Merger Time Research Articles

Market Optimism and Merger Waves

We argue that stock and bond market booms and merger waves are both driven by increases in optimism in financial markets and discuss two behavioral hypotheses, the managerial discretion and overvaluation hypotheses that claim that merger waves are driven by market optimism. Empirical support for the managerial theory is provided by evidence that the amounts of assets acquired increase as optimism in financial markets increases and that the returns to acquiring companies are inversely related to market optimism at the time of mergers. Our measures of market optimism also explain managerial choices of finance for mergers. Copyright © 2012 John Wiley & Sons, Ltd.

THE ELM SURVEY. III. A SUCCESSFUL TARGETED SURVEY FOR EXTREMELY LOW MASS WHITE DWARFS

Extremely low mass (ELM) white dwarfs (WDs) with masses <0.25 Msun are rare objects that result from compact binary evolution. Here, we present a targeted spectroscopic survey of ELM WD candidates selected by color. The survey is 71% complete and has uncovered 18 new ELM WDs. Of the 7 ELM WDs with follow-up observations, 6 are short-period binaries and 4 have merger times less than 5 Gyr. The most intriguing object, J1741+6526, likely has either a pulsar companion or a massive WD companion making the system a possible supernova Type Ia or .Ia progenitor. The overall ELM Survey has now identified 19 double degenerate binaries with <10 Gyr merger times. The significant absence of short orbital period ELM WDs at cool temperatures suggests that common envelope evolution creates ELM WDs directly in short period systems. At least one-third of the merging systems are halo objects, thus ELM WD binaries continue to form and merge in both the disk and the halo.

Imprint of the merger and ring-down on the gravitational wave background from black hole binaries coalescence

We compute the gravitational wave background (GWB) generated by a cosmological population of black hole-black hole (BH-BH) binaries using hybrid waveforms recently produced by numerical simulations of (BH-BH) coalescence, which include the inspiral, merger, and ring-down contributions. A large sample of binary systems is simulated using the population synthesis code SeBa, and we extract fundamental statistical information on (BH-BH) physical parameters (primary and secondary BH masses, orbital separations and eccentricities, formation, and merger time scales). We then derive the binary birth and merger rates using the theoretical cosmic star formation history obtained from a numerical study which reproduces the available observational data at redshifts $z&lt;8$. We evaluate the contributions of the inspiral, merger, and ring-down signals to the GWB, and discuss how these depend on the parameters which critically affect the number of coalescing (BH-BH) systems. We find that Advanced LIGO/Virgo have a chance to detect the GWB signal from the inspiral phase with a $(S/N)=10$ only for the most optimistic model, which predicts the highest local merger rate of $0.85\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}\text{ }{\mathrm{Myr}}^{\ensuremath{-}1}$. Third generation detectors, such as the Einstein Telescope (ET), could reveal the GWB from the inspiral phase predicted by any of the considered models. In addition, ET could sample the merger phase of the evolution at least for models which predict local merger rates between $[0.053--0.85]\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}\text{ }{\mathrm{Myr}}^{\ensuremath{-}1}$, which are more than a factor 2 lower than the upper limit inferred from the analysis of the LIGO S5 run [J. Abadie et al., Phys. Rev. D 83, 122005 (2011)]. The frequency dependence and amplitude of the GWB generated during the coalescence is very sensitive to the adopted core mass threshold for BH formation. This opens up the possibility to better understand the final stages of the evolution of massive stellar binaries using observational constraints on the associated gravitational wave emission.

The dynamics of mergers and acquisitions in oligopolistic industries

This paper embeds an oligopolistic industry structure in a real options framework in which synergy gains of horizontal mergers arise endogenously and vary stochastically over time. We find that (i) mergers are more likely in more concentrated industries; (ii) mergers are more likely in industries that are more exposed to industry-wide shocks; (iii) returns to merger and rival firms arising from restructuring are higher in more concentrated industries; (iv) increased industry competition delays the timing of mergers; (v) in sufficiently concentrated industries, bidder competition induces a bid premium that declines with product market competition; and (vi) mergers are more likely and yield larger returns in industries with higher dispersion in firm size.

