WISDOM project – VI. Exploring the relation between supermassive black hole mass and galaxy rotation with molecular gas

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) 500 (2020) 1933-1952

MD Smith, M Bureau, TA Davis, M Cappellari, L Liu, K Onishi, S Iguchi, EV North, M Sarzi

<jats:title>ABSTRACT</jats:title> <jats:p>Empirical correlations between the masses of supermassive black holes (SMBHs) and properties of their host galaxies are well established. Among these is the correlation with the flat rotation velocity of each galaxy measured either at a large radius in its rotation curve or via a spatially integrated emission-line width. We propose here the use of the deprojected integrated CO emission-line width as an alternative tracer of this rotation velocity, which has already been shown useful for the Tully–Fisher (luminosity–rotation velocity) relation. We investigate the correlation between CO line widths and SMBH masses for two samples of galaxies with dynamical SMBH mass measurements, with spatially resolved and unresolved CO observations, respectively. The tightest correlation is found using the resolved sample of 25 galaxies as $\log (M_\mathrm{BH}/\mathrm{M_\odot })=(7.5\pm 0.1)+(8.5\pm 0.9)[\log (W_\mathrm{50}/\sin i \, \mathrm{km\, s}^{-1})-2.7]$, where MBH is the central SMBH mass, W50 is the full width at half-maximum of a double-horned emission-line profile, and i is the inclination of the CO disc. This relation has a total scatter of $0.6\,$ dex, comparable to those of other SMBH mass correlations, and dominated by the intrinsic scatter of $0.5\,$ dex. A tight correlation is also found between the deprojected CO line widths and the stellar velocity dispersions averaged within one effective radius. We apply our correlation to the COLD GASS sample to estimate the local SMBH mass function.</jats:p>

The Evolution of Gas-Phase Metallicity and Resolved Abundances in Star-forming Galaxies at z ≈ 0.6 – 1.8

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2020)

S Gillman, A Tiley, A Swinbank, U Dudzevičiūtė, R Sharples, I Smail, C Harrison, AJ Bunker, M Bureau, M Cirasuolo, GE Magdis, T Mendel, JP Stott

&lt;jats:title&gt;Abstract&lt;/jats:title&gt; &lt;jats:p&gt;We present an analysis of the chemical abundance properties of &#x2248;650 star-forming galaxies at z&#xA0;&#x2248;&#xA0;0.6&#xA0;&#x2013;&#xA0;1.8. Using integral-field observations from the K&#xA0;-&#xA0;band Multi-Object Spectrograph (KMOS), we quantify the [N&#x2009;ii]/H&#x3B1; emission-line ratio, a proxy for the gas-phase Oxygen abundance within the interstellar medium. We define the stellar mass&#xA0;&#x2013;&#xA0;metallicity relation at z&#xA0;&#x2248;&#xA0;0.6&#xA0;&#x2013;&#xA0;1.0 and z&#xA0;&#x2248;&#xA0;1.2&#xA0;&#x2013;&#xA0;1.8 and analyse the correlation between the scatter in the relation and fundamental galaxy properties (e.g. H&#x3B1; star-formation rate, H&#x3B1; specific star-formation rate, rotation dominance, stellar continuum half-light radius and Hubble-type morphology). We find that for a given stellar mass, more highly star-forming, larger and irregular galaxies have lower gas-phase metallicities, which may be attributable to their lower surface mass densities and the higher gas fractions of irregular systems. We measure the radial dependence of gas-phase metallicity in the galaxies, establishing a median, beam smearing-corrected, metallicity gradient of &#x394;Z/&#x394;R=&#xA0;0.002&#xA0;&#xB1;&#xA0;0.004 dex kpc&#x2212;1, indicating on average there is no significant dependence on radius. The metallicity gradient of a galaxy is independent of its rest-frame optical morphology, whilst correlating with its stellar mass and specific star-formation rate, in agreement with an inside-out model of galaxy evolution, as well as its rotation dominance. We quantify the evolution of metallicity gradients, comparing the distribution of &#x394;Z/&#x394;R in our sample with numerical simulations and observations at z&#xA0;&#x2248;&#xA0;0&#xA0;&#x2013;&#xA0;3. Galaxies in our sample exhibit flatter metallicity gradients than local star-forming galaxies, in agreement with numerical models in which stellar feedback plays a crucial role redistributing metals.&lt;/jats:p&gt;

