Balmer and metal absorption feature gradients in M32

New data sources are used to assess Lick/IDS feature strength gradients inside the half-light radius Re of the compact Local Group elliptical galaxy M32. A Hubble Space Telescope (HST) STIS spectrum seemed to indicate ionized gas and a very young central stellar population. In fact, this conclusion is entirely spurious because of incomplete removal of ion hits. More robust ground-based spectra taken at the MDM Observatory are, in contrast, the most accurate measurements of Lick/IDS indices yet obtained for M32. All but a few ( of 24 measured) indices show a statistically significant gradient. The CN indices show a maximum at 400 radius, dropping off both toward the nucleus and away from it. At 200 radius there is a discontinuity in the surface brightness profile, but this feature is not reflected in any spectral feature. Comparing with models, the index gradients indicate a mean age and abundance gradient in the sense that the nucleus is a factor of 2.5 younger and a factor of 0.3 dex more metal-rich than at 1R(e). This conclusion is only weakly dependent on which index combinations are used and is robust to high accuracy. Stars near the M32 nucleus have a mean age and heavy element abundance [M/H] of (4.7 Gyr, + 0.02), judging from models by Worthey with variable abundance ratios. This result has very small formal random errors, although, of course, there is significant age-metallicity degeneracy along an ( age, abundance) line segment from (5.0 Gyr, 0.00) to (4.5 Gyr, + 0.05). An abundance pattern of [C/M] = +0.077 (carbon abundance affects CN, C(2)4668, and the bluer Balmer features), [N/M] = - 0.13, [Mg/M] = -0.18, [Fe/M] approximate to 0.0, and [Na/M] = +0.12 is required to fit the feature data, with a fitting precision of about 0.01 dex (with two caveats: the [Fe/M] guess has about twice this precision because of the relative insensitivity of the Fe5335 feature to iron, and the [Na/M] value may be falsely amplified because of interstellar absorption). Model uncertainties make the accuracies of these values at least twice the magnitude of the precision. Forcing scaled-solar abundances does not change the age very much, but it increases the rms goodness of model-data fit by a factor of 3 and broadens the allowed range of age to +/-1 Gyr. The abundance ratios do not show strong trends with radius, except for the nuclear weakening of CN ( measuring mainly N) mentioned above, which needs reconfirming with better data. The overall abundance pattern contrasts with larger elliptical galaxies, in which all measurable lighter elements are enhanced relative to iron and calcium. Nucleosynthetic theory does not provide a ready explanation for these mixtures.