Download Introduction Contact Weak Lensing: Method The NOAO Deep Wide

Observational Cosmology, Gravitational Lensing and Astrophysics Group
Ian Dell’Antonio, Jeffery
*
Kubo ,
Hossein Khiabanian, Wessyl Kelly
Kaitlin Goldstein, Stephan Janiszewski, Hannah Singer, Alexander Cerjan, Amandeep Gill
Introduction
Weak Lensing: Method
A JDEM Project: Destiny
The goal of observational cosmology is to determine the properties of the Universe today, and
how it has evolved with time. One of the most fundamental questions to ask about the Universe
is: how much matter is there, and how is it distributed? This is a deceptively hard question to
answer. Most of the matter in the Universe is dark, it emits no light (of any kind!) A picture of the
visible matter is not necessarily representative of what is there. To overcome this difficulty, we
are using a variety of techniques that measure the mass directly, the main one being
gravitational lensing. Gravitational lensing uses the fact that the presence of mass causes the
space around the mass to deform. The light from distant background objects bends in response
to the deformation, distorting the images of the distant galaxies. By measuring the amount the
light is bent, we can measure the curvature of space and thus the mass! Measurements of the
clustering of the dark matter may give us clues as to the nature of dark matter.
The presence of mass causes background galaxies to appear
shifted in position and stretched tangentially to the vector
connecting the galaxies to the mass (see figure below). In
weak lensing, the deflection of the position is not measurable.
(We cannot remove the mass to see where the galaxy really
is!) But the tangential ellipticity eT is. In general the distortion
of a galaxy’s shape is much less than the random variation in
shape and orientation from galaxy to galaxy.
Our aim is to optimize the capability of DESTINY while minimizing cost. In the case of gravitational
lensing, our goal is to recover the distortion in galaxy shapes that is the result of intervening mass
between distant galaxies and Earth. In order to gauge the suitability of a set of telescope parameters, we
simulate an image with the depth, size, and resolution of the Universe as it would be seen through the
“eyes” of the telescope.
Observations of Supernovae have revealed that the expansion of the Universe is accelerating.
Because dark matter decelerates the expansion, this points to a new component to the Universe
—the Dark Energy. Experiments like the JDEM missions and LSST will use gravitational lensing
as a tool to measure dark energy and its properties.
There are two types of gravitational lensing: strong lensing occurs when the curvature is great
enough to cause multiple imaging—the same background object is seen in multiple directions!
This yields very detailed information about the mass, but requires a significant mass density. In
weak lensing, the distortion of each galaxy is too small to be reliably measured. However, the
ensemble statistical effect on many background galaxies can be measured. This allows us to
probe the distribution of mass even in low-density environments. Our research group is heavily
involved in the study of gravitational lensing using both techniques and data from the Hubble
Space Telescope as well as ground-based telescopes.
However,
by
considering the
average shape and
orientation of an
ensemble of galaxies
in a patch of the sky,
we can measure the
average tangential
ellipticity <eT>. If we
average over enough
galaxies, the random
component will
average to zero,
allowing us to
measure the lensinginduced ellipticity!
To do so, small galaxy “postage stamps”, taken from
Hubble Deep Fields, are scaled to reflect the size,
shape, orientation, redshift, and magnitude
distribution of galaxies in the real Universe. Once
we simulate a full image, consisting of tens of
thousands of galaxies, we add an artificial lensing
signal and analyze how well we recover it.
One of the critical aspects of the Destiny mission is
the plan to obtain slitless spectroscopy of all the
imaged fields. This will allow us to measure lowresolution (R~75) spectra of every object in the
frame, and greatly improve our ability to measure
distances for the lensed galaxies.
Left: Artist’s rendition of the Destiny spacecraft.
Above: A Schematic showing of the path of
light from distant galaxies through the dark
matter and how coherent distortion in the
galaxy shapes are produced.
As the pictures below show, however, one of the drawbacks of slitless
spectroscopy is that the spectra of objects will overlap. To disentangle the spectra
will require rotating the spacecraft and repeating exposures. We are generating
simulations of this effect to test the optimal combination of roll angles.
Above: Full simulation field 20784 by 4096 pixels,
while the image above is solely 250 by 250 pixels.
Weak Lensing: Mass Maps
The relation between surface mass
density (κ) and the shear due to the
gravitational field (γ) is
Our goal is to produce a map of the
surface mass density. There are two
classes of reconstruction methods using
weak gravitational lensing data. The
direct methods, approximate a local
value for the shear from the observed
ellipticities of the background galaxies (γT
= eT). The tangential ellipticity as a
function of angular distance about each
point is related to the mass density at
that point by
There are also indirect methods of producing mass maps. Inverse methods aim to find the best fit to the data.
By minimizing
we are able to find the best answer for κ that satisfies the first equation. The expected ellipticity of each
The
Deep
Lens
Survey
source is derived from the deflection potential (ψ) which is related to κ at xg. These methods have the benefit
of not only utilizing all the shear information provided by each source galaxy, but also incorporating extra The DLS is a NOAO Survey program—it uses the 4-meter
information from other observables such as magnification.
telescopes at Kitt Peak in Arizona (right) and Cerro Tololo in
Chile to make maps of several 4-square degree regions of the
We can also produce maps with multiple
sky, to a depth of about R=26. (Some 10 billion times fainter
resolutions in the different parts of the observed
than the naked eye can see.)
field. Therefore, we achieve a uniform signal to
Approximately 140 nights of 4-meter time will have been
noise level and are able to better study the suballocated to this project. The background of the poster is 1.6%
structure of massive clusters.
of the survey area.
Left:
The
analytical mass
map
of
a
simulated field
with five clusters
of galaxies with
masses ranging
from 1013 to 1015
Solar masses.
This can be used to map out the surface
density of matter and reveal the
distribution of dark matter. In these
methods the data must be smoothed.
The picture below shows a map of the
surface mass density for a four squaredegree field obtained by the Deep Lens
Survey. The bright spots represent mass
concentrations of about or greater than
1014 Solar masses.
Above: The mass map of one of the four square-degree DLS fields. Bottom Left: The Optical
data of the same field. Bottom Right: The brightest blob in the mass map is due to a know cluster
of galaxies called Abell 781. Its mass is greater than 1014 Solar masses
The NOAO Deep Wide-Field Survey
Right: The mass map of the same field produced by an inverse method.
We can also produce mass maps by only
using the magnification information. The
gravitational lensing changes the
average number density of background
galaxies by changing both the flux of the
galaxies (therefore making the faint ones
brighter) and the apparent solid angle.
Thus, from a measurement of the local
number density of galaxies, we can
estimate κ. The left image shows such a
mass map for the same DLS field.
The Deep Lens Survey is one of several data sets currently being
used to investigate cosmology and dark matter. Another, the
NDWFS is a deep optical and near-infrared imaging survey that
covers two 9.3 square degree fields. It was designed primarily for
the study of the existence and evolution of large scale structures
at redshifts z > 1 as sampled by diverse populations of objects.
Our current project is using the Bootes field to detect and analyze
galaxy-galaxy weak lensing as a way to constrain the dark matter
in the universe.
Contact
For more information visit our group webpage at http://www.het.brown.edu/people/ian/astro/ or
email Ian Dell’Antonio at [email protected].