nmagic: a fast parallel implementation of a χ2-made-to-measure algorithm for modelling observational data

We describe a made-to-measure (M2M) algorithm for constructing N -particle models of stellar systems from observational data (χ²M2M), extending earlier ideas by Syer & Tremaine. The algorithm properly accounts for observational errors, is flexible, and can be applied to various systems and geometries. We implement this algorithm in a parallel code nmagic and carry out a sequence of tests to illustrate its power and performance. (i) We reconstruct an isotropic Hernquist model from density moments and projected kinematics and recover the correct differential energy distribution and intrinsic kinematics. (ii) We build a self-consistent oblate three-integral maximum rotator model and compare how the distribution function is recovered from integral field and slit kinematic data. (iii) We create a non-rotating and a figure rotating triaxial stellar particle model, reproduce the projected kinematics of the figure rotating system by a non-rotating system of the same intrinsic shape, and illustrate the signature of pattern rotation in this model. From these tests, we comment on the dependence of the results from χ²M2M on the initial model, the geometry, and the amount of available data.     

A comparative study of the electron and photon components in photon-induced air showers

A detailed simulation of the electromagnetic component of extensive air showers generated by 10¹¹–10¹⁵ eV photons has been carried out by means of the EPAS code. We present and discuss the results concerning the longitudinal, lateral and temporal distributions of electrons and photons down to 1 MeV energy threshold.     

Properties of the infrared dark cloud G79.2+0.38

The MSX infrared dark cloud G79.2+0.38 has been observed over a 11′×′ region simultaneously in the J=1-0 rotational transition lines of the ¹²CO and its isotopic molecules ¹³CO and ¹⁸CO. The dense molecular cores defined by the C¹⁸O line are found to be associated with the two high-extinction patches shown in the MSX A-band image. The two dense cores have the column density N (H₂) (5 – 12) × 10²² cm⁻² and the mean number density n (3 ± 1) × 10⁴ cm⁻³. Their sizes are 1.7 and 1.2 pc in ¹³CO(1-0) line, 1.2 and 0.6 pc in C¹⁸O(1-0) line, respectively. The masses of these cloud cores are estimated to be in the range from 2 × 10² to 2 × 10³ M. The profile of radial mean density of the cloud core can be described by the exponential function ¯n(p) p^{−0.34±0.02}. Compared with the cases of typical optical dark clouds, the abundances of the CO isotopic molecules ¹³CO and C¹⁸O in this MSX infrared dark cloud appear to be depleted by a factor of 4–11, but at present there is no evidence for any obvious variation of the relative abundance ratio X_13/18 between ¹³CO and C¹⁸O with the column density.     

Generalized limits to the number of light particle degrees of freedom from big bang nucleosynthesis

We compute the big bang nucleosynthesis limit on the number of light neutrino degrees of freedom in a model-independent likelihood analysis based on the abundances of ⁴He and ⁷Li. We use the two-dimensional likelihood functions to simultaneously constrain the baryon-to-photon ratio and the number of light neutrinos for a range of ⁴He abundances Y_p = 0.225–0.250, as well as a range in primordial ⁷Li abundances from (1.6 to 4.1) ×10⁻¹⁰. For (⁷Li/H)_p = 1.6 × 10⁻¹⁰, as can be inferred from the ⁷Li data from Population II halo stars, the upper limit to N_ν based on the current best estimate of the primordial ⁴He abundance of Y_p = 0.238 is N_ν < 4.3 and varies from N_ν < 3.3 (at 95% C.L.) when Y_p = 0.225 to N_ν < 5.3 when Y_p = 0.250. If ⁷Li is depleted in these stars the upper limit to N_ν is relaxed. Taking (⁷Li/H)_p = 4.1 × 10⁻¹⁰, the limit varies from N_ν < 3.9 when Y_p = 0.225 to N_ν 6 when Y_p = 0.250. We also consider the consequences on the upper limit to N_ν if recent observations of deuterium in high-redshift quasar absorption-line systems are confirmed.     

