arXiv subjects

Enrico Ramirez-Ruiz

Publications and source records attributed to Enrico Ramirez-Ruiz.

At least 55 records · Page 3Linked to original sources

arXiv2024

Tidal Disruption Events from Stripped Stars

Observations of tidal disruption events (TDEs) show signs of Nitrogen enrichment reminiscent of other astrophysical sources such as active galactic nuclei (AGN) and star-forming galaxies. Given that TDEs probe the gas from a single star, it is possible to test if the observed enrichment is consistent with expectations from the CNO cycle by looking at the observed Nitrogen/Carbon (N/C) abundance ratios. Given that $\approx 20\%$ of solar mass stars (and an even larger fraction of more massive stars) live in close binaries, it is worthwhile to also consider what TDEs from stars influenced by binary evolution would look like. We show here that TDEs from stars stripped of their Hydrogen-rich (and Nitrogen-poor) envelopes through previous binary-induced mass loss can produce much higher observable N/C enhancements than even TDEs from massive stars. Additionally, we predict that the time-dependence of the N/C abundance ratio in the mass fallback rate of stripped stars will follow the inverse behavior of main-sequence stars, enabling a more accurate characterization of the disrupted star.

astro-ph.HE↗

arXiv2024

The Peculiar Radio Evolution of the Tidal Disruption Event ASASSN-19bt

We present detailed radio observations of the tidal disruption event (TDE) ASASSN-19bt/AT2019ahk, obtained with the Australia Telescope Compact Array (ATCA), the Atacama Large Millimeter/submillimeter Array (ALMA), and the MeerKAT radio telescopes, spanning 40 to 1464 days after the onset of the optical flare. We find that ASASSN-19bt displays unusual radio evolution compared to other TDEs, as the peak brightness of its radio emission increases rapidly until 457 days post-optical discovery and then plateaus. Using a generalized approach to standard equipartition techniques, we estimate the energy and corresponding physical parameters for two possible emission geometries: a non-relativistic spherical outflow and a relativistic outflow observed from an arbitrary viewing angle. We find that the non-relativistic solution implies a continuous energy rise in the outflow from $E\sim10^{46}$ erg to $E\sim10^{49}$ erg with $β\approx 0.05$, while the off-axis relativistic jet solution instead suggests $E\approx10^{52}$ erg with $Γ\sim10$ erg at late times in the maximally off-axis case. We find that neither model provides a holistic explanation for the origin and evolution of the radio emission, emphasizing the need for more complex models. ASASSN-19bt joins the population of TDEs that display unusual radio emission at late times. Conducting long-term radio observations of these TDEs, especially during the later phases, will be crucial for understanding how these types of radio emission in TDEs are produced.

astro-ph.HE↗

arXiv2024

SN 2022oqm: A Bright and Multi-peaked Calcium-rich Transient

We present the photometric and spectroscopic evolution of SN 2022oqm, a nearby multi-peaked hydrogen- and helium-weak calcium-rich transient (CaRT). SN 2022oqm was detected 13.1 kpc from its host galaxy, the face-on spiral galaxy NGC 5875. Extensive spectroscopic coverage reveals an early hot (T >= 40,000 K) continuum and carbon features observed $\sim$1~day after discovery, SN Ic-like photospheric-phase spectra, and strong forbidden calcium emission starting 38 days after discovery. SN 2022oqm has a relatively high peak luminosity (MB = -17 mag) for (CaRTs), making it an outlier in the population. We determine that three power sources are necessary to explain the light curve (LC), with each corresponding to a distinct peak. The first peak is powered by an expanding blackbody with a power law luminosity, suggesting shock cooling by circumstellar material (CSM). Subsequent LC evolution is powered by a double radioactive decay model, consistent with two sources of photons diffusing through optically thick ejecta. From the LC, we derive an ejecta mass and 56Ni mass of ~0.6 solar masses and ~0.09 solar masses. Spectroscopic modeling suggests 0.6 solar masses of ejecta, and with well-mixed Fe-peak elements throughout. We discuss several physical origins for SN 2022oqm and find either a surprisingly massive white dwarf progenitor or a peculiar stripped envelope model could explain SN 2022oqm. A stripped envelope explosion inside a dense, hydrogen- and helium-poor CSM, akin to SNe Icn, but with a large 56Ni mass and small CSM mass could explain SN 2022oqm. Alternatively, helium detonation on an unexpectedly massive white dwarf could also explain SN 2022oqm.

