A New IW And-Type Star: Karachurin 12 with Tilted Disks and Diverse cycles
Qi-Bin Sun Sheng-Bang Qian Li-Ying Zhu Qin-Mei Li Fu-Xing Li Min-Yu Li Ping Li

	
	Resolving Twin Jets and Twin Disks with JWST and ALMA:  

The Young WL 20 Multiple System
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	keywords: Binary stars; Cataclysmic variable stars; Dwarf novae; individual (Karachurin 12)
	
	
	


§ INTRODUCTION
 

Cataclysmic variables (CVs) are of considerable interest due to their unique characteristics and their contributions to astrophysical research. These systems typically consist of a white dwarf (the primary) and a late main-sequence star (the secondary). Key types of CVs include classical novae, recurrent novae, novae-like stars (NLs), dwarf novae (DNe), and magnetic CVs <cit.>. In these binary systems, the secondary star overflows its Roche lobe and transfers mass to the primary, forming a semi-detached close binary system.
When the magnetic field of the white dwarf is weak (below 1 MG), it allows for the formation of accretion disks around the white dwarf. In contrast, a stronger magnetic field (exceeding 1 MG) disrupts the accretion disk, leading to the formation of accretion curtains or columns ().

Dwarf novae (DNe) represent a subclass of CVs, which are weakly magnetic or non-magnetic CVs. In these systems, the variability is primarily driven by the accretion disks, which cause outbursts that, while less intense than those seen in novae (which involve thermonuclear reactions), occur more frequently. DNe are typically categorized into three main types: Z Camelopardalis, SU Ursae Majoris, and U Geminorum. Normal DN outbursts result from luminosity variations driven by thermal instabilities in the accretion disk. This behavior is commonly explained by the accretion disk instability model (DIM; ).

DIM posits that the accretion disk undergoes transitions between three states—cold and stable, thermally unstable, and hot and stable—driven by changes in opacity with temperature. In the low-temperature state where hydrogen is neutral (below ∼ 6000 K), the accretion disk is stable and exhibits low viscosity. As the temperature increases and hydrogen becomes partially ionized, the disk becomes hotter, more viscous, and thermally unstable. When the temperature rises sufficiently to fully ionize hydrogen (above ∼ 8000 K), the disk stabilizes again, at which point it has high viscosity, and its thermal behavior can be described by a classical S-shaped stability curve (See, e.g., ; ;  for details).


Z Camelopardalis (Z Cam) are particularly distinguished by their “standstill” behavior during the decline phase of outbursts, where their brightness stabilizes approximately 0.7 magnitudes below the peak level. DIM explains typical “standstill” by describing the disk as being in a hot stable state. When the mass transfer rate from the secondary star exceeds a critical value (Ṁ_crit), the disk remains in a hot stable state, similar to that observed in Z Cam and NLs. Z Cam have mass transfer rates close to Ṁ_crit, with slight variations potentially triggering the “standstill” phenomenon <cit.>.
However, during the “Z CamPaign” observation campaign, <cit.> observed for the first time that the “standstill” in IW And and V513 Cas did not conclude by returning to the quiescent state but instead culminated in an outburst, followed immediately by a dip and then a rapid return to “standstill”. This unusual behavior, identified as the “anomalous standstill phenomenon” by <cit.>. <cit.> categorized these objects as “IW And-type objects (or phenomena)” and proposed the existence of a previously unknown type of limit-cycle oscillation in IW And-type stars. Multiple IW And-type objects have been found in subsequent studies, such as V507 Cyg <cit.>, ST Cha <cit.>, IM Eri <cit.>, KIC 9406652 <cit.> and HO Pup <cit.>.

IW And-type phenomenon is a new challenge to DIM, and the specific physical processes about it are still under debate. 
<cit.> was one of the first to systematically explanation the IW And-type phenomenon, suggesting that mass-transfer burst is the primary cause and partially reproducing the observed effects. However, the exact trigger for these mass-transfer oburst remains unresolved.
<cit.> conducted numerical simulations based on the tilted thermal-viscous instability model, which also successfully reproduces the IW And-type phenomenon. They suggest that a tilted accretion disk allows mass from the secondary star to more easily reach the inner disk, establishing a new cycle. In this cycle, the inner disk remains nearly always in a hot state, while the outer disk undergoes repeated outbursts, producing the observed light curve characteristics of the IW And-type phenomenon.

The precession of tilted accretion disks has been observed across various types of celestial systems <cit.> and is particularly common in CVs, where the periods are typically only a few days <cit.>. In CVs, tilted accretion disks often exhibit signals known as “negative superhumps” (NSHs), with periods approximately 5% shorter than orbital period <cit.>. This phenomenon is thought to result from the retrograde precession of the tilted disk combined with the effects of mass stream from the secondary <cit.>.

Our recent research has uncovered that the depth of eclipses, the brightness minima during eclipses, the amplitude of NSHs, and their frequencies all display periodic variations that align with the precession period of the tilted disk (e.g., TV Col, SDSS J0812 and HS 2325+8205 ; ). These findings provide strong evidence for the existence of tilted disks and the origin of NSH associated with the precession of tilted disks. Furthermore, we have observed a correlation between DNe outbursts and the formation of NSHs, offering new perspectives on the origins of NSHs and the mechanisms behind DN outbursts (e.g., AH Her, ASAS J1420, TZ Per, and V392 Hya; ).

