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We report a new hot-PAGB star identified in the Galactic GC E3, which is one of the first to show a binary signature among the identified PAGB stars of GCs. We present a detailed photometric and spectroscopic analysis to study the evolutionary status of the newly identified hot-PAGB star. We use Gaia EDR3 proper motion (PM) and parallax measurements to confirm the cluster membership. We supplement the photometric observations with radial velocities (RVs) from multi-epoch high resolution (R$\sim$28000) spectroscopic observations. We fitted the spectral energy distribution of 30 photometric fluxes of the PAGB star from ultraviolet to infra-red passbands with the TLUSTY BSTAR2006 stellar atmosphere model to derive its physical parameters, \Teff, $\log g$, \Lbol, and R. We derive the chemical abundances of nine elements (He, C, N, O, Ne, Al, Si, S, and Fe) using spectroscopic measurements. The derived chemical abundances, kinematic information, and stellar parameters are used to study the evolution history of the star. The PM and parallax of the identified PAGB star match well with cluster parameters, which confirms its cluster membership. We find that the RVs vary over $\sim$6 \kms\ between the two epochs. This is an indication of the star being in a binary orbit. A simulation of possible binary systems with the observed RVs suggests a binary period of either 39.12 days or 17.83 days with mass ratio, q$\geq$1.0. The [Fe/H] derived using the high-resolution spectra is $\sim -$0.7 dex matches well with the cluster metallicity. Various PAGB evolutionary tracks on the H-R diagram suggest a current mass of the identified PAGB star in the range 0.51$-$0.55 \Msun. The star is enriched with C and O abundances, showing similar CNO abundances compared to the other PAGB stars of GCs with the evidence of 3rd dredge-up on the AGB phase., Comment: Submitted to A&A Letters

Double neutron star (DNS) systems offer excellent opportunities to test gravity theories. We report the timing results of PSR J1901+0658, the first pulsar discovered in the FAST Galactic Plane Pulsar Snapshot (GPPS) survey. Based on timing observations by FAST over 5 years, we obtain the phase-coherent timing solutions and derive the precise measurements of its position, spin parameters, orbital parameters, and dispersion measure (DM). It has a period of 75.7 ms, a period derivative of 2.169(6)$\times 10^{-19}$ s s$^{-1}$, and a characteristic age of 5.5 Gyr. This pulsar is in an orbit with a period of 14.45 days and an eccentricity of 0.366. One post-Keplerian parameter, periastron advance, has been well measured as being 0.00531(9) deg/yr, from which the total mass of this system is derived to be 2.79(7) $M_{\odot}$. The pulsar has the mass upper limit of 1.68 $M_{\odot}$, so the lower limit for the companion mass is 1.11 $M_{\odot}$. Because PSR J1901+0658 is a partially recycled pulsar in an eccentric binary orbit with such a large companion mass, it should be in a DNS system according to the evolution history of the binary system., Comment: 6 pages, 6 figures, accepted by MNRAS

The strict periodicity of pulsars is the primary source of information we have to learn about their nature and environment, it allows us to challenge general relativity and measure gravitational waves. Identifying such a periodicity from a discrete set of arrival times is a difficult algorithmic problem, particularly when the pulsar is in a binary system. This challenge is especially acute in $\gamma$-ray pulsar astronomy as there are hundreds of unassociated Fermi-LAT sources awaiting a timing solution that will reveal their nature, and may allow adding them to pulsar timing arrays. The same issue arises when attempting to recover a strict periodicity for repeating fast radio bursts (FRBs). Such a detection would be a major breakthrough, providing us with the FRB source's age, magnetic field, and binary orbit. The problem of recovering a timing solution from sparse time-of-arrival (TOA) data is currently unsolvable for pulsars in binary systems and incredibly hard even for single pulsars. In a series of papers, we will develop an algorithmic set of tools that will allow us to solve the timing recovery problem under different regimes. In this paper, we frame the timing recovery problem as the problem of finding a short vector in a lattice and obtain the solution using off-the-shelf lattice reduction and sieving techniques. As a proof of concept, we solve PSR J0318+0253, a millisecond $\gamma$-ray pulsar discovered by FAST in a $\gamma$-ray directed search, in a few CPU-minutes. We discuss the assumptions of the standard lattice techniques and quantify their performance and limitations., Comment: 11 pages, 3 figures

