Roles of statistical mechanics in determining the density profile of mild relaxation

The r ^?4 law of cold collapse has been explained in other work. Here we try to explain the density profile of mild relaxation by statistical mechanics. In this paper we first generate many kinds of initial conditions with the same mass and energy to see whether there are other initial factors that can change the density profile of an isolated equilibrium self-gravitating system; then for a more general initial condition we discuss the role of mass and energy in determining the final density profile. Next we use our previous results obtained from statistical mechanics to fit these simulations, and find that when the masses of the particles in clumps are less than 5 % of the total mass, or the initial density is shallower than r ^?2, the whole virialized density profile (VDF) can be fitted well by our equation of state with three parameters, and some other cases can be explained by the theory with the r ^?4 law. We conclude that statistical physics may play an important role in determining the shape of VDF in the mild relaxation, mass and energy can control the values of the central density and the system’s radius, but there are still other initial configurations that can affect the VDF.     

Vertical distribution of water vapor and mars model lower and middle atmosphere

Observations and model calculations of water vapor diffusion suggest that about half the amount of water vapor is distributed with constant mixing ratio in the Martian atmosphere, the other half is the excess water vapor in the lower troposphere. During 24 hr the total content of water vapor may vary by a factor of two. The eddy diffusion coefficient providing agreement between calculations and observations is K = (3–10) × 10⁶ cm² sec^?1 in the troposphere. An analytical expression is derived for condensate density in the stratosphere in terms of the temperature profile, the particle radius r, and K. The calculations agree with the Mars 5 measurements for r = 1.5 μm, condensate density 5 × 10^?12 g/cm³ in the layer maximum at 30 to 35 km, condensate column density 7 × 10^?6 cm^?2, K = (1?3) × 10⁶ cm² sec^?1, and the temperature profile T = 185 ? 0.05z ? 0.01z² at 20 to 40 km. Condensation conditions yield a temperature of 160°K at 60 km in the evening; the scale height for scattered radiation yields T = 110°k at 80 to 90 km. The Mars model atmosphere has been developed up to 125 km.     

Some further comments on approximations of the radial dependence of the electron temperature in two-fluid models of the solar wind

In a previous paper (Cosmic Electrodyn.3, 116) we had suggested the use of the radialr ^?2/5 dependence rather than the often usedr ^?2/7 one in approximations of the electronic temperature profile in some two-fluid models. This note is intended to clarify and restate some points on this subject.     

Measurements of the initial radii of the ionization columns of bright meteors

A multi-wavelength radar backscatter study of the echo characteristics of radio-meteors has yielded measurements of the height dependence of the radii, r_i, of overdense plasma meteor columns. For electron line densities α ～ 10¹⁵ m^?1 it is found that r_i ∝ ?^?0.63 (? atmospheric density) with r_i = 5 m at a height of 100 km.     

Correlation properties of galaxies from the Main Galaxy Sample of the SDSS survey

The apparatus of correlation gamma function (Γ^*(r)) is used to analyze volume-limited samples from the DR4 Main Galaxy Sample of the SDSS survey with the aim of determining the characteristic scales of galaxy clustering. Up to 20h ^?1 Mpc (H ₀ = 65 km s^?1 Mpc^?1), the distribution of galaxies is described by a power-law density—distance dependence, Γ^*(r) ∝ r ^?γ , with an index γ ≈ 1.0. A change in the state of clustering (a significant deviation from the power law) was found on a scale of (20–25) h ^?1 Mpc. The distribution of SDSS galaxies becomes homogeneous (γ ～ 0) from a scale of ～60h ^?1 Mpc. The dependence of γ on the luminosity of galaxies in volume-limited samples was obtained. The power-law index γ increases with decreasing absolute magnitude of sample galaxies M _abs. At M _abs ～ ?21.4, which corresponds to the characteristic value M _r ^* of the SDSS luminosity function, this dependence exhibits a break followed by a more rapid increase in γ.     

