Long-term Light Curve Research Articles

A Radio Quasi-periodic Oscillation of 176 days in the Radio-loud Narrow-line Seyfert 1 Galaxy J0849+5108

Abstract We analyze the 11 yr long-term light curve of the Radio-loud Narrow-line Seyfert 1 galaxy J0849+5108 and the nearly simultaneous γ-ray data of the source. The data were obtained with the Owens Valley Radio Observatory 40 m telescope at 15 GHz and with the Large Area Telescope onboard the Fermi Gamma-ray Space Telescope, respectively. A quasi-periodic oscillation (QPO) signal at a significance of >5σ is found in the radio light curve, but no similar modulation is seen in the γ-ray light curve. The QPO signal was present for 21 cycles, the longest among the reported radio QPOs, and likely disappeared after 2019 January 16. Different mechanisms proposed to explain the observed QPOs in active galactic nuclei (AGNs) are discussed for this QPO case. Either a secular instability in the inner accretion disk or a helical structure in the jet of J0849+5108 may explain the radio QPO, while for the latter scenario the jet has to be collimated up to ∼200 pc, similar to that seen in the nearby AGN M87. It will be of interest to keep monitoring the source at radio frequencies, seeing whether similar QPO signals appear again.

The rare X-ray flaring activity of the ultraluminous X-ray source NGC 4559 X7

ABSTRACT Ultraluminous X-ray sources are considered amongst the most extremely accreting objects in the local Universe. The recent discoveries of pulsating neutron stars in ULXs strengthened the scenario of highly super-Eddington accretion mechanisms on stellar mass compact objects. In this work, we present the first long-term light curve of the source NGC 4559 X7 using all the available Swift/XRT, XMM–Newton, Chandra, and NuSTAR data. Because of the high quality 2019 XMM–Newton and NuSTAR observations, we investigated in an unprecedented way the spectral and temporal properties of NGC 4559 X7. The source displayed flux variations of up to an order of magnitude and an unusual flaring activity. We modelled the spectra from NGC 4559 X7 with a combination of two thermal components, testing also the addition of a further high energy cut-off power law. We observed a spectral hardening associated with a luminosity increase during the flares, and a spectral softening in the epochs far from the flares. Narrow absorption and emission lines were also found in the RGS spectra, suggesting the presence of an outflow. Furthermore, we measured hard and (weak) soft lags with magnitudes of a few hundreds of seconds whose origin is possibly due to the accretion flow. We interpret the source properties in terms of a super-Eddington accretion scenario assuming the compact object is either a light stellar mass black hole or a neutron star.

Quasi-periodic oscillations in the long-term radio light curves of the blazar AO 0235+164

ABSTRACT We present time series analyses of three-decade long radio observations of the BL Lacertae object AO 0235+164 made at the University of Michigan Radio Astronomical Observatory operating at three central frequencies of 4.8, 8.0, and 14.5 GHz. We detected a quasi-periodic oscillation of ∼965 d in all three frequency bands in the light curve of the effectively simultaneous observations, along with strong signals at ∼1950, ∼1350, and ∼660 d. The periodicity is analysed with three methods: data-compensated discrete Fourier transform, generalized Lomb–Scargle periodogram, and Weighted Wavelet Z-transform. These methods are chosen as they have different analysis approaches toward robust measurement of claimed periodicities. The quasi-periodic oscillation at 965 ± 50 d is found to be significant (at least 3.5σ) and is persistent throughout the observation for all three radio frequencies, and the others, which may be harmonics, are comparably significant in at least the 8.0 and 14.5 GHz bands. We briefly discuss plausible explanations for the origin of such long and persistent periodicity.

Dynamical modelling of CXOGBS J175553.2−281633: a 10 h long orbital period cataclysmic variable

