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NASA NTRS2003

Velocity Structure and Plasma Properties in Halo CMEs

We have identified a set of 23 Halo CMEs through July 2002 and 21 Partial Halo CMEs from the LASCO Halo CME Mail Archive for which Ultraviolet Coronagraph Spectrometer (UVCS) spectra exist. For each event we have collected basic information such as the event speed, whether or not UVCS caught the bright front, lines detected, Doppler shift and associated flare class. We have also obtained excellent observations of some of the spectacular events in November 2003, and we have made theoretical calculations pertaining to CME expansion at the heights observed by UVCS. We first analyzed the halo CMEs on 21 April and 24 August 2002 and the partial halo on 23 July 2002, because the X-class flares associated with these CMEs were extensively observed by RHESSI and other instruments as part of the MAX MILLENIUM campaign. These very fast CMEs showed extremely violent disruption of the pre-CME streamers, little or no cool prominence material, and the unusual (for UVCS heights) hot emission line [Fe XVIII]. Results, including a discussion of the current sheet interpretation for the [Fe XVIII] emission, are published in Raymond et al. and presented at the Fall 2002 AGU meeting and the solar physics summer school in L'Aquila, Italy. We are currently preparing two papers on the Dec. 28, 2000 partial halo event. This event was chosen to take advantage of the SEP event measured by WIND and ACE, and because a Type II radio burst coincides with the time that broad, blue-shifted O VI emission appeared in the UVCS spectra. One paper deals with a new density and velocity diagnostic for very fast CMEs; pumping of O VI lambda 1032 by Ly beta and pumping of O VI lambda 1038 by O VI lambda 1032. The other discusses physics of the shock wave and association with the SEP event. In the coming year we plan to expand the list of Halo and Partial Halo events observed by UVCS through the end of 2003. We will look at those events as a class to search for correlation between UV spectral characteristics and other CME and flare parameters. We will also choose several events for more detailed study, probably including the November 2003 events. We expect to support extended visits to CfA by S. Mancuso and A. Ciaravella. In the past year the grant covered some salary support for members of the SAO UVCS team and a 1 month visit to CfA by Angela Ciaravella, along with trips to meetings by J. Lin and J. Raymond and page charges for two papers.

Wagner, William↗

NASA NTRS2013

Abort Options for Human Missions to Earth-Moon Halo Orbits

Abort trajectories are optimized for human halo orbit missions about the translunar libration point (L2), with an emphasis on the use of free return trajectories. Optimal transfers from outbound free returns to L2 halo orbits are numerically optimized in the four-body ephemeris model. Circumlunar free returns are used for direct transfers, and cislunar free returns are used in combination with lunar gravity assists to reduce propulsive requirements. Trends in orbit insertion cost and flight time are documented across the southern L2 halo family as a function of halo orbit position and free return flight time. It is determined that the maximum amplitude southern halo incurs the lowest orbit insertion cost for direct transfers but the maximum cost for lunar gravity assist transfers. The minimum amplitude halo is the most expensive destination for direct transfers but the least expensive for lunar gravity assist transfers. The on-orbit abort costs for three halos are computed as a function of abort time and return time. Finally, an architecture analysis is performed to determine launch and on-orbit vehicle requirements for halo orbit missions.

