases CMB autocorrelation atsmall l and induces positivecorrelation with galaxies
Global ISW 3Thermal Sunyaev-Zel’dovich Effect• Hot electron gas surrounds galaxyfilaments and clusters• CMB photons inverse Comptonscatter off of electrons, shiftingphotons to higher energies• CMB in Rayleigh-Jeans region oforiginal spectrum gives observedtemperature decrement ⇒anti-correlation with foregroundstructure
Global ISW 4Weak Lensing Magnification• High redshift galaxies are lensedby foreground structure, leading todistortions in their angulardistribution• These low redshift potentials aredecaying due to ISW, so thiscorrelation is imprinted on highredshift galaxies as well asintrinsic ISW signal.• Amplitude and sign depends onslope of galaxy number counts(zero effect for field galaxies).
Global ISW 5• Expect ISW to dominate on largeangles, SZ to become importanton smaller angles• 2 free parameters in linear theory:galaxy bias (δ gal = b gal δ DM ) andelectron gas-bias (T e b P ). b galcontrols overall amplitude of thesignal and T e b P determines therelative importance of the SZeffect• Very important to maximize skycoverage (cosmic variance) andkeep Poisson noise lowExpected Signal
Global ISW 6The Plan• Collect footprints & galaxy data from 2MASS, SDSS, FIRST and NVSS• 15 total maps covering 0 < z < 2.5:⋆ 3 2MASS magnitude limited samples (10.5 < k < 11.5, 11.5 < k < 12.5,12.5 < k < 13.5)⋆ 5 magnitude limited SDSS galaxy samples over 16 < r < 21⋆ 3 SDSS LRG redshift slices⋆ NVSS radio galaxies⋆ 2 FIRST samples (star forming galaxies with flux < 10 mJy, AGNs with flux> 50 mJy)⋆ Photometric SDSS QSOs with 1 < z < 2.5• Cross-correlate with smoothed 3 year WMAP w channel map• Generate global covariance matrix using 10,000 CMB realizations on Teragrid
Global ISW 7STOMP: Space and Time Ordered Mapping Packagehttp://nvogre.phyast.pitt.edu/gestalt/• All cosmological statistics aremeasurements of spatial properties(area, angular distance, density)• Describe complex geometries onthe sphere and possibly spatialvariations• Find unions, intersections, andoverlaps between large numbers ofobservations• It has to be fast
Global ISW 8STOMP: Space and Time Ordered Mapping Package• Pixelize arbitrary survey footprints with 1” resolution• Hierarchical scheme: extremely rapid localization & efficient angular statistics.• All footprints & analysis done with current STOMP code
Global ISW 9CMB SideWMAP w channel – smoothed & masked (??)
Global ISW 102MASS2MASS – |b| > 20, A k < 0.03
Global ISW 112MASS2MASS Over-Density – 12.5 < k < 13.5, z ∼ 0.1
Global ISW 12NVSSNVSS – |b| > 20
Global ISW 13NVSSNVSS Over-Density – |b| > 20
Global ISW 14FIRSTFIRST – background flux < 0.17 mJy
Global ISW 15FIRSTFIRST – flux > 50 mJy (AGNs with z ∼ 1.5)
Global ISW 16FIRSTFIRST – flux < 10 mJy (star-forming galaxies with z ∼ 1)
Global ISW 17SDSSSDSS DR5 – Mask out bad seeing, extinction, sky brightness
Global ISW 18SDSSSDSS DR5 Magnitude-Limited (20 < r < 21, z ∼ 0.3)
Global ISW 19SDSSSDSS DR5 LRG (z ∼ 0.55)
Global ISW 20SDSS Photometric QSOsSDSS DR4 Photometric Survey – A g < 0.15
Global ISW 21SDSSSDSS DR4 Photometric QSOs (1 < z < 2.5)
Global ISW 22Results: 2MASS• Strong SZ signal at small angles; increasing as z → 0• χ 2 = 59.8 for 45 angular bins: 1.3σ
Global ISW 23Results: SDSS Magnitude Limited• Increasing S/N as z increases• χ 2 = 136.4 for 75 angular bins: 3.0σ
Global ISW 24Results: SDSS LRGs• Dropped lowest redshift bin from Scranton et al (2003); lower S/N• χ 2 = 87.2 for 45 angular bins: 2.7σ
Global ISW 25Results: High Redshift• Huge χ 2 for NVSS; probably contaminated.• χ 2 = 130.7 for 60 angular bins: 3.6σ
Global ISW 26Results: Global Sample 0 < z < 2.5
Global ISW 27Results: Global Sample 0 < z < 2.5