Circumbinary disks are found in a variety of astrophysical scenarios, spanning binary star formation to accreting supermassive black hole binaries. The interaction with a circumbinary disk can yield opposite effects on the binary orbit leading to circularization, or exciting the eccentricity, widening the orbit or shrinking it and facilitating mergers. We present a new formalism for the long-term evolution of the disk-binary interaction based on the results of recent suites of hydrodynamic simulations, which resolve the complex geometry of the gas in the vicinity of the binary and fully account for the gravitational and accretion forces. We release a python package, \texttt{spindler}, that implements our model. We show that, unless the mass reservoir feeding the disk is comparable to the mass of the binary, accretion onto the binary depletes the disk mass before inducing a significant change in orbital separation or mass ratio. This finding implies that, in most scenarios, interaction with a circumbinary disk is not an efficient mechanism to shrink the orbit of the binary. However, as long as the mass of the disk is at least a few percent of the mass of the binary, the interaction can excite the eccentricity up to an equilibrium value, and induce a statistical correlation between mass ratio and eccentricity. We consider the applicability of our model to a variety of astrophysical scenarios: during star formation, in evolved stellar binaries, triples and in supermassive black hole binaries. We discuss the theoretical and observational implications of our predictions., Comment: 18 pages, 12 figures. Submitted. Comments welcome. Spindler available as a Python package on Zenodo: https://doi.org/10.5281/zenodo.10529060

Neutron star (NS) binaries can be potentially intriguing gravitational wave (GW) sources, with both high- and low-frequency radiations from the possibly aspherical individual stars and the binary orbit, respectively. The successful detection of such a dual-line source could provide fresh insights into binary geometry and NS physics. In the absence of electromagnetic observations, we develop a strategy for inferring the spin-orbit misalignment angle using the tight dual-line double NS system under the spin-orbit coupling. Based on the four-year joint detection of a typical dual-line system with LISA and Cosmic Explorer, we find that the misalignment angle and the NS moment of inertia can be measured with sub-percentage and 5% accuracy, respectively., Comment: 8 pages, 3 figures. Accepted by PRD

We study the dynamical evolution of quasi-circular equal mass massive black hole binaries embedded in circumbinary discs from separations of $\sim 100R_{\rm g}$ down to the merger, following the post merger evolution. The binary orbit evolves owing to the presence of the gaseous disc and the addition of Post-Newtonian (PN) corrections up to the 2.5 PN order, therefore including the dissipative gravitational wave back-reaction. We investigate two cases of a relatively cold and warm circumbinary discs, with aspect ratios $H/R=0.03,\,0.1$ respectively, employing 3D hyper-Lagrangian resolution simulations with the {\sc gizmo}-MFM code. We extract spectral energy distributions and light curves in different frequency bands (i.e. X-ray, optical and UV) from the simulations. We find a clear two orders of magnitude drop in the X-ray flux right before merger if the disc is warm while we identify a significant increase in the UV flux regardless of the disc temperature. The optical flux shows clear distinctive modulations on the binary orbital period and on the cavity edge period, regardless of the disc temperature. We find that the presence of a cold disc can accelerate the coalescence of the binary by up to 130 seconds over the last five days of inspiral, implying a phase shift accumulation of about $\pi\,$radians compared to the binary evolution in vacuum. These differences are triggered by the presence of the gaseous disc and might have implications on the waveforms that can be in principle detected. We discuss the implications that these distinctive signatures might have for existing and upcoming time domain surveys and for multimessenger astronomy., Comment: 10 pages, A&A submitted

We propose a model of a twisted accretion disc around a Kerr black hole interacting with a secondary black hole of a smaller mass on an inclined eccentric orbit. We use parameters of the system, which may be appropriate for the so-called 'precessing massive' model of OJ 287. We calculate expressions for torque exerted on the disc by the secondary and a contribution of the secondary to the apsidal precession of disc elements by a double averaging procedure over the periods of the secondary and the disc elements. These expressions are used at all scales of interest, including the ones inside the binary orbit. We calculate numerically the evolution of the disc tilt and twist assuming a flat initial configuration. We consider the disc aspect ratio $h/r=10^{-3}$, a rather large viscosity parameter $\alpha=0.1$ and several values of the primary rotational parameter, $\chi$. We find that, after a few periods of Lense-Thirring precession of the orbit, the disc relaxes to a quasi-stationary configuration in the precessing frame with a non-trivial distribution of the disc inclination angle, $\beta$, over the radial scale. We propose an analytic model for this configuration. We show that the presence of the twisted disc leads to multiple crossings of the disc by the secondary per one orbital period, with time periods between the crossings being different from the flat disc model. Our results should be taken into account in the modelling of OJ 287. They can also be applied to similar sources., Comment: to be published in MNRAS

