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Chaz ShapiroInstitute of Cosmology & Gravitation, Portsmouth

Collaborators: David Bacon (ICG), Dr. Ben Hoyle (ICG), Martin Hendry (Glasgow)

RemovingLensing Noise fromGravitational Wave Standard-Sirens

Hendry & Woan 07

+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.

+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 =DL

true m-1/2

Lensing blows up distance uncertainty to several % at high redshift.

+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

+Solution: Map the 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)2 that can be removed by mapping m is

Map must be deep and wide and have many high-z galaxies

HST/COSMOS, Massey et al. (2005)

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I’m so sensitive!

Wow, a talking

banana!

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

+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

+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/arcmin2 zmed=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)

+Reduction in distance uncertainty with an ELT:z = 2, s(DL)lens=4%

s(DL)corrected / s(DL)lens

Limited by small-scale resolution, mass-sheet degeneracy

Realistic

Idealized

+

s(DL)corrected / s(DL)lens

Limited by small-scale resolution, mass-sheet degeneracy

Reduction in distance uncertainty with an ELT:z = 3, s(DL)lens=5%

Realistic

Idealized

+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/arcmin2

zmed=1.5

+Reduction in distance uncertainty with an ELT + JDEM: z = 2, s(DL)lens=4%

s(DL)corrected / s(DL)lens

Limited by small-scale resolution only

ELT only

With JDEM

+Reduction in distance uncertainty with an ELT + JDEM: z = 3, s(DL)lens=5%

s(DL)corrected / s(DL)lens

Limited by small-scale resolution only

ELT only

With JDEM

+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 imageNo redshift information