Explanations for Historical Merger and Current Variation of the English Morpheme -ing

The morpheme -ing is variably realized as non-standard [?n] or the standard [?ŋ] in present-day English, showing a stable sociolinguistic variation. Historical documents suggest that the origin of the [?n] variant is related to the OE verbal ending -ende and the spelling -ing is the result of the merger with the OE nominal ending -inge. As progressive is becoming more popular today, the [?n] variant is found in almost all English speaking communities, but rather differently as a sociolinguistic marker to express the nature of the context as well as the speaker’s identity in terms of region, social class, gender, and ethnicity. This paper attempts to provide a cogent explanation of why the two morphemes in the 12th century had merged into -ing. Phonological salience of the syllable -ing /?ŋ/ along with the unmarked nature of velar nasal /ŋ/ in the coda position can be taken into consideration. The fact that the progressive aspect did not exist at the time of merger, so that the frequency of verbal endings were lower than the nominal endings, also can be supportive evidence for the selection of -ing and current variation with the alveolar nasal pronunciation as a consequence.

BLINDLY DETECTING ORBITAL MODULATIONS OF JETS FROM MERGING SUPERMASSIVE BLACK HOLES

In the last few years before merger, supermassive black hole binaries will rapidly inspiral and precess in a magnetic field imposed by a surrounding circumbinary disk. Multiple simulations suggest this relative motion will convert some of the local energy to a Poynting-dominated outflow, with a luminosity 10^{43} erg/s * (B/10^4 G)^2(M/10^8 Msun)^2 (v/0.4 c)^2, some of which may emerge as synchrotron emission at frequencies near 1 GHz where current and planned wide-field radio surveys will operate. On top of a secular increase in power on the gravitational wave inspiral timescale, orbital motion will produce significant, detectable modulations, both on orbital periods and (if black hole spins are not aligned with the binary's total angular momenta) spin-orbit precession timescales. Because the gravitational wave merger time increases rapidly with separation, we find vast numbers of these transients are ubiquitously predicted, unless explicitly ruled out (by low efficiency $\epsilon$) or obscured (by accretion geometry f_{geo}). If the fraction of Poynting flux converted to radio emission times the fraction of lines of sight accessible $f_{geo}$ is sufficiently large (f_{geo} \epsilon > 2\times 10^{-4} for a 1 year orbital period), at least one event is accessible to future blind surveys at a nominal 10^4 {deg}^2 with 0.5 mJy sensitivity. Our procedure generalizes to other flux-limited surveys designed to investigate EM signatures associated with many modulations produced by merging SMBH binaries.

Convergence of galaxy properties with merger tree temporal resolution

Dark matter halo merger trees are now routinely extracted from cosmological simulations of structure formation. These trees are frequently used as inputs to semi-analytic models of galaxy formation to provide the backbone within which galaxy formation takes place. By necessity, these merger trees are constructed from a finite set of discrete "snapshots" of the N-body simulation and so have a limited temporal resolution. To date, there has been little consideration of how this temporal resolution affects the properties of galaxies formed within these trees. In particular, the question of how many snapshots are needed to achieve convergence in galaxy properties has not be answered. Therefore, we study the convergence in the stellar and total baryonic masses of galaxies, distribution of merger times, stellar mass functions and star formation rates in the Galacticus model of galaxy formation as a function of the number of "snapshot" times used to represent dark matter halo merger trees. When utilizing snapshots between z=20 and z=0, we find that at least 128 snapshots are required to achieve convergence to within 5% for galaxy masses. This convergence is obtained for mean quantities averaged over large samples of galaxies - significant variance for individual galaxies remains even when using very large numbers of snapshots. We find only weak dependence of the rate of convergence on the distribution of snapshots in time - snapshots spaced uniformly in the expansion factor, uniformly in the logarithm of expansion factor or uniformly in the logarithm of critical overdensity for collapse work equally well in almost all cases. We provide input parameters to Galacticus which allow this type of convergence study to be tuned to other simulations and to be carried out for other galaxy properties.

What determines the fraction of elliptical galaxies in clusters?

