Mass reconstruction of subhalos by weak lensing analysis

Mass reconstruction of subhalos by
weak lensing analysis
Student : Li-Yen Hsu
Advisers : Dr. Keiichi Umetsu & Prof. Pisin Chen

Outlines
● Introduction – Weak gravitational lensing
● galaxy-galaxy lensing
● Strategy
● Results
● Summery

Lens equation (cluster gravitational lensing)

Lensing Jacobian matrix, Convergence &
Shear
● Lensing Jacobian matrix : image -> source
where
with the formula of the lensing effective potential:

Effect of convergence & shear
● Convergence
=> size
● Shear
=> shape

Weak Lensing Distortion Observables
● Ellipticity (spin-2):

Weak Lensing Distortion Observables
● Ellipticity in turns of quadrupole moments of the surface
brightness distribution
● Ellipticity transforms under the lens mapping :
● In the weak lensing limit :
assuming that the sources are randomly oriented :

Lensing distortion profiles
● The tangential and cross-component shears
rotate the basis axis :
=>
(The ref. point is often taken to be the cluster center)
● Statistics
● Comparing observed tangential shear profiles with models

Lensing distortion profiles
● Fitting the model to the distortion profiles

Galaxy-galaxy lensing
● Assumption: Each Cluster's galaxy resides in a
subhalo
● Background galaxies are lensed by galaxysized
halos
● Galaxy-galaxy lensing requires that lenses must
be stacked in order to enhance S/N ratio
=> expect to get of the stacking subhalos

Strategy
● Averaging out the smooth
part induce by the cluster
potential In the polar
coordinates

● The aperture of each
target subhalo should
not include another
subhalo.
● Treating subhalos as
point sources
=> Inverse-square law
Aperture

Simulation-N body data
● Binning the sample of subhals into 3 mass bins

Simulation-N body data
● Binning the field into 3 radial bins

Working on Cl0024+1654 data (z=0.395)
● Binning the field and the sample of cluster galaxies into a
few radial bins or a few luminosity bins
● Using the R-band for the luminosity (or flux, magnitude)
measurements
● Trying to avoid those region that shear induced by the host
halo varies too much as r changes
● We expect to see a tendency of increasing M with
increasing luminosity, or increasing distance from the
cluster's center due to dynamics.

Stacking all the lenses without bins

● Mass reconstruction
3 radial bins

1 st R bin

2 nd R bin

3 rd R bin

● Mass reconstruction
3 luminosity bins

1 st L bin

2 nd L bin

3 rd L bin

Summery
● It is a model dependent (point source) method.
● It is a pure lensing analysis without scaling
relations.
● The mass of subhalos should increase as the
luminosity or radius increases.
● We must try more strategy to improve S/N ratio.
● How to subtract the cluster's potential
contribution exactly is still a problem.

● Keiichi Umetsu
References
lecture:“Cluster Weak gravitational lensing”
arXiv:0908.0069v2 [astro-ph.CO] 11 Aug 2009
arXiv:astro-ph/0004400v2 29 Apr 2000
● Peter Schneider & Carolin Seitz, astro-ph/9407032 12 Jul 1994
● Priyamvada Natarajan, arXiv:astro-ph/9609008v2 24 Apr 1997
● Priyamvada Natarajan, arXiv:0711.4587v2 [astro-ph] 5 Nov 2008
● Dodelson “Modern Cosmology”