SDSS-IV MaNGA: the indispensable role of bars in enhancing the central star formation of low-z galaxies

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2020)

L Lin, C Li, C Du, E Wang, T Xiao, M Bureau, A Fraser-McKelvie, K Masters, L Lin, D Wake, L Hao

&lt;jats:title&gt;Abstract&lt;/jats:title&gt; &lt;jats:p&gt;We analyse two-dimensional maps and radial profiles of EW(H&#x3B1;), EW(H&#x3B4;A), and Dn(4000) of low-redshift galaxies using integral field spectroscopy from the MaNGA survey. Out of &#x2248;1400 nearly face-on late-type galaxies with a redshift z &amp;amp;lt; 0.05, we identify 121 &#x201C;turnover&#x201D; galaxies that each have a central upturn in EW(H&#x3B1;), EW(H&#x3B4;A) and/or a central drop in Dn(4000), indicative of ongoing/recent star formation. The turnover features are found mostly in galaxies with a stellar mass above &#x223C;1010 M&#x2299; and NUV-r colour less than &#x2248;5. The majority of the turnover galaxies are barred, with a bar fraction of 89&#xB1;3%. Furthermore, for barred galaxies the radius of the central turnover region is found to tightly correlate with one third of the bar length. Comparing the observed and the inward extrapolated star formation rate surface density, we estimate that the central SFR have been enhanced by an order of magnitude. Conversely, only half of the barred galaxies in our sample have a central turnover feature, implying that the presence of a bar is not sufficient to lead to a central SF enhancement. We further examined the SF enhancement in paired galaxies, as well as the local environment, finding no relation. This implies that environment is not a driving factor for central SF enhancement in our sample. Our results reinforce both previous findings and theoretical expectation that galactic bars play a crucial role in the secular evolution of galaxies by driving gas inflow and enhancing the star formation and bulge growth in the center.&lt;/jats:p&gt;

Resolving the Disc-Halo Degeneracy II: NGC 6946

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2020)

S Aniyan, A Ponomareva, K Freeman, M Arnaboldi, O Gerhard, L Coccato, K Kuijken, M Merrifield

&lt;jats:title&gt;Abstract&lt;/jats:title&gt; &lt;jats:p&gt;The mass-to-light ratio (M/L) is a key parameter in decomposing galactic rotation curves into contributions from the baryonic components and the dark halo of a galaxy. One direct observational method to determine the disc M/L is by calculating the surface mass density of the disc from the stellar vertical velocity dispersion and the scale height of the disc. Usually, the scale height is obtained from near-IR studies of edge-on galaxies and pertains to the older, kinematically hotter stars in the disc, while the vertical velocity dispersion of stars is measured in the optical band and refers to stars of all ages (up to &#x223C; 10&#xA0;Gyr) and velocity dispersions. This mismatch between the scale height and the velocity dispersion can lead to underestimates of the disc surface density and a misleading conclusion of the sub-maximality of galaxy discs. In this paper we present the study of the stellar velocity dispersion of the disc galaxy NGC&#xA0;6946 using integrated star light and individual planetary nebulae as dynamical tracers. We demonstrate the presence of two kinematically distinct populations of tracers which contribute to the total stellar velocity dispersion. Thus, we are able to use the dispersion and the scale height of the same dynamical population to derive the surface mass density of the disc over a radial extent. We find the disc of NGC&#xA0;6946 to be closer to maximal with the baryonic component contributing most of the radial gravitational field in the inner parts of the galaxy ($\rm V_{max}(bar)=0.76(\pm 0.14)V_{max}$).&lt;/jats:p&gt;

