Multifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr
aa r X i v : . [ a s t r o - ph . S R ] M a r Mon. Not. R. Astron. Soc. , 1–17 (2009) Printed 4 November 2018 (MN L A TEX style file v2.2)
Multifrequency nature of the 0.75 mHz feature in theX-ray light curves of the nova V4743 Sgr
A. Dobrotka ⋆ , J.-U. Ness † Department of Physics, Institute of Materials Science, Faculty of Materials Science and Technology, Slovak Universityof Technology in Bratislava, J´ana Bottu 25, 91724 Trnava, The Slovak Republic European Space Astronomy Centre, PO Box 78, 28691 Villanueva de la Ca˜nada, Madrid, Spain: [email protected]
Accepted ???. Received ???; in original form 4 November 2018
ABSTRACT
We present timing analyses of eight X-ray light curves and one optical/UV light curveof the nova V4743 Sgr (2002) taken by
Chandra and
XMM-Newton on days after out-burst: 50 (early hard emission phase), 180, 196, 302, 371, 526 (super soft source, SSS,phase), and 742 and 1286 (quiescent emission phase). We have studied the multifre-quency nature and time evolution of the dominant peak at ∼ .
75 mHz using the stan-dard Lomb-Scargle method and a 2-D sine fitting method. We found a double structureof the peak and its overtone for days 180 and 196. The two frequencies were closertogether on day 196, suggesting that the difference between the two peaks is graduallydecreasing. For the later observations, only a single frequency can be detected, whichis likely due to the exposure times being shorter than the beat period between the twopeaks, especially if they are moving closer together. The observations on days 742 and1286 are long enough to detect two frequencies with the difference found for day 196,but we confidently find only a single frequency. We found significant changes in theoscillation frequency and amplitude. We have derived blackbody temperatures fromthe SSS spectra, and the evolution of changes in frequency and blackbody temperaturesuggests that the 0.75-mHz peak was modulated by pulsations. Later, after nuclearburning had ceased, the signal stabilised at a single frequency, although the X-rayfrequency differs from the optical/UV frequency obtained consistently from the OMonboard
XMM-Newton and from ground-based observations. We believe that the latefrequency is the white dwarf rotation and that the ratio of spin/orbit period stronglysupports that the system is an intermediate polar.
Key words: stars: novae: cataclysmic variables - stars: individual: V4743 Sgr - X-ray:stars
Cataclysmic variables are interacting binary systems, con-sisting of a white dwarf primary and a late main sequencestar, where accretion takes place from the cool companionto the white dwarf. If the accretion rate is in the range be-tween (1 − × − M ⊙ yr − , steady nuclear burning canestablish, thus the hydrogen content of the accreted mate-rial is fused to helium at the accretion rate upon arrivalon the white dwarf surface van den Heuvel et al. (1992). Ifthe accretion rate is < − M ⊙ yr − then the hydrogen-richmaterial settles on the white dwarf surface and ignites explo-sively in a thermonuclear runaway, after a critical amount ofmass of 10 − − − M ⊙ (depending on white dwarf mass) ⋆ E-mail: [email protected] † E-mail: [email protected] has been reached. Such outbursts are commonly known as aClassical Nova outbursts. Within hours after outburst, thewhite dwarf is engulfed in an envelope of optically thick ma-terial that is driven away from the white dwarf by radiationpressure. Early in the evolution, the nova is bright in opti-cal, but the peak of the spectral energy distribution shiftsto higher energies as the mass ejection rate (and thus theopacity) decreases, exposing successively hotter layers (see,e.g., Bode & Evans 2008). A few weeks after outburst, thenova becomes bright in X-rays, and the observed X-ray spec-tra resemble those of the class of Super Soft Binary X-raySources (SSSs).The nova V4743 Sgr was discovered in September2002 by Haseda et al. (2002). The first measured enve-lope ejection velocities exceeded 1200 km s − Kato et al.(2002). Nielbock & Schmidtobreick (2003) studied the novaat λ c (cid:13) A. Dobrotka and J.-U. Ness the dominant emission source is the heated dust rather thanfree-free emission. The spectrum of the Nova was classified asFe II type by Morgan et al. (2003). Petz et al. (2005) foundsignificant absorption from Fe and N from atmosphere mod-elling to a SSS X-ray spectrum taken with
Chandra
180 daysafter outburst, that had been presented earlier by Ness et al.(2003). Ness et al. found large-amplitude fast variabilitywith a period of ∼
22 minutes with clear overtones of thissignal in the periodogram. During this observation a strongdecline in X-ray brightness was observed with simultaneousspectral change from continuum spectrum to emission lines.The count rate dropped from 44 counts per second to 0.6within ∼ ∼
24 minutes. The authors at-tributed this signal to the beat period between the orbitaland spin period of the white dwarf, where the 22 minute sig-nal present in X-ray (Ness et al. 2003) was assumed to bethe spin period of the central white dwarf. Sophisticated X-ray period studies were presented by Leibowitz et al. (2006).They reanalysed the
Chandra data taken on day 180, to-gether with an
XMM-Newton observation taken on day 196.The large-amplitude variations were also found in the
XMM-Newton data set. They detected at least 6 frequencies onday 180 and at least 12 on day 196. Most of the variabil-ity was explained by a combination of oscillations at a setof discrete frequencies, and the main feature with a periodof ∼
22 minutes has a double peak in the periodogram. Atleast 5 signals were constant between the two observations.Leibowitz et al. (2006) suggested that the main feature inthe periodogram at ∼
22 minutes ( ∼ .
75 mHz) is related tothe white dwarf spin and that the other observed frequenciesare produced by non-radial white dwarf pulsations.In this paper we present timing analyses of all
Chan-dra and
XMM-Newton observations, including those alreadyanalysed, for consistency. The main goal is to characterisethe main feature at ∼ .
75 mHz and its possible multiplestructure as well as following the evolution of the oscilla-tions. We address the question whether these variations areproduced by the white dwarf rotation or by its pulsations.In Sect. 2 we present all analysed X-ray data sets, and inSect. 3 we describe our period analysis methods. The resultsare described in Sect. 4. This section is structured into thepresentation of two different methods described in Sect. 3,the evolution of the oscillation amplitude of the main signal,studies on beat periods, and other signals within a larger fre-quency radius around the main signal as well as overtones.Our results are discussed in Sect. 5, and a summary withconclusions is given in Sect. 6.
In Table 1 we sumarise the analysed observations of the novaV4743 Sgr. The
Chandra /ACIS (Nousek et al. 1987) lightcurve for day 50.2 was extracted from the level-two eventsfile using a circular extraction region with radius 20 pixels.
Table 1.
Journal of observations. Given are ’Day’, days afteroutburst, ’Mission’, name of observing mission, ’ t ’, exposure timein seconds, ’ N ’, the number of time bins, ’∆ t ’, the duration ofone time bin in seconds, and ’cr’, and mean count rate (countsper second). For day 180 we excluded the declining part of thelight curve. In the text we refer to observations using days afteroutburst. For the optical/UV observation on day 742 we do notquote the mean count rate because of different filters used in theobservation.Day Mission t N ∆ t cr50.23 Chandra . ± . Chandra . ± . XMM /RGS 35280 1408 25 52 . ± . Chandra . ± . Chandra . ± . Chandra . ± . XMM /MOS1 22100 885 25 0 . ± . XMM /MOS1 34050 682 50 0 . ± . XMM /OM 21722 206 100 –
The
Chandra /LETGS (Brinkman et al. 2000) light curvesfor days 180, 302, 371 and 526 were extracted from the non-dispersed photons (0th order), and the
XMM-Newton /RGSlight curve for day 196 was extracted from the dispersedphotons. The two
XMM-Newton /MOS (Turner et al. 2001)light curves for days 742 and 1286 were extracted from theevents file using an extraction region with radius 200 pixels.In both observations, the source was on a chip gap in thepn, and only the MOS1 observations can be used.In the
XMM-Newton observation on day 742, additionaloptical/UV data from the Optical Monitor (OM, Talavera2009) are available. Five light curves have been taken inseries using the filters U, B, UVW1, UVM2, and UVW2 at50-second time resolution. The different sensitivities of eachfilter are not of relevance to this paper, and the light curvesshown in Fig. 2 are normalised. For the other
XMM-Newton observations, the source was either too bright, or no timingmode was used.Our focus is on the ∼ .
