Planetary nebulae in the elliptical galaxy NGC 821: kinematics and distance determination

Using a slitless spectroscopy method with the 8.2 m Subaru telescope and its FOCAS Cassegrain spectrograph, we have increased the number of planetary nebula (PN) detections and PN velocity measurements in the flattened elliptical galaxy NGC 821. A comparison with the detections reported previously by the Planetary Nebula Spectrograph (PN.S) group indicates that we have confirmed most of their detections. The velocities measured by the two groups, using different telescopes, spectrographs and slitless techniques, are in good agreement. We have built a combined sample of 167 PNs and have confirmed the keplerian decline of the line-of-sight velocity dispersion reported previously. We also confirm misaligned rotation from the combined sample. A dark matter halo may exist around this galaxy, but it is not needed to keep the PN velocities below the local escape velocity as calculated from the visible mass. We have measured the m(5007) magnitudes of 145 PNs and produced a statistically complete sample of 40 PNs in NGC 821. The resulting PN luminosity function (PNLF) was used to estimate a distance modulus of 31.4 mag, equivalent to 19 Mpc. We also estimated the PN formation rate. NGC 821 becomes the most distant galaxy with a PNLF distance determination. The PNLF distance modulus is smaller than the surface brightness fluctuation (SBF) distance modulus by 0.4 mag. Our kinematic information permits to rule out the idea that a shorter PNLF distance could be produced by the contamination of the PNLF by background galaxies with emission lines redshifted into the on-band filter transmission curve.Comment: Accepted for publication in ApJ; 16 figure

Solution to the Landau-Zener problem via Susskind-Glogower operators

We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.Comment: 6 pages, 5 figure