Mathematics – Logic
Scientific paper
Jan 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aas...21334003m&link_type=abstract
American Astronomical Society, AAS Meeting #213, #340.03; Bulletin of the American Astronomical Society, Vol. 41, p.403
Mathematics
Logic
Scientific paper
The faint source correlation function (FSCF) has previously been a barely measured and totally unused quantity. While it had been tentatively observed down to scales of a few arcseconds in the HDF, its amplitude was on the order of 10-1. I show, using a combination of higher quality data (GOODS and UDF), superior pair-finding source extraction and extensive use of custom image simulations to counter systematics, that the FSCF is not only measurable down to scales of 0.3'' (2.6 kpc at most) but that on such short distance scales it also exceeds unity for 25 < V < 28 sources. My measurement of the FSCF as a power law with an index of -2.5 rather than the measured large-scale index of -0.7 shows that the physics of galactic-scale correlation functions is different from that of the cosmological correlation function. I also measured a reduced three point correlation function, confirming that the FSCF is non-Gaussian, and used the measurement of close pairs to set upper limits on the cosmic string density. Applications of lensing on the FSCF are most interesting. I show, theoretically, that gravitational lenses induce a local anisotropy in the FSCF that is proportional to the lensing shear. For lenses of known mass profile, we can invert the lens equation to solve for the distance to the source using the shear and the induced anisotropy. This produces a distance estimate of the faintest sources without using any spectral information. I establish the framework for using this technique with a large population of galaxy scale lenses, a single large cluster lens or a large field with cosmic shear. Large future datasets with a wide range of lens redshifts will allow us to measure this effect precisely to gain a true, non-spectral distance distribution of the faintest sources.
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