The Long-term Activity of the Postnovae Q Cygni and BK Lyncis

We show the postnova activity of Q Cyg (Nova Cyg 1876) and BK Lyn (probable Nova Lyn 101). We use both CCD and photographic photometric observations. We show that both systems lie close to the upper limit of the luminosity in which dwarf nova (DN) outbursts occur. Q Cyg shows a novalike high-state activity. Random fluctuations (typically 0.6 mag) from a well-defined curve of the moving averages of brightness often occur on the timescale of weeks. The random fluctuations were suppressed during one fainter interval lasting several months but increased during another. In the author’s interpretation, clumps in the disk wind are likely to play a role in these fluctuations, especially when the luminosity of Q Cyg is near the upper limit of the range in which DN outbursts occur. BK Lyn was observed to spend about 100 yr in a very long state of a high luminosity on the upper limit of the region of DN outbursts before undergoing a time segment in which DN outbursts were present. We find that the individual DN outbursts in BK Lyn all show similar decay rates and fade more gradually than those of DNe that do not also show classical nova eruptions. We attribute it, along with the low amplitude of DN outbursts and the high quiescent luminosity, to the role of extra light. These outburst peaks, higher than the surrounding segments of the flat light curve, speak in favor of the ER UMa-type with superoutburst cycles and standstills rather than the high state in a novalike variable.


Introduction
Cataclysmic variables (CVs) are close binary systems in which gas transfers onto the white dwarf (WD) from its companion, a lobe-filling secondary star (donor; e.g., Warner 1995).Their orbital periods P orb span from several minutes to about 5 days (Ritter & Kolb 2003).
CVs display various activity types that depend on the value of mass transfer rate m tr  from the donor to the accretion disk (if it exists).The disk embedding of a relatively nonmagnetized WD is subject to thermal-viscous instability (TVI) if the value of m tr  in a given CV is between some limits (Smak 1984;Cannizzo 1994;Hameury et al. 1998).It leads to episodic ionization and accretion of matter from the disk onto the WD when the critical column density of the disk is achieved.This gives rise to dwarf nova (DN) outbursts.
The value of m tr  above the upper limit of the TVI zone leads to a high state in which the disk is ionized, and no DN outbursts occur.These so-called novalike variables have bright absolute magnitudes M opt (in the optical band in the V-filter or its vicinity), comparable to those of the DN outburst peaks (Warner 1987).The variations of m tr  govern the changes of their M opt .
An eruption of a classical nova (CN) is caused by episodic hydrogen burning of the accreted matter on the WD (Bode & Evans 1989;Warner 1995).Shara et al. (1986) hypothesize that the mass transfer rate of postnovae decreases on the timescale of decades or centuries and increases again only a few decades before another CN eruption.Also, the activity of a postnova can be modified by changes in the secondary star leading to enhanced mass transfer rates caused by irradiation by the WD (Kovetz et al. 1988).In the model of Ginzburg & Quataert (2021), irradiation of the donor during a CN eruption can cause a very high time-averaged mass transfer rate.In some cases, it may remain at a selfsustaining rate of about 10 −7 M e yr −1 for up to 1000 yr since the CN outburst.
Q Cyg erupted as Nova Cyg 1876; it ranged from 3.0v to 15.6v (Schmidt 1877;Duerbeck 1987).It is a novalike variable, and its P orb is 10.08 hr (Kafka et al. 2003).The hot component is dominated by accretion light from a luminous disk surrounding the WD (Kolobow & Sion 2011).Bianchini (1987) and Bianchini (1990) found a period of 6.4 yr with an amplitude of about 0.5 mag in its light curve, and explained it by postulating a solar-type cycle in the late-type donor that can modulate the mass transfer rate into the disk.Shara et al. (1989) found significant photometric (0.6 mag) variability even on shorter timescales, with an initially monotonic dimming followed by 2 weeks of fluctuations with an amplitude of 0.4 mag.The later observations of Kafka & Honeycutt (2004) in 1991-2003 showed that Q Cyg varied by more than 1 mag, but with the brightness varying only by a few tenths of mag for the time segments of hundreds of days, sometimes replaced by steep rises or decreases of brightness by about 0.7 mag.Q Cyg spent only short times in the peak and bottom limits of brightness.A belt of brightness between these limits was the most densely populated.Pavlenko et al. (2008) found that the brightness of Q Cyg in 1995-1996 varied between 14.3 and15.3mag (V ).The power spectrum showed a signal at 20 days.In two brightening episodes, Q Cyg grew bluer in V − R by about 0.3 mag.
