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1.
We obtained U BV R photometric and spectroscopic observations during the outburst of V838 Mon. Before its outburst, the B brightness of the star had been stable ( $\tilde15.^m 85$ ) for 45 years. This was a blue star with the color index $(B - V)_0 = - 0\mathop .\limits^m 03 \pm 0\mathop .\limits^m 1$ and may have been a cataclysmic variable. In the middle of March 2002, the outburst amplitude reached $8\mathop .\limits^m 1$ in B. The star has the counterpart V 1006/7 in M 31 in luminosity at maximum and in spectrum. The unusual spectrum at the premaximum stage originated in the expanding photosphere of a cool K-type giant. The expansion velocity of the photosphere was 150 km s?1; the maximum velocity in the expanding stellar envelope reached 500 km s?1. The absorption components of neutral metal lines were enhanced by a factor of 3 or 4 compared to a normal K-type star. No overabundance of s-process elements was found. One day before the brightness peak, an intense Hα emission line with broad wings, FWZI=3100 km s?1, and numerous lines of ionized metals appeared in V838 Mon, which is characteristic of normal classical novae. We show light, color, and spectral variations of the object.  相似文献   

2.
New photoelectric UBVRI observations of the eclipsing variable V 1016 Ori have been obtained with the AZT-11 telescope at Crimean Astrophysical Observatory and with the Zeiss-600 telescope at Mount Maidanak Observatory. Light curves are constructed from the new observations and from published and archival data. We use a total of 340, 348, 386, 185, and 62 magnitude estimates in the bands from U to I, respectively. An analysis of these data has yielded the following results. The photometric elements were refined; their new values are $Min I = JDH 2441966.820 + 65\mathop .\limits^d 4331E$ . The UBVRI magnitudes outside eclipse were found to be $5\mathop .\limits^m 95$ , $6\mathop .\limits^m 77$ , $6\mathop .\limits^m 75$ , $6\mathop .\limits^m 68$ , and $6\mathop .\limits^m 16$ , respectively. No phase effect was detected. We obtained two light-curve solutions: (1) assuming that the giant star was in front of the small one during eclipse, we determined the stellar radii, r s=0.0141 and r g=0.0228 (in fractions of the semimajor axis of the orbit); and (2) assuming that the small star was in front of the giant one, we derived r g=0.0186 and r s=0.0180 for the V band. The brightness of the primary star in the bands from U to I is L 1=0.96, 0.92, 0.90, 0.89, and 0.88, the orbital inclination is $i = 87^\circ .1$ , and the maximum eclipse phase is α0= 0.66. In both cases, we accepted the U hypothesis, assumed the orbit to be elliptical, and took into account the flux from the star Θ1 Ori E that fell within the photometer aperture. The first solution leads to a discrepancy between the primary radius determined by solving the light curve and the radial-velocity curve and its value estimated from the luminosity and temperature. This discrepancy is eliminated in the second solution, and it turns out that, by all parameters, the primary corresponds to a normal zero-age main-sequence star.  相似文献   

3.
We analyze ultraviolet spectra of DF Tau, a binary system whose primary component is a classical T Tauri star. The spectra were obtained from the Hubble Space Telescope and the IUE satellite. The stellar emission in the wavelength range covered is shown to originate in an accretion shock wave. The gas infall velocity is ～250 km s?1. The accreted-gas density is typically N 0≤1011 cm?3, but it can occasionally be higher by one and a half orders of magnitude. The continuum intensity near λ=1900 Å was found to be virtually constant for such a significant change in N 0. The star’s photometric variability is probably attributable to variations in accreted-gas density and velocity, as well as to variations in the area of a hot spot on the stellar surface and in its orientation relative to the observer. The mean accretion rate is $\dot M \sim 3 \times 10^{ - 9} M_ \odot yr^{ - 1}$ . The interstellar extinction for DF Tau is $A_V \simeq 0\mathop .\limits^m 5$ , the stellar radius is ≤2R ⊙, and the luminosity of the primary component is most likely no higher than 0.3 L ⊙. We argue that the distance to DF Tau is about 70 pc. Upper limits are placed on the primary’s coronal emission measure: EM(T=107 K)<3×1054 cm?3 and EM(T=1.3×106 K)<3×1055 cm?3. Absorption lines originating in the stellar wind were detected in the star’s spectrum. Molecular hydrogen lines have essentially the same radial velocity as the star, but their full width at half maximum is FWHM ?50 km s?1. We failed to explain why the intensity ratio of the C IV λ1550 doublet components exceeds 2.  相似文献   

