The nearby population of M dwarfs with WISE: A search for warm circumstellar dust

Circumstellar debris disks are important because of their connection to planetary systems. An efficient way to identify these systems is through their infrared excess. Most studies so far concentrated on early-type or solar-type stars, but less effort has gone into investigating M dwarfs. We characterize the mid-infrared photometric behavior of M dwarfs and search for infrared excess in nearby M dwarfs taken from the volume-limited RECONS sample using data from the WISE satellite and the 2MASS catalog. Our sample consists of 85 sources encompassing 103 M dwarfs. We derive empirical infrared colors from these data and discuss their errors. Based on this, we check the stars for infrared excess and discuss the minimum excess we would be able to detect. Other than the M8.5 dwarf SCR 1845-6357 A, where the excess is produced by a known T6 companion, we detect no excesses in any of our sample stars. The limits we derive for the 22um excess are slightly higher than the usual detection limit of 10-15% for Spitzer studies, but including the [12]-[22] color in our analysis allows us to derive tight constraints on the fractional dust luminosity L_dust/L_star. We show that this result is consistent with M dwarf excesses in the mid-inrared being as frequent as excesses around earlier-type stars. The low detection rate could be an age effect. We also present a tentative excess detection at 22um around the known cold debris disk M dwarf AU Mic, which is not part of our statistical sample. There is still no clear detection of a mid-infrared excess around any old (>30 Myr) main-sequence M dwarf. It is unclear whether this is due to a different dust evolution around M dwarfs or whether this is an age effect combined with the diffculties involved in searching M dwarfs for infrared excesses. A significantly larger sample of well-studied M dwarfs is required to solve this question.Comment: Accepted for publication in A&A, 15 pages, 7 figure

Bayesian Inverse Regression and Discrimination: An Application of Credibility Theory

Many measurement problems can be formulated as follows: a certain linear relationship between two variables is to be estimated by using pairs of input and output data; the value of an unknown input variable is then estimated, given an observation of the corresponding output variable. This problem is often referred to as inverse regression or discrimination. In this paper, we formulate a general Bayesian calibration and measurement model for this problem, in which prior information is assumed to be available on the relationship parameters, the possible values of the unknown input, and the output observation error. Simplified and easily interpreted formulae for estimating the posterior mean and variance of the input are then developed using the methods of credibility theory, a linearized Bayesian analysis developed originally for insurance estimation problems. A numerical example of the calibration of a calorimeter to measure nuclear material is given

Systems Aspects of Environmental Accountability

Human activities have increased in such a way that there now exists the danger that some global balances will be disturbed. As a result, there is today a widespread effort to get precise knowledge about these balances themselves as well as about the consequences of possible disturbances in these balances. Because of their magnitude, these problems are inter-related with other problems. Additionally, effects which were considered earlier to be side effects become important. All this means that for the treatment of these problems a systems approach seems necessary. This paper recommends use of the general concept of material accountability for the analysis and treatment of these problems. This has already been proposed by different groups. The reason it is emphasized here is that the material accountability concept has proven extremely valuable in the establishment of the IAEA safeguards system for nuclear material in the peaceful nuclear industry. It is especially the organization of this system in the plant operator's responsibility (generation and reporting of source data for material balance) and in the safeguards authority's responsibility (verification of these data by means of independent measurements) which allowed the acceptance of this system on a broad international scale and which GROSSO MODO could serve as an example for any future global monitoring system. In the first part of this paper, examples for balances existing in nature are given: oxygen, carbon dioxide, radiation balance of the earth atmosphere system. Models for these balances and their disturbances as well as the respective measurements are reported. In the second part we have tried to explain why the treatment of these problems necessarily leads into the field of systems analysis. Special reference is made to the problems outlined in this paper. As an example for this kind of approach and for an existing global control system, the IAEA safeguards system and the mathematical models developed in the course of establishing that system are sketched in the third part. In the fourth part, the economic implications of material accountability are described using the input-output approach; for the example of sulphur it is demonstrated in which way the consequences of constraints -- e.g. in the form of emission standards -- can be analyzed. The paper ends with a schematic representation of the complex interrelations between the basic concepts: material accountability, verification by means of measurements, and economic implications

Material Accountability and Its Verification: A Special Example of Multivariate Statistical Inference

