Broken Power Law Research Articles

On the Mass Function of GWTC-2 Binary Black Hole Systems and Their Progenitors

The distribution of LIGO black hole binaries (BBH) shows an intermediate-mass range consistent with the Salpeter initial mass function (IMF) in black hole formation by core-collapse supernovae, subject to preserving binary association. They are effectively parameterized by the mean mass μ with a Pearson correlation coefficient of r = 0.93 ± 0.06 of secondary to primary masses with a mean mass ratio of , q = M 2/M 1, consistent with the paucity of intermediate-mass X-ray binaries. The mass function of LIGO BBHs is well approximated by a broken power law with a tail μ ≳ 31.4 M ⊙ in the mean binary mass . Its power-law index of α B,true = 4.77 ± 0.73 inferred from the tail of the observed mass function is found to approach the upper bound 2α S = 4.7 of the uncorrelated binary IMF, defined by the Salpeter index α S = 2.35 of the IMF of stars. The observed low scatter in BBH mass ratio q evidences equalizing mass transfer in binary evolution prior to BBH formation. At the progenitor redshift , furthermore, the power-law index satisfies in a flat ΛCDM background cosmology. The bound hereby precludes early formation at arbitrarily high redshifts , which may be made more precise and robust with extended BBH surveys from upcoming LIGO O4-5 observations.

Synchrotron Self-Compton Afterglow Closure Relations and Fermi-LAT-detected Gamma-Ray Bursts

The Fermi Large Area Telescope (Fermi-LAT) Collaboration reported the Second Gamma-ray Burst Catalog (2FLGC), which comprises a subset of 29 bursts with photon energies above 10 GeV. Although the standard synchrotron forward-shock model has successfully explained the gamma-ray burst (GRB) afterglow observations, energetic photons higher than 10 GeV from these transient events can hardly be described in this scenario. We present the closure relations (CRs) of the synchrotron self-Compton (SSC) afterglow model in the adiabatic and radiative scenario, and when the central engine injects continuous energy into the blast wave to study the evolution of the spectral and temporal indexes of those bursts reported in 2FLGC. We consider the SSC afterglow model evolving in stellar-wind and the interstellar medium (ISM), and the CRs as a function of the radiative parameter, the energy injection index, and the electron spectral index for 1 < p < 2 and 2 ≤ p. We select all GRBs that have been modeled with both a simple or a broken power law in the 2FLGC. We found that the CRs of the SSC model can satisfy a significant fraction of the burst that cannot be interpreted in the synchrotron scenario, even though those that require an intermediate density profile (e.g., GRB 130427A) or an atypical fraction of total energy given to amplify the magnetic field (ε B ). The value of this parameter in the SSC model ranges (ε B ≈ 10−5 − 10−4) when the cooling spectral break corresponds to the Fermi-LAT band for typical values of GRB afterglow. The analysis shows that the ISM is preferred for the scenario without energy injection and the stellar-wind medium for an energy injection scenario.

Arecibo observations of a burst storm from FRB 20121102A in 2016

ABSTRACT FRB 20121102A is the first known fast radio burst (FRB) from which repeat bursts were detected, and one of the best-studied FRB sources in the literature. Here we report on the analysis of 478 bursts (333 previously unreported) from FRB 20121102A using the 305-m Arecibo telescope – detected during approximately 59 hours of observations between December 2015 and October 2016. The majority of bursts are from a burst storm around September 2016. This is the earliest available sample of a large number of FRB 20121102A bursts, and it thus provides an anchor point for long-term studies of the source’s evolving properties. We observe that the bursts separate into two groups in the width-bandwidth-energy parameter space, which we refer to as the low-energy bursts (LEBs) and high-energy bursts (HEBs). The LEBs are typically longer duration and narrower bandwidth than the HEBs, reminiscent of the spectro-temporal differences observed between the bursts of repeating and non-repeating FRBs. We fit the cumulative burst rate-energy distribution with a broken power law and find that it flattens out toward higher energies. The sample shows a diverse zoo of burst morphologies. Notably, burst emission seems to be more common at the top than the bottom of our 1150–1730 MHz observing band. We also observe that bursts from the same day appear to be more similar to each other than to those of other days, but this observation requires confirmation. The wait times and burst rates that we measure are consistent with previous studies. We discuss these results, primarily in the context of magnetar models.