Karachurin 12 was discovered by Raul Karachurin, and we used the naming convention of the American Association of Variable Star Observers (AAVSO). Other name examples include 
FBS1726+618, ASASSN-V J172710.78+614528.0, and SDSS J172710.79+614527.8. Kato et al. (2018)(vsnet-chat 7938)[http://ooruri.kusastro.kyoto-u.ac.jp/mailarchive/vsnet-chat/7938] suggests that Karachurin 12 be classified as a Z Cam-type DN.
There has been no in-depth analysis of Karachurin 12 to date, making this paper the first detailed study. This paper will determine the parameters and light curve characteristics, and use dip as an index and NSH as a probe to investigate the IW And-type phenomenon in Karachurin 12, offering new observational evidence to better understand this phenomenon.



The structure of this paper is outlined as follows:
Section <ref> details the data sources utilized in this paper.
Section <ref> focuses on identifying periodic information for Karachurin 12.
Section <ref> provides an in-depth analysis of the IW And-type phenomenon.
Section <ref> explores the evolution of the NSH in relation to the IW And phenomenon.
Section <ref> discusses the physical processes of the IW And phenomenon in the context of current research advances and the results presented in this paper.
Finally, Section <ref> presents the conclusions.











§ SOURCES OF OBSERVATION DATA
 


The All-Sky Automated Survey for Supernovae (ASAS-SN; ) is a long-term initiative dedicated to rapid supernova monitoring across the sky (V < 17 mag) and also tracking numerous variable stars <cit.>. Karachurin 12 was photometrically observed in the V-band by ASAS-SN from HJD 2456675.131 to HJD 2458372.751, with an average magnitude of 14.33 mag (see Fig. <ref>). Data were retrieved from the ASAS-SN Variable Stars Database [https://asas-sn.osu.edu/variables].

The Zwicky Transient Facility (ZTF; ) is a northern-sky optical survey focused on high-cadence time-domain astronomy, utilizing the 48-inch Samuel Oschin Schmidt Telescope at Palomar Observatory. ZTF operates with three custom filters: ZTF_zg, ZTF_zr, and ZTF_zi. Karachurin 12 was observed in these bands over approximately 6 years (from HJD 2458198.8895 to HJD 2460363.9715; see Fig. <ref>). Data were obtained from the Lasair database [https://lasair.roe.ac.uk/].

The Transiting Exoplanet Survey Satellite (TESS; ) is primarily designed for exoplanet detection but has also collected a significant amount of variable star data. TESS conducts sky surveys in sectors, observing each sector for approximately one month in the 600 to 1000 nm wavelength range, utilizing both long-cadence (30 minutes) and short-cadence (2 minutes) modes. It produces Simple Aperture Photometry (SAP) and Pre-Search Data Conditional Simple Aperture Photometry (PDCSAP) light curves (see  and  for details). Karachurin 12 was observed across 35 sectors over approximately 5 years in short-cadence mode (see Fig. <ref>), with detailed observation data listed in Table <ref>. In this paper, we used the SAP data, which were downloaded from the Mikulski Archive for Space Telescopes (MAST)[https://mast.stsci.edu/].











§ PERIOD DETERMINATION
 


The ASAS-SN, ZTF, and TESS observations all exhibit IW And-type phenomena with notable variations in outburst amplitudes. We analyzed the periods for each dataset individually using the  software (details in ). For ZTF, frequency analyses were conducted separately on the ZTF_zg, ZTF_zr, and ZTF_zi bands. The period of IW And-type phenomena was determined to be 31.98(5) days from ASAS-SN data (see Fig. <ref> a) and 38.095(2) days from TESS data (see Fig. <ref> c). For ZTF, the cycle periods were 35.82(3) days for ZTF_zg, 35.97(3) days for ZTF_zr, and 36.60(6) days for ZTF_zi (see Fig. <ref> b). Averaging these values, the period of the IW And-type phenomena is found to be 35.69(3) days.

The TESS data, with a 120-second exposure time, provides crucial insights into detailed variations in our study. Frequency analysis reveals periodic signals with periods of f_2 = 0.201662(6) d^-1, f_3 = 3.155674(13) d^-1, f_4 = 3.355861(9) d^-1, and f_5 = 6.311376(7) d^-1, in addition to the IW And phenomenon. 
Notably, f_5 is approximately 2 × f_2, confirming it as the second harmonic of f_2. The relationship among f_2, f_3, and f_4 can be expressed as f_2 ≈ f_4 - f_3, reflecting the connection between the precession period of the accretion disk, the orbital period, and the NSH period (1/P_prec = 1/P_nsh - 1/P_orb). 
From this, we infer that f_2 corresponds to a precession signal with a period of 4.9588(2) days for the tilted disk, f_3 represents an orbital period of 0.3168895(13) days, f_4 corresponds to the NSH period of 0.2979861(8) days, and f_5 denotes the second harmonic of the orbital period. No eclipses were observed in Karachurin 12, aside from the ellipsoidal modulation, suggesting that it is a low-inclination CV.
Excess is a key parameter in the study of NSHs, defined as ϵ^- = (P_nsh - P_orb) / P_orb. For Karachurin 12, ϵ^- is determined to be -0.059653(7). Comparing this value with the empirical relationship between orbital period and ϵ^- derived by <cit.> from a large sample of NSHs, we find a general agreement with their results (see Fig. <ref>).



We have identified for the first time that Karachurin 12 not only exhibits the IW And phenomenon but also represents a new NSH system with a tilted disk precession signal. Recent studies suggest that the IW And phenomenon may be linked to tilted disks <cit.>. The observation of both the IW And phenomenon and the tilted disk in Karachurin 12 supports these recent findings and aligns with these expectations.





