Counter evidence against multiple frequency nature of 0.75 mHz oscillation in V4743 Sgr
aa r X i v : . [ a s t r o - ph . S R ] F e b Mon. Not. R. Astron. Soc. , 1– ?? (2017) Printed 21 July 2018 (MN L A TEX style file v2.2)
Counter evidence against multiple frequency nature of0.75 mHz oscillation in V4743 Sgr
A. Dobrotka ⋆ , J.-U. Ness Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technologyin Bratislava, Bottova 25, 917 24 Trnava, Slovakia XMM-Newton Science Operations Center, European Space Astronomy Center, Camino Bajo del Castillo s/n, Urb. Villafranca delCastillo, 28692 Villanueva de la Ca˜nada, Madrid, Spain
Accepted ???. Received ???; in original form 21 July 2018
ABSTRACT
All X-ray light curves of nova V4743 Sgr (2002), taken during and after outburst,contain a 0.75 mHz periodic signal that can most plausibly be interpreted as beingexcited by the rotation of the white dwarf in an intermediate polar system. Thisinterpretation faces the challenge of an apparent multi-frequency nature of this signalin the light curves taken days 180 and 196 after outburst. We show that the multi-sine fit method, based on a superposition of two sine functions, yields two inherentlyindistinguishable solutions, i.e. the presence of two close frequencies, or a single signalwith constant frequency but variable modulation amplitude. Using a power spectrumtime map, we show that on day 180, a reduction of the modulation amplitude of thesignal coincides with a substantial overall flux decline while on day 196, the signalwas only present during the first half of the observation. Supported by simulations, weshow that such variations in amplitude can lead to false beating that manifests itselfas a multiple signal if computing a periodogram over the full light curve. Therefore,the previously proposed double frequency nature of both light curves was probablyan artefact while we consider a single signal with frequency equal to the white dwarfrotation as more plausible.
Key words: stars: novae: cataclysmic variables - stars: individual: V4743 Sgr - X-ray:binaries
Cataclysmic variables are interacting binary systems, con-sisting of a white dwarf primary and a late main sequencestar (see e.g. Warner 1995 for a review). Accretion takesplace from the cool companion to the white dwarf causingaccumulation of hydrogen-rich material onto the white dwarfsurface. If the accretion rate is in the range between (1 − × − M ⊙ yr − , steady nuclear burning can be established,thus hydrogen is fused to helium at the accretion rate uponarrival on the white dwarf surface (van den Heuvel et al.1992). If the accretion rate is lower, then slow accumulationof hydrogen-rich material leads to building up a hydrogen-rich surface layer that ignites explosively in a thermonu-clear runaway when ignition conditions are reached. A crit-ical amount of mass of 10 − − − M ⊙ (depending onwhite dwarf mass) is needed for such an explosion which arecommonly known as Classical Nova outburst. Subsequently, ⋆ E-mail: [email protected] within hours, the white dwarf is engulfed in an envelope ofoptically thick material that is driven away from the whitedwarf by radiation pressure. The nova is first bright in op-tical, but the peak of the spectral energy distribution shiftsto higher energies as the mass ejection rate (and thus theopacity) decreases. As a consequence, the expanding enve-lope is becoming less opaque, and successively hotter layersbecome visible (see, e.g., Bode & Evans 2008). A few weeksto months after outburst, the nova becomes bright in X-rayswith a dominant supersoft blackbody-like spectral compo-nent.The nova V4743 Sgr was discovered in September 2002by Haseda et al. (2002). Ness et al. (2003) found large-amplitude variability in
Chandra data taken 180 day afterthe maximum brightness with a period of ∼