ABSTRACT We present modelling of the long-term optical light and radial velocity curves of the binary stellar system CXOGBS J175553.2−281633, first detected in X-rays in the Chandra Galactic Bulge Survey. We analysed 7 yr of optical I-band photometry from Optical Gravitational Lensing Experiment and found long-term variations from year to year. These long-term variations can most likely be explained with by either variations in the luminosity of the accretion disc or a spotted secondary star. The phased light curve has a sinusoidal shape, which we interpret as being due to ellipsoidal modulations. We improve the orbital period to be P = 10.34488 ± 0.00006 h with a time of inferior conjunction of the secondary star T0 = HJD 2455260.8204 ± 0.0008. Moreover, we collected 37 spectra over 6 non-consecutive nights. The spectra show evidence for an evolved K7 secondary donor star, from which we obtain a semi-amplitude for the radial velocity curve of K2 = 161 ± 6 km s−1. Using the light-curve synthesis code xrbinary, we derive the most likely orbital inclination for the binary of i = 63.0 ± 0.7 deg, a primary mass of M1 = 0.83 ± 0.06 M⊙, consistent with a white dwarf accretor, and a secondary donor mass of M2 = 0.65 ± 0.07 M⊙, consistent with the spectral classification. Therefore, we identify the source as a long orbital period cataclysmic variable star.

Long-term light curve variations of AGB stars: episodic mass-loss or binarity?

AbstractA significant fraction of the stars near the tip of the AGB phase become regular or semi-regular (Mira-type, SRs) pulsators. However, some of these light curves have shown intriguing secondary minima or sharp dips with much longer periods. Although this phenomenon shows some resemblance with the R CrB variables, the light curve is generally symmetric before and after the dip, whereas in R CrB the luminosity recovers slower after its minimum. More recently, high-resolution ALMA CO observations revealed a spiral structure around some of these stars, which suggests the presence of a stellar or sub-stellar companion. In these cases, the long-term light curve minima could be caused by periodic eclipses of the primary by a spiral circumstellar structure, and the long-period would be related to the orbital period. In this paper we discuss the pros and cons of the various proposed scenarios for the long-term minima of pulsating AGB stars.

Asteroseismology of High-Mass Stars: New Insights of Stellar Interiors With Space Telescopes

Massive stars are important metal factories in the Universe. They have short and energetic lives, and many of them inevitably explode as a supernova and become a neutron star or black hole. In turn, the formation, evolution and explosive deaths of massive stars impact the surrounding interstellar medium and shape the evolution of their host galaxies. Yet the chemical and dynamical evolution of a massive star, including the chemical yield of the ultimate supernova and the remnant mass of the compact object, strongly depend on the interior physics of the progenitor star. We currently lack empirically calibrated prescriptions for various physical processes at work within massive stars, but this is now being remedied by asteroseismology. The study of stellar structure and evolution using stellar oscillations -- asteroseismology -- has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2 and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modelling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars. Thus asteroseismology has opened a new window into calibrating stellar physics within a highly degenerate part of the Hertzsprung--Russell diagram. In this review, I provide a historical overview of the progress made using ground-based and early space missions, and discuss more recent advances and breakthroughs in our understanding of massive star interiors by means of asteroseismology with modern space telescopes.

TheXMM-Newtonserendipitous survey

Context.TheXMM-NewtonSurvey Science Centre Consortium (SSC) develops software in close collaboration with the Science Operations Centre to perform a pipeline analysis of allXMM-Newtonobservations. In celebration of the twentieth anniversary of theXMM-Newtonlaunch, the SSC has compiled the fourth generation of serendipitous source catalogues, 4XMM.Aims.The catalogue described here, 4XMM-DR9s, explores sky areas that were observed more than once byXMM-Newton. These observations are bundled in groups referred to as stacks. Stacking leads to a higher sensitivity, resulting in newly discovered sources and better constrained source parameters, and unveils long-term brightness variations.Methods.The 4XMM-DR9s catalogue was constructed from simultaneous source detection on overlapping observations. As a novel feature, positional rectification was applied beforehand. Observations with all filters and suitable camera settings were included. Exposures with a high background were discarded. The high-background thresholds were determined through a statistical analysis of all exposures in each instrument configuration. The X-ray background maps used in source detection were modelled via an adaptive smoothing procedure with newly determined parameters. Source fluxes were derived for all contributing observations, irrespective of whether the source would be detectable in an individual observation.Results.The new catalogue lists the X-ray sources detected in 1329 stacks with 6604 contributing observations over repeatedly covered 300 square degrees in the sky. Most stacks are composed of two observations, the largest one comprises 352 observations. We find 288 191 sources of which 218 283 were observed several times. The number of observations of a source ranges from 1 to 40. Auxiliary products, like X-ray full-band and false-colour images, long-term X-ray light curves, and optical finding charts, are published as well.Conclusions.4XMM-DR9s contains new detections and is considered a prime resource to explore long-term variability of X-ray sources discovered byXMM-Newton. Regular incremental releases, including new public observations, are planned.