Hard-X-ray-selected active galactic nuclei – II. Spectral energy distributions in the 5–45 GHz domain

ABSTRACT A wide-frequency radio study of active galactic nuclei (AGN) is crucial to evaluate the intervening radiative mechanisms responsible for the observed emission and relate them with the underlying accretion physics. We present wide-frequency (5–45 GHz), high-sensitivity (few $\mathrm{{\mu }Jy\, beam^{-1}}$), (sub)-kpc Jansky Very Large Array (JVLA) observations of a sample of 30 nearby ($0.003\, \le \, z\, \le \, 0.3$) AGN detected by the International Gamma-Ray Astrophysics Laboratory (INTEGRAL)/Imager on Board the INTEGRAL Satellite (IBIS) at hard X-ray. We find a high detection fraction of radio emission at all frequencies, i.e. ≥95 per cent at 5, 10, and 15 GHz and ≥80 per cent at 22 and 45 GHz. Two sources out of 30 remain undetected at our high sensitivities. The nuclear radio morphology is predominantly compact, sometimes accompanied by extended jet-like structures, or more complex features. The radio spectral energy distributions (SEDs) of the radio cores appear either as single or as a broken power law, a minority of them exhibit a peaked component. The spectral slopes are either flat/inverted or steep, up to a break/peak or over the whole range. The sample mean SED shows a flat slope up to 15 GHz that steepens between 15 and 22 GHz and becomes again flat above 22 GHz. Significant radio–X-ray correlations are observed at all frequencies. About half of the sample features extended emission, clearly resolved by the JVLA, indicating low-power jets or large-scale outflows. The unresolved cores, which often dominate the radio power, may be of jet, outflow, and/or coronal origin, depending on the observed frequency.

Revisiting the Mass–Size Relation of Structures in Molecular Clouds

We revisit the mass–size relation of molecular cloud structures based on the column density map of the Cygnus-X molecular cloud complex. We extract 135 column density peaks in Cygnus-X and analyze the column density distributions around these peaks. The averaged column density profiles, N(R), around all the peaks can be well fitted with broken power-laws, which are described by an inner power-law index n, outer power-law index m, and the radius R TP and column density N TP at the transition point. We then explore the M–R relation with different samples of cloud structures by varying the N(R) parameters and the column density threshold, N 0, which determines the boundary of a cloud structure. We find that only when N 0 has a wide range of values, the M–R relation may largely probe the density distribution, and the fitted power-law index of the M–R relation is related to the power-law index of N(R). On the contrary, with a constant N 0, the M–R relation has no direct connection with the density distribution; in this case, the fitted power-law index of the M–R relation is equal to 2 (when N 0 ≥ N TP and n has a narrow range of values), larger than 2 (when N 0 ≥ N TP and n has a wide range of values), or slightly less than 2 (when N 0 < N TP).

Luminosity Function and Event Rate Density of XMM-Newton-selected Supernova Shock Breakout Candidates

Abstract A dozen X-ray supernova shock breakout (SN SBO) candidates were reported recently based on XMM-Newton archival data, which increased the X-ray-selected SN SBO sample by an order of magnitude. Assuming that they are genuine SN SBOs, we study the luminosity function (LF) by improving on the method used in our previous work. The light curves and the spectra of the candidates were used to derive the maximum volume within which these objects could be detected with XMM-Newton by simulation. The results show that the SN SBO LF can be described by either a broken power law (BPL) with indices (at the 68% confidence level) of 0.48 ± 0.28 and 2.11 ± 1.27 before and after the break luminosity at log ( L b / erg s − 1 ) = 45.32 ± 0.55 or a single power law (SPL) with an index of 0.80 ± 0.16. The local event rate densities of SN SBOs above 5 × 1042 erg s−1 are consistent for two models, i.e., 4.6 − 1.3 + 1.7 × 10 4 Gpc−3 yr−1 and 4.9 − 1.4 + 1.9 × 10 4 Gpc−3 yr−1 for BPL and SPL models, respectively. The number of fast X-ray transients of SN SBO origin can be significantly increased by wide-field X-ray telescopes such as the Einstein Probe.

