Power-law Shape Research Articles

On the nature of the X-ray pulsar XTE J1859+083 and its broad-band properties

ABSTRACT This work is devoted to the study of the broad-band 0.8–79 keV spectral and timing properties of the poorly studied X-ray pulsar XTE J1859+083 during its 2015 outburst based on the data from the NuSTAR and Swift observatories. We show that the source pulse profile has complex shape that depends on the energy band. Pulse fraction of XTE J1859+083 has constant value around 35 per cent in the broad energy band, this behaviour is atypical for X-ray pulsars. At the same time its energy spectrum is typical of this class of objects and has a power-law shape with an exponential cutoff at high energies. No cyclotron absorption line was discovered in the source spectrum. On the basis of indirect method and the absence of a cyclotron line, an estimation was made for the magnetic field strength as less than 5 × 1011 G or belonging to the interval from 5 × 1012 to $2.0^{+0.9}_{-1.2}\times 10^{13}$ G. Data from the NOT and SALT telescopes as well as optical and IR sky surveys allowed us also to study the nature of its optical companion. We have proposed and studied new possible candidates for the optical companion of XTE J1859+083 and the most likely candidate was identified. The results of the optical and IR photometry and spectroscopy of these possible companions showed that the system is a Be X-ray binary, showing Brγ, He i, and strong H α spectral lines.

Comprehensive Analysis of a Dense Sample of FRB 121102 Bursts

Abstract We present an analysis of a densely repeating sample of bursts from the first repeating fast radio burst, FRB 121102. We reanalyzed the data used by Gourdji et al. and detected 93 additional bursts using our single-pulse search pipeline. In total, we detected 133 bursts in three hours of data at a center frequency of 1.4 GHz using the Arecibo telescope, and develop robust modeling strategies to constrain the spectro-temporal properties of all of the bursts in the sample. Most of the burst profiles show a scattering tail, and burst spectra are well modeled by a Gaussian with a median width of 230 MHz. We find a lack of emission below 1300 MHz, consistent with previous studies of FRB 121102. We also find that the peak of the log-normal distribution of wait times decreases from 207 to 75 s using our larger sample of bursts, as compared to that of Gourdji et al. Our observations do not favor either Poissonian or Weibull distributions for the burst rate distribution. We searched for periodicity in the bursts using multiple techniques, but did not detect any significant period. The cumulative burst energy distribution exhibits a broken power-law shape, with the lower- and higher-energy slopes of −0.4 ± 0.1 and −1.8 ± 0.2, with the break at (2.3 ± 0.2) × 1037 erg. We provide our burst fitting routines as a Python package burstfit 4 4 https://github.com/thepetabyteproject/burstfit that can be used to model the spectrogram of any complex fast radio burst or pulsar pulse using robust fitting techniques. All of the other analysis scripts and results are publicly available. 5 5 https://github.com/thepetabyteproject/FRB121102