75 mHz period, and we thusremoved all long-term variations by dividing the light curvesby fifth-order polynomial fits. In Fig. 1 we show the de-trended, rebinned (100-s bins) light curves. For day 180,we only analyse the first 17 ks of data in order to avoidcontamination by the steep decline that occurred shortlyafter (Ness et al. 2003). No such event occurred in any ofthe other observations, and the full data sets were used forall other observations.For consistency checks, we have also extracted separatelight curves for a hard and a soft band (15-30 ˚A and 30-40 ˚A, respectively), filtering on the wavelengths in the level2 event files.
The goal of this work is to study the dominant 0.75 mHzfeature detected by Ness et al. (2003) and analysed in moredetail by Leibowitz et al. (2006). The principal problem isthe multifrequency nature of this dominant peak on day c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr Figure 1.
Detrended and normalised X-ray light curves of allobservations, indicated by the days after outburst given in theright legend of each panel (for observation log see Table 1). Thedetrending and normalisation was done using a 5-th order poly-nomial.
Figure 2.
Optical/UV light curve taken in series with the
XMM-Newton /OM on day 742 using different filters (upper panel) andcorresponding Lomb-Scargle power spectrum with candidate fre-quency marked by dotted line (lower panel).
196 (Leibowitz et al. 2006). While Ness et al. (2003) re-ported only one period in the power spectrum for day 180,Leibowitz et al. (2006) found two nearby frequencies, usinga least square fitting approach. We note that the observationon day 180 is much shorter than that taken on day 196 (see Fig. 1 or Table 1), and a clear separation of multi-frequencyoscillations is more difficult.For our period analysis we use three different meth-ods. First, we apply the standard Lomb-Scargle algorithm(Scargle 1982). This method calculates the normalised powerfor every frequency from the interval of interest with a se-lected frequency step. The result is a 2-D periodogram show-ing normalised power vs. tested frequency. The significantmaxima are the significant signals.We also use a linear combination of one or multiple sinecurves that is fitted to the light curve. If t i defines a timegrid, with i indicating the index of each time bin, the model s i is defined on the same grid as s i = P i + B i + n X j =1 A j sin(2 πt i f j + φ j ) , (1)where P i denotes a 5-th order polynomial used for detrend-ing, B i is the mean value of the instrumental backgroundcounts in each time bin, and n is the number of assumedsine curves with A j , f j , and φ j being the respective ampli-tudes, frequencies, and phase shifts.Instead of standard least square fitting (i.e., minimisa-tion of χ ), we use maximum likelihood iteration. The rea-son is that some of our light curves have low count rates forwhich Poissonian noise has to be assumed. With s i given inEq. 1 and c i the observed light curve (in units counts perbin on the same time grid), the likelihood is defined as L = − N X i =1 [ c i ln( s i ) − s i ] . (2)Note that c i is not background subtracted, because thatwould destroy the Poissonian nature of the data. Instead,we do forward fitting, i.e., instead of subtracting the back-ground B i , we add it to the model as defined in Eq. 1.In the fitting procedure, the parameters A j , f j , and φ j are iterated to minimise L as defined in Eq. 2. The 1- σ , 2- σ ,and 3- σ uncertainties (equivalent to 68.3%, 95.4% and 99.7%confidence levels) for the frequencies f j can be determinedby interpolating the L ( f j )-surface to values of L + ∆ L , L + ∆ L , and L + ∆ L , respectively, where the values of∆ L , , depend on the number of degrees of freedom (thusthe number of sine curves, n ). For n = 1, ∆ L , , assumesvalues of 1.0, 4.0, and 8.85, respectively, while for n = 2,∆ L , , takes the respective values of 2.30, 6.16, and 11.6.The uncertainties in the Lomb-Scargle methodhave been derived from the false alarm probability(Horne & Baliunas 1986) of 0.3%, which is equivalent to the3- σ confidence. In cases where the errors are not constrainedwithin 3- σ confidence because of low normalised power of thepeaks, we used higher false alarm probabilities of 4.6% and31.7%, equivalent to 2 and 3- σ confidence, respectively. Inthe cases with even lower normalised power we quote onlythe nominal values without errors.In this paper we refer to the n = 1 case as the ’1-Dmethod’, while we call the n = 2 case the ’2-D method’.We illustrate the results of our 2-D method in the form ofcontour plots. Examples of such contour plots are shownin Figs. 3 and 4 for two different synthetic light curveswhich are sampled as the Chandra light curve taken onday 180 with comparable amplitude. We modulated thesynthetic light curves with one and two frequencies and c (cid:13) , 1–17 A. Dobrotka and J.-U. Ness f1 [mHz] f [ m H z ] Figure 3.
Contour plots of the 2-D sine fit period analysis appliedto a test light curve. The test light curve is modulated with thetwo frequencies 0.72 and 0.76 mHz (marked by dotted lines), andis sampled as the day 180 light curve. The lines are the contoursof the likelihood from sine fitting of the analysed data set and theaxes are the tested intervals of the frequencies f and f . Shownare the 1- σ , 2- σ and 3- σ contours. The solid lines intersectingat 0.740 mHz indicates the result (with errors equivalent to 0.3%false alarm probability) from the Lomb-Scargle algorithm. added Poissonian noise and then applied the 2-D methodto each synthetic light curve. In Fig. 3, the result for thesynthetic light curve that has been modulated with two fre-quencies is shown. The input frequencies are f = 0 .
72 and f = 0 .
76 mHz (see horizontal and vertical dotted lines inFig. 3), and it can be seen that these values can be recov-ered. Closed contour lines, centred around the coordinates( f , f ) and ( f , f ) are the result. In contrast the case ofa synthetic light curve that is modulated with only one fre-quency, yields a different contour plot (see Fig. 4). Again,the input frequency of 0.72 mHz is marked by dotted lines,and open contours around these lines are the result.Meanwhile, both, the 1-D and the Lomb-Scargle meth-ods, applied to the light curve that is modulated with twofrequencies, yield only a single period at a frequency of0.740 mHz (Fig. 5). In Fig. 3, this frequency is marked withthe horizontal and vertical lines, the length of which indi-cate the error bars. This demonstrates that our 2-D methodallows us to discriminate between light curves that are mod-ulated with one and with two frequencies. We have employed the techniques described in Sect. 3 to alldata sets and summarise our results in Table 2. In the fol-lowing subsections we describe the results from the 1-D and2-D methods. We focus on the multifrequency nature of thedominant peak at 0.75 mHz employing the 1-D method andthe 2-D method in Sects. 4.1 and 4.2, respectively. We dis-cuss the role of the beat period in relation to the exposuretime in Sect. 4.3. The evolution of the oscillation amplitudesis determined in Sect. 4.4, and the expected harmonic fre-quencies of 0.75 mHz in Sect. 4.5. f1 [mHz] f [ m H z ] Figure 4.
Same as Fig. 3 for a test light curve modulated with asingle frequency of 0.72 mHz (marked by dotted lines) and sam-pled as the day 180 light curve.