Ambilateral collimation study of the twin-jets in NGC 1052

Context. With the increase in the sensitivity and resolution of radio interferometry within recent years, the study of the collimation and acceleration region of extragalactic jets in active galactic nuclei (AGN) has come into focus. Whereas a large fraction of AGN jets show a change from parabolic to conical collimation profile around the Bondi radius, there is a small number of sources that display a deviation from this standard picture, including the radio galaxy NGC 1052. Aims. We study the jet width profile, which provides valuable information about the interplay between the central engine and accretion disk system and the formation, acceleration, and collimation of the jets. Methods. We observed the double-sided, low-radio-power active galaxy NGC 1052 at six frequencies with the VLBA in 2017 and at 22 GHz with RadioAstron in 2016. These data are combined with archival 15, 22, and 43 GHz multi-epoch VLBA observations. From ridge-line fitting we obtained width measurements along the jet and counter-jet which were fitted with single and broken power laws. Results. We find a clear break point in the jet collimation profile at ∼104 RS (Schwarzschild radii). Downstream of the break, the collimation is conical with a power-law index of 1.0 − 1.2 (cylindrical 0; parabolic 0.5; conical 1) for both jets. On the other hand, the upstream power-law index of 0.36 for the approaching jet is neither cylindrical nor parabolic, and the value of 0.16 for the receding jet suggests this latter is close-to cylindrical. For both jets we find a large opening angle of ∼30° at a distance of ∼103 RS and well-collimated structures with an opening angle of &lt; 10° downstream of the break. Conclusions. There are significant differences between the upstream collimation profiles of the approaching (eastern) and receding (western) jets. Absorption or scattering in the surrounding torus as well as an accretion wind may mimic a cylindrical profile. We need to increase the observing frequencies, which do not suffer from absorption, in order to find the true jet collimation profile upstream of 104 RS.

A Comprehensive Consistency Check between Synchrotron Radiation and the Observed Gamma-Ray Burst Spectra

Abstract We performed a time-resolved spectral analysis of 53 bright gamma-ray bursts (GRBs) observed by Fermi/GBM. Our sample consists of 1117 individual spectra extracted from the finest time slices in each GRB. We fitted them with the synchrotron radiation model by considering the electron distributions in five different cases: monoenergetic, single power law, Maxwellian, traditional fast cooling, and broken power law. Our results were further qualified through the Bayesian information criterion (BIC) by comparing with the fit by empirical models, namely, the so-called Band function and cutoff power-law models. Our study showed that the synchrotron models, except for the fast-cooling case, can successfully fit most observed spectra, with the single power-law case being the most preferred. We also found that the electron distribution indices for the single power-law synchrotron fit in more than half of our spectra exhibit flux-tracking behavior, i.e., the index increases/decreases with the flux increasing/decreasing, implying that the distribution of the radiating electrons is increasingly narrower with time before the flux peaks and becomes more spreading afterward. Our results indicate that the synchrotron radiation is still feasible as a radiation mechanism of the GRB prompt emission phase.

Double-power-law Feature of Energetic Particles Accelerated at Coronal Shocks

Abstract Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as E B ∼ (Q/A) α , with α varying from 0.16 to 1.2 by considering different turbulence spectral indices. We suggest that the double-power-law distribution may emerge as a result of the superposition of energetic particles from different source regions where the acceleration rates differ significantly due to particle diffusion. The diffusion and mixing of energetic particles could also provide an explanation for the increase of Fe/O at high energies as observed in some SEP events. Although further mixing processes may occur, our simulations indicate that either a power-law break or rollover can occur near the Sun and predict that the spectral forms vary significantly along the shock front, which may be examined by upcoming near-Sun SEP measurements from the Parker Solar Probe and Solar Orbiter.