The cosmic ray primary composition in the “knee” region through the EAS electromagnetic and muon measurements at EAS-TOP

The evolution of the cosmic ray primary composition in the energy range 10⁶–10⁷ GeV (i.e. the “knee” region) is studied by means of the e.m. and muon data of the Extensive Air Shower EAS-TOP array (Campo Imperatore, National Gran Sasso Laboratories). The measurement is performed through: (a) the correlated muon number (N_μ) and shower size (N_e) spectra, and (b) the evolution of the average muon numbers and their distributions as a function of the shower size. From analysis (a) the dominance of helium primaries at the knee, and therefore the possibility that the knee itself is due to a break in their energy spectrum (at E_k^He=(3.5±0.3)×10⁶ GeV) are deduced. Concerning analysis (b), the measurement accuracies allow the classification in terms of three mass groups: light (p,He), intermediate (CNO), and heavy (Fe). At primary energies E₀≈10⁶ GeV the results are consistent with the extrapolations of the data from direct experiments. In the knee region the obtained evolution of the energy spectra leads to: (i) an average steep spectrum of the light mass group (γ_p,He>3.1), (ii) a spectrum of the intermediate mass group harder than the one of the light component (γ_CNO2.75, possibly bending at E_k^CNO≈(6–7)×10⁶ GeV), (iii) a constant slope for the spectrum of the heavy primaries (γ_Fe2.3–2.7) consistent with the direct measurements. In the investigated energy range, the average primary mass increases from lnA=1.6–1.9 at E₀1.5×10⁶ GeV to lnA=2.8–3.1 at E₀1.5×10⁷ GeV. The result supports the standard acceleration and propagation models of galactic cosmic rays that predict rigidity dependent cut-offs for the primary spectra of the different nuclei. The uncertainties connected to the hadronic interaction model (QGSJET in CORSIKA) used for the interpretation are discussed.     

Compton scattered transition radiation from very high energy particles

X-ray transition radiation can be used to measure the Lorentz factor of relativistic particles. At energies approaching γ=E/mc²=10⁵, transition radiation detectors can be optimized by using thick (5–10 mil) foils with large (5–10 mm) spacings. This implies X-ray energies 100 keV and the use of scintillators as the X-ray detectors. Compton scattering of the X-rays out of the particle beam then becomes an important effect. We discuss the design of very high energy detectors, the use of metal radiator foils rather than the standard plastic foils, inorganic scintillators for detecting Compton scattered transition radiation, and the application to the ACCESS cosmic ray experiment.     

An auroral F-region study using in situ measurements by the Atmosphere Explorer-C satellite

On 14 July 1974 the Atmosphere Explorer-C satellite flew through an aurora at F-region altitudes just after local midnight. The effects of the particle influx are clearly evident in the ion densities, the 6300 Å airglow, and the electron and ion temperatures. This event provided an opportunity to study the agreement between the observed ion densities and those calculated from photochemical theory using in situ measurements of such atmospheric parameters as the neutral densities and the differential electron energy spectra obtained along the satellite track. Good agreement is obtained for the ions O₂⁺, NO⁺ and N₂⁺ using photochemical theory and measured rate constants and electron impact cross sections. Atomic nitrogen densities are calculated from the observed [NO⁺]/[O₂⁺] ratio. In the region of most intense electron fluxes (20 erg cm⁻² sec⁻¹) at 280 km, the N density is found to be between 2 and 7 × 10⁷ cm⁻³. The resulting N densities are found to account for approx. 60% of the production of N⁺ through electron impact on N and the resonant charge exchange of O⁺(²P) with N(⁴S). This reaction also provides a significant source of O(¹S) in the aurora at F-region altitudes. In the region of intense fast electron influx, the reaction with atomic nitrogen is found to be the main loss of O⁺(²P).     

Space–time foam and cosmic-ray interactions

It has been proposed that propagation of cosmic-rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (“foam”). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of space–time foam. The strength of the foam is characterized by the factor (E/M_P)^a, where a is a phenomenological suppression parameter. We find that there exists a critical value of a (dependent on the particular reaction: a_crit3 for cosmic-rays, 1 for gamma-rays), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. In the context of this foam model, we find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10⁸ TeV for the scale of gravity. We also find that suppression of p→pπ⁰ and γ→e⁻e⁺ “decays” favors values aa_crit. Finally, we comment on the apparent non-conservation of particle energy–momentum, and speculate on its re-emergence as dark energy in the foamy vacuum.     

