A novel 3D technique to study the kinematics of lensed galaxies

August 01, 2018
Gravitational lensing offers the possibility to study faint, far-away galaxies. MPA researchers have now developed the first three dimensional lens modelling method, which allows not only the reconstruction of the mass distribution of the foreground galaxy but also the kinematics of the background galaxy. Consequently, the matter content can now be studied also in young galaxies. 

This schematic view shows lensed images in the top row and the source plane in the bottom row. Lensed data are shown for three representative velocity channels of the data cube; the respective grid on the image plane is regular. For each velocity channel, the position of a pixel in the image plane corresponds to a position on the source plane (lower panel), determined by the lens equation. The points form the vertices of a triangular adaptive grid on the source plane. The source grid automatically adapts with the lensing magnification, so that there is a high pixel density in the high-magnification regions close to the caustics.

In the standard model of cosmology, galaxies form as the baryonic gas cools at the centre of dark matter halos. They subsequently grow through accretion and mergers, leading to the hierarchical build-up of galaxy mass. While this general picture is well known, there are numerous physical mechanisms determining the relative contribution of baryons and dark matter within a galaxy and several open questions remain: What are the most important physical mechanisms that lead to the variety of galaxies we observe today? How do these mechanisms influence the matter content within galaxies? The answer to these questions is one of the significant challenges of modern astrophysics.

The study of galaxy kinematics has played a key role in this context. For example, in the local universe, the flatness of observed rotation curves is a well-established fact. The outer parts of the observed rotation curves cannot be explained by the mass predicted from the observed stellar and gas distribution and this discrepancy has been interpreted as evidence for the presence of a "dark matter" halo. Within high redshift galaxies, however, the relative content of baryons and dark matter is poorly known and also its evolution with cosmic time is not well understood. Neither current numerical simulations nor observational studies were able to produce consistent results on the fraction of dark matter within young galaxies.

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.

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).

For different mock background galaxies, these plots show the velocity fields (upper panels) and rotation curves (bottom panels). The velocity field is colour coded (see bar on the side) with red areas moving away from the observer and blue areas moving towards the observer. The original rotation curves are shown in blue and the best fit kinematic model is shown in red. The orange band shows the possible errors from uncertainties of the parameters that defined the rotation curves.

The mock data M1-M3 have input rotation curves described by functional forms, while for M4-M6 the rotation curves were taken from real galaxies. The rotation curves of M1 and M4 are typical of dwarf galaxies, the rotation curves of M2 and M5 are prototypes of spirals, while those of M3 and M6 are typical of massive spirals with a prominent bulge.

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).

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