22 minutes(0.75 mHz) with clear overtones of this signal in the peri-odogram. During this observation a strong decline in X-raybrightness was observed with a simultaneous spectral changefrom a continuum spectrum to emission lines.More detailed period analyses of the
Chandra and c (cid:13) A. Dobrotka and J.-U. Ness
XMM-Newton
X-ray data taken 196 days after outburst werepresented by Leibowitz et al. (2006). The large-amplitudevariations albeit with lower amplitude were also found inthe
XMM-Newton light curve, while the main feature at0.75 mHz showed two peaks leading to an interpretation ofa multiple signal. The authors confirmed the double naturealso in the earlier
Chandra data taken on day 180. Moreover,at least 6 and 12 additional frequencies were identified ondays 180 and 196, respectively. Leibowitz et al. (2006) sug-gested that the main feature at 0.75 mHz is related to thewhite dwarf rotation and that the other observed frequenciesare produced by non-radial white dwarf pulsations.Kang et al. (2006) presented CCD unfiltered opticalphotometry analyses from observations taken one and threeyears after the outburst. They detected two periods of 6.7 hand ∼
24 minutes. The authors attributed the longer sig-nal to the orbital period of the underlying binary sys-tem. Assuming that the 22 minute signal present in X-ray(Ness et al. 2003) is the rotation period of the central whitedwarf, the longer optical period of 24 min was interpreted asthe beat period between the orbital and rotation period ofthe white dwarf, respectively. This suggests an intermediatepolar nature of the V4743 Sgr binary.Dobrotka & Ness (2010) performed a complex timingstudy of all X-ray data taken up to 3.5 years after maxi-mum brightness using two different period analysis meth-ods. They confirmed that the
Chandra data taken 180 daysand
XMM-Newton data taken 196 days after outburst canbe modulated with two signals with close frequencies as de-tected previously by Leibowitz et al. (2006). In later obser-vations only a single signal was detected supporting the in-termediate polar interpretation. Other unstable or multiplesignificant signals are compatible with pulsations.Zemko et al. (2016) reanalysed the latest X-ray obser-vations taken 2 and 3.5 years after maximum brightness to-gether with a new SALT optical spectrum taken 11.5 yearsafter outburst. Besides the same procedure as performedby Dobrotka & Ness (2010), the authors performed sepa-rate timing studies for a hard and a soft band. While theyfound the 0.75 mHz signal in both bands at 2 years afteroutburst, they were only able to detect it in the hard bandat 3.5 years after outburst. The X-ray spectra from bothobservations had the characteristics in common with knownintermediate polars, with a hard thermal plasma fitted witha partially covering absorber. The earlier spectrum had alsoa supersoft blackbody-like component possibly originatingfrom the polar regions irradiated by an accretion column.The authors emphasised the intermediate polar nature ofthe nova V4743 Sgr.Apparently the multifrequency nature of the oscillationsin nova V4743 Sgr is a challenge to the interpretation of amodulation arrising from the rotation of the white dwarf.We have revisited the two X-ray light curves with multiplesignals, taken 180 and 196 days after maximum brightness,in order to elucidate whether the data are modulated witha single or multiple signals.
In this work we reanalyse some of the data studied inDobrotka & Ness (2010). We focus on the
Chandra
LETGS light curve (ObsID 3775) taken 180.39 days (hereafter day180) after maximum and the
XMM-Newton
EPIC-pn lightcurve (ObsID 0127720501) obtained 196.14 days (hereafterday 196) after the maximum brightness. All details aboutobservations and data reduction are summarised in Table 1.We also refer to Section 2 in Dobrotka & Ness (2010).