Figure 5. χ and Lomb-Scargle normalised power curves for arange of frequencies around the input frequencies of two syntheticlight curves. The solid lines indicate the χ curves for the syn-thetic light curve that was modulated with a single frequency at0.72 mHz, while the dashed curves indicate the χ curves for thesynthetic light curve that was modulated with two frequencies at0.72 mHz and 0.76 mHz (see lower right legend in top panel). Inthe top panel, the respective χ curves for the 1-D method areshown, and in the bottom panel the same for the Lomb-Scargleresults. The single frequency can be recovered with both meth-ods, but the 2-frequency light curve yields only a single frequencyin between the two input frequencies. The Lomb-Scargle and 1-D sine fitting methods give similarresults. In Fig. 6 we show the Lomb-Scargle periodograms ofall light curves. Except for the observation taken on day 196,all observations yield only a single peak around 0.75 mHz.For day 196, a more complicated structure can be seen. ”Issuch complex nature of the main peak present only at this c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr day?” Such a question motivates this project of searching forthe two central dominant peaks in the other light curves. Inthe L-S column of Table 2 we give the signals detected withthe Lomb-Scargle method near the value of 0.75 mHz for alllight curves.Following the tests with the synthetic light curves de-scribed in the previous section, the non-detection of a mul-tifrequency structure with the Lomb-Scargle analysis doesnot necessarily rule out the presence of two or more nearbyfrequencies. In order to test for the presence of such addi-tional signals, we have pre-whitened the data with the de-tected frequencies. By subsequent period search we find forday 180 another dominant peak at (0 . ± . XMM-Newton /OM light curve taken on day 742 is shown in Fig. 2.The frequency found is 0 . ± .
020 mHz. Pre-whitening ofthe data with this frequency yields a complete disappearanceof any other signal. Therefore, this is the only signal.
In contrast to the Lomb-Scargle method, the 2-D sine fittingmethod is a direct fitting approach, and the fits can be illus-trated. In Fig. 8, we show the original (not detrended) lightcurves and the best-fit models, s i , according to Eq. 1, forthe observations taken on days 180, 196, 742, and 1286. Ineach panel, the dashed line indicates the 5-th order polyno-mial, P i , that was used for detrending. The light curve takenon day 196 is the most complex of all, and Leibowitz et al.(2006) reported the presence of multiple frequencies fromthe power spectrum and from least squares fitting. Theyalso reported that they resolved two frequencies (0.728 and0.782 mHz) with least squares fitting to the day-180 data,yielding better fits than single- or three-frequency fits.In order to investigate the detailed structure of the 0.75-mHz signal, we closely inspect our contour plots for eachfit. As a detection criterion we choose the 99.7% confidence,i.e., the 3- σ significance level. In Table 2 we list the resultingfrequencies with corresponding 3- σ uncertainties. Figure 6.
Power spectra of all X-ray data sets using the Lomb-Scargle algorithm. The candidate frequencies summarised in Ta-ble 2 are marked by dotted lines in each panel. H W H M [ m H z ] duration [ks]50 180 196302371526 742 1286 Figure 7.
Half width at half maximum of the peaks in the Lomb-Scargle power spectrum of X-ray data versus respective exposurestimes. Long exposure times yield narrow peaks, and multiple sig-nals can only be detected if the exposure time covers at leastone beating cycle. The horizontal line represents the differencebetween the detected frequencies from day 196.
The first observation on day 50 is too short to yield anysignificant detection of a second period. Even the presenceof the 0.75-mHz signal itself as a single frequency can onlybe established on the 1- σ level, and the uncertainties givenin Table 2 for this observation are only 1- σ errors.The result of the analysis of the day-180 light curve isshown in Fig. 9 (solid contour lines in the bottom right).We find closed contours around the pair of frequencies0 . ± .
004 and 0 . ± .
003 mHz. This is consistentwithin the errors with our result from the pre-whitening(Sect. 4.1). We emphasise, however, that the error from the1-D method is much larger, i.e. 0.062 mHz (Tab. 2). The c (cid:13) , 1–17 A. Dobrotka and J.-U. Ness
Figure 8.
Original X-ray light curves and best-fit 2-D models fordays 180, 196, 742, and 1286. For illustration purposes, the dataand model are rebinned to a time bin size of 250 sec. The solidline is the 2-D sine best fit and the dotted line is the detrendingpolynomial. result from Leibowitz et al. (2006) is marked with a plussymbol in Fig. 9. While it is just outside of our 3- σ contourlines, it is yet close enough to argue that the two indepen-dent results are reasonably consistent within the combinederrors (Leibowitz et al. have given no errors, which we esti-mate from their periodogram as ∼ .
02 mHz).For day 196, two peaks are clearly detected, and the re-sult from our 2-D approach is included in the top left cornerof Fig. 9 (dotted contour lines). The two frequencies are welllocalised and form a deep minimum at 0 . ± .
005 and0 . ± .
004 mHz. These values also agree with Leibowitzet al. (2006) within the combined uncertainties. The contourlines of day 180 (solid lines) and from day 196 (dotted lines)do not overlap, and the frequencies are thus significantly dif-ferent. Apparently, the two detected frequencies are closertogether on day 196.For the well-exposed observations taken on days 180 and196, we have also analysed separate light curves extractedfrom a soft band (30-40 ˚A) and a hard band (15-30 ˚A). Thesoft light curve for day 180 delivers exactly the same result.The frequencies derived from the other three light curves areconsistent within the statistical 3- σ uncertainty ranges, andthe conclusion that the two signals on days 180 and 196 aredifferent is robust against the chosen energy band.For the observations taken on days 302, 526, 742, and1286, no indication for a double frequency structure can bedetected. This is illustrated in Fig. 10 and Figs. 12–14, re-spectively, where only a single frequency is found with the2-D method. While for days 526, 742 and 1286, closed con-tour lines are encountered at the 1- σ significance level, thiscan not be considered significant enough for a secure detec-tion of two frequencies. However, the detection of a singlefrequency is significant at the 99.7% confidence level.Meanwhile, for day 371 a deep minimum with closed f1 [mHz] f [ m H z ] Figure 9.
Same as Fig. 4 for days 180 (solid line) and 196 (dashedline). The values derived by Leibowitz et al. (2006) are markedby two crosses. f1 [mHz] f [ m H z ] Figure 10.
Same as Fig. 4 for day 302. The shape contour linesresembles that in Fig. 4, indicating that only a single frequencyis present with f = 0 . ± .
01 mHz (see Table 2). contours is found (Fig. 11), indicating the presence of twofrequencies (0 . ± . . ± . . ± .
015 mHz which is consistent with ourLomb-Scargle finding. c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr f1 [mHz] f [ m H z ] Figure 11.
Same as Fig. 4 for day 371. The closed contour linesindicate two frequencies at f = 0 .
72 mHz and f = 0 .
87 mHz.The latter is not near the main 0.75-mHz signal and is thus be-yond the scope of this paper. f1 [mHz] f [ m H z ] Figure 12.
Same as Fig. 4 for day 526.
The superposition of two sine functions with different fre-quencies f and f results in beating at frequency | f − f | .We expect that two frequencies can only be separated witha given observation duration if it is longer than the beat pe-riod, 1 / | f − f | . The only observations for which we are ableto find two frequencies are those on days 180 and 196. The f1 [mHz] f [ m H z ] Figure 13.
Same as Fig. 4 for day 742 in X-ray band. f1 [mHz] f [ m H z ] Figure 14.
Same as Fig. 4 for day 1286.
Figure 15.
Phased light curves (detrended, binned into 50-s bins)for the frequencies found by 2-D sine fitting (see 3-rd column ofTable 2). f1 [mHz] f [ m H z ] Figure 16.
Same as Fig. 4 for optical/UV from
XMM-Newton /OM data obtained on day 742.c (cid:13) , 1–17
A. Dobrotka and J.-U. Ness
Table 2.