Gaseous Halos of Simulated Milky Way-like Galaxies

Abstract In order to investigate the role of the host halo in quenching satellite galaxies, we have characterized a single Milky Way-like host galaxy from the FIRE simulations from z = 0–1.76 by quantifying the gas density of the host halo environment with respect to distance from the host and galactocentric latitude. The gas density decreases with increasing distance from the host according to a broken power law. At earlier times (2–10 Gyr ago), the density in the inner regions of the host halo was enhanced relative to z = 0. Thus, earlier infalling satellites experienced more ram-pressure and were more efficiently quenched compared to later infalling satellites. We also find that in the inner halo (&lt;150 kpc) the density is 2–3 times larger close to the plane of the host galaxy disk versus above or below the disk, so satellites that orbit at low galactocentric latitudes may be more efficiently quenched.

Searching for an additional high-energy component in Fermi-LAT GRB afterglows

Context. The very high-energy (VHE; ≥100 GeV) component from at least two gamma-ray bursts (GRBs), that is, GRB 180720B and GRB 190114C, has been detected in the afterglow phase. It is widely discussed that the GeV to TeV emission originated from a synchrotron self-Compton (SSC) process. The VHE component may cause an upturn at the high-energy spectral ends in the Fermi-Large Area Telescope (Fermi-LAT) observing band. Aims. We aim to find out whether an additional high-energy component commonly exists in the afterglows of Fermi-LAT GRBs. This study will help us to better understand how common it is for a GRB afterglow detected by Fermi-LAT to involve a VHE component. Methods. First, we selected the GRBs that emit ≥10 GeV photons. The ≥10 GeV photons can be considered as a plausible proxy for a VHE component. We systematically analyzed 199 GRBs detected by Fermi-LAT from 2008–2019. If an additional high-energy component exists in the afterglows of Fermi-LAT GRBs, the best-fit spectral model could be a broken power law (BPL) model with an upturn above a break energy. We compared the afterglow spectra using power-law (PL) and BPL representations. Results. Out of the 30 GRBs with ≥10 GeV photons that arrived after T90 (the time duration when 90% of the prompt emission was detected), 25 GRBs are tentatively or significantly detected at 0.1–200 GeV after 2 × T90. The spectrum of GRB 131231A shows an upturn above an energy break of 1.6 ± 0.8 GeV, supporting the BPL model. For GRB 131231A, we performed a modeling of its X-ray and γ-ray spectra and found that the SSC model can explain the upturn with acceptable parameter values. In the cases of GRB 190114C, GRB 171210A, GRB 150902A, GRB 130907A, GRB 130427A, and GRB 090902B, the improvement of the BPL fit compared to the PL fit is tentative or marginal. Conclusions. There is no conclusive evidence that an additional higher energy component commonly exists in Fermi-LAT GRB afterglows, except for the group of Fermi-LAT GRBs mentioned above. Such an additional high-energy component may be explained by the SSC mechanism. Current and future VHE observations will provide important constraints on the issue.

Characteristics of discharge frequency and their effects on flood channel formation in the middle and lower reaches of the Yangtze River before/after the impoundment of the Three Gorges Reservoir