astro-ph.HE↗

arXiv2024

Mid-Infrared Outbursts in Nearby Galaxies: Nuclear Obscuration and Connections to Hidden Tidal Disruption Events and Changing-Look Active Galactic Nuclei

We study the properties of galaxies hosting mid-infrared outbursts in the context of a catalog of five hundred thousand galaxies from the Sloan Digital Sky Survey. We find that nuclear obscuration, as inferred by the surrounding dust mass, does not correlate with host galaxy type, stellar properties (e.g. total mass and mean age), or with the extinction of the host galaxy as estimated by the Balmer decrement. This implies that nuclear obscuration may not be able to explain any over-representation of tidal disruption events in particular host galaxies. We identify a region in the galaxy catalog parameter space that contains all unobscured tidal disruption events but only harbors $\lesssim $ 11\% of the mid-infrared outburst hosts. We find that mid-infrared outburst hosts appear more centrally concentrated and have higher galaxy Sérsic indices than galaxies hosting active galactic nuclei (AGN) selected using the BPT classification. We thus conclude that the majority of mid-infrared outbursts are not hidden tidal disruption events but are instead consistent with being obscured AGN that are highly variable, such as changing-look AGN.

astro-ph.GA↗

arXiv2023

Accelerating pathways to leadership for underrepresented groups in STEM

The vision of 2030STEM is to address systemic barriers in institutional structures and funding mechanisms required to achieve full inclusion in Science, Technology, Engineering, and Mathematics (STEM) and accelerate leadership pathways for individuals from underrepresented populations across STEM sectors. 2030STEM takes a systems-level approach to create a community of practice that can test, learn and promote programs and policies that affirm and value cultural identities in STEM. To achieve parity and full representation in the STEM workforce, a variety of changes are needed across academia and STEM professional industries (e.g., business, finance, biotech, government) to accelerate underrepresented groups into positions of leadership throughout the STEM ecosystem. Through a series of subject matter interviews, roundtables, and curated analysis four major themes have surfaced, which, if implemented, could exponentially accelerate the creation of critical pathways to leadership, break down pre-existing barriers and biases, intentionally elevate the voices, value, and research of underrepresented groups in STEM, and implement new structural strategies at scale. This white paper provides a summary of innovative new practices designed to accelerate inclusion, including expanding on known global toolkits, new funding strategies, and the structural changes required throughout various STEM professions to propel pathways to leadership for underrepresented groups.

physics.soc-ph↗

arXiv2023

Machine-Learning Enhanced Photometric Analysis of the Extremely Bright GRB 210822A

We present analytical and numerical models of the bright long GRB 210822A at $z=1.736$. The intrinsic extreme brightness exhibited in the optical, which is very similar to other bright GRBs (e.g., GRBs 080319B, 130427A, 160625A 190114C, and 221009A), makes GRB 210822A an ideal case for studying the evolution of this particular kind of GRB. We use optical data from the RATIR instrument starting at $T+315.9$ s, with publicly available optical data from other ground-based observatories, as well as Swift/UVOT, and X-ray data from the Swift/XRT instrument. The temporal profiles and spectral properties during the late stages align consistently with the conventional forward shock model, complemented by a reverse shock element that dominates optical emissions during the initial phases ($T<300$ s). Furthermore, we observe a break at $T=80000$s that we interpreted as evidence of a jet break, which constrains the opening angle to be about $θ_\mathrm{j}=(3-5)$ degrees. Finally, we apply a machine-learning technique to model the multi-wavelength light curve of GRB 210822A using the AFTERGLOWPY library. We estimate the angle of sight $θ_{obs}=(6.4 \pm 0.1) \times 10^{-1}$ degrees, the energy $E_0=(7.9 \pm 1.6)\times 10^{53}$ ergs, the electron index $p=2.54 \pm 0.10$, the thermal energy fraction in electrons $ε_\mathrm{e}=(4.63 \pm 0.91) \times 10^{-5}$ and in the magnetic field $ε_\mathrm{B}= (8.66 \pm 1.01) \times 10^{-6}$, the efficiency $χ= 0.89 \pm 0.01$, and the density of the surrounding medium $n_\mathrm{0} = 0.85 \pm 0.01 cm^{-3}$.

astro-ph.HE↗

arXiv2023

Transients stemming from collapsing massive stars: The missing pieces to advance joint observations of photons and high-energy neutrinos

