Search

We report a comprehensive study by the UV spectrograph LAMP (Lyman-Alpha Mapping Project) onboard the Lunar Reconnaissance Orbiter to map the spatial distribution and temporal evolution of helium atoms in the lunar exosphere, via spectroscopy of the He i emission line at 58.4 nm. Comparisons with several Monte Carlo models show that lunar exospheric helium is fully thermalized with the surface (accommodation coefficient of 1.0). LAMP-derived helium source rates are compared to the flux of solar wind alpha particles measured in situ by the ARTEMIS twin spacecraft. Our observations confirm that these alpha particles (He++) are the main source of lunar exospheric helium, representing 79 per cent of the total source rate, with the remaining 21 per cent presumed to be outgassing from the lunar interior. The endogenic source rate we derive, (1.49 ± 0.08) × 106 cm−2 s−1, is consistent with previous measurements but is now better constrained. LAMP-constrained exospheric surface densities present a dawn/dusk ratio of ∼1.8, within the value measured by the Apollo 17 surface mass spectrometer LACE (Lunar Atmosphere Composition Experiment). Finally, observations of lunar helium during three Earth’s magnetotail crossings, when the Moon is shielded from the solar wind, confirm previous observations of an exponential decay of helium with a time constant of 4.5 d

Pluto energies of a few kiloelectron volts and suprathermal ions with tens of kiloelectron volts and above. We measure this population using the Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI) instrument on board the New Horizons spacecraft that flew by Pluto in 2015. Even though the measured ions have gyroradii larger than the size of Pluto and the cross section of its magnetosphere, we find that the boundary of the magnetosphere is depleting the energetic ion intensities by about an order of magnitude close to Pluto. The intensity is increasing exponentially with distance to Pluto and reaches nominal levels of the interplanetary medium at about 190

We investigate what can be learned about a population of distant Kuiper Belt Objects (KBOs) by studying the statistical properties of their light curves. Whereas others have successfully inferred the properties of individual, highly variable KBOs, we show that the fraction of KBOs with low amplitudes also provides fundamental information about a population. Each light curve is primarily the result of two factors: shape and orientation. We consider contact binaries and ellipsoidal shapes, with and without flattening. After developing the mathematical framework, we apply it to the existing body of KBO light curve data. Principal conclusions are as follows. (1) When using absolute magnitude H as a proxy for the sizes of KBOs, it is more accurate to use the maximum of the light curve (minimum H) rather than the mean. (2) Previous investigators have noted that smaller KBOs tend to have higher-amplitude light curves, and have interpreted this as evidence that they are systematically more irregular in shape than larger KBOs; we show that a population of flattened bodies with uniform proportions, independent of size, could also explain this result. (3) Our method of analysis indicates that prior assessments of the fraction of contact binaries in the Kuiper Belt may be artificially low. (4) The pole orientations of some KBOs can be inferred from observed changes in their light curves over time scales of decades; however, we show that these KBOs constitute a biased sample, whose pole orientations are not representative of the population overall. (5) Although surface topography, albedo patterns, limb darkening, and other surface properties can affect individual light curves, they do not have a strong influence on the statistics overall. (6) Photometry from the Outer Solar System Origins Survey (OSSOS) survey is incompatible with previous results and its statistical properties defy easy interpretation. We also discuss the promise of this approach for the analysis of future, much larger data sets such as the one anticipated from the upcoming Vera C. Rubin Observatory.

NASA's Lucy mission is the 13th Discovery-class mission, and it will be the first to visit the Jupiter Trojan asteroids. Over the course of 12 years, the mission will encounter 7 Trojan asteroids in a series of 5 flybys. Each of these flyby occurs over a short period of time, such that careful planning of time-critical observations must be performed to ensure that the mission's Science Requirement are achieved. Additionally, various sources of uncertainty in the spacecraft's attitude and pointing accuracy must be thoroughly tested and constrained to determine how they impact instrument operation and the resulting data. In order to develop and test observations sequences, we have developed the Science Encounter Simulation Software (SESS). This powerful software allows one to simulate the spacecraft's encounter with each of Lucy's target, and to perform a series of commands to adjust the spacecraft's attitude and trigger data acquisitions with the various instruments of the Lucy payload. The software outputs a variety of information that allows one to construct resolution maps which can be used to determine whether a given observation sequence produces adequate data that meet the Science Requirements. The code also performs numerous checks to ensure that the spacecraft, its instrument pointing platform, and the L'Ralph scan mirror, are operated within their capabilities.

