+
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)
+
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