Collapsing massive stars lead to a broad range of astrophysical transients, whose multi-wavelength emission is powered by a variety of processes including radioactive decay, activity of the central engine, and interaction of the outflows with a dense circumstellar medium. These transients are also candidate factories of neutrinos with energy up to hundreds of PeV. We review the energy released by such astrophysical objects across the electromagnetic wavebands as well as neutrinos, in order to outline a strategy to optimize multi-messenger follow-up programs. We find that, while a significant fraction of the explosion energy can be emitted in the infrared-optical-ultraviolet (UVOIR) band, the optical signal alone is not optimal for neutrino searches. Rather, the neutrino emission is strongly correlated with the one in the radio band, if a dense circumstellar medium surrounds the transient, and with X-rays tracking the activity of the central engine. Joint observations of transients in radio, X-rays, and neutrinos will crucially complement those in the UVOIR band, breaking degeneracies in the transient parameter space. Our findings call for heightened surveys in the radio and X-ray bands to warrant multi-messenger detections.

astro-ph.HE↗

arXiv2023

Type II-P Supernova Progenitor Star Initial Masses and SN 2020jfo: Direct Detection, Light Curve Properties, Nebular Spectroscopy, and Local Environment

We present optical, ultraviolet, and infrared data of the type II supernova (SN II) 2020jfo at 14.5 Mpc. This wealth of multiwavelength data allows to compare different metrics commonly used to estimate progenitor masses of SN II for the same object. Using its early light curve, we infer SN 2020jfo had a progenitor radius of $\approx$700 $R_{\odot}$, consistent with red supergiants of initial mass $M_{\rm ZAMS}=$11-13 $M_{\odot}$. The decline in its late-time light curve is best fit by a ${}^{56}$Ni mass of 0.018$\pm$0.007 $M_{\odot}$ consistent with that ejected from SN II-P with $\approx$13 $M_{\odot}$ initial mass stars. Early spectra and photometry do not exhibit signs of interaction with circumstellar matter, implying that SN 2020jfo experienced weak mass loss within the final years prior to explosion. Our spectra at $>$250 days are best fit by models from 12 $M_{\odot}$ initial mass stars. We analyzed integral field unit spectroscopy of the stellar population near SN 2020jfo, finding its massive star population had a zero age main sequence mass of 9.7$\substack{+2.5\\-1.3} M_{\odot}$. We identify a single counterpart in pre-explosion imaging and find it has an initial mass of at most $7.2\substack{+1.2\\-0.6} M_{\odot}$. We conclude that the inconsistency between this mass and indirect mass indicators from SN 2020jfo itself is most likely caused by extinction with $A_{V}=2$-3 mag due to matter around the progenitor star, which lowered its observed optical luminosity. As SN 2020jfo did not exhibit extinction at this level or evidence for interaction with circumstellar matter between 1.6-450 days from explosion, we conclude that this material was likely confined within $\approx$3000 $R_{\odot}$ from the progenitor star.

astro-ph.SR↗

arXiv2023

Jetted and Turbulent Stellar Deaths: New LVK-Detectable Gravitational Wave Sources

Upcoming LIGO/Virgo/KAGRA (LVK) observing runs are expected to detect a variety of inspiralling gravitational-wave (GW) events, that come from black-hole and neutron-star binary mergers. Detection of non-inspiral GW sources is also anticipated. We report the discovery of a new class of non-inspiral GW sources - the end states of massive stars - that can produce the brightest simulated stochastic GW burst signal in LVK bands known to date, and could be detectable in the LVK run A+. Some dying massive stars launch bipolar relativistic jets, which inflate a turbulent energetic bubble - cocoon - inside of the star. We simulate such a system using state-of-the-art 3D general-relativistic magnetohydrodynamic simulations and show that these cocoons emit quasi-isotropic GW emission in the LVK band, $\sim 10-100$ Hz, over a characteristic jet activity timescale, $\sim 10-100$ s. Our first-principles simulations show that jets exhibit a wobbling behavior, in which case cocoon-powered GWs might be detected already in LVK run A+, but it is more likely that these GWs will be detected by the third generation GW detectors with estimated rate of $ \sim 10 $ events/year. The detection rate drops to $ \sim 1\% $ of that value if all jets were to feature a traditional axisymmetric structure instead of a wobble. Accompanied by electromagnetic emission from the energetic core-collapse supernova and the cocoon, we predict that collapsars are powerful multi-messenger events.