For timing analysis we use two different methods. One is tocompute a standard 1-D periodogram (power vs. frequency)over the entire (detrended) light curves using the Lomb-Scargle algorithm by Scargle (1982) as in Dobrotka & Ness(2010). This approach yields a representation of the overalllight curve behaviour and is useful when dealing with lightcurves that are modulated with a discrete coherent and sta-ble signal. As a visualisation of variations in signal strengthand/or frequency during an observation, we display a seriesof periodograms as in Ness et al. (2015) to form a time map.We divide a light curve into equally spaced, overlapping,subsets, and compute a 1-D (Lomb Scargle) periodogramfor each of them. The subsets overlap with 50%, i.e., for aduration of each subset of ∆ t , the periodograms are calcu-lated for time intervals of 0 - 2∆ t , ∆ t - 3∆ t , 2∆ t - 4∆ t ,etc. All 1-D periodograms are tagged together to form a 2-Dtime map. The 1-D periodograms derived from the light curves takenon days 180 and 196 are presented in Dobrotka & Ness(2010) while the 2-D maps are in Figs. 1 and 2 in this pa-per, respectively. Fig. 1 shows a more or less constant mainfrequency until 13 ks from observation start after which astrong flux decline started that may be accompanied byan increase of frequency until it becomes undetectable. InFig. 2, the main 0.75 mHz signal seems slightly variable upto approximately 15-16 ks with some weak signals possiblypresent up to 26 ks.Both time maps suggest that the 0.75 mHz signal haschanged both in terms of amplitude and frequency, mak-ing the analysis more complicated than previously assumed(Dobrotka & Ness 2010). The simultaneous change of fre-quency and X-ray flux on day 180 has to be taken into ac-count in order to study whether the flux decrease may havemislead us to conclude a multifrequency signal. Moreover,the variations of the frequency and its later disappearanceon day 196 can significantly influence the periodogram ofthe full light curve, and the multi-frequency nature of themain feature at 0.75 mHz needs more detailed analysis.For this re-analysis we used the same detrended lightcurve from day 180 and the non-detrended light curve fromday 196 as in Dobrotka & Ness (2010). Subtracting a fifth-order polynomial fit to the data.c (cid:13) , 1– ?? .75 mHz oscillation in V4743 Sgr is not multiple Figure 1.
Time map of the
Chandra observation from day 180.The whole light curve is divided into 15 equally spaced subsetsin order to calculate individual periodograms. The light curve isadded for direct comparison in the right panel. The top panelshows the overall periodogram and two selected periodogramscalculated from subsets marked as red a blue shaded areas in theright panel.
Figure 2.
The same as Fig. 1 but for day 196. The whole lightcurve is divided into 20 equally spaced subsets.
While for the observation on day 196, the multiple nature ofthe 0.75 mHz signal was already detectable with standardapproaches by Leibowitz et al. (2006), Ness et al. (2003)only reported a single signal for day 180. We developed amore sensitive approach using a multi-sine fitting algorithmto investigate whether also on day 180 the signal actuallyconsists of two components (Dobrotka & Ness 2010).While the multi-sine fit was based on a superposition oftwo sine functions, the underlying basic mathematical rela-tionsin( f ) + sin( f ) = 2 cos (cid:16) f − f (cid:17) sin (cid:16) f + f (cid:17) (1)actually allows two solutions on the right-hand side. We per-formed direct fittings with the GNUPLOT software using bothsolutions in the form of -10-5 0 5 10 0 2 4 6 8 10 12 14 16 f l u x [ c t s / s ] time [ks] observationcos x sinsin + sin Figure 3.
Detrended light curve from day 180. The data areaveraged (every 250 s) for clarity. The lines are different fits usingequation (2).
Table 1.
Frequencies from fits to the day 180 data using eq. (2).The right column is recalculated from eq. (3) using frequenciesfrom middle column.frequency from fits from eq. (3)(mHz) (mHz) f . ± .
004 0 . ± . f . ± .
007 0 . ± . F . ± .
002 0 . ± . F . ± .