The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain

Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable to the Δ=1 isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to anisotropy Δ>1. The aim of this paper is the study of the (k,ω)-plane line shape of the spin dynamical structure factor components S+−(k,ω), S−+(k,ω), and Szz(k,ω) of the Δ>1 spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field near their (k,ω)-plane sharp peaks. However, the extension of the theory to anisotropy Δ>1 requires as a first step the clarification of the nature of a specific type of elementary magnetic configurations in terms of physical spins 1/2. To reach that goal, that the spin SU(2) symmetry of the isotropic Δ=1 point is in the case of anisotropy Δ>1 replaced by a continuous quantum group deformed q-spin SUq(2) symmetry plays a key role. For Δ>1, spin projection Sz remains a good quantum number whereas spin S is not, being replaced by the q-spin Sq in the eigenvalue of the Casimir generator of the continuous SUq(2) symmetry. Based on the isomorphism between the irreducible representations of the Δ=1 spin SU(2) symmetry and Δ>1 continuous SUq(2) symmetry and on their relation to the occupancy configurations of the Bethe-ansatz quantum numbers one finds that the elementary magnetic configurations under study are q-spin neutral. This determines the form of S matrices on which the extended dynamical theory relies. They are found in this paper to describe the scattering of n-particles whose relation to configurations of physical spins 1/2 is established. Specifically, their internal degrees of freedom refer to unbound q-spin singlet pairs of physical spins 1/2 described by n=1 real single Bethe rapidities and to n=2,3,... bound such q-spin singlet pairs described by Bethe n-strings for n>1. There is a relationship between the negativity and the length of the momentum k interval of the k dependent exponents that control the power-law line shape of the spin dynamical structure factor components near the lower threshold of a given (k,ω)-plane continuum and the amount of spectral weight over the latter. Using such a relationship, one finds that in the thermodynamic limit the significant spectral weight contributions from Bethe n-strings at a finite longitudinal magnetic field refer to specific two-parametric (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factor components S+−(k,ω) and Szz(k,ω). In contrast to the Δ=1 isotropic chain, excited energy eigenstates including up to n=3 Bethe n-strings lead to finite spectral-weight contributions to S+−(k,ω). Most spectral weight stems though from excited energy eigenstates whose q-spin singlet Sz=Sq=0 pairs of physical spins 1/2 are all unbound. It is associated with (k,ω)-plane continua in the spectra of the spin dynamical structure factor components that are gapless at some specific momentum values. We derive analytical expressions for the line shapes of S+−(k,ω), S−+(k,ω), and Szz(k,ω) valid in the vicinity of (k,ω)-plane lines of sharp peaks. Those are mostly located at and just above lower thresholds of (k,ω)-plane continua associated with both states with only unbound q-spin singlet pairs and states populated by such pairs and a single n=2 or n=3n-particle. Our results provide physically interesting and important information on the microscopic processes that determine the dynamical properties of the non-perturbative spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field.

The first simultaneous X-ray broadband view of Mrk 110 with XMM-Newton and NuSTAR

Context. Soft and hard X-ray excesses, compared to the continuum power-law shape between ∼2−10 keV, are common features observed in the spectra of active galactic nuclei (AGN) and are associated with the accretion disc-corona system around the supermassive black hole. However, the dominant process at work is still highly debated and has been proposed to be either relativistic reflection or Comptonisation. Such an investigation can be problematic for AGN that have significant intrinsic absorption, either cold or warm, which can severely distort the observed continuum. Therefore, AGN with no (or very weak) intrinsic absorption along the line-of-sight, called bare AGN, are the best targets for directly probing disc-corona systems. Aims. We aim to characterise the main X-ray spectral physical components from the bright bare broad-line Seyfert 1 AGN Mrk 110, as well as the physical process(es) at work in its disc-corona system viewed almost face-on. Methods. We perform the X-ray broadband spectral analysis thanks to two simultaneous XMM-Newton and NuSTAR observations performed on November 16−17, 2019, and April 5−6, 2020. We also use a deep NuSTAR observation obtained in January 2017 for the spectral analysis above 3 keV. Results. The broadband X-ray spectra of Mrk 110 are characterised by the presence of a prominent and absorption-free smooth soft X-ray excess, moderately broad O VII and Fe Kα emission lines, and a lack of a strong Compton hump. The continuum above ∼3 keV is very similar at both epochs, while some variability (stronger when brighter) is present for the soft X-ray excess. A combination of soft and hard Comptonisation by a warm and hot corona, respectively, plus mildly relativistic disc reflection reproduce the broadband X-ray continuum very well. The inferred warm corona temperature, kTwarm ∼ 0.3 keV, is similar to the values found in other sub-Eddington AGN, whereas the hot corona temperature, kThot ∼ 21−31 keV (depending mainly on the assumed hot corona geometry), is found to be in the lower range of the values measured in AGN.

