Stellar Collisions Research Articles

Dynamics of binary black holes in young star clusters: the impact of cluster mass and long-term evolution

ABSTRACT Dynamical interactions in dense star clusters are considered one of the most effective formation channels of binary black holes (BBHs). Here, we present direct N-body simulations of two different star cluster families: low-mass (∼500–800 M⊙) and relatively high-mass star clusters (≥5000 M⊙). We show that the formation channels of BBHs in low- and high-mass star clusters are extremely different and lead to two completely distinct populations of BBH mergers. Low-mass clusters host mainly low-mass BBHs born from binary evolution, while BBHs in high-mass clusters are relatively massive (chirp mass up to ∼100 M⊙) and driven by dynamical exchanges. Tidal disruption dramatically quenches the formation and dynamical evolution of BBHs in low-mass clusters on a very short time-scale (≲100 Myr), while BBHs in high-mass clusters undergo effective dynamical hardening until the end of our simulations (1.5 Gyr). In high-mass clusters, we find that 8 per cent of BBHs have primary mass in the pair-instability mass gap at metallicity Z = 0.002, all of them born via stellar collisions, while only one BBH with primary mass in the mass gap forms in low-mass clusters. These differences are crucial for the interpretation of the formation channels of gravitational-wave sources.

Light-curve Model for Luminous Red Novae and Inferences about the Ejecta of Stellar Mergers

The process of unstable mass transfer in a stellar binary can result in either a complete merger of the stars or successful removal of the donor envelope leaving a surviving more compact binary. Luminous red novae (LRNe) are the class of optical transients believed to accompany such merger/common envelope events. Past works typically model LRNe using analytic formulae for supernova light curves that make assumptions (e.g., radiation-dominated ejecta, neglect of hydrogen recombination energy) not justified in stellar mergers due to the lower velocities and specific thermal energy of the ejecta. We present a one-dimensional model of LRN light curves that accounts for these effects. Consistent with observations, we find that LRNe typically possess two light-curve peaks, an early phase powered by initial thermal energy of the hot, fastest ejecta layers and a later peak powered by hydrogen recombination from the bulk of the ejecta. We apply our model to a sample of LRNe to infer their ejecta properties (mass, velocity, and launching radius) and compare them to the progenitor donor star properties from pretransient imaging. We define the maximum luminosity achievable for a given donor star in the limit that the entire envelope is ejected, finding that several LRNe violate this limit. Shock interaction between the ejecta and predynamical mass loss may provide an additional luminosity source to alleviate this tension. Our model can also be applied to the merger of planets with stars or stars with compact objects.

The nuclear transient AT 2017gge: a tidal disruption event in a dusty and gas-rich environment and the awakening of a dormant SMBH

ABSTRACT We present the results from a dense multwavelength [optical/UV, near-infrared (IR), and X-ray] follow-up campaign of the nuclear transient AT 2017gge, covering a total of 1698 d from the transient’s discovery. The bolometric light curve, the blackbody temperature and radius, the broad H and He i λ5876 emission lines and their evolution with time, are all consistent with a tidal disruption event (TDE) nature. A soft X-ray flare is detected with a delay of ∼200 d with respect to the optical/UV peak and it is rapidly followed by the emergence of a broad He ii λ4686 and by a number of long-lasting high ionization coronal emission lines. This indicate a clear connection between a TDE flare and the appearance of extreme coronal line emission (ECLEs). An IR echo, resulting from dust re-radiation of the optical/UV TDE light is observed after the X-ray flare and the associated near-IR spectra show a transient broad feature in correspondence of the He i λ10830 and, for the first time in a TDE, a transient high-ionization coronal NIR line (the [Fe xiii] λ10798) is also detected. The data are well explained by a scenario in which a TDE occurs in a gas-and-dust rich environment and its optical/UV, soft X-ray, and IR emission have different origins and locations. The optical emission may be produced by stellar debris stream collisions prior to the accretion disc formation, which is instead responsible for the soft X-ray flare, emitted after the end of the circularization process.