Testing two-component models on very high-energy gamma-ray-emitting BL Lac objects

Context. It has become evident that one-zone synchrotron self-Compton models are not always adequate for very high-energy (VHE) gamma-ray-emitting blazars. While two-component models perform better, they are difficult to constrain due to the large number of free parameters. Aims. In this work, we make a first attempt at taking into account the observational constraints from very long baseline interferometry (VLBI) data, long-term light curves (radio, optical, and X-rays), and optical polarisation to limit the parameter space for a two-component model and test whether or not it can still reproduce the observed spectral energy distribution (SED) of the blazars. Methods. We selected five TeV BL Lac objects based on the availability of VHE gamma-ray and optical polarisation data. We collected constraints for the jet parameters from VLBI observations. We evaluated the contributions of the two components to the optical flux by means of decomposition of long-term radio and optical light curves as well as modelling of the optical polarisation variability of the objects. We selected eight epochs for these five objects based on the variability observed at VHE gamma rays, for which we constructed the SEDs that we then modelled with a two-component model. Results. We found parameter sets which can reproduce the broadband SED of the sources in the framework of two-component models considering all available observational constraints from VLBI observations. Moreover, the constraints obtained from the long-term behaviour of the sources in the lower energy bands could be used to determine the region where the emission in each band originates. Finally, we attempt to use optical polarisation data to shed new light on the behaviour of the two components in the optical band. Our observationally constrained two-component model allows explanation of the entire SED from radio to VHE with two co-located emission regions.

Optical counterpart to Swift J0243.6+6124

Context.Swift J0243.6+6124 is a unique system. It is the first and only ultra-luminous X-ray source in our Galaxy. It is the first and only high-mass Be X-ray pulsar showing radio jet emission. It was discovered during a giant X-ray outburst in October 2017. While there are numerous studies in the X-ray band, very little is known about the optical counterpart.Aims.Our aim is to characterize the variability timescales in the optical and infrared bands in order to understand the nature of this intriguing system.Methods.We performed optical spectroscopic observations to determine the spectral type. Long-term photometric light curves together with the equivalent width of the Hαline were used to monitor the state of the circumstellar disk. We usedBVRIphotometry to estimate the interstellar absorption and distance to the source. Continuous photometric monitoring in theBandVbands allowed us to search for intra-night variability.Results.The optical counterpart to Swift J0243.6+6124 is aV = 12.9, O9.5Ve star, located at a distance of ∼5 kpc. The optical extinction in the direction of the source isAV = 3.6 mag. The rotational velocity of the O-type star is 210 km s−1. The long-term optical variability agrees with the growth and subsequent dissipation of the Be circumstellar disk after the giant X-ray outburst. The optical and X-ray luminosity are strongly correlated during the outburst, suggesting a common origin. We did not detect short-term periodic variability that could be associated with nonradial pulsations from the Be star photosphere.Conclusions.The long-term optical and infrared pattern of variability of Swift J0243.6+6124 is typical of Be/X-ray binaries. However, the absence of nonradial pulsations is unusual and adds another peculiar trait to this unique source.

The 2020 April–June super-outburst of OJ 287 and its long-term multiwavelength light curve with Swift: binary supermassive black hole and jet activity

ABSTRACT We report detection of a very bright X-ray–UV–optical outburst of OJ 287 in 2020 April–June, the second brightest since the beginning of our Swift multiyear monitoring in late 2015. It is shown that the outburst is predominantly powered by jet emission. Optical–UV–X-rays are closely correlated, and the low-energy part of the XMM–Newton spectrum displays an exceptionally soft emission component consistent with a synchrotron origin. A much harder X-ray power-law component (Γx = 2.4, still relatively steep when compared to expectations from inverse Compton models) is detected out to 70 keV by NuSTAR. We find evidence for reprocessing around the Fe region, consistent with an absorption line. If confirmed, it implies matter in outflow at ∼0.1c. The multiyear Swift light curve shows multiple episodes of flaring or dipping with a total amplitude of variability of a factor of 10 in X-rays, and 15 in the optical–UV. The 2020 outburst observations are consistent with an after-flare predicted by the binary black hole model of OJ 287, where the disc impact of the secondary black hole triggers time-delayed accretion and jet activity of the primary black hole.

