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The IW And phenomenon in cataclysmic variables presents a significant challenge to the accretion disk instability model. Using photometric data from the All-Sky Automated Survey for Supernovae, the Zwicky Transient Facility, and the Transiting Exoplanet Survey Satellite, we identify Karachurin 12 as a new IW And-type object with a cycle period of 35.69(3) days. We also report for the first time that Karachurin 12 is a negative superhump (NSH) system featuring a precessing tilted disk, with precession, orbital, and NSH periods of 4.9588(2) days, 0.3168895(13) days, and 0.2979861(8) days, respectively. Our analysis, using dips as indexes and NSHs as probes, reveals diverse cycle patterns in Karachurin 12, with NSH amplitude varying throughout the cycle. Analyses of NSH behaviour using multiple methods shows that the amplitude decreases with increasing outbursts and increases with weakening outbursts, which we suggest is related to changes in the radius of the accretion disk. The mass transfer outburst model fails to explain the observed NSH amplitude variations, whereas the tilted thermally unstable disk model accounts for most of the observed cycles and dip patterns, particularly the disappearance of the IW And phenomenon when NSHs become undetectable. However, no significant changes in the NSH period were observed. These findings suggest a potential link between the IW And phenomenon and a tilted disk. Further improvements in simulations are needed to better understand the detailed dynamics of these cycles., Comment: 22 pages, 9 figures and 3 tables

Tilted disk precession exists in different objects. Negative superhumps (NSHs) in cataclysmic variable stars (CVs) are believed to arise from the interaction between the reverse precession of a tilted disk and the streams from the secondary star.Utilizing TESS photometry, we present a comprehensive investigation into the tilted disk precession and NSHs in the dwarf nova (DN) HS 2325+8205, employing eclipse minima, eclipse depths, NSH frequencies, and NSH amplitudes and the correlation between them as the windows. We identified NSHs with a period of 0.185671(17) days in HS 2325+8205. The NSH frequency exhibits variability with a period of 3.943(9) days, akin to the tilted disk precession period validated in novae-like stars (NLs, SDSS J0812) and intermediate polars (IPs, TV Col).The O-C of eclipse minima were similarly found to vary cyclically in period 4.135(5) days, characterized by a faster rise than fall. Furthermore, the NSH amplitude exhibits complex and diverse variations, which may be linked to changes in the disk radius, mass transfer rate, and the apparent area of the hot spot. For the first time in DNe, we observe bi-periodic variations in eclipse depth (P1= 4.131(4) d and P2= 2.065(2) d ~ Pprec/2), resembling those seen in IPs, suggesting that variations with P2 are not attributable to an accretion curtain, as previously suspected. Moreover, NSH amplitude and eclipse depth decrease with increasing NSH frequency, while NSH amplitude correlates positively with eclipse depth.These complex variations observed across multiple observational windows provide substantial evidence for understanding of tilted disk precession and NSHs., Comment: 19 pages, 10 figures and 3 tables; accepted for publication in ApJ

The merger of compact binary stars produces short gamma-ray bursts (sGRBs), involving channels such as neutron star - neutron star (BNS) and neutron star - black hole (NS-BH). The association between sGRB 170817A and gravitational wave GW 170817 provides reliable evidence for the BNS channel. The spatial distribution and merger rate differ between BNS mergers and NS-BH mergers. Some speculations suggest that sGRBs with extended emission (EE) may represent another distinct population. We compared the offset distributions of these two types of samples and found that they follow the same distribution. Utilizing non-parametric methods, we investigated the origin of these burst types in terms of their formation rate. We examined the luminosity function and formation rate of sGRBs without any assuming. The luminosity function can be described as $\psi(L_{0}) \propto L_{0}^{-0.09 \pm 0.01}$ for $L_{0} < L_0^b$ ($\psi(L_{0}) \propto L_{0}^{-0.57 \pm 0.02}$ for $L_{0} > L_0^b$) for standard sGRBs and $\psi(L_{0}) \propto L_{0}^{-0.11 \pm 0.004}$ for $L_{0} < L_0^b$ ($\psi(L_{0}) \propto L_{0}^{-0.61 \pm 0.01}$ for $L_{0} > L_0^b$) for sGRBs with EE. The formation rate is characterized as $\rho(z) \propto (1 + z)^{-4.21 \pm 0.22}$ for $z < 0.8$ and $\rho(z) \propto (1 + z)^{-0.22 \pm 0.74}$ for $0.8 < z < 3$ for standard sGRBs, while for sGRBs with EE, it is $\rho(z) \propto (1 + z)^{-4.30 \pm 0.13}$ for $z < 0.8$ and $\rho(z) \propto (1 + z)^{-0.33 \pm 0.66}$ for $0.8 < z < 3$. Based on these findings, we suggest that there is no significant difference in the progenitor stars of sGRBs with and without EE, considering the spatial offset and formation rate perspectives., Comment: 16 pages, 11 figures and 2 tables