astro-ph.HE↗

arXiv2023

Tidal Disruption Events from the Combined Effects of Two-Body Relaxation and the Eccentric Kozai-Lidov Mechanism

Tidal disruption events (TDEs) take place when a star ventures too close to a supermassive black hole (SMBH) and becomes ruptured. One of the leading proposed physical mechanisms often invoked in the literature involves weak two-body interactions experienced by the population of stars within the host SMBH's sphere of influence, commonly referred to as two-body relaxation. This process can alter the angular momentum of stars at large distances and place them into nearly radial orbits, thus driving them to disruption. On the other hand, gravitational perturbations from an SMBH companion via the eccentric Kozai-Lidov (EKL) mechanism have also been proposed as a promising stellar disruption channel. Here we demonstrate that the combination of EKL and two-body relaxation in SMBH binaries is imperative for building a comprehensive picture of the rates of TDEs. Here we explore how the density profile of the surrounding stellar distribution and the binary orbital parameters of an SMBH companion influence the rate of TDEs. We show that this combined channel naturally produces disruptions at a rate that is consistent with observations and also naturally forms repeated TDEs, where a bound star is partially disrupted on multiple orbits. Recent observations show stars being disrupted in short-period orbits, which is challenging to explain when these mechanisms are considered independently. However, the diffusive effect of two-body relaxation, combined with the secular nature of the eccentricity excitations from EKL, is found to drive stars on short eccentric orbits at a much higher rate.

astro-ph.GA↗

arXiv2023

Uncovering Hidden Massive Black Hole Companions with Tidal Disruption Events

Dynamical perturbations from supermassive black hole (SMBH) binaries can increase the rates of tidal disruption events (TDEs). However, most previous work focuses on TDEs from the heavy black hole in the SMBH binary (SMBHB) system. In this work, we focus on the lighter black holes in SMBHB systems and show that they can experience a similarly dramatic increase in their TDE rate due to perturbations from a more massive companion. While the increase in TDEs around the more massive black hole is mostly due to chaotic orbital perturbations, we find that, around the smaller black hole, the eccentric Kozai-Lidov (EKL) mechanism is dominant and capable of producing a comparably large number of TDEs. In this instance, the mass derived from the light curve and spectra of TDEs triggered by the lighter SMBH companion are expected to be significant smaller than the SMBH mass estimated from galaxy scaling relations, which are dominated by the more massive companion. This apparent inconsistency can help find SMBHB candidates that are not currently accreting as active galactic nuclei (AGN) and that are at separations too small to be resolved as two distinct sources. TDEs thus provide us with an exciting opportunity to study SMBHB, in particular when they might be detected from galaxies hosting SMBHs that are too massive to disrupt sun-like stars.

astro-ph.HE↗

arXiv2023

Collapsar Black Holes are Likely Born Slowly Spinning

Collapsing stars constitute the main black hole (BH) formation channel, and are occasionally associated with the launch of relativistic jets that power $ γ$-ray bursts (GRBs). Thus, collapsars offer an opportunity to infer the natal (before spin-up/down by accretion) BH spin directly from observations. We show that once the BH saturates with large-scale magnetic flux, the jet power is dictated by the BH spin and mass accretion rate. Core-collapse simulations by Halevi et al. 2023 and GRB observations favor stellar density profiles that yield an accretion rate $ \dot{m} \approx 10^{-2} M_\odot~{\rm s^{-1}} $, weakly dependent on time. This leaves the spin as the main factor that governs the jet power. By comparing the jet power to characteristic GRB luminosities, we find that the majority of BHs associated with jets are likely born slowly spinning with a dimensionless spin $ a \simeq 0.2 $, or $ a \lesssim 0.5 $ for wobbling jets, with the main uncertainty originating in the unknown $ γ$-ray radiative efficiency. This result could be applied to the entire core-collapse BH population, unless an anti-correlation between the stellar magnetic field and angular momentum is present. In a companion paper, Jacquemin-Ide et al. 2023, we show that regardless of the natal spin, the extraction of BH rotational energy leads to spin-down to $ a \lesssim 0.2 $, consistent with gravitational-wave observations. We verify our results by performing the first 3D general relativistic magnetohydrodynamic simulations of collapsar jets with characteristic GRB energies, powered by slowly spinning BHs. We find that jets of typical GRB power struggle to escape from the star, providing the first numerical indication that many jets fail to generate a GRB.

astro-ph.HE↗

arXiv2023

A binary origin for the first isolated stellar-mass black hole detected with astrometric microlensing

