Black hole mass measurement using molecular gas kinematics: what ALMA can do

We study the limits of the spatial and velocity resolution of radio interferometry to infer the mass of supermassive black holes (SMBHs) in galactic centres using the kinematics of circum-nuclear molecular gas, by considering the shapes of the galaxy surface brightness profile, signal-to-noise ratios (S/Ns) of the position-velocity diagram (PVD) and systematic errors due to the spatial and velocity structure of the molecular gas. We argue that for fixed galaxy stellar mass and SMBH mass, the spatial and velocity scale that need to be resolved increase and decrease, respectively, with decreasing \sersic\ index of the galaxy surface brightness profile. We validate our arguments using simulated PVDs for varying beam size and velocity channel width. Furthermore, we consider the systematic effects on the inference of the SMBH mass by simulating PVDs including the spatial and velocity structure of the molecular gas, which demonstrates that their impacts are not significant for a PVD with good S/N unless the spatial and velocity scale associated with the systematic effects are comparable to or larger than the angular resolution and velocity channel width of the PVD from pure circular motion. Also, we caution that a bias in a galaxy surface brightness profile owing to the poor resolution of a galaxy photometric image can largely bias the SMBH mass by an order of magnitude. This study shows the promise and the limit of ALMA observations for measuring SMBH mass using molecular gas kinematics and provides a useful technical justification for an ALMA proposal with the science goal of measuring SMBH mass.Comment: MNRAS publishe

Comparative study between N-body and Fokker-Planck simulations for rotating star clusters: I. Equal-mass system

We have carried out N-body simulations for rotating star clusters with equal mass and compared the results with Fokker-Planck models. These two different approaches are found to produce fairly similar results, although there are some differences with regard to the detailed aspects. We confirmed the acceleration of the core collapse of a cluster due to an initial non-zero angular momentum and found a similar evolutionary trend in the central density and velocity dispersion in both simulations. The degree of acceleration depends on the initial angular momentum. Angular momentum is being lost from the cluster due to the evaporation of stars with a large angular momentum on a relaxation time scale.Comment: 11 pages, 13 eps figures, accepted for the publication of MNRA

A remarkably simple and accurate method for computing the Bayes Factor from a Markov chain Monte Carlo Simulation of the Posterior Distribution in high dimension

Weinberg (2012) described a constructive algorithm for computing the marginal likelihood, Z, from a Markov chain simulation of the posterior distribution. Its key point is: the choice of an integration subdomain that eliminates subvolumes with poor sampling owing to low tail-values of posterior probability. Conversely, this same idea may be used to choose the subdomain that optimizes the accuracy of Z. Here, we explore using the simulated distribution to define a small region of high posterior probability, followed by a numerical integration of the sample in the selected region using the volume tessellation algorithm described in Weinberg (2012). Even more promising is the resampling of this small region followed by a naive Monte Carlo integration. The new enhanced algorithm is computationally trivial and leads to a dramatic improvement in accuracy. For example, this application of the new algorithm to a four-component mixture with random locations in 16 dimensions yields accurate evaluation of Z with 5% errors. This enables Bayes-factor model selection for real-world problems that have been infeasible with previous methods.Comment: 14 pages, 3 figures, submitted to Bayesian Analysi

Spinning Nanoparticles Impacted by C-shock: Implications for Radio-millimeter Emission from Star-forming Regions

We investigate the impact of anomalous microwave emission (AME) on the radio-millimeter spectral energy distribution for three typical interstellar medium (ISM) conditions surrounding star-forming regions -- cold neutral medium, warm neutral medium, and photodissociation region -- by comparing the emissivities of three major contributors: free-free, thermal dust emission, and AME. In particular, for spinning nanoparticles (i.e., potential carriers of AME), we consider a known grain destruction mechanism due to a centrifugal force from spin-up processes caused by collisions between dust grains and supersonic neutral streams in a magnetized shock (C-shock). We demonstrate that, if the ISM in a magnetic field is impacted by a C-shock developed by a supernova explosion in the early phase of massive star-formation ($\lesssim 10$ Myr), AME can be significantly or almost entirely suppressed relative to free-free and thermal dust continuum emission if the grain tensile strength is small enough. This study may shed light on explaining the rare observations of AME from extragalactic star-forming regions preferentially observed from massive star clusters and suggest a scenario of "the rise and fall of AME" in accordance with the temporal evolution of star-forming regions.Comment: 20 pages, 8 figures, Accepted for publication in Ap

