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Young stars in Epsilon Cha and their disks: disk evolution in sparse associations

(abridge) The nearby young stellar association Epsilon Cha association has an estimated age of 3-5 Myr, making it an ideal laboratory to study the disk dissipation process and provide empirical constraints on the timescale of planet formation. We combine the available literature data with our Spitzer IRS spectroscopy and VLT/VISIR imaging data. The very low mass stars USNO-B120144.7 and 2MASS J12005517 show globally depleted spectral energy distributions pointing at strong dust settling. 2MASS J12014343 may have a disk with a very specific inclination where the central star is effectively screened by the cold outer parts of a flared disk but the 10 micron radiation of the warm inner disk can still reach us. We find the disks in sparse stellar associations are dissipated more slowly than those in denser (cluster) environments. We detect C_{2}H_{2} rovibrational band around 13.7 micron on the IRS spectrum of USNO-B120144.7. We find strong signatures of grain growth and crystallization in all Epsilon Cha members with 10 micron features detected in their IRS spectra. We combine the dust properties derived in the Epsilon Cha sample with those found using identical or similar methods in the MBM 12, Coronet cluster, Eta Cha associations, and in the cores to disks (c2d) legacy program. We find that disks around low-mass young stars show a negative radial gradient in the mass-averaged grain size and mass fraction of crystalline silicates. A positive correlation exists between the mass-averaged grain sizes of amorphous silicates and the accretion rates if the latter is above ~10^{-9} Msun/yr, possibly indicating that those disks are sufficiently turbulent to prevent grains of several microns in size to sink into the disk interior.