Jesick, Mark C.↗

NASA NTRS2019

Cloud Computing Methods for Near Rectilinear Halo Orbit Trajectory Design

Complicated mission design problems require innovative computational solutions. As spacecraft depart from a proposed Gateway in a Near Rectilinear Halo Orbit (NRHO), recontact analysis is required to avoid risk of collision and ensure safe operations. Escape dynamics from NRHOs are governed by multiple gravitational bodies, yielding a trajectory design space that is exhaustively large. This paper summarizes the recontact analysis for departure from the NRHO and describes how the Deep Space Trajectory Explorer (DSTE) trajectory design software incorporates high performance cloud computing to compute and visualize the orbit design space. Recent focus on exploration missions to cislunar space has kindled accelerated interest in multibody orbit solutions. Trajectory analysis in the presence of multiple gravity fields is complex, and innovative computational tools are needed to simplify complicated design spaces, to generate large quantities of data quickly, and to visualize the output for user accessibility. The Gateway mission is a prime example. The Gateway1 is proposed as a human outpost in deep space. The current baseline orbit for the Gateway is a Near Rectilinear Halo Orbit (NRHO) near the Moon.2 The NRHO exists in a regime that experiences the gravitational effects of the Earth and the Moon simultaneously, complicating orbit analysis. The mission design process benefits greatly from updated computational tools for multibody missions like the Gateway. As an example, consider the problem of assessing the risk of collision in an NRHO. As a staging location to missions to the lunar surface and beyond the Earth-Moon system, the Gateway will experience spacecraft and other objects regularly arriving and departing. Departing objects potentially include spent logistics modules, visiting crew vehicles, debris objects, wastewater particles, and cubesats. Each departure is governed by the dynamics of the Gateway orbit and the surrounding dynamical environment. Over time, any unmaintained object in such an orbit eventually departs due to the small instabilities associated with the NRHOs. A separation maneuver speeds the departure from the NRHO, but the effects of the maneuver on the spacecraft behavior depend on the location, magnitude, and direction of the burn. Escape dynamics from the NRHO with regard to these maneuver options open up an enormous potential trajectory design space where subtle changes in input can produce dramatically large changes in the results. Any departing object must avoid recontacting the Gateway as it leaves the lunar vicinity, and a recontact analysis thus involves a significant number of computations and extensive output data. To explore the dynamics of this extensive design space, the Deep Space Trajectory Explorer3 (DSTE) trajectory design software incorporates new High Performance Computing (HPC) services and novel interactive visualizations. This paper details the HPC and cloud infrastructure techniques that are implemented in the DSTE, applying the new capabilities to analysis of recontact risk with the Gateway in NRHO. NEAR RECTILINEAR HALO ORBITS The Gateway is planned to fly in a lunar NRHO as its baseline orbit. The NRHO families of orbits are subsets of the larger halo families, which originate from planar orbits near the L1 and L2 libration points; the Earth-Moon L2 halo family appears in Figure 1. Each halo orbit is perfectly periodic in the Circular Restricted 3-Body Problem (CR3BP) and becomes a quasi-periodic orbit in a higher fidelity ephemeris force model. The NRHOs are defined as those members of the halo family with bounded stability properties;2 they pass near the Moon at perilune and are nearly polar. Families exist with apolunes located both above the lunar north pole and above the lunar south pole; the Gateway is planned to reside in a southern L2 NRHO in a 9:2 resonance with the lunar synodic period. The 9:2 NRHO is characterized by a period of about 6.5 days, a perilune radius of about 3,500 km, and an apolune radius of about 71,000 km; it is strongly affected by the gravity of both the Earth and the Moon simultaneously. This NRHO offers extended communications with assets on the south pole of the Moon,4 as well as low-cost orbit maintenance and attitude control,5 favorable eclipse avoidance properties,6 and inexpensive transfers from Earth and to other destinations.5,7 The NRHO portion of the southern L2 halo family is highlighted in black in Figure 1, and the 9:2 NRHO appears in blue.

Phillips, Sean M.↗

NASA NTRS1984

Discovery of solar system-size halos around young stars

Near-infrared speckle interferometric observations of five pre-main-sequence stars reveal a core-halo structure around two of these stars: HL Tau and R Mon. The halo light distribution is shown to arise from scattered light from small circumstellar particles. Halo sizes of 320 x 200 AU (alpha x delta FWHM) and 1300 x 1300 AU are deduced for HL Tau and R Mon, respectively, and the halo light is substantially bluer than the stellar light. The minimum mass of small particles in the scattering regions is comparable to the earth's mass in HL Tau and ten times greater in R Mon. Mass loss from the stars is almost certainly insufficient to produce the halo matter. The halos probably consist of relatively slowly moving matter bound gravitationally to the stars. From the size and mass of the circumstellar matter, it appears likely that these halos are in the early stage in the formation of planet-forming disks around the young stars.