In addition, Q Cyg was observed to undergo 11 stunted outbursts with a typical amplitude of 0.5 mag and duration of Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.9-23 days in 19919-23 days in -19969-23 days in (Honeycutt et al. 1998; see also Pavlenko et al. 2008).Honeycutt (2001) argued in favor of the TVI as the cause of these outbursts with the contribution of an extra light source.Downes et al. (1995) detected significant spectral changes of Q Cyg-a decrease in strength of Hγ and He I 5876, and a disappearance of He II 4686 and C III/N III 4650 that occurred during 5 days.Kafka & Honeycutt (2004) show that most wind episodes in a group of CVs including Q Cyg occur when the system is brightest, either as part of a state transition or as part of a stunted outburst.The data also confirm the erratic nature of the wind.Also, Kolobow & Sion (2011) discovered spectroscopic peculiarities in the optical, including the presence of variable wind outflow in P Cyg profiles.The accretion light of a luminous accretion disk dominates the far-UV flux of the hot component in Q Cyg.
BK Lyn was discovered as an object with UV excess in the Palomar-Green survey (Green et al. 1986).The value of P orb of 1.7995 hr and blue spectrum with the long-term light curve without DN outbursts make it the first disk novalike variable known below the period gap of CVs (Ringwald et al. 1996).Spectroscopic observations show that BK Lyn contains an accretion disk (Dobrzycka & Howell 1992).Patterson et al. (2013) show that two apparent superhumps dominate in BK Lyn, with periods 4.6% longer and 3.0% shorter than its P orb .BK Lyn's light curve transitioned from a novalike variable and became indistinguishable from a DN for several years since 2005.It showed both outbursts and superoutbursts.While the TVI operates in normal DN outbursts, both TVI and a tidal instability of the disk operate in superoutbursts (Hellier 2001a).BK Lyn thus belonged to the ER UMa type (Hellier 2001b).Hellier (2001b) used the scheme of CVs proposed by Osaki (1996) and suggested that the ER UMa type with echo outbursts and ultrashort supercycles (<40 days) can occur in binaries with mass ratios of q < 0.07.Patterson et al. (2013) ascribe this transition to postnova evolution.If BK Lyn is associated with the remnant of the probable CN on 101 December 30 (Hsi 1958;Hertzog 1986;Kemp et al. 2012), it required almost 2000 yr for the accretion rate to drop sufficiently to permit DN outbursts (Patterson et al. 2013).
Because BK Lyn returned to the novalike state in 2013 (Kato et al. 2014b), even if the average mass transfer rate of a postnova is decreasing over millennia, it is not doing so monotonically since BK Lyn did not stay in the DN outbursting state.Instead, the supercycle length did not significantly vary before the transition to the novalike state, indicating that m tr  did not change significantly.They argue that the signal of negative superhumps showed a dramatic disappearance in 2013.This fact may be related to the transition to the novalike state.
The postnovae Q Cyg and BK Lyn have good data coverage of several decades or about a century.Their absolute magnitudes indicate that their accretion disks are close to the thermally stable or unstable limit (e.g., Smak 1984;Warner 1995).These CVs thus deserve analysis of their long-term activity, especially as regards the search for possible outbursts that could indicate transitions of their disks to the TVI zones.A preliminary version of part of this analysis was presented by Šimon (2021).
DASCH allows examination of the appearance of the scans of the field of objects (with possible zooming).It also produces a file with the timings of each exposure, the studied star's magnitude, its rms, and the plate limiting magnitude.It also allows seeing information about the exposure time and plate emulsion.It is thus also possible to inspect and assess plates.Therefore, only the plates with reliable magnitudes of the observed stars were used.
BK Lyn was detected on 417 DASCH plates starting in 1892.Usually, one plate of BK Lyn was obtained per night.The Q Cyg field was not included in the available DASCH digitized plates.
The Catalina Real-time Transient Survey (CRTS; 4 Drake  et al. 2009) obtained CCD images of BK Lyn between the years 2005 and 2013.5 CRTS data are unfiltered with a V zero-point.In total, 337 images of BK Lyn were obtained (usually, four images per night).A typical separation of the neighboring images in a night series was about 8-16 minutes.CRTS did not observe Q Cyg because it was in a too-crowded field.