Examining Arrokoth The New Horizons spacecraft flew past the Kuiper Belt object (486958) Arrokoth (also known as 2014 MU 69 ) in January 2019. Because of the great distance to the outer Solar System and limited bandwidth, it will take until late 2020 to downlink all the spacecraft's observations back to Earth. Three papers in this issue analyze recently downlinked data, including the highest-resolution images taken during the encounter (see the Perspective by Jewitt). Spencer et al. examined Arrokoth's geology and geophysics using stereo imaging, dated the surface using impact craters, and produced a geomorphological map. Grundy et al. investigated the composition of the surface using color imaging and spectroscopic data and assessed Arrokoth's thermal emission using microwave radiometry. McKinnon et al. used simulations to determine how Arrokoth formed: Two gravitationally bound objects gently spiraled together during the formation of the Solar System. Together, these papers determine the age, composition, and formation process of the most pristine object yet visited by a spacecraft. Science , this issue p. eaay3999 , p. eaay3705 , p. eaay6620 ; see also p. 980

The Lyman-Alpha Mapping Project (LAMP) UV spectrograph on board the Lunar Reconnaissance Orbiter (LRO) performed a campaign to observe the Moon's nanodust exosphere, evidence for which was provided by the Lunar Atmosphere and Dust Environment Explorer (LADEE) Ultraviolet and Visible Spectrometer (UVS) during the 2014 Quadrantid meteoroid stream. These LADEE/UVS observations were consistent with a nanodust exosphere modulated by meteoroid impacts. LRO performed off-nadir maneuvers around the peak of the 2016 Quadrantids, in order to reproduce, as closely as possible, the active meteoroid environment and observing geometry of LADEE/UVS. We analyzed LAMP spectra to search for sunlight backscattering from nanodust. No brightness enhancement attributable to dust, of any size, was observed. We determine an upper limit for dust column concentration of ~10(^ 5) sq. cm for grains of radius ~25 nm, and an upper limit for dust column mass of ~10 11 g sq. cm, nearly independent of grain size for radii

We investigate the density and spatial distribution of the H2 exosphere of the Moon assuming various source mechanisms. Owing to its low mass, escape is non-negligible for H2. For high-energy source mechanisms, a high percentage of the released molecules escape lunar gravity. Thus, the H2 spatial distribution for high-energy release processes reflects the spatial distribution of the source. For low energy release mechanisms, the escape rate decreases and the H2 redistributes itself predominantly to reflect a thermally accommodated exosphere. However, a small dependence on the spatial distribution of the source is superimposed on the thermally accommodated distribution in model simulations, where density is locally enhanced near regions of higher source rate. For an exosphere accommodated to the local surface temperature, a source rate of 2.2 g s-1 is required to produce a steady state density at high latitude of 1200 cm-3. Greater source rates are required to produce the same density for more energetic release mechanisms. Physical sputtering by solar wind and direct delivery of H2 through micrometeoroid bombardment can be ruled out as mechanisms for producing and liberating H2 into the lunar exosphere. Chemical sputtering by the solar wind is the most plausible as a source mechanism and would require 10-50 of the solar wind H+ inventory to be converted to H2 to account for the observations.

Micro-Channel Plate (MCP) detectors can suffer from a form of degradation known as gain sag in regions with significant fluence. We have developed a method to recover the total Lyman-Alpha (Ly-[Formula: see text]) emission line (121.6[Formula: see text]nm) flux for the Lyman-Alpha Mapping Project (LAMP) UV imaging spectrograph onboard of the Lunar Reconnaissance Orbiter (LRO), where gain sag issues are important. The constant ratio between the Ly-[Formula: see text] emission line and its ghost image at shorter wavelengths allows for a useful correction factor for the true flux at the Ly-[Formula: see text] region of the detector. A similar method could be used in other spectrographs whenever a ghost image of sufficient brightness is present.