We study the correlation between the morphological mix of cluster galaxies and the assembly history of the parent cluster by taking advantage of two independently developed semi-analytic models for galaxy formation and evolution. In our models, both the number of cluster members and that of elliptical members increase as a function of cluster mass, in such a way that the resulting elliptical fractions are approximately independent of cluster mass. The population of cluster ellipticals exhibits a marked bimodal distribution as a function of galaxy stellar mass, with a dip at masses ∼1010 M⊙. In the framework of our models, this bimodality originates from the combination of a strongly decreasing number of galaxies with increasing stellar mass, and a correspondingly increasing probability of experiencing major mergers. We show that the correlation between the measured elliptical fraction and the assembly history of the parent cluster is weak, and that it becomes stronger in models that adopt longer galaxy merger times. We argue that this results from the combined effect of a decreasing bulge production due to a reduced number of mergers, and an increasing survival probability of pre-existing ellipticals, with the latter process being more important than the former.

ACCELERATING COMPACT OBJECT MERGERS IN TRIPLE SYSTEMS WITH THE KOZAI RESONANCE: A MECHANISM FOR “PROMPT” TYPE Ia SUPERNOVAE, GAMMA-RAY BURSTS, AND OTHER EXOTICA

White dwarf-white dwarf (WD-WD) and neutron star-neutron star (NS-NS) mergers may produce Type Ia supernovae and gamma-ray bursts (GRBs), respectively. A general problem is how to produce binaries with semi-major axes small enough to in significantly less than the Hubble time (t_H), and thus accommodate the observation that these events closely follow episodes of star formation. I explore the possibility that such systems are not binaries at all, but actually coeval, or dynamical formed, triple systems. The tertiary induces Kozai oscillations in the inner binary, driving it to high eccentricity, and reducing its gravitational wave (GW) merger timescale. This effect significantly increases the allowed range of binary period P such that the merger time is t_merge < t_H. In principle, Chandrasekhar-mass binaries with P ~ 300 days can merge in < t_H if they contain a prograde solar-mass tertiary at high enough inclination. For retrograde tertiaries, the maximum P such that t_merge < t_H is yet larger. In contrast, P < 0.3 days is required in the absence of a tertiary. I discuss implications of these findings for the production of transients formed via compact object binary mergers. Based on the statistics of solar-type binaries, I argue that many such binaries should be in triple systems affected by the Kozai resonance. If true, expectations for the mHz GW signal from individual sources, the diffuse background, and the foreground for GW experiments like LISA are modified. This work motivates future studies of triples systems of A, B,and O stars, and new types of searches for WD-WD binaries in triple systems.

Valuing a Listed Property Fund or Trust on the Johannesburg Securities Exchange (JSE) Using a Real Options Technique

The empirical study was undertaken to critically analyse if there was any other value other than the calculated market value during the time of the merger of the two property funds listed on the Johannesburg Securities Exchange. In doing so, the real options technique is used, because according to option valuation theory, real options have the flexibility that traditional valuation techniques do not have. The optionality that existed in this case was due to one listed property fund merging with another listed property fund. The listed property fund that acquires the other fund will be exercising its call on the acquired fund. Most of the written research papers on optionalities within real estate market are on the option to develop on a vacant land or build a new building. It seems that there is not much literature on listed real estate funds and optionality at the moment. From South Africa’s perspective, there are relatively no research papers on real estate and real options. Normally, when an investor applies a hedging strategy, he or she buys the cheapest asset, selling the expensive one. In this case, it is recommended that the investor should exercise a long call option and short the underlying, as the price of the call option is relatively cheap than the of a Freestone Property Fund.

Quantified H i morphology - III. Merger visibility times from H i in galaxy simulations

Major mergers of disk galaxies are thought to be a substantial driver in galaxy evolution. To trace the fraction and the rate galaxies are in mergers over cosmic times, several observational techniques, including morphological selection criteria, have been developed over the last decade. We apply this morphological selection of mergers to 21 cm radio emission line (HI) column density images of spiral galaxies in nearby surveys. In this paper, we investigate how long a 1:1 merger is visible in HI from N-body simulations. We evaluate the merger visibility times for selection criteria based on four parameters: Concentration, Asymmetry, M20, and the Gini parameter of second order moment of the flux distribution (GM). Of three selection criteria used in the literature, one based on Concentration and M20 works well for the HI perspective with a merger time scale of 0.4 Gyr. Of the three selection criteria defined in our previous paper, the GM performs well and cleanly selects mergers for 0.69 Gyr. The other two criteria (A-M20 and C-M20), select isolated disks as well, but perform best for face-on, gas-rich disks (T(merger) ~ 1 Gyr). The different visibility scales can be combined with the selected fractions of galaxies in any large HI survey to obtain merger rates in the nearby Universe. All-sky surveys such as WALLABY with ASKAP and the Medium Deep Survey with the APETIF instrument on Westerbork are set to revolutionize our perspective on neutral hydrogen and will provide an accurate measure of the merger fraction and rate of the present epoch.