We study the formation of Population III stars by performing radiation hydrodynamic simulations for three different initial clouds extracted from cosmological hydrodynamic simulations. Starting from the cloud collapse stage, we follow the growth of protostars by accretion for ∼10⁵ yr until the radiative feedback from the protostars suppresses the accretion and the stellar properties are nearly fixed. We find that Population III stars form in massive and wide binary/small-multiple stellar systems, with masses >30 M⊙ and separations >2000 au. We also find that the properties of the final stellar system correlate with those of the initial clouds: the total mass increases with the cloud-scale accretion rate, and the angular momentum of the binary orbit matches that of the initial cloud. While the total mass of the system in our simulations is consistent with our previous single-star formation simulations, individual masses are lower due to mass sharing, suggesting potential modification in the extent of feedback from Population III stars in the subsequent evolution of the Universe. We also identify such systems as mini-binaries embedded in a wider outer multiple-star system, which could evolve into progenitors for observed gravitational wave events.

The origin of magnetic fields and their role in chemical spot formation on magnetic Ap stars is currently not understood. Here, we contribute to solving this problem with a detailed observational characterization of the surface structure of 45 Her, a weak-field Ap star. We find this object to be a long-period, single-lined spectroscopic binary and determine the binary orbit as well as fundamental and atmospheric parameters of the primary. We study magnetic field topology and chemical spot distribution of 45 Her with the help of the Zeeman Doppler imaging technique. Magnetic mapping reveals the stellar surface field to have a distorted dipolar topology with a surface-averaged field strength of 77 G and a dipolar component strength of 119 G - confirming it as one of the weakest well-characterized Ap-star fields known. Despite its feeble magnetic field, 45 Her shows surface chemical inhomogeneities with abundance contrasts of up to 6 dex. Of the four chemical elements studied, O concentrates at the magnetic equator, whereas Ti, Cr, and Fe avoid this region. Apart from this trend, the positions of Fe-peak element spots show no apparent correlation with the magnetic field geometry. No signs of surface differential rotation or temporal evolution of chemical spots on the time-scale of several years were detected. Our findings demonstrate that chemical spot formation does not require strong magnetic fields to proceed and that both the stellar structure and the global field itself remain stable for sub-100 G field strengths contrary to theoretical predictions.

We develop in detail a recently proposed optical-path modification of astronomical intensity interferometers. Extended-Path Intensity Correlation (EPIC) introduces a tunable path extension, enabling differential astrometry of multiple compact sources such as stars and quasars at separations of up to a few arcseconds. Combined with other recent technological advances in spectroscopy and fast single-photon detection, a ground-based intensity interferometer array can achieve microarcsecond resolution and even better light-centroiding accuracy on bright sources of magnitude $m \lesssim 15$. We lay out the theory and technical requirements of EPIC, and discuss the scientific potential. Promising applications include astrometric lensing of stars and quasar images, binary-orbit characterization, exoplanet detection, Galactic acceleration measurements and calibration of the cosmic distance ladder. The introduction of the path extension thus significantly increases the scope of intensity interferometry while reaching unprecedented levels of relative astrometric precision., Comment: 58+21 pages, 22 figures; companion paper to arXiv:2307.03221

The recurring transient outbursts in low-mass X-ray binaries (LMXBs) provide ideal laboratories to study the accretion process. Unlike their supermassive relatives, LMXBs are far too small and distant to be imaged directly. Fortunately, phase-resolved spectroscopy can provide an alternative diagnostic to study their highly complex, time-dependent accretion discs. The primary spectral signature of LMXBs are strong, disc-formed emission lines detected at optical wavelengths. The shape, profile, and appearance/disappearance of these lines change throughout a binary orbit, and thus, can be used to trace how matter in these discs behaves and evolves over time. By combining a \textit{Swift} multi-wavelength monitoring campaign, phase-resolved spectroscopy from the Gran Telescopio Canarias (GTC) and Liverpool Telescope, and modern astrotomography techniques, we find a clear empirical connection between the line emitting regions and physical properties of the X-rays heating the disc in the black hole LMXB MAXI J1820+070 during its 2018 outburst. In this paper, we show how these empirical correlations can be used as an effective observational tool for understanding the geometry and structure of a LMXB accretion disc and present further evidence for an irradiation-driven warped accretion disc present in this system., Comment: 14 pages, 7 figures, accepted for publication in MNRAS

