arXiv subjects

Tiziana Di Matteo

Publications and source records attributed to Tiziana Di Matteo.

At least 91 records · Page 5Linked to original sources

arXiv2020

On the possibility of Baryon Acoustic Oscillation measurements at redshift $z>7.6$ with the Roman Space Telescope

The Nancy Grace Roman Space Telescope (RST), with its field of view and high sensitivity will make surveys of cosmological large-scale structure possible at high redshifts. We investigate the possibility of detecting Baryon Acoustic Oscillations (BAO) at redshifts $z>7.6$ for use as a standard ruler. We use data from the hydrodynamic simulation \textsc{BlueTides} in conjunction with the gigaparsec-scale Outer Rim simulation and a model for patchy reionization to create mock RST High Latitude Survey grism data for Lyman-alpha emission line selected galaxies at redshifts $z=7.4$ to $z=10$, covering 2280 square degrees. We measure the monopoles of galaxies in the mock catalogues and fit the BAO features. We find that for a line flux of $L = 7\times 10^{-17} \ {\rm erg/s/cm}^{2}$, the $5 σ$ detection limit for the current design, the BAO feature is partially detectable (measured in three out of four survey quadrants analysed independently). The resulting root mean square error on the angular diameter distance to $z=7.7$ is 7.9$\%$. If we improve the detection sensitivity by a factor of two (i.e. $L = 3.5\times 10^{-17} \ {\rm erg/s/cm}^{2}$), the distance error reduces to $1.4\%$. We caution that many more factors are yet to be modelled, including dust obscuration, the damping wing due to the intergalactic medium, and low redshift interlopers. If these issues do not strongly affect the results, or different observational techniques (such as use of multiple lines) can mitigate them, RST or similar instruments may be able to constrain the angular diameter distance to the high redshift Universe.

astro-ph.CO↗

arXiv2020

Mocking Faint Black Holes during Reionization

To investigate the potential abundance and impact of nuclear black holes (BHs) during reionization, we generate a neural network that estimates their masses and accretion rates by training it on 23 properties of galaxies harbouring them at $z=6$ in the cosmological hydrodynamical simulation Massive-Black II. We then populate all galaxies in the simulation from $z=18$ to $z=5$ with BHs from this network. As the network allows to robustly extrapolate to BH masses below those of the BH seeds, we predict a population of faint BHs with a turnover-free luminosity function, while retaining the bright (and observed) BHs, and together they predict a Universe in which intergalactic hydrogen is $15\%$ ionized at $z=6$ for a clumping factor of 5. Faint BHs may play a stronger role in H reionization without violating any observational constraints. This is expected to have an impact also on pre-heating and -ionization, which is relevant to observations of the 21 cm line from neutral H. We also find that BHs grow more efficiently at higher $z$, but mainly follow a redshift-independent galaxy-BH relation. We provide a power law parametrisation of the hydrogen ionizing emissivity of BHs.

astro-ph.GA↗

arXiv2020

The host galaxies of z=7 quasars: predictions from the BlueTides simulation

We examine the properties of the host galaxies of $z=7$ quasars using the large volume, cosmological hydrodynamical simulation BlueTides. We find that the 10 most massive black holes and the 191 quasars in the simulation (with $M_{\textrm{UV,AGN}} 10^{6.5}M_\odot$ black hole, indicating that minor mergers play at least some role in growing black holes in the early Universe.

astro-ph.GA↗

arXiv2020

Large scale simulations of H and He reionization and heating driven by stars and more energetic sources

We present simulations of cosmic reionization and reheating from $z=18$ to $z=5$, investigating the role of stars (emitting soft UV-photons), nuclear black holes (BHs, with power-law spectra), X-ray binaries (XRBs, with hard X-ray dominated spectra), and the supernova-associated thermal bremsstrahlung of the diffuse interstellar medium (ISM, with soft X-ray spectra). We post-process the hydrodynamical simulation Massive-Black II (MBII) with multifrequency ionizing radiative transfer. The source properties are directly derived from the physical environment of MBII, and our only real free parameter is the ionizing escape fraction $f_{\rm esc}$. We find that, among the models explored here, the one with an escape fraction that decreases with decreasing redshift yields results most in line with observations, such as of the neutral hydrogen fraction and the Thomson scattering optical depth. Stars are the main driver of hydrogen reionization and consequently of the thermal history of the intergalactic medium (IGM). We obtain $\langle x_{\rm HII} \rangle = 0.99998$ at $z=6$ for all source types, with volume averaged temperatures $\langle T \rangle \sim 20,000~{\rm K}$. BHs are rare and negligible to hydrogen reionization, but conversely they are the only sources which can fully ionize helium, increasing local temperatures by $\sim 10^4~{\rm K}$. The thermal and ionization state of the neutral and lowly ionized hydrogen differs significantly with different source combinations, with ISM and (to a lesser extent) XRBs, playing a significant role and, as a consequence, determining the transition from absorption to emission of the 21 cm signal from neutral hydrogen.