Density profiles of dark matter halos with anisotropic velocity tensors

We present density profiles, that are solutions of the spherical Jeans equation, derived under the following two assumptions: (i) the coarse grained phase-density follows a power-law of radius, ρ/σ³ ∝ r⁻, and (ii) the velocity anisotropy parameter is given by the relation β_a(r)=β₁+2β₂ (r/r_*)/[1+(r/r_*)²] where β₁, β₂ are parameters and r_* equals twice the virial radius, r_vir, of the system. These assumptions are well motivated by the results of N-body simulations. Density profiles have increasing logarithmic slopes γ, defined by γ=−d ln ρ/d ln r. The values of γ at r=10^−2.5r_vir, a distance where the systems could be resolved by large N-body simulations, lie in the range 1.0–1.6. These inner values of γ increase for increasing β₁ and for increasing concentration of the system. On the other hand, slopes at r=r_vir lie in the range 2.42–3.82. A model density profile that fits well the results at radial distances between 10⁻³r_vir and r_vir and connects kinematic and structural characteristics of spherical systems is described.     

A parallel TreeSPH code for galaxy formation

We describe a new implementation of a parallel TreeSPH code with the aim of simulating galaxy formation and evolution. The code has been parallelized using shmem , a Cray proprietary library to handle communications between the 256 processors of the Silicon Graphics T3E massively parallel supercomputer hosted by the Cineca Super-computing Center (Bologna, Italy). ¹
The code combines the smoothed particle hydrodynamics (SPH) method for solving hydrodynamical equations with the popular Barnes & Hut tree-code to perform gravity calculation with an N ×log  N scaling, and it is based on the scalar TreeSPH code developed by Carraro et al. Parallelization is achieved by distributing particles along processors according to a workload criterion.
Benchmarks, in terms of load balance and scalability, of the code are analysed and critically discussed against the adiabatic collapse of an isothermal gas sphere test using 2×10⁴ particles on 8 processors. The code results balance at more than the 95 per cent level. Increasing the number of processors, the load balance slightly worsens. The deviation from perfect scalability for increasing number of processors is almost negligible up to 32 processors. Finally, we present a simulation of the formation of an X-ray galaxy cluster in a flat cold dark matter cosmology, using 2×10⁵ particles and 32 processors, and compare our results with Evrard's P³M–SPH simulations.
Additionally we have incorporated radiative cooling, star formation, feedback from SNe of types II and Ia, stellar winds and UV flux from massive stars, and an algorithm to follow the chemical enrichment of the interstellar medium. Simulations with some of these ingredients are also presented.     

High-performance direct gravitational N-body simulations on graphics processing units

We present the results of gravitational direct N-body simulations using the commercial graphics processing units (GPU) NVIDIA Quadro FX1400 and GeForce 8800GTX, and compare the results with GRAPE-6Af special purpose hardware. The force evaluation of the N-body problem was implemented in Cg using the GPU directly to speed-up the calculations. The integration of the equations of motions were, running on the host computer, implemented in C using the 4th order predictor–corrector Hermite integrator with block time steps. We find that for a large number of particles (N  10⁴) modern graphics processing units offer an attractive low cost alternative to GRAPE special purpose hardware. A modern GPU continues to give a relatively flat scaling with the number of particles, comparable to that of the GRAPE. The GRAPE is designed to reach double precision, whereas the GPU is intrinsically single-precision. For relatively large time steps, the total energy of the N-body system was conserved better than to one in 10⁶ on the GPU, which is impressive given the single-precision nature of the GPU. For the same time steps, the GRAPE gave somewhat more accurate results, by about an order of magnitude. However, smaller time steps allowed more energy accuracy on the grape, around 10⁻¹¹, whereas for the GPU machine precision saturates around 10⁻⁶ For N  10⁶ the GeForce 8800GTX was about 20 times faster than the host computer. Though still about a factor of a few slower than GRAPE, modern GPUs outperform GRAPE in their low cost, long mean time between failure and the much larger onboard memory; the GRAPE-6Af holds at most 256k particles whereas the GeForce 8800GTX can hold 9 million particles in memory.     

OH masers in W 33A

This paper presents observations of OH maser lines of W 33A for the transitions ²Π_3/2, J = 3/2, F = 1 → 1 and F = 2 → 2. Two models, a thin tube and a sphere, were used for modelling the masing region and a molecular hydrogen density of about 10⁷ cm⁻³ was obtained. To give a maser photon emission of the order of 10⁴⁶ s⁻¹, both models require a pump rate of 1 OH cm⁻³s⁻¹, while the sphere model requires a higher pump efficiency.     