4.
We present photoelectric and spectroscopic observations of the protoplanetary object V 1853 Cyg, a B supergiant with an IR excess. Over two years of its observations, the star exhibited rapid irregular light variations with amplitudes $\Delta V = 0\mathop .\limits^m 3$ , $\Delta B = 0\mathop .\limits^m 3$ , $\Delta U = 0\mathop .\limits^m 4$ and no correlation between color and magnitude. Its mean magnitude has not changed since the first UBV observations in 1973 (Drilling 1975). Low-resolution spectroscopic observations show that the spectrum of V 1853 Cyg in 2000 corresponded to that of a B1–B2 star with T eff ～ 20000 K. High-resolution spectroscopic observations confirm the conclusion that the profiles of absorption and emission lines are variable. We identified the star’s spectral lines and measured the equivalent widths of more than 40 lines. The star’s radial velocity is 〈V r 〉= ?49 × 5 km s?1, as measured from absorption lines, and ranges from–50 to–85 km s–1 for different lines, as measured from shell emission lines. The velocity of the dust clouds on the line of sight determined from diffuse interstellar bands (DIBs) and from interstellar Na I lines is 〈V r 〉= ?16 × 5 km s?1. The P Cyg profiles of the He I λ5876 Å and λ6678 Å lines suggest an ongoing mass loss by the star. An analysis of the observational data confirms the conclusion that the star belongs to the class of intermediatemass protoplanetary objects.  相似文献   

5.
We present results based on the systematic analysis of Chandra archive data on the X-ray bright Abell Richness class-I type cluster Abell 1991 with an objective to investigate properties of the X-ray cavities hosted by this system. The unsharp masked image as well as 2-d β model subtracted residual image of Abell 1991 reveals a pair of X-ray cavities and a region of excess emission in the central ～12 kpc region. Both the cavities are of ellipsoidal shape and exhibit an order of magnitude deficiency in the X-ray surface brightness compared to that in the undisturbed regions. Spectral analysis of X-ray photons extracted from the cavities lead to the temperature values equal to $1.77_{-0.12}^{+0.19}~\mathrm{keV}$ for N-cavity and $1.53_{-0.06}^{+0.05}~\mathrm{keV}$ for S-cavity, while that for the excess X-ray emission region is found to be equal to $2.06_{-0.07}^{+0.12}~\mathrm{keV}$ . Radial temperature profile derived for Abell 1991 reveals a positive temperature gradient, reaching to a maximum of 2.63 keV at ～76 kpc and then declines in outward direction. 0.5–2.0 keV soft band image of the central 15′′ region of Abell 1991 reveals relatively cooler three different knot like features that are about 10′′ off the X-ray peak of the cluster. Total power of the cavities is found to be equal to ${\sim}8.64\times10^{43}~\mathrm{erg\,s}^{-1}$ , while the X-ray luminosity within the cooling radius is found to be $6.04 \times10^{43}~\mathrm{erg\,s}^{-1}$ , comparison of which imply that the mechanical energy released by the central AGN outburst is sufficient to balance the radative loss.  相似文献   

6.
We compute the ultra-high energy (UHE) neutrino fluxes from plausible accreting supermassive black holes closely linking to the 377 active galactic nuclei (AGNs). They have well-determined black hole masses collected from the literature. The neutrinos are produced via simple or modified URCA processes, even after the neutrino trapping, in superdense proto-matter medium. The resulting fluxes are ranging from: (1) (quark reactions)— $J^{q}_{\nu\varepsilon}/(\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1})\simeq8.29\times 10^{-16}$ to 3.18×10?4, with the average $\overline{J}^{q}_{\nu\varepsilon}\simeq5.53\times 10^{-10}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ , where ε d ～10?12 is the opening parameter; (2) (pionic reactions)— $J^{\pi}_{\nu\varepsilon} \simeq0.112J^{q}_{\nu\varepsilon}$ , with the average $J^{\pi}_{\nu\varepsilon} \simeq3.66\times 10^{-11}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ ; and (3) (modified URCA processes)— $J^{URCA}_{\nu\varepsilon}\simeq7.39\times10^{-11} J^{q}_{\nu\varepsilon}$ , with the average $\overline{J}^{URCA}_{\nu\varepsilon} \simeq2.41\times10^{-20} \varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ . We conclude that the AGNs are favored as promising pure neutrino sources, because the computed neutrino fluxes are highly beamed along the plane of accretion disk, peaked at high energies and collimated in smaller opening angle θ～ε d .  相似文献   

