Ion transition heights from topside electron density profiles

Theoretical electron density profiles are calculated for the topside ionosphere to determine the major factors controlling the profile shape. Only the mean temperature, the vertical temperature gradient and the $\text{O}{}^{\mathrm{+}}\text{H}{}^{\mathrm{+}}$ ion transition height are important. Vertical proton fluxes alter the ion transition height but have no other effect on the profile shape. Diffusive equilibrium profiles including only these three effects fit observed profiles, at all latitudes, to within experimental accuracy.Values of plasma temperature, temperature gradient and ion transition height h_tT were determined by fitting theoretical models to 60,000 experimental profiles obtained from Alouette l ionograms, at latitudes of 75°S–85°N near solar minimum. Inside the plasmasphere h_T varies from about 500 km on winter nights to 850 km on summer days. Diurnal variations are caused primarily by the production and loss of O⁺ in the ionosphere. The approximately constant winter night value of h_T is close to the level for chemical equilibrium. In summer h_T is always above the equilibrium level, giving a continual production of protons which travel along lines of force to aid in maintaining the conjugate winter night ionosphere. Outside the plasmasphere h_T is 300–600 km above the equilibrium level at all times. This implies a continual near-limiting upwards flux of protons which persists down to latitudes of about 60° at night and 50° during the day.     

Estimation of the galactic spiral pattern speed from Cepheids

To study the peculiarities of the Galactic spiral density wave, we have analyzed the space velocities of Galactic Cepheids with propermotions from the Hipparcos catalog and line-of-sight velocities from various sources. First, based on the entire sample of 185 stars and taking R ₀ = 8 kpc, we have found the components of the peculiar solar velocity (u _⊙, v _⊙) = (7.6, 11.6) ± (0.8, 1.1) km s^?1, the angular velocity of Galactic rotation Ω₀ = 27.5 ± 0.5 km s^?1 kpc^?1 and its derivatives Ω′₀ = ?4.12 ± 0.10 km s^?1 kpc^?2 and Ω″₀ = 0.85 ± 0.07 km s^?1 kpc^?3, the amplitudes of the velocity perturbations in the spiral density wave f _R = ?6.8 ± 0.7 and f _θ = 3.3 ± 0.5 km s^?1, the pitch angle of a two-armed spiral pattern (m = 2) i = ?4.6° ± 0.1° (which corresponds to a wavelength λ = 2.0 ± 0.1 kpc), and the phase of the Sun in the spiral density wave χ_⊙ = ?193° ± 5°. The phase χ_⊙ has been found to change noticeably with the mean age of the sample. Having analyzed these phase shifts, we have determined the mean value of the angular velocity difference Ω _p ? Ω, which depends significantly on the calibrations used to estimate the individual ages of Cepheids. When estimating the ages of Cepheids based on Efremov’s calibration, we have found |Ω _p ? Ω₀| = 10 ± 1_stat ± 3_syst km s^?1 kpc^?1. The ratio of the radial component of the gravitational force produced by the spiral arms to the total gravitational force of the Galaxy has been estimated to be f _r0 = 0.04 ± 0.01.     

II. Combined numerical model of ion and neutral composition above 120 km

A coupled neutral-ionic photochemical model has been used to interpret the ionic composition of the Venusian dayside ionosphere measured by the orbiter retarding potential analyser (ORPA) experiment on board the NASA Pioneer-Venus orbiter spacecraft. The electron and ion temperatures also measured by the ORPA are used for calculating the plasma-diffusion coefficients and scale heights for ions. The neutral temperature profiles and the densities of neutral constituents, particularly CO₂ and O, play key roles in the determination of the height profiles of the ionic constituents. All these quantities vary substantially in the Venusian thermosphere near the terminator; the models presented are representatives of the solar zenith angle ～65°. The predicted O₂⁺ densities below ～200km agree particularly well with observations by the ORPA, but the model values are significantly less than those measured by the orbiter ion mass spectrometer (OIMS). Models predict much smaller densities than observed values for all molecular ions above ～200km. The reason for the turn-up trend of the concentration gradient of molecular ions observed at these heights by both ORPA and OIMS is unknown. One of the models can predict O⁺ ion densities above ～200km compatible with observations, if an effective vertical escape flux (φ10⁸cm^?2sec^?1) is assumed at the ionopause. The neutral air density required to explain the observed ion composition is about 1.4 times larger than the values measured by the orbiter neutral mass spectrometer (ONMS).     