The Kuiper Belt is a distant region of the Solar System. On 1 January 2019, the New Horizons spacecraft flew close to (486958) 2014 MU69, a Cold Classical Kuiper Belt Object, a class of objects that have never been heated by the Sun and are therefore well preserved since their formation. Here we describe initial results from these encounter observations. MU69 is a bi-lobed contact binary with a flattened shape, discrete geological units, and noticeable albedo heterogeneity. However, there is little surface color and compositional heterogeneity. No evidence for satellites, ring or dust structures, gas coma, or solar wind interactions was detected. By origin MU69 appears consistent with pebble cloud collapse followed by a low velocity merger of its two lobes., 43 pages, 8 figure

Lunar swirls – the enigmatic, magnetically-anomalous regions – are observed for the first time at far-UV (FUV) wavelengths using LRO/LAMP. Swirls in both highlands and mare regions are spectrally relatively red (or less blue) than surrounding terrains, indicating a difference in weathering and/or composition in the swirls vs. non-swirl regions. We compare spectra of the highlands swirl Gerasimovich with mature and immature low-Fe highlands regions as measured by LAMP and show that the swirl itself does not have the spectral characteristics of either the mature or the immature regions. Mature, weathered highlands regions are spectrally blue in the FUV; immature highlands are less blue, especially at wavelengths > ∼160 nm. In contrast, the Gerasimovich swirl is spectrally red at wavelengths > ∼160 nm. We also compare Reiner Gamma, a mare swirl, with mature and immature high-Ti mare regions as measured by LAMP. We find that the mature and immature high-Ti mare regions are spectrally indistinguishable while the Reiner Gamma spectra are less blue at wavelengths > ∼160 nm. We conclude that both swirls (Reiner Gamma and Gerasimovich) are consistent with less mature spectra than the immature terrains studied here, in accordance with the lower amounts of weathering expected in a solar wind standoff scenario. However, the swirl spectra are also consistent with greater abundances of feldspathic material, as we show that anorthite exhibits a characteristic red spectrum at wavelengths > ∼160 nm. Thus, the LAMP data are also consistent with a model wherein compositional sorting occurs at swirls.

We present results from Lunar Reconnaissance Orbiter’s (LRO) UV spectrograph LAMP (Lyman-Alpha Mapping Project) campaign to study the lunar atmosphere. Several off-nadir maneuvers (lateral rolls) were performed to search for resonantly scattering species, increasing the illuminated line-of-sight (and hence the signal from atoms resonantly scattering the solar photons) compared to previously reported LAMP’s “twilight observations” (Cook, J.C., Stern, S.A. [2014]. Icarus 236, 48–55). Helium was the only element distinguishable on a daily basis, and we present latitudinal profiles of its line-of-sight column density in December 2013. We compared the helium line-of-sight column densities with solar wind alpha particle fluxes measured from the ARTEMIS (Acceleration, Reconnection, Turbulence, & Electrodynamics of Moon’s Interaction with the Sun) twin spacecraft. Our data show a correlation with the solar wind alpha particle flux, confirming that the solar wind is the main source of the lunar helium. We also support the finding by Benna et al. (Benna, M. et al. [2015]. Geophys. Res. Lett. 42, 3723–3729) and Hurley et al. (Hurley, D.M. et al. [2015]. Icarus, this issue), that a non-zero contribution from endogenic helium, coming from radioactive decay of 232 Th and 238 U, is present. Moreover, our results suggest that not all of the incident alpha particles are converted to thermalized helium, allowing for a non-negligible fraction to escape as suprathermal helium or simply backscattered from the lunar surface. We compare LAMP-derived helium surface density with the one recorded by the mass spectrometer LACE (Lunar Atmospheric Composition Experiment) deployed on the lunar surface during the Apollo 17 mission, finding good agreement between the two measurements. The LRO/LAMP roll observations presented here are in agreement with the most recent lunar exospheric helium model (Hurley, D.M. et al. [2015]. Icarus, this issue) around mid- to high-latitudes (50–70°) regardless of the local solar time, while there is an underestimation of the model around the low- to mid-latitudes (10–30°), especially around the dawn terminator. The LRO/LAMP roll observations presented here provide unique coverage of local solar time and latitude of the lunar exospheric helium, filling a gap in the knowledge of the structure of the lunar exosphere as a whole. These observations will inform future models of transport of volatiles, since at the terminator the analytic expressions for the surface temperature, essential to determine the energy distribution, the residence time, and the hop length of the particles, is least accurate.

