Protostellar half-life: new methodology and estimates

(Abridged) Protostellar systems evolve from prestellar cores, through the deeply embedded stage and then disk-dominated stage, before they end up on the main sequence. Knowing how much time a system spends in each stage is crucial for understanding how stars and associated planetary systems form, because a key constraint is the time available to form such systems. Equally important is understanding what the spread in these time scales is. The most commonly used method for inferring protostellar ages is to assume the lifetime of one evolutionary stage, and then scale this to the relative number of protostars in the other stages, i.e., assuming steady state. This method does not account for the underlying age distribution and apparent stochasticity of star formation, nor that relative populations are not in steady state. To overcome this, we propose a new scheme where the lifetime of each protostellar stage follows a distribution based on the formalism of sequential nuclear decay. The main assumptions are: Class 0 sources follow a straight path to Class III sources, the age distribution follows a binomial distribution, and the star-formation rate is constant. The results are that the half-life of Class 0, Class I, and Flat sources are (2.4+/-0.2)%, (4.4+/-0.3)%, and (4.3+/-0.4)% of the Class II half-life, respectively, which translates to 47+/-4, 88+/-7, and 87+/-8 kyr, respectively, for a Class II half-life of 2 Myr for protostars in the Gould Belt clouds with more than 100 protostars. The mean age of these clouds is 1.2+/-0.1 Myr, and the star formation rate is (8.3+/-0.5)x10^-4 Msun/yr. The critical parameters in arriving at these numbers are the assumed half-life of the Class II stage, and the assumption that the star-formation rate and half-lives are constant. This method presents a first step in moving from steady-state to non-steady-state solutions of protostellar populations.Comment: Accepted for publication in A&

Modelling diverse root density dynamics and deep nitrogen uptake — a simple approach

We present a 2-D model for simulation of root density and plant nitrogen (N) uptake for crops grown in agricultural systems, based on a modification of the root density equation originally proposed by Gerwitz and Page in J Appl Ecol 11:773–781, (1974). A root system form parameter was introduced to describe the distribution of root length vertically and horizontally in the soil profile. The form parameter can vary from 0 where root density is evenly distributed through the soil profile, to 8 where practically all roots are found near the surface. The root model has other components describing root features, such as specific root length and plant N uptake kinetics. The same approach is used to distribute root length horizontally, allowing simulation of root growth and plant N uptake in row crops. The rooting depth penetration rate and depth distribution of root density were found to be the most important parameters controlling crop N uptake from deeper soil layers. The validity of the root distribution model was tested with field data for white cabbage, red beet, and leek. The model was able to simulate very different root distributions, but it was not able to simulate increasing root density with depth as seen in the experimental results for white cabbage. The model was able to simulate N depletion in different soil layers in two field studies. One included vegetable crops with very different rooting depths and the other compared effects of spring wheat and winter wheat. In both experiments variation in spring soil N availability and depth distribution was varied by the use of cover crops. This shows the model sensitivity to the form parameter value and the ability of the model to reproduce N depletion in soil layers. This work shows that the relatively simple root model developed, driven by degree days and simulated crop growth, can be used to simulate crop soil N uptake and depletion appropriately in low N input crop production systems, with a requirement of few measured parameters

ALMA CO J=6-5 observations of IRAS16293-2422: Shocks and entrainment

Observations of higher-excited transitions of abundant molecules such as CO are important for determining where energy in the form of shocks is fed back into the parental envelope of forming stars. The nearby prototypical and protobinary low-mass hot core, IRAS16293-2422 (I16293) is ideal for such a study. The source was targeted with ALMA for science verification purposes in band 9, which includes CO J=6-5 (E_up/k_B ~ 116 K), at an unprecedented spatial resolution (~0.2", 25 AU). I16293 itself is composed of two sources, A and B, with a projected distance of 5". CO J=6-5 emission is detected throughout the region, particularly in small, arcsecond-sized hotspots, where the outflow interacts with the envelope. The observations only recover a fraction of the emission in the line wings when compared to data from single-dish telescopes, with a higher fraction of emission recovered at higher velocities. The very high angular resolution of these new data reveal that a bow shock from source A coincides, in the plane of the sky, with the position of source B. Source B, on the other hand, does not show current outflow activity. In this region, outflow entrainment takes place over large spatial scales, >~ 100 AU, and in small discrete knots. This unique dataset shows that the combination of a high-temperature tracer (e.g., CO J=6-5) and very high angular resolution observations is crucial for interpreting the structure of the warm inner environment of low-mass protostars.Comment: Accepted for publication in A&A Letter

Investigating Optimal Progress Measures for Verification of the WebSocket Protocol

The sweep-line method is a state space reduction technique formemory-efficient on-the-fly verification of concurrent systems. Themethod relies on a progress measure capturing inherent progress in thesystem under verification to store only fragments of the state space inmemory at a time and thereby reduce peak memory usage. The sweep-line method has been applied to many concurrent systems, but theoptimality of progress measures in terms of the peak number of statesstored has not been investigated. Assessing the optimality of a progressmeasure is important since memory in most cases is the limiting factorin verification using state spaces. We derive lower bounds for the peaknumber states and present initial experimental results on near optimalprogress measures for verification of the IETF WebSocket protocol