PSR J1953+1844 (i.e., M71E) is a millisecond pulsar (MSP)in a 53 minute binary orbit discovered by the Five-hundred-meter Aperture Spherical radio Telescope. The mass function from pulsar timing is $2.3\times10^{-7}$ $M_\odot$. The possible redback origin of this system has been discussed by Pan et al. We discuss here an alternative evolution track for this binary system, namely that PSR J1953+1844 is a descendant of an ultra-compact X-ray binary (UCXB), which has a hydrogen-poor donor accreting onto a neutron star (NS) with an orbital period of $\leq1$ hr. We noticed that some of UCXB systems hold an accreting millisecond X-ray pulsars (AMXPs) and a donor with a mass of about 0.01 M$_\odot$. M71E has a very similar orbit to those of AMXPs, indicating that it might be evolved from a UCXB similar to PSR J1653--0158. The companion star of M71E should be significantly bloated and it most probably has a carbon and oxygen composition, otherwise a low inclination angle of the orbit is required for a helium companion. The discovery of this M71E binary system may shed light on when and how an NS in a UCXBs turns into a radio pulsar., Comment: Accepted for publication in ApJL. 5 pages, 2 figures

Neutron stars accreting from OB supergiants are often divided between persistently and transiently accreting systems, called Supergiant X-ray Binaries (SgXBs) and Supergiant Fast X-ray Transients (SFXTs). This dichotomy in accretion behaviour is typically attributed to systematic differences in the massive stellar wind, binary orbit, or magnetic field configuration, but direct observational evidence for these hypotheses remains sparse. To investigate their stellar winds, we present the results of pilot 100-GHz observations of one SFXT and one SgXB with the Northern Extended Millimetre Array. The SFXT, IGR J18410-0535, is detected as a point source at $63.4 \pm 9.6$ $\mu$Jy, while the SgXB, IGR J18410-0535 remains undetected. Radio observations of IGR J18410-0535 imply a flat or inverted low-frequency spectrum, arguing for wind emission and against non-thermal flaring. Due to the uncertain SFXT distance, however, the observations do not necessarily imply a difference between the wind properties of the SFXT and SgXB. We compare the mm constraints with other HMXBs and isolated OB supergiants, before considering how future mm campaigns can constrain HMXB wind properties by including X-ray measurements. Specifically, we discuss caveats and future steps to successfully measure wind mass loss rates and velocities in HMXBs with coordinated mm, radio, and X-ray campaigns., Comment: Accepted for publication in MNRAS Letters. 7 pages, 1 figure

In their third observing run, the LIGO-Virgo-KAGRA gravitational-wave (GW) observatory was sensitive to binary black hole (BBH) mergers out to redshifts $z_\mathrm{merge}\approx1$. Because GWs are inefficient at shrinking the binary orbit, some of these BBH systems likely experienced long delay times $\tau$ between the formation of their progenitor stars at $z_\mathrm{form}$ and their GW merger at $z_\mathrm{merge}$. In fact, the distribution of delay times predicted by isolated binary evolution resembles a power law $p(\tau)\propto\tau^{\alpha_\tau}$ with slope $-1\lesssim\alpha_\tau\lesssim-0.35$ and a minimum delay time of $\tau_\mathrm{min}=10$ Myr. We use these predicted delay time distributions to infer the formation redshifts of the $\sim70$ BBH events reported in the third GW transient catalog GWTC-3 and the formation rate of BBH progenitors. For our default $\alpha_\tau=-1$ delay time distribution, we find that GWTC-3 contains at least one system (with 90\% credibility) that formed earlier than $z_\mathrm{form}>4.4$. Comparing our inferred BBH progenitor formation rate to the star formation rate (SFR), we find that at $z_\mathrm{form}=4$, the number of BBH progenitor systems formed per stellar mass was $6.4^{+9.4}_{-5.5}\times10^{-6}\,M_\odot^{-1}$ and this yield dropped to $0.134^{+1.6}_{-0.127}\times10^{-6}\,M_\odot^{-1}$ by $z_\mathrm{form}=0$. We discuss implications of this measurement for the cosmic metallicity evolution, finding that for typical assumptions about the metallicity-dependence of the BBH yield, the average metallicity at $z_\mathrm{form}=4$ was $\langle\log_{10}(Z/Z_\odot)\rangle=-0.3^{+0.3}_{-0.4}$, although the inferred metallicity can vary by a factor of $\approx3$ for different assumptions about the BBH yield. Our results highlight the promise of current GW observatories to probe high-redshift star formation., Comment: Updates to some calculations following helpful referee comments. Accepted by ApJL. 17 pages, 8 figures

