Neutral hydrogen 21 cm absorption at redshift 2.6365 toward the gravitational lens MG J0414+0534

We report the detection of the 21 cm line of neutral hydrogen in absorption at a redshift of 2.6365 toward the gravitationally lensed radio source MG J0414+0534. The absorption shows two velocity components, each with a width of similar to 150 km s(-1), separated by about 200 km s(-1). We determine a total H I column density of 7.5 +/- 1.3 x 10(18) (T-s) cm(-2) assuming an H I covering factor of unity. Assuming a Galactic dust-to-gas ratio and that all the reddening toward the source is due to dust associated with the observed H I 21 cm absorption line, we derive an upper limit to the H I spin temperature T-s of 1300 K. We do not detect absorption in the HCN (J = 1-0) line toward MG J0414+0534 with a 3 sigma optical depth limit of 0.047 at 19.2 km s(-1) resolution. The implied upper limit on the HCN column density is 1 x 10(13) cm(-2). The redshift of the H I absorption centroid differs by 200 km s(-1) from the centroid of the recently discovered CO J = 3-2 emission from MG J0414+0534. We present two alternative scenarios that explain both the observed velocity offset between the CO emission and the H I absorption and the lack of molecular absorption toward MG J0414+0534. Either (1) the H I 21 cm line is absorbing the lensed active galactic nucleus and the regions giving rise to CO emission have a different spatial distribution than the radio continuum-emitting regions and ai-e affected differently by gravitational lensing or (2) the H I 21 cm absorption is toward an extended, steep-spectrum radio component, which contributes substantially to the radio continuum emission at low frequencies but has a negligible flux density at I higher frequencies. This latter model requires free-free absorption toward the steep-spectrum component in order to result in the observed Gigahertz-peaked spectrum of MG J0414+0534's integrated radio emission