Global ISW 28Results: Global Sample 0 < z < 2.5
Global ISW 29Results: Global Sample 0 < z < 2.5
Global ISW 30Results: Global Sample 0 < z < 2.5
Global ISW 31Results: Global Sample 0 < z < 2.5
Global ISW 32Results: Global Sample 0 < z < 2.5
Global ISW 33Results: Global Sample 0 < z < 2.5• Significant anti-correlations; magnification bias? Quite possibly (LoVerde, Hui& Gaztanaga, in preparation).• χ 2 = 461.5 for 225 angular bins: 6.2σ (5.3σ w/o NVSS)
Global ISW 34Graphic Magnification – PRELIMINARYPrelminary Results with SDSS QSOsPrelminary MagnificationContribution to LRG ISW Signal
Global ISW 35Summary• Current set of surveys all demonstrate ISW signal to one degree or another, butthe S/N of any given survey remains relatively small. Combining the detectionsfrom multiple surveys increases the overall S/N to roughly 5σ• Part of this increase appears to be due magnification bias between samples atdifferent redshifts. Depending on the sample, magnification can be a significantor even dominant part of the total signal at high z.• What’s been done since May:⋆ Cleaned up data sets (more thorough systematics checks and limits).⋆ Limited NVSS data to > 50 mJy and masked out foreground sources.⋆ Quantified expected signal from weak-lensing magnification.
Global ISW 36Summary• Current set of surveys all demonstrate ISW signal to one degree or another, butthe S/N of any given survey remains relatively small. Combining the detectionsfrom multiple surveys increases the overall S/N to roughly 5σ• Part of this increase appears to be due magnification bias between samples atdifferent redshifts. Depending on the sample, magnification can be a significantor even dominant part of the total signal at high z.• What remains to be done:⋆ Include correlations between galaxy data sets in covariance matrixgeneration. Also, error on χ 2 .⋆ Make magnification-only measurements.⋆ Generate cosmological constraints (redshift distributions & lensing).
Cosmic Magnification Appendix 37Two Effects of Gravitational Lensing• Weak lensing of background sources introduces shear and magnification
Cosmic Magnification Appendix 38Two Effects of Gravitational Lensing• Magnification (µ) increases flux (amplification); decreases density (dilution).
Cosmic Magnification Appendix 39Quantifying Cosmic Magnification• If we are in the weak lensing regime (µ ≈ 1),∫w GQ (θ) = 12π 2 Ω M (α(m) − 1)dχ dk k K(k, θ, χ) P gm (k, χ)= (α(m) − 1) × w 0 (θ), (1)where α(m) is the power-law slope of the QSO number counts, K depends onthe foreground and background redshift distributions and P gm (k) is thegalaxy-dark matter power spectrum.• For α(m) > 1, increasing amplification outweighs the dilution effect, yielding apositive cross-correlation. For α(m) < 1, dilution wins and the cross-correlationis negative.
Cosmic Magnification Appendix 40Magnification & ISW• Standard ISW redshift kernel:K ISW ∼∫dχW G (χ) ∂∂χ[ ] D(χ)a(χ)(2)where χ is the comoving distance, W G (χ) is the redshift distribution of thegalaxies and D(χ) is the linear growth factor. For ΛCDM, potential decaypeaks at z = 0, so amplitude increases as z → 0.• Magnification (convergence) kernel:∫K κ ∼ (α − 1)dχW F (χ) g B(χ)a(3)whereg B (χ) =∫dχ ′χ(χ′ − χ)χ ′ W B (χ ′ ) (4)
Cosmic Magnification Appendix 41• Magnification-ISW kernel:∫K ISW,κ ∼ (α − 1)dχ g G(χ)a∂∂χ[ ] D(χ)a(χ)(5)• For α − 1 ≠ 0 and z > 0.5, the pure ISW effect falls off sharply as Ω Λ → 0.Magnification is generated by foreground structure at lower redshift potentialswhere the decay is large, hence its contribution increases, relatively.• For field galaxies α − 1 ≈ 0, so need to choose galaxy subsets like LRGs, QSOor radio galaxies (or use an optimal estimator (?)).