Detected X-ray signals around the 0.75 mHz frequency,between 0.72 and 0.78 mHz (Other signals are listed in Table 4).The ’L-S’ column lists the results from the Lomb-Scargle analysiswith errors computed from the half width at half maximum in thepower spectrum. The ’2-D sine fit’ column lists the results fromour 2-D sine fitting analysis with errors calculated from the 3- σ contours. In the last column the results of Leibowitz et al (2006)are give for comparison.Day L-S 2-D sine fit LeibowitzmHz mHz et al. (2006)50 (0 . b . ± ( > . a –180 – 0 . ± .
004 0.7210 . ± .
062 – –– 0 . ± .
003 0.777196 0 . ± .
009 0 . ± .
005 0.7290 . ± .
011 0 . ± .
004 0.763302 0 . ± .
113 0 . ± .
012 –371 0 . ± .
051 0 . ± .
011 –526 0 . ± ( > . a . ± .
028 –742 0 . ± .
019 0 . ± .
011 –1286 0 . ± ( > . a . ± .
011 – a unconstrained on 3- σ level and only 1- σ level given b unconstrained on 1- σ level and only the nominal value is given Figure 17.
Illustration of detectability of two signals in our ob-servations. The star symbols, connected by the black line, are theexposure times listed in Table 1. If the beat period between twosignals is longer than the exposure time, then these frequenciescan not be detected as two separate signals, because the expo-sure time does not cover at least one beat cycle. The blue dottedand red dashed lines indicate the beat periods for days 180 and196. The limit imposed by too short exposure time prohibits thedetection of these two frequencies on days 50, 301, 371, and 526.But for days 742 and 1286, at least the two frequencies found forday 180 would be detectable, unless the ratio of the amplitudesof the two signals is less than 1:2 for a 99.7% confidence detection(for a 95,4% and 90% confidence detection, an amplitude ratio of1:3 and 1:4 is sufficient, respectively). difference between these two frequencies are 0.055 mHz and0.028 mHz, respectively (see Table 7), and the expected beatperiods are (18 . ± .
1) ks and (35 . ± .
2) ks, respectively.As can be seen from Table 1, the exposure times of thesetwo observations are sufficiently long to cover one cycle ofthe beat period. However, the observations taken on days301, 372, and 526 are significantly shorter, and two frequen-cies can not easily be separated. We tested this statement byanalysing a synthetic light curve, sampled and noised as day302 and modulated with two close frequencies of 0.72 and0.76 mHz. Our 2-D method did not find a closed minimumwithin 3- σ lines and the global minimum in the goodnesscontours is found for the combination of values of 0.678 and0.745 mHz. Since the exposure times for days 371 and 526are of the same order with lower signal to noise, we concludethat the exposure times for days 302, 371, and 526 are tooshort and the data are too noisy for a positive detection oftwo signals.The importance of the exposure time for the resolu-tion of two frequencies is illustrated in Fig. 17, where weplot the exposure times (in units ks) with the star symbols,connected by the black line and the beat periods for days180 and 196 for comparison. The best resolving power canbe achieved with the exposure times on days 196 and 1286when a full beating cycle is covered. Two signals with a fre-quency difference as observed for days 180 or 196 can notbe detected in any of the observations taken on days 50,301, 371, and 526. However, the observation taken on day742 was long enough to at least recover two frequencies if | f − f | was as large as on day 180. For day 1286, the situa-tion detected for day 196 would have been detectable. Thisconclusion is valid with comparable modulation amplitudes,but different amplitude ratios can affect the detectability.To test the effect, we have produced a synthetic data setsampled as day 742 and 1286, with amplitudes taken fromTable 3 and with Poissonian noise. With our 2-D method,we were able to identify both signals at 0.72 and 0.76 mHzfor the amplitude ratios 1:2, 1:3 and 1:4 at a confidence levelof 99.7%, 95,4%, and 90%, respectively.If on days 301, 372, and 526 the main peak was splitin two signals as on days 180 or 196, then we would detecta value somewhere in between the minimum and maximumvalue. We experimented with synthetic light curves modu-lated by two signals of different amplitudes and found thatthe resultant frequency would be closer to the signal with thehigher amplitude, and exactly in between if the amplitudeswere the same. Meanwhile, the formal 3- σ measurement un-certainties would be much smaller than the maximum fre-quency difference between two signals that could be detectedwith the given exposure times. As a consequence, the possi-bility of having detected an average frequency between twosignals introduces a source of systematic uncertainty of theorder of half the inverse exposure time, because this valuelimits the detectability of two signals.It is noteworthy from Fig. 17 that the beat periods thatcorrespond to the two signals on days 180 and 196 are sus-piciously close to their respective exposure times. This sim-ilarity might raise suspicions that the exposure time couldalready predetermine the difference between the two signals.In the case of such a bias the same two frequencies wouldhave resulted if the exposure times for days 180 and 196 hadbeen the same. While we can not test longer exposure, we c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr Figure 18.
Normalised X-ray light curves for days 196, 302, 371,and 526 as indicated in the legends (solid lines) in comparison today 180 (dotted line). have run several tests using reduced exposure times for bothlight curves. For day 196 we only found a single frequencyaround 0.76 mHz if only the first 17 ks of the light curveare used. This can be explained by the reduced coverage ofthe beat period, and the detected two periods apparentlyrequire the long exposure time. Our analyses of a sampleof reduced data sets for day 180 always resulted in two de-tected frequencies. The resulting values depend slightly onthe selected subset of the light curve, but no correlation be-tween effective exposure time and beat period is seen. Thereason for the clear detection of two signals for day 180 canbe seen in the well-pronounced sinusoidal form of the lightcurve with little contaminating noise, as can be seen fromFig. 8. The Lomb-Scargle method is limited by the require-ment to cover at least one beating cycle in order to detectthe respective two close signals (see Fig. 7). Meanwhile, ourfitting approach is only limited by the quality of the data,and two close signals can be detected, even if only a fractionof the beating cycle is covered, if only the data have sufficientsignal to noise. For day 196, the count rate is higher, but thelight curve shows more irregular patterns, and a clear detec-tion of two periods requires a more complete coverage of thebeat period. From all these considerations we conclude thatthe presence of two frequencies is real in both cases and thatthe similarity between exposure time and beat period in thetwo cases must therefore be a coincidence.
The comparison of normalised light curves in Fig. 18 illus-trates that the oscillation amplitudes vary considerably be-tween the observations. While only parts of the light curvesare shown for better clarity, it is clear, e.g., from Figs. 1and 8, that the amplitude of the first 10 ksec is represen-tative for the full observation in each case. We include the
Table 3.
Amplitude parameters A j from Eq. 1 for the days givenin the first column. Given are the X-ray absolute amplitudes (inunits counts per second, [cps]), and the X-ray amplitudes relativeto the mean count rates given in the last column of Table 1, eachfor the respective frequencies f j Day f [mHz] absolute [cps] relative50 0.760 < . < . . ± .
190 0 . ± . . ± .
190 0 . ± . . ± .
162 0 . ± . . ± .
163 0 . ± . . ± .
235 0 . ± . . ± .
158 0 . ± . . ± .
082 0 . ± . . ± .
008 0 . ± . . ± .
