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Register a new userA note on the interpretation of the statistical analysis of the $M_{bullet}-M_{G}sigma^2$ scaling relation
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Added by
Antonella Lucia Iannella
Publication date
2021
fields
Physics
and research's language is
English
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In the context of scaling relations between Supermassive Black Holes and host-galaxy properties, we aim to enhance the comparison between $M_{bullet} - M_{G}sigma^2$ and $M_{bullet} - sigma$ relations from a statistical point of view. First, it is suggested to take into account the predictive accuracy of the scaling relation, in addition to the classical measures of goodness of fit. Here, prediction accuracy is fairly evaluated according to a leave-one-out cross-validation strategy. Then, we spread more light on the analysis of residuals from the fitted scaling relation, in order to provide more useful information on the role played by the different variables in their correlation with the black hole mass. The findings from six samples are discussed.
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We have studied, in a series of papers, the properties of the $M_{bullet}$ versus $M_{G}sigma^2$ relation and we have found that it is useful to describe the evolution of galaxies in the same way as the HR diagram does for stars and to predict the masses of Supermassive Black Holes that are difficult to be guessed using other scaling relations. In this paper, analyzing five samples of galaxies, we find that this relation has intrinsic scatter similar to the $M_{bullet} - sigma$, but follows the theoretical models much better than the $M_{bullet} - sigma$. Furthermore, we analyze the role of the bulge mass in the behavior of $M_{bullet}$ versus $M_{G}sigma^2$ relation because the difference with the $M_{bullet} - sigma$ is often determined by the choice of the right sample of galactic masses.
In this paper we want to compare the theoretical predictions of a law proposed by Feoli and Mancini, with the most recent experimental data about galaxies and Supermassive black holes. The physical principle behind this law is the transformation of the angular momentum of the interstellar material, which falls into the black hole, into the angular momentum of the radiation emitted in this process. Despite the simplicity of the model, this law shows an excellent agreement with the experimental data for early-type galaxies while a new approach is proposed for spirals.
Strong scaling relations between host galaxy properties (such as stellar mass, bulge mass, luminosity, effective radius etc) and their nuclear supermassive black holes mass point towards a close co-evolution. In this work, we first review previous efforts supporting the fundamental importance of the relation between supermassive black hole mass and stellar velocity dispersion ($M_{rm BH}$-$sigma_{rm e}$). We then present further original work supporting this claim via analysis of residuals and principal component analysis applied to some among the latest compilations of local galaxy samples with dynamically measured supermassive black hole masses. We conclude with a review of the main physical scenarios in favour of the existence of a $M_{rm BH}$-$sigma_{rm e}$ relation, with a focus on momentum-driven outflows.
We use the stellar kinematics for $2458$ galaxies from the MaNGA survey to explore dynamical scaling relations between the stellar mass $M_{star}$ and the total velocity parameter at the effective radius, $R_e$, defined as $S_{K}^{2}=KV_{R_e}^{2}+sigma_{star_e}^{2}$, which combines rotation velocity $V_{R_e}$, and velocity dispersion $sigma_{star_e}$. We confirm that spheroidal and spiral galaxies follow the same $M_{star}-S_{0.5}$ scaling relation with lower scatter than the $M_{star}-V_{R_e}$ and $M_{star}-sigma_{star_e}$ ones. We also explore a more general Universal Fundamental Plane described by the equation $log(Upsilon_{e}) = log (S_{0.5}^{2}) - log (I_{e}) - log (R_{e}) + C$, which in addition to kinematics, $S_{0.5}$, and effective radius, $R_e$, it includes surface brightness, $I_e$, and dynamical mass-to-light ratio, $Upsilon_e$. We use sophisticated Schwarzschild dynamical models for a sub-sample of 300 galaxies from the CALIFA survey to calibrate the so called Universal Fundamental Plane. That calibration allows us to propose both: (i) a parametrization to estimate the difficult-to-measure dynamical mass-to-light ratio at the effective radius; and (ii) a new dynamical mass proxy consistent with dynamical models within $0.09 dex$. We reproduce the relation between the dynamical mass and the stellar mass in the inner regions of galaxies. We use the estimated dynamical mass-to-light ratio from our analysis, $Upsilon_{e}^{fit}$, to explore the Universal Fundamental Plane with the MaNGA data set. We find that all classes of galaxies, from spheroids to disks, follow this Universal Fundamental Plane with a scatter significantly smaller $(0.05 dex)$ than the one reported for the $M_{star}-S_{0.5}$ relation $(0.1 dex)$, the Fundamental Plane $(sim 0.09 dex)$ and comparable with Tully-Fisher studies $(sim 0.05 dex)$, but for a wider range of galaxy types.
We present a re-calibration of the $M_{BH}-sigma_{star}$ relation, based on a sample of 16 reverberation-mapped galaxies with newly determined bulge stellar velocity dispersions ($sigma_{star}$) from integral-field spectroscopy (IFS), and a sample of 32 quiescent galaxies with publicly available IFS. For both samples, $sigma_{star}$ is determined via two different methods that are popular in the literature, and we provide fits for each sample based on both sets of $sigma_{star}$. We find the fit to the AGN sample is shallower than the fit to the quiescent galaxy sample, and that the slopes for each sample are in agreement with previous investigations. However, the intercepts to the quiescent galaxy relations are notably higher than those found in previous studies, due to the systematically lower $sigma_{star}$ measurements that we obtain from IFS. We find that this may be driven, in part, by poorly constrained measurements of bulge effective radius ($r_{e}$) for the quiescent galaxy sample, which may bias the $sigma_{star}$ measurements low. We use these quiescent galaxy parameterizations, as well as one from the literature, to recalculate the virial scaling factor $f$. We assess the potential biases in each measurement, and suggest $f=4.82pm1.67$ as the best currently available estimate. However, we caution that the details of how $sigma_{star}$ is measured can significantly affect $f$, and there is still much room for improvement.
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