arXiv subjects

Christopher Wegg

Publications and source records attributed to Christopher Wegg.

At least 19 recordsLinked to original sources

arXiv2020

The bar resonances and low angular momentum moving groups in the Galaxy revealed by stellar ages

We use the second Gaia data release in combination with the catalog of Sanders & Das (2018) to dissect the Milky Way disc in phase-space and relative ages. We confirm and report the existence of multiple velocity moving groups at low azimuthal velocities and angular momenta, below Arcturus, regularly separated by $\sim~18-20\,\rm{km s^{-1}}$ in azimuthal velocity. Such features were predicted to exist more than ten years ago from the reaction of the Milky Way to a perturbation in the disc undergoing phase-mixing. These structures appear slightly younger than their phase-space surroundings, arguing against an extra-galactic origin. We also identify in relative age many of the classical ridges in the plane of azimuthal velocity vs. Galactocentric radius, traditionally associated with resonance features. These ridges are also younger than their phase-space surroundings in accordance with predictions from recent state-of-the-art cosmological hydrodynamical simulations of Milky Way-like galaxies. We study the response of dynamically young and old stellar disc populations to resonances from an analytic model of a large bar, which, remarkably, qualitatively reproduces the trends seen in the data. Our results re-inforce the idea that the Galactic disc is currently being shaped by both internal and external perturbations, and that, while absolute isochrone ages have to be taken with great care, exploring the dynamical structure of the disc in stellar ages, especially with future asteroseismic data, will provide much stronger constraints than metallicity/abundance trends alone.

astro-ph.GA↗

arXiv2019

The Milky Way bar/bulge in proper motions: a 3D view from VIRAC & Gaia

We have derived absolute proper motions of the entire Galactic bulge region from VIRAC and Gaia. We present these as both integrated on-sky maps and, after isolating standard candle red clump (RC) stars, as a function of distance using RC magnitude as a proxy. These data provide a new global, 3-dimensional view of the Milky Way barred bulge kinematics. We find a gradient in the mean longitudinal proper motion, $<μ_l^\star>$, between the different sides of the bar, which is sensitive to the bar pattern speed. The split RC has distinct proper motions and is colder than other stars at similar distance. The proper motion correlation map has a quadrupole pattern in all magnitude slices showing no evidence for a separate, more axisymmetric inner bulge component. The line-of-sight integrated kinematic maps show a high central velocity dispersion surrounded by a more asymmetric dispersion profile. $σ_{μ_l} / σ_{μ_b}$ is smallest, $\sim1.1$, near the minor axis and reaches $\sim1.4$ near the disc plane. The integrated $<μ_b>$ pattern signals a superposition of bar rotation and internal streaming motion, with the near part shrinking in latitude and the far part expanding. To understand and interpret these remarkable data, we compare to a made-to-measure barred dynamical model, folding in the VIRAC selection function to construct mock maps. We find that our model of the barred bulge, with a pattern speed of 37.5 $\mathrm{km \, s^{-1} \, kpc^{-1}}$, is able to reproduce all observed features impressively well. Dynamical models like this will be key to unlocking the full potential of these data.

astro-ph.GA↗

arXiv2019

The signatures of the resonances of a large Galactic bar in local velocity space

The second data release of the Gaia mission has revealed a very rich structure in local velocity space. In terms of in-plane motions, this rich structure is also seen as multiple ridges in the actions of the axisymmetric background potential of the Galaxy. These ridges are probably related to a combination of effects from ongoing phase-mixing and resonances from the spiral arms and the bar. We have recently developed a method to capture the behaviour of the stellar phase-space distribution function at a resonance, by re-expressing it in terms of a new set of canonical actions and angles variables valid in the resonant region. Here, by properly treating the distribution function at resonances, and by using a realistic model for a slowly rotating large Galactic bar with pattern speed 39 km/s/kpc, we show that no less than six ridges in local action space can be related to resonances with the bar. Two of these at low angular momentum correspond to the corotation resonance, and can be associated to the Hercules moving group in local velocity space. Another one at high angular momentum corresponds to the outer Lindblad resonance, and can tentatively be associated to the velocity structure seen as an arch at high azimuthal velocities in Gaia data. The other ridges are associated to the 3:1, 4:1 and 6:1 resonances. The latter can be associated to the so-called 'horn' of the local velocity distribution. While it is clear that effects from spiral arms and incomplete phase-mixing related to external perturbations also play a role in shaping the complex kinematics revealed by Gaia data, the present work demonstrates that, contrary to common misconceptions, the bar alone can create multiple prominent ridges in velocity and action space.