§ IW AND-TYPE PHENOMENON
 



 §.§ Identification of dips
 

Typical IW And objects are characterized by standstill or quasi-standstill phases interrupted by brightening events or outbursts, which are collectively referred to as outbursts. Unlike Z Cam-type stars that return to a quiescent state, these systems undergo damping oscillations following outbursts, resulting in a cycle of standstill–outburst–damping oscillations <cit.>.

In the case of Karachurin 12, we observe a notable IW And phenomenon where the typical cyclic sequence includes a quasi-standstill phase interrupted by an outburst, followed immediately by a dip. Unlike other IW And objects, the quasi-standstill phase in Karachurin 12 does not show significant damping oscillations. Instead, it reflects the signal of accretion disk precession, although this precession signal is not prominent in every quasi-standstill phase (see Fig. <ref>). In addition to the standard cycles, Karachurin 12 exhibits unique variations, with relatively stable outburst and quasi-standstill phases, and variations mainly arising from the dip. Therefore, we use the dip as an index to study these special cycles.

The IW And phenomenon has been documented through surveys conducted by ASAS-SN, ZTF, and TESS. ASAS-SN data, being relatively dispersed, contrasts with the more precise photometric results provided by TESS. Our initial approach involved identifying the positions of the dips based on their occurrence times and labeling them accordingly (e.g., dip2459830, as shown in Table <ref>). To determine the precise location of these dips, we employed Gaussian fitting and identified the minimum points of the dips.

For TESS data, where the dip profiles were relatively complete, we used Gaussian fitting to calculate the dip parameters. For ZTF and ASAS-SN data, we determined the timing of the dips from the minimum points. For ZTF data, the ZTF_zg band, with its greater detail and larger amplitude variations, was used to define the dip parameters. In the ASAS-SN dataset, only one particularly complete profile was identified. In total, we recognized 23 dips, 8 of which were determined through Gaussian fitting (see Table <ref>).




 §.§ Different types of dip and corresponding cycles
 

Next, we use dips as indices to study the cyclical nature of the IW And phenomenon. Among the identified dips, 16 are classified as normal cycles, characterized by a quasi-standstill phase interrupted by an outburst, followed by a dip. We designate these as Type_I dips (see Fig. <ref>). For Type_I, eight dips were analyzed using Gaussian fitting (see Figs. <ref> and <ref>). The width of each dip was determined as twice the full width at half maximum (FWHM) of the fit, with an average width of 3.86(10) days and a depth of 0.32(8) mag. The quasi-standstill duration typically ranges from about 14.0 to 14.5 mag and lasts between 10 and 20 days.

The deepest dip observed in Karachurin 12 is dip2459057 (see Fig. <ref>), with a depth of approximately 1.5 mag and a duration of about 15 days. This dip is notably 4 to 5 times wider and deeper than a typical dip. Unusually, it was discovered not following an outburst phase but rather within a cycle that included an outburst, a quasi-standstill, and then the dip (outburst - quasi-standstill - dip - outburst). This deviation from the Type_I pattern leads us to classify it as Type_II. Another example of Type_II is dip2457977 (see Fig. <ref>a).

Another distinct case is dip2458284 (see Fig. <ref>), where the cycle consists of an outburst followed by a 30-day standstill, which is then truncated by a dip. This is followed by a new standstill phase, truncated by another outburst, resulting in the cycle: outburst - quasi-standstill - dip - quasi-standstill - outburst. We designate this as Type_III. The key difference between Type_III and Type_II is that Type_III is followed by another standstill. Similar variations may be present in dip2458375 (see Fig. <ref>), though the data is less clear due to gaps.

In dips 2459336 and 2459344, two dips occur within a single IW And cycle, approximately 8 days apart (see Fig. <ref>). This pattern can be attributed to precession (4.9588(2) days) followed by a quasi-standstill. A similar pattern is observed in dips 2458318 and 2458326 (see Fig. <ref>a). Unlike Type_I, where only a single dip is observed, these double dips are classified as Type_IV. This type of variation may be analogous to the damping oscillations observed in IM Eri <cit.>. However, further observational data is needed to confirm these double-dip occurrences.

To compare the four types of dips, we calculated the time intervals between clearly defined dips and the preceding and following outburst peaks, with an uncertainty of 2 days. Results show that Type_I dips typically occur about 11 days after the previous outburst peak and 15 to 35 days before the next outburst peak (see Fig. <ref>b). This suggests that the interval between Type_I dips and the preceding outburst is relatively stable, while the duration of the quasi-standstill phase varies.

In contrast, Type_II dips occur much further from the preceding outburst and closer to the subsequent one compared to Type_I (see Fig. <ref>b). Type_III dips are separated from both preceding and following outbursts by more than 20 days (see Fig. <ref>b). For Type_IV, the first dip in the double-dip structure shows intervals to the preceding and following outbursts consistent with those of Type_I.

By indexing dips according to their position within the cycle, we observed various dip types and their corresponding cycles in Karachurin 12. Our study reveals the following:
(i) Among the 23 dips analyzed, 18 occur after an outburst, indicating that dips are more likely to follow an outburst phase.
(ii) However, a dip does not always follow an outburst phase, as seen in Type_II and Type_III (see Fig. <ref>).
(iii) A dip does not always have to be followed by a quasi-standstill and can directly transition into an outburst phase, as observed in Type_II (see Fig. <ref>).
(iv) Not every cycle must include a dip (see the yellow regions of dip2459057 in Fig. <ref>).










