Variation of Molecular Cloud Properties across the Spiral Arm in M 51

We present the results of high-resolution 13CO(1-0) mapping observations with the NRO 45m telescope of the area toward the southern bright arm region of M51, including the galactic center. The obtained map shows the central depression of the the circumnuclear ring and the spiral arm structure.The arm-to-interarm ratio of the 13CO(1-0) integrated intensity is 2-4. We also have found a feature different from that found in the 12CO results. The 12CO/13CO ratio spatially varies, and shows high values (~20) for the interarm and the central region, but low values(~10) for the arm. These indicate that there is a denser gas in the spiral arm than in the interarm. The distribution of the 13CO shows a better correspondence with that of the H\alpha emission than with the 12CO in the disk region, except for the central region. We found that the 13CO emission is located on the downstream side of the 12CO arm, namely there is an offset between the 12CO and the 13CO as well as the H\alpha emission. This suggests that there is a time delay between the accumulation of gas caused by the density wave and dense gas formation, accordingly star formation. This time delay is estimated to be ~10^7 yr based on the assumption of galactic rotation derived by the rotation curve and the pattern speed of M51. It is similar to the growth timescale of a gravitational instability in the spiral arm of M51, suggesting that the gravitational instability plays an important role for dense gas formation.Comment: 23 pages, 10 figures, PASJ Vol.54, No.2 (2002), in pres

"A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments"

We compare four dffierent estimation methods for a coefficient of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum emirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. We prove several theorems on the asymptotic optimality of the LIML estimator when the number of instruments is large, which are new as well as old, and we relate them to the results in some recent studies. Tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most of interest. We have found that the LIML estimator has good performance when the number of instruments is large, that is, the micro-econometric models with many instruments in the terminology of recent econometric literature.

"On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments"

We consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large; some of these results are new and we relate them to results in some recent studies. We have found that the variance of the LIML estimator and its modifications often attain the asymptotic lower bound when the number of instruments is large and the disturbance terms are not necessarily normally distributed, that is, for the micro-econometric models with many instruments.

XMM-Newton Observation of IC 310 in the Outer Region of the Perseus Cluster of Galaxies

We present results from an XMM-Newton observation of the head-tail radio galaxy IC 310 located in the southwest region of the Perseus cluster. The spectrum is well-fitted by an absorbed power-law model with a photon index of $2.50 \pm 0.02$ with no significant absorption excess. The X-ray image shows a point-like emission at IC 310 without any signs of a structure correlated with the radio halo tail. The temperature of the intracluster medium surrounding IC 310 declines as a function of distance from the cluster center, from $kT \sim 6$ keV in the northeast corner of the field of view to about 3 keV in the southwest region. Although we do not find any sharp edges in the surface brightness profile, a brightness excess over a smooth $\beta$ model by about 20% is seen. The temperature also rises by about 10% in the same region. This indicates that the IC 310 region is a subcluster probably infalling into the Perseus cluster, and the gas in front of IC 310 towards the Perseus cluster is likely to be compressed by the large-scale motion, which supports the view that the IC 310 system is undergoing a merger.Comment: 7 pages, 8 figures (including color), accepted for publication in PAS