005 0 . ± . normalised light curve for day 180 with a dotted line for ref-erence. Clearly, on days 196 and 302, the relative amplitudewas much smaller than on day 180, and it seems that it hasalmost recovered by day 372 but is smaller again on day 526.The amplitude parameters, A j in Eq. 1, are representa-tive of the evolution of the oscillation amplitude, as can beseen from, e.g., Figs. 8 and 15.The evolution of the best-fit amplitude parameters A j ,relative to the mean count rates given in the last column ofTable 1, is illustrated in Fig. 19. The values are listed in thelast column of Table 3, where also the absolute amplitudesare given for each observation and each frequency. The ab-solute amplitudes have been determined directly from thedetrended light curves before normalisation. In the bottompanel of Fig. 19 we show X-ray band fluxes (0.3-2.5 keV) forcomparison. The description of flux measurements can befound in Sect.4.6. The sharp drop in brightness on day 180first reported by Ness et al. (2003) can be identified in thebottom panel, and it coincides with a significant reduction inoscillation amplitude. While the brightness has completelyrecovered by day 196, the oscillation amplitudes remainedlow until the end of the SSS phase after day 526. While the focus of this paper is the substructure and evolu-tion of the strongest signal around 0.75 mHz, other nearbysignals are present. Leibowitz et al. (2006) found at least12 significant frequencies for day 196, and for five of these,similar frequencies were also found for day 180. However,without uncertainty ranges it is difficult to decide whetheror not these frequencies are related to each other.In Table 4 we list all 3- σ detections of frequencies in therange between 0.6 and 0.9 mHz for days 180-371. Basically,three significant frequencies can be detected in this rangefor days 180 and 196. Their values differ on a statisticallysignificant level, and either these three frequencies are vari-able, or they occurred at random and are not related to each c (cid:13) , 1–17 A. Dobrotka and J.-U. Ness
Figure 19.
Top: Time evolution of the relative amplitudes A j listed in the last column of Table 3. Bottom: Evolution of X-rayfluxes (see Sect. 4.6) for comparison. The connection between thedecline on day 180 and a sudden drop in relative amplitude canbe recognised. Table 4.
Significant detections of other X-ray frequencies in therange 0.6-0.9 mHz.day 1st 2nd 3rd180 f [mHz] 0 . ± .
004 0 . ± (0 . a . ± . A (abs) 0 . ± .
196 1 . ± .
193 1 . ± . A (rel) 0 . ± .
006 0 . ± .
005 0 . ± . f [mHz] 0 . ± .
004 0 . ± .
007 0 . ± . A (abs) 0 . ± .
230 0 . ± .
232 0 . ± . A (rel) 0 . ± .
004 0 . ± .
004 0 . ± . f [mHz] – 0 . ± .
030 0 . ± . A (abs) – 0 . ± .
179 0 . ± . A (rel) – 0 . ± .
010 0 . ± . a unconstrained on 3- σ level and only 2- σ level given other. However, the two frequencies found for day 371 areboth in good agreement with the corresponding frequencieson day 180, and these frequencies may have undergone asimilar evolution as the main peak, i.e. reduction betweendays 180 and 196, followed by a slow increase back to thelevel seen on day 180. This is supported by the fact thatthe same trends of the third frequency in the last column ofTable 4 can be seen as in Fig. 21. This behaviour could berelated to the sharp decay that occurred on day 180. Thebeat periods between the main frequency of 0.75 mHz andthe signals at 0.67 mHz and 0.87 mHz are both of order 10 ks,which is short enough to separate these frequencies from themain frequency, but too long in order to be detectable in thepower spectrum. Along the definitions of amplitudes set out in Sect. 4.4, we calculated the relative and absolute ampli-tudes, which are also listed in Table 4.Both, Ness et al. (2003) and Leibowitz et al. (2006) un-derlined the presence of overtones at ∼ . σ contours, and the 1- σ un-certainty range is given in round brackets. For days 180 and196, we clearly detected two frequencies from both methods.The beat periods from the 2-D results are 17.8 and 19.6 ks,respectively, and such splitting of the main signal is thusdetectable in the given observing durations (Table 1). Wealso found two frequencies in the day 742 observation withboth techniques, yielding a beat period of ∼
16 ks. With the2-D method, both frequencies are only significant on the 2- σ level. For the other light curves, only a single frequency, ifany, could be identified.The detected overtone frequencies listed in Table 5 needto be compared to the expected overtone frequencies basedon the measured ground harmonics listed in Table 2, whichare given in the last three columns, assuming the resultsfrom the 2-D sine fitting listed in the second column of Ta-ble 2. Expected overtones are those from f + f , 2 × f , and2 × f . Within the combined uncertainties, all observed over-tone frequencies can be uniquely associated to one of the ex-pected overtone frequencies. The overtones determined fromusing the Lomb-Scargle algorithm are also in satisfactoryagreement within the larger uncertainties. These findingsare also in agreement with Leibowitz et al. (2006). On order to compare our photometric results with the spec-tral evolution, we have extracted the high-resolution X-raygrating spectra taken during the SSS phase, thus on days180, 196, 302, 371, and 526, using standard data reduc-tion packages provided by the
Chandra and
XMM-Newton missions. For details on spectral analyses, we refer to, e.g.,Ness et al. (2007). The SSS spectrum taken on day 180has been shown in fig. 3 of Ness et al. (2003). We havealso extracted the low-resolution spectra taken on day 50with
Chandra /ACIS and on days 742 and 1286 with
XMM-Newton /MOS1.From the spectra, we have determined X-ray bandfluxes over the energy range 0.3-2.5 keV, which is coveredby all instruments. For the high-resolution grating spectra,the fluxes can be obtained directly by integrating the photonenergies from each spectral bin. The low-resolution spectrasuffer from photon redistribution, but reliable fluxes can beobtained by fitting a spectral model to the data that is foldedthrough the instrumental response matrix. The evolution ofX-ray fluxes is shown in Fig. 19.For the SSS spectra, we have determined the spectralcolour for each spectrum, following two approaches. First, wecomputed two different hardness ratios HR = ( H − S ) / ( H + S ) were H and S are the number of counts within a hard anda soft energy band, respectively. We computed two differenthardness ratios from different energy cuts. The first hardnessratio has been computed with 0 . − . . − . c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr Table 5.
First overtone X-ray frequencies expected around 1.5 mHz. For comparison, three linear combinations of the observed groundharmonics from the second column in Table 2 are given in the last three columns.Linear combinations of ground harmonics (Table 2):Day L-S 2-D sine fit Leibowitz f + f × f × f et al. (2006) from 2-D sine fit from 2-D sine fit from 2-D sine fit50 (1 . c . ± ( > . a – – 1 . ± ( > . a –180 1 . ± .
018 1 . ± .
009 1.482 1 . ± .
005 1 . ± .
004 1 . ± . . c . ± .
015 –196 (1 . c . ± .
010 1.459 1 . ± .
006 1 . ± .
005 1 . ± . . c . ± .
008 1.504302 (1 . c . ± .
044 – – 1 . ± .
012 –371 – – – – 1 . ± .
011 –526 (1 . c – – – 1 . ± .
028 –742 (1 . c . ± ( > . b – – 1 . ± .
011 –(1 . c . ± ( > . b –1286 (1 . c . ± .
037 – – 1 . ± .
011 – a unconstrained on 3- σ level and only 1- σ level given b unconstrained on 3- σ level and only 2- σ level given c unconstrained on 1- σ level and only the nominal value is given Figure 20.
Parameterisation of the spectral evolution during theSSS phase. In the top panel, spectral hardness ratios with twodifferent energy cuts, as detailed in the bottom right legend, areshown. In the bottom panel, best-fit colour temperatures derivedfrom blackbody fits are shown, that show the same evolution asthe hardness ratio curve plotted in black. for soft and hard bands, respectively, and a second one usingthe two bands 0 . − . . − evolution , we assume thatthe evolution of the blackbody temperature reflects the evo-lution of the effective temperature. While this remains to beproven, we use this assumption as our working hypothesis.In the bottom panel of Fig. 20 we show the evolution ofthe blackbody temperature. We have calculated statisticaluncertainties accounting for correlations with other param-eters, but these errors are smaller than the plot symbols.We caution, however, that a χ goodness criterion indi-cates poor fits, and statistical errors are of little use in thissituation. The reason for poor fits is the presence of deepabsorption lines that are not reproduced by a blackbody.Since the continuum is well reproduced in each case, westill consider the blackbody fits a good approximation forthe spectral shape. The best-fit blackbody temperatures arelisted in Table 6. From day 180 to 196, the blackbody tem-perature decreases and recovers to a somewhat higher valueon day 302. The temperature then stays approximately con-stant until day 371, after which time it decreases by a largeamount. This behaviour resembles that of the evolution ofthe softer hardness ratio shown with the black line in the top c (cid:13) , 1–17 A. Dobrotka and J.-U. Ness
Figure 21.