Analysis of the Z distribution of young objects in the Galactic thin disk

We have obtained new estimates of the Sun’s distance from the symmetry plane Z _⊙ and the vertical disk scale height h using currently available data on stellar OB associations, Wolf–Rayet stars, HII regions, and Cepheids. Based on individual determinations, we have calculated the mean Z _⊙ = ?16 ± 2 pc. Based on the model of a self-gravitating isothermal disk for the density distribution, we have found the following vertical disk scale heights: h = 40.2 ± 2.1 pc from OB associations, h = 47.8 ± 3.9 pc from Wolf–Rayet stars, h = 48.4 ± 2.5 pc from HII regions, and h = 66.2 ± 1.6 pc from Cepheids. We have estimated the surface, Σ = 6 kpc^?2, and volume, D(Z _⊙) = 50.6 kpc^?3, densities from a sample of OB associations. We have found that there could be ～5000 OB associations in the Galaxy.     

Galactic kinematics from a sample of young massive stars

Based on published sources, we have created a kinematic database on 220 massive (> 10 M _⊙) young Galactic star systems located within ≤3 kpc of the Sun. Out of them, ≈100 objects are spectroscopic binary and multiple star systems whose components are massive OB stars; the remaining objects are massive Hipparcos B stars with parallax errors of no more than 10%. Based on the entire sample, we have constructed the Galactic rotation curve, determined the circular rotation velocity of the solar neighborhood around the Galactic center at R ₀ = 8kpc, V ₀ = 259±16 km s^?1, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations f _R = ?10.8 ± 1.2 km s^?1 and f _θ = 7.9 ± 1.3 km s^?1, respectively; the pitch angle for a two-armed spiral pattern i = ?6.0° ± 0.4°, with the wavelength of the spiral density wave near the Sun being λ = 2.6 ± 0.2 kpc; and the radial phase of the Sun in χ _⊙ = ?120° ± 4°. We show that such peculiarities of the Gould Belt as the local expansion of the system, the velocity ellipsoid vertex deviation, and the significant additional rotation can be explained in terms of the density wave theory. All these effects decrease noticeably once the influence of the spiral density wave on the velocities of nearby stars has been taken into account. The influence of Gould Belt stars on the Galactic parameter estimates has also been revealed. Eliminating them from the kinematic equations has led to the following new values of the spiral density wave parameters: f _θ = 2.9 ± 2.1 km s^?1 and χ _⊙ = ?104° ± 6°.     

VLF goniometer observations at halley bay,Antarctica—II. Magnetospheric structure deduced from whistler observations

On 26 July 1967, a magnetically quiet day (ΣK_p = 12?) with high whistler activity at Halley Bay, it was found possible, by measurement of whistler nose-frequency and dispersion and the bearings of the whistler exit points, to make a detailed study of the magnetospheric structure associated with the whistler ducts.During the period 0509–2305 UT most of the exit points of whistlers inside the plasmasphere were situated along a strip about 100km wide passing through Halley Bay in an azimuthal direction 30°E of N between 57° and 62° invariant latitude. A mechanism which can give rise to such a well-defined locus which co-rotates with the Earth is not clear. Nevertheless, it does appear that the locus coincides with the contour of solar zenith angle 102° at 1800 UT 25 July. This was also the time of occurrence of a sub-storm and it is suggested that the magnetospheric structure was initiated by proton precipitation along the solar zenith angle 102° contour.At mid-day knee-whistlers observed outside the plasmapause had exit points which were closely aligned along an L-shell at an invariant latitude of 62.5°. They exhibited a marked variation (~ 3:1) in electron tube content over about 12° of invariant longitude and a drift of about 8 msec^?1 to lower L-shells.Throughout the period of observation the plasmapause lay about 2° polewards of the mean position found by Carpenter (1968) for moderately disturbed days.     