The AAVSO International Database (Massachusetts, USA;6 Kafka 2023) contains both the visual and CCD measurements of Q Cyg and BK Lyn.We used only the V-band and CV (with a sensitivity similar to the V-band) CCD data for both objects.
The Zwicky Transient Facility (ZTF) is a robotic timedomain survey using the Palomar 48 inch Schmidt Telescope.ZTF uses a 47 degree 2 field with a 600 megapixel camera to scan the entire northern visible sky (Masci et al. 2019).Bellm et al. (2019) described a complement of three custom filters, ZTF-g, ZTF-r, and ZTF-i.They did not attempt to match any existing filter bandpasses exactly.We used the ZTF-g filter in our analysis.The reason is that observations in this filter are similar to those in the V filter and unfiltered, used in the AAVSO.It enables meaningful comparison of the light curves.In total, 547 1 day means of Q Cyg were obtained (consisting of one to eight CCD images, usually two images (∼51%) per night).They span JD 2 458 208 (2018 March) and JD 2 460 125 (2023 June).The ZTF-g observations of BK Lyn spanning JD 2 458 203 (2018 March) and JD 2 460 078 (2023 May) covered only the time segment after the finish of a segment with outbursts, and their brightnesses continued a flat light curve.
The B band could approximate the photographic data band (older than the CCD ones) of BK Lyn.We compared the photographic measurements with CCD observations similar to the V band.Still, the peak-to-peak amplitude of the brightness variations was considerably higher than the possible changes in the color indices.These indices only slightly modified M opt of BK Lyn.The color variations do not influence our results dramatically because the difference between the B and V mag of a blue CV like BK Lyn is small (see also Bruch 1984).To pick out the structures in the light curve and to evaluate how the brightness varied during the times of considerable scatter across the brightness fluctuations, the two-sided moving averages (TMAs) of brightness smoothed the light curve consisting of the 1 day means of brightness.This method is described in Brockwell & Davis (1987).TMAs enable us to suppress the high-frequency variations and thus obtain a better insight into the properties of the long-term light curve.This method allows us to analyze variations through the data set without further presumptions.
Fittings by TMA for AAVSO and ZTF data were separate from each other.TMAs of the data were calculated for several values of the filter half-width Q.The parameter Q refers to the interval of days within which the data were averaged.We made an ensemble of TMAs for various values of Q. Steps of 10 days were used for the time evolution of the smoothed curve.The AAVSO data were truncated at the line at JD 2 458 400 + Q to compare the TMA fits to the AAVSO and ZTF data and their offset.While the AAVSO data were fragmented beyond this line, the ZTF data dominated.Inspection selected the Q values for which the TMA already converged to a good fit.They are displayed in Figure 1.
These TMAs washed out the scatter of the light curve of the 1 day means.They emphasized the general trend in the light curve and showed the gradual evolution of the brightness on the timescale of hundreds of days.The difference between the brightness of the TMA of Set 1 and Set 2 is about 0.07 mag (measured at the dashed vertical line in Figure 1(a)), considerably smaller than the peak-to-peak amplitude of the light curve.We ascribed this difference to the slightly different filters (V versus ZTF-g).
We also smoothed the residuals of the fit to the brightness by the TMA again.This yielded the σ resMA curve (Figure 1(b)).It represents the standard deviation of the brightness of every calculated TMA point, giving thus information about the current scatter caused by the brightness variations of the observations included in a given bin.The value of σ resMA in Figure 1(b) only barely depends on the long-term M opt (e.g., weeks).The TMA showed a depression of brightness near JD 2 457 600 that coincided with a temporary decrease of σ resMA with respect to its surroundings.In contrast, a bump of σ resMA accompanied a depression of brightness defined by the TMA near JD 2 459 400 (Figure 1(b)).The difference between these two brightness minima in the TMA was that TMA ran through an extended depression of brightness near JD 2 457 600 where flares (outbursts?) were absent.In contrast, TMA ran through a series of brightness fluctuations (flares?) from a depressed brightness in the second case (i.e., in the surroundings of JD 2 459 400).
A detail of the variable amplitude of the short-time (a few days) variations in the light curve of Q Cyg at different times is shown in Figure 1(c).A gradual brightness decrease and a subsequent plateau, emphasized by TMAs running through the fluctuations, can be resolved.A considerable scatter of brightness is visible in the segment between JD 2 457 300 and JD 2 457 520.