7.
We present the results of measurements of the total X-ray flux from the Andromeda galaxy (M31) in the 3-100 keV band based on data from the RXTE/PCA, INTEGRAL/ISGRI, and SWIFT/BAT space experiments. We show that the total emission from the galaxy has a multicomponent spectrum whose main characteristics are specified by binaries emitting in the optically thick and optically thin regimes. The galaxy’s luminosity at energies 20–100 keV gives about 6% of its total luminosity in the 3–100 keV band. The emissivity of the stellar population in M31 is L 2–20 keV ～ 1.1 × 1029 erg s?1 M ⊙ ?1 in the 2–20 keV band and L 20–100 keV ～ 8 × 1027 erg s?1 M ⊙ ?1 in the 20–100 keV band. Since low-mass X-ray binaries at high luminosities pass into a soft state with a small fraction of hard X-ray emission, the detection of individual hard X-ray sources in M31 requires a sensitivity that is tens of times better (up to 10?13 erg s?1 cm?2) than is needed to detect the total hard X-ray emission from the entire galaxy. Allowance for the contribution from the hard spectral component of the galaxy changes the galaxy’s effective Compton temperature approximately by a factor of 2, from ～1.1 to ～2.1 keV.  相似文献   

8.
We examine the possibility that the observed cosmic-ray protons are of primary extragalactic origin. The present \(\bar p\) data are consistent with a primary extragalactic component having \(\bar p\) /p?3.2±0.7 x 10-4 independent of energy. Following the suggestion that most extragalactic cosmic rays are from active galaxies, we propose that most of the observed \(\bar p\) 's are alos from the same sites. This would imply the possibility of destroying the corresponding \(\bar \alpha \) 'sat the source, thus leading to a flux ratio \(\bar \alpha \) /α< \(\bar p\) /p. We further predict an estimate for \(\bar \alpha \) α～10-5, within the range of future cosmic-ray detectors. the cosmological implications of this proposal are discussed.  相似文献   

9.
We present our photometric observations of an early B supergiant with an infrared excess, the protoplanetary object LSIV-12°111, and the previously suspected variable star NSV 24971. We confirm its photometric variability. During two observing seasons (2000–2001), the star exhibited rapid irregular light variations with amplitudes $\Delta V \sim 0\mathop .\limits^m 3$ , $\Delta B \sim 0\mathop .\limits^m 3$ , and $\Delta U \sim 0\mathop .\limits^m 4$ and a time scale of ～1d. There is no correlation between the colors and magnitudes of the star. The variability patterns of LSIV-12°111 and two other hot post-AGB stars, V886 Her and V1853 Cyg, are shown to be similar.  相似文献   

10.
Published photoelectric measurements over a wide wavelength range (0.36–18 µm) are used to study the continuum spectrum of the star Θ1 Ori C. The model that assumes the following three radiation sources is consistent with observations: (1) a zero-age main-sequence O7 star (object 1) of mass M 1=20M ⊙, radius R 1=7.4R ⊙, effective temperature T 2=37 000 K, and absolute bolometric magnitude $M\mathop {bol}\limits^1 = - 7\mathop .\limits^m 7$ ; (2) object 2 with M 2=15M ⊙, R 2=16.2R ⊙, T 2=4000 K, and $M\mathop {bol}\limits^2 = - 5\mathop .\limits^m 1$ ; and (3) object 3 with R 310 700 R ⊙, T 3=190 K, and $M\mathop {bol}\limits^3 = - 0\mathop .\limits^m 6$ . The visual absorption toward the system is $A_V = 0\mathop .\limits^m 95$ and obeys a normal law. The nature of objects 2 and 3 has not been elucidated. It can only be assumed that object 2 is a companion of the primary star, its spectral type is K7, and it is in the stage of gravitational contraction. Object 3 can be a cocoon star and a member of the system, but can also be a dust envelope surrounding the system as a whole.  相似文献   