Searching for the next Galactic Luminous red nova

ABSTRACT Luminous red novae (LRNe) are astrophysical transients believed to be caused by the partial ejection of a binary star’s common envelope (CE) and the merger of its components. The formation of the CE is likely to occur during unstable mass transfer, initiated by a primary star which is evolving off the main sequence (a Hertzsprung gap star) and a lower mass companion. In agreement with observations, theoretical studies have shown that outflows from the pre-CE phase produce a detectable brightening of the progenitor system a few years before the ejection event. Based on these assumptions, we present a method to identify Galactic LRNe precursors, the resulting precursor candidates, and our follow-up analysis to uncover their nature. We begin by constructing a sample of progenitor systems, i.e. Hertzsprung gap stars, by statistically modelling the density of a colour magnitude diagram formed from ‘well behaved’ Gaia DR2 sources. Their time-domain evolution from the Zwicky Transient Facility (ZTF) survey is used to search for slowly brightening events, as pre-CE precursor candidates. The nature of the resulting candidates is further investigated using archival data and our own spectroscopic follow-up. Overall, we constructed a sample of ∼5.4 × 104 progenitor sources, from which 21 were identified as candidate LRNe precursors. Further analysis revealed 16 of our candidates to be Hα emitters, with their spectra often suggesting hotter (albeit moderately extincted) A-type or B-type stars. Because of their long-term variability in optical and mid-infrared wavelengths, we propose that many of our candidates are mass-transferring binaries with compact companions surrounded by dusty circumstellar discs or alternatively magnetically active stellar merger remnants.

Evolution of massive stellar triples and implications for compact object binary formation

ABSTRACT Most back hole and neutron star progenitors are found in triples or higher multiplicity systems. Here, we present a new triple stellar evolution code, ${\tt TSE}$, which simultaneously takes into account the physics of the stars and their gravitational interaction. ${\tt TSE}$ is used to simulate the evolution of massive stellar triples in the galactic field from the zero-age main sequence until they form compact objects. To this end, we implement initial conditions that incorporate the observed high correlation between the orbital parameters of early-type stars. We show that the interaction with a tertiary companion can significantly impact the evolution of the inner binary. High eccentricities can be induced by the third-body dynamical effects, leading to a Roche lobe overflow or even to a stellar merger from initial binary separations 103–$10^5\, \rm R_\odot$. In $\sim 5\, {{\ \rm per\ cent}}$ of the systems, the tertiary companion itself fills its Roche lobe, while $\sim 10\, {{\ \rm per\ cent}}$ of all systems become dynamically unstable. We find that between $0.3{{\ \rm per\ cent}}$ and $5{{\ \rm per\ cent}}$ of systems form a stable triple with an inner compact object binary, where the exact fraction depends on metallicity and the natal kick prescription. Most of these triples are binary black holes with black hole companions. We find no binary neutron star in any surviving triple, unless zero natal kicks are assumed. About half of all black hole binaries formed in our models are in triples, where in the majority, the tertiary black hole can perturb their long-term evolution. Our results show that triple interactions are key to a full understanding of massive star evolution and compact object binary formation.

The Effect of Metallicity on the Formation of Massive Black Holes through Stellar Collisions in Young Massive Star Clusters

Dynamical interactions facilitated by the high densities in massive star clusters can lead to large numbers of stellar collisions and unique stellar evolution pathways not possible for stars evolving in isolation. Using N-body cluster models, we study the role of stellar collisions in the formation of massive black holes, specifically studying the effect of stellar metallicity on this process. We show that at high metallicity (up to solar), the number of massive black holes formed may be reduced by up to a factor of ten compared to low-metallicity clusters. We also examine the role of collisions in the production of pair-instability supernovae and predict event rates of these transients in the local universe.

Revisiting the V1309 Sco 2008 outburst spectra

Context. V1309 Sco is the only confirmed non-compact stellar merger, identified thanks to the match of its pre-outburst light curve to that of a contact binary. Therefore, anything that can be deduced from existing observations may serve as benchmark constraints for models. Aims. We present some observational evidence to guide future hydrodynamical simulations and common envelope studies. Methods. Using archive spectra taken at high and mid spectral resolution during the V1309 Sco outburst and late decline, together with the inferential methods we developed to study nova ejecta through panchromatic high resolution spectroscopic follow ups, we constrained the physical state, structure, dynamics, and geometry of the transient that originated in the stellar merger. Results. We found that the emitted spectra arise from two distinct contributions: matter expelled during the 2008 outburst and circumbinary gas produced during historic mass-loss episodes. These two components are likely to exhibit orthogonal geometry, with the 2008 mass loss displaying a dust-laden bipolar ejecta produced by a time limited rapidly accelerating wind and the circumbinary gas having a donut-like shape. A central source powers them both, having produced a fluorescent light pulse, but we cannot precisely determine the time it started or its spectral energy distribution. We can, however, place its upper energy cutoff at about 54 eV and the bulk of its emission at < 20 eV. We also know that the central source turned off within months after the outburst and before the ejecta turned optically thin.