§ EVOLUTION OF NSH WITH THE IW AND PHENOMENON
 



 §.§ Extraction of NSH information
 

Current research indicates that the IW And phenomenon is associated with tilted accretion disks. To explore the relationship between NSHs and the IW And phenomenon and to provide new observational evidence, we propose using NSHs as a diagnostic tool. The origin of NSHs is closely linked with mass transfer streams from the secondary star and variations within the accretion disk. Given their higher completeness and continuity compared to precession signals observed in Karachurin 12, NSHs are an ideal probe for this investigation.

To study the evolution of NSHs, we follow the methodology outlined by <cit.> for excluding long-term trends and orbital signals. We employed locally weighted regression (LOWESS; ) to remove the long-term trend (see Fig. <ref>a). Orbital signals were subsequently removed using  software (details in ). The evolution of NSH amplitude and period is calculated as follows:

(i) Frequency Analysis: Using , we performed a frequency analysis of the light curves after removing the long-term trend for each sector, identifying signals with signal-to-noise ratios greater than 3. The periodogram for each sector is shown in Figure <ref>, and the statistical results are listed in Table <ref>.

(ii) Amplitude and Phase Determination: The amplitude and phase information for each signal were obtained using the fitting equation provided by  (see Fig. <ref>c):

    mag(t) = Z + ∑Amplitude_i ·sin(2π· (frequency_i · t + phase_i))

where Z, Amplitude_i, frequency_i, and phase_i are the fitted intercept, amplitude, frequency, and phase, respectively.

(iii) Isolation of NSH Signal: Based on the fit results, we adjusted the detrended light curve to isolate the NSH signal by subtracting both the orbital signal and its second harmonic (as illustrated in Fig. <ref>c). A sinusoidal fit was then applied to the residual data (see Fig. <ref>d).

(iv) Gaussian Fitting: To determine the NSH maxima and minima, we applied a Gaussian fit (see Fig. <ref>e). The NSH amplitude was calculated using the following equation:

    ΔAmplitude_nsh = ( minima_before, mag + minima_after, mag) / 2 - maxima_mag/2

Here, minima_before, mag and minima_after, mag refer to the minima before and after the NSH maxima, respectively. The calculated amplitudes are shown as black points in Figure <ref>b. Note that some NSH amplitudes could not be determined due to significant weakening of the NSHs.

(v) Segmented Frequency Analysis: To validate the NSH results from step (iv) and address issues with unclear contours, we performed a segmented frequency analysis of the light curves after removing long-term trends and orbital signals. The data were initially divided into one-day segments for periodic analysis (indicated by the blue points in Fig. <ref>b and Fig. <ref>c). The data were then re-divided into two-day segments for further analysis (shown by the red points in Figs. <ref>b and <ref>c). This approach aimed to provide a clearer profile of the frequency and amplitude evolution of the NSHs.

(vi) Continuous Wavelet Transform (CWT): Finally, in agreement with <cit.>, we applied the CWT <cit.> to the light curves after removing long-term trends and orbital signals. This method complemented steps (iv) and (v) and facilitated cross-validation of the NSH information (see Fig. <ref>c).



 §.§ The evolution of NSH
 

A comparison of the results from steps (iv), (v), and (vi) reveals consistent trends with the following characteristics:

(a) The NSH shows a marked weakening starting from sector 73, becoming undetectable in sectors 76 and 77, and then weakly recovering in sectors 78 and 79. For detailed information, refer to Figures <ref> and <ref>c. Notably, no significant IW And phenomenon is observed after the outburst ends in sector 75 (see Fig. <ref>d), suggesting a potential link between the IW And phenomenon and NSHs.

(b) No discernible regularity in the period of NSHs was detected (see Fig. <ref>c), indicating that the NSH frequency does not vary with the IW And cycle in Karachurin 12.

(c) The amplitude of the NSH is significantly correlated with the outburst phases, decreasing during the rise of an outburst and increasing during its recession. The maximum NSH amplitude is observed during the quasi-standstill phase (see Figs. <ref> and <ref>).

(d) We analyzed the dip in three phases: ingress dip, minima, and egress dip. The ingress and egress dips are highlighted in yellow and magenta, respectively, in Figures <ref>a and <ref>b. A linear fit was applied to the NSH amplitude during the relatively complete ingress dip (fitting the black points). The results indicate that the NSH amplitude for the ingress dip continues to rise, reflecting the trend of the outburst recession phase. There is no evidence that the NSH amplitude evolution reverses at the dip minima, suggesting that the dip minima may not represent a turning point. Additionally, the NSH amplitudes during the egress dips of dip2458870 and dip2459711 continue to show an increasing trend.












§ DISCUSSION
 

The DIM explains the standstill phase observed in regular Z Cam systems by proposing that Z Cam has a mass transfer rate that approaches a critical value <cit.>. Fluctuations in this mass transfer rate can drive the system into a hot state, resulting in a brightness standstill <cit.>. According to the DIM, such a standstill should eventually end with a return to quiescence. However, the IW And phenomenon, where the standstill ends with an outburst, poses a challenge to this model. The DIM alone cannot account for recurring outbursts while the accretion disk remains in a hot state <cit.>.

The origin of NSHs is theorized to be linked to periodic variations in the energy released by the impact of mass streams from the secondary star interacting with a tilted, retrogradely precessing disk <cit.>. Several researchers have successfully modeled NSHs based on this framework <cit.>. However, there is still no consensus on the specific physical mechanisms responsible for the tilt and retrograde precession of the disk.
In this section, we propose using NSHs as a diagnostic tool to explore the origins of the IW And phenomenon, integrating recent discoveries to gain further insights.