astro-ph.CO↗

arXiv2020

The early growth of supermassive black holes in cosmological hydrodynamic simulations with constrained Gaussian realizations

The paper examines the early growth of supermassive black holes (SMBHs) in cosmological hydrodynamic simulations with different BH seeding scenarios. Employing the constrained Gaussian realization, we reconstruct the initial conditions in the large-volume BlueTides simulation and run them to $z=6$ to cross-validate that the method reproduces the first quasars and their environments. Our constrained simulations in a volume of $(15\, h^{-1}{\rm Mpc})^3$ successfully recover the evolution of large-scale structure and the stellar and BH masses in the vicinity of a $\sim10^{12}\, M_{\odot}$ halo which we identified in BlueTides at $z\sim7$ hosting a $\sim10^9\, M_{\odot}$ SMBH. Among our constrained simulations, only the ones with a low-tidal field and high-density peak in the initial conditions induce the fastest BH growth required to explain the $z>6$ quasars. We run two sets of simulations with different BH seed masses of $5\times10^3$, $5\times10^4$, and $5\times10^5\, h^{-1}M_{\odot}$, (a) with the same ratio of halo to BH seed mass and (b) with the same halo threshold mass. At $z=6$, all the SMBHs converge in mass to $\sim10^9\, M_{\odot}$ except for the one with the smallest seed in (b) undergoing critical BH growth and reaching $10^8$ -- $10^9\, M_{\odot}$, albeit with most of the growth in (b) delayed compared to set (a). The finding of eight BH mergers in the small-seed scenario (four with masses $10^4$ -- $10^6\, M_{\odot}$ at $z>12$), six in the intermediate-seed scenario, and zero in the large-seed scenario suggests that the vast BHs in the small-seed scenario merge frequently during the early phases of the growth of SMBHs. The increased BH merger rate for the low-mass BH seed and halo threshold scenario provides an exciting prospect for discriminating BH formation mechanisms with the advent of multi-messenger astrophysics and next-generation gravitational wave facilities.

astro-ph.GA↗

arXiv2020

Testing the fidelity of simulations of black hole - galaxy co-evolution at z ~ 1.5 with observations

We examine the scaling relations between the mass of a supermassive black hole (SMBH) and its host galaxy properties at $1.2<z<1.7$ using both observational data and simulations. Recent measurements of 32 X-ray-selected broad-line Active Galactic Nucleus (AGNs) are compared with two independent state-of-the-art efforts, including the hydrodynamic simulation MassiveBlackII (MBII) and a semi-analytic model (SAM). After applying an observational selection function to the simulations, we find that both MBII and SAM agree well with the data, in terms of the central distribution. However, the dispersion in the mass ratio between black hole mass and stellar mass is significantly more consistent with the MBII prediction ($\sim0.3~$dex), than with the SAM ($\sim0.7~$dex), even when accounting for observational uncertainties. Hence, our observations can distinguish between the different recipes adopted in the models. The mass relations in the MBII are highly dependent on AGN feedback while the relations in the SAM are more sensitive to galaxy merger events triggering nuclear activity. Moreover, the intrinsic scatter in the mass ratio of our high-$z$ sample is comparable to that observed in the local sample, all but ruling out the proposed scenario the correlations are purely stochastic in nature arising from some sort of cosmic central limit theorem. Our results support the hypothesis of AGN feedback being responsible for a causal link between the SMBH and its host galaxy, resulting in a tight correlation between their respective masses.