The Lunar Reconnaissance Orbiter’s (LRO) Lyman Alpha Mapping Project (LAMP) is a lightweight (6.1 kg), lowpower (4.5 W), ultraviolet spectrograph based on the Alice instruments aboard the European Space Agency’s Rosetta spacecraft and NASA’s New Horizons spacecraft. Its primary job is to identify and localize exposed water frost in permanently shadowed regions (PSRs) near the Moon’s poles, and to characterize landforms and albedos in PSRs. LRO launched on June 18, 2009 and reached lunar orbit four days later. LAMP operated with its failsafe door closed for its first seven years in flight. The failsafe door was opened in October 2016 to increase light throughput during dayside operations at the expense of no longer having the capacity to take further dark observations and slightly more operational complexity to avoid saturating the instrument. This one-time irreversible operation was approved after extensive review, and was conducted flawlessly. The increased throughput allows measurement of dayside hydration in one orbit, instead of averaging multiple orbits together to reach enough signal-to-noise. The new measurement mode allows greater time resolution of dayside water migration for improved investigations into the source and loss processes on the lunar surface. LAMP performance and optical characteristics after the failsafe door opening are described herein, including the new effective area, wavelength solution, and resolution.

The New Horizons mission has provided resolved measurements of Pluto's moons Styx, Nix, Kerberos, and Hydra. All four are small, with equivalent spherical diameters of $\approx$40 km for Nix and Hydra and ~10 km for Styx and Kerberos. They are also highly elongated, with maximum to minimum axis ratios of $\approx$2. All four moons have high albedos ( $\approx$50-90 %) suggestive of a water-ice surface composition. Crater densities on Nix and Hydra imply surface ages $\gtrsim$ 4 Ga. The small moons rotate much faster than synchronous, with rotational poles clustered nearly orthogonal to the common pole directions of Pluto and Charon. These results reinforce the hypothesis that the small moons formed in the aftermath of a collision that produced the Pluto-Charon binary., Comment: in Science 351, aae0030 (2016)

Watering the Moon About a year ago, a spent upper stage of an Atlas rocket was deliberately crashed into a crater at the south pole of the Moon, ejecting a plume of debris, dust, and vapor. The goal of this event, the Lunar Crater Observation and Sensing Satellite (LCROSS) experiment, was to search for water and other volatiles in the soil of one of the coldest places on the Moon: the permanently shadowed region within the Cabeus crater. Using ultraviolet, visible, and near-infrared spectroscopy data from accompanying craft, Colaprete et al. (p. 463 ; see the news story by Kerr ; see the cover) found evidence for the presence of water and other volatiles within the ejecta cloud. Schultz et al. (p. 468 ) monitored the different stages of the impact and the resulting plume. Gladstone et al. (p. 472 ), using an ultraviolet spectrograph onboard the Lunar Reconnaissance Orbiter (LRO), detected H 2 , CO, Ca, Hg, and Mg in the impact plume, and Hayne et al. (p. 477 ) measured the thermal signature of the impact and discovered that it had heated a 30 to 200 square-meter region from ∼40 kelvin to at least 950 kelvin. Paige et al. (p. 479) mapped cryogenic zones predictive of volatile entrapment, and Mitrofanov et al. (p. 483 ) used LRO instruments to confirm that surface temperatures in the south polar region persist even in sunlight. In all, about 155 kilograms of water vapor was emitted during the impact; meanwhile, the LRO continues to orbit the Moon, sending back a stream of data to help us understand the evolution of its complex surface structures.

Out of the Oort Cloud Long-period comets originate from the Oort cloud, a vast reservoir of icy bodies that surrounds the solar system. These bodies are thought to be remnants from the formation of the solar system. But did they all form in the Sun's protoplanetary disk, or could they have been generated in the protoplanetary disks of other stars in the cluster where the Sun probably formed? Levison et al. (p. 187 , published online 10 June) used detailed numerical simulations to investigate what fraction of comets might transfer from the outer reaches of one stellar system to another. The simulations suggest that a substantial number of comets can be captured through this mechanism, which may explain why the number of bodies in the Oort cloud is larger than models predict.