Stellar collisions in globular clusters: Constraints on the initial mass function of the first generation of stars

Globular clusters display an anticorrelation between the fraction of the first generation of stars (N(G1)/N(tot)) and the slope of the present-day mass function of the clusters (αpd), which is particularly significant for massive clusters. In the framework of the binary-mediated collision scenario for the formation of the second-generation stars in globular clusters, we test the effect of a varying stellar initial mass function (IMF) of the G1 stars on the (N(G1)/N(tot)) − αpd anticorrelation. We use a simple collision model that has only two input parameters, the shape of the IMF of G1 stars and the fraction of G1 stars that coalesce to form second-generation stars. We show that a variable efficiency of the collision process is necessary in order to explain the (N(G1)/N(tot)) − αpd anticorrelation; however, the scatter in the anticorrelation can only be explained by variations in the IMF, and in particular by variations in the slope in the mass interval ≈(0.1–0.5) M⊙. Our results indicate that in order to explain the scatter in the (N(G1)/N(tot)) − αpd relation, it is necessary to invoke variations in the slope in this mass range between ≈ − 0.9 and ≈ − 1.9. Interpreted in terms of a Kroupa-like broken power law, this translates into variations in the mean mass of between ≈0.2 and 0.55 M⊙. This level of variation is consistent with what is observed for young stellar clusters in the Milky Way and may reflect variations in the physical conditions of the globular cluster progenitor clouds at the time the G1 population formed or may indicate the occurrence of collisions between protostellar embryos before stars settle on the main sequence.

Von Zeipel – Lidov – Kozai cycles in action: Kepler triples with eclipse depth variations: KICs 6964043, 5653126, 5731312, and 8023317

ABSTRACT We report the results of the photodynamical analyses of four compact, tight triple stellar systems, KICs 6964043, 5653126, 5731312, and 8023317, based largely on Kepler and TESS data. All systems display remarkable eclipse timing and eclipse depth variations, the latter implying a non-aligned outer orbit. Moreover, KIC 6964043 is also a triply eclipsing system. We combined photometry, ETV curves, and archival spectral energy distribution data to obtain the astrophysical parameters of the constituent stars and the orbital elements with substantial precision. KICs 6964043 and 5653126 were found to be nearly flat with mutual inclinations imut = 4${_{.}^{\circ}}$1 and 12${_{.}^{\circ}}$3, respectively, while KICs 5731312 and 8023317 (imut = 39${_{.}^{\circ}}$4 and 55${_{.}^{\circ}}$7, respectively) are found to lie in the high imut regime of the von Zeipel-Kozai-Lidov (ZKL) theorem. We show that, currently, both high inclination triples exhibit observable unusual retrograde apsidal motion. Moreover, the eclipses will disappear in all but one of the four systems within a few decades. Short-term numerical integrations of the dynamical evolution reveal that both high inclination triples are currently subject to ongoing, large amplitude (Δe ∼ 0.3) inner eccentricity variations on centuries-long time-scales, in accord with the ZKL theorem. Longer-term integrations predict that two of the four systems may become dynamically unstable on ∼ Gyr time-scales, while in the other two triples common envelope phases and stellar mergers may occur. Finally, we investigate the dynamical properties of a sample of 71 KIC/TIC triples statistically, and find that the mutual inclinations and outer mass ratios are anticorrelated at the 4σ level. We discuss the implications for the formation mechanisms of compact triples.

Extreme Eccentricities of Triple Systems: Analytic Results

Triple stars and compact objects are ubiquitously observed in nature. Their long-term evolution is complex; in particular, the von Zeipel–Lidov–Kozai (ZLK) mechanism can potentially lead to highly eccentric encounters of the inner binary. Such encounters can lead to a plethora of interacting binary phenomena, as well as stellar and compact-object mergers. Here we find implicit analytical formulae for the maximal eccentricity, , of the inner binary undergoing ZLK oscillations, where both the test-particle limit (parameterized by the inner-to-outer angular momentum ratio η) and the double-averaging approximation (parameterized by the period ratio, ϵ SA) are relaxed, for circular outer orbits. We recover known results in both limiting cases (either η or ϵ SA → 0) and verify the validity of our model using numerical simulations. We test our results with two accurate numerical N-body codes, rebound for Newtonian dynamics and tsunami for general-relativistic dynamics, and find excellent correspondence. We discuss the implications of our results for stellar triples and both stellar and supermassive triple black hole mergers.