astro-ph.GA↗

arXiv2020

Unveil stock correlation via a new tensor-based decomposition method

Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this question and proposes a new methodology to estimate the correlation matrix which doesn't depend on the chosen sample period. This new methodology is based on tensor factorization techniques. In particular, combining and normalizing factor components, we build a correlation matrix which shows emerging structural dependency properties not affected by the sample period. To retrieve the factor components, we propose a new tensor decomposition (which we name Slice-Diagonal Tensor (SDT) factorization) and compare it to the two most used tensor decompositions, the Tucker and the PARAFAC. We have that the new factorization is more parsimonious than the Tucker decomposition and more flexible than the PARAFAC. Moreover, this methodology applied to both simulated and empirical data shows results which are robust to two non-parametric tests, namely Kruskal-Wallis and Kolmogorov-Smirnov tests. Since the resulting correlation matrix features stability and emerging structural dependency properties, it can be used as alternative to other correlation matrices type of measures, including the Person correlation.

q-fin.RM↗

arXiv2020

Stochastic Processes as the Origin of the Double-Power Law Shape of the Quasar Luminosity Function

The Quasar Luminosity Function (QLF) offers insight into the early co-evolution of black holes and galaxies. It has been characterized observationally up to redshift $z\sim6$ with clear evidence of a double power-law shape, in contrast to the Schechter-like form of the underlying dark-matter halo mass function. We investigate a physical origin for the difference in these distributions by considering the impact of stochasticity induced by the processes that determine the quasar luminosity for a given host halo and redshift. We employ a conditional luminosity function and construct the relation between median quasar magnitude versus halo mass $M_{UV,\rm{c}}(M_{\rm{h}})$ with log-normal in luminosity scatter $Σ$, and duty-cycle $ε_{\rm{DC}}$, and focus on high redshift $z\gtrsim4$. We show that, in order to reproduce the observed QLF, the $Σ=0$ abundance matching requires all of the brightest quasars to be hosted in the rarest most massive dark-matter halos (with an increasing $M_{UV,\rm{c}}/M_{\rm{h}}$ in halo mass). Conversely, for $Σ>0$ the brightest quasars can be over-luminous outliers hosted in relatively common dark-matter halos. In this case, the median quasar magnitude versus halo mass relation, $M_{UV,\rm{c}}$, flattens at the high-end, as expected in self-regulated growth due to feedback. We sample the parameter space of $Σ$ and $ε_{\rm{DC}}$ and show that $M_{UV,\rm{c}}$ flattens above $M_{\rm{h}}\sim 10^{12}M_{\odot}$ for $ε_{\rm{DC}}<10^{-2}$. Models with $ε_{\rm{DC}}\sim1$ instead require a high mass threshold close to $M_{\rm{h}}\gtrsim10^{13}M_{\odot}$. We investigate the impact of $ε_{\rm{DC}}$ and $Σ$ on measurements of clustering and find there is no luminosity dependence on clustering for $Σ>0.3$, consistent with recent observations from Subaru HSC.

astro-ph.GA↗

arXiv2020

TXS 2116$-$077: A Gamma-ray Emitting Relativistic Jet Hosted in a Galaxy Merger

What triggers collimated relativistic outflows or jets, from the centers of galaxies remains a fundamental question in astrophysics. The merging of two galaxies has been proposed to realize the conditions to successfully launch and drive such jets into the intergalactic medium. However, evidences for the operation of this mechanism are scarce. Here we report the first unambiguous detection of an ongoing merger of a narrow-line Seyfert 1 galaxy, TXS 2116$-$077, hosting a closely aligned, $γ$-ray emitting relativistic jet with a Seyfert 2 galaxy at a separation of $\sim$12 kpc, using the observations taken with 8.2 m Subaru telescope. Our subsequent followup observations with 10.4 m Gran Telescopio Canarias, 4.2 m William Herschel Telescope, and Chandra X-ray observatory have provided what is likely to be the first glimpse of the merging environment hosting a closely aligned relativistic jet. Our finding that the jet is considerably younger than the merger demonstrates that jet activity can be triggered by galaxy mergers and that $γ$-ray detected narrow-line Seyfert 1 galaxies represent the beginning phase of that activity. These results also highlight the crucial role of mergers in shaping the fate of galaxies in their cosmological evolution and are consistent with recent studies focused on the host galaxy imaging of this enigmatic class of active galactic nuclei.

