Yu. A. Shibanov

Optical photometry of the PSR B0656+14 and its neighborhood

We present the results of broad-band photometry of the nearby middle-aged radio pulsar PSR B0656+14 and its neighborhood obtained with the 6-meter telescope of the SAO RAS and with the Hubble Space Telescope. The broad-band spectral flux F of the pulsar decreases with increasing frequency in the near-IR range and increases with frequency in the near-UV range. The increase towards UV can be naturally interpreted as the Rayleigh-Jeans tail of the soft thermal component of the X-ray spectrum emitted from the surface of the cooling neutron star. Continuation of the power-law component, which dominates in the high-energy tail of the X-ray spectrum, to the IR-optical-UV frequencies is consistent with the observed fluxes. This suggests that the non- thermal pulsar radiation may be of the same origin in a broad frequency range from IR to hard X-rays. We also studied 4 objects detected within 5 00 from the pulsar.

The young pulsar PSR B0540-69.3 and its synchrotron nebula in the optical and X-rays

The young PSR B0540-69.3 in the LMC is the only pulsar (except the Crab pulsar) for which a near-UV spec- trum has been obtained. However, the absolute flux and spectral index of the HST/FOS spectrum are significantly higher than suggested by previous broad-band time-resolved groundbased UBVRI photometry. To investigate this difference, observations with ESO/VLT/FORS1 and analysis of HST/WFPC2 archival data were done. We show that the HST and VLT spectral data for the pulsar have >50% nebular contamination and that this is the reason for the above-mentioned difference. The broadband HST spectrum for the range 3300-8000 A is clearly nonthermal and has a negative spectral index, Fν ∝ ν −α with αν = 1.07 +0.20 −0.19 . This is different from the almost flat spectrum of the Crab pulsar, and also steeper than for the previously published broadband photometry of PSR B0540-69.3. We have also studied the spatial variations of the brightness and spectral index of the Pulsar Wind Nebula (PWN) around the pulsar, and find no significant spectral index variation over the PWN. The HST data show a clear asymmetry of the surface brightness distribution along the major axis of the torus-like structure of the PWN with respect to the pulsar position, also seen in Chandra/HRC X-ray images. This is different from the Crab PWN and likely linked to the asymmetry of the surrounding SN ejecta. The HST/WFPC2 archival data have an epoch separation of 4 years, and this allows us to estimate the proper motion of the pulsar. We find a motion of 4.9 ± 2. 3m as yr −1 (corresponding to a transverse velocity of 1190 ± 560 km s −1 ) along the southern jet of the PWN. If this is confirmed at a higher significance level by future observations, this makes PSR B0540-69.3 the third pulsar with a proper motion aligned with the jet axis of its PWN, which poses constraints on pulsar kick models. To establish the multiwavelength spectrum of the pulsar and its PWN, we have included recent Chandra X-ray data, and discuss the soft pulsar X-ray spectrum based on spectral fits including absorption by interstellar gas in the Milky Way, LMC as well as the supernova ejecta. We have compared the multiwavelength spectra of PSR B0540-69.3 and the Crab pulsar, and find that both PSR B0540-69.3 and the Crab pulsar have a weaker flux in the optical than suggested by a low-energy power-law extension of the X-ray spectrum. This optical depression is more severe for PSR B0540-69.3 than for the Crab pulsar. The same trend is seen for the PWNe of the two pulsars, and continues for low energies also out in the radio band. We discuss possible interpretations of this behavior.

The Vela pulsar in the near-infrared

We report on the first detection of the Vela pulsar in the near-infrared with the VLT/ISAAC in the Js and H bands. The pulsar magnitudes are Js = 22.71 ± 0.10 and H = 22.04 ± 0.16. We compare our results with the available multiwavelength data and show that the dereddened phase-averaged optical spectrum of the pulsar can be fitted with a power law Fν ∝ ν −αν with αν = 0.12 ± 0.05, assuming the color excess EB−V = 0.055 ± 0.005 based on recent spectral fits of the emission of the Vela pulsar and its supernova remnant in X-rays. The negative slope of the pulsar spectrum is different from the positive slope observed over a wide optical range in the young Crab pulsar spectrum. The near-infrared part of the Vela spectrum appears to have the same slope as the phase-averaged spectrum in the high energy X-ray tail, obtained in the 2−10 keV range with the RXTE. Both of these spectra can be fitted with a single power law suggesting their common origin. Because the phase-averaged RXTE spectrum in this range is dominated by the second X-ray peak of the pulsar light curve, coinciding with the second main peak of its optical pulse profile, we suggest that this optical peak can be redder than the first one. We also detect two faint extended structures in the 1. �� 5−3. �� 1 vicinity of the pulsar, projected on and aligned with the south-east jet and the inner arc of the pulsar wind nebula, detected in X-rays with Chandra. We discuss their possible association with the nebula.

