倾角函数及其导数的定积分计算方法

给出了一种倾角函数及其导数的定积分计算方法,表达式十分简单,其计算精度:倾角函数可达10^-15,导数可达10^-13,可与Gooding方法相媲美.该方法的稳定性和适用倾角范围均较好,可供倾角函数的最高阶数L_max≤50时使用.     

Laboratory kinetics of C2H radical reactions with ethane, propane, and n-butane at T = 96-296 K: implications for Titan

The kinetics of the reactions of C₂H radical with ethane (k₁), propane (k₂), and n-butane (k₃) are studied over the temperature range of T = 96-296 K with a pulsed Laval nozzle apparatus that utilizes a pulsed laser photolysis-chemiluminescence technique. The C₂H decay profiles in the presence of both the alkane reactant and O₂ are monitored by the CH(A²Δ) chemiluminescence tracer method. The results, together with available literature data, yield the following Arrhenius expressions: k₁(T) = (0.51 ± 0.06) × 10⁻¹⁰ exp[(−76 ± 30)K/T] cm³ molecule⁻¹ s⁻¹ (T = 96-800 K), k₂(T) = (0.98 ± 0.32) × 10⁻¹⁰exp[(−71 ± 60)K/T] cm³ molecule⁻¹ s⁻¹ (T = 96-361 K), and k₃(T) = (1.23 ± 0.26) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ (T = 96-297 K). At T = 296 K, k₁ is measured as a function of total pressure and has little or no pressure dependence. The results from this work support a direct hydrogen abstraction mechanism for the title reactions. Implications to the atmospheric chemistry of Titan are discussed.     

Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15R_J for Jupiter and rCS ∼ 22R_S for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (R_H), which we choose to be ∼R_H/5 (located at ∼150 R_J near the inner irregular satellites for Jupiter, and ∼200R_S near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼10⁶ years, Iapetus in 10⁶-10⁷ years, Ganymede in 10³-10⁴ years, and Titan in 10⁴-10⁵ years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100R_J. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH₃ present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H₂O as well as other issues that may help to test our model.     

HS 2333 + 3927: a new sdB binary with a large reflection effect

We report the discovery of a binary, HS 2233 + 3927, consisting of an sdB star with a faint companion. From its lightcurve the orbital period of 14,844 s, the mass ratio, the inclination, and other system parameters are derived. The companion does not contribute to the optical light of the system except through a strong reflection effect. The semi-amplitude of the radial velocity curve K ₁= 89.6 km/s^?1 and a mass function of f(m) = 0.013 M _⊙ are determined. A preliminary spectroscopic analysis of the blue spectra using NLTE model atmospheres results in T_eff= 36 500 K, log g= 5.70, and log(n _He/n _H) =?2.15. These parameters are typical for sdB stars, the companion is probably an M dwarf.     

Structure and chemical composition of the envelope of Nova V339 del in the nebular phase

Based on our spectrophotometric observations, we have investigated the envelope of Nova V339 Del in the nebular phase. Our modeling of the Hα line profiles and their comparison with the observed profiles have shown that the Nova envelope consists of circumpolar ejecta and a disk-shaped central component. The inclination of the orbital plane of the binary system, 65°, has been determined in the same way. We have estimated the mean electron density to be ~10⁶ cm^-3. Our estimates of the abundances of some chemical elements in the Nova envelope have shown that the concentrations of helium, neon, and iron are nearly solar, while the concentrations of nitrogen and oxygen exceed the solar ones by a factor of 120 ± 60 and 8 ± 1.6, respectively. The mass of the emission envelope in the nebular phase (from 253 to 382 days after the brightness maximum) has been estimated to be ~7 × 10^-5 M _⊙.     

An updated period analysis for ER Orionis: A definitive solution

An updated period analysis for the overcontact eclipsing binary ER Orionis is presented. Featured is an improved derivation of parameters for the light time effect (LTE) due to the third star (in actuality, a pair of stars) utilising the latest set of eclipse timings. The very good fit between the eclipse timing differences (ETD) plot (otherwise known as an O–C diagram) and the theoretical ETD curve makes possible an improved determination of the rate of mass interchange between the binary pair, dm₁/dt = +1.83(6) × 10⁻⁷ M_ʘ/year. In addition, the mass of the companion system (in actuality, m₃ sin i) and the elements of its orbit were computed. A suggestion is made for a method of future determination of the inclination of the orbit of the companion system.     

