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We explore the Kazakov-Solodukhin quantum deformed black hole spacetime, characterized by a single deformation parameter η that encodes quantum corrections to the classical Schwarzschild solution. The model preserves the correct general-relativistic limit as η → 0, while introducing significant and physically meaningful deviations in the strong-field regime. A central and remarkable feature of the geometry is the regularization of the classical singularity: curvature invariants remain finite near the minimal radius <mml:math><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>η</mml:mi></mml:mrow></mml:math>, effectively replacing the divergent core with a smooth and well-behaved region. This behavior naturally introduces a minimal length scale into the spacetime structure, offering a geometrically motivated resolution of the singularity problem. The deformation modifies the horizon structure, shifts the event horizon location, and alters the mass-radius relation. It also reduces the surface gravity, leading to a lower Hawking temperature and a slower evaporation process, thereby enhancing the thermodynamic stability of the black hole. Photon dynamics are correspondingly affected, resulting in a displaced photon sphere and modified strong-lensing characteristics. While the shadow remains perfectly circular due to spherical symmetry, its size depends sensitively on η. Observational constraints can be expressed through <mml:math><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>η</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>⩽</mml:mi><mml:mstyle><mml:mi>∆</mml:mi></mml:mstyle><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math> which places an upper bound on the deformation parameter. In the weak-field limit, the deflection angle acquires a quadratic correction proportional to η<SUP>2</SUP>, ensuring consistency with precision tests while allowing potentially detectable deviations in strong-gravity observations. These features make the model both theoretically appealing and observationally testable.

Quasars are among the most luminous objects. They are powered by accretion onto supermassive black holes. They are thought to impact cosmological evolution primarily through energetic winds, known as quasar-mode feedback, yet the efficiency and spatial extent of this process remain poorly constrained. Here we present X-Ray Imaging and Spectroscopy Mission (XRISM) observations of H1821+643---the nearest galaxy cluster with a central quasar (redshift z = 0.297)---which was a rare opportunity to directly probe quasar-mode feedback in the intracluster medium. High-resolution spectroscopy reveals exceptionally broadened Fe XXV emission lines from the intracluster medium, with a velocity dispersion of approximately 300 km/s, far exceeding values observed in nearby cluster cores. These lines originate predominantly at radii of 20-100 kpc from the centre. Assuming that turbulence from a quasar-driven shock led to the broadening of the lines, the energy injected by the quasar beyond galactic scales ($\gtrsim$20 kpc) is estimated to be $\gtrsim$1-10% of its radiative energy. Notably, this feedback efficiency exceeds previous multiwavelength estimates by orders of magnitude ($\lesssim$0.01%) and reaches the levels required by the latest cosmological hydrodynamical simulations. This finding of vigorous turbulence indicates that quasar-mode feedback plays a central role in regulating galaxy and cluster evolution at high redshift.

We present Syntriod, an orbital-phase domain radial velocity (RV) template-based algorithm designed to provide robust initial orbital parameter estimates for spectroscopic binaries across diverse observational sampling conditions. Rather than performing full orbital inference, Syntriod constrains the parameter space with physically consistent solutions to guide subsequent optimization procedures. We evaluate its performance using 10,000 synthetic Keplerian orbits spanning diverse configurations and sampling regimes. For well-sampled datasets ($N_{obs} \ge 8$), Syntriod recovers orbital periods with relative accuracies of order $10^{-3}$. At the theoretical sampling limit ($N_{obs} = 6$), the method maintains a ~94% success rate, while classical period-search techniques like Lomb-Scargle become increasingly affected by aliasing. Even below this limit ($N_{obs} = 5$), Syntriod recovers the correct orbital solution in ~83% of cases, showing gradual degradation rather than catastrophic failure. We further evaluate the method on 12 real spectroscopic binary systems (HD 160934, Phi Cyg, Capella A, Kepler 16, KIC 3858884, KIC 6867766, KIC 2445134, KIC 3003991, DU Boo, HL Dra, FP Boo, and AK Her) spanning broad orbital periods and eccentricities. Syntriod consistently reproduces literature solutions even when datasets are randomly subsampled to sparse regimes. Where a full Keplerian solution becomes underconstrained ($N_{obs} \le 4$), the algorithm transitions to linear dynamical relations, recovering parameters such as mass ratio ($q$) and systemic velocity ($γ$) with success rates exceeding 99%. These results demonstrate that Syntriod provides reliable, computationally efficient initial parameter estimates across well-sampled and sparse regimes, making it a practical pre-solver for modern orbit-fitting pipelines and large spectroscopic surveys.