Bayesian time series analysis of terrestrial impact cratering

Giant impacts by comets and asteroids have probably had an important influence on terrestrial biological evolution. We know of around 180 high velocity impact craters on the Earth with ages up to 2400Myr and diameters up to 300km. Some studies have identified a periodicity in their age distribution, with periods ranging from 13 to 50Myr. It has further been claimed that such periods may be causally linked to a periodic motion of the solar system through the Galactic plane. However, many of these studies suffer from methodological problems, for example misinterpretation of p-values, overestimation of significance in the periodogram or a failure to consider plausible alternative models. Here I develop a Bayesian method for this problem in which impacts are treated as a stochastic phenomenon. Models for the time variation of the impact probability are defined and the evidence for them in the geological record is compared using Bayes factors. This probabilistic approach obviates the need for ad hoc statistics, and also makes explicit use of the age uncertainties. I find strong evidence for a monotonic decrease in the recorded impact rate going back in time over the past 250Myr for craters larger than 5km. The same is found for the past 150Myr when craters with upper age limits are included. This is consistent with a crater preservation/discovery bias modulating an otherwise constant impact rate. The set of craters larger than 35km (so less affected by erosion and infilling) and younger than 400Myr are best explained by a constant impact probability model. A periodic variation in the cratering rate is strongly disfavoured in all data sets. There is also no evidence for a periodicity superimposed on a constant rate or trend, although this more complex signal would be harder to distinguish.Comment: Minor typos corrected in arXiv v2. Erratum (minor notation corrections) corrected in arXiv v3. (Erratum available from http://www.mpia-hd.mpg.de/~calj/craterTS_erratum.pdf

Selfgravitating Gas Spheres in a Box and Relativistic Clusters: Relation between Dynamical and Thermodynamical Stability

We derive a variational principle for the dynamical stability of a cluster as a gas sphere in a box. Newtonian clusters are always dynamically stable and, for relativistic clusters, the relation between dynamical and thermodynamical instabilities is analyzed. The boundaries between dynamically and thermodynamically stable and unstable models are found numerically for relativistic stellar systems with different cut off parameters. A criterion based on binding energy curve is used for determination of the boundary of dynamical stability.Comment: 10 figure

Tropospheric aerosol as a reactive intermediate

In tropospheric chemistry, secondary organic aerosol (SOA) is deemed an end product. Here, on the basis of new evidence, we make the case that SOA is a key reactive intermediate. We present laboratory results on the catalysis by carboxylate anions of the disproportionation of NO_2 ‘on water’: 2NO_2 + H_2O = HONO + NO_3^− + H^+ (R1), and supporting quantum chemical calculations, which we apply to reinterpret recent reports on (i) HONO daytime source strengths vis-à-vis SOA anion loadings and (ii) the weak seasonal and latitudinal dependences of NO_x decay kinetics over several megacities. HONO daytime generation via R1 should track sunlight because it is generally catalyzed by the anions produced during the photochemical oxidation of pervasive gaseous pollutants. Furthermore, by proceeding on the everpresent substrate of aquated airborne particulates, R1 can eventually overtake the photolysis of NO_2: NO_2 + hν = NO + O(^3P) (R2), at large zenith angles. Thus, since R1 leads directly to ˙OH-radical generation via HONO photolysis: HONO + hν = NO + ˙OH, whereas the path initiated by R2 is more circuitous and actually controlled by the slower photolysis of O_3: O_3 + hν (+H_2O) = O_2 + 2˙OH, the competition between R1 and R2 provides a mechanistic switch that buffers ˙OH concentrations and NO_2 decay (via R1 and/or NO_2^+ ˙OH = HNO_3) from actinic flux variations

Multi--Pressure Polytropes as Models for the Structure and Stability of Molecular Clouds. I. Theory

Molecular clouds are supported by thermal pressure, magnetic pressure, and turbulent pressure. Each of these can be modeled with a polytropic equation of state, so that overall the total pressure is the sum of the individual components. We model the turbulent pressure as being due to a superposition of Alfven waves. The theory of polytropes is generalized to allow for the flow of entropy in response to a perturbation, as expected for the entropy associated with wave pressure. The equation of state of molecular clouds is "soft", so that the properties of the clouds are generally governed by the conditions at the surface. In general, the polytropes are not isentropic, and this permits large density and pressure drops to occur between the center and the edge of the polytropes, as is observed.Comment: Submitted to ApJ with 10 figure