astro-ph.GA↗

arXiv2019

The Gravitational Force Field of the Galaxy Measured From the Kinematics of RR Lyrae in Gaia

From a sample of 15651 RR Lyrae with accurate proper motions in Gaia DR2, we measure the azimuthally averaged kinematics of the inner stellar halo between 1.5 kpc and 20 kpc from the Galactic centre. We find that their kinematics are strongly radially anisotropic, and their velocity ellipsoid nearly spherically aligned over this volume. Only in the inner regions $\lesssim$ 5 kpc does the anisotropy significantly fall (but still with $β>$ 0.25) and the velocity ellipsoid tilt towards cylindrical alignment. In the inner regions, our sample of halo stars rotates at up to 50 km s$^{-1}$, which may reflect the early history of the Milky Way, although there is also significant angular momentum exchange with the Galactic bar at these radii. We subsequently apply the Jeans equations to these kinematic measurements in order to non-parametrically infer the azimuthally averaged gravitational acceleration field over this volume, and by removing the contribution from baryonic matter, measure the contribution from dark matter. We find that the gravitational potential of the dark matter is nearly spherical with average flattening $q_Φ=$ 1.01 $\pm$ 0.06 between 5 kpc and 20 kpc, and by fitting parametric ellipsoidal density profiles to the acceleration field, we measure the flattening of the dark matter halo over these radii to be $q_ρ=$ 1.00 $\pm$ 0.09.

astro-ph.GA↗

arXiv2018

Sculpting Andromeda -- made-to-measure models for M31's bar and composite bulge: dynamics, stellar and dark matter mass

The Andromeda galaxy (M31) contains a box/peanut bulge (BPB) entangled with a classical bulge (CB) requiring a triaxial modelling to determine the dynamics, stellar and dark matter mass. We construct made-to-measure models fitting new VIRUS-W IFU bulge stellar kinematic observations, the IRAC-3.6$μ$m photometry, and the disc's HI rotation curve. We explore the parameter space for the 3.6$μ$m mass-to-light ratio $(Υ_{3.6})$, the bar pattern speed ($Ω_p$), and the dark matter mass in the composite bulge ($M^B_{DM}$) within 3.2kpc. Considering Einasto dark matter profiles, we find the best models for $Υ_{3.6}=0.72\pm0.02\,M_\odot/L_\odot$, $M^B_{DM}=1.2^{+0.2}_{-0.4}\times10^{10}M_\odot$ and $Ω_p=40\pm5\,km/s/kpc$. These models have a dynamical bulge mass of $M_{dyn}^B=4.25^{+0.10}_{-0.29}\times10^{10}M_{\odot}$ including a stellar mass of $M^B=3.09^{+0.10}_{-0.12}\times10^{10}M_\odot$(73%), of which the CB has $M^{CB}=1.18^{+0.06}_{-0.07}\times10^{10}M_\odot$(28%) and the BPB $M^{BPB}=1.91\pm0.06\times10^{10}M_\odot$(45%). We also explore models with NFW haloes finding that, while the Einasto models better fit the stellar kinematics, the obtained parameters agree within the errors. The $M^B_{DM}$ values agree with adiabatically contracted cosmological NFW haloes with M31's virial mass and radius. The best model has two bulge components with completely different kinematics that only together successfully reproduce the observations ($μ_{3.6},\upsilon_{los},σ_{los},h3,h4$). The modelling includes dust absorption which reproduces the observed kinematic asymmetries. Our results provide new constraints for the early formation of M31 given the lower mass found for the classical bulge and the shallow dark matter profile, as well as the secular evolution of M31 implied by the bar and its resonant interactions with the classical bulge, stellar halo and disc.