A note on the asymptotic density-potential relation of a spiral galaxy with a finite thickness

It is shown that the asymptotic σ₁(r) and ψ₁(r) relations can be derived very simply by using the method of double series expansion, where σ₁, ψ₁(r,0) and ψ₁ are the surface density perturbation, the gravitational potential perturbation at the symmetric plane Z=0 and the average potential perturbation respectively. The results are accurate to the order of both m²(kr)^?2 and k〈∣z∣〉, where m is the number of spiral arms, k is the radial wave number, r is the distance from the centre of the galaxy, and 〈∣z∣〉 is the average vertical distance of a star from the Symmetrie plane Z=0. Such an accuracy is usually sufficient for the discussion of spiral modes in a spiral galaxy of small but finite disk thickness. It is pointed out that ψ₁(r,0)～(σ₁(r) relation can be expressed in a unified form for different vertical density profiles if 〈∣z∣〉 is adopted as the thickness scale, and that ψ₁(r,0)～(σ₁(r) can be expressed in a unified form for different vertical density profiles if 〈∣z?z∣〉 the average vertical separation between two stars, is adopted as the thickness scale. Only the value of the ratio $\text{〈|z?z′|〉z}\text{〈|z|〉}$ is a functional of the vertical density profile. However, for the usual physically meaningful profiles, these values are very close to each other: It is $\text{2}$ for the Gaussian profile, $\text{1}\text{Ln}\text{2}\text{= 1.443}$ for the $\text{rmsech}{}^2\text{(}\text{z}\text{z}{}_1\text{(r)}\text{)}$ profile, and 1.5 for the $\text{exp}\text{[}\text{?|z|}\text{z}{}_1\text{(r)}\text{]}$ profile.     

The virial mass of the nucleus of M32

By means of the virial theorem we derive the dependence of the mass of an oblate spheroid in solid body rotation from the velocity dispersion and the space light density. The latter is obtained from a calibrated and seeing deconvolved brightness profile as numerical and stable solution of the Abel integral equation. The application of the nucleus of M32 gives a central density of 2.1×10^?5 M _⊙ pc^?3, a nuclear mass of 4.3×10^?7 M _⊙ and a mass-to-light ratio of 4.6 inV-band.     

Steady flow approximations to the heliumR-process

R-process yields for a helium layer have been calculated within a network of 6033 heavy nuclei using a steady flow approximation. The calculation of the neutron capture cross sections has been improved. The beta decay rates computed by Klapdor and his colleagues have been used in the calculation. We find that ther-process yield peaks near mass numbers 80 and 130 require a neutron number density of approximately 10²⁰ cm^?3 and a freezing time comparable to or less than 0.1 s. The peak near mass number 195 requires a neutron number density of about 10²¹ cm^?3 and a freezing time comparable to or less than about 0.01 s. The individual yield features of the steady flowr-process depend entirely upon the neutron capture cross sections of the nuclei along the flow path and the beta decay rates, which can shift the flow path and thereby introduce inappropriate capture cross sections into the determination of the yields.     

A galactic model with a pulsating active nucleus

The accumulation and distribution of rare-light elements in the Galaxy is investigated according to a model of the galaxy at which center there exists a pulsating active nucleus with decreasing activity with time. The abundances of rare-light elements rapidly decrease with approaching to the galactic center whereas the most abundant region of these elements is the annular region of the radial distance ofr=8～14 kpc from the galactic center. In the inner region ofr?8 kpc the abundances of these elements have varied by two to three orders of magnitude from the early days of the galactic history till now, but inr?8 kpc they have been almost constant within a factor of 2. It has become clear that if the nuclides D,³He,⁷Li,¹⁰B and¹¹B have been produced mainly by the shock process taking place in the outer envelope of type-II supernova, they must have been created by the mass fractions of the supernova of some 2.7×10^?3, 1.7×10^?4, 6.9×10^?8, 1.7×10^?7 and 7.9×10^?7, respectively, to account for the solar system abundances.     

Variable cosmological “constant” and motion of a test particle in a cloud of dust

We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ(x ⁱ ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ?Λ/? x ⁱ and, in the weak field approximation, causes an anomalous acceleration A～(Vc ²/γ ρ)?Λ/? t+(c ⁴/γ ρ)?Λ/? r where V=dr/dt, c=the speed of light, γ=8π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ(t) give A<10^?8 cm/s² when ρ>10^?29 g/cm³ i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.     

Similarity solution for unsteady accretion flow,II

Similarity solution for unsteady accretion flow is obtained. The density distribution of the initial state of the gas surrounding the star is given as ?₀ ∝r ^?ω. The flow patterns are compared with the results of the numerical computation by Zel'dovichet al. (1972), and it is shown that the similarity solution reproduces the results of the numerical computations well. An unsteady accretion model for the nova-like X-ray source is discussed briefly.     

A Molecular Filament Threaded by Helical Magnetic Fields?