002 0 . ± . a sin( f ) + a sin( f ) = a cos( F ) sin( F ) , (2)where F = f − f F = f + f . (3)The results are displayed in Fig. 3, and fitted frequen-cies are summarised in Table 1. Clearly, both fits yieldvery similar results with values (almost) satisfying equa-tion (3). Therefore, two solutions are possible to explain thelight curve from day 180, i.e. 1) two close signals as pub-lished by Dobrotka & Ness (2010), and 2) a single frequencyof 0.76 mHz with a variable amplitude on a longer timescale of approximately 38.5 ks (equivalent to a frequency of0.026 mHz). The latter is the cosine period. While only oneantinode loop is visible on day 180, only half of the beatingcycle (the light curve in Fig. 3) should be compared to thecosine cycle, which is 17 vs. 19 ks, respectively. These valuesmatch well as a rough estimate. In order to study different possible interpretations of the ob-served periodogram from day 196, we simulated light curveswith the same long term trend as the observed data butwith different modulations. We sampled and noised (usingGaussian noise) a sine function to get a similar scatter as inthe observed data. The first step is based on visual inspec-tion of the observed data. We divided the light curve intothree different intervals during which the variability differs(Fig. 4). The first interval is from 0 to 17.5 ks where the pe-riodic variability is clearest. The next interval ranges from Obtained by fitting a 7th-order polynomial.c (cid:13) , 1– ?? A. Dobrotka and J.-U. Ness
40 45 50 55 60 65 0 5 10 15 20 25 30 35 f l u x [ c t s / s ] time [ks]observationfitted frequency 0.756 mHzextrapolated fitted frequency 0.756 mHzfitted frequency 0.351 mHz Figure 4.
Different sine fits to the observed data from day 196.The data are averaged (every 250 s) for clarity. The differentwhite-gray areas represent different time intervals used for sinemodel fitting (see text and Table 2 for details).
Table 2.
Fitted sine parameters in different light curve segmentsfrom day 196, where a is the amplitude, f is the frequency and φ is the phase in the sine argument 2 πtf + φ ( t is time). The errorsare standard errors calculated from the covariance matrix by the GNUPLOT software.fitted int. a f φ (ks) (counts/s) (mHz)0 - 11.0 1 . ± .
250 0 . ± .
005 2 . ± . . ± .
455 0 . ± .
012 2 . ± . Gnuplot software. We fitted the firstinterval (0 - 17.5 ks) using as start parameters the fre-quencies of 0.730, 0.748 and 0.764 mHz that were derivedby Dobrotka & Ness (2010). All three cases converged toa value of 0.756 mHz. The second interval (17.5 - 26.5 ks)yields a lower frequency of 0.351 mHz. All fitted parametersare summarised in Table 2.We performed 100000 simulations using the two sinemodulations on the corresponding time intervals from Ta-ble 2 and computed a goodness parameter for each sim-ulation that assesses the agreement of the power spec-trum derived from the simulated light curve with the ob-served power spectrum. We choose the sum of unweightedsquared residua, Σ = P ni =0 ( m ( f i ) − d ( f i )) , where m ( f i )and d ( f i ) are model and data at frequency f i , respec-tively. We computed Σ probing two frequency intervals of f i = 0 . .. .
784 mHz and f i = 0 . .. .
819 mHz. The for-mer takes into account only the two dominant peaks, whilethe latter also includes the two small satellite peaks at ap-proximately 0.7 and 0.8 mHz.Out of all simulations, we select the 4 best ones forillustration in Fig. 5. The left column shows the best fits (from top to bottom) based on the narrow frequency intervalwhile the middle column shows the best simulations basedon the broader frequency interval. The light curves used forthe middle panel calculation are shown in the right column.Clearly a single frequency is sufficient to generate the ob-served main feature at 0.75 mHz and no multiple signals assuggested by Leibowitz et al. (2006) and Dobrotka & Ness(2010) are needed. Moreover, the signal is present or dom-inant in the interval 0 - 17.5 ks. The rest of the light curveis dominated by longer time scale modulations or just noisewithout any significant periodic signal. The time map cor-responding to the best simulated light curve is depicted inFig. 