The Milky Way is believed to host hundreds of millions of quiescent stellar-mass black holes (BHs). In the last decade, some of these objects have been potentially uncovered via gravitational microlensing events. All these detections resulted in a degeneracy between the velocity and the mass of the lens. This degeneracy has been lifted, for the first time, with the recent astrometric microlensing detection of OB110462. However, two independent studies reported very different lens mass for this event. Sahu et al. (2022) inferred a lens mass of 7.1 $\pm$ 1.3 Msun, consistent with a BH, while Lam et al. (2022) inferred 1.6-4.2 Msun, consistent with either a neutron star or a BH. Here, we study the landscape of isolated BHs formed in the field. In particular, we focus on the mass and center-of-mass speed of four sub-populations: isolated BHs from single-star origin, disrupted BHs of binary-star origin, main-sequence stars with a compact object companion, and double compact object mergers. Our model predicts that most ($\gtrsim$ 70%) isolated BHs in the Milky Way are of binary origin. However, non-interactions lead to most massive BHs ($\gtrsim$ 15-20 Msun) being predominantly of single origin. Under the assumption that OB110462 is a free-floating compact object we conclude that it is more likely to be a BH originally belonging to a binary system. Our results suggest that low-mass BH microlensing events can be useful to understand binary evolution of massive stars in the Milky Way, while high-mass BH lenses can be useful to probe single stellar evolution.

astro-ph.GA↗

arXiv2023

Hydrodynamics and survivability during post-main-sequence planetary engulfment

The engulfment of substellar bodies (SBs, such as brown dwarfs and planets) by giant stars is a possible explanation for rapidly rotating giants, lithium-rich giants, and the presence of SBs in close orbits around subdwarfs and white dwarfs. We simulate the flow in the vicinity of an engulfed SB in three-dimensional hydrodynamics. We model the SB as a rigid body with a reflective surface because it cannot accrete. This reflective boundary changes the flow morphology to resemble that of engulfed compact objects with outflows. We measure the drag coefficients for the ram pressure and gravitational drag forces acting on the SB, and use them to integrate its trajectory inside the star. We find that engulfment can increase the luminosity of a $1M_\odot$ star by up to a few orders of magnitude. The time for the star to return to its original luminosity is up to a few thousand years when the star has evolved to $\approx10R_\odot$ and up to a few decades at the tip of the red giant branch. No SBs can eject the envelope of a $1M_\odot$ star before it evolves to $\approx10R_\odot$, if the orbit of the SB is the only energy source contributing to the ejection. In contrast, SBs as small as $\approx10M_\text{Jup}$ can eject the envelope at the tip of the red giant branch. The numerical framework we introduce here can be used to study planetary engulfment in a simplified setting that captures the physics of the flow at the scale of the SB.

astro-ph.SR↗

arXiv2023

The hydrodynamic evolution of binary black holes embedded within the vertically stratified disks of active galactic nuclei

Stellar-mass black holes can become embedded within the gaseous disks of active galactic nuclei (AGNs). Afterwards, their interactions are mediated by their gaseous surroundings. In this work, we study the evolution of stellar-mass binary black holes (BBHs) embedded within AGN disks using a combination of three-dimensional hydrodynamic simulations and analytic methods, focusing on environments in which the AGN disk scale height $H$ is $\gtrsim$ the BBH sphere of influence. We model the local surroundings of the embedded BBHs using a wind tunnel formalism and characterize different accretion regimes based on the local properties of the disk, which range from wind-dominated to quasi-spherical. We use our simulations to develop prescriptions for mass accretion and drag for embedded BBHs. We use these prescriptions, along with AGN disk models that can represent the Toomre-unstable outer regions of AGN disks, to study the long-term evolution of the BBHs as they migrate through the disk. We find that BBHs typically merge within $\lesssim 5-30\,{\rm Myr}$, increasing their mass significantly in the process, allowing BBHs to enter (or cross) the pair-instability supernova mass gap. The rate at which gas is supplied to these BBHs often exceeds the Eddington limit, sometimes by several orders of magnitude. We conclude that most embedded BBHs will merge before migrating significantly in the disk. Depending on the conditions of the ambient gas and the distance to the system, LISA can detect the transition between the gas-dominated and gravitational wave dominated regime for inspiraling BBHs that are formed sufficiently close to the AGN ($\lesssim$ 0.1 pc). We also discuss possible electromagnetic signatures during and following the inspiral, finding that it is generally unlikely but not inconceivable for the bolometric luminosity of the BBH to exceed that of the host AGN.

