Ages and thermal luminosities of neutron stars, inferred from observations, can be interpreted with the aid of the neutron star cooling theory to gain information on the properties of superdense matter in neutron-star interiors. We present a survey of estimated ages, surface temperatures, and thermal luminosities of middle-aged neutron stars with relatively weak or moderately strong magnetic fields, which can be useful for these purposes. The catalogue includes results selected from the literature, supplemented with new results of spectral analysis of a few cooling neutron stars. The data are compared with the theory. We show that overall agreement of theoretical cooling curves with observations improves substantially for models where neutron superfluidity in stellar core is weak.

Context. PSR J1357−6429 is a Vela-like radio pulsar that has been recently detected in X-rays and γ-rays. It powers a compact taillike X-ray pulsar wind nebula and X-ray-radio plerion associated with an extended TeV source HESS J1356−645. Aims. We present our deep optical observations with the Very Large Telescope to search for an optical counterpart of the pulsar and its nebula. Methods. The observations were carried out using a direct imaging mode in the V, R, and I bands. We also analysed archival X-ray data obtained with Chandra and XMM-Newton. Results. In all three optical bands, we detect a point-like source with V = 27.3 ± 0.3, R = 25.52 ± 0.07, and I = 24.13 ± 0.05, whose position is within the 1σ error circle of the X-ray position of the pulsar, and whose colours are distinct from those of ordinary stars. We consider it as a candidate optical counterpart of the pulsar. If it is indeed the counterpart, its 5σ offset from the radio pulsar position, measured about 9 yr earlier, implies that the transverse velocity of the pulsar is in the range of 1600-2000 km s −1 at the distance of 2-2.5 kpc, making it the fastest moving pulsar known. The direction of the estimated proper motion coincides with the extension of the pulsar's X-ray tail, suggesting that this is a jet. The tentative optical luminosity and efficiency of the pulsar are similar to those of the Vela pulsar, which also supports the optical identification. However, the candidate undergoes an unusually steep dereddened flux increase towards the infrared with a spectral index α ν ∼ 5, that is not typical of optical pulsars. It implies a strong double-knee spectral break in the pulsar emission between the optical and X-rays. The reasons for the spectral steepness are unclear. It may be caused by a nebula knot projected onto the jet and strongly overlapping with the pulsar, as observed for the Crab, where the knot has a significantly steeper spectrum than the pulsar. We find no other signs of the pulsar nebula in the optical. Alternatively, the detected source may be a faint AGN, that has not yet been seen at other wavelengths. Conclusions. The position and peculiar colours of the detected source suggest that it is an optical counterpart of the pulsar. Further high spatial-resolution infrared observations can help to verify its real nature.

PSR J2021+3651 is a 17 kyr old rotation powered pulsar detected in the radio, X-rays, and γ-rays. It powers a torus-like pulsar wind nebula with jets, dubbed the Dragonfly, which is very similar to that of the Vela pulsar. The Dragonfly is likely associated with the extended TeV source VER J2019+368 and extended radio emission. We conducted first deep optical observations with the GTC in the Sloan r ′ band to search for optical counterparts of the pulsar and its nebula. No counterparts were detected down to r ′ 27.2 and 24.8 for the point-like pulsar and the compact X-ray nebula, respectively. We also reanalyzed Chandra archival X-ray data taking into account an interstellar extinction -distance relation, constructed by us for the Dragonfly line of sight using the red-clump stars as standard candles. This allowed us to constrain the distance to the pulsar, D = 1.8 +1.7 −1.4 kpc at 90% confidence. It is much smaller than the dispersion measure distance of ∼12 kpc but compatible with a γ-ray "pseudo-distance" of 1 kpc. Based on that and the optical upper limits, we conclude that PSR J2021+3651, similar to the Vela pulsar, is a very inefficient nonthermal emitter in the optical and X-rays, while its γ-ray efficiency is consistent with an average efficiency for γ-pulsars of similar age. Our optical flux upper limit for the pulsar is consistent with the longwavelength extrapolation of its X-ray spectrum while the nebula flux upper limit does not constrain the respective extrapolation.

Context. The Crab-like supernova remnant 3C 58 contains the young pulsar PSR J0295+6449, which powers a radio plerion and a compact torus-like pulsar wind nebula visible in X-rays. Aims. We have performed deep optical imaging of the 3C 58 field to detect the optical counterpart of the pulsar and its wind nebula. Methods. The imaging was carried out with the Nordic Optical Telescope. We also analyzed the archival images of the field obtained with the Chandra/ACIS-S and HRC-S in X-rays and with the Spitzer/IRAC in the mid-infrared. Results. We detect a faint extended elliptical optical object with B = 24. m 06 ± 0.08 and V = 23. m 11 ± 0.04, whose center and peak brightness position are consistent at the sub-arcsecond level with the position of the pulsar. The morphology of the object and the orientation of its major axis are in excellent agreement with the torus region of the pulsar wind nebula seen almost edge on in the X-rays, although its extension is only about a half of what is in X-rays. This suggests that in the optical we see only the brightest central part of the torus nebula with the pulsar. The position and morphology of the object are also practically identical to the counterpart of the torus region recently detected in the mid-infrared bands. We do not resolve any point-like source within the nebula that could be identified with the pulsar and estimate that the contribution of the pulsar to the observed optical flux is < ∼ 10%. Using the archival Chandra/ACIS-S data we analyzed the spectrum of the pulsar+nebula X-ray emission extracted from the spatial region constrained by the optical/infrared source position and extent and find that a single absorbed power law provides an acceptable spectral fit. Combining this fit with the optical and infrared fluxes of the detected candidate torus nebula counterpart, we compile a tentative multi-wavelength spectrum of the central part of the pulsar nebula. Within the uncertainties of the interstellar extinction towards 3C 58, it is reminiscent of either the Crab or PSR B0540-69 pulsar wind nebula spectra. Conclusions. The position, morphology, and spectral properties of the detected source strongly suggest that it is the optical/midinfrared counterpart of the 3C 58 pulsar + its wind nebula system. This makes 3C 58 the third member, together with the Crab and PSR B0540-69, of such a system as identified in the optical and mid-infrared.

We report detection of the likely companion of the binary millisecond pulsar J0740+6620 with the Gran Telescopio Canarias in the r ′ and i ′ bands. The position of the detected starlike source coincides with the pulsar coordinates within the 1σ uncertainty of ≈ 0.2 arcsec. Its magnitudes are r ′ = 26.51 ± 0.17 and i ′ = 25.49 ± 0.15. Comparing the data with the white dwarf cooling tracks suggests that it can be an ultracool helium-atmosphere white dwarf with the temperature 3500 K and cooling age 5 Gyr. The age is consistent with the pulsar characteristic age corrected for kinematic effects. This is the reddest source among known white dwarf companions of millisecond pulsars. Detection of the source in other bands would be useful to clarify its properties and nature.