Jeans modelling of the Milky Way’s nuclear stellar disc

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2020)

MC Sormani, J Magorrian, F Nogueras-Lara, N Neumayer, R Schönrich, RS Klessen, A Mastrobuono-Battisti

&lt;jats:title&gt;Abstract&lt;/jats:title&gt; &lt;jats:p&gt;The nuclear stellar disc (NSD) is a flattened stellar structure that dominates the gravitational potential of the Milky Way at Galactocentric radii 30 &#x2272; R &#x2272; 300&#x2009;pc. In this paper, we construct axisymmetric Jeans dynamical models of the NSD based on previous photometric studies and we fit them to line-of-sight kinematic data of APOGEE and SiO maser stars. We find that (i) the NSD mass is lower but consistent with the mass independently determined from photometry by Launhardt et&#xA0;al. (2002). Our fiducial model has a mass contained within spherical radius r = 100&#x2009;pc of $M(r&amp;amp;lt;100\, {\rm pc}) = 3.9 \pm 1 \times 10^8 \, \rm M_\odot$ and a total mass of $M_{\rm NSD} = 6.9 \pm 2 \times 10^8 \, \rm M_\odot$. (ii) The NSD might be the first example of a vertically biased disc, i.e. with ratio between the vertical and radial velocity dispersion &#x3C3;z/&#x3C3;R &amp;amp;gt; 1. Observations and theoretical models of the star-forming molecular gas in the central molecular zone suggest that large vertical oscillations may be already imprinted at stellar birth. However, the finding &#x3C3;z/&#x3C3;R &amp;amp;gt; 1 depends on a drop in the velocity dispersion in the innermost few tens of parsecs, on our assumption that the NSD is axisymmetric, and that the available (extinction corrected) stellar samples broadly trace the underlying light and mass distributions, all of which need to be established by future observations and/or modelling. (iii) We provide the most accurate rotation curve to date for the innermost 500&#x2009;pc of our Galaxy.&lt;/jats:p&gt;

Detecting Kozai–Lidov Imprints on the Gravitational Waves of Intermediate-mass Black Holes in Galactic Nuclei

The Astrophysical Journal American Astronomical Society 901 (2020) 125-125

B Deme, B-M Hoang, S Naoz, B Kocsis

Binary Intermediate-mass Black Hole Mergers in Globular Clusters

The Astrophysical Journal American Astronomical Society 899 (2020) 149-149

A Rasskazov, G Fragione, B Kocsis

Revealing the Intermediate Mass Black Hole at the Heart of Dwarf Galaxy NGC404 with Sub-parsec Resolution ALMA Observations

Monthly Notices of the Royal Astronomical Society Oxford University Press 496 (2020) 4061-4078

M Bureau, M Cappellari, L Liu, M Smith

We estimate the mass of the intermediate-mass black hole at the heart of the dwarf elliptical galaxy NGC 404 using Atacama Large Millimeter/submillimeter Array (ALMA) observations of the molecular interstellar medium at an unprecedented linear resolution of ≈0.5 pc, in combination with existing stellar kinematic information. These ALMA observations reveal a central disc/torus of molecular gas clearly rotating around the black hole. This disc is surrounded by a morphologically and kinematically complex flocculent distribution of molecular clouds, that we resolve in detail. Continuum emission is detected from the central parts of NGC 404, likely arising from the Rayleigh–Jeans tail of emission from dust around the nucleus, and potentially from dusty massive star-forming clumps at discrete locations in the disc. Several dynamical measurements of the black hole mass in this system have been made in the past, but they do not agree. We show here that both the observed molecular gas and stellar kinematics independently require a ≈ 5 × 105 M black hole once we include the contribution of the molecular gas to the potential. Our best estimate comes from the high-resolution molecular gas kinematics, suggesting the black hole mass of this system is 5.5+4.1−3.8×105 M (at the 99% confidence level), in good agreement with our revised stellar kinematic measurement and broadly consistent with extrapolations from the black hole mass – velocity dispersion and black hole mass – bulge mass relations. This highlights the need to accurately determine the mass and distribution of each dynamically important component around intermediate-mass black holes when attempting to estimate their masses.