The slab thickness of the mid-latitude ionosphere

The thickness of the peak of the ionosphere depends primarily on the temperature T _n of the neutral gas, and corresponds approximately to an α-Chapman layer at a temperature of 0.87T _n. The overall slab thickness, as given by Faraday rotation measurements, is then τ =0.22 _n + 7km. Expansion of the topside ionosphere, and changes in the E-andFl-regions increase τ by about 20 km during the day in summer. Near solar minimum τ is increased by a lowering of the O ⁺/H ⁺ transition height; if the neutral temperature T _n is estimated, this height can be obtained from observed values of τ.Hourly values of slab thickness were determined over a period of 6 yr at 34°S and 42°S. Near solar maximum the night-time values were about 260 km in all seasons. The corresponding neutral temperatures agree with satellite drag values; they show a semiannual variation of 14 per cent and a seasonal change of 5 per cent. Daytime values of τ were about 230 km in winter and 320 km in summer, implying a seasonal change of 30 per cent in T _n. Temperatures increase steadily throughout the day in all seasons, with a rapid post-sunset cooling in summer. Downwards movements produce a large peak in τ at 0600 hr in winter. A large upwards flux, equal to about 40 per cent of the maximum (limiting) value, reduces τ for several hours after sunrise in winter. The slab thickness increases near solar minimum showing a reduction of the O ⁺/H ⁺ transition height to about 700 km in summer and 500 km in winter.     

The intensity variation of the atomic oxygen red line during morning and evening twilight on 9–10 April 1969

During the evening of 9 April and the morning of 10 April 1969, the twilight zenith intensity of the atomic oxygen red line OI(³P-¹D) at 6300 Å was measured at the Blue Hill Observatory (42°N, 17°W). At the same time incoherent scatter radar data were being obtained at the Millstone Hill radar site 50 km distant. We have used a diurnal model of the mid-latitude F-region to calculate the ionospheric structure over Millstone Hill conditions similar to 9–10 April 1969. The measured electron temperature, ion temperature, and electron density at 800 km are used as boundary conditions for the model calculations. The diurnal variation of neutral composition and temperature were obtained from the OGO-6 empirical model and the neutral winds were derived from a semiempirical three-dimensional dynamic model of the neutral thermosphere. The solar EUV flux was adjusted to yield reasonable agreement between the calculated and observed ionospheric properties.This paper presents the results of these model computations and calculations of the red line intensity. The 6300 Å emission includes contributions from photoelectron excitation, dissociative recombination, Schumann-Runge photodissociation and thermal electron impact. The variations of these four components for morning and evening twilight between 90–120° solar zenith angles, and their relative contributions to the total 6300 Å emission line intensity, are presented and the total is compared to the observations. For this particular day the Schumann-Runge photodissociation component, calculated using the solar fluxes tabulated by Ackermann (1970), is the dominant component of the morning twilight 6300 Å emission. During evening twilight it is necessary to utilize a lower O₂ density than for the morning twilight in order to bring the calculated and observed 6300 Å emission rates into agreement. The implication that there may be a diurnal variation in the O₂ density at the base of the thermosphere is discussed in the light of available experimental data and current theoretical ideas.     

The dayside Venus ionosphere: I. Pioneer-Venus retarding potential analyzer experimental observations

The median values of the principal ionospheric quantities of the Venus dayside ionosphere are presented. The values are derived from the quantities measured by the Pioneer-Venus orbiter retarding potential analyzer over a period of two Earth yaers at solar cycle maximum. Quantities reported are total ion density, O⁺ density, O₂⁺ density, sum density (NO⁺ + N₂⁺ + CO⁺), CO₂⁺ density, ion temperature, electron temperature, and plasma particle pressure. The data are organized to reveal altitude, solar zenith angle, solar longitude, and latitude dependences. The O⁺ density exhibits both a solar longitude and a latitude dependence which we suggest is caused by superrotation of the thermosphere and/or ionosphere. Asymmetry between the dawn and dusk terminator regions in the behavior of other quantities is also descibed.     

Galactic rotation curve and spiral density wave parameters from 73 masers

Based on kinematic data on masers with known trigonometric parallaxes and measurements of the velocities of HI clouds at tangential points in the inner Galaxy, we have refined the parameters of the Allen-Santillan model Galactic potential and constructed the Galactic rotation curve in a wide range of Galactocentric distances, from 0 to 20 kpc. The circular rotation velocity of the Sun for the adopted Galactocentric distance R ₀ = 8 kpc is V ₀ = 239 ± 16 km s^?1. We have obtained the series of residual tangential, ΔV _θ , and radial, V _R , velocities for 73 masers. Based on these series, we have determined the parameters of the Galactic spiral density wave satisfying the linear Lin-Shu model using the method of periodogram analysis that we proposed previously. The tangential and radial perturbation amplitudes are f _θ = 7.0±1.2 km s^?1 and f _R = 7.8±0.7 km s^?1, respectively, the perturbation wave length is λ = 2.3±0.4 kpc, and the pitch angle of the spiral pattern in a two-armed model is i = ?5.2° ±0.7°. The phase of the Sun ζ _⊙ in the spiral density wave is ?50° ± 15° and ?160° ± 15° from the residual tangential and radial velocities, respectively.     