6. Similar patterns can be seen. Worth noting is thefake smooth frequency decrease below 20 ks from 0.756 to0.351 mHz resulting from the abrupt change in modulatingfrequencies.We also performed simulations assuming a single signalin the full light curve and with a constant amplitude. In sucha case only a single and dominant peak is detected. Thissupports the connection between the double peak featureand variable modulation amplitude, i.e. that the signal isnot present in the whole light curve.Moreover, we also performed some test simulations as-suming a variable frequency over different time intervals.The resulting periodograms showed a multiple peak struc-ture also in the case in which the variability was present inthe full light curve with constant amplitude. However, thepattern was very different, unacceptable and shifted towardlower frequencies or showed strong aliases not present in theobserved periodogram. Moreover, the resulting sum of Σ wasconsiderably worse than in the constant frequency case. Toget periodograms in better agreement with the observationswe needed to restrict the modulation only to the interval of0-17.5 ks, i.e. a variable amplitude is needed. Therefore, thedouble peak was probably again the result of a false beatingrather than a variable frequency. To study the profile of the modulation, we used detrendedlight curves. We folded the first 17 ks of the day 180 lightcurve using the frequency of 0.757 mHz from Table 1, andthe first 11 ks of the day 196 light curve, during which thevariability is most obvious, using the fitted frequency of0.756 mHz from Table 2. The folded and binned light curvesare depicted in Fig. 7. Apparently, the profile on day 180shows an obviously non sinusoidal profile with a constantplateau at the minimum. The profile on day 196 shows amore or less triangular and asymmetric shape of the pulse.Both profiles are similar, except that day 196 does not showthe obvious hump at phase 0.7 as in day 180.Following Fourier series theory, a non-sinusoidal shapemust yield harmonic signals in the periodogram. This is con-firmed by the clear presence of overtones in Figs. 1 and 2already mentioned in Ness et al. (2003). Since our simula-tions are based on pure sine functions, the overtones arenot present in the simulated time maps (Fig. 6). The exactvariability pattern depends on the shape of the accretionspot on the white dwarf surface, and a non-sinusoidal vari-ability profile is common in intermediate polars (see e.g.Beardmore et al. 1998). c (cid:13) , 1–, 1–
819 mHz. The for-mer takes into account only the two dominant peaks, whilethe latter also includes the two small satellite peaks at ap-proximately 0.7 and 0.8 mHz.Out of all simulations, we select the 4 best ones forillustration in Fig. 5. The left column shows the best fits (from top to bottom) based on the narrow frequency intervalwhile the middle column shows the best simulations basedon the broader frequency interval. The light curves used forthe middle panel calculation are shown in the right column.Clearly a single frequency is sufficient to generate the ob-served main feature at 0.75 mHz and no multiple signals assuggested by Leibowitz et al. (2006) and Dobrotka & Ness(2010) are needed. Moreover, the signal is present or dom-inant in the interval 0 - 17.5 ks. The rest of the light curveis dominated by longer time scale modulations or just noisewithout any significant periodic signal. The time map cor-responding to the best simulated light curve is depicted inFig. 6. Similar patterns can be seen. Worth noting is thefake smooth frequency decrease below 20 ks from 0.756 to0.351 mHz resulting from the abrupt change in modulatingfrequencies.We also performed simulations assuming a single signalin the full light curve and with a constant amplitude. In sucha case only a single and dominant peak is detected. Thissupports the connection between the double peak featureand variable modulation amplitude, i.e. that the signal isnot present in the whole light curve.Moreover, we also performed some test simulations as-suming a variable frequency over different time intervals.The resulting periodograms showed a multiple peak struc-ture also in the case in which the variability was present inthe full light curve with constant amplitude. However, thepattern was very different, unacceptable and shifted towardlower frequencies or showed strong aliases not present in theobserved periodogram. Moreover, the resulting sum of Σ wasconsiderably worse than in the constant frequency case. Toget periodograms in better agreement with the observationswe needed to restrict the modulation only to the interval of0-17.5 ks, i.e. a variable amplitude is needed. Therefore, thedouble peak was probably again the result of a false beatingrather than a variable frequency. To study the profile of the modulation, we used detrendedlight curves. We folded the first 17 ks of the day 180 lightcurve using the frequency of 