We propose that the polarization of the emission from the X-ray binary Cygnus X-1, measured using the Imaging X-ray Polarimetry Explorer (IXPE), is imprinted by bulk Comptonization of coronal emission in a mildly relativistic wind or jet with a hollow-cone geometry. Models based on scattering in a static corona overlying a thin accretion disc have difficulty reproducing the relatively high polarization degree (PD ~4%) concurrently with the low inclination (~30 deg) of the binary orbit. We show that bulk outflow with a Lorentz factor > 1.5 is adequate to reproduce the observed PD, with position angle parallel to the large-scale jet, provided that the scattering occurs in a conical sheath offset from the jet axis and our line of sight aligns roughly with the opening angle of the cone. Physically, this flow geometry could represent the entrainment of dense material near the base of an accelerating jet as it passes through the disc corona, or a slow (but still relativistic) sheath around a fast jet. If similar outflows are present in other X-ray binaries at higher inclination, we might expect to see still higher degrees of linear polarization ~10% with an orientation perpendicular to the jet direction., Comment: 4 pages, 3 figures, submitted to MNRAS Letters

We report the analysis of circumbinary discs formed in a radiation hydrodynamical simulation of star cluster formation. We consider both pure binary stars and pairs within triple and quadruple systems. The protostellar systems are all young (ages < $10^5$ yrs). We find that the systems that host a circumbinary disc have a median separation of $\approx 11$ au, and the median characteristic radius of the discs is $\approx 64$ au. We find that $89$ per cent of pure binaries with semi-major axes $a<1$ au have a circumbinary disc, and the occurrence rate of circumbinary discs is bimodal with log-separation in pure binaries with a second peak at $a \approx 50$ au. Systems with $a>100$ au almost never have a circumbinary disc. The median size of a circumbinary disc is between $\approx 5-6\ a$ depending on the order of the system, with higher order systems having larger discs relative to binary separation. We find the underlying distribution of mutual inclinations between circumbinary discs and binary orbit of both observed and simulated discs to not differ statistically., Comment: 12 pages, 11 figures, 1 table, accepted for publication in MNRAS

Wolf-Rayet (WR) 140 is the archetypal periodic dust-forming colliding-wind binary that hosts a carbon-rich WR (WC) star and an O-star companion with an orbital period of 7.93 years and an orbital eccentricity of 0.9. Throughout the past several decades, multiple dust-formation episodes from WR 140 have been observed that are linked to the binary orbit and occur near the time of periastron passage. Given its predictable dust-formation episodes, WR 140 presents an ideal astrophysical laboratory for investigating the formation and evolution of dust in the hostile environment around a massive binary system. In this paper, we present near- and mid-infrared (IR) spectroscopic and imaging observations of WR 140 with Subaru/SCExAO+CHARIS, Keck/NIRC2+PyWFS, and Subaru/COMICS taken between 2020 June and Sept that resolve the circumstellar dust emission linked to its most recent dust-formation episode in 2016 Dec. Our spectral energy distribution (SED) analysis of WR 140's resolved circumstellar dust emission reveals the presence of a hot ($T_\mathrm{d}\sim1000$ K) near-IR dust component that is co-spatial with the previously known and cooler ($T_\mathrm{d}\sim500$ K) mid-IR dust component composed of $300-500$ {\AA}-sized dust grains. We attribute the hot near-IR dust emission to the presence of nano-sized ("nanodust") grains and suggest they were formed from grain-grain collisions or the rotational disruption of the larger grain size population by radiative torques in the strong radiation field from the central binary. Lastly, we speculate on the astrophysical implications of nanodust formation around colliding-wind WC binaries, which may present an early source of carbonaceous nanodust in the interstellar medium., Comment: 21 pages, 8 figures, Accepted for publication in ApJ

