Unusual infrared fading of CH Cygni in 2006

Infrared observations of the unique symbiotic system CH Cyg in 2003–2006 are presented. Analysis of the observations has shown that a fairly dense dust structure (a cloud or a shell) appeared on the line of sight in August–November 2006. The dust grains in the new shell are similar in optical properties to graphite ones and their sizes are mostly within the range 0.14–0.16 μm. The dust shell is optically thick and its optical depth at 2.2 μm is τ(2.2) ≈ 0.97. The dust shell mass is M _d(06) ≈ 8 × 10⁻⁶ M _⊙ and the rate of matter flow into the shell has reached ∼2 × 10⁻⁵ M _⊙ yr⁻¹. Original Russian Text ? O.G. Taranova, V.I. Shenavrin, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 8, pp. 598–603.     

Interaction of the supernova remnant HB3 with the ambient interstellar gas

The well-known shell supernova remnant (SNR) HB3 is part of a feature-rich star-forming region together with the nebulae W3, W4, and W5. We study the HI structure around this SNR using five RATAN-600 drift curves obtained at a wavelength of 21 cm with an angular resolution of 2′ in one coordinate over the radial-velocity range ?183 to +60 km s^?1 in a wider region of the sky and with a higher sensitivity than in previous works by other authors. The spatial-kinematic distribution of HI features around the SNR clearly shows two concentric expanding shells of gas that surround the SNR and coincide with it in all three coordinates (α, δ, and V). The outer shell has a radius of 133 pc, a thickness of 24 pc, and an expansion velocity of 48 km s^?1. The mass of the gas in it is ≈2.3 × 10⁵M_⊙. For the inner shell, these parameters are 78 pc, 36 pc, 24 km s^{? 1}, and 0.9 × 10⁵M_⊙, respectively. The inner shell is immediately adjacent to the SNR. Assuming that the outer shell was produced by the stellar wind and the inner shell arose from the shock wave of the SNR proper, we estimated the age of the outer shell, ≈1.7 × 10⁶ yr, and the mechanical luminosity of the stellar wind, 1.5 × 10³⁸ erg s^?1. The inner shell has an age of ≈10⁶ yr and corresponds to a total supernova explosion energy of ≈10⁵² erg.     

Infrared photometry of the symbiotic novae V1016 Cyg and HM Sge in 1978–1999

The photometric JHKLM observations of the symbiotic novae V1016 Cyg and HM Sge in 1978–1999 are presented. Parameters of the cool stars themselves and the dust envelopes are estimated. The periods of 470±5 days (for V1016 Cyg) and 535±5 days (for HM Sge) are reliably determined from the entire set of our photometric J data for V1016 Cyg and HM Sge. In addition, monotonic light and color variations are observed on a time scale of several thousand days, with the increase in infrared brightness occurring with the simultaneous decrease in infrared color indices; i.e., the dust envelopes in which both components of the systems were embedded before the outburst of their hot sources in 1964 and 1975, respectively, had continued to disperse until late 1999. The amplitudes of these variations for HM Sge are almost twice those for V1016 Cyg. For HM Sge, the dust envelope reached a maximum density near JD 2447500 and then began to disperse. In the case of V1016 Cyg, a maximum density of the dust envelope was probably reached near JD 2444800, and its dispersal has been continuing for about 20 years. Thus, in both symbiotic novae, their dust envelopes reached a maximum density approximately eight years after the outburst of the hot component and then began to disperse. An analysis of the color-magnitude (J–K, J) diagram reveals that grains in the dust envelopes of V1016 Cyg and HM Sge are similar in their optical properties to impure silicates. The observed [J–K, K–L] color variations for the symbiotic novae under study can be explained in terms of the simple model we chose by variations in the Mira's photospheric temperature from 2400 to 3000 K and in the dust-envelope optical depth from 1 to 3 at a wavelength of 1.25 µm for a constant grain temperature. The observed J–K and K–L color indices for both symbiotic novae, while decreasing, tend to the values typical of Miras. The dust envelopes of both symbiotic novae are optically thick. The dust envelope around HM Sge is, on the average, twice as dense as that around V1016 Cyg; the Mira in V1016 Cyg is slightly cooler (~2800–2900 K) than that in HM Sge (~2600–2700 K). The dust-envelope density decreases as the Mira's temperature increases. The absolute bolometric magnitudes are $ - 5\mathop .\limits^m 1 \pm 0\mathop .\limits^m 15$ for V 1016 Cyg and $5\mathop .\limits^m 27 \pm 0\mathop .\limits^m 17$ for HM Sge. Their distances are 2.8±0.6 and 1.8±0.4 kpc, respectively; the luminosities and radii of their cool components (Miras) are 8.6×10³ L _⊙, 1×10⁴ L _⊙, 500R _⊙, and 540R _⊙. The radii of their dust envelopes are 1400R _⊙ and 1500R _⊙; the masses are (3?3.3) × 10^?5M_⊙ and (4?8) × 10^?5M_⊙ The dust envelope of V1016 Cyg disperses slower than that of HM Sge by almost a factor of 25.     

