Water on Mars: Inventory, distribution, and possible sources of polar ice

Theoretical considerations and various lines of morphologic evidence suggest that, in addition to the normal seasonal and climatic exchange of H2O that occurs between the Martian polar caps, atmosphere, and mid to high latitude regolith, large volumes of water have been introduced into the planet's long term hydrologic cycle by the sublimation of equatorial ground ice, impacts, catastrophic flooding, and volcanism. Under the climatic conditions that are thought to have prevailed on Mars throughout the past 3 to 4 b.y., much of this water is expected to have been cold trapped at the poles. The amount of polar ice contributed by each of the planet's potential crustal sources is discussed and estimated. The final analysis suggests that only 5 to 15 pct. of this potential inventory is now in residence at the poles

Workshop on the Polar Regions of Mars: Geology, Glaciology, and Climate History, part 1

Papers and abstract of papers presented at the workshop are presented. Some representative titles are as follows: Glaciation in Elysium; Orbital, rotational, and climatic interactions; Water on Mars; Rheology of water-silicate mixtures at low temperatures; Evolution of the Martian atmosphere (the role of polar caps); Is CO2 ice permanent; Dust transport into Martian polar latitudes; Mars observer radio science (MORS) observations in polar regions; and Wind transport near the poles of Mars (timescales of changes in deposition and erosion)

Carter-like constants of the motion in Newtonian gravity and electrodynamics

For a test body orbiting an axisymmetric body in Newtonian gravitational theory with multipole moments Q_L, (and for a charge in a non-relativistic orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes in general relativity, if the odd-L moments vanish, and the even-L moments satisfy Q_2L = m (Q_2/m)^L. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame-dragging (or if the electrostatic field is supplemented by a multipolar magnetic field), we are unable to find an analogous Carter-like constant. This further highlights the very special nature of the Kerr geometry of general relativity.Comment: 4 page

The evolution of the early Martian climate and the initial emplacement of crustal H2O

Given the geomorphic evidence for the widespread occurrence of water and ice in the early Martian crust, and the difficulty involved in accounting for this distribution given the present climate, it has been suggested that the planet's early climate was originally more Earth-like, permitting the global emplacement of crustal H2O by direct precipitation as snow or rain. The resemblance of the Martian valley networks to terrestrial runoff channels and their almost exclusive occurrence in the planet's ancient (approximately 4-b.y.-old) heavily cratered terrain are often cited as evidence of just such a period. An alternative school of thought suggests that the early climate did not differ substantially from that of today. Advocates of this view find no compelling reason to invoke a warmer, wetter period to explain the origin of the valley networks. Rather, they cite evidence that the primary mechanism of valley formation was groundwater sapping, a process that does not require that surface water exists in equilibrium with the atmosphere. However, while sapping may successfully explain the origin of the small valleys, it fails to address how the crust was initially charged with ice as the climate evolved towards its present state. Therefore, given the uncertainty regarding the environmental conditions that prevailed on early Mars, the initial emplacement of ground ice is considered here from two perspectives: (1) the early climate started warm and wet, but gradually cooled with time, and (2) the early climate never differed substantially from that of today

The hydrologic response of Mars to the onset of a colder climate and to the thermal evolution of its early crust

Morphologic similarities between the Martian valley networks and terrestrial runoff channel have been cited as evidence that the early Martian climate was originally more Earth-like, with temperatures and pressures high enough to permit the precipitation of H2O as snow or rain. Although unambiguous evidence that Mars once possessed a warmer, wetter climate is lacking, a study of the transition from such conditions to the present climate can benefit our understanding of both the early development of the cryosphere and the various ways in which the current subsurface hydrology of Mars is likely to differ from that of the Earth. Viewed from this perspective, the early hydrologic evolution of Mars is essentially identical to considering the hydrologic response of the Earth to the onset of a global subfreezing climate

Thermal and hydraulic considerations regarding the fate of water discharged by the outflow channels to the Martian northern plains