 §.§ Mass Transfer Outburst
 

Initially, variations in the mass transfer rate were proposed to explain DN outbursts through the mass-transfer burst model (MTB;  and ). However, this explanation is not universally accepted.
<cit.> used simulations of V513 Cas, assuming that mass-transfer bursts followed by dips could reproduce the outbursts and dips seen in the IW And cycle (see figure 2 in ). Despite this approach, they did not identify the underlying physical processes and suggested that the magnetic activity of the secondary star is a more likely cause. They explained the termination of standstills with outbursts (a scenario not predicted by the DIM) as a result of mass-transfer bursts from the secondary superimposed on the thermally stable state of Z Cam, with dips resulting from fluctuations in mass transfer.

In our study, we observed that the amplitude of the NSH varied with the IW And phenomenon in Karachurin 12. Specifically, the NSH amplitude decreased as the outburst intensified and increased as the outburst diminished. Notably, the NSH amplitude continued to rise during the ingress dip, with the maximum amplitude observed during the standstill.

It is widely accepted that the accretion disk radius expands during DN outbursts, a factor frequently considered in DN outburst models (e.g., ) and crucial in explaining the superoutbursts of SU UMa systems (e.g., ). During outbursts, the disk expands due to significant angular momentum transfer to the outer edge from the accretion of large amounts of matter at the inner edge. Conversely, during quiescence, the disk's outer radius contracts as it accumulates low angular momentum mass from the secondary star’s gas stream, which has less specific angular momentum than the outer disk (e.g., ).

If, as suggested by MTB, a standstill is interrupted by an outburst due to a burst in the mass transfer rate, the behavior of the accretion disk during this period becomes crucial. Specifically, mass-transfer rate bursts would lead to a shrinking of the accretion disk, which should increase the energy released by the mass streams from the secondary as the outburst rises and decrease it as the outburst weakens. This scenario would predict that the NSH amplitude should increase as the outburst rises and decrease as the outburst weakens, contrary to our observations in Karachurin 12.
Moreover, MTB implies that a dip is caused by a decrease in the mass transfer rate. According to this model, the combined effects of disk expansion and reduced mass streams should lead to a significant dip in NSH amplitude. However, our observations of Karachurin 12 show an increase in NSH amplitude during the ingress dip, contradicting the predictions of MTB. Therefore, we conclude that MTB does not adequately explain the variations in NSH amplitude observed in Karachurin 12.

Instead, we propose that the variation in NSH amplitude during outbursts in Karachurin 12 is consistent with observations from AH Her, ASAS J1420, TZ Per, and V392 Hya <cit.>. In this scenario, the mass transfer remains relatively stable. As the outburst progresses, the accretion disk expands, causing the Lagrangian point L1 to move closer to the disk. This reduces the energy released by the mass streams, leading to a decrease in NSH amplitude as the outburst intensifies and an increase in NSH amplitude as the outburst subsides.





 §.§ Tilted Thermally Unstable Disk
 

In studies of V507 Cyg, IM Eri, and FY Vul, <cit.> proposed that the IW And-type phenomenon represents a previously unknown limit cycle oscillation. Kato suggested that the standstill observed in IW And-type systems corresponds to an extended period during which the inner region of the accretion disk remains in a hot state. He also proposed that this standstill phase is eventually terminated by a thermal instability originating from the disk's outer regions, which leads to outbursts that interrupt the standstill.

Building on Kato's ideas, <cit.> explored different scenarios using a tilted, thermally unstable disk model (referred to as the tilted-DIM). Their three-dimensional hydrodynamic simulations, particularly Model B1, partially reproduced the IW And phenomenon under conditions of high mass transfer rates. Although they were able to reproduce some aspects of the IW And phenomenon, they acknowledged that their simulations needed further refinement to fully explain the details. They proposed that the tilted disk allows mass streams to enter the inner region, keeping it in a hot state for extended periods, thereby maintaining the standstill phase. Meanwhile, the outer disk remains relatively cool. Once enough matter accumulates, it triggers an outburst that interrupts the standstill. Oscillations during the standstill phase are caused by alternating cold and hot waves propagating through the middle region of the disk. A sufficiently strong cold wave reaching the inner disk can lead to a dip in brightness.

In our study of Karachurin 12, we analyzed IW And cycles indexed by dips and found diversity in their patterns:
(i) A dip is more likely to follow an outburst.
(ii) A dip can occur after a standstill.
(iii) A dip can be followed by an outburst without a preceding standstill.
(iv) Not every cycle includes a dip.

Except for the first pattern, the observed details in Karachurin 12 align with the simulation results of <cit.>. For example, their Model B1 shows multiple dips following a standstill (referred to as mid-brightness), and a dip can transition directly into an outburst (see figures 11 and 12 of ). Additionally, their Model C1 does not include a dip. The radius of the accretion disk increases with outbursts and decreases during dips, consistent with the changes in NSH amplitude observed in Karachurin 12 (where NSH amplitude decreases during disk expansion and increases during disk contraction). Most importantly, we observed a significant weakening of the NSH amplitude starting from sector 73, with complete undetectability and disappearance of the IW And phenomenon in sectors 76 and 77. This supports the existence of a correlation between the tilted disk and the IW And phenomenon.