We present a multitransition study in the ¹³CO(1-0), ¹²CO(2-1), ¹²CO(3-2) and ¹²CO(4-3) lines of a parsec scale elongated structure connected to a low-mass dense core. Densities larger than n _{H 2} = 10⁴ cm^?3 are inferred in the central regions of this structure, supporting the proposition that it is a genuine filament denser than its environment. The sharp observed drop of the ¹²CO and ¹³CO emissions requires a power law density fall-off steeper than r ^?1 although a single density law cannot reproduce the spatial shift of 0.1 pc between the ¹³CO and ¹²CO drops. Our results support the previous proposition that this elongated structure is a filament threaded by helical magnetic fields, channeling the gas inflow onto the dense core.     

Scaling relation between Sunyaev–Zel’dovich effect and X-ray luminosity and scale-free evolution of cosmic baryon field

It has been revealed recently that, in the scale free range, i.e. from the scale of the onset of nonlinear evolution to the scale of dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the self-similar log-Poisson hierarchy. As a consequence of this evolution, the relations among various physical quantities of cosmic baryon fluid should be scale invariant, if the physical quantities are measured in cells on scales larger than the dissipation scale, regardless the baryon fluid is in virialized dark halo, or in pre-virialized state. We examine this property with the relation between the Compton parameter of the thermal Sunyaev–Zel’dovich effect, y(r), and X-ray luminosity, L_x(r), where r being the scale of regions in which y and L_x are measured. According to the self-similar hierarchical scenario of nonlinear evolution, one should expect that (1) in the y(r) ? L_x(r) relation, y(r) = 10^A(r)[L_x(r)]^α(r), the coefficients A(r) and α(r) are scale-invariant; (2) The relation y(r) = 10^A(r)[L_x(r)]^α(r) given by cells containing collapsed objects is also available for cells without collapsed objects, only if r is larger than the dissipation scale. These two predictions are well established with a scale decomposition analysis of observed data, and a comparison of observed y(r) ? L_x(r) relation with hydrodynamic simulation samples. The implication of this result on the characteristic scales of non-gravitational heating is also addressed.     

Measurement of the lunar neutron density profile

Anin situ measurement of the lunar neutron density from 20 to 400 g cm^?2 depth below the lunar surface was made by the Apollo 17 Lunar Neutron Probe Experiment (LNPE) using particle tracks produced by the¹⁰B (n,α)⁷Li reaction. Both the absolute magnitude and the depth profile of the neutron density are in good agreement with theoretical calculations by Lingenfelter, Canfield, and Hampel. However, relatively small deviations between experiment and theory in the effect of Cd absorption on the neutron density and in the relative¹⁴⁹Sm to¹⁵⁷Gd capture rates reported previously (Russet al., 1972) imply that the true lunar¹⁵⁷Gd capture rate is about one half of that calculated theoretically.     

Solution of one-fluid model equations with short range retarding magnetic forces for the quiet solar wind

The discrepancy of the low predicted versus the observed coronal particle densities is investigated by considering radial magnetic forces acting at the base of the corona in the one fluid model equations with anomalous thermal conductivity for the quiet solar wind. If the short range retarding magnetic force is taken to fall asr ^?5,r being the heliocentric distance, then in order to obtain satisfactory agreement between the predicted and observed (about 3×10⁸ cm^?3 at 1R _⊙) coronal densities, the strength of the retarding magnetic force at 1R _⊙ should be 1.2 times that of the gravitational force.     

Further Evidence Suggestive of a Solar Influence on Nuclear Decay Rates

Recent analyses of nuclear decay data show evidence of variations suggestive of a solar influence. Analyses of datasets acquired at the Brookhaven National Laboratory (BNL) and at the Physikalisch-Technische Bundesanstalt (PTB) both show evidence of an annual periodicity and of periodicities with sidereal frequencies in the neighborhood of 12.25 year^?1 (at a significance level that we have estimated to be 10^?17). It is notable that this implied rotation rate is lower than that attributed to the solar radiative zone, suggestive of a slowly rotating solar core. This leads us to hypothesize that there may be an ??inner tachocline?? separating the core from the radiative zone, analogous to the ??outer tachocline?? that separates the radiative zone from the convection zone. The Rieger periodicity (which has a period of about 154 days, corresponding to a frequency of 2.37 year^?1) may be attributed to an r-mode oscillation with spherical-harmonic indices l=3,m=1, located in the outer tachocline. This suggests that we may test the hypothesis of a solar influence on nuclear decay rates by searching BNL and PTB data for evidence of a ??Rieger-like?? r-mode oscillation, with l=3,m=1, in the inner tachocline. The appropriate search band for such an oscillation is estimated to be 2.00??C?2.28 year^?1. We find, in both datasets, strong evidence of a periodicity at 2.11 year^?1. We estimate that the probability of obtaining these results by chance is 10^?12.     

