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Chaz Shapiro Institute of Cosmology & Gravitation, Portsmouth

Removing Lensing Noise from Gravitational Wave Standard-Sirens. Hendry & Woan 07. Hendry & Woan 07. Chaz Shapiro Institute of Cosmology & Gravitation, Portsmouth. Collaborators: David Bacon (ICG), Dr. Ben Hoyle (ICG), Martin Hendry (Glasgow). Black hole binaries are standard sirens.

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Chaz Shapiro Institute of Cosmology & Gravitation, Portsmouth

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  1. Removing Lensing Noise from Gravitational Wave Standard-Sirens Hendry & Woan 07 Hendry & Woan 07 Chaz ShapiroInstitute of Cosmology & Gravitation, Portsmouth Collaborators: David Bacon (ICG),Dr. Ben Hoyle (ICG), Martin Hendry (Glasgow)

  2. Black hole binaries are standard sirens • Gravitational wave analog of standard candles: obtain luminosity distance from amplitude of predictable chirp signal • “Hairless” 2-body system is relatively simple compared to SNeIa, then again… • IF E-M counterpart provides redshift, then we can construct a Hubble Diagram.

  3. The Problem of Lensing • Supermassive black hole binaries (SMBHB) found by LISA could determine distances to ~ 0.1%. • But large-scale structure lenses GWs! From a (de)magnified signal, we can only measure DLobs=DLtruem-1/2 • Lensing blows up distance uncertainty to several % at high redshift.

  4. Siren distances are uncertain due to an unknown magnification from weak lensing • Holz & Hughes (2005) • All parameters fixed except 2 • Expect ~few SMBHB per year z = 1.5

  5. Solution: Mapthe magnification to “delens” each BHB • A map of m can be reconstructed from weakly lensed galaxy images (m ≈ 1-2k) • Map will be imperfect due to • Intrinsic galaxy shapes • Smoothing • Source redshift distribution • Mass-sheet degeneracy • Dalal et al. (2006): The fraction of s(m)2that can be removed by mapping mis • Map must be deepand wide and have many high-z galaxies HST/COSMOS, Massey et al. (2005)

  6. The Power of FlexionGoldberg & Bacon / Bacon et al. (2006) • Flexion is the weak “arc-iness” or “bananification” of lensed galaxies • 2 flexion types, informally they are F ~ grad( k) G ~ grad( g) • High S/N galaxies have small intrinsic flexion • Flexion is more sensitive to substructure than shear is I’m so sensitive! Wow, a talking banana!

  7. Flexion attenuates small-scale noise [SKIP] • Average over galaxy shapes with filter of size q • For shear alone, noise in 1 pixel of k map is • Using dimensional analysis, expect flexion shape noise to be • In reality: Shear Shear + Flexion Flexion allows us to smooth on smaller scales, pick up fine features in m

  8. How well can we remove magnification uncertainty? Assumptions: • Follow up on each BHB with an Extremely Large Telescope (we’ll want to anyway!)gRMS= 0.2 FRMS= 0.15/arcmin GRMS= 0.5/arcmin • Assume depth & width similar to Hubble Ultra Deep Field: ngal~1000/arcmin2zmed=1.8 • Choose smoothing so pq2ngal = 10 • Assume lensing fields are weak and Gaussian; no intrinsic correlations • Nonlinear power from Smith et al. fitting formula, s8=0.8, ns=0.96 Coe et al. (2006)

  9. Reduction in distance uncertainty with an ELT:z= 2, s(DL)lens=4% s(DL)corrected/ s(DL)lens Realistic Idealized Limited by small-scale resolution, mass-sheet degeneracy

  10. Reduction in distance uncertainty with an ELT:z= 3, s(DL)lens=5% s(DL)corrected/ s(DL)lens Realistic Idealized Limited by small-scale resolution, mass-sheet degeneracy

  11. How could we do better? • Measuring redshifts for each source galaxy • Remove mass-sheet degeneracy • One strategy is to take wide images - not feasible with an ELT • Space survey telescope (e.g. JDEM, Euclid) has necessary width but not depth. Also, poor flexions! • Hybrid method: Combine survey data with narrow ELT images • We assume JDEM (shear only) and ngal=100/arcmin2zmed=1.5

  12. Reduction in distance uncertainty with an ELT + JDEM:z= 2, s(DL)lens=4% s(DL)corrected/ s(DL)lens ELT only With JDEM Limited by small-scale resolution only

  13. Reduction in distance uncertainty with an ELT + JDEM: z= 3, s(DL)lens=5% s(DL)corrected/ s(DL)lens ELT only With JDEM Limited by small-scale resolution only

  14. Summary • Binary black holes are precise standard sirens, but gravitational lensing hampers distance measurements. • Using deep images of BHB neighborhoods to make weak lensing maps, we can remove some uncertainty in BHB distances (delensing). • Shear and flexion maps from combining an ELT with a space telescope could reduce distance errors by more than a factor of 2. Error from lensing After delensing (ELT) After delensing (ELT+JDEM) 30 arcmin^2 ELT image No redshift information =

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