The dark matter assembly of the Local Group in constrained cosmological simulations of a Λ cold dark matter universe

We make detailed theoretical predictions for the assembly properties of the Local Group (LG) in the standard LambdaCDM cosmological model. We use three cosmological N-body dark matter simulations from the CLUES project, which are designed to reproduce the main dynamical features of the matter distribution down to the scale of a few Mpc around the LG. Additionally, we use the results of an unconstrained simulation with a sixty times larger volume to calibrate the influence of cosmic variance. We characterize the Mass Aggregation History (MAH) for each halo by three characteristic times, the formation, assembly and last major merger times. A major merger is defined by a minimal mass ratio of 10:1. We find that the three LGs share a similar MAH with formation and last major merger epochs placed on average \approx 10 - 12 Gyr ago. Between 12% and 17% of the halos in the mass range 5 x 10^11 Msol/h < M_h < 5 x 10^12 Msol/h have a similar MAH. In a set of pairs of halos within the same mass range, a fraction of 1% to 3% share similar formation properties as both halos in the simulated LG. An unsolved question posed by our results is the dynamical origin of the MAH of the LGs. The isolation criteria commonly used to define LG-like halos in unconstrained simulations do not narrow down the halo population into a set with quiet MAHs, nor does a further constraint to reside in a low density environment. The quiet MAH of the LGs provides a favorable environment for the formation of disk galaxies like the Milky Way and M31. The timing for the beginning of the last major merger in the Milky Way dark matter halo matches with the gas rich merger origin for the thick component in the galactic disk. Our results support the view that the specific large and mid scale environment around the Local Group play a critical role in shaping its MAH and hence its baryonic structure at present.

Accounting for mergers and reverse mergers: An instructional assignment using SEC Form 10-K and S-4 disclosures

► The assignment requires students to investigate two real-world mergers using disclosures in SEC Forms 10-K and S-4. ► Students must examine contextual factors surrounding the merger and reconstruct entries on the books of the acquirer. ► Contextual factors include reasons for the merger, determination of the “accounting acquirer,” and the legal environment. ► Students are given exposure to accounting for reverse mergers, where the legal acquirer is not the accounting acquirer . This instructional assignment explores two real-world business combinations, focusing on contextual factors surrounding the merger as well as accounting recognition by the legal acquirer. The business combinations studied in this assignment are Exxon Mobil Corporation’s (2010) acquisition of XTO Energy Inc. and the 2010 reverse merger between RRI Energy, Inc. and Mirant Corporation. Students must utilize disclosures in Forms 10-K and S-4 to: (1) investigate the reasons behind the merger, (2) examine the criteria used for determination of the “accounting acquirer” (in the case of RRI Energy and Mirant), and finally (3) prepare the entries to combine the firms at the time of merger. Students must learn the basics of reverse-acquisition accounting from relevant authoritative pronouncements as well as study the legal environment surrounding business combinations. Targeted for Advanced Accounting courses, this instructional assignment meets calls from the accounting profession and the Accounting Education Exchange Commission (1990) for instructors to integrate real-world problems that capture complex business transactions into the course curriculum.