0.757 mHz from Table 1, andthe first 11 ks of the day 196 light curve, during which thevariability is most obvious, using the fitted frequency of0.756 mHz from Table 2. The folded and binned light curvesare depicted in Fig. 7. Apparently, the profile on day 180shows an obviously non sinusoidal profile with a constantplateau at the minimum. The profile on day 196 shows amore or less triangular and asymmetric shape of the pulse.Both profiles are similar, except that day 196 does not showthe obvious hump at phase 0.7 as in day 180.Following Fourier series theory, a non-sinusoidal shapemust yield harmonic signals in the periodogram. This is con-firmed by the clear presence of overtones in Figs. 1 and 2already mentioned in Ness et al. (2003). Since our simula-tions are based on pure sine functions, the overtones arenot present in the simulated time maps (Fig. 6). The exactvariability pattern depends on the shape of the accretionspot on the white dwarf surface, and a non-sinusoidal vari-ability profile is common in intermediate polars (see e.g.Beardmore et al. 1998). c (cid:13) , 1–, 1– ?? .75 mHz oscillation in V4743 Sgr is not multiple L - S po w e r frequency [mHz/100] Σ = 230 0 5 10 15 L - S po w e r Σ = 215 0 5 10 15 L - S po w e r Σ = 183 0 5 10 15 L - S po w e r Σ = 169 0 5 10 1560 65 70 75 80 85frequency [mHz/100] Σ = 837 0 5 10 15 Σ = 748 0 5 10 15 Σ = 714 0 5 10 15 Σ = 535 40 45 50 55 0 5 10 15 20 25 f l u x [ c t s / s ] time [ks] 45 50 55 f l u x [ c t s / s ]
45 50 55 f l u x [ c t s / s ]
45 50 55 f l u x [ c t s / s ] simulatedobserved Figure 5.
The 4 best cases selected out of 100000 simulations described in Sect. 3.4, compared to the data taken on day 196. Left andmiddle column: simulated (red) and observed (black) periodograms with Σ in respective upper left corners, using two different frequencyintervals that are shown as gray-shaded areas. Right column: corresponding simulated (red) light curves compared to observed light curve(black) belonging to the PSD shown in the respective middle panels.
Figure 6.
Time map of the best simulated light curve depictedin the top right panel of Fig. 5.
The previous works about nova V4743 Sgr suggested thattwo X-ray observations taken 180 and 196 after the maxi-mum brightness were modulated with two signals with closefrequencies (Leibowitz et al. 2006, Dobrotka & Ness 2010).We now show that this result does not account for the possi-bility of variations during these observations which can man-ifest themselves as multiple signal in a time-averaged peri- -4-3-2-1 0 1 2 3 0 0.5 1 1.5 2 f l u x [ c t s / s ] phase f = 0.756 mHzday 196-6-4-2 0 2 4 6 8 f l u x [ c t s / s ] f = 0.757 mHzday 180 Figure 7.
Folded and binned light curves subsample between 0and 17 ks on day 180, and 0 and 11 ks on day 196. The foldingfrequency is marked in each panel. The error-bars are errors ofthe mean and two cycles are shown for clarity.c (cid:13) , 1– ?? A. Dobrotka and J.-U. Ness odogram. The review of the mentioned observations in thispaper and use of basic mathematics together with simula-tions reveals that a single signal can explain at least equallywell the observed behaviour.
Dobrotka & Ness (2010) showed with a two-component fit-ting of the
Chandra observation from day 180, that the datacan be well described by two close frequencies despite thefact, that the standard periodogram showed only one singlebut broad peak. In this paper we have shown, that this solu-tion is only one possible interpretation, while an additionaland totally equivalent solution exists because the ambivalentnature of the underlying mathematical description of twosummed sine functions. According to this second solution,the data are modulated by a single and constant frequency,while the modulation amplitude varies with another muchshorter frequency. This result is a sort of beating, which isalso a natural consequence when two sine functions withclose frequencies are summed. Therefore, both solutions areinherently equivalent and indistinguishable. However, thenova experienced a strong flux decline during the observa-tion on day 180 and the variability amplitude decreased simultaneously with the flux. Such amplitude decrease canmimic the mentioned beating. Therefore, the solution wherethe amplitude decreases can be generated by the flux declinewhich appears more probable to us. Another solution (andharder to believe) could be that the amplitude decrease isdue to real beating of two signals that conspicuously coin-cide with the flux decline.Moreover, the derived constant frequency has a value of0 . ± .