Anion-Catalyzed Dissolution of NO_2 on Aqueous Microdroplets

Fifty-seven years after NOx (NO + NO_2) were identified as essential components of photochemical smog, atmospheric chemical models fail to correctly predict •OH/HO_2• concentrations under NO_x-rich conditions. This deficiency is due, in part, to the uncertain rates and mechanism for the reactive dissolution of NO_2(g) (2NO_2 + H_2O = NO_3^− + H^+ + HONO) in fog and aerosol droplets. Thus, state-of-the-art models parametrize the uptake of NO_2 by atmospheric aerosol from data obtained on “deactivated tunnel wall residue”. Here, we report experiments in which NO_3^− production on the surface of microdroplets exposed to NO_2(g) for 1 ms is monitored by online thermospray mass spectrometry. NO_2 does not dissolve in deionized water (NO_3^− signals below the detection limit) but readily produces NO_3^− on aqueous NaX (X = Cl, Br, I) microdroplets with NO_2 uptake coefficients γ that vary nonmonotonically with electrolyte concentration and peak at γ_(max) ~ 10^(−4) for [NaX] ~ 1 mM, which is >10^3 larger than that in neat water. Since I^− is partially oxidized to I_2•^− in this process, anions seem to capture NO2(g) into X−NO_2•^− radical anions for further reaction at the air/water interface. By showing that γ is strongly enhanced by electrolytes, these results resolve outstanding discrepancies between previous measurements in neat water versus NaCl-seeded clouds. They also provide a general mechanism for the heterogeneous conversion of NO_2(g) to (NO_3^− + HONO) on the surface of aqueous media

Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method

We complete classical investigations concerning the dynamical stability of an infinite homogeneous gaseous medium described by the Euler-Poisson system or an infinite homogeneous stellar system described by the Vlasov-Poisson system (Jeans problem). To determine the stability of an infinite homogeneous stellar system with respect to a perturbation of wavenumber k, we apply the Nyquist method. We first consider the case of single-humped distributions and show that, for infinite homogeneous systems, the onset of instability is the same in a stellar system and in the corresponding barotropic gas, contrary to the case of inhomogeneous systems. We show that this result is true for any symmetric single-humped velocity distribution, not only for the Maxwellian. If we specialize on isothermal and polytropic distributions, analytical expressions for the growth rate, damping rate and pulsation period of the perturbation can be given. Then, we consider the Vlasov stability of symmetric and asymmetric double-humped distributions (two-stream stellar systems) and determine the stability diagrams depending on the degree of asymmetry. We compare these results with the Euler stability of two self-gravitating gaseous streams. Finally, we determine the corresponding stability diagrams in the case of plasmas and compare the results with self-gravitating systems

Vertical distribution of Galactic disk stars: III. The Galactic disk surface mass density from red clump giants

We used red clump stars to measure the surface mass density of the Galactic disk in the solar neighbourhood. High resolution spectra of red clump stars towards the NGP have been obtained with the ELODIE spectrograph at OHP for Tycho-2 selected stars, and nearby Hipparcos counterparts were also observed. We determined their distances, velocities, and metallicities to measure the gravitational force law perpendicular to the Galactic plane. As in most previous studies, we applied one-parameter models of the vertical gravitational potential. We obtained a disk surface mass density within 1.1kpc of the Galactic plane, Sigma_{1.1kpc}=64+/-5 Msun_pc^{-2}, with an excellent formal accuracy, however we found that such one-parameter models can underestimate the real uncertainties. Applying two-parameter models, we derived more realistic estimates of the total surface mass density within 800pc from the Galactic plane, Sigma_{0.8kpc}=57-66 Msun pc^{-2}, and within 1.1kpc, Sigma{1.1kpc}=57-79 Msun pc^{-2}. This can be compared to literature estimates of \sim40 Msun pc^{-2} in stars and to 13 Msun pc^{-2} in the less accurately measured ISM contribution. We conclude that there is no evidence of large amounts of dark matter in the disk and, furthermore, that the dark matter halo is round or not vey much flattened. A by-product of this study is the determination of the half period of oscillation by the Sun through the Galactic plane, 42+/-2Myr, which cannot be related to the possible period of large terrestrial impact craters \sim 33-37Myr.Comment: accepte

Habitable Zones in the Universe

Habitability varies dramatically with location and time in the universe. This was recognized centuries ago, but it was only in the last few decades that astronomers began to systematize the study of habitability. The introduction of the concept of the habitable zone was key to progress in this area. The habitable zone concept was first applied to the space around a star, now called the Circumstellar Habitable Zone. Recently, other, vastly broader, habitable zones have been proposed. We review the historical development of the concept of habitable zones and the present state of the research. We also suggest ways to make progress on each of the habitable zones and to unify them into a single concept encompassing the entire universe.Comment: 71 pages, 3 figures, 1 table; to be published in Origins of Life and Evolution of Biospheres; table slightly revise