K-CLASH: Strangulation and ram pressure stripping in galaxy cluster members at 0.3 &lt; z &lt; 0.6

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) 496 (2020) 3841-3861

SP Vaughan, AL Tiley, RL Davies, LJ Prichard, SM Croom, M Bureau, JP Stott, A Bunker, M Cappellari, B Ansarinejad, MJ Jarvis

&lt;jats:title&gt;ABSTRACT&lt;/jats:title&gt; &lt;jats:p&gt;Galaxy clusters have long been theorized to quench the star formation of their members. This study uses integral-field unit observations from the K-band MultiObject Spectrograph (KMOS) &#x2013; Cluster Lensing And Supernova survey with Hubble (CLASH) survey (K-CLASH) to search for evidence of quenching in massive galaxy clusters at redshifts 0.3 &amp;amp;lt; z &amp;amp;lt; 0.6. We first construct mass-matched samples of exclusively star-forming cluster and field galaxies, then investigate the spatial extent of their H&#x2009;&#x3B1; emission and study their interstellar medium conditions using emission line ratios. The average ratio of H&#x2009;&#x3B1; half-light radius to optical half-light radius ($r_{\mathrm{e}, {\rm {H}\,\alpha }}/r_{\mathrm{e}, R_{\mathrm{c} } }$) for all galaxies is 1.14&#xA0;&#xB1;&#xA0;0.06, showing that star formation is taking place throughout stellar discs at these redshifts. However, on average, cluster galaxies have a smaller $r_{\mathrm{e}, {\rm {H}\alpha }}/r_{\mathrm{e}, R_{\mathrm{c} } }$ ratio than field galaxies: &#x2329;$r_{\mathrm{e}, {\rm {H}\alpha }}/r_{\mathrm{e}, R_{\mathrm{c} } }$&#x232A;&#xA0;= 0.96&#xA0;&#xB1;&#xA0;0.09 compared to 1.22&#xA0;&#xB1;&#xA0;0.08 (smaller at a 98&#x2009;per&#x2009;cent credibility level). These values are uncorrected for the wavelength difference between H&#x2009;&#x3B1; emission and Rc-band stellar light but implementing such a correction only reinforces our results. We also show that whilst the cluster and field samples follow indistinguishable mass&#x2013;metallicity (MZ) relations, the residuals around the MZ relation of cluster members correlate with cluster-centric distance; galaxies residing closer to the cluster centre tend to have enhanced metallicities (significant at the 2.6&#x3C3; level). Finally, in contrast to previous studies, we find no significant differences in electron number density between the cluster and field galaxies. We use simple chemical evolution models to conclude that the effects of disc strangulation and ram-pressure stripping can quantitatively explain our observations.&lt;/jats:p&gt;

Spin Evolution of Stellar-mass Black Hole Binaries in Active Galactic Nuclei

The Astrophysical Journal American Astronomical Society 899 (2020) 26-26

H Tagawa, Z Haiman, I Bartos, B Kocsis

K-CLASH: spatially-resolving star-forming galaxies in field and cluster environments at z ≈ 0.2-0.6

Monthly Notices of the Royal Astronomical Society Oxford University Press (2020)

AL Tiley, JP Stott, R Davies, LJ Prichard, A Bunker, M Bureau, M Cappellari, M Jarvis, A Robotham, L Cortese, S Bellstedt, B Ansarinejad

