We present observations of HCN J = 1-0 and CH_3OH J(K_a, K_c) = 3(1, 3)-4(0, 4) A+ emission from comet C/2002 T7 (LINEAR) obtained simultaneously with the Owens Valley Radio Observatory (OVRO) and Berkeley-Illinois-Maryland Association (BIMA) millimeter interferometers. We combined the data from both arrays to increase the (u, v) sampling and signal to noise of the detected line emission. We also report the detection of CH_3OH J(K_a, K_c) = 8(0, 8)-7(1, 7) A^+ with OVRO data alone. Using a molecular excitation code that includes the effects of collisions with water and electrons, as well as pumping by the Solar infrared photons (for HCN alone), we find a production rate of HCN of 2.9 × 10^(26) s^(–1) and for CH_3OH of 2.2 × 10^(27) s^(–1). Compared to the adopted water production rate of 3 × 10^(29) s^(–1), this corresponds to an HCN/H_2O ratio of 0.1% and a CH_3OH/H_2O ratio of 0.7%. We critically assess the uncertainty of these values due to the noise (~10%), the uncertainties in the adopted comet model (~50%), and the uncertainties in the adopted collisional excitation rates (up to a factor of 2). Pumping by Solar infrared photons is found to be a minor effect for HCN, because our 15 synthesized beam is dominated by the region in the coma where collisions dominate. Since the uncertainties in the derived production rates are at least as large as one-third of the differences found between comets, we conclude that reliable collision rates and an accurate comet model are essential. Because the collisionally dominated region critically depends on the water production rate, using the same approximate method for different comets may introduce biases in the derived production rates. Multiline observations that directly constrain the molecular excitation provide much more reliable production rates.
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