astro-ph.GA↗

arXiv2017

The Hercules stream as seen by APOGEE-2 South

The Hercules stream is a group of co-moving stars in the Solar neighbourhood, which can potentially be explained as a signature of either the outer Lindblad resonance (OLR) of a fast Galactic bar or the corotation resonance of a slower bar. In either case, the feature should be present over a large area of the disc. With the recent commissioning of the APOGEE-2 Southern spectrograph we can search for the Hercules stream at $(l,b)=(270^\circ,0)$, a direction in which the Hercules stream, if caused by the bar's OLR, would be strong enough to be detected using only the line-of-sight velocities. We clearly detect a narrow, Hercules-like feature in the data that can be traced from the solar neighbourhood to a distance of about 4 kpc. The detected feature matches well the line-of-sight velocity distribution from the fast-bar (OLR) model. Confronting the data with a model where the Hercules stream is caused by the corotation resonance of a slower bar leads to a poorer match, as the corotation model does not predict clearly separated modes, possibly because the slow-bar model is too hot.

astro-ph.GA↗

arXiv2017

Chemodynamical Modelling of the Galactic Bulge and Bar

We present the first self-consistent chemodynamical model fitted to reproduce data for the galactic bulge, bar and inner disk. We extend the Made-to-Measure method to an augmented phase-space including the metallicity of stars, and show its first application to the bar region of the Milky Way. Using data from the ARGOS and APOGEE (DR12) surveys, we adapt the recent dynamical model from Portail et al. to reproduce the observed spatial and kinematic variations as a function of metallicity, thus allowing the detailed study of the 3D density distributions, kinematics and orbital structure of stars in different metallicity bins. We find that metal-rich stars with [Fe/H] > -0.5 are strongly barred and have dynamical properties that are consistent with a common disk origin. Metal-poor stars with [Fe/H] < -0.5 show strong kinematic variations with metallicity, indicating varying contributions from the underlying stellar populations. Outside the central kpc, metal-poor stars are found to have the density and kinematics of a thick disk while in the inner kpc, evidence for an extra concentration of metal-poor stars is found. Finally, the combined orbit distributions of all metallicities in the model naturally reproduce the observed vertex deviations in the bulge. This paper demonstrates the power of Made-to-Measure chemodynamical models, that when extended to other chemical dimensions will be very powerful tools to maximize the information obtained from large spectroscopic surveys such as APOGEE, GALAH and MOONS.

astro-ph.GA↗

arXiv2017

The Initial Mass Function of the Inner Galaxy Measured From OGLE-III Microlensing Timescales

We use the timescale distribution of ~3000 microlensing events measured by the OGLE-III survey, together with accurate new made-to-measure dynamical models of the Galactic bulge/bar region, to measure the IMF in the inner Milky Way. The timescale of each event depends on the mass of the lensing object, together with the relative distances and velocities of the lens and source. The dynamical model provides statistically these distances and velocities allowing us to constrain the lens mass function, and from this to infer the IMF. Parameterising the IMF as a broken power-law, we find slopes in the main sequence $α_{\rm ms}=1.31\pm0.10|_{\rm stat}\pm0.10|_{\rm sys}$ and brown dwarf region $α_{\rm bd}=-0.7\pm0.9|_{\rm stat}\pm0.8|_{\rm sys}$ where we use a fiducial 50% binary fraction, and the systematic uncertainty covers the range of binary fractions 0-100%. Similarly for a log-normal IMF we conclude $M_c=(0.17\pm0.02|_{\rm stat}\pm0.01|_{\rm sys})M_\odot$ and $σ_m=0.49\pm0.07|_{\rm stat}\pm0.06|_{\rm sys}$. These values are very similar to a Kroupa or Chabrier IMF respectively, showing that the IMF in the bulge is indistinguishable from that measured locally, despite the lenses lying in the inner Milky Way where the stars are mostly ~10Gyr old and formed on a fast $α$-element enhanced timescale. This therefore constrains models of IMF variation that depend on the properties of the collapsing gas cloud.

astro-ph.GA↗

arXiv2017

Revisiting the Tale of Hercules: how stars orbiting the Lagrange points visit the Sun