astro-ph.HE↗

arXiv2020

A new set of cluster driven composite development indicators

Composite development indicators used in policy making often subjectively aggregate a restricted set of indicators. We show, using dimensionality reduction techniques, including Principal Component Analysis (PCA) and for the first time information filtering and hierarchical clustering, that these composite indicators miss key information on the relationship between different indicators. In particular, the grouping of indicators via topics is not reflected in the data at a global and local level. We overcome these issues by using the clustering of indicators to build a new set of cluster driven composite development indicators that are objective, data driven, comparable between countries, and retain interpretabilty. We discuss their consequences on informing policy makers about country development, comparing them with the top PageRank indicators as a benchmark. Finally, we demonstrate that our new set of composite development indicators outperforms the benchmark on a dataset reconstruction task.

econ.GN↗

arXiv2020

Nebular Line Emission During the Epoch of Reionization

Nebular emission lines associated with galactic HII regions carry information about both physical properties of the ionised gas and the source of ionising photons as well as providing the opportunity of measuring accurate redshifts and thus distances once a cosmological model is assumed. While nebular line emission has been extensively studied at lower redshift there are currently only few constraints within the epoch of reionisation (EoR, $z>6$), chiefly due to the lack of sensitive near-IR spectrographs. However, this will soon change with the arrival of the Webb Telescope providing sensitive near-IR spectroscopy covering the rest-frame UV and optical emission of galaxies in the EoR. In anticipation of Webb we combine the large cosmological hydrodynamical simulation Bluetides with photoionisation modelling to predict the nebular emission line properties of galaxies at $z=8\to 13$. We find good agreement with the, albeit limited, existing direct and indirect observational constraints on equivalent widths though poorer agreement with luminosity function constraints.

astro-ph.GA↗

arXiv2020

Multiplicity functions of quasars: Predictions from the MassiveBlackII simulation

We examine multiple AGN systems (triples and quadruples, in particular) in the \texttt{MassiveBlackII} simulation over a redshift range of $0.06\lesssim z \lesssim 4$. We identify AGN systems (with bolometric luminosity $L_{\mathrm{bol}}>10^{42}~\mathrm{ergs/sec}$) at different scales~(defined by the maximum distance between member AGNs) to determine the AGN multiplicity functions. This is defined as the volume/ surface density of AGN systems per unit \textit{richness} $R$, the number of AGNs in a system. We find that gravitationally bound multiple AGN systems tend to populate scales of $\lesssim0.7~\mathrm{cMpc}/h$; this corresponds to angular separations of $\lesssim100~\mathrm{arcsec}$ and a line of sight velocity difference $\lesssim200~\mathrm{km/sec}$. The simulation contains $\sim 10$ and $\sim100$ triples/quadruples per $\mathrm{deg}^2$ up to depths of DESI ($g\lesssim24$) and LSST ($g\lesssim26$) imaging respectively; at least $20\%$ of these should be detectable in spectroscopic surveys. The simulated quasar ($L_{\mathrm{bol}}>10^{44}~\mathrm{ergs/sec}$) triples and quadruples predominantly exist at $1.5\lesssim z \lesssim 3$. Their members have black hole masses $10^{6.5}\lesssim M_{bh}\lesssim 10^{9}~M_{\odot}/h$ and live in separate (one central and multiple satellite) galaxies with stellar masses $10^{10}\lesssim M_{*}\lesssim 10^{12}~M_{\odot}/h$. They live in the most massive haloes (for e.g. $\sim 10^{13}~M_{\odot}/h$ at $z=2.5$; $\sim 10^{14}~M_{\odot}/h$ at $z=1$) in the simulation. Their detections provide an exciting prospect for understanding massive black hole growth and their merger rates in galaxies in the era of multi-messenger astronomy.

astro-ph.GA↗

arXiv2020

Disentangling shock diffusion on complex networks: Identification through graph planarity