The intranight CCD light curve of Q Cyg is displayed in Figure 1(d) to assess the influence of rapid changes, including orbital modulation, on the superorbital brightness activity.Although only part of the orbital period is covered, the amplitude of this modulation is considerably lower than that of the long-term light curve in Figure 1(a).This result is consistent with the light curve of Q Cyg over 4.3 hr of Kafka et al. (2003), showing fluctuations with the amplitude of about 0.1 mag, although not all orbital phases were covered by observations.
The histograms of M opt of Q Cyg are displayed in Figure 2. The application of TMAs considerably influences them.The histogram for the light curve consisting of the individual 1 day means is a relatively symmetric bump with broad wings (Figure 2 TMAs show that the scatter of the brightness significantly contributes to both the maximum and minimum M opt of Q Cyg.

Properties of the Light Curve of BK Lyn
Since we concentrated on investigating the long-term activity of BK Lyn, we binned AAVSO CCD data into night means.These observations were shorter or comparable to P orb .The diagrams used the standard deviations of the brightness of these means and the times of the bins' centers.This binning enabled analyzing light-curve features on timescales longer than rapid variations (potentially caused by spin modulation of the WD and the orbital modulation).
Figures 3(a) and (b) show the long-term activity of BK Lyn.The color variations are not expected to influence our results dramatically because the difference between the B and V mag of a blue CV like BK Lyn is close to zero (see also Bruch 1984).Despite some gaps in data coverage, the brightness in the very long time segment that BK Lyn spent in the high state (the DASCH data) was roughly consistent with a constant within the observing errors in JD < 2 450 000.A linear fit shows that although the mean brightness slightly decreased, it is still consistent with a constant within its standard deviation.Later, a series of brightness fluctuations with an amplitude sometimes reaching about 2 mag occurred.It was covered by CRTS and AAVSO data (we abbreviate this segment as S FL ).After finishing S FL near JD 2 456 000 (this JD represents the B set of the AAVSO data), the mean brightness coincides with a continuation of this linear fit.The ZTF-g observations spanning JD 2 458 203 and JD 2 460 078 covered only the time segment after the finish of S FL , and their brightnesses were consistent with the B set of the AAVSO data.They continued this flat light curve.
Figure 3(c) shows the histograms of the brightness of BK Lyn in various time segments of Figures 3(a) and (b).The DASCH data can be described as a single narrow peak (apart from several outliers).It is followed by a much broader bump in S FL .The data mapping S FL were split into the CRTS (segment S1 in Figure 3) observations and the AAVSO bins (S2).Inspection showed that the AAVSO means provided an accurate light curve while the more fragmented CRTS data enabled the extension of the coverage of S FL .The brightness of this bump in S FL asymmetrically expands toward both directions when compared with the surroundings of this time segment.The histogram does not show a secondary peak at the faintest levels.The profile of the narrow peak of AAVSO B data is similar to that of the previous DASCH data, with the mean brightness values before and after S FL differing at most by 0.3 mag.
Figure 3(d) shows a comparison of the limiting values of M opt determined from the brightness histograms of BK Lyn and the outburst light curves (mostly superoutburst peaks and quiescent M opt ) of DNe with P orb similar to BK Lyn.Table 1 lists the parameters and references.Notice that the quiescent M opt of most of these DNe are fainter than in BK Lyn, except for RZ LMi.
Superoutburst light curves of BK Lyn with sufficient coverage are shown in Figure 4(a).The individual events were shifted along the time axis.The slope of the rising branch is very stable for all four events.A peak of some superoutbursts displays a bump lasting for about 3 days and transitioning into a long plateau.A transition from the plateau to the steep final decay occurs at significantly different times since the outburst starts of the individual events.In one case (abbreviated as 56330.5 in Figure 4(a)), this transition was followed by several echo outbursts that do not subside back to the quiescent brightness.Echo outbursts are short brightenings on the decaying branches of some outbursts or immediately after them (Section 6.5.1 in Hellier (2001a)).
Figure 4(b) shows that the quiescent interval between outbursts of BK Lyn is generally very short, comparable to the outburst duty cycle.Quiescence may not even be reached in some cases (Figure 4(b)).