We propose a novel explanation for the Hercules stream consistent with recent measurements of the extent and pattern speed of the Galactic bar. We have adapted a made-to-measure dynamical model tailored for the Milky Way to investigate the kinematics of the solar neighborhood (SNd). The model matches the 3D density of the red clump giant stars (RCGs) in the bulge and bar as well as stellar kinematics in the inner Galaxy, with a pattern speed of 39 km s$^{-1}$ kpc$^{-1}$. Cross-matching this model with the $Gaia$ DR1 TGAS data combined with RAVE and LAMOST radial velocities, we find that the model naturally predicts a bimodality in the $U\!-\!V$-velocity distribution for nearby stars which is in good agreement with the Hercules stream. In the model, the Hercules stream is made of stars orbiting the Lagrange points of the bar which move outward from the bar's corotation radius to visit the SNd. While the model is not yet a quantitative fit of the velocity distribution, the new picture naturally predicts that the Hercules stream is more prominent inward from the Sun and nearly absent only a few $100$ pc outward of the Sun, and plausibly explains that Hercules is prominent in old and metal-rich stars.

astro-ph.GA↗

arXiv2016

Andromeda chained to the Box -- Dynamical Models for M31: Bulge & Bar

Andromeda is our nearest neighbouring disk galaxy and a prime target for detailed modelling of the evolutionary processes that shape galaxies. We analyse the nature of M31's triaxial bulge with an extensive set of N-body models, which include Box/Peanut (B/P) bulges as well as initial classical bulges (ICBs). Comparing with IRAC 3.6$μm$ data, only one model matches simultaneously all the morphological properties of M31's bulge, and requires an ICB and a B/P bulge with 1/3 and 2/3 of the total bulge mass respectively. We find that our pure B/P bulge models do not show concentrations high enough to match the Sérsic index ($n$) and the effective radius of M31's bulge. Instead, the best model requires an ICB component with mass $M^{\rm ICB}=1.1\times10^{10}{\rm M_{\odot}}$ and three-dimensional half-mass radius $r_{\rm half}^{\rm ICB}$=0.53 kpc (140 arcsec). The B/P bulge component has a mass of $M^{\rm B/P}=2.2\times10^{10}{\rm M_{\odot}}$ and a half-mass radius of $r_{\rm half}^{\rm B/P}$=1.3 kpc (340 arcsec). The model's B/P bulge extends to $r^{\rm B/P}$=3.2 kpc (840 arcsec) in the plane of the disk, as does M31's bulge. In this composite bulge model, the ICB component explains the velocity dispersion drop observed in the centre within $R<$190 pc (50 arcsec), while the B/P bulge component reproduces the observed rapid rotation and the kinematic twist of the observed zero velocity line. This model's pattern speed is $Ω_p$=38 km/s/kpc, placing corotation at $r_{\rm cor}$=5.8 kpc (1500 arcsec). The outer Lindblad resonance (OLR) is then at $r_{\rm OLR}$=10.4kpc, near the 10kpc-ring of M31, suggesting that this structure may be related to the bar's OLR. By comparison with an earlier snapshot, we estimate that M31's thin bar extends to $r_{\rm bar}^{\rm thin}\sim$4.0 kpc (1000 arcsec) in the disk plane, and in projection extends to $R_{\rm bar}^{\rm thin}\sim$2.3 kpc (600 arcsec).

astro-ph.GA↗

arXiv2016

Dynamical modelling of the Galactic bulge and bar: the Milky Way's bar pattern speed, stellar, and dark matter mass distribution

We construct a large set of dynamical models of the galactic bulge, bar and inner disk using the Made-to-Measure method. Our models are constrained to match the red clump giant density from a combination of the VVV, UKIDSS and 2MASS infrared surveys together with stellar kinematics in the bulge from the BRAVA and OGLE surveys, and in the entire bar region from the ARGOS survey. We are able to recover the bar pattern speed and the stellar and dark matter mass distributions in the bar region, thus recovering the entire galactic effective potential. We find a bar pattern speed of $39.0 \pm 3.5 \,\rm{km\,s^{-1}\,kpc^{-1}}$, placing the bar corotation radius at $6.1 \pm 0.5 \rm{kpc}$ and making the Milky Way bar a typical fast rotator. We evaluate the stellar mass of the long bar and bulge structure to be $M_{\rm{bar/bulge}} = 1.88 \pm 0.12 \times 10^{10} \, \rm{M}_{\odot}$, larger than the mass of disk in the bar region, $M_{\rm{inner\ disk}} = 1.29\pm0.12 \times 10^{10} \, \rm{M}_{\odot}$. The total dynamical mass in the bulge volume is $1.85\pm0.05\times 10^{10} \, \rm{M}_{\odot}$. Thanks to more extended kinematic data sets and recent measurement of the bulge IMF our models have a low dark matter fraction in the bulge of $17\%\pm2\%$. We find a dark matter density profile which flattens to a shallow cusp or core in the bulge region. Finally, we find dynamical evidence for an extra central mass of $\sim0.2\times10^{10} \,\rm{M}_{\odot}$, probably in a nuclear disk or disky pseudobulge.

