Modeling molecular hyperfine line emission

In this paper we discuss two approximate methods previously suggested for modeling hyperfine spectral line emission for molecules whose collisional transitions rates between hyperfine levels are unknown. Hyperfine structure is seen in the rotational spectra of many commonly observed molecules such as HCN, HNC, NH3, N2H+, and C17O. The intensities of these spectral lines can be modeled by numerical techniques such as Lambda-iteration that alternately solve the equations of statistical equilibrium and the equation of radiative transfer. However, these calculations require knowledge of both the radiative and collisional rates for all transitions. For most commonly observed radio frequency spectral lines, only the net collisional rates between rotational levels are known. For such cases, two approximate methods have been suggested. The first method, hyperfine statistical equilibrium (HSE), distributes the hyperfine level populations according to their statistical weight, but allows the population of the rotational states to depart from local thermodynamic equilibrium (LTE). The second method, the proportional method approximates the collision rates between the hyperfine levels as fractions of the net rotational rate apportioned according to the statistical degeneracy of the final hyperfine levels. The second method is able to model non-LTE hyperfine emission. We compare simulations of N2H+ hyperfine lines made with approximate and more exact rates and find that satisfactory results are obtained.Comment: 34 pages. Pages 22-34 are data tables. For ApJ

Indentation plasticity and fracture in silicon

Measurements of the ductile-brittle transition temperature of heavily doped silicon were carried out using indentation techniques. Diamond pyramid hardness tests were performed on the (100) face of heavily doped N-type and P-type and intrinsic silicon single crystals. Tests were performed over the range 200 C to 850 C and loads of 100 to 500 g were used. Samples were subsequently etched to reveal dislocation rosettes produced by indentation. Intrinsic silicon underwent a ductile-brittle transition at 660 C, P-type at 645 C and N-type at 625 C. Hardness values varied from 1.1 GPa at 700 C to 11.7 GPa at 200 C. Significant effects of hardness on doping were present only at the highest temperatures. Lower loads generally produced higher hardness but load did not affect the Ductile-Brittle Transition Temperature (DBTT). Fracture toughness values ranged from 0.9 MPa m(1/2) at 200 C to 2.75 MPa m(1/2) near the DBTT. Doping did not affect the fracture toughness of silicon. P-type doping increased the size of dislocation rosettes observed after indentation, but N-type did not, in contradiction of the expected results. Results are discussed in terms of the effect of doping on the dislocation mobility in silicon

Polarization of the \lya Halos Around Sources Before Cosmological Reionization

In Loeb & Rybicki (1999; paper I) it was shown that before reionization, the scattering of \lya photons from a cosmological source might lead to a fairly compact ($\sim 15''$) \lya halo around the source. Observations of such halos could constrain the properties of the neutral intergalactic medium (IGM), and in particular yield the cosmological density parameters of baryons and matter on scales where the Hubble flow is unperturbed. Paper I did not treat the polarization of this scattered radiation, but did suggest that the degree of such polarization might be large. In this Letter we report on improved calculations for these \lya halos, now accounting for the polarization of the radiation field. The polarization is linear and is oriented tangentially to the projected displacement from the center of the source. The degree of polarization is found to be 14% at the core radius, where the intensity has fallen to half of the central value. It rises to 32% and 45% at the radii where the intensity has fallen to one-tenth and one-hundreth of the central intensity, respectively. At larger radii the degree of polarization rises further, asymptotically to 60%. Such high values of polarization should be easily observable and provide a clear signature of the phenomenon of \lya halos surrounding sources prior to reionization.Comment: 8 pages, 2 Postscript figures, accepted by Astrophysical Journal Letters; some typos corrected; added two paragraphs at the end of section 3 concerning detectability of Lyman alpha halo

Magnification Ratio of the Fluctuating Light in Gravitational Lens 0957+561

Radio observations establish the B/A magnification ratio of gravitational lens 0957+561 at about 0.75. Yet, for more than 15 years, the optical magnfication ratio has been between 0.9 and 1.12. The accepted explanation is microlensing of the optical source. However, this explanation is mildly discordant with (i) the relative constancy of the optical ratio, and (ii) recent data indicating possible non-achromaticity in the ratio. To study these issues, we develop a statistical formalism for separately measuring, in a unified manner, the magnification ratio of the fluctuating and constant parts of the light curve. Applying the formalism to the published data of Kundi\'c et al. (1997), we find that the magnification ratios of fluctuating parts in both the g and r colors agrees with the magnification ratio of the constant part in g-band, and tends to disagree with the r-band value. One explanation could be about 0.1 mag of consistently unsubtracted r light from the lensing galaxy G1, which seems unlikely. Another could be that 0957+561 is approaching a caustic in the microlensing pattern.Comment: 12 pages including 1 PostScript figur

The Time Development of a Resonance Line in the Expanding Universe

The time-dependent spectral profile of a resonance line in a homogeneous expanding medium is studied by numerically solving an improved Fokker-Planck diffusion equation. The solutions are used to determine the time required to reach a quasi-static solution near the line center. A simple scaling law for this relaxation time is derived and is fitted to the numerical results. The results are applied to the case of Lyman alpha scattering during primordial recombination of hydrogen. For a wide range of cosmological models it is found that the relaxation times are smaller than the recombination timescale, although not by a very large factor. Thus the standard assumption of a quasi-static solution in cosmological recombination calculations is reasonably valid, and should not cause substantial errors in the solutions.Comment: 20 pages text and 10 figures, in 30 pages of uuencoded, compressed postscript. CFA preprint no. 375

Scattered Lyman-alpha Radiation Around Sources Before Cosmological Reionization

The spectra of the first galaxies and quasars in the Universe should be strongly absorbed shortward of their rest-frame Lyman-alpha wavelength by neutral hydrogen (HI) in the intervening intergalactic medium. However, the Lyman-alpha line photons emitted by these sources are not eliminated but rather scatter until they redshift out of resonance and escape due to the Hubble expansion of the surrounding intergalactic HI. We calculate the resulting brightness distribution and the spectral shape of the diffuse Lyman-alpha line emission around high redshift sources, before the intergalactic medium was reionized. Typically, the Lyman-alpha photons emitted by a source at z=10 scatter over a characteristic angular radius of order 15 arcseconds around the source and compose a line which is broadened and redshifted by about a thousand km/s relative to the source. The scattered photons are highly polarized. Detection of the diffuse Lyman-alpha halos around high redshift sources would provide a unique tool for probing the neutral intergalactic medium before the epoch of reionization. On sufficiently large scales where the Hubble flow is smooth and the gas is neutral, the Lyman-alpha brightness distribution can be used to determine the cosmological mass densities of baryons and matter.Comment: 21 pages, 5 Postscript figures, accepted by ApJ; figures 1--3 corrected; new section added on the detectability of Lyman alpha halos; conclusions update