The Lyman Alpha Mapping Project (LAMP) is a far-ultraviolet (FUV) imaging spectrograph on NASA’s Lunar Reconnaissance Orbiter (LRO) mission. Its main objectives are to (i) identify and localize exposed water frost in permanently shadowed regions (PSRs), (ii) characterize landforms and albedos in PSRs, (iii) demonstrate the feasibility of using natural starlight and sky-glow illumination for future lunar surface mission applications, and (iv) characterize the lunar atmosphere and its variability. As a byproduct, LAMP will map a large fraction of the Moon at FUV wavelengths, allowing new studies of the microphysical and reflectance properties of the regolith. The LAMP FUV spectrograph will accomplish these objectives by measuring the signal reflected from the night-side lunar surface and in PSRs using both the interplanetary HI Lyman-α sky-glow and FUV starlight as light sources. Both these light sources provide fairly uniform, but faint, illumination. With the expected LAMP sensitivity, by the end of the primary 1-year LRO mission, the SNR for a Lyman-α albedo map should be >100 in polar regions >1 km2, providing useful FUV constraints to help characterize subtle compositional and structural features. The LAMP instrument is based on the flight-proven Alice series of spectrographs flying on the Rosetta comet mission and the New Horizons Pluto mission. A general description of the LAMP instrument and its initial ground calibration results are presented here.

The Pluto system was recently explored by NASA's New Horizons spacecraft, making closest approach on 14 July 2015. Pluto's surface displays diverse landforms, terrain ages, albedos, colors, and composition gradients. Evidence is found for a water-ice crust, geologically young surface units, surface ice convection, wind streaks, volatile transport, and glacial flow. Pluto's atmosphere is highly extended, with trace hydrocarbons, a global haze layer, and a surface pressure near 10 microbars. Pluto's diverse surface geology and long-term activity raise fundamental questions about how small planets remain active many billions of years after formation. Pluto's large moon Charon displays tectonics and evidence for a heterogeneous crustal composition, its north pole displays puzzling dark terrain. Small satellites Hydra and Nix have higher albedos than expected., 8 pages - Initial Science paper from NASA's New Horizons Pluto Encounter

The central, or x1, family of periodic orbits is the most important one in almost all two-dimensional numerical models of galactic bars in the literature. However, we present evidence that in two-dimensional models with sufficiently large bar axial ratios (a/c 6), stable orbits having propeller shapes play the dominant role. In our models this propeller family is in fact a distant relative of the x1 family. There are also intermediate cases in which both families are important. The dominance of one family over the other may have direct consequences on the morphological properties of the bars that can be constructed from them, properties such as face-on bar thinness and strength as well as the boxiness of the outer isophotes.

NASA’s COST LESS Team is pursuing strategies to reduce the cost and complexity of planning and executing space missions. The team’s technical goal is to reverse the trend of constructing unique solutions for similar problems. To this end, the team is exploring ways to represent mission functionality in terms of building blocks and is discovering approaches that could accommodate the same building blocks for seemingly disparate activities, such as organizing processed telemetry data, controlling onboard experiments, searching science archives, reducing and presenting information to science users, and supporting educational outreach. Reusable object technology (UOT), a research undertaking by the authors, is showing promise in recognizing similarities in functions which were previously viewed as unique because they appeared in different programs or mission phases. Since UOT is aimed at being implementation independent (i.e. the function performed could be accomplished manually, by an automated process, by a specialized instrument, etc.), no premature judgment for automation or autonomy need be made. In this paper, the authors attempt to strike a balance between theory and reality as they describe UOT, including its beginnings, its underpinning, its utility, and its potential for achieving substantive reductions in cost and complexity for the Agency’s space programs. The authors discuss their collaboration with the Center for EUV Astrophysics, University of California, Berkeley to reduce the cost and complexity of science investigations. Their multi-disciplinary plan incorporates both UOT and a complementary technology introduced in this paper, called interactive archives.

[1] We present an analysis of Lunar Reconnaissance Orbiter (LRO) Lyman Alpha Mapping Project (LAMP) measurements of the dayside lunar surface at far-ultraviolet wavelengths. We use the strong 165 nm H2O absorption edge to look for diurnal variations in hydration. We find that diurnal variations in spectral slope are indeed present; they are superimposed on latitudinal and spatial variations related to composition and weathering. We use two different spectral regions (164–173 nm and 175–190 nm) to separate out these effects. Highlands and mare regions have distinct reflectance spectra, with mare regions being spectrally bluer than highlands regions, a consequence of the greater abundance of opaque minerals in mare regions. Bright ray terrains and areas known to be young such as Giordano Bruno crater, are found to be relatively spectrally flat or red in the far-UV; this is consistent with a lack of space weathering, which tends to make the far-UV spectrum bluer due to the spectral behavior of nanophase iron. Large-scale latitudinal variations in FUV slope are distinct and are likely due to a gradient in space weathering. The diurnal variation in hydration is consistent with a solar wind origin and with loss of H2O at temperatures above ∼320 K. Far-UV spectroscopy is thus shown to represent a viable method for mapping aqueous alteration, even on the dayside of the Moon, and potentially elsewhere in the solar system.

