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Astron. Astrophys. 350, 517-528 (1999)

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8. Discussion

The HST/FOS and IUE spectroscopy has revealed new insights in the UV variability of FO Aqr.

8.1. The periodic variations

The UV continuum and emission line fluxes are found to be strongly variable at the orbital period. This periodicity also dominates the optical range where FO Aqr was previously found to be spin dominated. The time series analysis indicates the presence of other periodicities, the negative [FORMULA] sideband being much stronger than the beat [FORMULA] in both UV and optical ranges. The presence of sidebands with different amplitudes at different epochs is rather common in FO Aqr, although the beat is usually the strongest (Patterson & Steiner 1983; Warner 1986; Semeniuk & Kaluzny 1988, Chiappetti et al. 1989; Paper 1, Marsh & Duck 1996). In particular the intermittent occurrence of a stronger pulsation at [FORMULA] frequency was already noticed (Warner 1986; Patterson et al. 1998). The strong negative sideband [FORMULA], cannot be produced by an amplitude modulation at [FORMULA] frequency of the rotational pulses, since the positive sideband [FORMULA] should have been present. Also, an orbital variability of the amplitude of the [FORMULA] modulation cannot be responsible alone since it is too weak. Hence the [FORMULA] pulsation should be dominated by the effects of an unmodulated illumination from the white dwarf, which naturally gives rise to the orbital variability (Warner 1986).

The occurrence of coherence between spin and beat pulsations appears to be different from epoch to epoch (Semeniuk & Kaluzny 1988; Osborne & Mukai 1989; Paper 1). It was proposed that phase coherence close to the optical orbital minimum could be possible if the reprocessing site(s) are viewing the lower accreting pole (Paper 1). The observed shift of half an orbital cycle would then imply that the reprocessing region(s), are now viewing the main accreting pole, as predicted by the standard reprocessing scenario (Warner 1986).

The behaviour of UV emission lines is different between fluxes and V/R ratios. The line fluxes are strongly variable at the orbital period, the spin variability being 1.6 times lower. On the other hand, their V/R ratios only show a rotational S-wave, but that of C IV line is surprisingly weak. The lack of detection of an orbital S-wave, can be ascribed to the low amplitude ([FORMULA] 300-400 km s-1) velocity displacements known from optical data (Hellier et al. 1989; Marsh & Duck 1996), which are not detected because of the low spectral resolution of the FOS data.

8.2. The rotational pulses

Both shapes and amplitudes of UV and optical continnum spin pulses indicate the presence of two components, one dominating the near-UV and optical ranges, already identified in Paper 1 and a new contribution dominating the far-UV pulses which lags by [FORMULA] 0.2 in phase the first one. Furthermore a different behaviour between emission line fluxes and V/R ratios is observed. While the latter show a spin S-wave in phase with the far-UV continuum, the line fluxes follow the near-UV and optical pulsations. The maximum blue-shift found at rotational maximum of the far-UV pulses indicates that the bulk of velocity motions in the emission lines maps the innermost regions of the accretion curtain. The outer curtain regions are then responsible for X-ray illumination effects seen in the line fluxes and near-UV and optical continua. A direct comparison with previous X-ray observations reported by Beardmore et al. (1998) is not possible since, adopting their linear spin ephemeris, the UV and optical maxima lag by [FORMULA]=0.4 their predicted optical maximum. However, the X-ray pulse maxima observed by Beardmore et al. (1998), typically lag by [FORMULA] =0.2 their optical phase zero (see their Fig. 3), consistently with the lag observed between the far-UV and optical pulses. Hence this difference is an indication that the far sides of the accretion curtain come into view earlier than the innermost regions.

The spectrum of the pulsation reveals regions at [FORMULA] 37 000 K covering a relatively large area, [FORMULA], with respect to typical X-ray fractional areas [FORMULA] (Rosen 1992). Such hot components have been also observed in the IPs PQ Gem (Stavroyiannopoulos et al. 1997) and EX Hya (de Martino 1998). The presence of the [FORMULA] absorption feature in this spectrum can be partially due to the photospheric absorption of the heated white dwarf with similar temperature and fractional area as a blackbody representation. On the other hand, both orbital and rotational modulated spectra give similar values of [FORMULA] if this absorption is of circumstellar nature. Hence, while only in AE Aqr the UV pulses are clearly associated with the heated white dwarf (Eracleous & Horne 1994, 1996), those in FO Aqr can be associated with either the innermost regions of the accretion curtain onto the white dwarf or its heated polar regions.

The second component identified as a cool 12 000 K region covers [FORMULA], a factor [FORMULA] lower than previously found in Paper 1. Thus the decrease in the optical amplitudes does not involve substantial changes in temperatures but in the size of the accretion curtain. Such lower temperatures characterizing the near-UV and optical pulses are also recognized in other IPs (de Martino et al. 1995; Welsh & Martell 1996; Stavroyiannopoulos et al. 1997; de Martino 1998). Although a two component pulsed emission might be a crude representation, it is clear that temperature gradients are present within the accretion curtain extending up to [FORMULA].

The bolometric flux involved in the spin modulation due to both components amounts to 6.3[FORMULA] ergs cm-2s-1. Although no contemporary X-ray observations are available this accounts for [FORMULA] the total accretion luminosity as derived from ASCA 1993 observations (Mukai et al. 1994).

