Noncommutative Deformation of Spinor Zero Mode and ADHM Construction

A method to construct noncommutative instantons as deformations from commutative instantons was provided in arXiv:0805.3373. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton background on noncommutative R^4, and we modify the index of the Dirac operator on the noncommutative space slightly and show that the number of the zero mode of the Dirac operator is preserved under the noncommutative deformation. We prove the existence of the Green's function associated with instantons on noncommutative R^4, as a smooth deformation of the commutative case. The feature of the zero modes of the Dirac operator and the Green's function derives noncommutative ADHM equations which coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one correspondence between the instantons on noncommutative R^4 and ADHM data. An example of a noncommutative instanton and a spinor zero mode are also given.Comment: 34 pages, no figures, v3: an appendix and some definitions added,typos correcte

Soft X-ray emission lines from a relativistic accretion disk in MCG-6-30-15 and Mrk 766

XMM-Newton Reflection Grating Spectrometer (RGS) spectra of the Narrow Line Seyfert 1 galaxies MCG -6-30-15 and Mrk 766 are physically and spectroscopically inconsistent with standard models comprising a power-law continuum absorbed by either cold or ionized matter. We propose that the remarkably similar features detected in both objects in the 5-35 Angstrom band are H-like oxygen, nitrogen, and carbon emission lines, gravitationally redshifted and broadened by relativistic effects in the vicinity of a Kerr black hole. We discuss the implications of our interpretation, and demonstrate that the derived parameters can be physically self-consistent

Cosmology with type-Ia supernovae

I review the use of type-Ia supernovae (SNe) for cosmological studies. After briefly recalling the main features of type-Ia SNe that lead to their use as cosmological probes, I briefly describe current and planned type-Ia SNe surveys, with special emphasis on their physics reach in the presence of systematic uncertainties, which will be dominant in nearly all cases.Comment: 15 pages, 10 figures. To appear in the proceedings of IRGAC 0

Gauge Theories in Noncommutative Homogeneous K\"ahler Manifolds

We construct a gauge theory on a noncommutative homogeneous K\"ahler manifold, where we employ the deformation quantization with separation of variables for K\"ahler manifolds formulated by Karabegov. A key point in this construction is to obtaining vector fields which act as inner derivations for the deformation quantization. We show that these vector fields are the only Killing vector fields. We give an explicit construction of this gauge theory on noncommutative ${\mathbb C}P^N$ and noncommutative ${\mathbb C}H^N$.Comment: 27 pages, typos correcte

The Soft X-ray Spectrum from NGC 1068 Observed with LETGS on Chandra

Using the combined spectral and spatial resolving power of the Low Energy Transmission Grating (LETGS) on board Chandra, we obtain separate spectra from the bright central source of NGC 1068 (Primary region), and from a fainter bright spot 4" to the NE (Secondary region). Both spectra are dominated by line emission from H- and He-like ions of C through S, and from Fe L-shell ions, but also include narrow radiative recombination continua, indicating that most of the soft X-ray emission arises in low-temperature (kT few eV) photoionized plasma. We confirm the conclusions of Kinkhabwala et al. (2002), based on XMM-Newton RGS observations, that the entire nuclear spectrum can be explained by recombination/radiative cascade following photoionization, and radiative decay following photoexcitation, with no evidence for hot, collisionally ionized plasma. In addition, this model also provides an excellent fit to the spectrum of the Secondary region, albeit with radial column densities a factor of three lower, as would be expected given its distance from the source of the ionizing continuum. The remarkable overlap and kinematical agreement of the optical and X-ray line emission, coupled with the need for a distribution of ionization parameter to explain the X-ray spectra, collectively imply the presence of a distribution of densities (over a few orders of magnitude) at each radius in the ionization cone. Relative abundances of all elements are consistent with Solar abundance, except for N, which is 2-3 times Solar. The long wavelength spectrum beyond 30 A is rich of L-shell transitions of Mg, Si, S, and Ar, and M-shell transitions of Fe. The velocity dispersion decreases with increasing ionization parameter, as deduced from these long wavelength lines and the Fe-L shell lines.Comment: 12 pages, 11 figures, accepted for publication in Astronomy and Astrophysic