11.
We present photoelectric and photographic observations of the supergiant HD 179821 with a large infrared excess, a candidate for protoplanetary objects. Over, ten years of our UBV observations, the star exhibited semiregular light variations with amplitudes $\Delta V = 0\mathop .\limits^m 10$ , $\Delta B = 0\mathop .\limits^m 15$ , and $\Delta U = 0\mathop .\limits^m 25$ , as well as systematic color and light variations. From 1990 until 1996, the yearly mean U-B and B-V color indices decreased by 0.25 and 0.15, respectively. After 1996, the motion of the star in the two-color (B-V)-(U-B) diagram upward and to the left slowed down. The color excess that we derived from our observations, by assuming that the star’s spectral type was F3 I in the 1990s, is E(B-V)=1.0. The photographic observations of HD 179821 from 1899 until 1989 show that its brightness m pg generally increased while significantly fluctuating. An analysis of the observational data suggests that HD 179821 is most likely a post-AGB star of intermediate or low mass.  相似文献   

12.
The planar problem of three bodies is described by means of Murnaghan's symmetric variables (the sidesa j of the triangle and an ignorable angle), which directly allow for the elimination of the nodes. Then Lemaitre's regularized variables \(\alpha _j = \sqrt {(\alpha ^2 - \alpha _j )}\) , where \(\alpha ^2 = \tfrac{1}{2}(a_1 + a_2 + a_3 )\) , as well as their canonically conjugated momenta are introduced. By finally applying McGehee's scaling transformation \(\alpha _j = r^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \tilde \alpha _j\) , wherer 2 is the moment of inertia a system of 7 differential equations (with 2 first integrals) for the 5-dimensional triple collision manifold \(T\) is obtained. Moreover, the zero angular momentum solutions form a 4-dimensional invariant submanifold \(N \subset T\) represented by 6 differential equations with polynomial right-hand sides. The manifold \(N\) is of the topological typeS 2×S 2 with 12 points removed, and it contains all 5 restpoint (each one in 8 copies). The flow on \(T\) is gradient-like with a Lyapounov function stationary in the 40 restpoints. These variables are well suited for numerical studies of planar triple collision.  相似文献   

13.
Catalogs of bright galaxies in the central regions of 11 clusters in the Ursa Major supercluster are presented. Absolute and relative coordinates and total B and R magnitudes are given for each galaxy. Plates taken with the 2-m Tautenburg Observatory telescope and CCD images obtained with the 6-m and 1-m SAO telescopes are used. The luminosity functions (LFs) for galaxies in the cluster nuclei (3 Mpc×3 Mpc) and the composite LF for the supercluster are constructed. The composite LF is well fitted by a Schechter function with $M_B^ * = - 20\mathop .\limits^m 91$ , α=?1.02 and with $M_R^ * = - 22\mathop .\limits^m 39$ , α=?1.06. A comparison with the LFs of field galaxies and of various samples of clusters and superclusters shows that the Ursa Major supercluster have LF parameters characteristic of the field and, thus, differ from those of the Corona Borealis supercluster, which is apparently at a later stage of dynamical evolution.  相似文献   

14.
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 ≤ LX,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 zspec ? 3; the remaining ones are quasar candidates with photometric redshift estimates zphot ? 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 LX,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.  相似文献   

15.
Hot spots similar to those in the radio galaxy Cygnus A can be explained by the strong shock produced by a supersonic but classical jet \(\left( {u_{jet}< c/\sqrt 3 } \right)\) . The high integrated radio luminosity (L?2×1044 erg s?1) and the strength of mean magnetic field (B?2×10?4 G) suggest the hot spots are the downstream flow of a very strong shock which generates the ultrarelativistic electrons of energy ?≥20 MeV. The fully-developed subsonic turbulence amplifies the magnetic field of the jet up to 1.6×10?4 G by the dynamo effect. If we assume that the post-shock pressure is dominated by relativistic particles, the ratio between the magnetic energy density to the energy density in relativistic particles is found to be ?2×10?2, showing that the generally accepted hypothesis of equipartition is not valid for hot spots. The current analysis allows the determination of physical parameters inside hot spots. It is found that:
  1. The velocity of the upstream flow in the frame of reference of the shock isu 1?0.2c. Radio observations indicate that the velocity of separation of hot spots isu sep?0.05c, so that the velocity of the jet isu jet=u 1+u sep?0.25c.
  2. The density of the thermal electrons inside the hot spot isn 2?5×10?3 e ? cm?3 and the mass ejected per year to power the hot spot is ?4M 0yr?1.
  3. The relativistic electron density is less than 20% of the thermal electron density inside the hot spot and the spectrum is a power law which continues to energies as low as 30 MeV.
  4. The energy density of relativistic protons is lower than the energy density of relativistic electrons unlike the situation for cosmic rays in the Galaxy.
  相似文献   