8.3. The sidebands variability

The UV continuum pulsations observed at the sideband frequencies, [FORMULA], [FORMULA] and [FORMULA], indicate the presence of a relatively hot component [FORMULA] 20 000-25 000 K. The lack of adequate data in the optical range does not allow one to confirm the cool ([FORMULA] 7 000 K), and hence possible second component, in the beat pulsed energy distribution as found in Paper 1. The phase lags of the far-UV maximum with respect to that in the near-UV in the [FORMULA] and [FORMULA] pulsations are similar to that observed in the rotational pulses. This is consistent with the pulsations being produced by amplitude variations of the spin pulses at the orbital period. In contrast, the prominent negative sideband [FORMULA] variability is not affected by phase shift effects, indicating that indeed such variability is mainly due to an aspect dependence of the reprocessing site at the orbital period.

No strong pulsation in the UV emission lines is observed at these frequencies except for the interesting anti-phased behaviour of these lines at the beat period. These are observed as weak absorption features in the modulated spectrum. Such behaviour, although much more prominent, is also observed in the IP PQ Gem (Stavroyiannopoulos et al. 1997). Though this is not easy to understand, a possibility could be that the reprocessing site, producing the [FORMULA] component in the emission lines, is viewing the lower pole instead of the main X-ray illuminating pole as also suggested by Stavroyiannopoulos et al. (1997).

8.4. The orbital variability

The present study confirms previous results where the orbital modulation is composed by two contributions, identified as the illuminated bulge and the heated face of the secondary star, the former being at superior conjunction at [FORMULA] = 0.86, while the latter is at superior conjunction at [FORMULA] = 0.0. The double-humped maximum in the optical light curve can be understood in terms of relative proportion of a strong bulge contribution with respect to that of the secondary star. Indeed no changes in the temperatures are found (the hot one is better constrained with the present data), but a substantial change by a factor of [FORMULA] since 1990 is found in the emitting area of the bulge itself. All this indicates that illumination effects are basically unchanged whilst the inflated part of the disc has increased.

The total bolometric flux involved in the orbital variability amounts to 2.7[FORMULA] ergs cm-2s-1 which is a factor [FORMULA] 4 larger than that of the rotational pulsation. Neglecting the sideband contributions at first approximation, the total modulated flux amounts to 3.3[FORMULA] ergs cm-2s-1 and corresponds to a reprocessed luminosity of [FORMULA] ergs s-1 which is approximately the order of magnitude of the accretion luminosity derived from X-rays (Mukai et al. 1994). Then assuming the balance of the energy budgets of the reprocessed and primary X-ray radiations, and hence of the accretion luminosity, an estimate of the accretion rate of [FORMULA] is derived.

8.5. The long term variability

FO Aqr has displayed a change in its power spectrum at optical and UV wavelengths on a time scale of five years. It was also brighter by 0.3 mag and 0.2 mag in the two ranges with respect to 1990. This difference is accounted for by the orbital modulated flux. The study of the spectra of the periodic variabilities has shown that a shrinking of the accretion curtain by a factor of [FORMULA] has occurred while the inflated part of the disc has increased in area by a factor of 2.6. Such changes indicate variations in the accretion parameters. Worth noticing is that the unmodulated UV and optical continuum component has not changed with time, indicating that the steady emission from the accretion disc (Paper 1) has not been affected. These results are in agreement with the long term trend of the X-ray power spectra (Beardmore et al. 1998) which showed that FO Aqr was dominated by the spin pulsation in 1990, while in 1988 and in 1993 prominent orbital and sideband variabilities were present. Changes from a predominant disc-fed accretion to a disc-overflow (or stream-fed) accretion have been the natural explanation for such changes in the X-ray power spectra. As proposed in Paper 1, the bulge provides a source for a variable mass transfer onto the white dwarf, and an increase in its dimensions accounts for a predominant disc-overflow towards the white dwarf.

Beardmore et al. (1998) suggested that changes in the accretion mode could be triggered by variations in the mass accretion rate and the analysis presented here is indeed in favour of this hypothesis. An estimate of changes in the accretion rate producing a shrinking of the accretion curtain can be inferred by the relation betwen magnetospheric radius, accretion rate and magnetic moment (Norton & Watson 1989):

[EQUATION]

where [FORMULA] is a dimensionless factor accounting for a departure from spherical symmetry, [FORMULA] is the magnetic moment in units of [FORMULA], [FORMULA] is the mass accretion rate in units of [FORMULA] and [FORMULA] is the white dwarf mass in units of [FORMULA]. Hence assuming that the accretion curtain reaches the magnetospheric boundary, a reduction of the linear extension by a factor of [FORMULA] 1.2 implies that the accretion rate has increased by a factor [FORMULA] 2 in five years.

The long term spin period variations observed from 1981 to 1997 in FO Aqr (Patterson et al. 1998), which changed from a spin-down to a recent spin-up since 1992, were proposed to be due to variations around the equilibrium period produced by long term variations in [FORMULA]. The increase in brightness level and the results found in the present analysis are strongly in favour of this interpretation.

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Online publication: October 4, 1999
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