Optical properties of single-component zodiacal light models

To provide material for interpretations of forthcoming zodiacal light measurements the characteristics of 468 single-component, in-ecliptic models are summarized in two survey diagrams. The models are based on Mie theory and on a power law dn ∞ r^?γα^?kdα for the dependence of the particle number density n on solar distance r and on the size parameter α (circumference/wavelength). The size range involves particles with α_min ≤ α ≤ 120; (α_min = 1,2,4,10,60), flat (k = 2·5) and steep (k = 4) size spectra, and complex refractive indices m = m₁ ? m₂i with m₁ = 1·33; 1·5; 1·7 and m₂ = 0; 0·01; 0·05; 0·1.The models suggest that the spatial variation of dust particle number densities should be less than about ∞ r^?0·5 in the ecliptic plane. Either dielectric particles of tenth-micron size or absorbing particles of half-micron size or very slightly absorbing particles of some tens of microns in size are able to produce polarization that agrees in sign and location of the maximum with the observations. Ambiguities can only be removed by considering intensity and polarization over a wide range of wavelengths.     

A model exciter for type III solar radiobursts

In an earlier paper (Harvey and Aubier, 1973) the large scale radial electron density gradient in the corona and solar wind was shown to cause the phase velocity of plasma waves to decrease as they propagate away from the Sun, thus leading to appreciable Landau damping of the plasma waves. It is proposed here that this same phase velocity decrease creates conditions which facilitate the stabilisation of a beam of exciter electrons of finite duration, provided that three conditions are fulfilled. Two of these conditions concern the velocity-time distribution of the exciter electrons at their point of ejection from the Sun, while the third is simply that, above a certain altitude, the coronal electron density decreases with altitude r faster than r ^?2. The plasma wave source is then associated with the leading edge of the electron stream. The spatial density of the power converted into plasma waves is calculated as a function of position and time, and is shown to be independent of the nature of the stabilisation mechanism. The maximum of this power density is found to move outwards from the Sun at a uniform speed when a simple electron injection model with a Maxwellian velocity distribution is introduced.     

New in the optical spectrum and kinematic state of the atmosphere of the variable V1027 Cyg (=IRAS 20004+2955)

Based on our high-spectral-resolution observations performed with the NES echelle spectrograph of the 6-m telescope, we have studied the peculiarities of the spectrum and the velocity field in the atmosphere and envelope of the cool supergiant V1027 Cyg, the optical counterpart of the infrared source IRAS 20004+2955. A splitting of the cores of strong absorptions of metals and their ions (Si II, Ni I, Ti I, Ti II, Sc II, Cr I, Fe I, Fe II, BaII) has been detected in the stellar spectrum for the first time. The broad profile of these lines contains a stable weak emission in the core whose position may be considered as the systematic velocity V _sys = 5.5 km s^?1. Small radial velocity variations with an amplitude of 5–6 km s^?1 due to pulsations have been revealed by symmetric low- and moderate-intensity absorptions. A long-wavelength shift of the Hα profile due to line core distortion is observed in the stellar spectrum. Numerous weak CN molecular lines and the KI 7696 Å line with a P Cyg profile have been identified in the red spectral region. The coincidence of the radial velocities measured from symmetric metal absorptions and CN lines suggests that the CN spectrum is formed in the stellar atmosphere. We have identified numerous diffuse interstellar bands (DIBs) whose positions in the spectrum, V _r (DIBs) = ?12.0 km s^?1, correspond to the velocity of the interstellar medium in the Local Arm of the Galaxy.     

Long time delay between the peaks of intense solar hard X-ray and microwave bursts

New solar wind data from Helios-2 are used to study, in a statistical fashion, the relation between proton number density n, flow speed u and heliocentric distance r. It is shown that the average of nu ² r ² does not depend on flow speed nor on distance, verifying the previously established invariance of momentum flux density (mnu²) carried by the solar wind. Averages of mnu² from different spacecraft do not show correlation with the solar cycle. Rather, the close agreement (to within 1.8%) of values from Helios-1 and Helios-2 suggests that the momentum flux density carried by the solar wind may be also constant during the solar cycle.