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Дата изменения: Wed Jun 15 19:38:40 2005 Дата индексирования: Sat Dec 22 10:22:33 2007 Кодировка: Поисковые слова: enceladus |
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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