Equilibrium and Dynamical Evolution of Self-Gravitating System Embedded in a Potential Well

Isothermal and self-gravitating systems bound by non-conducting and conducting walls are known to be unstable if the density contrast between the center and the boundary exceeds critical values. We investigate the equilibrium and dynamical evolution of isothermal and self-gravitating system embedded in potential well, which can be the situation of many astrophysical objects such as the central parts of the galaxies, or clusters of galaxies with potential dominated by dark matter, but is still limited to the case where the potential well is fixed during the evolution. As the ratio between the depth of surrounding potential well and potential of embedded system becomes large, the potential well becomes effectively the same boundary condition as conducting wall, which behaves like a thermal heat bath. We also use the direct N-body simulation code, NBODY6 to simulate the dynamical evolution of stellar system embedded in potential wells and propose the equilibrium models for this system. In deep potential well, which is analogous to the heat bath with high temperature, the embedded self-gravitating system is dynamically hot, and loosely bound or can be unbound since the kinetic energy increases due to the heating by the potential well. On the other hand, the system undergoes core collapse by self-gravity when potential well is shallow. Binary heating can stop the collapse and leads to the expansion, but the evolution is very slow because the potential as a heat bath can absorb the energy generated by the binaries. The system can be regarded as quasi-static. Density and velocity dispersion profiles from the N-body simulations in the final quasi-equilibrium state are similar to our equilibrium models assumed to be in thermal equilibrium with the potential well.Comment: 12 pages, 12 figures, Submitted to MNRA

Quantifying the detection likelihood of faint peaks in interferometric data through jackknifing:Test application on finding z > 10 galaxy candidates

Context. False-positive emission-line detections bias our understanding of astronomical sources; for example, falsely identifying z ∼ 3–4 passive galaxies as z > 10 galaxies leads to incorrect number counts and flawed tests of cosmology.Aims. In this work, we provide a novel but simple tool to better quantify the detection of faint lines in interferometric data sets and properly characterize the underlying noise distribution. We demonstrate the method on three sets of archival observations of z > 10 galaxy candidates, taken with the Atacama Large Millimeter/Submillimeter Array (ALMA).Methods. By jackknifing the visibilities using our tool, jackknify, we create observation-specific noise realizations of the interferometric measurement set. We apply a line-finding algorithm to both the noise cubes and the real data and determine the likelihood that any given positive peak is a real signal by taking the ratio of the two sampled probability distributions.Results. We show that the previously reported, tentative emission-line detections of these z > 10 galaxy candidates are consistent with noise. We further expand upon the technique and demonstrate how to properly incorporate prior information on the redshift of the candidate from auxiliary data, such as from the James Webb Space Telescope.Conclusions. Our work highlights the need to achieve a significance of ≳ 5σ to confirm an emission line when searching in broad 30 GHz bandwidths. Using our publicly available method enables the quantification of false detection likelihoods, which are crucial for accurately interpreting line detections

Why Post-Starburst Galaxies are Now Quiescent

Post-starburst or "E+A" galaxies are rapidly transitioning from star-forming to quiescence. While the current star formation rate of post-starbursts is already at the level of early type galaxies, we recently discovered that many have large CO-traced molecular gas reservoirs consistent with normal star forming galaxies. These observations raise the question of why these galaxies have such low star formation rates. Here we present an ALMA search for the denser gas traced by HCN (1--0) and HCO+ (1--0) in two CO-luminous, quiescent post-starburst galaxies. Intriguingly, we fail to detect either molecule. The upper limits are consistent with the low star formation rates and with early-type galaxies. The HCN/CO luminosity ratio upper limits are low compared to star-forming and even many early type galaxies. This implied low dense gas mass fraction explains the low star formation rates relative to the CO-traced molecular gas and suggests the state of the gas in post-starburst galaxies is unusual, with some mechanism inhibiting its collapse to denser states. We conclude that post-starbursts galaxies are now quiescent because little dense gas is available, in contrast to the significant CO-traced lower density gas reservoirs that still remain.Comment: accepted for publication in Ap