Atmospheric predictability of the martian atmosphere: from low-dimensional dynamics to operational forecasting?

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The stellar mass-halo mass relation of isolated field dwarfs: a critical test of Λ\LambdaCDM at the edge of galaxy formation

We fit the rotation curves of isolated dwarf galaxies to directly measure the stellar mass-halo mass relation ($M_*-M_{200}$) over the mass range $5 \times 10^5 < M_{*}/{\rm M}_\odot < 10^{8}$. By accounting for cusp-core transformations due to stellar feedback, we find a monotonic relation with little scatter. Such monotonicity implies that abundance matching should yield a similar $M_*-M_{200}$ if the cosmological model is correct. Using the 'field galaxy' stellar mass function from the Sloan Digital Sky Survey (SDSS) and the halo mass function from the $\Lambda$ Cold Dark Matter Bolshoi simulation, we find remarkable agreement between the two. This holds down to $M_{200} \sim 5 \times 10^9$M$_\odot$, and to $M_{200} \sim 5 \times 10^8$M$_\odot$ if we assume a power law extrapolation of the SDSS stellar mass function below $M_* \sim 10^7$M$_\odot$. However, if instead of SDSS we use the stellar mass function of nearby galaxy groups, then the agreement is poor. This occurs because the group stellar mass function is shallower than that of the field below $M_* \sim 10^9$M$_\odot$, recovering the familiar 'missing satellites' and 'too big to fail' problems. Our result demonstrates that both problems are confined to group environments and must, therefore, owe to 'galaxy formation physics' rather than exotic cosmology. Finally, we repeat our analysis for a $\Lambda$ Warm Dark Matter cosmology, finding that it fails at 68% confidence for a thermal relic mass of $m_{\rm WDM} < 1.25$keV, and $m_{\rm WDM} < 2$keV if we use the power law extrapolation of SDSS. We conclude by making a number of predictions for future surveys based on these results.Comment: 22 pages; 2 Tables; 10 Figures. This is the version accepted for publication in MNRAS. Key changes: (i) added substantially more information on the surveys used to measure the stellar mass functions; (ii) added tests of the robustness of our results. Results and conclusions unchanged from previously. Minor typos corrected from previous versio

Dark matter cores all the way down

We use high resolution simulations of isolated dwarf galaxies to study the physics of dark matter cusp-core transformations at the edge of galaxy formation: M200 = 10^7 - 10^9 Msun. We work at a resolution (~4 pc minimum cell size; ~250 Msun per particle) at which the impact from individual supernovae explosions can be resolved, becoming insensitive to even large changes in our numerical 'sub-grid' parameters. We find that our dwarf galaxies give a remarkable match to the stellar light profile; star formation history; metallicity distribution function; and star/gas kinematics of isolated dwarf irregular galaxies. Our key result is that dark matter cores of size comparable to the stellar half mass radius (r_1/2) always form if star formation proceeds for long enough. Cores fully form in less than 4 Gyrs for the M200 = 10^8 Msun and 14 Gyrs for the 10^9 Msun dwarf. We provide a convenient two parameter 'coreNFW' fitting function that captures this dark matter core growth as a function of star formation time and the projected stellar half mass radius. Our results have several implications: (i) we make a strong prediction that if LCDM is correct, then 'pristine' dark matter cusps will be found either in systems that have truncated star formation and/or at radii r > r_1/2; (ii) complete core formation lowers the projected velocity dispersion at r_1/2 by a factor ~2, which is sufficient to fully explain the 'too big to fail problem'; and (iii) cored dwarfs will be much more susceptible to tides, leading to a dramatic scouring of the subhalo mass function inside galaxies and groups.Comment: 20 pages; 9 figures; final version to appear in MNRAS including typos corrected in proo

Reduced-order models of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves

Teleconnection in the martian atmosphere during the 2001 planet-encircling dust storm

Introduction: In July 2001 (Martian year 25), Mars was enshrouded by a thick veil of dust which lasted for several months and obscured the observation of its surface to spacecraft cameras and ground-based telescopes. The emergence and rapid evolution (within a few days) of multiple, isolated, regional dust storms which eventually attained planetary scale extent were observed by NASA’s Mars Global Surveyor (MGS) spacecraft using high resolution camera images and the thermal profiles and dust opacity measurements pro-vided by the Thermal Emission Spectrometer (TES) [1, 2]. We have applied a technique used in Terrestrial meteorology (sequential data assimilation, [3]) to ob-tain a complete, four-dimensional evolution of all the atmospheric variables during the period of this planet-encircling dust storm, even those which were not di-rectly observed by the MGS satellite, such as surface pressure and winds. We assimilated TES nadir-pointing thermal profiles and total dust opacities in a global circulation model of the Martian atmosphere, developed jointly by the University of Oxford and the Open University in the United Kingdom, with the col-laboration of the Laboratoire de Météorologie Dyna-mique in Paris (UK-MGCM) [4, 5, 6]