We present the high-precision optical polarimetric observations of black hole X-ray binary Cyg X-1, spanning several cycles of its 5.6 day orbital period. Week-long observations on two telescopes located in opposite hemispheres allowed us to track the evolution of the polarization within one orbital cycle with the highest temporal resolution to date. Using the field stars, we determine the interstellar polarization in the source direction and subsequently its intrinsic polarization. The optical polarization angle is aligned with that in the X-rays as recently obtained with the Imaging X-ray Polarimetry Explorer. Furthermore, it is consistent, within the uncertainties, with the position angle of the radio ejections. We show that the intrinsic PD is variable with the orbital period with the amplitude of $\sim$0.2% and discuss various sites of its production. Assuming the polarization arises from a single Thomson scattering of the primary star radiation by the matter that follows the black hole in its orbital motion, we constrain the inclination of the binary orbit $i>120^\circ$ and its eccentricity $e<0.08$. The asymmetric shape of the orbital profiles of Stokes parameters implies also the asymmetry of the scattering matter distribution about the orbital plane, which may arise from the tilted accretion disk. We compare our data to the polarimetric observations made over 1975-1987 and find good, within $1^\circ$, agreement between the intrinsic polarization angles. On the other hand, the PD decreased by 0.4% over half a century, suggesting the presence of secular changes in the geometry of accreting matter., Comment: 12 pages, 18 figures

Recent studies have shown that AGN discs can host sources of gravitational waves. Compact binaries can form and merge in AGN discs through their interactions with the gas and other compact objects in the disc. It is also possible for the binaries to shorten the merging timescale due to eccentricity excitation caused by perturbations from the supermassive blackhole (SMBH). In this paper we focus on effects due to precession-induced (eviction-like) resonances, where nodal and apsidal precession rates of the binary is commensurable with the mean motion of the binary around the SMBH. We focus on intermediate mass black hole (IMBH)-stellar mass black hole (SBH) binaries, and consider binary orbit inclined from the circum-IMBH disk which leads to the orbital $J_2$ precession. We show that if a binary is captured in these resonances and is migrating towards the companion, it can undergo large eccentricity and inclination variations. We derive analytical expressions for the location of fixed points, libration timescale and width for these resonances, and identified two resonances in the near coplanar regime (the evection and eviction resonances) as well as two resonances in the near polar regime that can lead to mergers. We also derive analytical expressions for the maximum eccentricity that a migrating binary can achieve for given initial conditions. Specifically, the maximum eccentricity can reach 0.9 when captured in these resonances before orbital decay due to gravitational wave emission dominates, and the capture is only possible for slow migration ($\sim 10$ Myr) 2-3 order of magnitude longer than the resonance libration timescale. We also show that capture into multiple resonances is possible, and can further excite eccentricities., Comment: Accepted for publication in ApJ

Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a distinct dynamical channel to produce black hole mergers detected in gravitational waves by LIGO/Virgo. To understand their orbital evolution through interactions with the disc gas, we perform a suite of 2D high-resolution, local shearing box, viscous hydrodynamical simulations of equal-mass binaries. We find that viscosity not only smooths the flow structure around prograde circular binaries, but also greatly raises their accretion rates. The torque associated with accretion may be overwhelmingly positive and dominate over the gravitational torque at a high accretion rate. However, the accreted angular momentum per unit mass decreases with increasing viscosity, making it easier to shrink the binary orbit. In addition, retrograde binaries still experience rapid orbital decay, and prograde eccentric binaries still experience eccentricity damping. Our numerical experiments further show that prograde binaries are more likely to be hardened if the physical sizes of the accretors are sufficiently small such that the accretion rate is reduced. The dependency of the binary accretion rate on the accretor size can be weaken through boosted accretion either due to a high viscosity or a more isothermal-like equation of state (EOS). Our results widen the explored parameter space for the hydrodynamics of embedded BBHs and demonstrate that their orbital evolution in AGN discs is a complex, multifaceted problem., Comment: 13 pages, 8 figures, 1st revision submitted to MNRAS. arXiv admin note: text overlap with arXiv:2207.01125