Dwarf AGN serve as the ideal systems for identifying intermediate mass black holes (IMBHs) down to the most elusive regimes ($\sim 10^3 - 10^4 M_{\odot}$). However, the ubiquitously metal-poor nature of dwarf galaxies gives rise to ultraluminous X-ray sources (ULXs) that can mimic the spectral signatures of IMBH excitation. We present a novel photoionization model suite that simultaneously incorporates IMBHs and ULXs in a metal-poor, highly star-forming environment. We account for changes in $M_{BH}$ according to formation seeding channels and metallicity, and changes in ULX populations with post-starburst age and metallicity. We find that broadband X-rays and UV emission lines are insensitive to $M_{BH}$ and largely unable to distinguish between ULXs and IMBHs. Many optical diagnostic diagrams cannot correctly identify dwarf AGN. The notable exceptions include He~II~$\lambda$4686 and [O~I]~$\lambda$6300, for which we redefine typical demarcations to account for ULX contributions. Emission lines in the mid-IR show the most promise in separating stellar, ULX, IMBH, and shock excitation while presenting sensitivity to $M_{BH}$ and $f_{\text{AGN}}$. Overall, our results expose the potential biases in identifying and characterizing dwarf AGN purely on strong line ratios and diagnostic diagrams rather than holistically evaluating the entire spectrum. As a proof of concept, we argue that recently discovered over-massive BHs in high-$z$ JWST AGN might not represent the overall BH population, with many galaxies in these samples potentially being falsely classified as purely star-forming. less

One of the most profound empirical laws of star formation is the Gao-Solomon relation, a linear correlation between the star formation rate (SFR) and the dense molecular gas mass. It is puzzling how the complicated physics in star-formation results in this surprisingly simple proportionality. Using archival Herschel and Atacama Large Millimeter/submillimeter Array Observations, we derived the masses of the most massive cores ($M^{\rm max}_{\rm core}$) and masses of the gravitationally bound gas ($ M_{\rm gas}^{\rm bound}$) in the parent molecular clouds for a sample of low-mass and high-mass star-forming regions. We discovered a significant correlation $\log(M^{\rm max}_{\rm core}/M_{\odot}) = 0.506 \log(M_{\rm gas}^{\rm bound}/M_{\odot})-0.32$. Our discovered $M^{\rm max}_{\rm core}$-$M_{\rm gas}^{\rm bound}$ correlation can be approximately converted to the Gao-Solomon relation if there is (1) a constant 30% efficiency of converting $M^{\rm max}_{\rm core}$ to the mass of the most massive star ($m^{\rm max}_{\rm star}$), and (2) if SFR and $m^{\rm max}_{\rm star}$ are tightly related through $\log({\rm SFR}/(M_{\odot} {\rm yr}^{-1})) = 2.04 \log(m^{\rm max}_{\rm star}/M_{\odot})-5.80$. Intriguingly, both requirements have been suggested by previous theoretical studies (c.f. Yan et al. 2017). Based on this result, we hypothesize that the Gao-Solomon relation is a consequence of combining the following three non-trivial relations (i) SFR vs. $m^{\rm max}_{\rm star}$, (ii) $m^{\rm max}_{\rm star}$ vs. $M^{\rm max}_{\rm core}$, and (iii) $M^{\rm max}_{\rm core}$ vs. $M_{\rm gas}^{\rm bound}$. This finding may open a new possibility to understand the Gao-Solomon relation in an analytic sense. less

UV radiation from OB stars can drive ``external'' photoevaporative winds from discs in clusters, that have been shown to be important for disc evolution and planet formation. However, cluster dynamics can complicate the interpretation of this process. A significant fraction of OB stars are runaways, propagating at high velocity which might dominate over the wider cluster dynamics in setting the time variation of the UV field in part of the cluster. We explore the impact of a runaway OB star on discs and the observational impact that may have. We find that discs exposed to even short periods of strong irradiation are significantly truncated, and only rebound slightly following the ``flyby'' of the UV source. This is predicted to leave an observable imprint on a disc population, with those downstream of the OB star vector being more massive and extended than those upstream. Because external photoevaporation acts quickly, this imprint is less susceptible to being washed out by cluster dynamics for faster runaway OB stars. The Gaia proper motion vector of the B star 42 Ori in NGC 1977 is transverse to the low mass stellar population and so may make a good region to search for this signature in resolved disc observations. less

To describe a general bound binary black hole system, we need to consider orbital eccentricity and the misalignment of black holes' spin vectors with respect to the orbital angular momentum. While binary black holes produced through many formation channels have negligible eccentricity close to merger, they often have a non-negligible eccentricity at formation, and dynamical interactions could produce binaries with non-negligible eccentricity in the bands of current and proposed gravitational-wave (GW) detectors. Another quantity that carries information about the formation channel is the angle between each black hole's spin vector and the binary's orbital angular momentum (referred to as the spin tilt) at formation. The spin tilts inferred in GW astronomy are usually those when the binary is in the band of a GW detector, but these can differ significantly from those at formation. Therefore, it is necessary to evolve the binary back in time to compute the tilts at formation. For many formation scenarios, the tilts in the formal limit of infinite orbital angular momentum, also known as tilts at infinity, are a good approximation to those at formation. We thus generalize the publicly available \texttt{tilts\_at\_infinity} code to compute the tilts at infinity for eccentric, spin-precessing binaries. This code employs hybrid post-Newtonian evolution, starting with orbit-averaged evolution for higher frequencies and then transitioning to precession-averaged evolution to compute the tilts at infinity. We find that the transition frequency used in the quasicircular case still gives acceptably small errors in the eccentric case, and show that eccentricity and hybrid evolution both have a significant effect on the tilts at infinity for many binaries. Finally, we give examples of cases where the tilts at infinity are and are not a good approximation to the tilts at formation in the eccentric case. less

Flows around compact objects are necessarily transonic. Due to their dissipative nature, finding of sonic points is not trivial. Becker and Le in 2003 (BL03) proposed a novel methodology to obtain global transonic solutions, using iterative relaxation technique and exploiting the inner boundary conditions of the central object. In the current work, we propose a generic methodology -- IRM-SP and IRM-SHOCK to obtain any class of global accretion and wind solutions, given a set of constants of motion. We have considered viscosity in the system, which transports angular momentum outwards. In addition, it heats the system. Radiative processes like bremsstrahlung which cools the system is also incorporated. An interplay between heating and cooling process, along with gravity and centrifugal forces gives rise to multiple sonic points and hence shocks. The proposed methodology successfully generates any class of accretion as well as wind solutions, allowing us to unify them. Additionally, we report here rigorously the mathematical as well as the computational algorithm needed, to find sonic point(s) and thus obtain global transonic flows around compact objects. less