[1] Using a Monte Carlo model, we analyze the evolution of the vapor plume emanating from the Lunar Crater Observation and Sensing Satellite (LCROSS) impact into Cabeus as seen by the Lyman Alpha Mapping Project (LAMP), a far-ultraviolet (FUV) imaging spectrograph onboard the Lunar Reconnaissance Orbiter. The best fit to the data utilizes a bulk velocity between 3.0 and 4.0 km/s. The fits to the light curve comprised of Hg, Ca, and Mg are not strongly dependent on the temperature. In contrast, the best fit to the light curve from H2 and CO corresponds to a 500 K thermal velocity distribution. The LAMP field of view primarily encounters particles released at low angles to the horizontal and misses fast moving particles released at more vertical angles. The isotropic model suggests that 117 ± 16 kg H2, 41 ± 3 kg CO, 16 ± 1 kg Ca, 12.4 ± 0.8 kg Hg, and 3.8 ± 0.3 kg Mg are released by the LCROSS impact. Additional errors could arise from an anisotropic plume, which cannot be distinguished with LAMP data. Mg and Ca are likely incompletely volatilized owing to their high vapor temperatures. The highly volatile components (H2 and CO) might derive from a greater mass of material. To agree with predicted abundances by weight of 0.047%, 0.023%, 11%, 0.28% and 3.4% for H2, CO, Ca, Hg, and Mg, respectively, the species would be released from 250,000 kg, 180,000 kg, 140 kg, 4400 kg, and 110 kg of regolith, respectively. This is consistent with the relative volatility of these species.

[1] Although of great interest for science and resource utilization, the Moon's permanently shadowed regions (PSRs) near each pole present difficult targets for remote sensing. The Lyman Alpha Mapping Project (LAMP) instrument on the Lunar Reconnaissance Orbiter (LRO) mission is able to map PSRs at far-ultraviolet (FUV) wavelengths using two faint sources of illumination from the night sky: the all-sky Ly α glow produced as interplanetary medium (IPM) H atoms scatter the Sun's Ly α emissions, and the much fainter source from UV-bright stars. The reflected light from these two sources produces only a few hundred events per second in the photon-counting LAMP instrument, so building maps with useful signal-to-noise (SNR) ratios requires the careful accumulation of the observations from thousands of individual LRO orbits. In this paper we present the first FUV albedo maps obtained by LAMP of the Moon's southern and northern polar regions. The results show that (1) most PSR regions are darker at all FUV wavelengths, consistent with their surface soils having much larger porosities than non-PSR regions (e.g., ∼70% compared to ∼40% or so), and (2) most PSRs are somewhat “redder” (i.e., more reflective at the longer FUV wavelengths) than non-PSR regions, consistent with the presence of ∼1–2% water frost at the surface.

We report observations of the lunar helium exosphere made between December 29, 2011, and January 26, 2012, with the Lyman Alpha Mapping Project (LAMP) ultraviolet spectrograph on NASA's Lunar Reconnaissance Orbiter Mission (LRO). The observations were made of resonantly scattered He I 584 from illuminated atmosphere against the dark lunar surface on the dawn side of the terminator. We find no or little variation of the derived surface He density with latitude but day-to-day variations that likely reflect variations in the solar wind alpha flux. The 5-day passage of the Moon through the Earth's magnetotail results in a factor of two decrease in surface density, which is well explained by model simulations., Comment: 21 pages, 5 figures, 3 supplementary figures, accepted for publication in Icarus

We present results of numerical simulations of bar-unstable disks that include a dissipative gas component. The simulations have been carried out using a two-dimensional polar grid for the force calculations. The gas component has been modelled as a collection of finite-sized particles that dissipate a fraction of their relative motion during collisions.

We study the dynamical behavior at the regions of resonances in N-body simulations with long-lived spiral structure. We find in several cases a main mode, the strong bisymmetric part of which ends at its 4:1 resonance region. This distance is found to be at 2.5→3 disk scale lengths. In real spiral galaxies this corresponds to the distance of termination of the observed prominent inner 2-armed spirals. In general other modes are found coexisting with the main one. In some cases they are found to be important in the outer part of the disks.