Figure 4(c) shows a composition of the light curves of the well-covered decaying branches of the normal (not super) outbursts of BK Lyn, mainly from Figure 4(b).The decaying branches of the well-observed outbursts of this object contained four 1 day means.Preferably, such outbursts were used for a reliable merging.The individual events were shifted along the time axis to match the decaying branch of the template.All normal outbursts reach similar decay rates after crossing the dashed vertical line (see a linear fit to this ensemble); only a decline of a probable partly covered superoutburst (empty circles in Figure 4(c)) joins from its plateau in a lower brightness than normal outbursts.

Discussion
Our analysis of the data sets of both postnovae (Q Cyg = Nova Cyg 1876) and BK Lyn (probable Nova Lyn 101)) shows that their maximum optical brightnesses were as expected for DNe of their P orb at the peaks of their outbursts (Patterson 2011).This, together with their positions in the M opt versus P orb diagram (Figure 6 in Šimon (2022)), suggests that their disks are close to the upper limit of the TVI region (see, e.g., models of Smak 1984;Cannizzo 1994;Hameury et al. 1998).
We assessed a possible increase of the mass transfer rate m tr  in Q Cyg predicted for some postnovae in models of Ginzburg & Quataert (2021).Applying a relation of the V-band absolute magnitude M V and P orb of CVs with the accretion disk (Figure 9.8 in Warner 1995), the observed M ≈ + 3 of Q Cyg implies m tr  of about 10 −8 M e yr −1 .The enormous value of m tr  of 10 −7 M e yr −1 predicted by Ginzburg & Quataert (2021) would imply M V ≈ + 1.5 for Q Cyg, significantly brighter than observed.Therefore, the observed value of mass transfer rate in Q Cyg is consistent with a novalike in the high state with M V similar to the upper limit of the TVI region or sometimes slightly below it.Because of its relatively long P orb , Q Cyg's disk is larger and M V is brighter than most CVs, consistent with the extrapolation of the peaks of the DN outbursts with P orb < 8 hr in Patterson (2011).Its m tr  does not appear remarkably high.This optical luminosity of Q Cyg is similar to that reported by Schmidt (1877) and Duerbeck (1987) shortly after its CN eruption.
The years-long brightness variations of Q Cyg seen in the TMAs may represent a continuation of the 6.6 yr solar-type cycles suggested by Bianchini (1987).Q Cyg appears to modify the activity features (or their profiles) on the timescale of years.The clusters of brightness peaks with an amplitude of about 0.5 mag (stunted outbursts), like those observed by Honeycutt et al. (1998) and Pavlenko et al. (2008Pavlenko et al. ( ) in 1995Pavlenko et al. ( -1996, are either absent in part of our data set or their amplitude is reduced.The TMAs in Figure 1 run through random fluctuations (including possible low-amplitude stunted outbursts); it smoothed their contribution, giving a resulting novalike variable high state with only two shallow lower-state events.Some brightness fluctuations superimposed on the long waves of the TMAs occur in all states of Q Cyg's activity in our data set, as suggested by truncating both wings of the brightness histogram by the TMA fit.
The difference between these two brightness minima in the TMA fit was that TMA ran through an extended depression of brightness near JD 2 457 600 where flares were absent (Figure 1).In contrast, TMA ran through a series of fluctuations from a depressed brightness in the second case (in the surroundings of JD 2 459 400).We ascribe these fluctuations to a cluster of stunted outbursts.In the author's interpretation, drops of brightness into a similar M opt inside the TVI instability region of Q Cyg do not always lead to the propagation of the cooling and heating fronts in the disk.
In this context, Downes et al. (1995) showed that when the V-band flux decreased by a factor of 2 over 6 days, the highexcitation emission lines He II 4686 and C II/ N III 4650 disappeared.Kafka & Honeycutt (2004) detected the erratic nature of the wind and its episodes in the optical spectra of Q Cyg, showing that most occur when the system is brightest.Also, Kolobow & Sion (2011) discovered spectroscopic peculiarities in the optical, including variable wind outflow in P Cyg profiles.The models by Kirilov et al. (2023) show that the total luminosity of a CV with the accretion disk varies on the timescales longer than the wind spikes.The reason is that clumps of this wind start in the inner disk region while a response of the outer disk smooths these luminosity changes.
In the author's interpretation, the features and σ resMA variations in the light curve of Q Cyg in Figure 2 are caused by the wind episodes and the disk responses, mainly in the higher state when Q Cyg got close to or exceeded the upper border of the TVI regime.The value of σ resMA speaks in favor of the fluctuations caused by a disk responding to the wind clumps (model by Kirilov et al. 2023) that are more intense when the M opt on superorbital timescales increase.