Fermi-LAT Detection of a GeV Afterglow from a Compact Stellar Merger

It is usually thought that long-duration gamma-ray bursts (GRBs) are associated with massive star core collapse, whereas short-duration GRBs are associated with mergers of compact stellar binaries. The discovery of a kilonova associated with a nearby (350 Mpc) long-duration GRB—GRB 211211A, however, indicates that the progenitor of this long-duration GRB is a compact object merger. Here we report the Fermi-LAT detection of gamma-ray (>100 MeV) afterglow emission from GRB 211211A, which lasts ∼20,000 s after the burst, the longest event for conventional short-duration GRBs ever detected. We suggest that this gamma-ray emission results from afterglow synchrotron emission. The soft spectrum of GeV emission may arise from a limited maximum synchrotron energy of only a few hundreds of MeV at ∼20,000 s. The usually long duration of the GeV emission could be due to the proximity of this GRB and the long deceleration time of the GRB jet that is expanding in a low-density circumburst medium, consistent with the compact stellar merger scenario.

Detectability of a spatial correlation between stellar mass black hole mergers and active galactic nuclei in the local Universe

ABSTRACT The origin of the binary black hole (BBH) mergers detected through gravitational waves (GWs) by the LIGO-Virgo-KAGRA (LVK) collaboration remains debated. One fundamental reason is our ignorance of their host environment, as the typical size of an event’s localization volume can easily contain thousands of galaxies. A strategy around this is to exploit statistical approaches to assess the spatial correlation between these mergers and astrophysically motivated host galaxy types, such as active galactic nuclei (AGNs). We use a likelihood ratio method to infer the degree of GW–AGN connection out to z = 0.2. We simulate BBH mergers whose components’ masses are sampled from a realistic distribution of the underlying population of black holes (BHs). Localization volumes for these events are calculated assuming two different interferometric network configurations. These correspond to the configuration of the third (O3) and of the upcoming fourth (O4) LVK observing runs. We conclude that the 13 BBH mergers detected during the third observing run at z ≤ 0.2 are not enough to reject with a 3σ significance the hypothesis according to which there is no connection between GW and AGNs more luminous than $\approx 10^{44.3}\rm {erg}\ \rm {s}^{-1}$, that have number density higher than 10−4.75 Mpc−3. However, 13 detections are enough to reject this no-connection hypothesis when rarer categories of AGNs are considered, with bolometric luminosities greater than $\approx 10^{45.5}\rm {erg}\ \rm {s}^{-1}$. We estimate that O4 results will potentially allow us to test fractional contributions to the total BBH merger population from AGNs of any luminosity higher than $80{{\ \rm per\ cent}}$.

Understanding the physical state of hot plasma formed through stellar wind collision in WR140 using high-resolution X-ray spectroscopy

ABSTRACT We analyse a series of XMM–Newton RGS data of the binary Wolf–Rayet star WR140 that encompasses one entire orbit. We find that the RGS detects X-rays from optically thin thermal plasma only during orbital phases when the companion O star is on the near side of the WR star. Although such X-rays are believed to be emitted from the shock cone formed through collision of the stellar winds, temperature and density profiles of the plasma along the cone have not been measured observationally. We find that the temperature of the plasma producing Ne emission lines is 0.4–0.8 keV, using the intensity ratio of Kα lines from He-like and H-like Ne. We also find, at orbital phases 0.816 and 0.912, that the electron number density in the Ne line-emission site is approximately 1012 cm−3 from the observed intensity ratios f/r and i/r of the He-like triplet. We calculated the shock cone shape analytically, and identify the distance of the Ne line-emission site from the shock stagnation point to be 0.9–8.9 × 1013 cm using the observed ratio of the line-of-sight velocity and its dispersion. This means that we will be able to obtain the temperature and density profiles along the shock cone with emission lines from other elements. We find that the photoexcitation rate by the O star is only 1.3–16.4 per cent of that of the collisional excitation at orbital phase 0.816. This implies that our assumption that the plasma is collisionally excited is reasonable, at least at this orbital phase.