Beckwith, S.↗

NASA NTRS1986

Measuring interstellar grains from the haloes of binary X-ray sources

Coherent forward scattering of X-rays by interstellar grains creates a halo around the X-ray image of a compact source. The fractional halo brightness at 2 keV is typically of order 10% moderately reddened galactic sources. The angular brightness distribution of the halo, which extends over several arcminutes, indicates the size distribution of the grains, and the spectrum of the halo indicates the composition of the grains. The halo will persist for several hours after the point source vanishes during an eclipse of a binary source; this provides a way to avoid systematic errors in measuring halo brightness due to an extended point response function of the X-ray telescope. Indeed, it is possilbe to infer the size distribution and composition of the grains without an imaging X-ray telescope by observing the time-dependence of the halo spectrum during eclipse.

Xu, Y.↗

NASA NTRS1990

Brown dwarfs as dark galactic halos

The possibility that the dark matter in galactic halos can consist of brown dwarf stars is considered. The radiative signature for such halos consisting solely of brown dwarfs is calculated, and the allowed range of brown dwarf masses, the initial mass function (IMF), the stellar properties, and the density distribution of the galactic halo are discussed. The prediction emission from the halo is compared with existing observations. It is found that, for any IMF of brown dwarfs below the deuterium burning limit, brown dwarf halos are consistent with observations. Brown dwarf halos cannot, however, explain the recently observed near-IR background. It is shown that future satellite missions will either detect brown dwarf halos or place tight constraints on the allowed range of the IMF.

Adams, Fred C.↗

NASA NTRS1992

Solar wind halo electrons from 1-4 AU

Observations from the Ulysses solar wind electron spectrometer are used to make a first examination of the evolution of the solar wind suprathermal or halo electron population as a function of heliocentric distance beyond 1 AU. As the core population cools with increasing heliocentric distance, no gap is formed between the core and halo populations. Rather, the halo electrons extend to increasingly lower energies. As predicted previously on theoretical grounds, the ratio of the core electron temperature to the low energy cutoff of the halo population appears to be roughly constant with a value of about 7.5. The total integrated heat flux drops rapidly with increasing heliocentric distance; a best fit power law of R exp -2.36 is found. In addition, it is found that the ratio of the halo to core densities is roughly constant over heliocentric distance with the halo representing 4 percent of the total electron distribution. These results suggest that the halo population may not consist of truly noninteractive test particles over the heliocentric range of 1-4 AU.

Mccomas, D. J.↗

NASA NTRS1991

Large-scale gas dynamical processes affecting the origin and evolution of gaseous galactic halos

Observations of galactic halo gas are consistent with an interpretation in terms of the galactic fountain model in which supernova heated gas in the galactic disk escapes into the halo, radiatively cools and forms clouds which fall back to the disk. The results of a new study of several large-scale gas dynamical effects which are expected to occur in such a model for the origin and evolution of galactic halo gas will be summarized, including the following: (1) nonequilibrium absorption line and emission spectrum diagnostics for radiatively cooling halo gas in our own galaxy, as well the implications of such absorption line diagnostics for the origin of quasar absorption lines in galactic halo clouds of high redshift galaxies; (2) numerical MHD simulations and analytical analysis of large-scale explosions ad superbubbles in the galactic disk and halo; (3) numerical MHD simulations of halo cloud formation by thermal instability, with and without magnetic field; and (4) the effect of the galactic fountain on the galactic dynamo.

Shapiro, Paul R.↗

NASA NTRS1994

Can MACHOs probe the shape of the galaxy halo ?

Microlensing searches in our galaxy have recently discovered several candidates in the direction of the Large Magellanic Cloud (LMC). We study the prospects for such searches to yield useful information about the flattening of the Galaxy dark matter halo, using a self-consistent oblate halo model and allowing for the possibility of misalignment between the disk and halo symmetry axes. The microlensing optical depth for the LMC, tau(LMC), depends sensitively on the disk-halo tilt angle in the Milky Way, as does the ratio tau(SMC)/tau(LMC). If the tilt angle is as large as 30 deg, a much larger spread in values for tau(LMC) is consistent with rotation curve constraints than previously thought. Disk-halo tilt and halo flattening do not significantly affect the massive compact halo object (MACHO) masses inferred from event durations.