Radiation GRMHD Simulations of the Hard State of Black Hole X-Ray Binaries and the Collapse of a Hot Accretion Flow

Abstract We present global radiation GRMHD simulations of strongly magnetized accretion onto a spinning, stellar mass black hole at sub-Eddington rates. Using a frequency-dependent Monte Carlo procedure for Compton scattering, we self-consistently evolve a two-temperature description of the ion–electron fluid and its radiation field. For an Eddington ratio L/L Edd ≳ 10−3, the emergent spectrum forms an apparent power-law shape from thermal Comptonization up to a cutoff at ≃100 keV, characteristic of that seen in the hard spectral states of black hole X-ray binary systems. At these luminosities, the radiative efficiency is high (≈24%) and results in a denser midplane region where magnetic fields are dynamically important. For L/L Edd ∼ 10−2, our hot accretion flow appears to undergo thermal runaway and collapse. Our simulations demonstrate that hot accretion flows can be radiatively efficient and provide an estimate of their maximum luminosity.

VLBI Data Processing on Coronal Radio-sounding Experiments of Mars Express

Abstract The ESA’s Mars Express solar corona experiments were performed at two solar conjunctions in the years 2015 and 2017 by a number of radio telescopes in the European VLBI Network. This paper presents the methods to measure the frequency and phase fluctuations of the spacecraft radio signal, and the applications to study the characteristics of the plasma turbulence effects on the signal at a single station and at multiple stations via cross correlation. The power spectra of the frequency fluctuations observed between 4.9 and 76.3 R s have a power-law shape close to a Kolmogorov spectrum over the frequency interval ν lo < ν < ν up, where the nominal value of ν lo is set to 3 mHz and ν up is in the range of 0.03–0.15 Hz. The rms of the frequency fluctuations is presented as a function of the heliocentric distance. Furthermore, we analyze the variations of the electron column density fluctuations at solar offsets 4.9 R s and 9.9 R s and the cross-correlation products between the VLBI stations. The power density of the differential fluctuations between different stations decreases at ν < 0.01 Hz. Finally, the fast flow speeds of solar wind >700 km s−1 are derived from the cross correlation of frequency fluctuations at ν < 0.01 Hz. The fast flow speeds of solar wind correspond to the high heliolatitude of the coronal region that the radio rays passed. The VLBI observations and analysis methods can be used to study the electron column density fluctuations and the turbulence at multiple spatial points in the inner solar wind by providing multiple lines of sight between the Earth and the spacecraft.

Machine learning application to detect light echoes around black holes

ABSTRACT X-ray reverberation has become a powerful tool to probe the disc-corona geometry near black holes. Here, we develop machine learning (ML) models to extract the X-ray reverberation features imprinted in the power spectral density (PSD) of active galactic nucleus (AGN). The machine is trained using simulated PSDs in the form of a simple power-law encoded with the relativistic echo features. Dictionary learning and sparse coding algorithms are used for the PSD reconstruction, by transforming the noisy PSD to a representative sparse version. Then, the support vector machine is employed to extract the interpretable reverberation features from the reconstructed PSD that holds the information of the source height. The results show that the accuracy of predicting the source height, h, is genuinely high and the misclassification is only found when h > 15rg. When the test PSD has a bending power-law shape, which is completely new to the machine, the accuracy is still high. Therefore, the ML model does not require the intrinsic shape of the PSD to be determined in advance. By focusing on the PSD parameter space observed in real AGN data, classification for h ≤ 10rg can be determined with 100 per cent accuracy, even using a PSD in an energy band that contains a reflection flux as low as $10{{\ \rm per\ cent}}$ of the total flux. For h > 10rg, the data, if misclassified, will have small uncertainties of Δh ∼ 2–4rg. This work shows, as a proof of concept, that the ML technique could shape new methodological directions in the X-ray reverberation analysis.