Magnetic massive stars from stellar mergers

Magnetic massive stars from stellar mergers

Stellar triples on the edge

Context. Hierarchical triple stars are ideal laboratories for studying the interplay between orbital dynamics and stellar evolution. Both mass loss from stellar winds and strong gravitational perturbations between the inner and outer orbit cooperate to destabilise triple systems. Aims. Our current understanding of the evolution of unstable triple systems is mainly built upon results from extensive binary-single scattering experiments. However, destabilised hierarchical triples cover a different region of phase space. Therefore, we aim to construct a comprehensive overview of the evolutionary pathways of destabilised triple-star systems. Methods. Starting from generic initial conditions, we evolved an extensive set of hierarchical triples using the code TRES, combining secular dynamics and stellar evolution. We detected those triples that destabilise due to stellar winds and/or gravitational perturbations. Their evolution was continued with a direct N-body integrator coupled to stellar evolution. Results. The majority of triples (54–69%) preserve their hierarchy throughout their evolution, which is in contradiction with the commonly adopted picture that unstable triples always experience a chaotic, democratic resonant interaction. The duration of the unstable phase was found to be longer than expected (103 − 4 crossing times, reaching up to millions), so that long-term stellar evolution effects cannot be neglected. The most probable outcome is dissolution of the triple into a single star and binary (42–45%). This occurs through the commonly known democratic channel, during which the initial hierarchy is lost and the lightest body usually escapes, but also through a hierarchical channel, during which the tertiary is ejected in a slingshot, independent of its mass. Collisions are common (13–24% of destabilised triples), and they mostly involve the two original inner binary components still on the main sequence (77–94%). This contradicts the idea that collisions with a giant during democratic encounters dominate (only 5–12%). Together with collisions in stable triples, we find that triple evolution is the dominant mechanism for stellar collisions in the Milky Way. Lastly, our simulations produce runaway and walk-away stars with speeds up to several tens of km/s, with a maximum of a few 100 km s−1. We suggest that destabilised triples can explain – or at least alleviate the tension behind – the origin of the observed (massive) runaway stars. Conclusions. A promising indicator for distinguishing triples that will follow the democratic or hierarchical route, is the relative inclination between the inner and outer orbits. Its influence can be summed up in two rules of thumb: (1) prograde triples tend to evolve towards hierarchical collisions and ejections, and (2) retrograde triples tend to evolve towards democratic encounters and a loss of initial hierarchy, unless the system is compact, which experience collision preferentially. The trends found in this work complement those found previously from binary-single scattering experiments, and together they will help to generalise and improve our understanding on the evolution of unstable triple systems of various origins.

Constraints on the origins of hypervelocity stars: velocity distribution, mergers, and star formation history

ABSTRACT In recent years surveys have identified several dozen B stars in the Milky Way halo moving faster than the local escape speed. The origin of most of these hypervelocity stars (HVSs) is still poorly constrained. Here we show that the velocity distribution, and in particular the deficiency in >700 km s−1 HVSs is inconsistent with binary disruptions by the massive black hole (MBH) in the Galactic Centre. This conclusion holds in the full and empty loss-cone regime, and for secular instabilities in eccentric discs. Accounting for multiple close encounters between binaries and the MBH does not qualitatively change the results. Moreover, there is no observed counterpart population in the Galactic Centre that is consistent with the HVSs. The star formation history could be tuned explain the HVS velocity distribution, but this tuning would produce a mismatch with the observed HVS flight times. Frequent stellar collisions of the binary components due to interactions with the MBH do not significantly impact the velocity distribution in the Galactic halo. Such collisions, however, can leave observable remnants in the Galactic Centre, and potentially explain the origins of G2-like dust clouds.

Stellar collisions in globular clusters: the origin of multiple stellar populations

ABSTRACT Two generations of stars, G1 and G2, typically populate Galactic globular clusters (GCs). The origin of G2 stars is unclear. We uncover two empirical dependencies between GC characteristics, which can be explained by the formation of G2 main-sequence (MS) stars due to collision/merging of their primordial counterparts (G1). A similar genesis of both G2 stars and peculiar objects like low-mass X-ray binaries and millisecond pulsars is also implied. Indeed, we find a significant (at a confidence level ${\gt} 99.9{{\ \rm per\ cent}}$) anticorrelation between the fraction of G1 red giants (NG1/Ntot) and stellar encounter rates among 51 GCs. Moreover, a Milky Way-like initial mass function requires at least ∼50 per cent of MS stars located in the mass range [0.1–0.5] M⊙. Unlike cluster mass loss, stellar collisions/merging retain these G1 stars by converting them into more massive G2 ones, with mainly MMS > 0.5 M⊙. This process coupled with a decreasing relative mass loss with increasing GC masses implies a smaller (NG1/Ntot) in more massive GCs with a shallower present-day mass function. From data for 35 GCs, we find that such an anticorrelation is significant at 98.3 per cent confidence level (Spearman’s correlation) for the 12 most massive GCs (MGC > 105.3 M⊙) and it is at a confidence level of 89 per cent for the 12 least massive GCs (MGC < 105.1 M⊙). Other fractions of G1 and G2 stars observed at the bottom of the MS as compared with the red giant branch in a few GCs are consistent with the scenario proposed.