Frieman, Joshua↗

NASA NTRS1994

Design of a Flush Airdata System (FADS) for the Hypersonic Air Launched Option (HALO) Vehicle

This paper presents a design study for a pressure based Flush airdata system (FADS) on the Hypersonic Air Launched Option (HALO) Vehicle. The analysis will demonstrate the feasibility of using a pressure based airdata system for the HALO and provide measurement uncertainty estimates along a candidate trajectory. The HALO is a conceived as a man-rated vehicle to be air launched from an SR-71 platform and is proposed as a testbed for an airbreathing hydrogen scramjet. A feasibility study has been performed and indicates that the proposed trajectory is possible with minimal modifications to the existing SR71 vehicle. The mission consists of launching the HALO off the top of an SR-71 at Mach 3 and 80,000 ft. A rocket motor is then used to accelerate the vehicle to the test condition. After the scramjet test is completed the vehicle will glide to a lakebed runway landing. This option provides reusability of the vehicle and scramjet engine. The HALO design will also allow for various scramjet engine and flowpath designs to be flight tested. For the HALO flights, measurements of freestream airdata are considered to be a mission critical to perform gain scheduling and trajectory optimization. One approach taken to obtaining airdata involves measurement of certain parameters such as external atmospheric winds, temperature, etc to estimate the airdata quantities. This study takes an alternate approach. Here the feasibility of obtaining airdata using a pressure-based flush airdata system (FADS) methods is assessed. The analysis, although it is performed using the HALO configuration and trajectory, is generally applicable to other hypersonic vehicles. The method to be presented offers the distinct advantage of inferring total pressure, Mach number, and flow incidence angles, without stagnating the freestream flow. This approach allows for airdata measurements to be made using blunt surfaces and significantly diminishes the heating load at the sensor. In the FADS concept a matrix of flush ports is placed in the vicinity of the aircraft nose, and the airdata are inferred indirectly from the measured pressures.

Whitmore, Stephen A.↗

NASA NTRS2002

Characterization of Polar Mesospheric Clouds Using Infrared Measurements from HALOE

Measurements from the Halogen Occultation Experiment (HALOE) revealed the infrared signature of polar mesospheric clouds (PMCs), for the first time, HALOE PMC observations at eight wavelengths (2.45 - 10 microns) show remarkable agreement with model PMC spectra based on ice particle extinction, and thus provide the first confirmation that water ice is the primary component of PMCs. Because PMCs respond to changes in temperature and water vapor, they are considered an indicator of global climate change. We propose to further the understanding of PMCs using a decade of infrared measurements form HALOE. This effort will characterize PMC spectral properties, extinction profiles, and size distributions. Using this information, HALOE measurements will be used to make simultaneous retrievals of H2O3, and temperature, in the presence of PMCs. The simultaneous retrievals of particle properties, H2O3, and temperature will be used with HALOE NO data to provide a significant step forward in the knowledge of PMC characteristics and formation conditions. We will challenge fundamental theories of PMC formation, and investigate changes in PMC properties and related conditions over the length of the HALOE measurement record. HALOE has been operating without flaw since it was launched on October 11, 1991. Consequently, ten southern and ten northern PMC seasons have been observed thus far, providing a wealth of data for the study of PMC and related parameters.

Hervig, Mark E.↗

NASA NTRS2002

Characterization of Polar Mesospheric Clouds Using Infrared Measurements From HALOE

Measurements from the Halogen Occultation Experiment (HALOE) revealed the infrared signature of polar mesospheric clouds (PMCs), for the first time, HALOE PMC observations at eight wavelengths (2.45 - 10 microns) show remarkable agreement with model PMC spectra based on ice particle extinction, and thus provide the first confirmation that water ice is the primary component of PMCs. Because PMCs respond to changes in temperature and water vapor, they are considered an indicator of global climate change. We propose to further the understanding of PMCs using a decade of infrared measurements form HALOE. This effort will characterize PMC spectral properties, extinction profiles, and size distributions. Using this information, HALOE measurements will be used to make simultaneous retrievals of H2O, O3, and temperature, in the presence of PMCs. The simultaneous retrievals of particle properties, H2O, O3, and temperature will be used with HALOE NO data to provide a significant step forward in the knowledge of PMC characteristics and formation conditions. We will challenge fundamental theories of PMC formation, and investigate changes in PMC properties and related conditions over the length of the HALOE measurement record. HALOE has been operating without flaw since it was launched on October 11, 1991. Consequently, ten southern and ten northern PMC seasons have been observed thus far, providing a wealth of data for the study of PMCs and related parameters.