Runaway stars as progenitors of supernovae and gamma-ray bursts

When a core-collapse supernova occurs in a binary system, the surviving star as well as the compact remnant emerging from the supernova may reach a substantial space velocity. With binary population synthesis modelling at solar and one-fifth of solar metallicity, we predict the velocities of such runaway stars or binaries. We compile predictions for runaway OB stars, red supergiants and Wolf–Rayet stars, either isolated or with a compact companion. For those stars or binaries which undergo a second stellar explosion we compute their further evolution and the distance travelled until a Type II or Type Ibc supernova or a long or short gamma-ray burst (GRB) occurs. We find our predicted population of OB runaway stars broadly matches the observed population of stars but, to match the fastest observed Wolf–Rayet runaway stars, we require that black holes receive an asymmetric kick upon formation. We find that at solar metallicity Type Ic supernova progenitors travel shorter distances than the progenitors of other supernova types because they are typically more massive and thus have shorter lifetimes. Those of Type IIP supernovae can fly farthest about 48 pc on average at solar metallicity, with about 8 per cent of them reaching 100 pc. In considering the consequences of assuming that the progenitors of long GRBs are spun-up secondary stars that experience quasi-homogeneous evolution, we find that such evolution has a dramatic effect on the population of runaway Wolf–Rayet stars and that some 30 per cent of GRBs could occur a hundred parsec or more from their initial positions. We also consider mergers of double compact object binaries consisting of neutron stars and/or black holes. We find the most common type of visible mergers are neutron star–black hole mergers that are roughly 10 times more common than neutron star–neutron star mergers. All compact mergers have a wide range of merger times from years to Gyr and are predicted to occur 300 times less often than supernovae in the Milky Way. We also find that there may be a population of low-velocity neutron stars that are ejected from a binary rather than by their own natal kick. These neutron stars need to be included when the distribution of neutron star kicks is deduced from observations.

Times, environments and channels of bulge formation in a Lambda cold dark matter cosmology

We analyze predictions from two independently developed galaxy formation models to study the mechanisms, environments, and characteristic times of bulge formation in a LambdaCDM cosmogony. For each model, we test different prescriptions for bulge formation in order to quantify the relative importance of different channels. Our results show that the strong correlation between galaxy and halo mass for central galaxies, and the richer merger history of more massive systems naturally give rise to a strong correlation between galaxy mass and morphology, and between halo mass and morphological type of central galaxies. Large fractions of the bulge mass are acquired through major and minor mergers, but disc instability plays an important role, particularly for intermediate mass galaxies. We find that the modelling of disc instability events, as well as of the galaxy merger times, can affect significantly the timing of bulge formation, and the relative importance of different channels. Bulge dominated galaxies acquire their morphology through major mergers, but this can be modified by cooling of gas from the surrounding hot halo. We find that disc regrowth is a non negligible component of the evolution of bulge dominated galaxies, particularly for low to intermediate masses, and at high redshifts.

GRAVITATIONAL MEMORY IN BINARY BLACK HOLE MERGERS

In addition to the dominant oscillatory gravitational wave signals produced during binary inspirals, a non-oscillatory component arises from the nonlinear "memory" effect, sourced by the emitted gravitational radiation. The memory grows significantly during the late inspiral and merger, modifying the signal by an almost step-function profile, and making it difficult to model by approximate methods. We use numerical evolutions of binary black holes to evaluate the nonlinear memory during late-inspiral, merger and ringdown. We identify two main components of the signal: the monotonically growing portion corresponding to the memory, and an oscillatory part which sets in roughly at the time of merger and is due to the black hole ringdown. Counter-intuitively, the ringdown is most prominent for models with the lowest total spin. Thus, the case of maximally spinning black holes anti-aligned to the orbital angular momentum exhibits the highest signal-to-noise (SNR) for interferometric detectors. The largest memory offset, however, occurs for highly spinning black holes, with an estimated value of h^tot_20 \approx 0.24 in the maximally spinning case. These results are central to determining the detectability of nonlinear memory through pulsar timing array measurements.

Post-Merger Integration Duration and Leverage Dynamics of Mergers: Theory and Evidence

We introduce the concept of the post-merger integration duration (PMID) which is the time delay that it takes a merged entity to fully capture synergistic gains. Using a dynamic model, we examine the effects of this duration on acquiring firms’ financing behavior around mergers. When facing a longer PMID, acquiring firms optimally choose lower leverage prior to and at the time of a merger, and gradually levers up as the integration period nears completion. We hand collect a unique data set on the integration duration of mergers and provide strong empirical support for the model implications.