16.
We analyzed the luminosity-temperature-mass of gas (L X ?T?M g ) relations for a sample of 21 Chandra galaxy clusters. We used the standard approach (β?model) to evaluate these relations for our sample that differs from other catalogues since it considers galaxy clusters at higher redshifts (0.4<z<1.4). We assumed power-law relations in the form $L_{X} \sim(1 +z)^{A_{L_{X}T}} T^{\beta_{L_{X}T}}$ , $M_{g} \sim(1 + z)^{A_{M_{g}T}} T^{\beta_{M_{g}T}}$ , and $M_{g} \sim(1 + z)^{A_{M_{g}L_{X}}} L^{\beta_{M_{g}L_{X}}}$ . We obtained the following fitting parameters with 68 % confidence level: $A_{L_{X}T} = 1.50 \pm0.23$ , $\beta_{L_{X}T} = 2.55 \pm0.07$ ; $A_{M_{g}T} = -0.58 \pm0.13$ and $\beta_{M_{g}T} = 1.77 \pm0.16$ ; $A_{M_{g}L_{X}} \approx-1.86 \pm0.34$ and $\beta_{M_{g}L_{X}} = 0.73 \pm0.15$ , respectively. We found that the evolution of the M g ?T relation is small, while the M g ?L X relation is strong for the cosmological parameters Ω m =0.27 and Ω Λ =0.73. In overall, the clusters at high-z have stronger dependencies between L X ?T?M g correlations, than those for clusters at low-z. For most of galaxy clusters (first of all, from MACS and RCS surveys) these results are obtained for the first time.  相似文献   

17.
We analyze flyby-type triple approaches in the plane isosceles equal-mass three-body problem and in its vicinity. At the initial time, the central body lies on a straight line between the other two bodies. Triple approaches are described by two parameters: virial coefficient k and parameter $\mu = \dot r/\sqrt {\dot r^2 + \dot R^2 }$ , where $\dot r$ is the relative velocity of the extreme bodies and $\dot R$ is the velocity of the central body relative to the center of mass of the extreme bodies. The evolution of the triple system is traceable until the first turn or escape of the central body. The ejection length increases with closeness of the triple approach (parameter k). The longest ejections and escapes occur when the extreme bodies move apart with a low velocity at the time of triple approach. We determined the domain of escapes; it corresponds to close triple approaches (k>0.8) and to μ in the range ?0.2<μ<0.7. For small deviations from the isosceles problem, the evolution does not differ qualitatively from the isosceles case. The domain of escapes decreases with increasing deviations. In general, the ejection length increases for wide approaches and decreases for close approaches.  相似文献   

18.
We examine the stability of the triangular Lagrange points L 4 and L 5 for secondary masses larger than the Gascheau??s value ${\mu_{\rm G}= (1-\sqrt{23/27}/2)= 0.0385208\ldots}$ (also known as the Routh value) in the restricted, planar circular three-body problem. Above that limit the triangular Lagrange points are linearly unstable. Here we show that between??? G and ${\mu \approx 0.039}$ , the L 4 and L 5 points are globally stable in the sense that a particle released at those points at zero velocity (in the corotating frame) remains in the vicinity of those points for an indefinite time. We also show that there exists a family of stable periodic orbits surrounding L 4 or L 5 for ${\mu \ge \mu_G}$ . We show that??? G is actually the first value of a series ${\mu_0 (=\mu_G), \mu_1,\ldots, \mu_i,\ldots}$ corresponding to successive period doublings of the orbits, which exhibit ${1, 2, \ldots, 2^i,\ldots}$ cycles around L 4 or L 5. Those orbits follow a Feigenbaum cascade leading to disappearance into chaos at a value ${\mu_\infty = 0.0463004\ldots}$ which generalizes Gascheau??s work.  相似文献   