We present the KMOS-CLASH (K-CLASH) survey, a K-band Multi-Object Spectrograph (KMOS) survey of the spatially-resolved gas properties and kinematics of 191 (predominantly blue) Hα-detected galaxies at 0.2 ≲ z ≲ 0.6 in field and cluster environments. K-CLASH targets galaxies in four Cluster Lensing And Supernova survey with Hubble (CLASH) fields in the KMOS IZ-band, over 7′ radius (≈2–3 Mpc) fields-of-view. K-CLASH aims to study the transition of star-forming galaxies from turbulent, highly star-forming disc-like and peculiar systems at z ≈ 1–3, to the comparatively quiescent, ordered late-type galaxies at z ≈ 0, and to examine the role of clusters in the build-up of the red sequence since z ≈ 1. In this paper, we describe the K-CLASH survey, present the sample, and provide an overview of the K-CLASH galaxy properties. We demonstrate that our sample comprises star-forming galaxies typical of their stellar masses and epochs, residing both in field and cluster environments. We conclude K-CLASH provides an ideal sample to bridge the gap between existing large integral-field spectroscopy surveys at higher and lower redshifts. We find that star-forming K-CLASH cluster galaxies at intermediate redshifts have systematically lower stellar masses than their star-forming counterparts in the field, hinting at possible “downsizing” scenarios of galaxy growth in clusters at these epochs. We measure no difference between the star-formation rates of Hα-detected, star-forming galaxies in either environment after accounting for stellar mass, suggesting that cluster quenching occurs very rapidly during the epochs probed by K-CLASH, or that star-forming K-CLASH galaxies in clusters have only recently arrived there, with insufficient time elapsed for quenching to have occured.