X-Ray Emission from Candidate Stellar Merger Remnant TYC 2597-735-1 and Its Blue Ring Nebula

Abstract Tight binary or multiple-star systems can interact through mass transfer and follow vastly different evolutionary pathways than single stars. The star TYC 2597-735-1 is a candidate for a recent stellar merger remnant resulting from a coalescence of a low-mass companion with a primary star a few thousand years ago. This violent event is evident in a conical outflow (“Blue Ring Nebula”) emitting in UV light and surrounded by leading shock filaments observed in Hα and UV emission. From Chandra data, we report the detection of X-ray emission from the location of TYC 2597-735-1 with a luminosity log ( L X / L bol ) = − 5.5 . Together with a previously reported period of ~14 days, this indicates ongoing stellar activity and the presence of strong magnetic fields on TYC 2597-735-1. Supported by stellar evolution models of merger remnants, we interpret the inferred stellar magnetic field as dynamo action associated with a newly formed convection zone in the atmosphere of TYC 2597-735-1, though internal shocks at the base of an accretion-powered jet cannot be ruled out. We speculate that this object will evolve into an FK Com–type source, i.e., a class of rapidly spinning magnetically active stars for which a merger origin has been proposed but for which no relic accretion or large-scale nebula remains visible. We also detect likely X-ray emission from two small regions close to the outer shock fronts in the Blue Ring Nebula, which may arise from inhomogeneities either in the circumstellar medium or in the mass and velocity distribution in the merger-driven outflow.

Stellar mergers as the origin of the blue main-sequence band in young star clusters

Recent high-quality Hubble Space Telescope (HST) photometry shows that the main sequences (MS) stars of young star clusters form two discrete components in the color-magnitude diagram (CMD). Based on their distribution in the CMD, we show that stars of the blue MS component can be understood as slow rotators originating from stellar mergers. We derive the masses of the blue MS stars, and find that they follow a nearly flat mass function, which supports their unusual formation path. Our results imply that the cluster stars gain their mass in two different ways, by disk accretion leading to rapid rotation, contributing to the red MS, or by binary merger leading to slow rotation and populating the blue MS. We also derive the approximate merger time of the individual stars of the blue MS component, and find a strong early peak in the merger rate, with a lower level merger activity prevailing for tens of Myr. This supports recent binary formation models, and explains new velocity dispersion measurements for members of young star clusters. Our findings shed new light on the origin of the bi-modal mass, spin, and magnetic field distributions of main-sequence stars.

Black hole spectroscopy horizons for current and future gravitational wave detectors

Black hole spectroscopy is the proposal to observe multiple quasinormal modes in the ringdown of a binary black hole merger. In addition to the fundamental quadrupolar mode, overtones and higher harmonics may be present and detectable in the gravitational wave signal, allowing for tests of the no-hair theorem. We analyze in detail the strengths and weaknesses of the standard Rayleigh criterion supplied with a Fisher matrix error estimation, and we find that the criterion is useful, but too restrictive. Therefore we motivate the use of a conservative high Bayes factor threshold to obtain the black hole spectroscopy horizons of current and future detectors, i.e., the distance (averaged in sky location and binary inclination) up to which one or more additional modes can be detected and confidently distinguished from each other. We set up all of our searches for additional modes starting at $t = 10(M_1+M_2)$ after the peak amplitude in simulated signals of circular nonspinning binaries. An agnostic multimode analysis allows us to rank the subdominant modes: for nearly equal mass binaries we find $(\ell, m, n) = (2,2,1)$ and $(3,3,0)$ and, for very asymmetric binaries, $(3,3,0)$ and $(4,4,0)$, for the secondary and tertiary modes, respectively. At the current estimated rates for heavy stellar mass binary black hole mergers, with primary masses between 45 and 100 solar masses, we expect an event rate of mergers within our conservative estimate for the $(2,2,1)$ spectroscopy horizon of $0.03 - 0.10\ {\rm yr}^{-1}$ for LIGO at design sensitivity and $(0.6 - 2.4) \times 10^3\ {\rm yr}^{-1}$ for the future third generation ground-based detector Cosmic Explorer.