Regarding the observation that a dip is more likely to occur after an outburst in Karachurin 12, this can still be explained by the tilted-DIM. During a standstill, the inner disk remains hot, the outer disk is cool, and the middle of the disk has an intermediate temperature. When a significant amount of mass accumulates in the outer disk and an outburst begins, the entire accretion disk transitions into a high-viscosity state (higher than during the standstill phase). This enhanced mass transport facilitates the propagation of a cooling wave into the inner disk as the outburst subsides, leading to the formation of a deep dip following the outburst.

In <cit.>'s simulations, they also estimated the precession rate, suggesting that the precession rate (v_pre / v_orb) of the accretion disk varies periodically with outbursts. However, we found that the NSH frequency (v_nsh = v_pre + v_orb) for Karachurin 12 does not vary significantly, indicating no substantial change in the precession rate. Therefore, we suggest that the tilted-DIM simulations need further refinement.

In conclusion, while the tilted-DIM is a valid framework for explaining the IW And phenomena observed in Karachurin 12, further optimization of the simulations is required to account for the detailed variations in the IW And cycle.








§ CONCLUSIONS
 


This paper presents a detailed analysis of the newly identified IW And object, Karachurin 12, using photometric data from ASAS-SN, ZTF, and TESS. Our main findings are summarized as follows:


(1) Frequency analysis of the data reveals that the IW And cycle period for Karachurin 12 is 35.69(3) days. TESS data analysis identifies Karachurin 12 as a new NSH system with an accretion disk precession signal. We have determined the accretion disk precession period, orbital period, and NSH period for Karachurin 12 to be 4.9588(2) days, 0.3168895(13) days, and 0.2979861(8) days, respectively.

(2) This paper analyzes the IW And cycles in Karachurin 12 using dips as an index. A Gaussian fit to the relatively complete dip observed in the TESS photometry yields an average dip width of 3.86(10) days and a depth of 0.32(8) mag. The primary cycle patterns observed are as follows:
(i) outburst - dip - quasi-standstill - outburst;
(ii)outburst - quasi-standstill - outburst;
(iii) outburst - quasi-standstill - dip - quasi-standstill - outburst;
(iv) outburst - dip - dip - quasi-standstill - outburst;
(v) outburst - quasi-standstill - outburst. We counted the times of different dip distances from the peak of the outburst (both pre- and post-dip), again revealing the presence of different cycles.
These patterns highlight the diversity and complexity of IW And cycles. It is important to note that some of these cycles in Karachurin 12 have limited samples and require further validation. 

(3) We used the difference between the maxima and minima, segmented frequency analysis, and the Continuous Wavelet Transform method to calculate the information of NSH. The results show that NSH amplitude decreases with outburst rise and increases with outburst recession. In the ingress dip phase NSH amplitude is allowed to continue to increase seems to continue the trend of outburst recession. No significant changes in the NSH period with the IW And cycle were observed. We suggest that this behaviour is caused by a decrease in the energy released from the mass stream due to a larger radius of the accretion disk during the outburst interval, and an increase in the energy released from the mass stream due to a smaller radius of the outburst recession. Regarding the continuous increase during the ingress dip we still suggest that it corresponds to a decrease in the radius of the accretion disk. 



(4) We discuss the two dominant theories on the origin of the IW And phenomenon in conjunction with the phenomenon in Karachurin 12. We find that the mass-transfer burst model leads to changes in NSH amplitudes that are the opposite of those observed in Karachurin 12. Therefore, we suggest that the mass transfer burst model cannot explain the IW And cycle in Karachurin 12. Except for the feature of an outburst followed by a dip, most of the observed cycle details are consistent with the results from <cit.>'s simulations of a tilted, thermally unstable disk. For instance, their simulations reproduce scenarios where the standstill is interrupted by a dip, dips transition directly into outbursts, and some cycles lack significant dips. Furthermore, the tilted thermally unstable disk model can also account for the outburst followed by a dip scenario. In this model, the viscosity coefficient during an outburst is significantly higher than during the standstill phase, enhancing the material transport capability of the accretion disk. This increased transport capability facilitates the propagation of cooling waves into the inner disk as the outburst wanes.
Additionally, our results reveal that NSHs begin to decrease in sector 73 of the TESS data, with undetectability in sectors 76 and 77 coinciding with the disappearance of the IW And phenomenon. This suggests a potential link between the IW And phenomenon and a tilted disk. Therefore, we propose that the tilted thermally unstable disk model effectively explains the IW And phenomenon in Karachurin 12. However, improvements are needed in the simulations of this model to better capture the detailed dynamics of the IW And cycles.










§ ACKNOWLEDGEMENTS


This work was supported by National Key R&D Program of China (grant No. 2022YFE0116800), the National Natural Science Foundation of China (Nos. 11933008). We are grateful to the All-Sky Automated Survey for Supernovae for their valuable V-band photometric data of Karachurin 12, which were crucial for our analysis. Our thanks also go to the Zwicky Transient Facility for their high-cadence observations using their custom filters, which provided important temporal coverage of Karachurin 12. Additionally, we appreciate the contributions of the Transiting Exoplanet Survey Satellite for its comprehensive monitoring of variable stars, including Karachurin 12, which greatly enhanced our study. These datasets were instrumental in advancing our understanding of the IW And phenomenon and the behavior of Karachurin 12. 

cas-model2-names




§ APPENDIX

The appendix includes the following figures and tables:
Figure <ref>: Displays 16 standard cycles of Karachurin 12.
Figure <ref>: Shows special cycles and their corresponding dips relative to outburst distance.
Figure <ref>: Presents the periodograms for each sector.
Table <ref>: Contains details of the TESS observations.
Table <ref>: Provides information on the dips.
Table <ref>: Lists statistics of significant signals in each sector.




























cccccccccccccccccc
	
	
	Frequency analysis results for different sectors.