Quantum effects in cyclotron plasma absorption

It is shown that X-ray radiation of neutron stars with magnetic fieldsB=1011–1013 G near cyclotron resonancesω=sωB(s=1,2,...) is deeply affected by such quantum effects as electron-positron vacuum polarization (significant at V=3×1028ne−1(B/BC4)≳1, whereBC=4.4×1013G), the quantizing character of the magnetic field (significant atV=3 x 1028ne−1(B/Bc)4≳1 whereBc=4.4 x 1013G), the non-harmonic character of the Landau levels, and the quantum recoil of electrons. The latter two factors shift the resonances by the frequency −s2ωB(B/2Bc)sin2ϑ, ϑ being the angle between the direction of radiation propagation and the magnetic field. IfV≪V0 (for ϑ∼1,V0∼β−1=(mc2/2T)1/2), the normal mode (NM) polarizations, as well as the absorption coefficientk1 of the extraordinary NM in the Doppler core of the first resonance (|ω−ω| ≲ωBβ cos ϑ), is only slightly affected by varyingb and/orV, whereas for the ordinary NM (at ϑ∼1)k2∼k1β2[b + (3 + tan2ϑ−2V)2]≪k1. For sufficiently largeb and/orV the quantum effects amplify resonant absorption of the ordinary NM atω∼ωB, with spin-flip transitions playing a major role atb≳1+V2. IfV∼V0, the coefficientsk1 andk2 in the Doppler core of the resonance are of the same order and acquire some peculiar features (shifts, intersections, etc.), with the NM polarizations depending sharply on ω and being strongly non-orthogonal. AtV≫V0,k2=k1(cos2 ϑ+B/2BC) and the polarizations are almost linear. Near high resonances (s≥2), as a rule,k1,2α(1 + b)s−1β2s−3 i.e., absorption increases withb due to replacement of the thermal energy of the transverse motion of electron,T, by the magnetic energyħωB. The above effects should be taken into account for an interpretation of observational data on X-ray pulsars (e.g., Her X-1) and other X-ray sources associated with neutron stars.

Radiation from a strongly-magnetized plasma: The case of predominant scattering

On the basis of diffusion approach for normal modes, solutions of the radiative transfer problem are obtained and analysed for an optically thick tenuous plasma with a strong magnetic field. The case is considered when the scattering processes without change of photon frequency ω are dominant. The radiative transfer coefficients as well as spectra, angular dependences and polarization of the outgoing radiation are investigated in detail for a ‘cold’ plasma,kTe≩mc2, |ω−sωB|≫ωkTe/mc2 )1/2|cosϑ|, whereTe is the electron plasma temperature,ωB=eB/mc the electron cyclotron frequency,s=1,2,... the number of cyclotron harmonic and ϑ the angle between the magnetic field and wave vector. The effects of electronpositron vacuum polarization are taken into account and shown to be very significant. Simple analytic solutions are obtained for various limiting cases (small and large vacuum polarization; high, low and close to the cyclotron resonance radiation frequencies; different orientations of the magnetic field, etc). The results obtained are necessary for analysing X-ray and gamma-ray radiation from strongly magnetized neutron stars.

Multiband optical observations of the old PSR B0950+08

We report on deep UBVRI -imaging of the field of the 17.3 Myr radiopulsar PSR B0950+08  obtained with the ESO/VLT/FORS1. Firm detection of the candidate pulsar optical counterpart in the BVRI bands with the magnitudes

The radiation of a hot magnetized plasma accreted by degenerate stars with a strong magnetic field

B=27.06

Spectra of radiation from a strongly magnetized plasma

± 0.35,

The near-UV pulse profile and spectrum of the pulsar PSR B0656+14

V=27.05

Subaru optical observations of the old pulsar PSR B0950+08 ⋆

± 0.15,