Formation and Evolution of Compact-object Binaries in AGN Disks

ASTROPHYSICAL JOURNAL American Astronomical Society 898 (2020) ARTN 25

H Tagawa, Z Haiman, B Kocsis

The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra


R Ahumada, CA Prieto, A Almeida, F Anders, SF Anderson, BH Andrews, B Anguiano, R Arcodia, E Armengaud, M Aubert, S Avila, V Avila-Reese, C Badenes, C Balland, K Barger, JK Barrera-Ballesteros, S Basu, J Bautista, RL Beaton, TC Beers, BIT Benavides, CF Bender, M Bernardi, M Bershady, F Beutler, CM Bidin, J Bird, D Bizyaev, GA Blanc, MR Blanton, M Boquien, J Borissova, J Bovy, WN Brandt, J Brinkmann, JR Brownstein, K Bundy, M Bureau, A Burgasser, E Burtin, M Cano-Diaz, R Capasso, M Cappellari, R Carrera, S Chabanier, W Chaplin, M Chapman, B Cherinka, C Chiappini, PD Choi, SD Chojnowski, H Chung, N Clerc, D Coffey, JM Comerford, J Comparat, L da Costa, M-C Cousinou, K Covey, JD Crane, K Cunha, GDS Ilha, YS Dai, SB Damsted, J Darling, DJW Jr, R Davies, K Dawson, N De, A de la Macorra, ND Lee, AB de Andrade Queiroz, AD Machado, S de la Torre, F Dell'Agli, HDM des Bourboux, AM Diamond-Stanic, S Dillon, J Donor, N Drory, C Duckworth, T Dwelly, G Ebelke, S Eftekharzadeh, AD Eigenbrot, YP Elsworth, M Eracleous, G Erfanianfar, S Escoffier, X Fan, E Farr, JG Fernandez-Trincado, D Feuillet, A Finoguenov, P Fofie, A Fraser-McKelvie, PM Frinchaboy, S Fromenteau, H Fu, L Galbany, RA Garcia, DA Garcia-Hernandez, LAG Oehmichen, J Ge, MAG Maia, D Geisler, J Gelfand, J Goddy, V Gonzalez-Perez, K Grabowski, P Green, CJ Grier, H Guo, J Guy, P Harding, S Hasselquist, AJ Hawken, CR Hayes, F Hearty, S Hekker, DW Hogg, JA Holtzman, D Horta, J Hou, B-C Hsieh, D Huber, JAS Hunt, JI Chitham, J Imig, M Jaber, CEJ Angel, JA Johnson, AM Jones, H Jonsson, E Jullo, Y Kim, K Kinemuchi, CCK Iv, GW Kite, M Klaene, J-P Kneib, JA Kollmeier, H Kong, M Kounkel, D Krishnarao, I Lacerna, T-W Lan, RR Lane, DR Law, J-M Le Goff, HW Leung, H Lewis, C Li, J Lian, L Lin, D Long, P Longa-Pena, B Lundgren, BW Lyke, JT Mackereth, CL MacLeod, SR Majewski, A Manchado, C Maraston, P Martini, T Masseron, KL Masters, S Mathur, RM McDermid, A Merloni, M Merrifield, S Meszaros, A Miglio, D Minniti, R Minsley, T Miyaji, FG Mohammad, B Mosser, E-M Mueller, D Muna, A Munoz-Gutierrez, AD Myers, S Nadathur, P Nair, K Nandra, JC do Nascimento, RJ Nevin, JA Newman, DL Nidever, C Nitschelm, P Noterdaeme, JE O'Connell, MD Olmstead, D Oravetz, A Oravetz, Y Osorio, ZJ Pace, N Padilla, N Palanque-Delabrouille, PA Palicio, H-A Pan, K Pan, J Parker, R Paviot, S Peirani, KP Ramrez, S Penny, WJ Percival, I Perez-Fournon, I Perez-Rafols, P Petitjean, MM Pieri, M Pinsonneault, VJ Poovelil, JT Povick, A Prakash, AM Price-Whelan, MJ Raddick, A Raichoor, A Ray, SB Rembold, M Rezaie, RA Riffel, R Riffel, H-W Rix, AC Robin, A Roman-Lopes, C Roman-Zuniga, B Rose, AJ Ross, G Rossi, K Rowlands, KHR Rubin, M Salvato, AG Sanchez, L Sanchez-Menguiano, JR Sanchez-Gallego, C Sayres, A Schaefer, RP Schiavon, JS Schimoia, E Schlafly, D Schlegel, DP Schneider, M Schultheis, A Schwope, H-J Seo, A Serenelli, A Shafieloo, SJ Shamsi, Z Shao, S Shen, M Shetrone, R Shirley, VS Aguirre, JD Simon, MF Skrutskie, A Slosar, R Smethurst, J Sobeck, BC Sodi, D Souto, DV Stark, KG Stassun, M Steinmetz, D Stello, J Stermer, T Storchi-Bergmann, A Streblyanska, GS Stringfellow, A Stutz, G Suarez, J Sun, M Taghizadeh-Popp, MS Talbot, J Tayar, AR Thakar, R Theriault, D Thomas, ZC Thomas, J Tinker, R Tojeiro, HH Toledo, CA Tremonti, NW Troup, S Tuttle, E Unda-Sanzana, M Valentini, J Vargas-Gonzalez, M Vargas-Magana, JA Vazquez-Mata, M Vivek, D Wake, Y Wang, BA Weaver, A-M Weijmans, V Wild, JC Wilson, RF Wilson, N Wolthuis, WM Wood-Vasey, R Yan, M Yang, C Yeche, O Zamora, P Zarrouk, G Zasowski, K Zhang, C Zhao, G Zhao, Z Zheng, Z Zheng, G Zhu, H Zou

Cosmic Evolution of Stellar-mass Black Hole Merger Rate in Active Galactic Nuclei

