The frequency of window damage caused by bolide airbursts: A quarter century case study

We have empirically estimated how often fireball shocks produce overpressure (∆P) at the ground sufficient to damage windows. Our study used a numerical entry model to estimate the energy deposition and shock production for a suite of 23 energetic fireballs reported by U.S. Government sensors over the last quarter century. For each of these events, we estimated the peak ∆P on the ground and the ground area above ∆P thresholds of 200 and 500 Pa where light and heavy window damage, respectively, are expected. Our results suggest that at the highest ∆P, it is the rare, large fireballs (such as the Chelyabinsk fireball) which dominate the long-term areal ground footprints for heavy window damage. The height at the fireball peak brightness and the fireball entry angle contribute to the variance in ground ∆P, with lower heights and shallower angles producing larger ground footprints and more potential damage. The effective threshold energy for fireballs to produce heavy window damage is ~5–10 kT; such fireballs occur globally once every 1–2 years. These largest annual bolide events, should they occur over a major urban center with large numbers of windows, can be expected to produce economically significant window damage. However, the mean frequency of heavy window damage (∆P above 500 Pa) from fireball shock waves occurring over urban areas is estimated to be approximately once every 5000 yr. Light window damage (∆P above 200 Pa) is expected every ~600 yr.     

Cepheid parallaxes and the Hubble constant

Revised Hipparcos parallaxes for classical Cepheids are analysed together with 10 Hubble Space Telescope ( HST )-based parallaxes. In a reddening-free V , I relation we find that the coefficient of log  P is the same within the uncertainties in our Galaxy as in the Large Magellanic Cloud (LMC), contrary to some previous suggestions. Cepheids in the inner region of NGC 4258 with near solar metallicities confirm this result. We obtain a zero-point for the reddening-free relation and apply it to the Cepheids in galaxies used by Sandage et al. to calibrate the absolute magnitudes of Type Ia supernova (SNIa) and to derive the Hubble constant. We revise their result for H ₀ from 62 to 70 ± 5 km s⁻¹ Mpc⁻¹. The Freedman et al. value is revised from 72 to 76 ± 8 km s⁻¹ Mpc⁻¹. These results are insensitive to Cepheid metallicity corrections. The Cepheids in the inner region of NGC 4258 yield a modulus of 29.22 ± 0.03 (int.) compared with a maser-based modulus of 29.29 ± 0.15. Distance moduli for the LMC, uncorrected for any metallicity effects, are 18.52 ± 0.03 from a reddening-free relation in V , I ; 18.47 ± 0.03 from a period–luminosity relation at K ; 18.45 ± 0.04 from a period–luminosity–colour relation in J , K . Adopting a metallicity correction in V , I from Macri et al. leads to a true LMC modulus of 18.39 ± 0.05.     

