Measuring the correlation length of intergalactic magnetic fields from observations of gamma0ray induced cascades

The imaging and timing properties of ? ray emission from electromagnetic cascades initiated by very high energy (VHE) ? rays in the intergalactic medium depend on the strength B and correlation length ?B of intergalactic magnetic fields (IGMF). We study the possibility of measuring both B and ?B via observations of the cascade emission with ? ray telescopes. For each measurement method we find two characteristics of the cascade signal which are sensitive to the IGMF B and ?B values in different combinations. For the case of IGMF measurement using the observation of extended emission around extragalactic VHE ? ray sources the two characteristics are the slope of the surface brightness profile and the overall size of the cascade source. For the case of IGMF measurement from the time delayed emission these two characteristics are the initial slope of the cascade emission light curve and the overall duration of the cascade signal. We show that measurement of the slope of the cascade induced extended emission and/or light curve can both potentially provide measure of the IGMF correlation length provided it lies within the range 10 kpc ? ?B ? 1 Mpc. For correlation lengths outside this range gamma ray observations can provide an upper or lower bound on ?B. The latter of the two methods holds great promise in the near future for providing a measurement/constraint using measurements from present/next generation ? ray telescopes. Measurement of the IGMF correlation length will provide an important constraint on its origin. In particular it will enable to distinguish between an IGMF of galactic wind origin from an IGMF of cosmological origin.