Ultraluminous quasars as a gravitational mesolensing effect

Two quasars SDSS J010013.02+280225.8 and J030642.51+185315.8 with redshifts z = 6.30 and z = 5.363 were recently discovered. Their apparent magnitudes in the standard cosmological model give the luminosities of L_bol ～ 4.3 × 10¹⁴L_⊙ and L_bol ～ 3.4 × 10¹⁴L_⊙. In the framework of modern concepts it is accepted that the energy release of quasars is provided by the accretion onto black holes with masses of 1.24 ± 0.19 × 10¹⁰M_⊙ and 1.07 ± 0.27 × 10¹⁰M_⊙. As within the standard cosmological model the ages of these objects are about one billion years, this creates serious difficulties for the scenario of formation of such objects. Here we interpret the ultra-high luminosities of quasars as the effect of lensing of their radiation by the foreground globular clusters or dwarf galaxies.     

Disk models for cataclysmic variables

This paper presents disk models for cataclysmic variables in which convection in the central layers has been included. The calculation of the vertical structure at different points is presented. The models have a central mass of 1M _⊙ and matter fluxes of 10^?9, 10^?8, and 10^?7 M _⊙ yr^?1. The corresponding luminosities are 1.86, 1.86×10 and 1.86×10² L _⊙.     

Broadband spectrum of the total X-ray emission from the galaxy M31

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.     

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 _⊙).     

Neutral hydrogen in the vicinity of the supernova remnant HB 9

The neutral hydrogen emission at 21 cm has been investigated with the RATAN-600 radio telescope in the vicinity of the supernova remnant HB9. A clumpyHI shell with radial motions surrounding the remnant has been detected. Its measured parameters contradict the connection with a shock wave from a supernova explosion. The shell formation under the action of a wind from a star that exploded as a supernova at the end of its evolution seems more realistic. The characteristics of the star obtained from the observed shell parameters are the following: a wind power of 0.5 × 10³⁸ erg s^?1, a mass-loss rate of 3.7 × 10^?5 M _⊙ yr^?1, and an age of 3 × 10⁶ yr. Given the measurement errors, the mass of the star is estimated to be >8M _⊙.     

For infrared spectrophotometry of Jupiter and Saturn

Infrared spectral observations of Mars, Jupiter, and Saturn were made from 100 to 470 cm^?1 using NASA's G. P. Kuiper Airborne Observatory. Taking Mars as a calibration source, we determined brightness temperatures of Jupiter and Saturn with approximately 5 cm^?1 resolution. The data are used to determine the internal luminosities of the giant planets, for which more than 75% of the thermally emitted power is estimated to be in the measured bandpass: for Jupiter L_J = (8.0 ± 2.0) × 10^?10L_⊙ and for Saturn L_S = (3.6 ± 0.9) × 10^?10. The ratio R of thermally emitted power to solar power absorbed was estimated to be R_J = 1.6 ± 0.2, and R_S = 2.7 ± 0.8 from the observations when both planets were near perihelion. The Jupiter spectrum clearly shows the presence of the rotational ammonia transitions which strongly influence the opacity at frequencies ?250 cm^?1. Comparison of the data with spectra predicted from current models of Jupiter and Saturn permits inferences regarding the structure of the planetary atmospheres below the temperature inversion. In particular, an opacity source in addition to gaseous hydrogen and ammonia, such as ammonia ice crystals as suggested by Orton, may be necessary to explain the observed Jupiter spectrum in the vicinity of 250 cm^?1.     