Graphical illustration of the evolution of the mea-sured X-ray frequencies. The top panel shows the main frequencyaround 0.75 mHz, and in the bottom panel we show the first over-tone. The bullets, connected by the solid line are the results fromthe 2-D method. The results from the Lomb-Scargle method areincluded with the dashed lines for comparison. panel of Fig. 20. The temperature decrease between days 180and 196 may be associated to the steep decay on day 180,but it could also be an instrumental effect, as the spectrumon day 180 was taken with
Chandra while that on day 196was taken with
XMM-Newton .The normalisation can be converted to a radius assum-ing spherical geometry. With a distance of d = 3 . ∼ ,
000 km is overestimated and can beconsidered as upper limit.
With a data set covering more than three years of evolution,we see large changes in brightness between observations.On day 180, a sharp decline was observed by Ness et al.(2003), and brightness variations thus occur on long andshort time scales. The origin of the observed emission is notthe same in all observations. On day 50, the X-ray emis-sion likely originated from shocks within the ejecta, whileon days 180-526, the spectrum was dominated by SSS emis-sion that comes from the photosphere around the whitedwarf. The post-SSS phase in novae is usually dominatedby optically thin X-ray emission originating from the nebu-lar ejecta that are radiatively cooling like in V382 Vel (seeNess et al. 2005). V4743 Sgr has a quiescent X-ray emissionsource (Ness et al. 2007) that could resemble those typicallyobserved in intermediate polars, where X-ray emission orig-inates from an accretion shock close to the white dwarf. In addition, Kang et al. (2006) detected a similar frequency of0 . ± . . ± .
015 mHz during day 742 is consistentwith the Kang et al. (2006) optical finding within the er-rors. It thus stands to reason that the origin of the mainX-ray frequency is of a fundamental nature as, e.g., the spinperiod of the white dwarf. However, systematic inspectionof the frequency evolution yields some inconsistencies withthe interpretation of pure rotational modulation.We confirm the multifrequency substructure found byLeibowitz et al. (2006) for days 180 and 196. However, forday 180, we need the higher sensitivity of our 2-D sine fittingmethod, as the Lomb-Scargle method yields only a singlepeak. Similarly, Leibowitz et al. had to use a least squarefitting approach in order to detect the double nature of themain peak for day 180. Since in addition, the formal mea-surement uncertainties from the Lomb-Scargle method arehigher than for our 2-D sine fitting method, we concentrateonly on the results from the 2-D sine fitting method for thediscussion.
The evolution of the main frequency is illustrated in Fig. 21.In the early observations, it is split in two frequencies, as thetwo signals on days 180 and 196 are different at < .
7% con-fidence. Since they have moved closer together from day 180to day 196, it is possible that this was a monotonic trendthat continued until they merged into a single frequency.Since the exposure times on days 301, 372, and 526 weremuch shorter than the beat period that corresponds to thedifference between the two signals on day 180, this possi-bility can not be tested. However, as illustrated in Fig. 17,the observations on days 742 and 1286 were long enoughto detect two frequencies if they were as far apart as onday 180. Unless the relative amplitudes of the two signalshave changed significantly, we can confidently conclude forat least these two observations that only a single signal waspresent and that the double nature of the 0.75-mHz signalhas disappeared. These results are also supported by theovertone studies. The detected values satisfy the character-istics of a fundamental and a first harmonic.After day 196, the frequency appears to have decreasedand then increased again by day 742 (see Fig. 21). While thisis formally not statistically significant in the 3- σ level, othernearby signals have undergone such kind of change on astatistically significant level (see Table 4). Furthermore, thedecrease of the relative amplitude as illustrated in Fig. 19 ishighly significant. In addition to being split in two nearbyfrequencies in the early evolution, the main frequency is thusnot a stable signal.In spite of the likely different origin of the optical emis-sion observed by Kang et al. (2006), they found a similarperiod to our main frequency, yielding 0 . ± . XMM-Newton
OM on day 742. While their fre-quency is remarkably close to our main X-ray frequency, thestatistical uncertainty ranges indicate a significant difference c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr Figure 22.
Graphical illustration of the connection betweenchanges in X-ray frequency and colour temperature. Each datapoint represents a predicted temperature T i for each observationtaken at time day i after outburst (x-axis), according to the for-mula given in the top, where T j is the blackbody temperature (seeSect. 4.6) for day j as indicated by the plot symbol (see legend),and f j /f i is the ratio of frequencies from our measurements. Thedashed grey line represents the observed colour temperatures (seeFig. 20) for comparison with the predictions (the symbols thatare connected by this line are the cases i = j , thus the measuredtemperatures). from all our measurements (see Table 2), including the lateobservations up to 1286 days after outburst. Nevertheless,the similarity of the frequency is striking and suggests somefundamentally common underlying origin. However, if thespin period of the white dwarf were to be responsible for themodulations in X-ray and optical, then the frequencies inboth bands should be identical.The fact that the optical and the X-ray frequencies dif-fer, plus the obvious changes in frequency and amplitude,demonstrate that there is more than simply rotational mod-ulation from the spin of the white dwarf. While Kang et al. (2006) rule out pulsations, the new ev-idence from our analysis requires us to reopen the case.Kang et al. argued that the interpretation of this periodas white dwarf pulsations would yield a significant slow-down with time, owing to cooling of the temperature ofthe white dwarf (Somers & Naylor 1999). From their esti-mates of changes in effective temperature, derived from ob-served luminosity changes, they calculated that the periodreported by Ness et al. (2003) for day 180 should be 38 min-utes around day 1000, and they rule out pulsations becauseno such period is in their data. While it is true that we arealso not observing a 38 minute period in the X-ray dataaround day 1000, we do see significant frequency changes inFig. 21.Kang et al. (2006) suggested using equation 10 inKjeldsen & Bedding (1995) for the conversion of tempera-ture changes to expected pulsation frequency changes. InSect. 4.2 of Kjeldsen & Bedding (1995), a scaling relationbetween stellar parameters and pulsation frequencies is de-rived. It is argued that the acoustic cut off frequency, ν max ,that defines a typical time scale of the atmosphere, scaleswith the maximum envelope frequency of stellar pulsations.Linear adiabatic theory is applied to derive ν max and thusthe relation given in their equation 10. The ratio of two pul-sation frequencies in two different atmospheres scales with the square root of the inverse ratio of the respective effectivetemperatures (assuming the same mass and radius). Withthis method, our observed changes in frequency can be con-verted to expected changes in photospheric temperature, ifpulsations were assumed. In Table 6 we list squared ratiosof frequencies from our 2-D sine fitting method taken fromTable 2. We indicate the two respective observation dateswith numbers (1) and (2) for which the ratios were taken.For days 180 and 196 we indicate the high and low frequen-cies by superscript ’+’ and ’-’ behind the day of observation.Since the 3- σ uncertainties given in Table 6 do not includethe possibility that two unresolved frequencies are present,we used the larger uncertainty range resulting from half ofthe inverse exposure times for days 302, 371, and 526. Theinverse exposure time sets a strict limit on the detectabilityof two separate frequencies (see Sect. 4.3 and Fig. 17), and ifthe signal was split in two components on days 302, 371, and526, then a value somewhere in between would result (de-pending on the individual amplitudes), while the statisticaluncertainty would not include the upper or lower frequency.As an estimate of the evolution of the effective temper-ature, we use colour temperatures derived in Sect. 4.6. Aspointed out earlier, the blackbody temperature is not equiv-alent to the photospheric temperature, and also the evolu-tion might not follow the same trend. However, we considerit a strong possibility that changes in the blackbody tem-perature indicate equivalent changes in temperature and as-sume this as a working hypothesis. The following conclusionsdepend on whether or not this assumption is valid.In the last three columns of Table 6 we quote the colourtemperatures derived in Sect. 4.6 for the respective days andthe inverse ratios of these values for direct comparison withthe squared frequency ratios in the third column. The ex-tent of agreement between these ratios is an indicator for thevalidity of the underlying assumption of pulsations. Thoseratios which agree within the given uncertainty ranges of thefrequency measurement are indicated by underlined num-bers. For illustration we show in Fig. 22 the evolution of theobserved colour temperature in comparison with tempera-tures computed from T i = T j ∗ ( f j /f i ) , (3)where T i and f i are predicted temperature and observed fre-quency for day i , respectively, and T j and f j are the observedtemperature and frequency for day j .The best agreement between observed and predicted ef-fective temperature is seen for the observations on days 180and 302, and between days 196 and 371. All predictions de-rived from day 526 are far off the mark and are not includedin the plot. This can be seen from the predictions from otherobservations for day 526, which are too high, indicating thatthe frequency changes do not predict the decline in temper-ature. The agreement between predicted and observed tem-perature between days 196 and 302 and between days 180and 196 is poorer. In light of the underlying assumptionsmade by Kjeldsen & Bedding (1995), a main sequence (MS)stars with an effective temperature of order 5500 K, plus theconsiderable uncertainty in the effective temperature, theagreements are surprisingly good, strongly suggesting thatpulsations play an important role. The breakdown of therelationship towards the end of the SSS phase can be under-stood as the turn off of the central energy source, leading to c (cid:13) , 1–17 A. Dobrotka and J.-U. Ness a highly non-equilibrium situation, and pulsations may notpropagate the same way as in equilibrium. We thus arguethat the possibility of pulsations can at least not easily beruled out.It must be noted that for a frequency of ∼ .