astro-ph.GA↗

arXiv2016

MOA-II Galactic Microlensing Constraints: The Inner Milky Way has a Low Dark Matter Fraction and a Near Maximal Disk

Microlensing provides a unique tool to break the stellar to dark matter degeneracy in the inner Milky Way. We combine N-body dynamical models fitted to the Milky Way's Boxy/Peanut bulge with exponential disk models outside this, and compute the microlensing properties. Considering the range of models consistent with the revised MOA-II data, we find low dark matter fractions in the inner Galaxy: at the peak of their stellar rotation curve a fraction $f_v=(0.88\pm0.07)$ of the circular velocity is baryonic (at $1σ$, $f_v > 0.72$ at $2σ$). These results are in agreement with constraints from the EROS-II microlensing survey of brighter resolved stars, where we find $f_v=(0.9\pm0.1)$ at $1σ$. Our fiducial model of a disk with scale length 2.6kpc, and a bulge with a low dark matter fraction of 12%, agrees with both the revised MOA-II and EROS-II microlensing data. The required baryonic fractions, and the resultant low contribution from dark matter, are consistent with the NFW profiles produced by dissipationless cosmological simulations in Milky Way mass galaxies. They are also consistent with recent prescriptions for the mild adiabatic contraction of Milky Way mass haloes without the need for strong feedback, but there is some tension with recent measurements of the local dark matter density. Microlensing optical depths from the larger OGLE-III sample could improve these constraints further when available.

astro-ph.GA↗

arXiv2016

Gas dynamics in the Milky Way: a low pattern speed model

We present gas flow models for the Milky Way based on high-resolution grid-based hydrodynamical simulations. The basic galactic potential we use is from a N-body model constrained by the density of red clump giants in the Galactic bulge. We augment this potential with a nuclear bulge, two pairs of spiral arms and additional mass at the bar end to represent the long bar component. With this combined model we can reproduce many features in the observed ($l,v$) diagram with a bar pattern speed of $33\; {\rm km}\;{\rm s}^{-1}\;{\rm kpc}^{-1}$ and a spiral pattern speed of $23\; {\rm km}\;{\rm s}^{-1}\;{\rm kpc}^{-1}$. The shape and kinematics of the nuclear ring, Bania's Clump 2, the Connecting arm, the Near and Far 3-kpc arms, the Molecular Ring, and the spiral arm tangent points in our simulations are comparable to those in the observations. Our results imply that a low pattern speed model for the bar in our Milky Way reproduces the observations for a suitable Galactic potential. Our best model gives a better match to the ($l,v$) diagram than previous high pattern speed hydrodynamical simulations.

astro-ph.GA↗

arXiv2015

Interstellar Extinction Curve Variations Toward the Inner Milky Way: A Challenge to Observational Cosmology

We investigate interstellar extinction curve variations toward $\sim$4 deg$^{2}$ of the inner Milky Way in $VIJK_{s}$ photometry from the OGLE-III and $VVV$ surveys, with supporting evidence from diffuse interstellar bands and $F435W,F625W$ photometry. We obtain independent measurements toward $\sim$2,000 sightlines of $A_{I}$, $E(V-I)$, $E(I-J)$, and $E(J-K_{s})$, with median precision and accuracy of 2%. We find that the variations in the extinction ratios $A_{I}/E(V-I)$, $E(I-J)/E(V-I)$ and $E(J-K_{s})/E(V-I)$ are large (exceeding 20%), significant, and positively correlated, as expected. However, both the mean values and the trends in these extinction ratios are drastically shifted from the predictions of Cardelli and Fitzpatrick, regardless of how $R_{V}$ is varied. Furthermore, we demonstrate that variations in the shape of the extinction curve has at least two degrees of freedom, and not one (e.g. $R_{V}$), which we conform with a principal component analysis. We derive a median value of $ =13.44$, which is $\sim$60% higher than the "standard" value. We show that the Wesenheit magnitude $W_{I}=I-1.61(I-J)$ is relatively impervious to extinction curve variations. Given that these extinction curves are linchpins of observational cosmology, and that it is generally assumed that $R_{V}$ variations correctly capture variations in the extinction curve, we argue that systematic errors in the distance ladder from studies of type Ia supernovae and Cepheids may have been underestimated. Moreover, the reddening maps from the Planck experiment are shown to systematically overestimate dust extinction by $\sim$100%, and lack sensitivity to extinction curve variations.