Hydrodynamic processes in young binaries as a source of cyclic variations in circumstellar extinction

Hydrodynamic models of a young binary accreting matter from the remnants of a protostellar cloud have been calculated by the SPH method. Periodic variations in column density in projection onto the primary component are shown to take place at low inclinations of the binary plane to the line of sight. These can result in periodic extinction variations accompanied by brightness variations in the primary. Generally, there can be three periodic components. The first component has a period equal to the orbital one and is attributable to the streams of matter penetrating into the inner regions of the binary. The second component has a period that is a factor of 5–8 longer than the orbital one and is related to the density waves generated in a circumbinary (CB) disk. Finally, the third, longest period is attributable to the precession of the inner CB disk regions. The relationship between the amplitudes of these cycles depends on the model parameters as well as on the inclination and orientation of the binary in space. We show that at a dust-togas ratio of 1: 100 and amass extinction coefficient of 250 cm² g^?1, the amplitude of the V-band brightness variations in the primary component can reach 1 ^m at a mass accretion rate onto the binary components of 10.8^?8 M _⊙ yr^?1 and a 10° inclination of the binary plane to the line of sight. We discuss possible applications of the model to young, pre-main-sequence stars.     

Upper-atmosphere features revealed by the orbit of 1980-43A

The satellite NOAA-B (1980-43A) was launched in May 1980 into an orbit with perigee height near 260 km and apogee height 1440 km, at an inclination of 92.2°.The lifetime was 11 months. The orbit has been determined at 40 epochs between October 1980 and May 1981 from about 3000 radar and optical observations. The average orbital accuracy, radial and cross-track, was about 100 m, with rather better accuracy in the final 14 days.The variation of orbital inclination has been analysed to determine two good values of atmospheric rotation rate, namely 1.10 ± 0.10 rev day^?1 at 300 km (average local time) and 1.15 ± 0.06 rev day^?1 at 225 km (evening).The effect of atmospheric rotation on the precession of the orbital plane of an actual satellite has never previously been detected; it is clearly apparent for 1980-43A in its last days and conforms to the expected theoretical change.The variation of perigee height has been analysed to determine ten values of atmospheric density scale height, for heights of 280–370 km. These values, accurate to about 3%, exceed by 15% the values indicated by the COSPAR International Reference Atmosphere. Solar activity was higher in the years 1980–1981 than at any time since early 1958 and it appears that the CIRA model underestimates the density and density scale height at high levels of solar activity.     

Gyldén Model: The Slowly Changing Equivalent Gravitational Parameter

In the Gyldén problem, the case of slowly changing equivalent gravitational parameter (e.g.p.) is studied. Assuming the following law for the variation of the e.g.p.: μ (t) = μ₀+ εμ (εt), ε< μ₀, we obtained a) a O(ε⁴ T⁴)-approximation of the solution, on a shortened time scale (0,T), with T of order o(ε^-1),for the general case (i.e. the support function μ is O(1)-valued and admits an expansion in power series of its argument), and b) a O(ε²)-approximation of the solution, on a natural timescale of order O(1/ε), for the case of a bounded variation rate (i.e. the support function μ and its derivative are both O(1)-valued). For the study of the first problem we introduced a type of Lissajous variables and used the Lie-Hori normalization scheme; for the second problem we used the Delaunay variables and applied the von Zeipel method for approximate integration. The physical interpretation of the results is in both cases the same: within the corresponding limits of approximation, the variation of e.g.p. (i) has no effect on the size of the osculating ellipse, (ii) it sets the pericenter in slow rotation and (iii) it introduces a secular variation in the longitudes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observations of CO in the atmosphere of Mars with PFS onboard Mars Express

We have analyzed spectra of CO recorded with the instrument PFS onboard Mars Express in the (1-0) band. The dataset we used ranges in time from January until June 2004 (L_S=331^°.17 until L_S=51^°.61; end of Mars Year 26, beginning of Mars Year 27). The aim of this work was to determine the amplitude of the CO mixing ratio departures from the mean globally averaged value currently admitted (8±3×10^-4) [Kaplan, L.D., Connes, J., Connes, P., 1969. Carbon monoxide in the martian atmosphere. Astron. J. 157, L187-L192] as a function of season, local time and location on the planet. We therefore processed the data from 90 calibrated orbits. The globally averaged CO mixing ratio value we derive from our dataset, 11.1×10^-4, is compatible with the range found by Kaplan et al. [1969. Carbon monoxide in the martian atmosphere. Astron. J. 157, L187-L192], although somewhat higher than the “standard” value. However, the CO mixing ratio we retrieve exhibits large variations (roughly between 3×10^-4 and 18×10^-4). Such relative variations have been used on a statistical basis to derive main trends as a function of latitude for three L_S ranges: 331-360^°, 0-30^° and 30-52^°. For the first L_S range, we seem to have an enhancement of the CO mixing ratio towards the northern latitudes, probably linked to the CO₂ condensation in winter on the north polar cap. The situation for the two other L_S ranges is not so clear, mainly as we lack data on the southern hemisphere. We roughly agree with the work of Krasnopolsky [2007. Long-term spectroscopic observations of Mars using IRTF/CSHELL: mapping of O2 dayglow, CO and search for CH4. Icarus 190, 93-102] for L_S=331-360^°, thus confirming the effect of seasonal condensation of CO₂ on the north polar cap, but we have no agreement for other seasons.     