Characteristics of Resonant Electrons Interacting With Whistler Waves in the Nearest Dipolarizing Magnetotail

AbstractThe Magnetospheric Multiscale spacecraft observations in the burst mode allow the determination of the characteristics of resonant electrons interacting with quasi‐parallel whistler waves during prolonged dipolarizations in the near Earth magnetotail at −22 RE < X ≤ −8 RE. We have detected 163 whistler bursts observed during 48 dipolarization events. The bursts were registered within ∼13 min following the dipolarization onset when the burst mode observations were available. In the majority of events, electrons with energies Wres ≥ 10 keV and pitch angles αres ∼ 100°–130° and αres ∼ 50°–80°made the maximum positive contribution to the growth rate of whistler waves propagating quasi‐parallel and antiparallel to the ambient magnetic field, respectively. Our analysis shows that electrons with Wres ∼ 10–20 keV could potentially be scattered into the loss cone by the low frequency whistler waves with fw ∼ (0.05–0.2)fce (fw is the wave frequency and fce is the electron gyrofrequency). The electrons that are scattered into the loss cone can contribute to electron precipitation within ∼13 min following the dipolarization onset. We suggest that whistler waves that are excited due to cyclotron instability driven by the temperature anisotropy of suprathermal electrons (≥2 keV) may, in turn, affect electron distribution in this energy range. Specifically, lower energy resonant electrons transfer a part of their kinetic energy to waves, while more energetic electrons absorb wave energy increasing their kinetic energy. This may lead to the transformation of higher‐energy part of electron distribution from Maxwellian to the power law shape.

Gravity currents with internal stratification in channels of non-rectangular cross-section

We investigate by theoretical means the motion of a gravity current (GC) released from a lock into an ambient fluid in a horizontal channel of non-rectangular cross-section area (CSA) like triangle, trapezoid or semicircle. The lock contains an internal stratification, in particular a layer of density ρL overlain by a layer of density ρU, where ρo<ρU<ρL and ρo is the density of the ambient fluid. Assuming a Boussinesq and large Reynolds flow, we develop a new self-contained model for the prediction of the motion of the GC, in particular the position and speed of the nose xN(t) and uN(t), where t is the time from release. Upon an appropriate scaling the system of equations and boundary conditions is reduced to a form amenable to analysis and solution by the methods employed for the non-stratified flow. The solution reveals an initial slumping with constant uN, and eventually the transition at xV to the viscous regime. A self similar phase of the form xN∼tβ can develop only for CSA of power-law shape, in which case the constant β depends on the shape but not on the stratification. The stability is also considered, and we show that the flow is stable with few exception. Unfortunately, experimental data for comparisons are not available, and we hope that the sharp present results will motivate the performance of needed experimental tests.

Particle acceleration in winds of star clusters

ABSTRACT The origin of cosmic rays in our Galaxy remains a subject of active debate. While supernova remnant (SNR) shocks are often invoked as the sites of acceleration, it is now widely accepted that the difficulties of such sources in reaching PeV energies are daunting and it seems likely that only a subclass of rare remnants can satisfy the necessary conditions. Moreover, the spectra of cosmic rays escaping the remnants have a complex shape that is not obviously the same as the spectra observed at the Earth. Here, we investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by star clusters’ winds in the interstellar medium. While the main limitation to the maximum energy in SNRs comes from the need for effective wave excitation upstream so as to confine particles in the near-shock region and speed up the acceleration process, at the termination shock of star clusters the confinement of particles upstream is guaranteed by the geometry of the problem. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for powerful clusters in the high end of the luminosity tail for these sources. A crucial role in this problem is played by the dissipation of energy in the wind to magnetic perturbations. Under reasonable conditions, the spectrum of the accelerated particles has a power-law shape with a slope 4/4.3, in agreement with what is required based upon standard models of cosmic ray transport in the Galaxy.