Large scale networks delineating collective dynamics often exhibit cascading failures across nodes leading to a system-wide collapse. Prominent examples of such phenomena would include collapse on financial and economic networks. Intertwined nature of the dynamics of nodes in such network makes it difficult to disentangle the source and destination of a shock that percolates through the network, a property known as reflexivity. In this article, a novel methodology is proposed which combines vector autoregression model with an unique identification restrictions obtained from the topological structure of the network to uniquely characterize cascades. In particular, we show that planarity of the network allows us to statistically estimate a dynamical process consistent with the observed network and thereby uniquely identify a path for shock propagation from any chosen epicenter to all other nodes in the network. We analyze the distress propagation mechanism in closed loops giving rise to a detailed picture of the effect of feedback loops in transmitting shocks. We show usefulness and applications of the algorithm in two networks with dynamics at different time-scales: worldwide GDP growth network and stock network. In both cases, we observe that the model predicts the impact of the shocks emanating from the US would be concentrated within the cluster of developed countries and the developing countries show very muted response, which is consistent with empirical observations over the past decade.

q-fin.ST↗

arXiv2019

QSO obscuration at high redshift ($z \gtrsim 7$): Predictions from the BlueTides simulation

High-$z$ AGNs hosted in gas rich galaxies are expected to grow through significantly obscured accretion phases. This may limit or bias their observability. In this work, we use \textsc{BlueTides}, a large volume cosmological simulation of galaxy formation to examine quasar obscuration for the highest-redshift ($z \geq 7$) supermassive black holes residing in the center of galaxies. We find that for the bright quasars, most of the high column density gas ($>90\%$) resides in the innermost regions of the host galaxy, (typically within $< 10$ ckpc), while the gas in the outskirts is a minor contributor to the $N_\mathrm H$. The brightest quasars can have large angular variations in galactic obscuration, over 2 orders of magnitude, where the lines of sight with the lowest obscuration are those formed via strong gas outflows driven by AGN feedback. We find that for the overall AGN population, the mean $N_\mathrm H$ is generally larger for high luminosity and BH mass, while the $N_\mathrm H$ distribution is significantly broadened, developing a low $N_\mathrm H $ wing due to the angular variations driven by the AGN outflows/feedback. The obscured fraction P($N_{\rm H} > 10^{23} {\rm cm}^{-2}$) typically range from 0.6 to 1.0 for increasing $L_{X}$ (with $L_X > 10^{43} \rm{ergs/s}$), with no clear trend of redshift evolution. With respect to the galaxy host property, we find a linear relation between $N_{\rm H}$, $M_*$ and $M_{\rm H_2}$ with $\log N_{\rm H} = (0.24 \pm 0.03) \log M_{*} + (20.7 \pm 0.3)$ and $\log N_{\rm H} = (0.47 \pm 0.03) \log M_{\rm H_2} + (18.4 \pm 0.3)$. The dust optical depth in the UV band $τ_{\mathrm UV}$ has tight positive correlation with $N_{\rm H}$. Our dust extincted UVLF is about 1.5 dex lower than the intrinsic UVLF, implying that more than 99\% of the $z \sim 7$ AGNs are heavily dust extincted and therefore would be missed by the UV band observation.

astro-ph.GA↗

arXiv2019

A memory-based method to select the number of relevant components in Principal Component Analysis

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an exponential, giving rise to long memory effects. In comparison with other available methods present in the literature, our procedure does not rely on subjective evaluations and is computationally inexpensive. The underlying basic idea is to use a suitable factor model to analyse the residual memory after sequentially removing more and more components, and stopping the process when the maximum amount of memory has been accounted for by the retained components. We validate our methodology on both synthetic and real financial data, and find in all cases a clear and computationally superior answer entirely compatible with available heuristic criteria, such as cumulative variance and cross-validation.