astro-ph.HE↗

arXiv2023

Tidal disruption events from eccentric orbits and lessons learned from the noteworthy ASASSN-14ko

Stars grazing supermassive black holes (SMBHs) on bound orbits may survive tidal disruption, causing periodic flares. Inspired by the recent discovery of the periodic nuclear transient ASASSN-14ko, a promising candidate for a repeating tidal disruption event (TDE), we study the tidal deformation of stars approaching SMBHs on eccentric orbits. With both analytical and hydrodynamics methods, we show the overall tidal deformation of a star is similar to that in a parabolic orbit provided that the eccentricity is above a critical value. This allows one to make use of existing simulation libraries from parabolic encounters to calculate the mass fallback rate in eccentric TDEs. We find the flare structures of eccentric TDEs show a complicated dependence on both the SMBH mass and the orbital period. For stars orbiting SMBHs with relatively short periods, we predict significantly shorter-lived duration flares than those in parabolic TDEs, which can be used to predict repeating events if the mass of the SMBH can be independently measured. Using an adiabatic mass loss model, we study the flare evolution over multiple passages, and show the evolved stars can survive many more passages than main sequence stars. We apply this theoretical framework to the repeating TDE candidate ASASSN-14ko and suggest that its recurrent flares originate from a moderately massive ($M\gtrsim 1 \mathrm{M_\odot}$), extended ($\approx$ a few $\mathrm{R_\odot}$), evolved star on a grazing, bound orbit around the SMBH. Future hydrodynamics simulations of multiple tidal interactions will enable realistic models on the individual flare structure and the evolution over multiple flares.

astro-ph.HE↗

arXiv2022

A Multiwavelength Study of the Massive Colliding Wind Binary WR 20a: A Possible Progenitor for Fast-Spinning LIGO Binary Black Hole Mergers

WR 20a is the most massive close-in binary known in our Galaxy. It is composed of two $\approx$80 M$_\odot$ Wolf-Rayet stars with a short period of $\approx$3.7 days in the open cluster Westerlund 2. As such, WR 20a presents us with a unique laboratory for studying the currently uncertain physics of binary evolution and compact object formation as well as for studying the wind collision region in an massive eclipsing binary system. We use deep Chandra observations of WR 20a to study the time variability of the wind collision region between the two Wolf-Rayet stars and are able to produce an X-ray light curve covering $\approx$2/3 of its orbital period. We find that the X-ray light curve is asymmetric because the flux of one peak is 2.5$σ$ larger than the flux of the other peak. This asymmetry could be caused by asymmetric mass-loss from the two stars or by the lopsidedness of the wind collision region due to the unusually fast rotation of the system. The X-ray light curve is also shifted in phase space when compared to the optical light curves measured by TESS and ASAS-SN. Additionally, we explore the ultimate fate of this system by modeling the resultant binary black hole merger expected at the end of the two stars' lives. We conclude that this system will evolve to be a representative of the sub-population of LIGO progenitors of fast-spinning binary black hole merger events.

astro-ph.HE↗

arXiv2022

A revised energy formalism for common-envelope evolution: repercussions for planetary engulfment and the formation of neutron star binaries

Common-envelope evolution is a stage in binary system evolution in which a giant star engulfs a companion. The standard energy formalism is an analytical framework to estimate the amount of energy transferred from the companion's shrinking orbit into the envelope of the star that engulfed it. We show analytically that this energy transfer is larger than predicted by the standard formalism. As the orbit of the companion shrinks, the mass it encloses becomes smaller, and the companion is less bound than if the enclosed mass had remained constant. Therefore, more energy must be transferred to the envelope for the orbit to shrink further. We derive a revised energy formalism that accounts for this effect, and discuss its consequences in two contexts: the formation of neutron star binaries, and the engulfment of planets and brown dwarfs by their host stars. The companion mass required to eject the stellar envelope is smaller by up to $50\%$, leading to differences in common-envelope evolution outcomes. The energy deposition in the outer envelope of the star, which is related to the transient luminosity and duration, is up to a factor of $\approx7$ higher. Common-envelope efficiency values above unity, as defined in the literature, are thus not necessarily unphysical, and result at least partly from an incomplete description of the energy deposition. The revised energy formalism presented here can improve our understanding of stellar merger and common-envelope observations and simulations.

astro-ph.SR↗