Lensing and WIRE Data

Warning! This document is only in it's earliest phases! Much work remains to be done!

What is lensing?

Lensing is the bending of light by gravity. A particularly massive object, like a galaxy with a massive halo, acts as a lens, distorting the images of other galaxies at higher redshift that fall behind or near it. The practical side of this is that a lensed object has the same surface brightness as when it was unlensed, but subtends a larger angular size. As a result, it's integrated flux is higher.

Who Cares? Gravitational lenses can be exploited as natural "telescopes". Amplifications can be as high as 100 or more times. Lenses are in many cases the only way to study certain objects at high redshift. CO studies at high redshift, for example, are confined primarily to lensed objects like FSC 10214 and the Cloverleaf Quasar, because without lensing no telescope is sensitive enough to make the observations.

Will WIRE see Lenses?

Almost certainly. On the one hand, we may directly target several clusters that are known to contain giant gravitational arcs. In these cases, we will definitely detect the arcs. However, the more interesting case will be the discovery of serendipitous lenses in the primary survey data. As detailed below, we will probably detect on the order of 100 strong lenses (amplifications greater than 10) in the survey. Once identified, this catalog of new lenses will represent a major result from WIRE. Considering the amount of attention generated by FSC 10214, imagine what could be done with a sample size greater than one!

How will we detect lenses in the WIRE primary survey?

There is no way from the WIRE data alone to determine if a galaxy is lensed or not. Primarily, this is because the WIRE beam size is approximately 20" FWHM. This is too large to detect the tell-tale distortions in the appearance of lensed galaxies; even giant arcs are typically only of sizes similar to this. The actual identification of the lenses will have to be made in the follow-up ground-based observations.

A Lensing Model

In an attempt evaluate the number and distribution of lenses, a hybrid analytical/empirical model has been constructed. Namely, the lensing treatment is a monte carlo simulation with an analytic form for the underlying lensing, while the galaxy flux distribution uses real galaxy templates.

The entire thing runs on a G3 Macintosh in the Igor data analysis package. A typical simulation incorporates 1-100 million galaxy observations. The basic steps are:

  • Generate a random galaxy redshift distribution whose co-moving density evolves according to (1+z)^alpha. This is normalized to a unit area in the sky (i.e. dN/(dz dW).
  • For each galaxy, assign a flux according to a probability table based on Cong Xu's modeled galaxy flux distribution which is a function of the evolutionary model.
  • Compute the probability of lensing for each galaxy based on a probability distribution derived from Turner (1984) for lensing by a uniform field of isothermal sphere lenses.
  • For each lensed galaxy, compute an amplification based on the probability of a given amplification according to Trentham (198X).
  • Compute the relevant amplified fluxes and compare to the unlensed results. In particular, derive the number of high amplification lenses that make it above a specified flux limit.

    It is best to keep in mind that this is only a model, and was designed to give an order of magnitude estimate. Despite the fact that it is very complicated, many of the things in it are "hand-waving" approximations; the uncertainties in the guesses that went into the model dominate the expected errors.


    Over the range of redshifts of interest (i.e. 0.5 < z < 3), the probability of being lensed with an amplification greater than 2 is typically in the range of a few per thousand. The likelihood of being lensed by 10 or more is correspondingly much lower - this is where the magic of Amplification Bias comes in. Most of the galaxies are at high redshift, and hence there are many more that could be lensed. Correspondingly, the likelihood of being lensed increases with redshift. In any flux-limited sample, the number of lensed sources will be much higher than expected, since flux amplification pushes the faint, high redshift lensed objects above the detection threshold. The model above seems to indicate that the amplification bias will be fairly high (20-30).

    How does the lensing rate vary as a function of the evolutionary model?

    Both luminosity and density evolution affect the rate of detectable lenses. This is because most lensing occurs for galaxies at z>1. Pure luminosity evolution greatly increases the luminosity of distant objects, increasing the likelihood that the lensed population will make it above the survey cutoff. On the other hand, the number of unlensed objects will also increase dramatically. Under these circumstances, the survey will become shallower, and hence the increase in the lensed/unlensed ratio will actually decrease slightly. The most dramatic changes occur with strong density evolution. In this case the vast majority of galaxies are at high redshift, and hence the number of galaxies that are lensed strongly enough to make it above the survey flux limit increases greatly. In this case, as many as 1% of the detected galaxies may be strongly lensed. Furthermore, if there is no luminosity evolution, then a very large fraction of the high redshift WIRE sources will be lensed, since it is difficult for galaxies to make it above the flux limit otherwise.
    ModelFlux Limit (mJy)Lensed(A>10)/Unlensed
    No Evolution 1.5 0.0015
    0.69 0.0027
    L=(1+z)^3 1.5 0.0011
    0.69 0.0016
    Rho=(1+z)^3 1.5 0.0272
    0.69 0.0119

    How will lensing affect the results of the primary survey?

    Lensing will masquerade as luminosity evolution in the primary survey. Quantification of this is still underway, but the areal density of lenses is so low compared to the galaxies in the survey that it is unlikely to make any real difference. It is likely that only 0.5-1% of the galaxies detected by WIRE will be strongly lensed. In any given flux bin, it is unlikely that the number of lensed galaxies could ever exceed 5%, and hence the effect on the perceived number counts will be small.