The nature of flux variations in the continua and broad-line regions of selected active galactic nuclei

ABSTRACT We present a multifractal analysis of the long-term light curves of a small sample of type 1 active galactic nuclei: NGC 4151, Arp 102B, 3C 390.3, E1821+643 and NGC 7469. We aim to investigate how the degrees of multifractality of the continuum and Hβ line vary among the five different objects and to check whether the multifractal behaviours of the continuum and the Hβ line correlate with standard accretion parameters. The backward (θ = 0) one-dimensional multifractal detrended moving average procedure was applied to light curves covering the full observation period and partial observation periods containing an equal number of epochs for each object. We detected multifractal signatures for the continua of NGC 4151, Arp 102B and 3C 390.3 and for the Hβ lines of NGC 4151 and 3C 390.3. However, we found nearly monofractal signatures for the continua of E1821+643 and NGC 7469, as well as for the Hβ lines of Arp 102B, E1821+643 and NGC 7469. In addition, we did not find any correlations between the degree of multifractality of the Hβ line and accretion parameters, while the degree of multifractality of the continuum seems to correlate with the Eddington ratio (i.e. the smaller the ratio is, the stronger the degree of multifractality). The given method is not robust, and these results should be taken with caution. Future analysis of the sampling rate and other properties of the light curves should help with better constraining and understanding these results.

A flare in the optical spotted in the changing-look Seyfert NGC 3516

Context.We present observations from the short-term intensive optical campaign (from September 2019 to January 2020) of the changing-look Seyfert NGC 3516. This active galactic nucleus is known to have strong optical variability and has changed its type in the past. It has been in the low-activity state in the optical since 2013, with some rebrightening from the end of 2015 to the beginning of 2016, after which it remained dormant.Aims.We aim to study the photometric and spectral variability of NGC 3516 from the new observations inU- andB-bands and examine the profiles of the optical broad emission lines in order to demonstrate that this object may be entering a new state of activity.Methods.NGC 3516 has been monitored intensively for the past 4 months with an automated telescope inUandBfilters, enabling accurate photometry of 0.01 precision. Spectral observations were triggered when an increase in brightness was spotted. We support our analysis of past-episodes of violent variability with the UV and X-ray long-term light curves constructed from the archivalSwift/UVOT andSwift/XRT data.Results.An increase of the photometric magnitude is seen in bothUandBfilters to a maximum amplitude of 0.25 mag and 0.11 mag, respectively. During the flare, we observe stronger forbidden high-ionization iron lines ([Fe VII] and [Fe X]) than reported before, as well as the complex broad Hαand Hβlines. This is especially seen in Hα, which appears to be double-peaked. It seems that a very broad component of ∼10 000 km s−1in width in the Balmer lines is appearing. The trends in the optical, UV, and X-ray light curves are similar, with the amplitudes of variability being significantly larger in the case of UV and X-ray bands.Conclusions.The increase of the continuum emission, the variability of the coronal lines, and the very broad component in the Balmer lines may indicate that the AGN of NGC 3516 is finally leaving the low-activity state in which it has been for the last ∼3 years.

Diversity of γ-ray and radio variability of bright blazars and implications for γ-ray emission location

Abstract Violent multi-wavelength variabilities are observed in γ-ray-selected blazars. We present an analysis of long-term light curves for eight bright blazars to explore the co-variation pattern in the γ-ray and radio bands. We extract their γ-ray light curves and spectra with data observed by the Fermi Large Area Telescope (LAT) since 2008. We find diverse co-variation patterns between the γ-ray and radio (at 43 GHz) fluxes in these sources. The γ-ray and radio fluxes of 3C 454.3 and PKS 1633+382 are correlated without any time lag, suggesting that they are from the same radiation region. Similar correlation is also observed in 3C 273 and PKS 1222+216, but the radio flux lags behind the γ-ray flux by approximately ∼160 d and ∼290 d, respectively. This likely suggests that their γ-ray emission regions are located the upstream of their radio cores at 43 GHz. The γ-ray and radio fluxes of the other four blazars are not correlated, implying that the γ-ray and radio emission may be from different regions in their jets. The γ-ray light curves of the eight blazars can be decomposed into some components with long-timescale variability and some fast spike flares. We propose that they may be attributed to the central engine activity and the magnetic reconnection process or turbulence in the local emission region, respectively.