In the author's interpretation, the propagation of wind clumps across the disk can influence the propagation of the heating and cooling fronts, thus modifying the light curve.Photometric observations of the brightness fluctuations and a simultaneous spectroscopic search for the wind features in the lines may help further investigate the role of these phenomena and their evolutions with time in Q Cyg.
In the author's interpretation, BK Lyn in Figure 3 showed a novalike high-state activity with ionized disk (Smak 1984) except during segment S FL .Its M opt and position in the P orb versus M opt diagram in Figure 6 in Šimon (2022) are consistent with postnovae with recent CN eruptions and similar P orb .This finding of a bright M opt does not depend on whether BK Lyn is associated with a postnova of Nova Lyn 101.In this context, GQ Mus = Nova Muscae 1983 (Liller & Overbeek 1983) with P orb = 1.425 hr (Diaz & Steiner 1989) and V1974 Cyg = Nova Cygni 1992 (Collins et al. 1992) with P orb = 1.9503 hr (De Young & Schmidt 1994) are postnovae with similar M opt and P orb that were recently observed in a CN eruption.The current M opt of all these three CVs is consistent with ionized disks (apart from the recent time segment S FL in BK Lyn).In the author's interpretation, this similarity of M opt in BK Lyn, GQ Mus, and V1974 Cyg also favors BK Lyn recovering from a CN eruption.
The flat bump of segment S FL in the histogram in Figure 3(c) can be explained if M opt decreased into the TVI region, which triggered a series of DN outbursts (Smak 1984;Cannizzo 1994;Hameury et al. 1998).We ascribe the bump in segment S2 to the dominant viscous plateaux of superoutbursts.The absence of any secondary bump in the faint end of M opt indicates that the quiescent time between DN outbursts in BK Lyn was comparable to the outburst duty cycle.Moreover, M opt might not reach the quiescent value between some DN outbursts (Figure 4(b)), and hence the heating and cooling fronts (e.g., Smak 1984) traversed the disk all the time if BK Lyn was not in superoutburst plateau (Figure 4(a)).
The peak M opt of superoutbursts in BK Lyn are close to the ensemble of peak magnitudes of DN outbursts in Patterson (2011).This bright peak M opt , reaching the upper limit of the luminosity of BK Lyn in the TVI zone with a low amplitude of the DN outbursts (about 2 mag in comparison with about 3-4 mag in DN below the period gap) in Figure 3(d), speaks in favor of some extra light, especially in its quiescence.Honeycutt et al. (1998) used extra light to explain stunted outbursts in several CVs.
The decay rate of individual normal outbursts in BK Lyn was stable and reproducible for the individual events (Figure 4(c)).Therefore, the similar properties of the cooling front determine the decay rate and profile of these DN outbursts (e.g., Smak 1984;Hameury et al. 1998).These peaks of outbursts brighter than the surrounding segments of the flat light curve of BK Lyn, apart from S FL , speak in favor of the ER UMa-type DNe.These systems have P orb below the period gap and are counterparts of the Z Cam-type DN with P orb above the period gap (Hellier 2001a).The light curve, except S FL , supports standstills (Figure 1 in Kato et al. 2019 and In the author's interpretation, a transition from a plateau of the superoutburst to the final decay at M opt at least 0.6 mag lower than the decay start of normal outbursts (Figure 4(c)) suggests that the outer disk region remained ionized in a lower mass accretion rate in superoutburst than in normal outburst.Smith et al. (2007) show that the superhumping disk develops a bigger column density in its arms in the outer region than without superhumps.It is worth modeling whether it can keep such a disk in the hot state even at a lower mass accretion rate in the inner disk region in the outburst late phase.
The parameter τ D (in day mag −1 ) that measures the decay rate of outbursts serves to analyze the nature of these events, especially with respect to what corresponds to other DNe with similar P orb (the Bailey relation; Bailey 1975).The value of τ D in Figure 4(c) is 2.05 ± 0.10 day mag −1 for BK Lyn.It corresponds to a DN with a significantly longer P orb , about 3.5-4.0hr (i.e., above the period gap), using Figure 3.11 in Warner (1995).This τ D is thus significantly higher than in DNe of almost the same P orb without CN outburst observed in the past.We ascribe a decrease in the value of τ D of DN outbursts in BK Lyn to the abovementioned extra light.