Oxygen and carbon isotope ratios in the martian atmosphere

Oxygen and carbon isotope ratios in the martian CO₂ are key values to study evolution of volatiles on Mars. The major problems in spectroscopic determinations of these ratios on Mars are uncertainties associated with: (1) equivalent widths of the observed absorption lines, (2) line strengths in spectroscopic databases, and (3) thermal structure of the martian atmosphere during the observation. We have made special efforts to reduce all these uncertainties. We observed Mars using the Fourier Transform Spectrometer at the Canada–France–Hawaii Telescope. While the oxygen and carbon isotope ratios on Mars were byproducts in the previous observations, our observation was specifically aimed at these isotope ratios. We covered a range of 6022 to 6308 cm⁻¹ with the highest resolving power of ν/δν=3.5×10⁵ and a signal-to-noise ratio of 180 in the middle of the spectrum. The chosen spectral range involves 475 lines of the main isotope, 184 lines of ¹³CO₂, 181 lines of CO¹⁸O, and 119 lines of CO¹⁷O. (Lines with strengths exceeding 10⁻²⁷ cm at 218 K are considered here.) Due to the high spectral resolution, most of the lines are not blended. Uncertainties of retrieved isotope abundances are in inverse proportion to resolving power, signal-to-noise ratio, and square root of the number of lines. Laboratory studies of the CO₂ isotope spectra in the range of our observation achieved an accuracy of 1% in the line strengths. Detailed observations of temperature profiles using MGS/TES and data on temperature variations with local time from two GCMs are used to simulate each absorption line at various heights in each part of the instrument field of view and then sum up the results. Thermal radiation of Mars' surface and atmosphere is negligible in the chosen spectral range, and this reduces errors associated with uncertainties in the thermal structure on Mars. Using a combination of all these factors, the highest accuracy has been achieved in measuring the CO₂ isotope ratios: ¹³C/¹²C = 0.978 ± 0.020 and ¹⁸O/¹⁶O = 1.018 ± 0.018 times the terrestrial standards. Heavy isotopes in the atmosphere are enriched by nonthermal escape and sputtering, and depleted by fractionation with solid-phase reservoirs. The retrieved ratios show that isotope fractionation between CO₂ and oxygen and carbon reservoirs in the solid phase is almost balanced by nonthermal escape and sputtering of O and C from Mars.     

Bodily tides near spin–orbit resonances

Spin–orbit coupling can be described in two approaches. The first method, known as the “MacDonald torque”, is often combined with a convenient assumption that the quality factor Q is frequency-independent. This makes the method inconsistent, because derivation of the expression for the MacDonald torque tacitly fixes the rheology of the mantle by making Q scale as the inverse tidal frequency. Spin–orbit coupling can be treated also in an approach called “the Darwin torque”. While this theory is general enough to accommodate an arbitrary frequency-dependence of Q, this advantage has not yet been fully exploited in the literature, where Q is often assumed constant or is set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent to a corrected version of the MacDonald torque. However neither a constant nor an inverse-frequency Q reflect the properties of realistic mantles and crusts, because the actual frequency-dependence is more complex. Hence it is necessary to enrich the theory of spin–orbit interaction with the right frequency-dependence. We accomplish this programme for the Darwin-torque-based model near resonances. We derive the frequency-dependence of the tidal torque from the first principles of solid-state mechanics, i.e., from the expression for the mantle’s compliance in the time domain. We also explain that the tidal torque includes not only the customary, secular part, but also an oscillating part. We demonstrate that the lmpq term of the Darwin–Kaula expansion for the tidal torque smoothly passes zero, when the secondary traverses the lmpq resonance (e.g., the principal tidal torque smoothly goes through nil as the secondary crosses the synchronous orbit). Thus, we prepare a foundation for modeling entrapment of a despinning primary into a resonance with its secondary. The roles of the primary and secondary may be played, e.g., by Mercury and the Sun, correspondingly, or by an icy moon and a Jovian planet. We also offer a possible explanation for the “improper” frequency-dependence of the tidal dissipation rate in the Moon, discovered by LLR.     

Diurnal variation of electron density in Saturn’s ionosphere: Model comparisons with Saturn Electrostatic Discharge (SED) observations

Using the Saturn Thermosphere Ionosphere Model (STIM), we present a study of the diurnal variation of electron density, with a focus on comparisons with peak electron densities (N_MAX) inferred from the low-frequency cutoff of radio emission due to lightning in the lower atmosphere, called Saturn Electrostatic Discharges (SEDs). It is demonstrated that photochemistry in Saturn’s ionosphere cannot reproduce the SED-inferred diurnal variation in N_MAX unless additional production and loss sources outside of the current best estimates are considered. Additional explanations of the SED-inferred diurnal variation of N_MAX are presented and analyzed, such as the possibility that the low-frequency cutoff seen in SEDs is due to the presence of sharp low-altitude layers of plasma, as frequently seen in radio occultation measurements. Finally, we outline the observational constraints that must be fulfilled by any candidate explanations of the SED-inferred diurnal variation of N_MAX.