Hervig, Mark E.↗

NASA NTRS2003

A New Method to Resolve X-Ray Halos around Point Sources with Chandra Data and Its Application to Cygnus X-1

With excellent angular resolution, good energy resolution, and a broad energy band, the Chandra Advanced CCD Imaging Spectrometer (ACIS) is the best instrument for studying the X-ray halos around some Galactic X-ray point sources caused by the dust scattering of X-rays in the interstellar medium. However, the direct images of bright sources obtained with the ACIS usually suffer from severe pileup. Making use of the fact that an isotropic image could be reconstructed from its projection in to any direction, we can reconstruct the images of the X-ray halos from the data obtained with the High Energy Transition Grating Spectrometer (HETGS) and/or in continuos clocking (CC) mode. These data have no or less serious pileup and enable us to take full advantage of the excellent angular resolution of Chandra. With the reconstructed high-resolution images, we can probe the X-ray halos as close as 1" to their associated point sources. Applying this method to Cygnus X-1 observed with the Chandra HETGS in CC mode, we derived an energy-dependent radial halo flux distribution and concluded that in a circular region (2' in radius) centered a the point source: (1) relative to the total intensity, the fractional halo intensity is about 15% at keV and drops to aboout 5% at approximately 6 keV (2) about 50% of the halo photons are within the region of a radius less than 40 inches and (3) the spectrum of the pooint source is slightly distorted by the halo contamination.

Yao, Yangsen↗

NASA NTRS2017

The Geographic Distribution of Boulder Halo Craters at Mid-to-High Latitudes on Mars

Extensive evidence exists for ground ice at mid-to-high latitudes on Mars, including results from neutron spectroscopy [1-3], thermal properties [4-5], geomorphology [e.g., 6-9], and the in situ observations of Mars Phoenix [10]. This ground ice has been hypothesized to be emplaced diffusively and fill pores [11], or to have accumulated by ice and dust deposition that draped or mantled the terrain [7, 12]. These two processes are not mutually exclusive; both potentially have occurred on Mars [5]. One of the landforms found in areas where ground ice is common on Mars are boulder halo craters [e.g., 13-15] (Figure 1), which are topographically muted impact craters that are filled by ice-rich regolith. They are outlined by boulders that trace a circular outline of the original crater rim. Boulder halos generally have distinctly higher boulder densities than the surrounding background plains and have few boulders in their interiors. The mechanism of boulder halo crater formation is somewhat uncertain. Our working model is that an impact event occurs with sufficient size to excavate to a depth greater than the boulder-poor, ice-rich soils. Excavated boulders are deposited around the crater's rim and in its proximal ejecta. Quite rapidly [14], the crater becomes infilled by icy soil. Rather than being buried, boulders in the halo remain at the surface, perhaps be-cause they 'float' relative to finer-grained materials [14, 16]. Regardless of the details of this process, the life-time of boulders at the surface is much greater than the timescale needed to remove most of the craters' topography. Physical weathering of rocks must be greatly out-paced by crater infilling (the opposite of what is typical, e.g., on the Moon [17]). The rapidity of this infilling is easiest to understand if icy mantling material is deposited and accumulates, rather than simply being added by pore filling of soils. If this model is correct, boulder halos only form when they excavate rock-producing materials from beneath the upper surface. Thus, the distribution and size of craters that result in boulders halos may provide in-sight into the thickness of the ice-rich surface layer in different locations. Note that this thickness is necessarily that of the ice-rich layer at the time of impact, not at present. This study is an initial survey of boulder halo crater locations in the 50deg to 80degN and 50deg to 80degS latitude bands on Mars.

Ice↗

NASA NTRS2019

Observation and Attribution of Temperature Trends near the Stratopause from HALOE