The identification of possible shorelines in the Martian northern plains suggests that the water discharged by the circum-Chryse outflow channels may have led to the formation of transient seas, or possibly even an ocean, covering as much as one-third of the planet. Speculations regarding the possible fate of this water have included local ponding and reinfiltration into the crust; freezing, sublimation, and eventual cold-trapping at higher latitudes; or the in situ survival of this now frozen water to the present day -- perhaps aided by burial beneath a protective cover of eolian sediment or lavas. Although neither cold-trapping at higher latitudes nor the subsequent freezing and burial of flood waters can be ruled out, thermal and hydraulic considerations effectively eliminate the possibility that any significant reassimilation of this water by local infiltration has occurred given climatic conditions resembling those of today. The arguments against the local infiltration of flood water into the northern plains are two-fold. First, given the climatic and geothermal conditions that are thought to have prevailed on Mars during the Late Hesperian (the period of peak outflow channel activity in the northern plains), the thickness of the cryosphere in Chryse Planitia is likely to have exceeded 1 km. A necessary precondition for the widespread occurrence of groundwater is that the thermodynamic sink represented by the cryosphere must already be saturated with ice. For this reason, the ice-saturated cryosphere acts as an impermeable barrier that effectively precludes the local resupply of subpermafrost groundwater by the infiltration of water discharged to the surface by catastraphic floods. Note that the problem of local infiltration is not significantly improved even if the cryosphere were initially dry, for as water attempts to infiltrate the cold, dry crust, it will quickly freeze, creating a seal that prevents any further infiltration from the ponded water above. The second argument against the local infiltration of flood water in the northern plains is based on hydraulic considerations. Repeated impacts have likely brecciated the Martian crust down to a depth of roughly 10 km. Given a value of permeability no greater than that inferred for the top 10 km of the Earth's crust (approximately 10(exp -2) darcies), a timescale as much as a billion years or more for the Martian groundwater system to achieve hydrostatic equilibrium, and the approximately 2-4 km elevation difference between the outflow channel source regions and the northern plains, the water confined beneath the frozen crust of the northern plains should have been under a significant hydraulic head. Thus, the existence of a hydraulic pathway between the ponded flood waters above the northern plains and the confined aquifer lying beneath it would not have led to the infiltration of flood water back into the crust, but rather the additional expulsion of groundwater onto the surface

Response to the Letter to the Editor

This paper has attracted interest around the world from the media (both TV and newspapers). In addition, we have received letters, emails and telephone calls. One of our favorites was a voicemail message asking us to return a call to Australia at which point we would learn who really killed JFK. We welcome the opportunity to respond to the letter to the editor from Mr. Fiorentino. Mr. Fiorentino claims that our ``statement relating to the likelihood of a second assassin based on the premise of three or more separate bullets is demonstrably false.'' In response we would like to simply quote from page 327 of Gerald Posner's book Case Closed, one of the most well known works supporting the single assassin theory: ``If Connally was hit by another bullet, it had to be fired from a second shooter, since the Warren Commission's own reconstructions showed that Oswald could not have operated the bolt and refired in 1.4 seconds.'' Mr. Fiorentino also claims that the ``second fatal flaw is the use of a rather uncomplicated formula based on Bayes Theorem.'' Let $E$ denote the evidence and $T$ denote the theory that there were just two bullets (and hence a single shooter). We used Bayes Theorem to hypothetically calculate $P(T|E)$ from $P(E|T)$ and the prior probability $P(T)$. In order to make $P(T|E)$ ten times more likely than $P(\bar{T}|E)$, the ratio of the prior probabilities [i.e., $P(T) / P(\bar{T})$] would have to be greater than 15. Thus, we again conclude that this casts serious doubt on Dr. Guinn's conclusion that the evidence supported just two bullets. Sadly, this is far from the first time that probability has been misunderstood and/or misapplied in a case of public interest. A notable British example is the Clark case. See Nobles and Schiff (2005) for details. Finally, we welcome and, in fact, encourage members of the scientific community to provide alternative analyses of the data.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS154 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Temporal changes in the geographic distribution, elevation, and potential origin of the Martian outflow channels

Observational evidence of outflow channel activity on Mars suggests that water was abundant in the planet's early crust. However, with the decline in the planet's internal heat flow, a freezing front developed within the regolith that propagated downward with time and acted as a thermodynamic sink for crustal H2O. One result of this thermal evolution is that, if the initial inventory of water on Mars was small, the cryosphere may have grown to the point where all the available water was taken up as ground ice. Alternatively, if the inventory of H2O exceeds the current pore volume of the cryosphere, then Mars has always possessed extensive bodies of subpermafrost groundwater. We have investigated the relative age, geographic distribution, elevation, and geologic setting of the outflow channels in an effort to accomplish the following: (1) identify possible modes of origin and evolutionary trends in their formation; (2) gain evidence regarding the duration and spatial distribution of groundwater in the crust; and (3) better constraint estimates of the planetary inventory of H2O

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. V. Evidence for the strong equivalence principle to second post-Newtonian order

Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, non-spinning but arbitrarily shaped bodies. In particular we study the contributions of the internal structure of the bodies (such as self-gravity) that would diverge if the size of the bodies were to shrink to zero. Using a set of virial relations accurate to the first post-Newtonian order that reflect the stationarity of each body, and redefining the masses to include 1PN and 2PN self-gravity terms, we demonstrate the complete cancellation of a class of potentially divergent, structure-dependent terms that scale as s^{-1} and s^{-5/2}, where s is the characteristic size of the bodies. This is further evidence of the Strong Equivalence Principle, and supports the use of post-Newtonian approximations to derive equations of motion for strong-field bodies such as neutron stars and black holes. This extends earlier work done by Kopeikin.Comment: 14 pages, submitted to Phys. Rev. D; small changes to coincide with published versio

Free subgroups of one-relator relative presentations

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G= always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1. 4 page