Analysis of HST ultraviolet spectra for T Tauri stars: DR Tau

We analyze the spectra of DR Tau in the wavelength range 1200 to 3100 Å obtained with the GHRS and STIS spectrographs from the Hubble Space Telescope. The profiles for the C IV 1550 and He II 1640 emission lines and for the absorption features of some lines indicate that matter falls to the star at a velocity ～300 km s^?1. At the same time, absorption features were detected in the blue wings of the N I, Mg I, Fe II, Mg II, C II, and Si II lines, suggesting mass outflow at a velocity up to 400 km s^?1. The C II, Si II, and Al II intercombination lines exhibit symmetric profiles whose peaks have the same radial velocity as the star. This is also true for the emission features of the Fe II and H₂ lines. We believe that stellar activity is attributable to disk accretion of circumstellar matter, with matter reaching the star mainly through the disk and the boundary layer. At the time of observations, the accretion luminosity was L_ac ? 2L_⊙ at an accretion rate ?10^?7M_⊙ yr^?1. Concurrently, a small (<10%) fraction of matter falls to the star along magnetospheric magnetic field lines from a height ～R_*. Within a region of size ?3.5R_*, the disk atmosphere has a thickness ～0.1R_* and a temperature ?1.5 × 10⁴ K. We assume that disk rotation in this region significantly differs from Keplerian rotation. The molecular hydrogen lines are formed in the disk at a distance <1.4 AU from the star. Accretion is accompanied by mass outflow from the accretion-disk surface. In a region of size <10R_*, the wind gas has a temperature ～7000 K, but at the same time, almost all iron is singly ionized by H I L _α photons from inner disk regions. Where the warm-wind velocity reaches ?400 km s^?1, the gas moves at an angle of no less than 30° to the disk plane. We found no evidence of regions with a temperature above 10⁴ K in the wind and leave open the question of whether there is outflow in the H₂ line formation region. According to our estimate, the star has the following set of parameters: M_* ? 0.9M_⊙, R_* ? 1.8R_⊙, L_* ? 0.9L_⊙, and \(A_V \simeq 0\mathop .\limits^m 9\). The inclination i of the disk axis to the line of sight cannot be very small; however, i≤60°.     

Effective recombination coefficient and solar zenith angle effects on low-latitude D-region ionosphere evaluated from VLF signal amplitude and its time delay during X-ray solar flares

Excess solar X-ray radiation during solar flares causes an enhancement of ionization in the ionospheric D-region and hence affects sub-ionospherically propagating VLF signal amplitude and phase. VLF signal amplitude perturbation (ΔA) and amplitude time delay (Δt) (vis-á-vis corresponding X-ray light curve as measured by GOES-15) of NWC/19.8 kHz signal have been computed for solar flares which is detected by us during Jan–Sep 2011. The signal is recorded by SoftPAL facility of IERC/ICSP, Sitapur (22^° 27′N, 87^° 45′E), West Bengal, India. In first part of the work, using the well known LWPC technique, we simulated the flare induced excess lower ionospheric electron density by amplitude perturbation method. Unperturbed D-region electron density is also obtained from simulation and compared with IRI-model results. Using these simulation results and time delay as key parameters, we calculate the effective electron recombination coefficient (α _eff ) at solar flare peak region. Our results match with the same obtained by other established models. In the second part, we dealt with the solar zenith angle effect on D-region during flares. We relate this VLF data with the solar X-ray data. We find that the peak of the VLF amplitude occurs later than the time of the X-ray peak for each flare. We investigate this so-called time delay (Δt). For the C-class flares we find that there is a direct correspondence between Δt of a solar flare and the average solar zenith angle Z over the signal propagation path at flare occurrence time. Now for deeper analysis, we compute the Δt for different local diurnal time slots DT. We find that while the time delay is anti-correlated with the flare peak energy flux ? _max independent of these time slots, the goodness of fit, as measured by reduced-χ ², actually worsens as the day progresses. The variation of the Z dependence of reduced-χ ² seems to follow the variation of standard deviation of Z along the T _x -R _x propagation path. In other words, for the flares having almost constant Z over the path a tighter anti-correlation between Δt and ? _max was observed.     