002 mHz (Table 1) which agrees within the errorswith the white dwarf rotation frequency detected as stablesignal 2 and 3.5 years after maximum in Dobrotka & Ness(2010). Note that the X-ray observations taken 2 and 3.5years after maximum are much longer, leading to a well-constrained frequency.
Furthermore, we showed that the double periodogram peakof the main signal around 0.76 mHz detected in the
XMM-Newton observation taken 196 days after outburst can be anartefact with a single frequency being sufficient to explainthis observation (double peak). The signal is not presentduring the entire observation and a simple visual inspectionsuggests that the variability is only present during the first17.5 ks. After 17.5 ks the light curve passes a minimum witha constant and strong increase of brightness toward the endwith no obvious uniform modulations, only some lower fre-quency (0.351 mHz) peaks are observed between 17.5 and26.5 ks. However, following Fig. 2 in Dobrotka & Ness (2010) the frac-tional amplitude is not affected.
40 45 50 55 60 65 0 5 10 15 20 25 30 35 f l u x [ c t s / s ] time [ks]observation2 sine fit Figure 8.
Fit of the day 196 observation using superposition oftwo sine functions with close frequencies and the visualisation ofthe resulting beating (see text for details). The light curve dataare averaged (every 250 s) for clarity.
Dobrotka & Ness (2010) used a two-dimensional peri-odogram in order to study the multifrequency nature of themain 0.75 mHz feature. Their finding is in agreement withthe Lomb-Scargle periodogram, i.e. the data are modulatedwith two signals with close frequency values. Therefore, theobservation must have the characteristics described in Sec-tion 3.3 and based on equation (1), i.e. a beating shouldappear in the data. However, the disappearance of the main0.75 mHz signal after approximately 17.5 ks is identified bythe fitting algorithm as amplitude minimum which mim-ics the knot of a beat cycle (Fig. 8). The appearance of twopeaks between 30 and 35 ks sustain this potentially false ”in-terpretation” mimicking a second beating cycle. Therefore,an optimisation algorithm converges to a beating solution,falsely resulting in two superposed signals with two closefrequencies, while the amplitude decrease/disappearance ofthe main variability around 17.5 ks can have a totally differ-ent origin just as on day 180. This explains why the powerspectrum from the full light curve yields two close peaks.Finally, just as for the day 180 we conclude thatthe fitted frequency of 0 . ± .
005 mHz agrees well withthe white dwarf rotation frequency derived previously byDobrotka & Ness (2010).
As already suggested by Leibowitz et al. (2006) and con-firmed by Dobrotka & Ness (2010) other signals are presentin the light curve, supporting the presence of other formsof pulsation. In this work we mentioned an additional andobvious frequency of 0 . ± .
