We report laboratory measurements of the absorption coefficient of solid para-H2, within the wavelength range from 1 to 16.7 micron, at high spectral resolution. In addition to the narrow rovibrational lines of H2 which are familiar from gas phase sp
ectroscopy, the data manifest double transitions and broad phonon branches that are characteristic specifically of hydrogen in the solid phase. These transitions are of interest because they provide a spectral signature which is independent of the impurity content of the matrix. We have used our data, in combination with a model of the ultraviolet absorptions of the H2 molecule, to construct the dielectric function of solid para-H2 over a broad range of frequencies. Our results will be useful in determining the electromagnetic response of small particles of solid hydrogen. The dielectric function makes it clear that pure H2 dust would contribute to IR extinction predominantly by scattering starlight, rather than absorbing it, and the characteristic IR absorption spectrum of the hydrogen matrix itself will be difficult to observe.
We develop a theory of ``ad hoc Chern characters for twisted matrix factorizations associated to a scheme $X$, a line bundle ${mathcal L}$, and a regular global section $W in Gamma(X, {mathcal L})$. As an application, we establish the vanishing, in
certain cases, of $h_c^R(M,N)$, the higher Herbrand difference, and, $eta_c^R(M,N)$, the higher codimensional analogue of Hochsters theta pairing, where $R$ is a complete intersection of codimension $c$ with isolated singularities and $M$ and $N$ are finitely generated $R$-modules. Specifically, we prove such vanishing if $R = Q/(f_1, dots, f_c)$ has only isolated singularities, $Q$ is a smooth $k$-algebra, $k$ is a field of characteristic $0$, the $f_i$s form a regular sequence, and $c geq 2$.
Hochsters theta invariant is defined for a pair of finitely generated modules on a hypersurface ring having only an isolated singularity. Up to a sign, it agrees with the Euler invariant of a pair of matrix factorizations. Working over the complex
numbers, Buchweitz and van Straten have established an interesting connection between Hochsters theta invariant and the classical linking form on the link of the singularity. In particular, they establish the vanishing of the theta invariant if the hypersurface is even-dimensional by exploiting the fact that the (reduced) cohomology of the Milnor fiber is concentrated in odd degrees in this situation. In this paper, we give purely algebra
Cyclic spectroscopy is a signal processing technique that was originally developed for engineering applications and has recently been introduced into the field of pulsar astronomy. It is a powerful technique with many attractive features, not least o
f which is the explicit rendering of information about the relative phases in any filtering imposed on the signal, thus making holography a more straightforward proposition. Here we present methods for determining optimum estimates of both the filter itself and the statistics of the unfiltered signal, starting from a measured cyclic spectrum. In the context of radio pulsars these quantities tell us the impulse response of the interstellar medium and the intrinsic pulse profile. We demonstrate our techniques by application to 428 MHz Arecibo data on the millisecond pulsar B1937+21, obtaining the pulse profile free from the effects of interstellar scattering. As expected, the intrinsic profile exhibits main- and inter-pulse components that are narrower than they appear in the scattered profile; it also manifests some weak, but sharp features that are revealed for the first time at low frequency. We determine the structure of the received electric-field envelope as a function of delay and Doppler-shift. Our delay-Doppler image has a high dynamic-range and displays some pronounced, low-level power concentrations at large delays. These concentrations imply strong clumpiness in the ionized interstellar medium, on AU size-scales, which must adversely affect the timing of B1937+21.
We consider the possibility that solid molecular hydrogen is present in interstellar space. If so cosmic-rays and energetic photons cause ionisation in the solid leading to the formation of H6+. This ion is not produced by gas-phase reactions and its
radiative transitions therefore provide a signature of solid H2 in the astrophysical context. The vibrational transitions of H6+ are yet to be observed in the laboratory, but we have characterised them in a quantum-theoretical treatment of the molecule; our calculations include anharmonic corrections, which are large. Here we report on those calculations and compare our results with astronomical data. In addition to the H6+ isotopomer, we focus on the deuterated species (HD)3+ which is expected to dominate at low ionisation rates as a result of isotopic condensation reactions. We can reliably predict the frequencies of the fundamental bands for five modes of vibration. For (HD)3+ all of these are found to lie close to some of the strongest of the pervasive mid-infrared astronomical emission bands, making it difficult to exclude hydrogen precipitates on observational grounds. By the same token these results suggest that (HD)3+ could be the carrier of the observed bands. We consider this possibility within the broader picture of ISM photo-processes and we conclude that solid hydrogen may indeed be abundant in astrophysical environments.
A small number of quasars exhibit interstellar scintillation on time-scales less than an hour; their scintillation patterns are all known to be anisotropic. Here we consider a totally anisotropic model in which the scintillation pattern is effectivel
y one-dimensional. For the persistent rapid scintillators J1819+3845 and PKS1257-326 we show that this model offers a good description of the two-station time-delay measurements and the annual cycle in the scintillation time-scale. Generalising the model to finite anisotropy yields a better match to the data but the improvement is not significant and the two additional parameters which are required to describe this model are not justified by the existing data. The extreme anisotropy we infer for the scintillation patterns must be attributed to the scattering medium rather than a highly elongated source. For J1819+3845 the totally anisotropic model predicts that the particular radio flux variations seen between mid July and late August should repeat between late August and mid November, and then again between mid November and late December as the Earth twice changes its direction of motion across the scintillation pattern. If this effect can be observed then the minor-axis velocity component of the screen and the orientation of that axis can both be precisely determined. In reality the axis ratio is finite, albeit large, and spatial decorrelation of the flux pattern along the major axis may be observable via differences in the pairwise fluxes within this overlap region; in this case we can also constrain both the major-axis velocity component of the screen and the magnitude of the anisotropy.