Assessing the contribution of groundwater to catchment travel time distributions through integrating conceptual flux tracking with explicit Lagrangian particle tracking

Travel time distributions (TTDs) provide an effective way to describe the transport and mixing processes of water parcels in a subsurface hydrological system. A major challenge in characterizing catchment TTD is quantifying the travel times in deep groundwater and its contribution to the streamflow TTD. Here, we develop and test a novel modeling framework for an integrated assessment of catchment scale TTDs through explicit representation of 3D-groundwater dynamics. The proposed framework is based on the linkage between a flux tracking scheme with the surface hydrologic model (mHM) for the soil-water compartment and a particle tracking scheme with the 3D-groundwater model OpenGeoSys (OGS) for the groundwater compartment. This linkage provides us with the ability to simulate the spatial and temporal dynamics of TTDs in these different hydrological compartments from grid scale to regional scale. We apply this framework in the Nägelstedt catchment in central Germany. Simulation results reveal that both shape and scale of grid-scale groundwater TTDs are spatially heterogeneous, which are strongly dependent on the topography and aquifer structure. The component-wise analysis of catchment TTD shows a time-dependent sensitivity of transport processes in soil zone and groundwater to driving meteorological forcing. Catchment TTD exhibits a power-law shape and fractal behavior. The predictive uncertainty in catchment mean travel time is dominated by the uncertainty in the deep groundwater rather than that in the soil zone. Catchment mean travel time is severely biased by a marginal error in groundwater characterization. Accordingly, we recommend to use multiple summary statistics to minimize the predictive uncertainty introduced by the tailing behavior of catchment TTD.

Path Properties of a Generalized Fractional Brownian Motion

The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power-law shape function and non-stationary noises with a power-law variance function. In this paper, we study sample path properties of the generalized fractional Brownian motion, including Hölder continuity, path differentiability/non-differentiability, and functional and local law of the iterated logarithms.

Swimming Escherichia coli Cells Explore the Environment by Lévy Walk.

Escherichia coli cells swim in aqueous environment in a random walk of alternating runs and tumbles. The diffusion characteristics of this random walk remains unclear. In this study, by tracking the swimming of wild-type cells in a three-dimensional (3D) homogeneous environment, we found that their trajectories are superdiffusive, consistent with Lévy walk behavior. For comparison, we tracked the swimming of mutant cells that lack the chemotaxis signaling noise (the steady-state fluctuation of the concentration of the chemotaxis response regulator CheY-P) and found that their trajectories are normal diffusive. Therefore, wild-type E. coli cells explore the environment by Lévy walk, which originates from the chemotaxis signaling noise. This Lévy walk pattern enhances their efficiency in environmental exploration.IMPORTANCEE. coli cells explore the environment in a random walk of alternating runs and tumbles. By tracking the 3D trajectories of E. coli cells in an aqueous environment, we found that their trajectories are superdiffusive, with a power-law shape for the distribution of run lengths, which is characteristics of Lévy walk. We further show that this Lévy walk behavior is due to the random fluctuation of the output level of the bacterial chemotaxis pathway, and it enhances the efficiency of the bacteria in exploring the environment.

Correlating spectral and timing properties in the evolving jet of the microblazar MAXI J1836−194

ABSTRACT During outbursts, the observational properties of black hole X-ray binaries vary on time-scales of days to months. These relatively short time-scales make these systems ideal laboratories to probe the coupling between accreting material and outflowing jets as the accretion rate varies. In particular, the origin of the hard X-ray emission is poorly understood and highly debated. This spectral component, which has a power-law shape, is due to Comptonization of photons near the black hole, but it is unclear whether it originates in the accretion flow itself, or at the base of the jet, or possibly the interface region between them. In this paper, we explore the disc–jet connection by modelling the multiwavelength emission of MAXI J1836−194 during its 2011 outburst. We combine radio through X-ray spectra, X-ray timing information, and a robust joint-fitting method to better isolate the jet’s physical properties. Our results demonstrate that the jet base can produce power-law hard X-ray emission in this system/outburst, provided that its base is fairly compact and that the temperatures of the emitting electrons are subrelativistic. Because of energetic considerations, our model favours mildly pair-loaded jets carrying at least 20 pairs per proton. Finally, we find that the properties of the X-ray power spectrum are correlated with the jet properties, suggesting that an underlying physical process regulates both.