ASTROPHYSICAL JOURNAL American Astronomical Society 896 (2020) ARTN 138

Y Yang, I Bartos, Z Haiman, B Kocsis, S Marka, H Tagawa

Trapped orbits and solar-neighbourhood kinematics


J Binney

Angle-action variables for orbits trapped at a Lindblad resonance


J Binney

Electromagnetic transients and gravitational waves from white dwarf disruptions by stellar black holes in triple systems

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2020)

G Fragione, BD Metzger, R Perna, NWC Leigh, B Kocsis

Mergers of binaries comprised of compact objects can give rise to explosive transient events, heralding the birth of exotic objects which cannot be formed through single star evolution. Using a large number of direct N-body simulations, we explore the possibility that a white dwarf (WD) is dynamically driven to tidal disruption by a stellar-mass black hole (BH) as a consequence of the joint effects of gravitational wave (GW) emission and Lidov-Kozai oscillations imposed by the tidal field of a outer tertiary companion orbiting the inner BH-WD binary. We explore the sensitivity of our results to the distributions of natal kick velocities imparted to the BH and WD upon formation, adiabatic mass loss, semi-major axes and eccentricities of the triples, and stellar mass ratios. We find rates of WD-TDEs in the range $1.2\times 10^{-3}-1.4$ Gpc$^{-3}$ yr$^{-1}$ for $z\leq 0.1$, rarer than stellar TDEs in triples by a factor of $\sim 3$--$30$. The uncertainty in the TDE rates may be greatly reduced in the future using gravitational wave (GW) observations of Galactic binaries and triples with LISA. WD-TDEs may give rise to high energy X-ray or gamma-ray transients of duration similar to long gamma-ray bursts but lacking the signatures of a core-collapse supernova, while being accompanied by a supernova-like optical transient which lasts for only days. WD--BH and WD--NS binaries will also emit GWs in the LISA band before the TDE. The discovery and identification of triple-induced WD-TDE events by future time domain surveys and/or GWs could enable the study of the demographics of BHs in nearby galaxies.

Newton versus the machine: solving the chaotic three-body problem using deep neural networks

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) 494 (2020) 2465-2470

PG Breen, CN Foley, T Boekholt, SP Zwart

<jats:title>ABSTRACT</jats:title> <jats:p>Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system’s chaotic nature. We show that an ensemble of converged solutions for the planar chaotic three-body problem obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at a fixed computational cost and up to 100 million times faster than the numerical integrator. In addition, we demonstrate the importance of training an ANN using converged solutions from an arbitrary precise integrator, relative to solutions computed by a conventional fixed precision integrator, which can introduce errors in the training data, due to numerical round-off and time discretization, that are learned by the ANN. Our results provide evidence that, for computationally challenging regions of phase space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black hole binary systems or the origin of the core collapse in dense star clusters.</jats:p>

Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) 493 (2020) 3932-3937

TCN Boekholt, SF Portegies Zwart, M Valtonen

<jats:title>ABSTRACT</jats:title> <jats:p>Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work, we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to 5 per cent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable.</jats:p>

Intermediate-mass Black Holes' Effects on Compact Object Binaries

ASTROPHYSICAL JOURNAL American Astronomical Society 892 (2020) ARTN 130

B Deme, Y Meiron, B Kocsis

Although their existence is not yet confirmed observationally, intermediate mass black holes (IMBHs) may play a key role in the dynamics of galactic nuclei. In this paper, we neglect the effect of the nuclear star cluster itself and investigate only how a small reservoir of IMBHs influences the secular dynamics of stellar-mass black hole binaries, using N-body simulations. We show that our simplifications are valid and that the IMBHs significantly enhance binary evaporation by pushing the binaries into the Hill-unstable region of parameter space, where they are separated by the SMBH's tidal field. For binaries in the S-cluster region of the Milky Way, IMBHs drive the binaries to merge in up to 1-6% of cases, assuming five IMBHs within 5 pc of mass 10,000 solar masses each. Observations of binaries in the Galactic center may strongly constrain the population of IMBHs therein.