Another view of synodic solar rotation

Adding the angular velocity of sidereal solar rotation and the apparent rotational effect of the Earth's revolution vectorially, a new synodic solar rotation vector has been obtained. The sidereal and synodic solar rotation axes (and equators) are separated. Using the known parameters of the Earth's orbital motion, the synodic rotation angular velocity and the inclination of the synodic equator, the corresponding sidereal rotation parameters have been calculated (ω₁ = 2.915 × 10^#X2212;6 rad s^#X2212;1 and i ₁ = 6.076). Various linear rotational velocities at the solar globe are briefly described.     

Intensities and anisotropies of low energy solar protons measured aboard the satellites Azur,Explorer 35 and 41, November 1969–April 1970

The NRL SOLRAD 10 satellite carries six ionization chambers to measure solar X-radiation in the 0.5 to 60 Å wavelength band. The X-ray emission spectrum in this range is determined by the derivative of the coronal emission measure (∫ N _e ² dV) with respect to temperature when the thermal processes of bremsstrahlung, radiative recombination and line radiation are considered. If a simple model for this differential emission measure is used and detector responses to the calculated spectra are fitted to the SOLRAD data by a least squares method, the differential emission measure can be obtained for temperatures between 2 × 10⁶K and 64 × 10⁶K. Data during quiet and flaring periods are analyzed and the general behavior of the differential emission measure during flares is presented. This analysis is based on experimental measurements of the efficiencies of the SOLRAD detectors.     

Optical variability of Mrk 421

We observed Mrk 421 in V and R band using the 1.0 m telescope at Weihai Observatory of Shandong University since 2009 April to 2012 May. The available historical data in B and V band were also assembled for constructing light curves. The brightness of Mrk 421 ranges from 11.40 to 16.14 in the B band light curve, and from 11.38 to 14.56 in the V band. Analyses with the Jurkevich method and the structure function method showed a possible period of about 1.36 years for its long periodic variability. This period could be explained by a close binary black hole system (BBHS) model with a primary black hole mass of 1.70×10⁸ M _⊙ and a secondary ～(0.49–2.9)×10⁷ M _⊙. We showed the color variability of Mrk 421, a bluer when brighter behavior during its lower state. Analyses of spectral index variations show that only a host galaxy contribution is not sufficient to explain the spectral index variations in Mrk 421, and some intrinsic mechanism is needed.     

The polarization of optical radiation from the magnetic white dwarfs

It is pointed out that, because of the large Faraday rotation an outlet of linear polarization from the photosphere of a white dwarf is hampered. In accordance with this fact it is proposed to distinguish two types of magnetic white dwarfs. The first type (its representative is Grw 70°8247) has a linear polarization which is comparable in magnitude with the circular one. Polarization of radiation from the white dwarfs of the first type cannot arise in the photosphere. It arises in the corona of the star either as a result of cyclotron emission of hot electrons (T～10⁶ K) or as a result of scattering of slightly polarized emission from the photosphere in the corona. For the first type dwarfs such magnetic fields are required thatω _B ω_opt, i.e.B(1?3)×10⁸G. The white dwarfs of the second type (its representative is G 99-37) have their linear polarization much smaller than the circular one. Polarization of these white dwarfs can arise as a result of the transfer of radiation in the nonisothermal photosphere. Magnetic fields required for the second type can be much smaller:B cos γ=(1?10)×10⁶ G. It is shown that the photospheric model allows to obtain the quantitative accordance of the theory with all the observational data for G 99-37 and is not in accordance with the data for Grw 70°8247, at the same time the model with cyclotron emission from the corona explains the magnitude of both linear and circular polarization and their wavelength dependence for Grw 70°8247.     

