Sprinkler.md

SN Sprinkler pseudo code

Assumptions and discussion

• Cosmology is known. This cosmology should be whatever is used to compute time delays from the lenses. CatSim is cosmology dependent as well. This plays into the setup in two ways: Galaxy evolution is cosmology dependent, but this dependence is relatively weak, and smudged anyway in how we are populating SN. The second is that SN have distance moduli calculated according to the udnerlying cosmology, which will determine the sensitivity/discovery in images. This may need to be changed to match the time delay calculations.
• The OM10 cataloag provides us with an ensemble of lens-source systems. The number of lens source systems in a given area is a function of the number density of lens galaxies and the number density of sources. I do not understand the way we need to oversample these two quantities to make the procedure sensible. At this point, let us assume that we can find a catalog of lenses that would make sense in combination with the transients

The lens catalog

• Set up the lenses Lenses
  • Obtain the lens catalog from OM10, resample to obtain a sample of OM10 lenses that make the area of the sky under consideration
  • Distribute these lenses randomly in the Twinkles patch of sky in ra, dec keeping their redshifts fixed
• Set up a list of sources that could be strongly lensed:
  • Catalogs contain simulations of transient sources distributed according to some population statistics of these sources. (For SN, in the present construction, use sims.catUtils.mixins.sncat which inherit from sims.catalogs.measures.instance and sims.catUtils.mixins.snUniverse with self.suppressDimSN=False) which will give a list of all SN with their redshifts, ra, dec, and peak mjd in BessellB and SNID within z = self.maxz
  • From this obtain a list of potential sources that could be lensed, irrespective of whether these would be observed in a particular LSST strategy or not. This is largely to speed up things using hard priors and should be chosen conservatively. let us call this list Total Potential Sources
  • Iterate over lenses and determine the maximal spatial box in ra and dec where we might get lensed transients due to these lenses. This must iterate over the lenses. We assume that this should be easy to do as a function of ra, dec and a redshift extent Q. How do we set the redshift extent ? I assume that the ra, dec extents can be set up in terms of functions of Einstein radii like (8theta)^2 used in OM10. It would not be terrible to take a constant value for the ra, dec, z extents
  • Determine the maximal temporal range (due to time delays, this will be larger than the LSST 10 year time period, where we imagine that we get delayed SN visits in the first year, while the SN exploded a couple of years before, and would have been excluded from the list of interesting ovjects in usual SN queries). We can use the largest Delta T value from OM10 as a guide here. This would correspond to about 1.5 to 2 yrs from Fig. 8 of OM10.
  • The intersection of the above two sets form the set of potentially lensed sources.
• Actually find lensing events
  • Find Potential Sources for each lens in Lenses
    • Find sources from Total Potential Sources which fall into a spatial box of interest (redshift, ra, dec) defined by the parameters of the Lens (external shear, density profile parameters, position. To do this we could take a small box around the lensed source in OM10. I am guessing that the ra, dec extents would be some function of Einstein radius. Q. How do we quantitavely find the extents?
    • For every source in Potential Sources :
      • Calculate the position of lensed images **Q How: Do we have a way of calculating this for a source-lens pair, given the lens properties For a very close matches in relative positions, we can assign the lensed positions in the same way as it worked in OM10. What about the sources that do not match as closely. Those could still be lensed. Is there some perturbative calculation we can do, or do we have to calculate it from scratch? Does code exist to do that? **
      • Calculate the magnification of the lensed images Q. Same as for lensed positions
      • Calculate the time delay for each source above Q Same as for lensed positions

Questions:

• This is a question about OM10: I might be missing it, but I would expect that the abundance of lenses also depends on the absolute number density of lens galaxies. If keeping all other things constant, I increased the number of randomly positioned elliptical galaxies by a large factor, I would expect the number of lenses to increase. I may have missed it (or it may be hidden in a previous work generating the lenses), but I am not finding an equation in OM10 which describes this.
• However this was implemented in OM10, the exact realization of lenses (not statistics like the number density etc. would seem to be a property of the distribtion of lenses and sources. I am unable to understand why changing the realization of sources to the CatSim sources and keeping the OM10 lenses would give us correct results. For instance, in OM10, there may have been a galaxy at z=0.3 at a certain ra, dec, but no source at z corresponding to twice the releavant distance scale and that galaxy did not get tagged as a lens. On the other hand, maybe there was a source-lens system in OM10 with the lens at z=3.5. Not th catsim catalog may have a source at the source location corresponding to the lens at z = 3.0, but not at z=3.5. This would mean that we get 0 lenses in catsim using thsi kind of matching. I think we should be matching distributions.