Liverpool-Maidanak monitoring of the Einstein Cross in 2006–2019

Quasar microlensing offers a unique opportunity to resolve tiny sources in distant active galactic nuclei and study compact object populations in lensing galaxies. We therefore searched for microlensing-induced variability of the gravitationally lensed quasar QSO 2237+0305 (Einstein Cross) using 4374 optical frames taken with the 2.0 m Liverpool Telescope and the 1.5 m Maidanak Telescope. These gVrRI frames over the 2006–2019 period were homogeneously processed to generate accurate long-term multi-band light curves of the four quasar images A–D. Through difference light curves, we found strong microlensing signatures. We then focused on the analytical modelling of two putative caustic-crossing events in image C, finding compelling evidence that this image experienced a double caustic crossing. Additionally, our overall results indicate that a standard accretion disc accounts reasonably well for the brightness profile of UV continuum emission sources and for the growth in source radius when the emission wavelength increases: Rλ ∝ λα, α = 1.33 ± 0.09. However, we caution that numerical microlensing simulations are required before firm conclusions can be reached on the UV emission scenario because the VRI-band monitoring during the first caustic crossing and one of our two α indicators lead to a few good solutions with α ≈ 1.

Gamma-Ray Flares in the Long-term Light Curve of 3C 454.3

Abstract 3C 454.3 is frequently observed in the flaring state. The long-term light curve of this source has been analyzed with 9 yr (2008 August–2017 July) of data from the Fermi-LAT detector. We have identified five flares and one quiescent state. The flares have substructures with many peaks during the flaring phase. We have estimated the rise and decay time of the flares and compared with flares of other similar sources. The modeling of gamma-ray spectral energy distributions shows in most cases that a log-parabola function gives the best fit to the data. We have done time-dependent leptonic modeling of two of the flares, for which simultaneous multiwavelength data are available. These two long-lasting flares, Flare-2A and Flare-2D, continued for 95 and 133 days, respectively. We have used the average values of Doppler factor, injected luminosity in electrons, size of the emission region, and the magnetic field in the emission region in modeling these flares. The emission region is assumed to be in the broad-line region in our single-zone model. The energy losses (synchrotron, synchrotron self-Compton, external Compton) and escape of electrons from the emission region have been included while doing the modeling. Although the total jet powers required to model these flares with the leptonic model are higher compared to other sources, they are always found to be lower than the Eddington luminosity of 3C 454.3. We also select some flaring peaks and show that the time variation of the Doppler factor or the injected luminosity in electrons over short timescales can explain their light curves.

Characterization of optical light curves of extreme variability quasars over a ∼16-yr baseline

ABSTRACT We study the optical light curves – primarily probing the variable emission from the accretion disc – of ∼900 extreme variability quasars (EVQs, with maximum flux variations more than 1 mag) over an observed-frame baseline of ∼16 yr using public data from the SDSS Stripe 82, PanSTARRS-1 and the Dark Energy Survey. We classify the multiyear long-term light curves of EVQs into three categories roughly in the order of decreasing smoothness: monotonic decreasing or increasing (3.7 per cent), single broad peak and dip (56.8 per cent), and more complex patterns (39.5 per cent). The rareness of monotonic cases suggests that the major mechanisms driving the extreme optical variability do not operate over time-scales much longer than a few years. Simulated light curves with a damped random walk model generally under-predict the first two categories with smoother long-term trends. Despite the different long-term behaviours of these EVQs, there is little dependence of the long-term trend on the physical properties of quasars, such as their luminosity, BH mass, and Eddington ratio. The large dynamic range of optical flux variability over multiyear time-scales of these EVQs allows us to explore the ensemble correlation between the short-term (≲6 months) variability and the seasonal-average flux across the decade-long baseline (the rms-mean flux relation). We find that unlike the results for X-ray variability studies, the linear short-term flux variations do not scale with the seasonal-average flux, indicating different mechanisms that drive the short-term flickering and long-term extreme variability of accretion disc emission. Finally, we present a sample of 16 EVQs, where the approximately bell-shaped large amplitude variation in the light curve can be reasonably well fit by a simple microlensing model.

