Abstract. The concept of topographic steady state has substantially informed our understanding of the relationships between landscapes, tectonics, climate, and lithology. In topographic steady state, erosion rates are equal everywhere, and steepness adjusts to enable equal erosion rates in rocks of different strengths. This conceptual model makes an implicit assumption of vertical contacts between different rock types. Here we hypothesize that landscapes in layered rocks will be driven toward a state of erosional continuity, where retreat rates on either side of a contact are equal in a direction parallel to the contact rather than in the vertical direction. For vertical contacts, erosional continuity is the same as topographic steady state, whereas for horizontal contacts it is equivalent to equal rates of horizontal retreat on either side of a rock contact. Using analytical solutions and numerical simulations, we show that erosional continuity predicts the form of flux steady-state landscapes that develop in simulations with horizontally layered rocks. For stream power erosion, the nature of continuity steady state depends on the exponent, n, in the erosion model. For n = 1, the landscape cannot maintain continuity. For cases where n ≠ 1, continuity is maintained, and steepness is a function of erodibility that is predicted by the theory. The landscape in continuity steady state can be quite different from that predicted by topographic steady state. For n < 1 continuity predicts that channels incising subhorizontal layers will be steeper in the weaker rock layers. For subhorizontal layered rocks with different erodibilities, continuity also predicts larger slope contrasts than in topographic steady state. Therefore, the relationship between steepness and erodibility within a sequence of layered rocks is a function of contact dip. For the subhorizontal limit, the history of layers exposed at base level also influences the steepness–erodibility relationship. If uplift rate is constant, continuity steady state is perturbed near base level, but these perturbations decay rapidly if there is a substantial contrast in erodibility. Though examples explored here utilize the stream power erosion model, continuity steady state provides a general mathematical tool that may also be useful to understand landscapes that develop by other erosion processes.

There is a large observational scatter toward low velocities in the stellar mass Tully-Fisher relation if disturbed and compact objects are included. However, this scatter can be eliminated if one replaces rotation velocity with S 0.5 , a quantity that includes a velocity dispersion term added in quadrature with the rotation velocity. In this work we use a large suite of hydrodynamic N-body galaxy merger simulations to explore a possible mechanism for creating the observed relations. Using mock observations of the simulations, we test for the presence of observational effects and explore the relationship between S 0.5 and intrinsic properties of the galaxies. We find that galaxy mergers can explain the scatter in the TF as well as the tight S 0.5 -stellar mass relation. Furthermore, S 0.5 is correlated with the total central mass of a galaxy, including contributions due to dark matter.

We construct a physically motivated model for predicting the properties of the remnants of gaseous galaxy mergers, given the properties of the progenitors and the orbit. The model is calibrated using a large suite of smoothed particle hydrodynamics (SPH) merger simulations. It implements generalized energy conservation while accounting for dissipative energy losses and star formation. The dissipative effects are evaluated from the initial gas fractions and from the orbital parameters via an 'impulse' parameter, which characterizes the strength of the encounter. Given the progenitor properties, the model predicts the remnant stellar mass, half-mass radius and velocity dispersion to an accuracy of 25 per cent. The model is valid for both major and minor mergers. We provide an explicit recipe for semi-analytic models of galaxy formation.

There are strong correlations between the three structural properties of elliptical galaxies – stellar mass, velocity dispersion and size – in the form of a tight ‘Fundamental Plane’ and a ‘scaling relation’ between each pair. Major mergers of disc galaxies are assumed to be a mechanism for producing ellipticals, but semi‐analytic galaxy formation models (SAMs) have encountered apparent difficulties in reproducing the observed slope and scatter of the size–mass relation. We study the scaling relations of merger remnants using progenitor properties from two SAMs. We apply a simple merger model that includes gas dissipation and star formation based on theoretical considerations and simulations. Combining the SAMs and the merger model allows the calculation of the structural properties of the remnants of major mergers that enter the population of elliptical galaxies at a given redshift. Without tuning the merger model parameters for each SAM, the results roughly match the slope and scatter in the observed scaling relations and their evolution in the redshift range z = 0–3. Within this model, the observed scaling relations, including the tilt of the Fundamental Plane relative to the virial plane, result primarily from the decrease of gas fraction with increasing progenitor mass. The scatter in the size–mass relation of the remnants is reduced from that of the progenitors because of a correlation between progenitor size and gas fraction at a given mass.

[1] The responses of karstic aquifers to storms are often used to obtain information about aquifer geometry. In general, spring hydrographs are a function of both system geometry and recharge. However, the majority of prior work on storm pulses through karst has not studied the effect of recharge on spring hydrographs. To examine the relative importance of geometry and recharge, we break karstic aquifers into elements according to the manner of their response to transient flow and demonstrate that each element has a characteristic response timescale. These fundamental elements are full pipes, open channels, reservoir/constrictions, and the porous matrix. Taking the ratio of the element timescale with the recharge timescale produces a dimensionless number, g, that is used to characterize aquifer response to a storm event. Using sets of simulations run with randomly selected element parameters, we demonstrate that each element type has a critical value of g below which the shape of the spring hydrograph is dominated by the shape of the recharge hydrograph and above which the spring hydrograph is significantly modified by the system geometry. This allows separation of particular element/storm pairs into recharge-dominated and geometry-dominated regimes. While most real karstic aquifers are complex combinations of these elements, we draw examples from several karst systems that can be represented by single elements. These examples demonstrate that for real karstic aquifers full pipe and open channel elements are generally in the recharge-dominated regime, whereas reservoir/constriction elements can fall in either the recharge-or geometry-dominated regimes.