The DN outbursts of both postnovae BK Lyn and V446 Her (Šimon 2023) on the different sides of the period gap (e.g., Dantona & Mazzitelli 1982) have well-reproducible τ D corresponding to considerably longer P orb than radial velocities of the components show (Ringwald et al. 1996;Thorstensen & Taylor 2000) assuming their relation to the Bailey relation (Bailey 1975).In the author's interpretation, the extra light's contribution in these CVs is stable in time, at least on the timescale of several years.
Irradiation of the disk by the WD can give rise to an inner steady-state disk region surrounded by a thermally unstable outer annulus.Models of Mineshige et al. (1990) and Schreiber et al. (2000) show that TVI can operate in this annulus; irradiation only changes the M opt of the quiescent level but not the DN outburst peak.The inner thermally stable disk region may play a role in extra light in BK Lyn.It can also explain the position of the quiescent BK Lyn in Figure 3(d).
Echo outbursts of BK Lyn that follow the superoutburst abbreviated as 56330.5 in Figure 4(a) suggest that the disk contained enough matter to trigger a new heating front (Hameury et al. 1998) promptly.These echo outbursts with a bright quiescent M opt and small amplitude are similar to those in other DN, WZ Sge (Ishioka et al. 2002), in which Georganti et al. (2022) detected a high-density "veiling curtain".Its characteristic temperature was higher than 10,000 K and was present during this series of echo outbursts.In the author's interpretation, a similar curtain may also be associated with the extra light in BK Lyn.

ORCID iDs
Vojtěch Šimon https:/ /orcid.org/0000-0003-2446-0231 Figure1(a) shows the densely covered light curve of the long-term activity of postnova Q Cyg.A scatter of the brightness is considerably more prominent than the size of the error bars of the individual data points (CCD images).The lengths of the night series are variable.Although the highest number of observations per night is 44, only one CCD image was often obtained.The AAVSO (Set 1) and ZTF (Set 2) data were analyzed separately.A dashed vertical line at JD 2 458 400 in Figure1(a) marks a border.The 1 day means are displayed because the variable lengths of the night series would increase the scatter of observations and introduce bias into the histogram of the long-term brightness variations.To pick out the structures in the light curve and to evaluate how the brightness varied during the times of considerable scatter across the brightness fluctuations, the two-sided moving averages (TMAs) of brightness smoothed the light curve consisting of the 1 day means of brightness.This method is described inBrockwell & Davis (1987).TMAs enable us to suppress the high-frequency variations and thus obtain a better insight into the properties of the long-term light curve.This method allows us to analyze variations through the data set without further presumptions.Fittings by TMA for AAVSO and ZTF data were separate from each other.TMAs of the data were calculated for several values of the filter half-width Q.The parameter Q refers to the interval of days within which the data were averaged.We made an ensemble of TMAs for various values of Q. Steps of 10 days were used for the time evolution of the smoothed curve.The AAVSO data were truncated at the line at JD 2 458 400 + Q to compare the TMA fits to the AAVSO and ZTF data and their offset.While the AAVSO data were fragmented beyond this line, the ZTF data dominated.Inspection selected the Q values for which the TMA already converged to a good fit.They are displayed in Figure1.These TMAs washed out the scatter of the light curve of the 1 day means.They emphasized the general trend in the light curve and showed the gradual evolution of the brightness on the timescale of hundreds of days.The difference between the brightness of the TMA of Set 1 and Set 2 is about 0.07 mag (measured at the dashed vertical line in Figure1(a)), considerably smaller than the peak-to-peak amplitude of the light curve.We ascribed this difference to the slightly different filters (V versus ZTF-g).We also smoothed the residuals of the fit to the brightness by the TMA again.This yielded the σ resMA curve (Figure1(b)).It represents the standard deviation of the brightness of every calculated TMA point, giving thus information about the current scatter caused by the brightness variations of the observations included in a given bin.The value of σ resMA in Figure1(b) only barely depends on the long-term M opt (e.g., weeks).The TMA showed a depression of brightness near JD 2 457 600 that coincided with a temporary decrease of σ resMA with respect to its surroundings.In contrast, a bump of

Figure 1 .