The baryon content of groups and clusters of galaxies in the FABLE simulations

ABSTRACT We study the gas and stellar mass content of galaxy groups and clusters in the fable suite of cosmological hydrodynamical simulations, including the evolution of their central brightest cluster galaxies (BCGs), satellite galaxies, and intracluster light (ICL). The total gas and stellar mass of fable clusters are in good agreement with observations and show negligible redshift evolution at fixed halo mass for $M_{500} \gtrsim 3 \times 10^{14} \, \mathrm{M}_{\odot }$ at z ≲ 1, in line with recent findings from Sunyaev–Zel’dovich (SZ)-selected cluster samples. Importantly, the simulations predict significant redshift evolution in these quantities in the low-mass ($M_{500} \sim 10^{14} \, \mathrm{M}_{\odot }$) regime, which will be testable with upcoming SZ surveys such as SPT-3G. Whilst the stellar masses of fable BCGs are in reasonable agreement with observations, the total stellar mass in satellite galaxies is lower than observed and the total mass in ICL is somewhat higher. This may be caused by enhanced tidal stripping of satellite galaxies due to their large sizes. BCGs are characterized by moderate stellar mass growth at z &amp;lt; 1 coincident with a late-time development of the ICL. The level of BCG mass growth is in good agreement with recent observations; however, we caution that the inferred growth depends sensitively on the mass definition. We further show that in situ star formation contributes more than half the mass of a BCG over its lifetime, the bulk of which is gained at z &amp;gt; 1 where star formation rates are highest. The stellar mass profiles of the BCG+ICL component are similar to observed profiles out to ∼100 kpc at z ≈ 0 and follow a close to power law shape out to several hundred kpc. We further demonstrate that the inferred size growth of BCGs can be severely biased by the choice of parametric model and the outer radius of the fit.

Induced gravitational waves as a probe of thermal history of the universe

The scalar perturbation induced gravitational waves are a probe of the primordial density perturbation spectrum on small scales. In this paper, we show that they can also probe the thermal history of the universe. We assume the universe underwent a stage with a constant equation of state parameter w, followed by the radiation-dominated stage of the conventional big bang universe. We find that the infrared slope of the power spectrum of the induced stochastic gravitational wave background for decelerating cosmologies is related to the equation of state of the universe. Furthermore, the induced gravitational wave spectrum has in general a broken power-law shape around the scale of reheating. Interestingly, below the threshold 0w= of the equation of state parameter, the broken power-law presents a peak for a Dirac delta peak in the scalar spectrum. For a finite width peak, the threshold changes to w=−1/15 depending on the value of the width. In some cases, such a broken power-law gravitational wave spectrum may degenerate to the spectrum from other sources like phase transitions or global cosmic strings.

On the distribution of fluxes of gamma-ray blazars: hints for a stochastic process?

ABSTRACT We examine a model for the observed temporal variability of powerful blazars in the γ-ray band in which the dynamics is described in terms of a stochastic differential equation, including the contribution of a deterministic drift and a stochastic term. The form of the equation is motivated by the current astrophysical framework, accepting that jets are powered through the extraction of the rotational energy of the central supermassive black hole mediated by magnetic fields supported by a so-called magnetically arrested accretion disc. We apply the model to the γ-ray light curves of several bright blazars and we infer the parameters suitable to describe them. In particular, we examine the differential distribution of fluxes (dN/dFγ) and we show that the predicted probability density function for the assumed stochastic equation naturally reproduces the observed power-law shape at large fluxes $\mathrm{ d}N/\mathrm{ d}F_{\gamma } \propto F_{\gamma }^{-\alpha }$ with α &amp;gt; 2.