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.     

Vertical distribution and kinematics of protoplanetary nebulae in the galaxy

The catalogue of protoplanetary nebulae by Vickers et al. has been supplemented with the line-of-sight velocities and proper motions of their central stars from the literature. Based on an exponential density distribution, we have estimated the vertical scale height from objects with an age less than 3 Gyr belonging to the Galactic thin disk (luminosities higher than 5000 L _⊙) to be h = 146 ± 15 pc, while from a sample of older objects (luminosities lower than 5000 L _⊙) it is h = 568 ± 42 pc. We have produced a list of 147 nebulae in which there are only the line-of-sight velocities for 55 nebulae, only the proper motions for 25 nebulae, and both line-of-sight velocities and proper motions for 67 nebulae. Based on this kinematic sample, we have estimated the Galactic rotation parameters and the residual velocity dispersions of protoplanetary nebulae as a function of their age. We have established that there is a good correlation between the kinematic properties of nebulae and their separation in luminosity proposed by Vickers. Most of the nebulae are shown to be involved in the Galactic rotation, with the circular rotation velocity at the solar distance being V ₀ = 227 ± 23 km s^?1. The following principal semiaxes of the residual velocity dispersion ellipsoid have been found: (σ₁, σ₂, σ₃) = (47, 41, 29) km s^?1 from a sample of young protoplanetary nebulae (with luminosities higher than 5000 L _⊙), (σ₁, σ₂, σ₃) = (50, 38, 28) km s^?1 from a sample of older protoplanetary nebulae (with luminosities of 4000 L _⊙ or 3500 L _⊙), and (σ₁, σ₂, σ₃) = (91, 49, 36) km s^?1 from a sample of halo nebulae (with luminosities of 1700 L _⊙).     

On the structure of Mars' atmosphere at 120–220 km

Altitude dependences of [CO₂] and [CO₂⁺] are deduced from Mariner 6 and 7 CO₂⁺ airglow measurements. CO₂ densities are also obtained from n_e radio occultation measurements. Both [CO₂] profiles are similar and correspond to the model atmosphere of Barth et al. (1972) at 120 km, but at higher altitudes they diverge and at 200–220 km the obtained [CO₂] values are three times less the model. Both the airglow and radio occultation observations show that a correction factor of 2.5 should be included into the values for solar ionization flux given by Hinteregger (1970). The ratio of [CO₂⁺]/n_e is 0.15–0.2 and, hence, [O]/[CO₂] is ～3% at 135 km. An atmospheric and ionospheric model is developed for 120–220 km. The calculated temperature profile is characterized by a value of T ≈ 370°K at h ? 220 km, a steep gradient (～2°/km) at 200-160 km, a bend in the profile at 160 km, a small gradient (～0.7°/km) below and a value of T ≈ 250°K at 120 km. The upper point agrees well with the results of the Lyman-α measurements; the steep gradient may be explained by molecular viscosity dissipation of gravity and acoustical waves (the corresponding energy flux is 4 × 10^?2 erg cm^?2sec^?1 at 180 km). The bend at 160 km may be caused by a sharp decrease of the eddy diffusion coefficient and defines K ≈ 2 × 10⁸cm²sec^?1; and the low gradient gives an estimate of the efficiency of the atmosphere heating by the solar radiation as ? ≈ 0.1.     

A two-dimensional model of the ionosphere of Venus: Thermal structure

A two-dimensional spectral model of energetics in the ionosphere of Venus has been constructed. The effects of horizontal bulk transport of heat and the heat flux saturation have been taken into account. The model is capable of explaining the observed high ion temperatures for solar zenith angles greater than 140°. An external heat input to ions of 1–2 × 10⁻⁴ergs cm⁻²sec⁻¹ almost uniformly distributed over the entire planet gives good agreement with the average ion temperature data from the PVO retarding potential analyzer. The effects of varying the magnitude of the horizontal plasma velocity, including the vertical component of bulk velocity, changing the altitude dependence of the velocity profile, and making the ionopause height a function of solar zenith angle have been discussed.     