Figure 1.(a) The long-term activity of Q Cyg from 2012 to 2023.These observations are divided into Sets 1 (AAVSO data) and 2 (ZTF data).Only the 1 day means are plotted.Sizes of the error bars are often smaller than the symbol size.The smooth, thick line represents the two-sided moving averages (TMAs) for Q = 160 days of the 1 day means of brightness.The TMAs for AAVSO and ZTF data are separate (see the legend).The horizontal line marks the segment in panel (c).A vertical line represents a night series from panel (d).(b) Smoothed residuals, σ resMA , of the TMA of brightness.(c) Part of the light curve with a trend of brightness decrease and a subsequent plateau.While a considerable scatter of brightness is visible between JD 2 457 300 and JD 2 457 520, the scatter was smaller after JD 2 457 700.The smooth line represents TMAs with Q = 160 days running through the night-to-night fluctuations.(d) Intranight CCD light curve of Q Cyg.The error bars of the individual data points are marked.The horizontal lines and numbers at the edge of the panels represent M opt for its d and A V .See Section 3 for details.
(a)).In contrast, the wings of the histogram for TMAs with Q = 160 days in Figure 2(b) are much steeper.This histogram is considerably narrower and more asymmetric in comparison with the histogram for the individual 1 day means.

Figure 2 .
Figure 2. Histograms of the brightness of Q Cyg from Figure 1(a).The division into Sets 1 and 2 is JD 258 400.AAVSO data in these histograms have JD < 258 400.ZTF data in these histograms have JD > 258 400.The bar widths are 0.1 mag in both plots.The vertical lines and numbers at the upper edge of panel (a) represent M opt for its d and A V .The big × symbol denotes maxima's peaks of DN outbursts analyzed by Patterson (2011), appropriate to P orb of Q Cyg.The small × symbols mark its error bars.(a) Individual 1 day means of CCD observations.(b) TMAs with Q = 160 days.See Section 3 for details.

Figure 3 .
Figure 3. (a) The long-term activity of postnova BK Lyn from 1890 to 2023.(The photographic DASCH, CCD CRTS, and CCD AAVSO data).The error bars are marked.A linear fit and its standard deviation are included.The lines and numbers at the edge of panel (a) represent M opt for its d and A V .(b) Detail of the segment with outbursts and its surroundings.(c) Histogram of M opt of BK Lyn.Notice the prominent tail of the S1 and S2 time segments.(d) Parameters of the outburst light curves of DNe with P orb similar to BK Lyn (mostly superoutburst peaks and quiescent M opt ).The vertical long dashed lines in panels (c) and (d) represent a combination of the outburst and superoutburst peaks of DNe analyzed by Patterson (2011), appropriate to P orb of BK Lyn (the short dashed lines denote its standard deviation).See Section 4 for details.

Figure 4 .
Figure 4. (a) Light curves of superoutbursts in postnova BK Lyn (CCD data).The individual events were shifted along the time axis to match the rising branch of the template (circles) in crossing 14.5 mag (times of this crossing and the shifts are given).A horizontal dashed line marks a crossing of this line.The filled symbols denote the night means, while the empty symbols mark the isolated observations.The error bars of the night means are sometimes comparable to the size of the symbols.The individual events were connected by the line to guide the eye.(b) A segment of the light curve of BK Lyn between superoutbursts.The night means and their error bars are plotted.A horizontal line near JD 2 456 000 marks a remarkably long decay of a probable superoutburst.(c) The light curves of the well-covered decaying branches of outbursts of BK Lyn.The individual outbursts were shifted along the time axis to match the decaying branch of the template (empty squares).The time of crossing 15.5 mag of each event is marked.All normal outbursts reach similar decay rates after crossing the dashed vertical line (only a decline of a probable superoutburst (empty circles) joins later).A linear fit to the ensemble and its statistical deviation is displayed.The lines and numbers at the edge of the panels represent M opt for d and A V of BK Lyn.See Section 4 for details.

Table 1
Green et al. (2018).2021) Light Curves of DNe with P orb Similar to BK Lyn (Figure 3(d))Note.These objects are arranged according to the length of P orb (in hours).Mostly, superoutburst peaks were measured.The brightest and the faintest apparent magnitudes are abbreviated as mag max and mag min .The brightest and the faintest absolute magnitudes are abbreviated as M max and M min .Distance, denoted as d, is given in parsecs(Bailer-Jones et al. 2021).Extinction measured in magnitudes is abbreviated as A V , mainly determined from the maps ofGreen et al. (2018).