X-ray Luminosity Function of Quasars at 3 &lt; <Emphasis Type="Italic">z</Emphasis> &lt; 5 from XMM-Newton Serendipitous Survey Data

The X-ray luminosity function of distant (3 < z < 5.1) type 1 quasars has been measured. A sample of distant high-luminosity (10⁴⁵ erg s^?1 ≤ L_X,2?10 < 7.5×10⁴⁵ erg s^?1 in the 2–10 keV energy band) quasars from the catalog by Khorunzhev et al. (2016) compiled from the data of the 3XMM-DR4 catalog of the XMM-Newton serendipitous survey and the Sloan Digital Sky Survey (SDSS) has been used. This sample consists of 101 sources. Most of them (90) have spectroscopic redshifts z_spec ? 3; the remaining ones are quasar candidates with photometric redshift estimates z_phot ? 3. The spectroscopic redshifts of eight sources have been measured with the BTA and AZT-33IK telescopes. Owing to the record sky coverage area (?250 sq. deg at X-ray fluxes ~10^?14 erg s^?1 cm^?2 in the 0.5–2 keVband) from which the sample was drawn, we have managed to obtain reliable estimates of the space density of distant X-ray quasars with luminosities L_X,2?10 > 2×10⁴⁵ erg s^?1 for the first time. Their comoving space density remains constant as the redshift increases from z = 3 to 5 to within a factor of 2. The power-law slope of the X-ray luminosity function of distant quasars at its bright end (above the break) has been reliably constrained for the first time. The range of possible slopes for the quasar luminosity and density evolution model is γ₂ = 2.72 _?0.12 ^+0.19 ± 0.21, where initially the lower and upper boundaries of γ₂ with the remaining uncertainty in the detection completeness of X-ray sources in SDSS and subsequently the statistical error of the slope are specified.     

Analysis of the clustering of 2dFGRS galaxies using the method of a modified correlation gamma function

The apparatus of a correlation gamma function is used to analyze a sample of 2dFGRS galaxies. We suggest a modified gamma-function algorithm with nonintersecting working spheres, which ensures that the counts are independent at each step. The method of nonintersecting spheres has revealed a change in the regime of clustering (a break of the gamma function) on a scale of 10–16h^?1 Mpc (H₀ = 65 km s^?1 Mpc^?1). The standard method yields a scale of 30h^?1 Mpc. An artificial distribution is used as an example to show that, in some cases, the modified algorithm is more responsive to a mixture of distributions with various properties than the standard method.     

A limit for gravitational collapse

Earlier, under certain simplifying assumptions, on the basis of the General Theory of Relativity, it has been concluded by many authors that when the radius of a gravitationally collapsing spherical object of massM reaches the critical value of the Scharzschild radiusR _s=2GM/c ², then, in a co-moving frame, the object collapses catastrophically to a point. However, in drawing this conclusion due consideration has not been given to the nuclear forces between the nucleons. In particular, the very strong ‘hard-core’ repulsive interaction between the nucleons which has the range ～0.4×10^?13 cm has been totally ignored. On taking into account this ‘hard-core’ repulsive interaction, it is found that no spherical object of massM g can collapse to a volume of radius smaller thanR _min=(1.68×10^?6)M ^1/3 cm or to a density larger than ρ_max=5.0 × 10¹⁶ g cm^?3. It has also been pointed out that objects of mass smaller thanM _c～1.21×10³³ g can not cross the Schwarzschild barrier and gravitationally collapse. The only course left to the objects of mass less thanM _cis to reach the equilibrium as either a white dwarf or a neutron star.     

The ion H 3 + in a strong magnetic field

A first detailed study of the low-lying electronic states of the H ₃ ⁺ molecular ion in linear configuration, parallel to a magnetic field, is carried out for B=0–4.414×10¹³ G in the Born-Oppenheimer approximation. The variational method is employed with a single, physically adequate trial function which includes, in particular, explicitly the electronic correlation term in the form exp?(γ r ₁₂), where γ is a variational parameter. The state of the lowest total energy (ground state) depends on the magnetic field strength. It evolves from spin-singlet ¹Σ _g for small magnetic fields B?5×10⁸ G to weakly-bound spin-triplet ³Σ _u for intermediate fields and eventually to spin-triplet ³Π _u state for B?5×10¹⁰ G.     

On the spin distributions of ΛCDM haloes

We used merger trees realizations, predicted by the extended Press-Schechter theory, in order to study the growth of angular momentum of dark matter haloes. Our results showed that:

1. The spin parameter λ′ resulting from the above method, is an increasing function of the present day mass of the halo. The mean value of λ′ varies from 0.0343 to 0.0484 for haloes with present day masses in the range of 10⁹h^?1 M _⊙ to 10¹⁴h^?1 M _⊙.
2. The distribution of λ′ is close to a log-normal, but, as it is already found in the results of N-body simulations, the match is not satisfactory at the tails of the distribution. A new analytical formula that approximates the results much more satisfactorily is presented.
3. The distribution of the values of λ′ depends only weakly on the redshift.
4. The spin parameter of an halo depends on the number of recent major mergers. Specifically the spin parameter is an increasing function of this number.