A GMRT 150 MHz Search for Variables and Transients in Stripe 82

We have carried out a dedicated transient survey of 300 deg$^2$ of the SDSS Stripe 82 region using the Giant Meterwavelength Radio Telescope (GMRT) at 150 MHz. Our multi-epoch observations, together with the TGSS survey, allow us to probe variability and transient activity on four different timescales, beginning with 4 hours, and up to 4 years. Data calibration, RFI flagging, source finding and transient search were carried out in a semi-automated pipeline incorporating the SPAM recipe. This has enabled us to produce superior-quality images and carry out reliable transient search over the entire survey region in under 48 hours post-observation. Among the few thousand unique point sources found in our 5$sigma$ single-epoch catalogs (flux density thresholds of about 24 mJy, 20 mJy, 16 mJy and 18 mJy on the respective timescales), we find $<$0.08%, 0.01%, $<$0.06% and 0.05% to be variable (beyond a significance of 4$sigma$ and fractional variability of 30%) on timescales of 4 hours, 1 day, 1 month and 4 years respectively. This is substantially lower than that in the GHz sky, where $sim$1% of the persistent point sources are found to be variable. Although our survey was designed to probe a superior part of the transient phase space, our transient sources did not yield any significant candidates. The transient (preferentially extragalactic) rate at 150 MHz is therefore $<$0.005 on timescales of 1 month and 4 years, and $<$0.002 on timescales of 1 day and 4 hours, beyond 7$sigma$ detection threshold. We put these results in the perspective with the previous studies and give recommendations for future low-frequency transient surveys.