75 mHzand a mass of order 0.5-1.4 M ⊙ , equation 10 ofKjeldsen & Bedding (1995) yields effective radii of or-der 2-7 R ⊙ , which appears rather large for a hot WD and isabout an order of magnitude larger than the radii derivedin Sect. 4.6 from blackbody fits, which have been discussedto be unrealistically large. If this apparent discrepancycould be resolved by a larger scaling factor, then therelative changes of effective temperature and oscillationchanges would still hold for a hot white dwarf. Withoutcomputing new models for hot white dwarfs, the validityof the relation must be taken with care. However, if weassume this relation to be valid, then we have good reasonto conclude that pulsations are occurring between days 180and 371.A fact that complicates the interpretation is the similar-ity between the frequencies measured during the SSS phaseand during the last phase, long after the nova has turned off.This similarity suggests that a fundamentally similar originis accountable, which brings us back to the spin period ofthe white dwarf. While pulsations seem to be a valid expla-nation for the SSS phase, the spin period of the white dwarfshould also play a major role. We have no explanation buthesitate to believe in a coincidence. Perhaps magnetic fieldsthat are present in an intermediate polar might stir up theejecta during the SSS phase and stimulate pulsations. How-ever, this is pure speculation.Leibowitz et al. (2006) interpreted the 0.75 mHz struc-ture as due to the rotation of the white dwarf and otherclose signals as the nonradial pulsations of the central star.This explanation would be consistent with a similar inter-pretation by Drake et al. (2003) and Rohrbach et al. (2009)for the nova V1494 Aql. A dominant short-term oscillationwith a period of 2498.9 s with other close signals was de-tected. The authors interpreted the variability as the pulsa-tions of the central white dwarf. These central acretors afterthe nova explosion resemble planetary nebula nuclei wherepulsations were observed in the range of ∼ ∼ ∼ .
01 mHz per month. This is re-markably similar to our finding of changes in each of the twofrequencies detected on days 180 and 196 (Table 2), whichchange by the amount of ∼ .
01 mHz within two weeks. Suchfrequency changes are thus not unprecedented in pulsatingwhite dwarfs.Sastri & Simon (1973) studied instabilities in hydrogenburning nova shells and found pulsations as a possible phe-nomenon. However, while the multiperiodic and unstable be-haviour is consistent with our results, the predicted typicalperiods are much smaller. For example, the unstable 35 s X-ray oscillations in RS Oph (Beardmore et al. 2008) shortlyafter the start of the super soft phase would fall into thisrange.Another mechanism with periods in accordance to our
Table 6.
Comparison of squared X-ray frequency ratios (fre-quencies from 2-D method from Table 2) with inverse ratiosof colour temperature ( T col in 10 K, derived in Sect. 4.6. Fordays 180 and 196, the low and high frequencies are markedwith - and + superscripts, respectively. The errors include sys-tematic uncertainties from the exposure times (see text for de-tails). The underlined numbers indicate cases for which the rela-tion ( f /f ) ≃ T (2)col /T (1)col holds. Note that mismatches involveonly days 196 and 526, times of non-equilibrium situations (seeSect. 5.2).Day(1) Day(2) ( f /f ) T (1)col T (2)col T (2)col /T (1)col − − ± .
01 427 406 0.95180 + + . ± .
01 427 406 0.95196 −
302 0 . ± .
11 406 451 1.11196 +
302 1.05 ± .
11 406 451 1.11302 371 1.06 ± .
16 451 443 0.98371 526 0 . ± .
17 443 336 0.76180 +
302 1.08 ± .
11 427 451 1.06180 +
371 1.15 ± .
12 427 443 1.04180 +
526 1 . ± .
13 427 336 0.79302 526 1 . ± .
17 451 336 0.74 finding could be pulsations in isolated hot GW Vir whitedwarfs. The origin of these pulsations is the compression-induced opacity and ionisation increase in the partial ioni-sation zones of carbon and oxygen (Starrfield et al. 1984).Such nonradial pulsations are typical for hydrogen-deficientwhite dwarfs with carbon-oxygen envelopes. While in ac-creting white dwarfs like V4743 Sgr the white dwarf is nothydrogen poor on its surface, Dreizler et al. (1996) foundsome GW Vir stars that have pulsations and hydrogen ontheir surface. The X-ray spectra of V4743 Sgr contain rela-tively deep carbon and oxygen absorption lines (Ness et al.2003), which is an indication for V4743 Sgr being a CO-typenova as opposed to an ONe-type nova. Drake et al. (2003)proposed the same interpretation in the case of the novaV1494 Aql, but without any spectral indication of the whitedwarf to be the required CO type.
Leibowitz et al. (2006) and Kang et al. (2006) argued thatthe two nearby frequencies can arise from the white dwarfspin period on the one hand and the beat period betweenthe spin and the orbital period of the binary system on theother hand. The orbital period was reliably determined byKang et al. (2006) as 6 . ± .
005 hours from both observ-ing campaigns. This can be compared to the beat periodsbetween various pairs of observed frequencies. In Table 7 welist the detected periods in minutes, the difference betweentheir frequencies, and the derived beat periods. We calcu-lated the beat periods for the two signals in the X-ray lightcurves taken on days 180 and 196 (top two rows), for all pos-sible combinations between these two signals and the opticalperiod of 23.651 min (derived from the f = 0 . c (cid:13) , 1–17 ultifrequency nature of the 0.75 mHz feature in the X-ray light curves of the nova V4743 Sgr Table 7.
Beat periods P beat (last column in unit hours), derivedfrom various pairs of observed periods ’ P ’ and ’ P ’ (in unit min-utes) and their corresponding frequencies, f and f . In the toptwo rows, the beat periods for the two close frequencies that wefound in the X-ray light curves on days 180 and 196 (see Table 2)are given. Next, the beat period between each X-ray period andoptical period of 23.651 minutes, observed between days 1003 and1011 by Kang et al. (2006), are given. The last two rows show thebeat period between the late X-ray periods and the optical period,which compare well to the orbital period of 6.72 hours.Day P [min] P [min] f - f [mHz] P beat [h]180 23 .
