Partial Hasse invariants on splitting models of Hilbert modular varieties

Let $F$ be a totally real field of degree $g$, and let $p$ be a prime number. We construct $g$ partial Hasse invariants on the characteristic $p$ fiber of the Pappas-Rapoport splitting model of the Hilbert modular variety for $F$ with level prime to $p$, extending the usual partial Hasse invariants defined over the Rapoport locus. In particular, when $p$ ramifies in $F$, we solve the problem of lack of partial Hasse invariants. Using the stratification induced by these generalized partial Hasse invariants on the splitting model, we prove in complete generality the existence of Galois pseudo-representations attached to Hecke eigenclasses of paritious weight occurring in the coherent cohomology of Hilbert modular varieties $\mathrm{mod}$ $p^m$, extending a previous result of M. Emerton and the authors which required $p$ to be unramified in $F$.Comment: 24 pages, refereed version, index changed from the previous versio

Ongoing Mass Transfer in the Interacting Galaxy Pair NGC 1409/10

I present two-band HST STIS imaging, and WIYN spectral mapping, of ongoing mass transfer in the interacting galaxy pair NGC 1409/10 (where NGC 1410 is the Seyfert galaxy also catalogued as III Zw 55). Archival snapshot WFPC2 imaging from the survey by Malkan et al. showed a dust feature stretching between the galaxies, apparently being captured by NGC 1409. The new images allow estimates of the mass being transferred and rate of transfer. An absorption lane typically 0.25" (100 pc) wide with a representative optical depth tau_B = 0.2 cuts across the spiral structure of NGC 1410, crosses the 7-kpc projected space between the nuclei, wraps in front of and, at the limits of detection, behind NGC 1409, and becomes a denser (tau_B = 0.4) polar feature around the core of NGC 1409. Combination of extinction data in two passbands allows a crude three-dimensional recovery of the dust structure, supporting the front/back geometry derived from colors and extinction estimates. The whole feature contains of order $10^6$ solar masses in dust, implying about 2x10^7 solar masses of gas, requiring a mass transfer rate averaging ~1 solar mass per year unless we are particularly unlucky in viewing angle. Curiously, this demonstrable case of mass transfer seems to be independent of the occurrence of a Seyfert nucleus, since the Seyfert galaxy in this pair is the donor of the material. Likewise, the recipient shows no signs of recent star formation from incoming gas, although NGC 1410 has numerous luminous young star clusters and widespread H-alpha emission.Comment: 27 pages, 9 figures. Accepted for the Astronomical Journal, March 200

Attosecond Streaking in the Water Window: A New Regime of Attosecond Pulse Characterization

We report on the first streaking measurement of water-window attosecond pulses generated via high harmonic generation, driven by sub-2-cycle, CEP-stable, 1850 nm laser pulses. Both the central photon energy and the energy bandwidth far exceed what has been demonstrated thus far, warranting the investigation of the attosecond streaking technique for the soft X-ray regime and the limits of the FROGCRAB retrieval algorithm under such conditions. We also discuss the problem of attochirp compensation and issues regarding much lower photo-ionization cross sections compared with the XUV in addition to the fact that several shells of target gases are accessed simultaneously. Based on our investigation, we caution that the vastly different conditions in the soft X-ray regime warrant a diligent examination of the fidelity of the measurement and the retrieval procedure.Comment: 14 Pages, 12 figure

Disentangling conical intersection and coherent molecular dynamics in methyl bromide with attosecond transient absorption spectroscopy

Attosecond probing of core-level electronic transitions provides a sensitive tool for studying valence molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy to follow the valence dynamics of strong-field initiated processes in methyl bromide. By probing the 3d core-to-valence transition, we resolve the strong field excitation and ensuing fragmentation of the neutral σ* excited states of methyl bromide. The results provide a clear signature of the non-adiabatic passage of the excited state wavepacket through a conical intersection. We additionally observe competing, strong field initiated processes arising in both the ground state and ionized molecule corresponding to vibrational and spin-orbit motion, respectively. The demonstrated ability to resolve simultaneous dynamics with few-femtosecond resolution presents a clear path forward in the implementation of attosecond XUV spectroscopy as a general tool for probing competing and complex molecular phenomena with unmatched temporal resolution