Gravitational Flexion: Galaxy

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Gravitational Flexion Galaxy Lensing to Second
Order
David Goldberg Drexel University
Gravitational Lensing, Dark Energy and Dark
Matter January 7, 2005
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• Acknowledgements
• David Bacon (Edinburgh) - GG Lensing/Theory
• Richard Massey (Cal. Tech) - Shapelets
• John Peacock (Edinburgh) -Clusters
• Priya Natarajan (Yale) - Initial work
• Students
• Kara Blaine (Drexel)
• Michael French (Drexel)
• Thanks also to Tereasa Brainerd for helpful
• comments on the method and initial drafts.

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Outline

• What is Flexion?
• Results from Galaxy-Galaxy Lensing.
• The topic at hand - Dark Matter/Energy
• Make a better map of Clusters
• Tomography
• Constraints in time-delays?
• Cosmic Flexion?

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We all know gravitational lensing distorts
images of background sources...
A simulated lens- source system. An isothermal
sphere, with a lens separated by 5 in the
absence of lensing.
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In reality, this is not simply an elliptical
distortion
NOT an ellipse!
The Arciness of an image is also important
-- Flexion!
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• Why is Flexion useful?
• A local measurement of the
• underlying density field
• Intrinsic arciness has a smaller
• variance than intrinsic shear
• - higher S/N!
• Can be used in a lossless way
• to supplement shear!

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How does it work?
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We define the Flexion as a pair of
vectors giving us information not
otherwise accessible!
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But, as written, Flexion is VERY hard to invert,
so we use Shapelets (2d Hermite Polynomials)
From Refregier (2003)
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FlexionShapelets make a great pair. Flexion and
shear can transfer power between nearby
(complementary) coefficients
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This expands out to a rather nasty (but easily
code-able) set of operators
Let's invert our simulation from earlier...
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Analytic Solution for an isothermal sphere.
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We can look at the same effect in shapelet space.
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Goldberg Bacon (2004) measure the Flexion (
shear) from the Deep Lens Survey (Wittman
2001). As with Shear, Flexion has a preferred
direction.
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You might point out But the Meeting asked about
Dark Matter Energy! True enough...
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Clusters 1) As a local measure, Flexion can be
used to find/measure substructure in clusters.
Not to be interpreted As a real measurement!
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2) Measurement of Cluster ellipticity (similar
to aperture moment analysis in shear). 3)
Complement to shear estimates of
aperture masses.
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4) Tomography Galaxies at different redshifts
will be lensed by a different amount (Consider,
e.g. Jain Taylor 2004). The difference scales
as the angular diameter distance. We need a very
good knowledge of substructure! But - we could
measure w.
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Consider two arclets near one another
The R factor is a straightforward function of
cosmology!
A
B
We could use this to compute the equation of
state of Dark Energy!
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3) Using Flexion with Time-Delay Measurements
of Independent Measurements/Image Delays 1xN
-2 Deflections 2xN-1 Distortions 3xN-1 F
lexion 4xN-1
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Cosmic Flexion would be able to measure
perturbations on highly nonlinear scales!
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Conclusions and References

• Flexion is a powerful means of extracting new
  info from
• galaxy-galaxy lensing
• It is measurable, and can have high S/N.
• Flexion may also be applied to weak lensing in
  clusters,
• cosmic scales, etc.
• Strong Flexion effects may be useful in
  time-delay
• measurements and Tomography

• Bacon, Goldberg, et al. (2005), in preparation
  -- look for it soon!
• Goldberg Bacon (2005), ApJ 619.
  astro-ph/0406376
• Goldberg Natarajan (2004), ApJ 564, 65.
  astro-ph/0107187