The IAEA nuclear material safeguards system consists basically of two different parts. One is the data verification scheme: the operators of nuclear plants report all relevant data on nuclear material processed in the plant to the safeguards authority. These data are then verified by the safeguards authority with independent measurements. The other part is the material accountability scheme: in case there are no significant differences between the operator's and the safeguards authority's data, all of the operator's data are taken for the nuclear material balance establishment. The purpose of this paper is to evaluate the overall probability of detection of this system in case someone tries to divert material. This evaluation takes into account the different diversion strategies available. It is complicated because the two decision functions on which the evaluation is based -- the difference between operator's and inspector's data and the difference between book and physical inventory -- are stochastically dependent. Exact formulas are derived and applied to a realistic case; it is shown that with a good approximation, one may neglect the correlation and thus, use simplified formulas

Game Theoretical Treatment of Material Accountability Problems: Part II

In a previous paper, the optimal strategy for an inspection authority which has to safeguard material on the basis of material accountability principles has been determined with game theoretical methods: Sets of reasonable inspection and diversion strategies have been defined, and a saddlepoint of the overall probability of detection for n inventory periods during the reference time under consideration has been determined. In this paper the problem of the appropriate choice of the number of inventory periods per reference time has been analyzed: it has been shown that the overall probability of detection in the case of one inventory period per reference time is always larger than that in the case of n inventory periods for n>1, and further it has been shown in which way this result is reflected in the expected detection time

A Game Theoretic Framework for Dynamic Standard Setting Procedures

This paper presents a game-theoretic approach to modeling environmental standard setting procedures under specific consideration of the dynamic conflict situation in environmental decisions. Three idealized decision units are considered, the regulator, producer and impactee units: the regulator has to fix the standard. This standard causes a financial burden to the producer, who releases pollutants to the environment. By means of the standard the impactee has to be protected against this pollution. The starting point is a multistage model for a non-cooperative three person game. After the description of this model the range of its application is indicated by the cases of North Sea oil, sulphur dioxide, carbon dioxide, and noise. Since any game-theoretic analysis includes the choice of a solution concept, a class of concepts is discussed. The last part of the paper contains a brief survey of the results of two multistage cases where the relevance of the solution concepts is demonstrated

Application of Credibility Theory to Material Accountability Verification

The nuclear materials safeguards system of the International Atomic Energy Agency (IAEA) in Vienna consists of two parts: the verification of the material flow and inventory data reported by the operator of a nuclear plant; the establishment of a material balance at the end of an inventory period with the help of the operator's reported data, which means that the book inventory (initial physical inventory plus receipts minus shipments) is compared with the ending physical inventory. By definition it is necessary that the plant operator maintains a complete measurement system for all nuclear materials processed in the plant. In this paper, we consider an alternative inspection scheme which is based on material accountability too, but which does not make use of the data reported by the operator. Contrary to the IAEA safeguards system, the material balance in this system is closed only with the help of the data observed by the inspection team itself. Such a system could be important in situations where there is no reason for a plant operator to maintain a complicated measurement system, or where, for some reason, the records are not available. It is clear that if the inspection team cannot measure the data of all material batches processed in the plant under consideration (e.g. if the inspection budget or time is limited), then some prior information about the average material contents of the different batches as well as the batch-to-batch variation have to be used. Therefore, a Bayesian approach seems to be natural for the treatment of problems of this kind. On the other hand, this prior information will not be very detailed, and so we will use the principles of credibility theory where only the first two moments of the prior distribution have to be known. In this paper, we first consider only one class of material, and then R different classes (inputs, outputs, etc.) with the problem of material balance closure. Finally we discuss the problem of optimization of a given inspection effort. As the batch-to-batch variation of the true material contents within one class normally is much larger than the measurement variance, we will neglect the measurement errors here; they could easily be taken into account, if necessary

The Carbon Cycle of the Earth - A Material Balance Approach

In this paper an idealized model of the carbon cycle of the earth has been analyzed. The model consists of four boxes (atmosphere, biosphere, surface layer of the oceans, and deep sea) and the carbon cycle is described as a flow of the carbon through the four boxes. The mathematical analysis, using a discrete time formalism, is easily generalized to models with more boxes. The results of the analysis are applied to several practical problems. Consistency checks of data on inventories and transition coefficients reported in the literature are made, and the influence of disturbances of the cycle (especially the addition of carbon dioxide to the atmosphere by burning fossil fuels) with respect to their sizes and time scales is discussed