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Astron. Astrophys. 343, L15-L18 (1999)

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3. Discussion and conclusion

The magnitude limits obtained in Sect. 2 have theoretical implications which we briefly mention here. The optical radiation is expected to be produced by tertiary e[FORMULA]-pairs produced in outer gap discharges. These particle fluxes and energy spectra are in turn dependent upon those of the primary and secondary electrons and the particular radiation mechanism involved, and the optical fluxes may be correlated with the gamma-ray photon fluxes in such models.

Usov (1994, see his Eq. (24)) has estimated the scaling of the optical vs gamma-ray luminosities expected in the outer gap models by Cheng, Ho & Ruderman (1986a, 1986b) for Vela-like pulsars. Usov's analysis predicts that the frequency integrated optical flux (between [FORMULA] and [FORMULA] Hz), [FORMULA], should scale with the integrated gamma-ray flux as [FORMULA]. From Fig. 3 we estimate the pulsed [FORMULA] to be [FORMULA] JyHz for PSR1706-44. For a flat optical spectrum, this gives [FORMULA] erg s-1 cm-2 Hz-1 between [FORMULA] and [FORMULA] Hz. Assuming [FORMULA] to be the same in both the V and R bands, the magnitudes predicted by the outer gap models by Cheng, Ho & Ruderman (according to Usov 1994) are [FORMULA] and [FORMULA]. We will now compare these limits with the observed limits by CK98 and those found in this work.

[FIGURE] Fig. 3. Multiwavelength spectrum, [FORMULA] versus [FORMULA], for PSR1706-44. Data are taken from the compilations of Thompson et al. (1996, 1999), except for the points marked `V' which are from this work. The point marked `RXTE' is from Ray et al. (1999), and that marked `R' is from CK98. Our two V points correspond to two estimates which should bracket the dereddened upper limit in the visual: [FORMULA] assumes minimum extinction ([FORMULA]) and the pulsar lying outside the PSF of Star 1, [FORMULA] assumses maximum extinction ([FORMULA]) and the pulsar lying close to Star 1 in projection. The point by CK98 is likely to underestimate the extinction.

CK98 found an upper limit to the R magnitude for the pulsar of [FORMULA]. It is obvious that the data of CK98 do not constrain the outer gap model, in particular since extinction appears not to have been included by CK98.

We know that extinction in the direction to the pulsar must occur. The photometry of Star 1 by CK98 indicates that [FORMULA]. The extinction to the more distant PSR1706-44 is likely to be higher. A rough estimate of the visual extinction is one magnitude per kpc (Spitzer 1978), which would indicate [FORMULA] to the pulsar. This is consistent with the column density, [FORMULA] cm-2, indicated by the X-ray data of Finley et al. (1998). This limiting column density translates into [FORMULA]. A likely range for [FORMULA] is therefore [FORMULA] magnitudes. The dereddened R magnitude could therefore be much brighter than [FORMULA], and of little value in constraining the outer gap model for PSR1706-44.

The situation is different for our V estimates from the VLT observations. Even if we adopt maximum extinction ([FORMULA]), and if the pulsar would lie close to Star 1 in projection, the dereddened observed upper limit is only [FORMULA], which is [FORMULA] magnitudes fainter than the limit obtained from Usov's analysis. In Fig. 3 we have included our dereddened upper limit of V (for two combinations of [FORMULA] and projected distances from Star 1) in a multiwavelength spectrum of the pulsar. Similar spectra are presented by Thompson et al. (1999) for the Crab, Vela and Geminga pulsars, as well as PSR1509-58, PSR1951+32 and PSR1055-52. Our faint limit to the V, in comparison to the predictions of the standard outer-gap model, scaled from gamma-ray flux ([FORMULA]), requires a low frequency cutoff in the synchrotron emission spectrum for PSR1706-44.

In the prediction of the ratio of [FORMULA] for Vela-like pulsars like PSR1706-44, an important assumption is that the gap averaged magnetic field [FORMULA] is approximately equal to the magnetic field at the outer boundary of the outer gap. This average [FORMULA] is: [FORMULA], where the subscript `L' refers to the field at the light cylinder, [FORMULA] being the inner radius of the outer gap, and [FORMULA] is the spin frequency of the pulsar. For small inclination angle [FORMULA] between the magnetic moment and spin vectors one has [FORMULA], and [FORMULA]. This gives the synchrotron cutoff frequency [FORMULA] for tertiary photons near [FORMULA] Hz, so that optical emission from a pulsar active in the gamma-ray region should be observable (as estimated above). On the other hand, if [FORMULA], the synchrotron cutoff frequency is [FORMULA] Hz and in this case the flux of optical band radiation may be very small. Our faint limit from the VLT for PSR1706-44 in combination with the outer gap model could therefore point to a case of an unaligned rotating neutron star. (This is consistent with an analysis of the photon spectral break in the GeV regime, - see Ray et al. 1999).

As shown in Table 1, PSR1706-44 has similar P and [FORMULA] to those of the Vela pulsar. It is therefore of interest that also the Vela pulsar is faint in the optical with [FORMULA] and [FORMULA] (Nasuti et al. 1997). If PSR1706-44 would have the same optical luminosity as Vela, it could have a V magnitude of [FORMULA] (if its [FORMULA] is 0.9 magnitudes, and its distance is 1.8 kpc). Our non-detection of PSR1706-44 in V is consistent with this. However, theory indicates that the optical emission is sensitive to many parameters, so there is certainly room for PSR1706-44 to be intrinsically much brighter than the Vela pulsar. This is also consistent with our results, in particular if PSR1706-44 lies close to Star 1 in projection.

While completing this work, we found out that an independent analysis by Mignani, Caraveo & Bignami (1999), using the same VLT SV data as in this work, places a limit on V for PSR1706-44 which is [FORMULA]. In our analysis a star of [FORMULA] would have a peak pixel signal less than 1[FORMULA] above noise level. We doubt such a faint star could be seen, especially if positioned close to Star 1.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999