	
	
	
	
	Sector   Fre.   err   Amp.   err   Phase   err   S/N   Sector   Fre.   err   Amp.   err   Phase   err   S/N

	
	   [1/d]   [1/d]   [mag]   [mag]   [rad]   [rad]          [1/d]   [1/d]   [mag]   [mag]   [rad]   [rad]       

	16c
	Table  continued from previous page 

	Sector   Fre.   err   Amp.   err   Phase   err   S/N   Sector   Fre.   err   Amp.   err   Phase   err   S/N

	
	   [1/d]   [1/d]   [mag]   [mag]   [rad]   [rad]          [1/d]   [1/d]   [mag]   [mag]   [rad]   [rad]       

	16c
	  

	ALL   0.026    1.10E-06   0.115    4.11E-04   0.267    5.68E-04   20.56    49   3.150    1.68E-02   0.009    2.71E-04   0.249    3.04E-02   4.14

	ALL   0.202    6.17E-06   0.020    4.11E-04   0.149    3.20E-03   4.13    49   3.368    4.65E-03   0.040    3.34E-04   0.359    8.44E-03   18.76

	ALL   3.156    1.33E-05   0.009    4.11E-04   0.722    6.90E-03   14.09    49   6.314    1.28E-02   0.013    2.95E-04   0.057    2.31E-02   13.74

	ALL   3.356    8.87E-06   0.014    4.11E-04   0.293    4.60E-03   22.05    50   3.177    2.47E-02   0.006    2.75E-04   0.566    4.47E-02   3.04

	ALL   6.311    8.62E-06   0.015    4.11E-04   0.585    4.47E-03   43.07    50   3.356    6.03E-03   0.031    3.38E-04   0.179    1.09E-02   15.29

	14   3.159    1.05E-02   0.018    3.43E-04   0.348    1.90E-02   9.09    50   6.312    1.04E-02   0.016    3.02E-04   0.348    1.89E-02   13.34

	14   3.360    6.11E-03   0.034    3.75E-04   0.437    1.11E-02   17.74    51   3.341    7.39E-03   0.032    4.34E-04   0.423    1.34E-02   13.26

	14   6.313    1.17E-02   0.016    3.28E-04   0.781    2.12E-02   14.63    51   6.307    1.55E-02   0.013    3.67E-04   0.530    2.82E-02   9.01

	15   3.154    1.45E-02   0.011    2.96E-04   0.942    2.63E-02   6.39    52   3.370    6.50E-03   0.035    4.14E-04   0.623    1.18E-02   16.69

	15   3.355    8.98E-03   0.021    3.37E-04   0.851    1.63E-02   12.05    52   6.312    1.51E-02   0.013    3.66E-04   0.340    2.75E-02   11.96

	15   6.307    1.04E-02   0.017    3.15E-04   0.260    1.89E-02   14.12    53   3.353    4.45E-03   0.043    3.48E-04   0.131    8.08E-03   20.67

	16   3.156    1.40E-02   0.011    2.77E-04   0.385    2.54E-02   8.09    53   6.311    1.14E-02   0.015    3.09E-04   0.714    2.07E-02   13.78

	16   3.348    1.15E-02   0.014    2.86E-04   0.254    2.08E-02   10.42    54   3.359    5.24E-03   0.039    3.70E-04   0.044    9.50E-03   17.81

	16   6.311    1.14E-02   0.015    3.02E-04   0.246    2.07E-02   13.43    54   6.312    1.30E-02   0.013    3.09E-04   0.937    2.35E-02   11.47

	17   3.155    1.01E-02   0.017    3.09E-04   0.235    1.84E-02   9.22    55   3.365    5.41E-03   0.039    3.78E-04   0.135    9.82E-03   18.09

	17   3.360    7.84E-03   0.024    3.39E-04   0.927    1.42E-02   13.30    55   6.313    1.32E-02   0.014    3.44E-04   0.544    2.40E-02   12.84

	17   6.313    9.85E-03   0.016    2.87E-04   0.794    1.79E-02   15.12    56   3.145    3.06E-02   0.005    2.89E-04   0.097    5.55E-02   3.12

	19   3.154    8.33E-03   0.018    2.75E-04   0.010    1.51E-02   10.98    56   3.357    6.93E-03   0.026    3.29E-04   0.603    1.26E-02   15.22

	19   3.352    6.88E-03   0.024    3.00E-04   0.302    1.25E-02   14.77    56   6.315    1.09E-02   0.016    3.06E-04   0.422    1.97E-02   14.04

	19   6.311    1.03E-02   0.014    2.60E-04   0.307    1.87E-02   15.43    57   3.148    3.12E-02   0.007    4.23E-04   0.792    5.67E-02   3.51

	20   3.152    1.00E-02   0.014    2.50E-04   0.780    1.82E-02   9.22    57   3.357    8.39E-03   0.030    4.59E-04   0.037    1.52E-02   14.41

	20   3.352    6.95E-03   0.023    2.85E-04   0.334    1.26E-02   15.39    57   6.310    1.93E-02   0.012    4.34E-04   0.641    3.51E-02   10.99

	20   6.313    9.99E-03   0.015    2.64E-04   0.695    1.81E-02   16.20    58   3.156    2.29E-02   0.009    3.82E-04   0.312    4.15E-02   5.11

	21   3.157    7.66E-03   0.020    2.72E-04   0.580    1.39E-02   11.83    58   3.354    9.26E-03   0.025    4.21E-04   0.182    1.68E-02   14.32