Determination of ionospheric electron content from the Faraday rotation of geostationary satellite signals

Calculations using a wide range of model ionospheres (with a peak at 300 km) show that the integrated electron content up to the height of the satellite could be up to four times the value deduced from Faraday rotation measurements. However, using a fixed mean field height of 400 km, the observed Faraday rotation gives the electron content up to a height h_F of 2000 km with an accuracy of ±3 per cent. For observations at different magnetic and geographic latitudes, and geostationary satellites at different longitudes, the optimum value of h_F varies by only ±200 km. Night-time increases in the height of the ionosphere have little effect on h_F, but increase the mean field height to about 470 km. Using a fixed value of 420 km, with h_F = 2000 km, gives an accuracy of ±5 per cent under most conditions.     

The Venus ionosphere at grazing incidence of solar radiation: Transport of plasma to the night ionosphere

Using a quasi-two-dimensional model of the Venus ionosphere, we calculated the ion number densities and horizontal ion bulk velocities expected for a range of solar zenith angles near the terminator (80 to 100°), and compared them with data obtained from the Pioneer Venus Orbiter retarding potential analyzer. The calculated ion bulk velocity arises entirely from the solar EUV-induced plasma pressure gradient and has a magnitude consistent with observations; ionization by suprathermal electrons is neglected in those computations. We find that while photoionization is the dominant source of ionospheric plasma for solar zenith angles less than 92°, plasma transport from the dayside is the dominant plasma source for solar zenith angles greater than 95°. We also show that the main nightside plasma peak at approximately 140 km altitude is of the F₂ type (i.e., is diffusion controlled). Its altitude and shape are thus quite insensitive to the altitude of the ion source.     

Dynamics of the Venus ionosphere: A two-dimensional model study

A two-dimensional model of the ionosphere of Venus which simulates ionospheric dynamics by self-consistently solving the plasma equations of motion, including the inertial term, in finite difference form has been constructed. The model, which is applied over the solar zenith angle range extending from 60 to 140° and the altitude range 100 to 480 km, simulates the measured horizontal velocity field quite satisfactorily. The ion density field is somewhat overestimated on the dayside because of the choice model neutral atmosphere and underestimated on the nightside because of setting the ionopause height at too low an altitude. It is concluded that solar photoionization on the dayside and ion recombination on the nightside are the processes mainly responsible for accelerating the plasma to the observed velocities. The plasma flow appears to be sufficient to maintain the nightside ionosphere at or near the observed median level of ion densities.     

Corrections for the Lutz-Kelker bias for Galactic masers

Based on published data, we have collected information about Galactic maser sources with measured distances. In particular, 44 Galactic maser sources located in star-forming regions have trigonometric parallaxes, proper motions, and radial velocities. In addition, ten more radio sources with incomplete information are known, but their parallaxes have been measured with a high accuracy. For all 54 sources, we have calculated the corrections for the well-known Lutz-Kelker bias. Based on a sample of 44 sources, we have refined the parameters of the Galactic rotation curve. Thus, at R ₀ = 8kpc, the peculiar velocity components for the Sun are (U _⊙, V _⊙, W _⊙) = (7.5, 17.6, 8.4) ± (1.2, 1.2, 1.2) km s^?1 and the angular velocity components are ω ₀ = ?28.7 ± 0.5 km s^?1 kpc^?1, ω ₀′ = +4.17 ± 0.10 km s^?1 kpc^?2, and ω₀″ = ?0.87 ± 0.06 km s^?1 kpc^?3. The corresponding Oort constants are A = 16.7 ± 0.6 km s^?1 kpc^?1 and B = ?12.0 ± 1.0 km s^?1 kpc^?1; the circular rotation velocity of the solar neighborhood around the Galactic center is V ₀ = 230 ± 16 km s^?1. We have found that the corrections for the Lutz-Kelker bias affect the determination of the angular velocity ω ₀ most strongly; their effect on the remaining parameters is statistically insignificant. Within themodel of a two-armed spiral pattern, we have determined the pattern pitch angle $i = - 6_.^ \circ 5$ and the phase of the Sun in the spiral wave χ ₀ = 150°.