三峡水库蓄水前后长江中下游流量特征变化及其对造床作用的影响一直受到学者的关注.采用枝城等6个水文站日均流量资料，分别统计了各站流量的经验频率分布，检验了8种概率密度函数的适用性，并讨论了三峡水库蓄水前后流量频率分布特征与造床流量的关系.研究表明：长江中下游干流洪中枯各级流量的频率分布具有分段特性，无法用皮尔逊Ш型或对数正态等常见函数来整体描述，但中洪流量区段符合分段幂函数；拟合得到的分段幂函数转折点可近似反映造床流量，包括临界值在内的函数特征参数受洞庭湖等调蓄作用影响，在螺山站上下游差异较大；三峡水库蓄水后，洪水削减使得各站的流量频率分段特性增强，分段幂函数仍然适用；由于三峡水库蓄水后流量过程变化和频率调整的影响，枝城、沙市、监利站造床流量将变为蓄水前的0.79、0.73、0.74倍，螺山、汉口、大通站造床流量将变为蓄水前的0.89、0.90、0.93倍.本文的方法和认识对于长江中下游径流特征分析和造床流量计算具有参考价值.;The variations of flow characteristics and their effects on channel formation in the middle and lower reaches of the Yangtze River before and after the impoundment of the Three Gorges Reservoir (TGR) have drawn much concern. Based on the data of the average daily discharge at six hydrological stations including Zhicheng Station, the empirical flow frequency distributions were calculated, and the applicabilities of eight probability density functions were tested. Furthermore, the relationships between the flow frequency distribution characteristics and the channel-forming discharges before and after the impoundment of the TGR were discussed. The results show that the flow frequency distributions in the study reach are segmented, which cannot be described as a whole by common functions such as Pearson Ш or Lognormal distribution. However, the frequency distributions of the medium-high flow conform to the broken power-law (BPL). The turning point of the BPL obtained by fitting approximately reflects the channel-forming discharge. Moreover, affected by the regulation and storage of Lake Dongting, the characteristic parameters including the critical values quite differently in the upper and lower reaches of Luoshan Station. After the TGR is impounded, the subsection characteristics of the flow frequency distributions are enhanced by the flood reduction, and the applicability of BPL are still considerable. Due to the influence of the flow process change and frequency adjustment by the impoundment of the TGR, the channel-forming discharge at Zhicheng, Shashi, Jianli, Luoshan, Hankou and Datong stations will be 0.79, 0.73, 0.74, 0.89, 0.90 and 0.93 times of that before the impoundment, respectively. The method presented in this paper are of reference value for the analysis of runoff characteristics and the calculation of channel-forming discharge in the middle and lower reaches of the Yangtze River.

X-ray timing and spectral variability properties of blazars S5 0716 + 714, OJ 287, Mrk 501, and RBS 2070

ABSTRACT The X-ray emission from blazars has been widely investigated using several space telescopes. In this work, we explored statistical properties of the X-ray variability in the blazars S5 0716+714, OJ 287, Mkn 501, and RBS 2070 using the archival observations from the XMM-Newton telescope between the period 2002–2020. Several methods of timing and spectral analyses, including fractional variability, minimum variability time-scale, power spectral density analyses, and countrate distribution, were performed. In addition, we fitted various spectral models to the observations, as well as estimated hardness ratio. The results show that the sources are moderately variable within the intraday time-scale. Three of the four sources exhibited a clear bi-modal pattern in their countrate distribution, revealing possible indication of two distinct countrate states, that is, hard and soft countrate states. The slope indices of the power spectral density were found to be centred around 0.5. Furthermore, the spectra of the sources were fitted with single power law, broken power law, log-parabolic, and blackbody + log-parabolic models (the latter only for OJ 287). We conclude that for most of the observations log-parabolic model was the best fit. The power-spectral-density analysis revealed the variable nature of PSD slopes in the source light curves. The results of this analysis could indicate the non-stationary nature of the blazar processes on intraday time-scales. The observed features can be explained within the context of current blazar models, in which the non-thermal emission mostly arises from kilo-pc scale relativistic jets.

Creep behaviour of different microstructural zones of TIG-welded semisolid cast AXE622 alloy

The impression creep behaviour of a TIG-welded semisolid cast AXE622 Mg alloy is investigated at the temperature range of 423–498 K and the stress range of 450–600 MPa. After creep, the (Mg–Al)2Ca phase loses its continuity in the HAZ, and some evidence of particle fracture is obvious. Except at 423 K, where the HAZ exhibits a higher creep resistance than in the FZ, the creep resistance decreases from BM to FZ. The power-law break dawn is the rate-controlling creep in BM though the dislocation creep is dominant in HAZ and FZ. Moreover, the creep is controlled by pipe diffusion in BM while a dislocation nucleation mechanism at the boundary surface is activated in the HAZ and FZ.