01 mHz (blue line in Fig. 4)which is close to the value of 0.38 mHz listed in Table 1 inLeibowitz et al. (2006).It is worth noting that the shorter frequency of 0.35 mHzappeared at the brightness decrease at ∼
17 ks into the ob-servation at the same time as main frequency of 0.76 mHzdisappeared. This can be a result of some physical processesduring which the observable emission experienced a tem-porary reduction, accompanied by some types of pulsation,while the radiation from the accretion flow on the whitedwarf surface vanished or weakened considerably making the The data were fitted with two sine functions with frequenciesas input mesh parameters in order to calculate the residuals, i.e.a 2 dimensional equivalent of a standard periodogram.c (cid:13) , 1– ?? .75 mHz oscillation in V4743 Sgr is not multiple main signal disappear. Possible processes that could lead tosuch a reduction in brightness could be obscurations or pho-tospheric expansion.Visual inspection of the Fig. 4 suggests that the lowfrequency peaks (blue line) are coherent in phase with alter-nate peaks of the high frequency modulation (red line). Thiswould suggest that the lower frequency of 0.35 mHz above17 ks is the same modulation bellow 17 ks but continuingwith alternate peaks vanishing. The red dashed line is theextrapolation of the modulation bellow 17 ks and it is clearthat the low frequency peaks are not in phase. Therefore,this supports the interpretation of an independent variabil-ity source. The main feature around 0.75 mHz has two possible inter-pretations, either pulsations or modulations excited by therotation of the white dwarf (Dobrotka & Ness 2010). Thedouble-peak solution of the main signal would be a strongcounter argument against white dwarf rotation, but the newinterpretation of a single signal that is variable in amplituderevitalises the interpretation of rotation. The same periodwas also seen, as a single signal, on days 302, 371 and 526,thus in all observations taken during the SSS phase. Whilepulsations might occur during the SSS phase one would ex-pect them to disappear when the nova turns off, but thesame period was also detected in the quiescent light curveson days 742 and 1286. If pulsations of 0.75 mHz occur in thequiescent white dwarf, one would expect it to be disturbedor damped within the expanding nova ejecta during the out-burst, but detecting the same pulsation period both duringand after the nova outburst would be a challenge. We thusstrongly prefer the interpretation of a magnetic white dwarfin an intermediate polar whose rotation stimulates observ-able periods.This paper has also some technical implications. De-tailed period analysis of rather short satellite data shouldbe taken with caution, and any standard periodogram studyshould be accompanied with simulations or more detailedtreatment in order to investigate any false beating. Thesame amplitude variation, probably generated by a flux dip,is also noticeable in the X-ray light curve of V2491 Cyg,yielding a double-peak feature as a main signal in the cor-responding periodogram (Ness et al. 2011). The presence ofthe first harmonics in the first part of the observation playedalso a significant role. The false beating was proposed as aprobable reason of the double peak nature. This was con-firmed by simulating light curves with a single signal andthe amplitude as observed, while a double peak emerged inthe corresponding periodograms. Apparently dips, flux de-clines, variable amplitudes are common in novae during out-burst. Therefore, any multiple peak detection in this stage ofnova evolution is an indicator for an instable signal that de-serves a closer look with time mapping techniques as shownin Fig. 1.
The results of this work can be summarised as follows: (i) The X-ray observation taken 180 days after maxi-mum brightness has two inherently indistinguishable inter-pretations: 1) the data are modulated with two signals withclose frequency values, 2) a single and constant frequencyis present, but the periodogram is influenced by the strongflux decrease and a contemporaneous reduction of the mod-ulation amplitude.(ii) Simulations reveal that also the double peak natureof the main 0.75 mHz feature during the X-ray observationtaken on day 196 can be explained by a single signal, if itis only present during the first 17 ks. The double nature ofthe main peak in the full power spectrum is then the resultof a fake beating because the period is only present duringa fraction of the whole light curve.(iii) Other signals are present as summarised byLeibowitz et al. (2006), but some of them can have a similarexplanation as the double nature of the main signal, i.e. fakemultiple nature due to fake beating.(iv) The false double peak nature of the signal duringa nova outburst is not unique for V4743 Sgr. It has alsobeen detected in X-ray data of the nova V2491 Cyg duringoutburst. A false beating generated by variability amplitudechange was also proposed as a reason in that case.The main conclusion of this work is that the new findingabout the main signal together with the folded variabilityprofile converges toward an intermediate polar interpreta-tion rather than pulsations.
ACKNOWLEDGEMENTS
AD was supported by the Slovak grant VEGA 1/0335/16and by the ERDF - Research and Development OperationalProgramme under the project ”University Scientific ParkCampus MTF STU - CAMBO” ITMS: 26220220179.
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