This study considers time series of temperature versus pressure, T(p), from the Halogen Occultation Experiment (HALOE) across the stratopause region, where the effects of radiative forcings from the greenhouse gases (CO2 and H2O) and from ozone are most pronounced. Trend analyses are from 1993-2005 for HALOE T(p) values at seven levels from 3.0 to 0.3 hPa with a vertical resolution of about 4 km and for eight latitude zones from 65°S to 65°N. The HALOE trends at 2.0 hPa are of the order of -1.0 K/decade across the tropics and subtropics, but then become smaller (-0.5 K/decade) at the middle latitudes. The near-global HALOE trend profile has a minimum cooling rate of -0.2 K/decade at 1.0 hPa, although it is more negative in the southern hemisphere and slightly positive in the northern hemisphere. The combined radiative forcings from CO2, H2O, and ozone are from -0.4 to -0.6 K/decade for 1993-2005 and are hemispherically symmetric. HALOE temperature trend and total radiative cooling profiles differ from those reported from observations and calculations for 1980-2000, mainly because the ozone trends changed from clearly negative in the 1980s through mid-1990s to slightly positive during the time of HALOE. Trends for the tracer, HALOE methane (CH4), increase from 2 to 4 %/decade from 50 hPa to 10 hPa, indicating an acceleration of the Brewer/Dobson circulation. Analyses of time series of CH4 across the stratopause reveal more variability in the northern hemisphere, where wave dissipation likely contributes to the heating.

Remsberg, Ellis↗

NASA NTRS1986

Measuring interstellar dust grains from the haloes of binary X-ray sources

A method for determining the location, size distribution, and composition of interstellar dust grains from the haloes of binary X-ray sources is described. The method is based on the time dependence of the halo X-ray emission during an eclipse of the point source. The distance of the dust cloud is inferred directly from observations of the growth of the dark circle around the eclipsed point source. Grain size distribution in the interstellar dust clouds is derived from the halo brightness profile at a given photon energy. The composition of the grains is obtained by observing the spectral features in the total optical depth due to X-ray scattering near the photoionization thresholds of the elements in the grains. The haloes become dim just below the ionization threshold, and sharply increase in function brightness as the photon energy increases beyond the absorption edge of the relevant atom. The method makes it possible to observe and analyze the halo emission during eclipse even without imaging the source. It is suggested that haloes probably account for the soft X-rays observed during eclipses and dips observed in sources including 4U1915-05 and X1755-338.

Xu, Y.↗

NASA NTRS1990

On planetary nebulae as sources of carbon dust: Infrared emission from planetary nebulae of the galactic halo

Planetary nebulae of the galactic disk are generally seen to emit a thermal continuum due to dust grains heated by stellar and nebular photons. This continuum typically peaks between 25 and 60 micron m, so that the total power emitted by the dust is sampled well by the broad-band measurements made by IRAS. Researchers examine here the characteristics of the infrared emission from the four planetary nebulae which are believed on the basis of their low overall metallicities to belong to the halo population. These nebulae are of particular interest because they are the most metal-poor ionized nebulae known in our Galaxy, and offer the opportunity to probe possible dependences of the dust properties on nebular composition. Researchers present fluxes extracted from co-addition of the IRAS data, as well as ground-based near infrared measurements. Each of the four halo objects, including the planetary nebula in the globular cluster M15, is detected in at least one infrared band. Researchers compare the estimated infrared excesses of these nebulae (IRE, the ratio of measured infrared power to the power available in the form of resonantly-trapped Lyman alpha photons) to those of disk planetary nebulae with similar densities but more normal abundances. Three of the halo planetaries have IRE values similar to those of the disk nebulae, despite the fact that their Fe- and Si-peak gas phase abundances are factors of 10 to 100 lower. However, these halo nebulae have normal or elevated C/H ratios, due to nuclear processing and mixing in their red giant progenitors. Unlike the other halo planetaries, DDDM1 is deficient in carbon as well as in the other light metals. This nebula has a substantially lower IRE than the other halo planetaries, and may be truly dust efficient. Researchers suggest that the deficiency is due to a lack of the raw material for producing carbon-based grains, and that the main bulk constituent of the dust in these planetary nebulae is carbon.

Dinerstein, Harriet L.↗

NASA NTRS1994

Cold dark matter. 1: The formation of dark halos

We use numerical simulations of critically closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to 256(exp 3) particles using the particle-mesh (PM) method and with up to 144(exp 3) particles using the adaptive particle-particle-mesh (P3M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations, and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all omega = 1 CDM models for linear amplitude sigma(sub 8) greater than or approximately = 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low-mass halos. The distribution of halos characterized by their circular velocities for the P3M simulations is in reasonable agreement with the observations for 150 km/s less than or = V(sub circ) less than or = 350 km/s.

Gelb, James M.↗