The isotropic energy function and formation rate of short gamma-ray bursts

Gamma-ray bursts (GRBs) are brief, intense, gamma-ray flashes in the universe, lasting from a few milliseconds to a few thousand seconds. For short gamma-ray bursts (sGRBs) with duration less than 2 seconds, the isotropic energy (E iso) function may be more scientifically meaningful and accurately measured than the luminosity (L p) function. In this work we construct, for the first time, the isotropic energy function of sGRBs and estimate their formation rate. First, we derive the L p – E p correlation using 22 sGRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi sGRBs. Then, we adopt the Lynden-Bell c − method to study isotropic energy functions and formation rate of sGRBs without any assumption. A strong evolution of isotropic energy E iso ∝ (1+z)5.79 is found, which is comparable to that between L p and z. After removing effect of the cosmic evolution, the isotropic energy function can be reasonably fitted by a broken power law, which is for dim sGRBs and for bright sGRBs, with the break energy 4.92 × 1049 erg. We obtain the local formation rate of sGRBs is about 17.43 events Gpc−3 yr−1. If assuming a beaming angle is 6° to 26°, the local formation rate including off-axis sGRBs is estimated as ρ 0,all = 155.79 – 3202.35 events Gpc−3 yr−1.

Exploring black hole scaling relations via the ensemble variability of active galactic nuclei

ABSTRACT An empirical model is presented that links, for the first time, the demographics of active galactic nuclei (AGN) to their ensemble X-ray variability properties. Observations on the incidence of AGN in galaxies are combined with (i) models of the power spectrum density (PSD) of the flux variations of AGN and (ii) parametrizations of the black hole mass versus stellar mass scaling relation to predict the mean excess variance of active black hole populations in cosmological volumes. We show that the comparison of the model with observational measurements of the ensemble excess variance as a function of X-ray luminosity provides a handle on both the PSD models and the black hole mass versus stellar mass relation. We find strong evidence against a PSD model that is described by a broken power law and a constant overall normalization. Instead, our analysis indicates that the amplitude of the PSD depends on the physical properties of the accretion events, such as the Eddington ratio and/or the black hole mass. We also find that current observational measurements of the ensemble excess variance are consistent with the black hole mass versus stellar mass relation of local spheroids based on dynamically determined black hole masses. We also discuss future prospects of the proposed approach to jointly constrain the PSD of AGN and the black hole mass versus stellar mass relation as a function of redshift.

NICER, NuSTAR, and Swift follow-up observations of the γ-ray flaring blazar BL Lacertae in 2020 August–October

ABSTRACT During a period of strong γ-ray flaring activity from BL Lacertae, we organized Swift, Neutron star Interior Composition Explorer (NICER), and Nuclear Spectroscopic Telescope Array (NuSTAR) follow-up observations. The source has been monitored by Swift-XRT (X-ray Telescope) between 2020 August 11 and October 16, showing a variability amplitude of 65, with a flux varying between 1.0 × 10−11 and 65.3 × 10−11 erg cm−2 s−1. On 2020 October 6, Swift-XRT has observed the source during its historical maximum X-ray flux. A softer-when-brighter behaviour has been observed by XRT, suggesting an increasing importance of the synchrotron emission in the X-ray part of the spectrum covered by XRT during this bright state. Rapid variability in soft X-rays has been observed with both the Swift-XRT and NICER observations with a minimum variability time-scale of 60 and 240 s, and a doubling time-scale of 274 and 1008 s, respectively, suggesting very compact emitting regions (1.1 × 1014 and 4.0 × 1014 cm). At hard X-rays, a minimum variability time-scale of ∼5.5 ks has been observed by NuSTAR. We report the first simultaneous NICER and NuSTAR observations of BL Lacertae during 2020 October 11–12. The joint NICER and NuSTAR spectra are well fitted by a broken power law with a significant difference of the photon index below (2.10) and above (1.60) an energy break at ∼2.7 keV, indicating the presence of two different emission components (i.e. synchrotron and inverse Compton) in the broad-band X-ray spectrum. Leaving the total hydrogen column density towards BL Lacertae free to vary, a value of NH,tot = (2.58 ± 0.09) × 1021 cm−2 has been estimated.

