Data
and modelling for one simulated 3D dataset. The rows show three
representative channel maps, corresponding to three velocities. Column 1
shows the input source, a rotating disc with its approaching (first
row) and receding side (third row); the middle row shows the component
which is at rest relative to the observer. Each row is then lensed
forward to obtain the mock lensed data in Column 2. The model obtained
with the 3D-lens modelling method is shown in column 3 and the residuals
(difference of the data and the model) in column 4. From this model,
both the source (column 5) and its kinematics (column 6) can be
reconstructed. © MPA
The diverging results on the kinematics of high-redshift galaxies -
and in consequence on their matter content - can be ascribed to the
different methods used to overcome the observational limitations. The
study of kinematics is mainly hampered by two factors: low spatial
resolution and low signal-to-noise ratio.
These observational limitations can be successfully overcome by
targeting galaxies for which the line of sight lies very close to a
foreground galaxy. The gravitational field of the foreground galaxy then
deflects the light from the distant background galaxy, producing
distorted, magnified, and even multiple images of the background object.
This effect is known as strong gravitational lensing and it offers the
opportunity to study the background galaxies at high physical resolution
and with good signal-to-noise. Furthermore, the magnifying power of
gravitational lensing opens the possibility to study faint galaxies with
low stellar masses, which are not easily accessible by surveys
targeting unlensed galaxies.
The gravitational lensing group at MPA developed the first three
dimensional lens modelling method (see Figure 1). This can be applied to
3D (IFU or radio) data, characterized by two spatial dimensions and one
spectral dimension (velocity, frequency or wavelength), to
simultaneously reconstruct both the mass distribution of the foreground
galaxy and the kinematics of the background galaxy (see Figure 2).
Our method represents a significant improvement over those used until
now, since it does not require the use of high-resolution imaging data
for the derivation of the lens parameters, as these are derived from the
same 3D data used for the kinematics of the background galaxy.
Moreover, the latter is not obtained by fitting on the source plane, but
directly the lensed data. This is achieved in a hierarchical Bayesian
fashion, where the kinematics on the source plane is essentially a
hyper-parameter of the model (i.e. a parameter defining the prior). We
are thus able to study the possible degeneracies between the lens and
kinematic parameters and estimate the uncertainties consistently.
With our technique we are able to recover both the lens and the
kinematics parameters with great accuracy under different observational
conditions. Furthermore, we have successfully tested the capability of
this new method in recovering a variety of rotation curves with shapes
which are prototypes of different morphological galaxy types, from dwarf
to massive spiral galaxies (see Figure 3).
Authors
Francesca Rizzo
PhD student
Phone: 2019
Email: frizzo@mpa-garching.mpg.de
Room: 107
Simona Vegetti
Scientific Staff
Phone: 2285
Email: svegetti@mpa-garching.mpg.de
Room: 105
Original Publication
A novel 3D technique to study the kinematics of lensed galaxies
Submitted to MNRAS in June 2018