astro-ph.SR↗

arXiv2015

Dust within the old nuclear star cluster in the Milky Way

The mean absolute extinction towards the central parsec of the Milky Way is A_K~3 mag, including both foreground and Galactic center dust. Here we present a measurement of dust extinction within the Galactic old nuclear star cluster (NSC), based on combining differential extinctions of NSC stars with their u_l proper motions along Galactic longitude. Extinction within the NSC preferentially affects stars at its far side, and because the NSC rotates, this causes higher extinctions for NSC stars with negative u_l, as well as an asymmetry in the u_l-histograms. We model these effects using an axisymmetric dynamical model of the NSC in combination with simple models for the dust distribution. Comparing the predicted asymmetry to data for ~7100 stars in several NSC fields, we find that dust associated with the Galactic center mini-spiral with extinction A_K~=0.15-0.8 mag explains most of the data. The largest extinction A_K~=0.8 mag is found in the region of the Western arm of the mini-spiral. Comparing with total A_K determined from stellar colors, we determine the extinction in front of the NSC. Finally, we estimate that for a typical extinction of A_K~=0.4 the statistical parallax of the NSC changes by ~0.4%.

astro-ph.GA↗

arXiv2015

The Structure of the Milky Way's Bar Outside the Bulge

While it is incontrovertible that the inner Galaxy contains a bar, its structure near the Galactic plane has remained uncertain, where extinction from intervening dust is greatest. We investigate here the Galactic bar outside the bulge, the long bar, using red clump giant (RCG) stars from UKIDSS, 2MASS, VVV, and GLIMPSE. We match and combine these surveys to investigate a wide area in latitude and longitude, |b|<9deg and |l|<40deg. We find: (1) The bar extends to l~25deg at |b|~5deg from the Galactic plane, and to l~30deg at lower latitudes. (2) The long bar has an angle to the line-of-sight in the range (28-33)deg, consistent with studies of the bulge at |l|<10deg. (3) The scale-height of RCG stars smoothly transitions from the bulge to the thinner long bar. (4) There is evidence for two scale heights in the long bar. We find a ~180pc thin bar component reminiscent of the old thin disk near the sun, and a ~45pc super-thin bar component which exists predominantly towards the bar end. (5) Constructing parametric models for the RC magnitude distributions, we find a bar half length of 5.0+-0.2kpc for the 2-component bar, and 4.6+-0.3kpc for the thin bar component alone. We conclude that the Milky Way contains a central box/peanut bulge which is the vertical extension of a longer, flatter bar, similar as seen in both external galaxies and N-body models.

astro-ph.GA↗

arXiv2014

The Galactic Bar

The Milky Way's bar dominates the orbits of stars and the flow of cold gas in the inner Galaxy, and is therefore of major importance for Milky Way dynamical studies in the Gaia era. Here we discuss the pronounced peanut shape of the Galactic bulge that has resulted from recent star count analysis, in particular from the VVV survey. We also discuss the question whether the Milky Way has an inner disky pseudo-bulge, and show preliminary evidence for a continuous transition in vertical scale-height from the peanut bulge-bar to the planar long bar.

astro-ph.GA↗

arXiv2013

Production of EMRIs in Supermassive Black Hole Binaries

We consider the formation of extreme mass-ratio inspirals (EMRIs) sourced from a stellar cusp centred on a primary supermassive black hole (SMBH) and perturbed by an inspiraling less massive secondary SMBH. The problem is approached numerically, assuming the stars are non-interacting over these short timescales and performing an ensemble of restricted three-body integrations. From these simulations we see that not only can EMRIs be produced during this process, but the dynamics are also quite rich. In particular, most of the EMRIs are produced through a process akin to the Kozai-Lidov mechanism, but with strong effects due to the non-Keplerian stellar potential, general relativity, and non-secular oscillations in the angular momentum on the orbital timescale of the binary SMBH system.

astro-ph.CO↗