A 3D model reflecting the dynamic generating process of pore networks for geological porous media

Pore-network models are useful for simulating physical processes in geological porous media. Here in this paper, the network theories are used to analyze X-ray computed tomography (CT) images of geological porous media. Results show the traditional mathematical degree which represents the coordination number of pore networks is insufficient to describe the preferential-attachment mechanism of pore networks. Thus a new parameter, physical degree, was proposed, which represents a physical quantity of both a specific pore and its attached throats to facilitate the description of pore networks. By analyzing X-ray CT images of different geological porous media, it was found the mathematical degree follows a Poisson law whereas the physical degree can be fitted by a power law. This indicates the pore network of geological porous media is randomly scale free. But the scale free is volume dependent. When the power law breaks down, the scale-free quantity, such as porosity, becomes scale variant. Based on these findings, a pore-network model was proposed, which reflects the dynamic generating process of the pore network. And the randomness featured in mathematical degrees and volume-dependent scale free featured in physical degrees are contained in this model.

A bottom-heavy initial mass function for the likely-accreted blue-halo stars of the Milky Way

ABSTRACT We use Gaia DR2 to measure the initial mass function (IMF) of stars within 250 pc and masses in the range of 0.2 &amp;lt; m/M⊙ &amp;lt; 1.0, separated according to kinematics and metallicity, as determined from Gaia transverse velocity, vT, and location on the Hertzsprung–Russell diagram (HRD). The predominant thin-disc population (vT &amp;lt; 40 km s−1) has an IMF similar to traditional (e.g. Kroupa) stellar IMFs, with star numbers per mass interval dN/dm described by a broken power law, m−α, and index $\alpha _\textrm {high}=2.03^{+0.14}_{-0.05}$ above m ∼ 0.5, shallowing to $\alpha _\textrm {low}=1.34^{+0.11}_{-0.22}$ at m ≲ 0.5. Thick-disc stars (60 km s−1 &amp;lt;vT &amp;lt; 150 km s−1) and stars belonging to the ‘high-metallicity’ or ‘red-sequence’ halo (vT &amp;gt; 100 km s−1 or vT &amp;gt; 200 km s−1, and located above the isochrone on the HRD with a metallicity [M/H] &amp;gt; −0.6) have a somewhat steeper high-mass slope, $\alpha _\textrm {high}=2.35^{+0.97}_{-0.19}$ (and a similar low-mass slope $\alpha _\textrm {low}=1.14^{+0.42}_{-0.50}$). Halo stars from the ‘blue sequence’, which are characterized by low metallicity ([M/H] &amp;lt; −0.6), however, have a distinct, bottom-heavy IMF, well described by a single power law with $\alpha =1.82^{+0.17}_{-0.14}$ over most of the mass range probed. The IMF of the low-metallicity halo is reminiscent of the Salpeter-like IMF that has been measured in massive early-type galaxies, a stellar population that, like Milky Way halo stars, has a high ratio of α elements to iron, [α/Fe]. Blue-sequence stars are likely the debris from accretion by the Milky Way, ∼10 Gyr ago, of the Gaia-Enceladus dwarf galaxy, or similar events. These results hint at a distinct mode of star formation common to two ancient stellar populations – elliptical galaxies and galaxies possibly accreted early-on by ours.

The spatial power spectrum and derived turbulent properties of isolated galaxies

ABSTRACT The turbulent dynamics of nearby and extragalactic gas structures can be studied with the column density power spectrum that is often described by a broken power law. In an extragalactic context, the breaks in the power spectra have been interpreted to constrain the disc scale height, which marks a transition from 2D disc-like to 3D motion. However, this interpretation has recently been questioned when accounting for instrumental effects. We use numerical simulations to study the spatial power spectra of isolated galaxies and investigate the origins of the break scale. We split the gas into various phases and analyse the time evolution of the power spectrum characteristics, such as the slope(s) and the break scale. We find that the break scale is phase dependent. The physics traced by the break scale also differ: in the warm gas it marks the transition from 2D (disc-like) to 3D (isotropic) turbulence. In the cold gas, the break scale traces the typical size of molecular clouds. We further show that the break scale almost never traces the disc scale height. We study turbulent properties of the interstellar medium (ISM) to show that, in the case where the break scale traces a transition to isotropic turbulence, the fraction of required accretion energy to sustain turbulent motions in the ISM increases significantly. Lastly, we demonstrate through simulated observations that it is crucial to account for observational effects, such as the beam and instrumental noise, in order to accurately recover the break scale in real observations.