Binary black hole coalescence in the extreme-mass-ratio limit: Testing and improving the effective-one-body multipolar waveform

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $\ensuremath{\mu}$ and $M$ in the extreme-mass-ratio limit $\ensuremath{\mu}/M=\ensuremath{\nu}\ensuremath{\ll}1$. We focus on the transition from quasicircular inspiral to plunge, merger, and ringdown. We compare the EOB waveform to a Regge-Wheeler-Zerilli waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by a leading-order $\mathcal{O}(\ensuremath{\nu})$ analytically resummed radiation reaction. The EOB and the Regge-Wheeler-Zerilli waveforms have an initial dephasing of about $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{rad}$ and maintain then a remarkably accurate phase coherence during the long inspiral ($\ensuremath{\sim}33$ orbits), accumulating only about $\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{rad}$ until the last stable orbit, i.e. $\ensuremath{\Delta}\ensuremath{\phi}/\ensuremath{\phi}\ensuremath{\sim}\ensuremath{-}5.95\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. We obtain such accuracy without calibrating the analytically resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for studies concerning the Laser Interferometer Space Antenna. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasicircular corrections in both the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasicircular parameters by requiring compatibility between EOB and Regge-Wheeler-Zerilli waveforms at the light ring. The resulting phase difference around the merger time is as small as $\ifmmode\pm\else\textpm\fi{}0.015\text{ }\text{ }\mathrm{rad}$, with a fractional amplitude agreement of 2.5%. This suggest that next-to-quasicircular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical-relativity waveforms.

Latent Value, Synergistic Effect and Merger Decision-Making: A Study on the Internet Industry

This paper studies the and acquisition (M&A hereafter) in the Internet industry, and constructs a theoretical model to anatomize the motivations of the M&A and the factors that impact the performance of M&A. The model analyzes three motivations on M&A: Synergistic Effect Motivation, Latent Value Motivation and Merger Timing Motivation. Among these three motivations, our study shows that the Latent Value motivation is the leading factor that causes the manager's decision on M&A in the case when the M&A result in a financial loss. For the first time, we quantify the synergistic effect and the latent value of M&A in the internet industry. We also develop the concepts of development merger and the prevention merger, and use the model to deduct the optimal timing and price of the M&A in the internet industry.

Recoiling black holes in merging galaxies: relationship to active galactic nucleus lifetimes, starbursts and the MBH-σ* relation

Gravitational-wave recoil of merging supermassive black holes (SMBHs) may influence the co-evolution of SMBHs and their host galaxies. We examine this possibility using smoothed particle hydrodynamic/N-body simulations of gaseous galaxy mergers, including SMBH accretion, in which the merged BH receives a recoil kick. This enables us to follow the trajectories and accretion of recoiling BHs in self-consistent, evolving merger remnants. In contrast to recent studies on similar topics, we conduct a large parameter study, generating a suite of over 200 simulations with more than 60 merger models and a range of recoil velocities (vk). With this, we can identify systematic trends in the behaviour of recoiling BHs. Our main results are as follows. (1) BHs kicked at nearly the central escape speed (vesc) may oscillate on large orbits for up to a Hubble time, but in gas-rich mergers, BHs kicked with up to ∼0.7vesc may be confined to the central few kpc of the galaxy, owing to gas drag and steep central potentials. (2) vesc in gas-rich mergers may increase rapidly during final coalescence, in which case recoil trajectories may depend sensitively on the timing of the BH merger relative to the formation of the central potential well. Delays of even a few times 107 yr in the BH merger time may substantially suppress recoiling BH motion for a fixed kick speed. (3) Recoil events generally reduce the lifetimes of bright active galactic nuclei (AGNs), but short-period recoil oscillations may actually extend AGN lifetimes at lower luminosities. (4) Bondi–Hoyle accretion dominates recoiling BH growth for vk/vesc≲ 0.6–0.8; for higher vk, the BH accretes primarily from its ejected gas disc, which we model as a time-dependent accretion disc. (5) Kinematically offset AGNs may be observable either immediately after a high-velocity recoil or during pericentric passages through a gas-rich remnant. In either case, AGN lifetimes may be up to ∼10 Myr (for Δv > 800 km s−1), though the latter generally have higher luminosities. (6) Spatially offset AGNs can occur for vk≳ 0.5–0.7vesc (for ΔR > 1 kpc); these generally have low luminosities and lifetimes of ∼1–100 Myr. (7) Rapidly recoiling BHs may be up to approximately five times less massive than their stationary counterparts. These mass deficits lower the normalization of the MBH–σ* relation and contribute to both intrinsic and overall scatter. (8) Finally, the displacement of AGN feedback after a recoil event enhances central star formation rates in the merger remnant, thereby extending the starburst phase of the merger and creating a denser, more massive stellar cusp.