The cosmic ray energy spectrum between 10 and 10 eV

The energy spectrum of cosmic rays with primary energies between 10¹⁴ eV and 10¹⁶ eV has been studied with the CASA-MIA air shower array. The measured differential energy spectrum is a power law (dj/dE ∝ E^−y) with spectral indices γ of 2.66±0.02 below approximately 10¹⁵ eV and 3.00±0.05 above. A new method is used for measuring primary energy derived from ground-based data in a compositionally insensitive way. In contrast with some previous reports, the “knee” of the energy spectrum does not appear sharp, but rather a smooth transition over energies from 10¹⁵ eV to 3.0 × 10¹⁵ eV.     

Comparison of high-energy galactic and atmospheric tau neutrino flux

We compare the tau neutrino flux arising from the galaxy and the earth atmosphere for 10³E/GeV10¹¹. The intrinsic and oscillated tau neutrino fluxes from both sources are calculated. The intrinsic galactic ν_τ flux (E10³ GeV) is calculated by considering the interactions of high-energy cosmic-rays with the matter present in our galaxy, whereas the oscillated galactic ν_τ flux is coming from the oscillation of the galactic ν_μ flux. For the intrinsic atmospheric ν_τ flux, we extend the validity of a previous calculation from E10⁶ GeV up to E10¹¹ GeV. The oscillated atmospheric ν_τ flux is, on the other hand, rather suppressed. We find that, for 10³E/GeV5×10⁷, the oscillated ν_τ flux along the galactic plane dominates over the maximal intrinsic atmospheric ν_τ flux, i.e., the flux along the horizontal direction. We also briefly mention the presently envisaged prospects for observing these high-energy tau neutrinos.     

Comparison of AGASA data with CORSIKA simulation

An interpretation of Akeno giant air shower array (AGASA) data by comparing the experimental results with the simulated ones by cosmic ray simulation for KASCADE (CORSIKA) has been made. General features of the electromagnetic component and low energy muons observed by AGASA can be well reproduced by CORSIKA. The form of the lateral distribution of charged particles agrees well with the experimental one between a few hundred metres and 2000 m from the core, irrespective of the hadronic interaction model studied and the primary composition (proton or iron). It does not depend on the primary energy between 10^17.5 and 10²⁰ eV as the experiment shows. If we evaluate the particle density measured by scintillators of 5 cm thickness at 600 m from the core S₀(600), suffix 0 denotes the vertically incident shower) by taking into account the similar conditions as in the experiment, the conversion relation from S₀(600) to the primary energy is expressed as E (eV)=2.15×10¹⁷S₀(600)^1.015 within 10% uncertainty among the models and composition used, which suggests the present AGASA conversion factor is the lower limit. Although the form of the muon lateral distribution fits well to the experiment within 1000 m from the core, the absolute values change with hadronic interaction model and primary composition. The slope of the ρ_μ(600) (muon density above 1 GeV at 600 m from the core) vs. S₀(600) relation in experiment is flatter than that in simulation of any hadronic model and primary composition. As the experimental slope is constant from 10¹⁵ to 10¹⁹ eV, we need to study this relation in a wide primary energy range to infer the rate of change of chemical composition with energy.     

Twilight effects of solar ionizing radiation

The absorption of solar ionizing radiation during twilight is investigated. Ion production rates are obtained as a function of altitude and twilight intensities and altitude profiles of emissions arising from the fluorescence of solar ionizing radiation are calculated for various solar depression angles. For an atmosphere with an exospheric temperature of 750°K, the predicted overhead intensity from fluorescence of the O⁺(²P — ²D) lines at 7319–7330 diminishes from 175 R at dusk to 10 R at a solar depression angle of 10°. The predicted overhead intensities from fluorescence of the N₂⁺ Meinel and first negative systems are respectively about 175 R and 20 R at dusk diminishing to respectively 1.5 R and 0.1 R at a solar depression angle of 10°.

