Andrej Cadez and Mirjam Galicic
University of Ljubljana, Department of Physics, Slovenia
Keywords: pulsars: Crab; stars: neutron
We are looking for possible short-time small-amplitude periodicities in Crab pulsar optical light-curve. We analysed two different types of data: Hubble Space Telescope data which were obtained by the instrument High Speed Photometer in 1993, and stroboscopic photometrical data obtained at the 1.82m telescope in Asiago. We found that both data show a weak modulation at the period of 60 seconds.
The Hubble data comprise of four approximately half-hour long HSP runs in visible light (Percival et al. 1993). Each of the data sets is organized in two columns: the first one giving the photon arrival time (), and the second one the number of photons detected at this time (). We Fourier analysed Hubble data considering the Hubble signal to be the function , where is the Dirac delta function, so that . has peaks at , where k is an integer and P is pulsar's period. The first ten peaks are of about equal height while higher frequencies are represented in the signal with much smaller amplitudes. A possible phase or amplitude modulation with frequency would show up as two side-bands at frequencies . We added the side-band spectra of the ten peaks and subtracted the central peak. In Figure 1 (left side), the sum of spectra for data sets 2 and 3 is shown. Negative and positive frequency amplitudes have been added, so that symmetrical peaks, if present, amplify. The
Figure: The sum of ten side-band spectra for HST data sets 2 and 3 (left: x-axis gives channel number, units on y-axis are arbitrary), and Fourier spectra of pulsar (number 6) and five other field stars' magnitudes from Asiago (right: x-axis is logarithmic, numbers mark period in seconds, units on y-axis are arbitrary; the lower horizontal line on each spectrum marks average Fourier amplitude, and the following two lines the +1 sigma and +2 sigma levels, respectively).
peak at the channel number 295 is indicated by an arrow. The corresponding frequency is Hz
We observed the Crab pulsar optically with the 1.82m telescope of the Asiago Observatory (Asiago and Padova Observatories). A stroboscopic method was applied, whereby the pulsar along with a few field stars is monitored with a CCD camera through a rotating chopper. The chopper blade, which is frequency and phase controlled by an external clock to match the phase of the pulsar, is periodically cutting the light beam to the camera. The chopper blade is open for ten percent of the pulsar's period (main pulse) and closed for the remaining part of the period. Thus, we decreased the background luminosity of Crab nebula by ten times which gave a better signal-to-noise ratio for pulsar magnitude determination. In this way we took several hundred consecutive CCD frames. 275 consecutive frames (22.68 seconds apart, 15 seconds exposure and (on average) 7.68 seconds of image storing) are included in the Fourier analysis of pulsar's magnitude as a function of time. Five other field stars are also analysed in the same way for comparison. Figure 1 (right side) shows their Fourier spectra. Pulsar magnitude spectrum is indicated by number 6. The pulsar spectrum displays a 3.3-sigma peak at the period of 60 seconds. The actual frequency is Hz. Its amplitude is magnitude.
The search for modulation side-bands in HST data is very different from the modulation search with the Earth-based Asiago telescope. Yet, both searches give the same side-band modulation frequency:
Both frequencies are in the same error-box! The same can be said for corresponding modulation amplitudes, which are: and .
This work is based in part on observations with the Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. We thank HSP team, R. C. Bless, PI, and in particular J. Dolan for sending us the data, and M. Calvani from Padua Astronomical Observatory for his encouragement. This project is partially supported by EEC grant under contract PECO 94 n.ERBCIPDCT940028.
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