Monitoring of the Blazar J0238+1636 with the RATAN-600 and RT-32 in 2014−2019

The presented observation results of the blazar J0238+1636 were obtained in: 2014–2019 with the RATAN-600 radio telescope from the Special Astrophysical Observatory of the Russian Academy of Sciences at 2.3, 4.8, 8.2, 11.2, and 21.7 GHz; and 2015–2017 with the 32-m Zelenchuk and Badary radio telescopes of the Institute of Applied Astronomy of the Russian Academy of Sciences at 4.84 and 8.57 GHz. Two flares were detected on the long-term light curve. The time scale for variability on the rising branch of the first flare is τvar = 0.5 year, and the upper limit for the linear and angular sizes of the emitting region at 21.7 GHz are 0.3 pc and 0.05 mas, respectively. The brightness temperature is Tb ≥ 2.6 × 1013 K, and the Doppler factor is δ ≥ 3. In three sets of the source’s daily observations, which lasted up to three months each, no significant variability on the day-to-day scale was found after subtracting the long-term variability. In the RT-32 data, the intraday variability (IDV) was found at a frequency of 4.84 GHz in three out of 15 sessions and at 8.57 GHz in two out of 13 sessions. The characteristic times for variability are 4−5 hours.

X-ray spectral and flux variability of the microquasar GRS 1758−258 on timescales from weeks to years

We present the spectral and timing evolution of the persistent black hole X-ray binary GRS 1758−258 based on almost 12 years of observations using theRossiX-ray Timing Explorer Proportional Counter Array. While the source was predominantly found in the hard state during this time, it entered the thermally dominated soft state seven times. In the soft state GRS 1758−258 shows a strong decline in flux above 3 keV rather than the pivoting flux around 10 keV more commonly shown by black hole transients. In its 3–20 keV hardness intensity diagram, GRS 1758−258 shows a hysteresis of hard and soft state fluxes typical for transient sources in outburst. The RXTE-PCA and RXTE-ASM long-term light curves do not show any orbital modulations in the range of 2–30 d. However, in the dynamic power spectra significant peaks drift between 18.47 and 18.04 d for the PCA data, while less significant signatures between 19 d and 20 d are seen for the ASM data as well as for theSwift/BAT data. We discuss different models for the hysteresis behavior during state transitions as well as possibilities for the origin of the long term variation in the context of a warped accretion disk.

REVISITING FS AURIGAE AND ITS TRIPLE CATACLYSMIC VARIABLE SYSTEM HYPOTHESIS

A very long term variability (VLPP), with period of 875 days, was observed in the long-term light curve of FS Aurigae (FS Aur) in 2011. This periodicity was calculated over 6 cycles. We re-examined the periodicity with new observations over the past 5 yrs. A total of 18 years of observations confirm the hypothesis of a third body perturbing in a secular way the cataclysmic variable (CV). Improvements to the model such as eccentric and inclined orbits for the third body and a binary post-Newtonian correction are considered. We confirm the VLPP of FS Aur and find the new period of 857 ± 78 days. The secular perturbations are most efficient when the mass of the third body is M₃≈ 29MJ, much less than the 50MJ reported in 2011. We estimate the effect of the third body on the mass transfer rate and on the brightness of the system. We consider alternative scenarios for the VLPP. New data and analysis support the hypothesis that FS Aur is a CV in a triple system.

Spot Model for Identifications of Periods in Asynchronous Polars

Abstract We improved the discless accretion models in Wynn & King considering the effects of the changing aspect due to the white dwarf (WD) spin and the variable feeding intensity caused by the asynchronism, and set up a more general spot model that is not sensitive to the different forms of these effects and can be applied for the period analysis of the optical and X-ray light curve. The spot model can produce the power spectra compatible with the observations, and its simulations limit the ratio P spin/P orb < 2 between the powers at the WD spin and the binary orbital frequencies, which is a strong criterion for identification of periods. Then we recognize the periods for CD Ind, BY Cam, and 1RXS J083842.1-282723. The spot model reveals a complex accretion geometry in the asynchronous polars (APs), which may indicate that the complex magnetic field causes their asynchronism. We think 1RXS J083842.1-282723 is a prepolar because of its highest asynchronism and stable light curve. Giving the unstable accretion process in APs, the period analysis of the long-term light curve will make the orbital signal prominent.