19.
We present new photometric UBVRI and spectroscopic observations of the symbiotic star YY Her during its return to quiescence after a strong outburst in 1993. High-resolution spectra of YY Her at similar phases at outburst maximum ?=0.48) and in quiescence ?=0.37) are presented for the first time. The ephemeris of YY Her has been refined P=586d). The last two observed minima (in 1999 and 2000) differed radically in shape from the 1997 minimum described previously. Both were sharp and deep $(\Delta U \sim 1\mathop .\limits^m 6, \Delta V \sim 0\mathop .\limits^m 9)$ . To explain this shape of the V light curve, which is only slightly affected by nebular emission, it should be assumed that the cool component of YY Her fills much of its Roche lobe and has a hot spot on the hemisphere facing the hot component. The emission spectrum rich in Fe II lines, which is characteristic of symbiotic stars, was observed during the outburst, but high-ionization lines (He II λ4686) were also observed. The He I λλ5876, 7065 lines exhibit distinct P Cyg profiles; the centers of the absorption components are shifted from the emission ones by V r≈100 km s?1, suggesting moderate outflow velocities.  相似文献   

20.
In the now classical Lindblad-Lin density-wave theory, the linearization of the collisionless Boltzmann equation is made by assuming the potential functionU expressed in the formU=U 0 + \(\tilde U\) +... WhereU 0 is the background axisymmetric potential and \(\tilde U<< U_0 \) . Then the corresponding density distribution is \(\rho = \rho _0 + \tilde \rho (\tilde \rho<< \rho _0 )\) and the linearized equation connecting \(\tilde U\) and the component \(\tilde f\) of the distribution function is given by $$\frac{{\partial \tilde f}}{{\partial t}} + \upsilon \frac{{\partial \tilde f}}{{\partial x}} - \frac{{\partial U_0 }}{{\partial x}} \cdot \frac{{\partial \tilde f}}{{\partial \upsilon }} = \frac{{\partial \tilde U}}{{\partial x}}\frac{{\partial f_0 }}{{\partial \upsilon }}.$$ One looks for spiral self-consistent solutions which also satisfy Poisson's equation $$\nabla ^2 \tilde U = 4\pi G\tilde \rho = 4\pi G\int {\tilde f d\upsilon .} $$ Lin and Shu (1964) have shown that such solutions exist in special cases. In the present work, we adopt anopposite proceeding. Poisson's equation contains two unknown quantities \(\tilde U\) and \(\tilde \rho \) . It could be completelysolved if a second independent equation connecting \(\tilde U\) and \(\tilde \rho \) was known. Such an equation is hopelesslyobtained by direct observational means; the only way is to postulate it in a mathematical form. In a previouswork, Louise (1981) has shown that Poisson's equation accounted for distances of planets in the solar system(following to the Titius-Bode's law revised by Balsano and Hughes (1979)) if the following relation wasassumed $$\rho ^2 = k\frac{{\tilde U}}{{r^2 }} (k = cte).$$ We now postulate again this relation in order to solve Poisson's equation. Then, $$\nabla ^2 \tilde U - \frac{{\alpha ^2 }}{{r^2 }}\tilde U = 0, (\alpha ^2 = 4\pi Gk).$$ The solution is found in a classical way to be of the form $$\tilde U = cte J_v (pr)e^{ - pz} e^{jn\theta } $$ wheren = integer,p =cte andJ v (pr) = Bessel function with indexv (v 2 =n 2 + α2). By use of the Hankel function instead ofJ v (pr) for large values ofr, the spiral structure is found to be given by $$\tilde U = cte e^{ - pz} e^{j[\Phi _v (r) + n\theta ]} , \Phi _v (r) = pr - \pi /2(v + \tfrac{1}{2}).$$ For small values ofr, \(\tilde U\) = 0: the center of a galaxy is not affected by the density wave which is onlyresponsible of the spiral structure. For various values ofp,n andv, other forms of galaxies can be taken into account: Ring, barred and spiral-barred shapes etc. In order to generalize previous calculations, we further postulateρ 0 =kU 0/r 2, leading to Poisson'sequation which accounts for the disc population $$\nabla ^2 U_0 - \frac{{\alpha ^2 }}{{r^2 }}U_0 = 0.$$ AsU 0 is assumed axisymmetrical, the obvious solution is of the form $$U_0 = \frac{{cte}}{{r^v }}e^{ - pz} , \rho _0 = \frac{{cte}}{{r^{2 + v} }}e^{ - pz} .$$ Finally, Poisson's equation is completely solvable under the assumptionρ =k(U/r 2. The general solution,valid for both disc and spiral arm populations, becomes $$U = cte e^{ - pz} \left\{ {r^{ - v} + } \right.\left. {cte e^{j[\Phi _v (r) + n\theta ]} } \right\},$$ The density distribution along the O z axis is supported by Burstein's (1979) observations.  相似文献   

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