Infrared luminosities of local-volume galaxies

Based on data from the Two-Micrometer All-Sky Survey (2MASS), we analyzed the infrared properties of 451 Local-Volume galaxies at distances D ≤ 10 Mpc. We determined the K-band luminosity function of the galaxies in the range of absolute magnitudes from ?25^m to ?11^m. The local luminosity density within 8 Mpc is 6.8 × 10⁸L_⊙ Mpc^?3, a factor of 1.5 ± 0.1 higher than the global mean K-band luminosity density. We determined the ratios of the virial mass to the K-band luminosity for nearby groups and clusters of galaxies. In the luminosity range from 5 × 10¹⁰ to 2 × 10¹³L_⊙, the dependence log(M/L_K) ∝ (0.27 ± 0.03) log L_K with a dispersion of ～0.1 comparable to the measurement errors of the masses and luminosities of the systems of galaxies holds for the groups and clusters of galaxies. The ensemble-averaged ratio, 〈M/L_K〉 ? (20–25) M_⊙/L_⊙, was found to be much smaller than the expected global ratio, (80–90)M_⊙/L_⊙, in the standard model with Ω_m = 0.27. This discrepancy can be eliminated if the bulk of the dark matter in the Universe is not associated with galaxies and their systems.     

On the origin and initial temperature of Jupiter and Saturn

A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 10⁷ years in Jupiter's zone and ～2 × 10⁸ years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～10²⁸ g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m_⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m₁ ≈ 50 m_⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m₂ ≈ 130 m_⊕), the width of the exhausted zone being $\text{～}\text{built1}\text{3}$ of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 10⁵?10⁶ years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m₁ > m₂ ≈ 30 m_⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m_⊕, when the luminosity of the planet reaches 3 × 10^?3 L_⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m_⊕) and a luminosity up to 10^?4 L_⊙.     

Radial pulsations of helium stars with masses from 10 to 50<Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We have performed hydrodynamic calculations of the radial pulsations of helium stars with masses 10M_⊙ ≤ M ≤ 50M_⊙, luminosity-to-mass ratios 5 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2.5 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for helium and heavy-element mass fractions of Y=0.98 and Z=0.02, respectively. We show that the high-temperature boundary of the instability region for radial pulsations at L/M ? 10⁴L_⊙/M_⊙ extends to T_eff≈10⁵ K. The amplitude of the velocity variations for outer layers is several hundred km s^?1, while the brightness variations in the B band of the UBV photometric system are within the range from several hundredths to half a magnitude. At constant luminosity-to-mass ratio, the radial pulsation period is determined only by the effective temperature of the star. In the ranges of luminosity-to-mass ratios 10⁴L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙ and effective temperatures 5 × 10⁴ K ≤ T_eff ≤ 9 × 10⁴ K, the periods of the radial modes are within 6 min ?Π?10³ min.     

Radial pulsations of helium stars with masses from 1 to 10 <Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We present the results of our hydrodynamic calculations of radial pulsations in helium stars with masses 1 M_⊙ ≤ M ≤ 10 M_⊙, luminosity-to-mass ratios 1 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for mass fractions of helium Y=0.98 and heavy elements Z=0.02. We show that the lower boundary of the pulsation-instability region corresponds to L/M ～ 10³L_⊙/M_⊙ and that the instability region for L/M ? 5 × 10³L_⊙/M_⊙ is bounded by effective temperatures T_eff ? 3 × 10⁴ K. As the luminosity rises, the instability boundary moves into the left part of the Hertzsprung-Russell diagram and radial pulsations can arise in stars with effective temperatures T_eff ? 10⁵ K at L/M ? 7 × 10³L_⊙/M_⊙. The velocity amplitude for the outer boundary of the hydrodynamic model increases with L/M and lies within the range 200 ? ΔU ? 700 km s^?1 for the models under consideration. The periodic shock waves that accompany radial pulsations cause a significant change of the gas-density distribution in the stellar atmosphere, which is described by a dynamic scale height comparable to the stellar radius. The dynamic instability boundary that corresponds to the separation of the outer stellar atmospheric layers at a superparabolic velocity is roughly determined by a luminosity-to-mass ratio L/M ～ 3 × 10⁴L_⊙/M_⊙.     

