0. 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)

1. 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.

2. The Problem of Lensing DLobs =DLtrue m-1/2
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 =DLtrue m-1/2
Lensing blows up distance uncertainty to several % at high redshift.

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

4. 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)

5. The Power of Flexion Goldberg & 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
F: spin 1 (vector), G: spin 3 (tensor)
Wow, a talking banana!
I’m so sensitive!

6. 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

7. 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)
HST has .05 arcsec pixels – high pixel noise for small galaxies
ELT should give 40milli-arcsec resolution

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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 =