User:TallJimbo/WeakLensing/Galaxy

Galaxy-galaxy lensing is a specific type of weak (and occasionally strong) gravitational lensing, in which the foreground object responsible for distorting the shapes of background galaxies is itself an individual field galaxy (as opposed to a galaxy cluster or the large-scale structure of the cosmos). Of the three typical mass regimes in weak lensing, galaxy-galaxy lensing produces a “mid-range” signal (shear correlations of ~1%) that is weaker than the signal due to cluster lensing, but stronger than the signal due to cosmic shear.

History
J.A. Tyson and collaborators first postulated the concept of galaxy-galaxy lensing in 1984, though the observational results of their study were inconclusive. It was not until 1996 that evidence of such distortion was tentatively discovered, with the first statistically significant results not published until the year 2000. Since those initial discoveries, the construction of larger, high resolution telescopes and the advent of dedicated wide field galaxy surveys have greatly increased the observed number density of both background source and foreground lens galaxies, allowing for a much more robust statistical sample of galaxies, making the lensing signal much easier to detect. Today, measuring the shear signal due to galaxy-galaxy lensing is a widely used technique in observational astronomy and cosmology, often used in parallel with other measurements in determining physical characteristics of foreground galaxies.

Stacking
Much like in cluster-scale weak lensing, detection of a galaxy-galaxy shear signal requires one to measure the shapes of background source galaxies, and then look for statistical shape correlations (specifically, source galaxy shapes should be aligned tangentially, relative to the lens center.) [WE SHOULD HAVE A FIGURE HERE, I THINK] In principle, this signal could be measured around any individual foreground lens. In practice however, due to the relatively low mass of field lenses and the inherent randomness in intrinsic shape of background sources (the so called galaxy “shape noise”)[MAYBE A SHAPE NOISE IMAGE…?], the signal is impossible to measure on a galaxy by galaxy basis. However, by combining the signals of many individual lens measurements together (a technique known as “stacking”), the signal to noise ratio will improve, allowing one to determine a statistically significant signal, averaged over the entire lens set.

Source/Lens Redshift Determination
In order to properly interpret shear signals from any gravitational lensing study, accurate redshifts must be determined for both the lenses themselves and the background source galaxies. In galaxy-galaxy lensing, this is particularly crucial, for two reasons:


 * 1) Unlike in cluster-scale weak lensing, where the lensing cluster members can often be easily differentiated from their source galaxy counterparts (images of galaxy clusters display a noticeable increase in galaxy density at the location of the cluster, and cluster members also form a distinct red-sequence on a color-magnitude diagram), galaxy-galaxy lenses are virtually indistinguishable from sources. By obtaining spectroscopic or – often in the case of large surveys – photometric redshifts however, the difference between background source galaxies and foreground lens galaxies becomes readily apparent.  (Though, in the absence of redshift information, it is still possible to estimate between source and lens populations using a simple  magnitude cut.  This technique is much less accurate, however.)
 * 2) Galaxy-galaxy lensing requires the stacking of many lenses before a coherent shear signal can be observed, and to properly combine this stack, each individual shear field must be appropriately weighted. Included in this weight factor are lens and source redshifts (where often, the source redshift is determined to be the ensemble average of all background galaxies), since gravitational shear is affected not only by foreground mass, but also by the geometry (angular diameter distances) between the observer, the lens, and the source.
 * 1) Galaxy-galaxy lensing requires the stacking of many lenses before a coherent shear signal can be observed, and to properly combine this stack, each individual shear field must be appropriately weighted. Included in this weight factor are lens and source redshifts (where often, the source redshift is determined to be the ensemble average of all background galaxies), since gravitational shear is affected not only by foreground mass, but also by the geometry (angular diameter distances) between the observer, the lens, and the source.

Scientific Applications
Galaxy-galaxy lensing (like all other types of gravitational lensing) is used to measure several quantities pertaining to mass:

Mass Density Profiles
Using techniques similar to those in cluster-scale lensing, galaxy-galaxy lensing can provide information about the shape of mass density profiles, though these profiles correspond to galaxy-sized objects, instead of larger clusters or groups. Given a high enough number density of background sources, a typical galaxy-galaxy mass density profile can cover a wide range of distances (from ~1 to ~100 effective radii). Since the effects of lensing are insensitive to the matter type, a galaxy-galaxy mass density profile can be used to probe a wide range of matter environments: from the central cores of galaxies where baryons dominate the total mass fraction, to the outer halos where dark matter is more prevalent.

Mass-to-Light Ratios
Comparing the measured mass to the luminosity (averaged over the entire galaxy stack) in a specific filter, galaxy-galaxy lensing can also provide insight into the mass to light ratios of field galaxies. Specifically the quantity measured through lensing is the total (or virial) mass to light ratio – again due to the insensitivity of lensing to matter type. Assuming that luminosity can trace luminous matter, this quantity is of particular importance, since measuring the ratio of luminous (baryonic) matter to total matter can provide information regarding the overall ratio of baryonic to dark matter in the universe.

Galaxy Mass Evolution
Since the speed of light is finite, an observer on the Earth will see distant galaxies not as they look today, but rather as they appeared at some earlier time. By restricting the lens sample of a galaxy-galaxy lensing study to lie at only one particular redshift, it is possible to understand the mass properties of the field galaxies that existed during this earlier time. Comparing the results of several such redshift-restricted lensing studies (with each study encompassing a different redshift), one can begin to observe changes in the mass features of galaxies over a period of several epochs, leading towards a better understanding of the evolution of mass on the smallest cosmological scales.

Other Mass Trends
Lens redshift is not the only quantity of interest that can be varied when studying mass differences between galaxy populations, and often there are several parameters used when segregating objects into galaxy-galaxy lens stacks. Two widely used criteria are galaxy color and morphology, which act as tracers of (among other things) stellar population, galaxy age, and local mass environment. By separating lens galaxies based on these properties, and then further segregating samples based on redshift, it is possible to use galaxy-galaxy lensing to see how several different types of galaxies evolve through time.