Normal galaxies in the all-sky survey by the eROSITA X-ray telescope of the Spectrum-X-Gamma observatory

We analyze the statistical properties of normal galaxies to be detected in the all-sky survey by the eROSITA X-ray telescope of the Spectrum-X-Gamma observatory. With the current configuration and parameters of the eROSITA telescope, the sensitivity of a 4-year-long all-sky survey will be ≈10^?14 erg s^?1 in the 0.5–2 keV band. This will allow ～(1.5–2) × 10⁴ normal galaxies with approximately the same contribution of star-forming and elliptical galaxies to be detected. All galaxies of the X-ray survey are expected to enter into the existing far-infrared (IRAS) or near-infrared (2MASS) catalogs; the sample of star-forming galaxies will be approximately equivalent in sensitivity to the sample of star-forming galaxies in the IRAS catalog of infrared sources. Thus, a large homogeneous sample of normal galaxies with measured X-ray, near-infrared, and far-infrared fluxes will be formed. About 90% of the galaxies in the survey are located within ～200–400 Mpc. A typical (most probable) galaxy will have a luminosity log L _X ～ 40.5–41.0, will be located at a distance of ～70–90 Mpc, and will be either a star-forming galaxy with a star formation rate of ～20M _⊙ yr^?1 whose X-ray emission is produced by ultraluminous X-ray sources (ULXs) or an elliptical galaxy with amass log M _* ～ 11.3 emitting through to a hot interstellar gas. The galaxies within 35 Mpc will collectively contain ～10² ULXs with luminosities log L _X > 40, ～80% of whichwill be the only luminous source in the galaxy. Thus, although the angular resolution of the eROSITA telescope is too low for the luminosity function of compact sources in galaxies to be studied in detail, the survey data will allow one to investigate its bright end and, possibly, to impose constraints on the maximum luminosity of ULXs.     

Relation between the X-ray and optical luminosities in binary systems with accreting nonmagnetic white dwarfs

We investigate the relation between the optical (g-band) and X-ray (0.5–10 keV) luminosities of accreting nonmagnetic white dwarfs. According to the present-day counts of the populations of star systems in our Galaxy, these systems have the highest space density among the close binary systems with white dwarfs. We show that the dependence of the optical luminosity of accreting white dwarfs on their X-ray luminosity forms a fairly narrow one-parameter curve. The typical half-width of this curve does not exceed 0.2–0.3 dex in optical and X-ray luminosities, which is essentially consistent with the amplitude of the aperiodic flux variability for these objects. At X-ray luminosities L _x ～ 10³² erg s^?1 or lower, the optical g-band luminosity of the accretion flow is shown to be related to its X-ray luminosity by a factor ～2–3. At even lower X-ray luminosities (L _x ? 10³⁰ erg s^?1), the contribution from the photosphere of the white dwarf begins to dominate in the optical spectrum of the binary system and its optical brightness does not drop below M _g ～ 13–14. Using the latter fact, we show that in current and planned X-ray sky surveys, the family of accreting nonmagnetic white dwarfs can be completely identified to the distance determined by the sensitivity of an optical sky survey in this region. For the Sloan Digital Sky Survey (SDSS) with a limiting sensitivity m _g ～ 22.5, this distance is ～400–600 pc.     