The Pre-explosion Mass Distribution of Hydrogen-poor Superluminous Supernova Progenitors and New Evidence for a Mass–Spin Correlation

Abstract Despite indications that superluminous supernovae (SLSNe) originate from massive progenitors, the lack of a uniformly analyzed statistical sample has so far prevented a detailed view of the progenitor mass distribution. Here we present and analyze the pre-explosion mass distribution of hydrogen-poor SLSN progenitors as determined from uniformly modeled light curves of 62 events. We construct the distribution by summing the ejecta mass posteriors of each event, using magnetar light-curve models presented in our previous works (and using a nominal neutron star remnant mass). The resulting distribution spans 3.6–40 M ⊙, with a sharp decline at lower masses, and is best fit by a broken power law described by at 3.6–8.6 M ⊙ and at 8.6–40 M ⊙. We find that observational selection effects cannot account for the shape of the distribution. Relative to Type Ib/c SNe, the SLSN mass distribution extends to much larger masses and has a different power-law shape, likely indicating that the formation of a magnetar allows more massive stars to explode as some of the rotational energy accelerates the ejecta. Comparing the SLSN distribution with predictions from single and binary star evolution models, we find that binary models for a metallicity of Z ≲ 1/3 Z ⊙ are best able to reproduce its broad shape, in agreement with the preference of SLSNe for low metallicity environments. Finally, we uncover a correlation between the pre-explosion mass and the magnetar initial spin period, where SLSNe with low masses have slower spins, a trend broadly consistent with the effects of angular momentum transport evident in models of rapidly rotating carbon–oxygen stars.

Basis function expansions for galactic dynamics: Spherical versus cylindrical coordinates

Aims. The orbital structure of galaxies is strongly influenced by the accuracy of the force calculation during orbit integration. We explore the accuracy of force calculations for two expansion methods and determine which one is preferable for orbit integration. Methods. We specifically compare two methods, one was introduced by Hernquist &amp; Ostriker (HO), which uses a spherical coordinate system and was built specifically for the Hernquist model, and the other by Vasiliev &amp; Athanassoula (CylSP) has a cylindrical coordinate system. Our comparisons include the Dehnen profile, its triaxial extension (of which the Hernquist profile is a special case) and a multicomponent system including a bar and disk density distributions for both analytical models and N-body realizations. Results. For the generalized Dehnen density, the CylSP method is more accurate than the HO method for nearly all inner power-law indices and shapes at all radii. For N-body realizations of the Dehnen model, or snapshots of an N-body simulation, the CylSP method is more accurate than the HO method in the central region for the oblate, prolate, and triaxial Hernquist profiles if the particle number is more than 5 × 105. For snapshots of the Hernquist models with spherical shape, the HO method is preferred. For the Ferrers bar model, the force from the CylSP method is more accurate than the HO method. The CPU time required for the initialization of the HO method is significantly shorter than that for the CylSP method, while the HO method costs subsequently much more CPU time than the CylSP method if the input corresponds to particle positions. From surface of section analyses, we find that the HO method creates more chaotic orbits than the CylSP method in the bar model. This could be understood to be due to a spurious peak in the central region when the force is calculated with the HO expansion. Conclusions. For an analytical model, the CylSP method with an inner cutoff radius of interpolation Rmin as calculated by the AGAMA software, is preferred due to its accuracy. For snapshots or N-body realizations not including a disk or a bar component, a detailed comparison between these two methods is needed if a density model other than the Dehnen model is used. For multicomponent systems, including a disk and a bar, the CylSP method is preferable.

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

Abstract The quasar luminosity function (QLF) offers insight into the early coevolution of black holes and galaxies. It has been characterized observationally up to redshift z ∼ 6 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 with log-normal in luminosity scatter Σ, and duty-cycle ϵ DC, and focus on high redshift z ≳ 4. 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 in halo mass). Conversely, for Σ &gt; 0 the brightest quasars can be overluminous outliers hosted in relatively common dark-matter halos. In this case, the median quasar magnitude versus halo mass relation, M UV,c, flattens at the high-end, as expected in self-regulated growth due to feedback. We sample the parameter space of Σ and ϵ DC and show that M UV,c flattens above for . Models with ϵ DC ∼ 1 instead require a high mass threshold close to . We investigate the impact of ϵ DC and Σ on measurements of clustering and find there is no luminosity dependence on clustering for Σ &gt; 0.3, consistent with recent observations from Subaru HSC.