180 21 .
533 0 . ± .
005 5 . ± . .
707 21 .
872 0 . ± .
006 9 . ± . .
180 23 . a . ± .
003 4 . ± . .
533 23 . a . ± .
004 19 . ± . .
707 23 . a . ± .
004 4 . ± . .
872 23 . a . ± .
005 9 . ± . .
252 23 . a . ± .
011 6 . ± . .
282 23 . a . ± .
011 6 . ± . a Detected optical period between days 1003 and 1011 ( f =0 . ± . riod. Also, the beat periods between these frequencies andthe optical frequency are not consistent with the orbital pe-riod. Only the beat periods between the frequencies derivedfrom the late X-ray observations and the optical frequencyare in agreement with the orbital period. The latter agree-ment suggests that either the optical or the late X-ray periodis the spin period, while the respective other one is the beatbetween orbital and spin period. The most probable situa-tion is that the X-ray signal is the spin of the white dwarf.The fact that none of the earlier frequencies are connectedto the orbit-spin relation, lends additional support to ourinterpretation that the oscillations during the SSS phase aremore than only the spin period of the white dwarf. In Sect. 5.2 we have discussed that during the SSS phase, themain period could be characterised by pulsations, while thefrequency detected in the later observations is more likelythe spin period of the white dwarf. In that case we wonderwhy the frequencies are so similar, despite of their differentnature (see, e.g., Fig. 6).We consider it unlikely that the spin period of the whitedwarf has changed, yet small but significant changes in theobserved oscillation frequency are undeniable. We can onlyspeculate about how to explain the presence of a persistentsignal that is variable at the same time. Perhaps, the spinperiod of the white dwarf could be modulated by additionalprocesses that could depend on the physical conditions of theemitting plasma. One possibility would be that the magneticfield axis is not aligned with the rotation axis, and the spin-ning of the non-aligned magnetic dipole stirs up the ejectasurrounding the white dwarf. In this way pulsations could bestimulated by the spin period of the white dwarf. The fluxis then modulated by these pulsations and the time evolu-tion would depend on the properties of the ejecta. We also note that the expansion of the shell during the SSS phasethat rotates at a slower velocity in the outer layers, owingto conservation of angular momentum, could slow down theoscillation frequency. We caution, however, that these ideasare unsubstantiated without theoretical support and are assuch highly speculative.
In Figs. 19 and 21 it can be seen that the largest changesin frequency and amplitude as well as the shrinking differ-ence between the two components of the main peak ap-peared shortly after the sudden brightness decline on day180 that was accompanied by spectral changes from soft op-tically thick to hard optically thin (Ness et al. 2003). Sincethis decline has only been seen in the first SSS observation,thus during the early SSS phase, it may be part of an earlyvariability phase similar to that first seen by Swift in RSOph (e.g., Beardmore et al. 2008). Such an early variabil-ity phase is now routinely being observed, e.g., in V458 Vul(see figure 6 in Ness et al. 2009). Since these novae did notshow any persistent oscillations as in V4743 Sgr, our find-ings are a unique contribution to the discussion about theorigin of the early variations in the SSS phase. Additional ev-idence comes from high-resolution spectroscopy. Ness (2010,in preparation) reports the rapid disappearance of some ofthe nebular emission lines that were seen during the darkphase (Ness et al. 2003). This indicates that the surroundingnebular emission was recombining after the bright central X-ray source had disappeared. One possibility for the completedisappearance of the X-ray source could be an expansion ofthe photospheric radius, followed by photospheric adjust-ment, thus shifting the peak of the SED back into the ultra-violet. This would be consistent with the spectral changesparameterised in Fig. 20. From day 180 to day 196, a sig-nificant drop in the blackbody temperature and hardness isseen which could indicate a lower photospheric temperatureon day 196. In that case, the atmospheric structure couldchange significantly, which could lead to changes in pulsationfrequency and amplitude, as the conditions for the propa-gation of pulsations through the atmosphere would change.Our observations of changes in the oscillations are importantevidence for a physical explanation of the variations ratherthan geometrical causes such as an eclipse.
In this paper, all available X-ray light curves of the novaV4743 Sgr are presented and analysed. Our results have tobe viewed in light of three different phases of evolution, eachwith a different origin of X-ray emission: • Early hard X-ray emission phase with X-rays likely orig-inating from shocks within the ejecta. This phase is charac-terised by weak emission line spectra that can be modeledwith optically thin thermal models. Our observation takenon day 50 belongs to this phase. • Super Soft Source (SSS) phase with the X-ray emis-sion originating from a pseudo photosphere around the whitedwarf. This phase is characterised by extremely bright con-tinuum emission. The broad-band spectrum can be fitted c (cid:13) , 1–17 A. Dobrotka and J.-U. Ness by a blackbody, and high-resolution X-ray spectra show ab-sorption lines that are blue shifted (see Ness et al. 2009).Our observations taken on days 180, 196, 302, 371, and 526belong to this phase. • Quiescent phase. In Classical novae, the radiativelycooling ejecta can be observed in X-rays. The spectra fromdays 742 and 1286 resemble more those of quiescent inter-mediate polars (Ness et al. in prep).Despite of all the differences in the emission origin, thesame main frequency was observed at all times. In addition,a similar frequency was observed in the optical (Kang et al.2006 and our
XMM-Newton optical/UV OM data), althoughthe optical light has a different origin. If the optical period isinterpreted as the beat period between the WD spin and theorbit, then the optical light must originate from somethingfixed in the orbiting system, for example from the secondarystar or the disc-stream impact region. Not many periodicprocesses in a cataclysmic variable can leave their footprintin all forms of light, leading us to the conclusion that thespin period of the white dwarf must play a major role.Meanwhile, the different phases can lead to differentkinds of modulation of the main frequency, and we haveinvestigated small anomalies that require detailed analysis.Our main results are: • On days 180 and 196, the main signal consists of twonearby frequencies. The difference between these two com-ponents shrinks from day 180 to day 196. While only a singlefrequency was found for days 302 to 526, these observationswere too short to detect such close signals. Either, the trendof a shrinking difference has continued until it merged intoa single signal, or roughly the same difference has remainedthrough the SSS phase. • The observations of days 742 and 1286 contained only asingle signal, and the double nature has not continued intothe quiescent phase. • The average frequency decreased slightly after day 196and then increased again after day 526. Colour temperaturesderived in Sect. 4.6 from fits to the SSS spectra on days180, 302, and 371, seem to change in relation to the changesin frequency. This suggests pulsations as an origin for themodulations. • The relative amplitude of the oscillations decreased af-ter day 196 and then increased again to the original valueafter day 526. • The largest change in frequency and oscillation ampli-tude occurred after the sudden brightness decline on day 180and could thus be connected to this event. • We found overtones at ∼ . ∼ .
75 mHz. • The beat period between the X-ray period and the op-tical period during the quiescent phase coincides with theorbital period.We believe that during the SSS phase, pulsations are themajor source for the oscillations, while the oscillations seenduring the quiescent phase are the spin period of the whitedwarf. The similarity of the spin period and pulsation periodis puzzling, and no mechanism that could co-align the pe-riods is known to us. Based on the spin period, we support the interpretation by Kang et al. (2006) that V4743 Sgr isan intermediate polar.
ACKNOWLEDGEMENT
AD acknowledges the Slovak Academy of Sciences GrantNo. 2/0078/10. We thank V.Antonuccio-Delogu from INAFCatania for providing computing facilities. We acknowledgefinancial support from the Faculty of the European SpaceAstronomy Centre.
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