q-fin.ST↗

arXiv2019

The evolution of galaxy intrinsic alignments in the MassiveBlack II universe

We investigate the redshift evolution of the intrinsic alignments (IA) of galaxies in the \texttt{MassiveBlackII} (MBII) simulation. We select galaxy samples above fixed subhalo mass cuts ($M_h>10^{11,12,13}~M_{\odot}/h$) at $z=0.6$ and trace their progenitors to $z=3$ along their merger trees. Dark matter components of $z=0.6$ galaxies are more spherical than their progenitors while stellar matter components tend to be less spherical than their progenitors. The distribution of the galaxy-subhalo misalignment angle peaks at $\sim10~\mathrm{deg}$ with a mild increase with time. The evolution of the ellipticity-direction~(ED) correlation amplitude $ω(r)$ of galaxies (which quantifies the tendency of galaxies to preferentially point towards surrounding matter overdensities) is governed by the evolution in the alignment of underlying dark matter~(DM) subhaloes to the matter density of field, as well as the alignment between galaxies and their DM subhaloes. At scales $\sim1~\mathrm{cMpc}/h$, the alignment between DM subhaloes and matter overdensity gets suppressed with time, whereas the alignment between galaxies and DM subhaloes is enhanced. These competing tendencies lead to a complex redshift evolution of $ω(r)$ for galaxies at $\sim1~\mathrm{cMpc}/h$. At scales $>1~\mathrm{cMpc}/h$, alignment between DM subhaloes and matter overdensity does not evolve significantly; the evolution of the galaxy-subhalo misalignment therefore leads to an increase in $ω(r)$ for galaxies by a factor of $\sim4$ from $z=3$ to $0.6$ at scales $>1~\mathrm{cMpc}/h$. The balance between competing physical effects is scale dependant, leading to different conclusions at much smaller scales($\sim0.1~\mathrm{Mpc}/h$).

astro-ph.CO↗

arXiv2019

Predictions for the Abundance of High-redshift Galaxies in a Fuzzy Dark Matter Universe

During the last decades, rapid progress has been made in measurements of the rest-frame ultraviolet (UV) luminosity function (LF) for high-redshift galaxies ($z \geq 6$). The faint-end of the galaxy LF at these redshifts provides powerful constraints on different dark matter models that suppress small-scale structure formation. In this work we perform full hydrodynamical cosmological simulations of galaxy formation using an alternative DM model composed of extremely light bosonic particles ($m \sim 10^{-22}$ eV), also known as fuzzy dark matter (FDM), and examine the predictions for the galaxy stellar mass function and luminosity function at $z \geq 6$ for a range of FDM masses. We find that for FDM models with bosonic mass $m = 5\times10^{-22}$ eV, the number density of galaxies with stellar mass $\rm M_* \sim 10^7 M_{\odot}$ is suppressed by $\sim 40\%$ at z = 9, $\sim 20\%$ at z = 5, and the UV LFs within magnitude range of -16 < $M_{\rm UV}$ < -14 is suppressed by $\sim 60\%$ at $z = 9$, $\sim 20\%$ at $z = 5$ comparing to the CDM counterpart simulation. Comparing our predictions with current measurements of the faint-end LFs ($-18 \leqslant M_{\rm UV} \leqslant -14$), we find that FDM models with $m_{22} < 5\times10^{-22}$ are ruled out at $3σ$ confidence level. We expect that future LF measurements by James Webb Space Telescope (JWST), which will extend down to $M_{\rm UV} \sim -13$ for $z \lesssim 10$, with a survey volume that is comparable to the Hubble Ultra Deep Field (HUDF) would have the capability to constrain FDM models to $m\; \gtrsim 10^{-21}$ eV.

astro-ph.CO↗

arXiv2019

The Fundamental Plane of Black Hole Accretion and its Use as a Black Hole-Mass Estimator

We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole ($M$), its 5 GHz radio continuum luminosity ($νL_ν$), and its 2-10 keV X-ray power-law continuum luminosity ($L_X$). We compile a sample of black holes with primary, direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a mass-predictor function of the form $\log(M/10^{8}\,M_{\scriptscriptstyle \odot}) = μ_0 + ξ_{μR} \log(L_R / 10^{38}\,\mathrm{erg\,s^{-1}}) + ξ_{μX} \log(L_X / 10^{40}\,\mathrm{erg\,s^{-1}})$. Our best-fit results are $μ_0 = 0.55 \pm 0.22$, $ξ_{μR} = 1.09 \pm 0.10$, and $ξ_{μX} = -0.59^{+0.16}_{-0.15}$ with the natural logarithm of the Gaussian intrinsic scatter in the log-mass direction $\lnε_μ= -0.04^{+0.14}_{-0.13}$. This result is a significant improvement over our earlier mass scaling result because of the increase in active galactic nuclei sample size (from 18 to 30), improvement in our X-ray binary sample selection, better identification of Seyferts, and improvements in our analysis that takes into account systematic uncertainties and correlated uncertainties. Because of these significant improvements, we are able to consider potential influences on our sample by including all sources with compact radio and X-ray emission but ultimately conclude that the fundamental plane can empirically describe all such sources. We end with advice for how to use this as a tool for estimating black hole masses.

astro-ph.HE↗