It is suggested that a charge transfer reaction of O⁺²D in N₂ is a significant source of N₂⁺ ions. This reaction offers a possible explanation for the high apparent rotational temperatures in the first negative system observed by Broadfoot and Hunten. Other excitation and ionization mechanisms are briefly discussed.     

A possible gas for solar neutrino spectroscopy

We discuss the possibility of using pure CF₄ to fill a 2000 m³ Time Projection Chamber in order to detect the solar neutrinos through the elastic scattering v_ee⁻ → v_ee⁻, with the threshold of 100 keV on the kinetic energy of the recoiling electron. In a volume of 2000 m³ of CF₄ at normal pressure and room temperature, which corresponds to a mass of 7.4 ton, we expect ~ 3300 of such events per year. The detector can give the spectrum of the low energy neutrinos from the Sun and it can identify solar neutrinos of different origin: pp, ⁷Be, and, eventually, ⁸B. We find that ¹⁴C is a possible severe source of background: it is necessary to have a ratio ¹⁴C/¹²C lower than 10⁻¹⁹ in order to be able to identify the pp neutrinos.     

Reanalysis of GU miniarray data using CORSIKA

The GU miniarray is a ultra high energy cosmic ray (UHECR) detector consisting of eight plastic scintillators of carpet area 2 m², each viewed by fast PMTs. It is used to detect Giant EAS by the method of time spread measurement of secondary particles produced in the atmosphere. The energies of the air showers have been reestimated using CORSIKA program. As in the original analysis the Cosmic Ray energy was determined via its relation to the ground level parameter N_s, the shower size. This relation was obtained previously through a best fit relation in agreement with QGS model and Yakutsk data. In this work we use CORSIKA code with QGSJET model of high energy hadronic interactions to simulate miniarray data leading to a modified relation between primary energy and shower size. A revised energy spectrum is reported for 10¹⁷–10¹⁹ eV primary energy.     

A prediction for three neutrino masses and mixings and similarity between quark and lepton mixings

If neutrinos have mass, we give reasons for a possible pattern of three (squaed) mass eigenvalues: m₁² (2.8−5.8) (eV)², m₂² 0.01 (eV)², m₃² (1.5−1) × 10⁻⁴ (eV)². The flavor states ν_μ and ν_e are mixtures of the eigenstates with m₂ and m₃ with a significant mixing, corresponding to an effective mixing angle of about 0.45. The ν_τ is nearly the state with m₁; the other two effective mixing angles are about an order of magnitude smaller than 0.45. There is a marked similarity to mixing in the quark sector.     

Observation and Study of the CO, CO, HCO and N2H Molecular Lines Towards IRAS 02232+6138

Using the 13.7 m millimeter-wave telescope at the Qinghai Station of Purple Mountain Observatory, we have made observations of ¹³CO, C¹⁸O, HCO⁺ and N₂H⁺ molecular lines towards IRAS 02232+6138. As the excitation density of the probe molecule increases from ¹³CO to HCO⁺, the size of the cloud core associated with IRAS 02232+6138 decreases from 2.40 pc to 0.54 pc, and the virial mass of the cloud core decreases from 2.2 × 10³M to 5.1 × 10²M. A bipolar molecular outflow is found towards IRAS 02232+6138. Using the power function n(r) ∝ r⁻ to fit the spatial density structure of the cloud core, we obtain the power-law index  = 2.3 − 1.2; and we find that, as the probed density increases, the power function becomes more flat. The abundance ratio of ¹³CO to C¹⁸O is 12.4 ± 6.9, comparable with the values 11.8 ± 5.9 for dark clouds and the values 9.0–15.6 for massive cores. The abundance of N₂H⁺ molecules is 3.5 ± 2.5 × 10⁻¹⁰, consistent with the value 1.0 − 5.0 × 10⁻¹⁰ for dark cloud cores and the value 1.2 − 12.8 × 10⁻¹⁰ for massive cores. The abundance of HCO⁺ molecules is 0.9 ± 0.5 × 10⁻⁹, close to the value 1.6 − 2.4 × 10⁻⁹ for massive cores. An increase of HCO⁺ abundance in the outflow region was not found. Combining with the IRAS data, the luminosity-mass ratio of the cloud core is obtained in the range 37–163(L/M). Based on the IRAS luminosity, it is estimated that a main-sequence O7.5 star is probably embedded in the IRAS 02232+6138 cloud core.