	21   3.360    5.80E-03   0.028    2.95E-04   0.399    1.05E-02   17.26    58   6.309    1.81E-02   0.012    4.00E-04   0.025    3.29E-02   12.32

	21   6.314    8.54E-03   0.016    2.55E-04   0.693    1.55E-02   17.95    59   3.164    2.57E-02   0.011    5.14E-04   0.614    4.66E-02   5.37

	22   3.157    5.97E-03   0.028    3.00E-04   0.544    1.08E-02   13.78    59   3.347    1.79E-02   0.017    5.36E-04   0.213    3.25E-02   8.20

	22   3.359    5.90E-03   0.030    3.24E-04   0.119    1.07E-02   15.29    59   6.310    2.48E-02   0.012    5.25E-04   0.184    4.49E-02   8.73

	22   6.314    1.04E-02   0.014    2.70E-04   0.647    1.88E-02   15.86    60   3.160    2.01E-02   0.017    6.03E-04   0.775    3.64E-02   8.15

	23   3.161    1.05E-02   0.016    2.97E-04   0.763    1.90E-02   7.59    60   3.356    2.38E-02   0.014    5.84E-04   0.359    4.32E-02   6.71

	23   3.357    5.32E-03   0.036    3.45E-04   0.918    9.65E-03   17.61    60   6.310    2.71E-02   0.012    5.67E-04   0.733    4.92E-02   8.65

	23   6.310    1.09E-02   0.016    3.16E-04   0.342    1.97E-02   14.97    73   3.155    2.43E-02   0.011    4.88E-04   0.970    4.41E-02   5.73

	24   3.152    1.39E-02   0.015    3.67E-04   0.341    2.52E-02   7.31    73   3.349    4.86E-02   0.006    4.75E-04   0.449    8.81E-02   3.01

	24   3.349    1.03E-02   0.021    3.84E-04   0.714    1.86E-02   10.65    73   6.314    2.01E-02   0.014    5.06E-04   0.664    3.65E-02   9.22

	24   6.311    1.50E-02   0.013    3.53E-04   0.417    2.72E-02   12.50    74   3.159    2.52E-02   0.010    4.44E-04   0.838    4.58E-02   5.98

	25   3.157    9.91E-03   0.019    3.43E-04   0.485    1.80E-02   8.26    74   3.368    1.98E-02   0.013    4.53E-04   0.914    3.60E-02   8.15

	25   3.364    5.68E-03   0.041    4.19E-04   0.912    1.03E-02   17.81    74   6.311    1.51E-02   0.017    4.75E-04   0.593    2.74E-02   12.92

	25   6.311    9.73E-03   0.021    3.72E-04   0.422    1.76E-02   17.89    75   3.158    2.02E-02   0.013    4.76E-04   0.920    3.67E-02   5.91

	26   3.156    7.72E-03   0.022    3.02E-04   0.463    1.40E-02   12.59    75   3.354    2.94E-02   0.009    4.67E-04   0.287    5.33E-02   4.20

	26   3.365    7.54E-03   0.024    3.24E-04   0.998    1.37E-02   13.99    75   6.310    1.72E-02   0.016    4.89E-04   0.980    3.12E-02   12.83

	26   6.313    1.19E-02   0.013    2.87E-04   0.410    2.16E-02   14.78    76   3.154    2.82E-02   0.010    5.02E-04   0.727    5.11E-02   5.66

	40   3.153    8.71E-03   0.015    2.31E-04   0.652    1.58E-02   10.08    76   6.313    1.38E-02   0.021    5.19E-04   0.889    2.50E-02   14.25

	40   3.358    5.71E-03   0.026    2.67E-04   0.569    1.04E-02   17.86    77   3.158    1.64E-02   0.019    5.54E-04   0.843    2.97E-02   9.86

	40   6.312    8.62E-03   0.016    2.43E-04   0.363    1.56E-02   18.98    77   6.311    1.90E-02   0.015    5.30E-04   0.998    3.44E-02   9.68

	41   3.158    9.31E-03   0.014    2.36E-04   0.386    1.69E-02   9.69    78   3.151    1.67E-02   0.019    5.84E-04   0.006    3.03E-02   7.87

	41   3.355    6.80E-03   0.022    2.66E-04   0.845    1.23E-02   15.14    78   3.357    3.96E-02   0.008    5.49E-04   0.478    7.18E-02   3.27

	41   6.312    9.34E-03   0.015    2.48E-04   0.370    1.69E-02   18.34    78   6.306    2.27E-02   0.014    5.68E-04   0.932    4.12E-02   8.54

	47   3.159    1.06E-02   0.016    3.02E-04   0.518    1.92E-02   7.70    79   3.360    3.75E-02   0.005    3.64E-04   0.478    6.80E-02   4.57

	47   3.349    5.66E-03   0.033    3.34E-04   0.883    1.03E-02   15.99    79   6.311    1.12E-02   0.019    3.84E-04   0.985    2.03E-02   17.86

	47   6.309    1.21E-02   0.013    2.79E-04   0.870    2.20E-02   13.30    -   -   -   -   -   -   -   -

	48   3.161    1.66E-02   0.011    3.35E-04   0.209    3.01E-02   4.91    -   -   -   -   -   -   -   -

	48   3.358    5.21E-03   0.040    3.77E-04   0.849    9.44E-03   17.80    -   -   -   -   -   -   -   -

	48   6.315    1.62E-02   0.011    3.25E-04   0.195    2.94E-02   9.95    -   -   -   -   -   -   -   -

	