Recent advances in the development of a European Mars climate model in Oxford

Since the early 1990s, efforts have been under way in Oxford to develop a range of numerical weather and climate prediction models for various studies of the Martian atmosphere and near-surface environment. Early versions of the Oxford model were more in the way of 'process models', aimed at relatively idealised studies e.g. of baroclinic instability[1] and low-level western boundary currents in the cross-equatorial solsticial Hadley circulation[2]. Since the mid-1990s, however, the group in Oxford have worked closely with the modelling group at LMD in Paris to develop a joint suite of more sophisticated and comprehensive numerical models of Mars' atmosphere. This collaboration, partly sponsored in recent years by the European Space Agency in connection with the associated development of a climate database for Mars[3], culminated in a suite of global circulation models[4], in which both groups share a library of parametrisation schemes, but in which the Oxford team use a spectral representation of horizontal fields (in the form of spherical harmonics) and the LMD group use a grid-point finite difference representation. These models were described in some detail by Forget et al.[4], and their preliminary validation and use in the construction of first versions of the European Mars Climate Database by Lewis et al.[3]. In the present report, we will review further developments which have taken place since the latter papers were published. Aspects of these developments which are common to both the LMD and Oxford groups will also be covered in the companion contribution by Forget et al. in this meeting, and so will only be touched on briefly here. Instead, we will concentrate on those advances which are more specific to the Oxford version of the model. In the following sections, we outline the main new developments to the model formulation since 1999. Subsequent sections then describe some recent examples where the new model is being utilised to advance a diverse range of studies of Mars atmospheric science

Wick's Theorem and a New Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems

A new type of perturbation expansion in the mixing $V$ of localized orbitals with a conduction-electron band in the $U\to\infty$ Anderson model is presented. It is built on Feynman diagrams obeying standard rules. The local correlations of the unperturbed system (the atomic limit) are included exactly, no auxiliary particles are introduced. As a test, an infinite-order ladder-type resummation is analytically treated in the Kondo regime, recovering the correct energy scale. An extension to the Anderson-lattice model is obtained via an effective-site approximation through a cumulant expansion in $V$ on the lattice. Relation to treatments in infinite spatial dimensions are indicated.Comment: selfextracting postscript file containing entire paper (10 pages) including 3 figures, in case of trouble contact author for LaTeX-source or hard copies (prep0994

Localization in disordered superconducting wires with broken spin-rotation symmetry

Localization and delocalization of non-interacting quasiparticle states in a superconducting wire are reconsidered, for the cases in which spin-rotation symmetry is absent, and time-reversal symmetry is either broken or unbroken; these are referred to as symmetry classes BD and DIII, respectively. We show that, if a continuum limit is taken to obtain a Fokker-Planck (FP) equation for the transfer matrix, as in some previous work, then when there are more than two scattering channels, all terms that break a certain symmetry are lost. It was already known that the resulting FP equation exhibits critical behavior. The additional symmetry is not required by the definition of the symmetry classes; terms that break it arise from non-Gaussian probability distributions, and may be kept in a generalized FP equation. We show that they lead to localization in a long wire. When the wire has more than two scattering channels, these terms are irrelevant at the short distance (diffusive or ballistic) fixed point, but as they are relevant at the long-distance critical fixed point, they are termed dangerously irrelevant. We confirm the results in a supersymmetry approach for class BD, where the additional terms correspond to jumps between the two components of the sigma model target space. We consider the effect of random $\pi$ fluxes, which prevent the system localizing. We show that in one dimension the transitions in these two symmetry classes, and also those in the three chiral symmetry classes, all lie in the same universality class

Active-distributed temperature sensing to continuously quantify vertical flow in boreholes

We show how a distributed borehole flowmeter can be created from armored Fiber Optic cables with the Active-Distributed Temperature Sensing (A-DTS) method. The principle is that in a flowing fluid, the difference in temperature between a heated and unheated cable is a function of the fluid velocity. We outline the physical basis of the methodology and report on the deployment of a prototype A-DTS flowmeter in a fractured rock aquifer. With this design, an increase in flow velocity from 0.01 to 0.3 m s−1 elicited a 2.5°C cooling effect. It is envisaged that with further development this method will have applications where point measurements of borehole vertical flow do not fully capture combined spatiotemporal dynamics