Ultraviolet Spectral Behavior of TVCol During and After Flaring Activity

We studied the intermediate polar TVCol during and after its flare in November 1982 observed in the ultraviolet range with the International Ultraviolet Explorer. Two spectra revealing the variations of emission lines at different times are presented. We have estimated a new value of the reddening from the 2200 Å absorption feature, E (B ? V ) = 0.12 ± 0.02, and calculated the line fluxes of C IV and He II emission lines produced in the outer accretion disk. The average ultraviolet luminosity of emitting region during and after the flare is approximately 4 × 10³² erg s^?1 and 9 × 10³⁰ erg s^?1, the corresponding average mass accretion rate is nearly 3 × 10¹⁵ erg s^?1 (4.76 × 10^?11M_⊙ yr^?1) and 5 × 10¹³ erg s^?1 (7.9³ × 10^?13M_⊙ yr^?1), and the average temperature of the emitting region during and after flare is estimated to be of about 3.5 × 10³ K and 2 × 10³ K. We attribute this flare to a sudden increase in the mass accretion rate leading to the outburst activity.     

Neutral hydrogen around the oxygen-sequence Wolf-Rayet star WR 102 and the nebula G2.4+1.4

We carried out the first 21-cm line observations of an extended region around the Wolf-Rayet star WR 102 and the associated nebula G2.4+1.4 with the RATAN-600 radio telescope. An irregular H I shell was identified. Its maximum expansion velocity reaches ～50 km s^?1, and its outer diameter (at a distance of 3 kpc) is 56 pc. The mechanical luminosity of the stellar wind required to produce the observed shell is estimated to be ～0.8×10³⁸ erg s^?1; the age of the shell is ～3.4×10⁵ yr. We compare the inferred parameters of the H I shell with the structure and kinematics of the ionized nebula and with the dust distribution in the region.     

Dust ring formation due to ice sublimation of radially drifting dust particles under the Poynting-Robertson effect in debris disks

In a disk with a low optical depth, dust particles drift radially inward by the Poynting-Robertson (P-R) drag rather than are blown out by stellar radiation pressure following destructive collisions. We investigate the radial distribution of icy dust composed of pure ice and refractory materials in dust-debris disks taking into account the P-R drag and ice sublimation. We find that icy dust particles form a dust ring by their pile-ups at the edge of their sublimation zone, where they sublime substantially at the temperature 100-110 K. The distance of the dust ring is 20-35 AU from the central star with its luminosity L_??30L_⊙ and 65(L_?/100L_⊙)^1/2 AU for L_??30L_⊙, where L_⊙ is the solar luminosity. The effective optical depth is enhanced by a factor of 2 for L_??100L_⊙ and more than 10 for L_??100L_⊙. The optical depth of the outer icy dust disk exceeds that of the inner disk filled with refractory particles, namely, the residue of ice sublimation, which are further subjected to the P-R effect. As a result, an inner hole is formed inside the sublimation zone together with a dust ring along the outer edge of the hole.     

Diagnostics of the early explosion phase of a classical nova using its X-ray emission: A model for the X-ray outburst of CI Camelopardalis in 1998

We have computed a spherically symmetric model for the interaction of matter ejected during the outburst of a classical nova with the stellar wind from its optical component. This model is used to describe the intense X-ray outburst (the peak 3–20 keV flux was ～2 Crab) of the binary system CI Camelopardalis in 1998. According to our model, the stellar wind from the optical component heated by a strong shock wave produced when matter is ejected from the white dwarf as the result of a thermonuclear explosion on its surface is the emission source in the standard X-ray band. Comparison of the calculated and observed time dependences of the mean radiation temperature and luminosity of the binary system during its outburst has yielded very important characteristics of the explosion. We have been able to measure the velocity of the ejected matter immediately after the onset of the explosion for the first time: it follows from our model that the ejected matter had a velocity of ～2700 km s^?1 even on 0.1–0.5 day after the outburst onset and it flew with such a velocity for the first 1–1.5 day under an external force, possibly, the radiation pressure from the white dwarf. Subsequently, the matter probably became transparent and began to decelerate. The time dependence of the mean radiation temperature at late expansion phases has allowed us to estimate the mass of the ejected matter, ～10^?7–10^?6 M _⊙. The mass loss rate in the stellar wind required to explain the observed peak luminosity of the binary system during its outburst has been estimated to be \(\dot M\) ～ (1 ? 2) × 10^?6 M _⊙ yr^?1.     

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.