Bright Supernova Precursors by Outbursts from Massive Stars with Compact Object Companions

A fraction of core-collapse supernovae (SNe) with signs of interaction with a dense circumstellar matter are preceded by bright precursor emission. While the precursors are likely caused by a mass ejection before core collapse, their mechanism to power energetic bursts—sometimes reaching 1048–1049 erg, which is larger than the binding energies of red supergiant envelopes—is still under debate. Remarkably, such a huge energy deposition should result in an almost complete envelope ejection and hence a strong sign of interaction, but the observed SNe with precursors show in fact typical properties among the interacting SNe. More generally, the observed luminosity of 1040−1042 erg s−1 is shown to be challenging for a single SN progenitor. To resolve these tensions, we propose a scenario where the progenitor is in a binary system with a compact object (CO) and an outburst from the star leads to a super-Eddington accretion onto the CO. We show that for sufficiently short separations outbursts with moderate initial kinetic energies of 1046–1047 erg can be energized by the accreting CO so that their radiative output can be consistent with the observed precursors. We discuss the implications of our model in relation to CO binaries detectable with Gaia and gravitational-wave detectors.


INTRODUCTION
Mass loss is an important process in massive stars that characterizes their evolution and the appearances of their final supernova (SN) explosions (e.g., Smith 2014).A wide variety of core-collapse explosions show signatures of dense circumstellar matter (CSM) around the progenitor, indicating suddenly enhanced massloss months to centuries prior to core-collapse.These span from SNe with narrow lines classified as Type IIn/Ibn/Icn (Schlegel 1990;Pastorello et al. 2008;Gal-Yam et al. 2022), and possibly Type II-P/L SNe that comprise about half of core-collapse SNe (Moriya et al. 2011;Khazov et al. 2016;Morozova et al. 2017Morozova et al. , 2018;;Yaron et al. 2017;Förster et al. 2018;Bruch et al. 2021Bruch et al. , 2023)).
Corresponding author: Daichi Tsuna tsuna@caltech.eduFor a fraction of these SNe, the dense CSM is linked to bright optical flares observed from months to years before core-collapse, often called SN precursors.Since the first finding of a precursor in a Type Ibn SN 2006jc two years before the SN (Nakano et al. 2006;Pastorello et al. 2007), precursors have been observed in many Type IIn SNe (e.g., Mauerhan et al. 2013;Fraser et al. 2013;Ofek et al. 2013Ofek et al. , 2014a;;Margutti et al. 2014;Elias-Rosa et al. 2016;Strotjohann et al. 2021;Fransson et al. 2022;Hiramatsu et al. 2023) and a few SNe of other types including Type Ibn SN 2019uo (Strotjohann et al. 2021) and Type II-P SN 2020tlf (Jacobson-Galán et al. 2022).A recent study with a large sample of interacting SNe (Strotjohann et al. 2021) finds that bright precursors months before core-collapse occur in 5-69 % of Type IIn SNe and ∼ 10 % of Type Ibn SNe.Understanding these precursors is important as clues to probing the mass-loss mechanism that produces dense CSM in the final years of massive stars.
The observed precursors are bright with luminosities of 10 40 -10 42 erg s −1 , which are orders of magnitude higher than the Eddington limit of massive stars.While the super-Eddington energy injection may naturally explain the generation of dense CSM (e.g., Matsumoto & Metzger 2022a), the mechanism that triggers such powerful energy injection is yet unclear.For the wavedriven mass loss mechanism where specific predictions exist, the luminosity of the (possible) outbursts months to years before core-collapse are estimated to be only ≲ 10 6 L ⊙ (Shiode & Quataert 2014;Fuller 2017;Fuller & Ro 2018;Leung et al. 2021;Wu & Fuller 2022a, see also discussion in Strotjohann et al. 2021).Model-agnostic radiation hydrodynamical simulations of partial envelope ejection triggered by energy injection from the core, aimed to phenomenologically reproduce the CSM of interacting SNe, find a similar upper limit in the precursor luminosity (e.g., Quataert et al. 2016;Kuriyama & Shigeyama 2020, 2021;Tsang et al. 2022;Tsuna et al. 2023b).
In this work, we suggest that the observed bright precursors can be reproduced if the progenitor is in a binary system with a compact object (CO) companion, i.e., a stellar-mass black hole (BH) or a neutron star (NS).Most of young massive stars (> 70%) live as interacting binaries (Sana et al. 2012), and a significant fraction of them can result in such star-CO systems.Binary interaction is also considered to be the main formation channel for stripped-envelope SNe of Type Ibc (e.g., Shigeyama et al. 1990;Podsiadlowski et al. 1992;Eldridge et al. 2008;Smith et al. 2011;Chen et al. 2024), where the companions can be COs if they were the more massive of the initial binary and underwent core-collapse first.
The schematic picture of our model is shown in Figure 1.The erupted material that encounters the CO's Bondi sphere would be accreted, forming a disk around it.For binaries close enough the accretion can become super-Eddington and launch an energetic outflow, which can lead to additional energy injection into the remaining CSM (e.g., Dexter & Kasen 2013;Kimura et al. 2017;Moriya et al. 2018a).This can boost the energy budget of the precursor (e.g., Mcley & Soker 2014;Danieli & Soker 2019), drastically reducing the required energy deposition for the partial eruption to values in line with proposed theoretical models.
In Section 2 we first elaborate on the difficulty of reproducing the observed bright precursors by eruptions of single massive stars.Then in Section 3 we describe our detailed modeling of precursors from massive starcompact object (CO) binary systems, and in Section 4 demonstrate that such systems can generally explain the energetics of the observed precursor emission.In Section 5 we discuss the formation channel of these binaries, as well as ways to test the model with independent observations.We conclude in Section 6.

PRECURSORS FROM SINGLE STARS
In this section, we estimate the radiative output of a single mass eruption event from an isolated (non-binary) star, and show its difficulty to reproduce the observed precursor events.
The radiated energy in the observed precursors, of 10 47 -10 49 erg and typically of the order of 10 48 erg (see e.g., Table 4 of Strotjohann et al. 2021 and Table 1 of Matsumoto & Metzger 2022a), requires that at least a comparable energy is injected to the envelope.This disfavors an eruption from a red supergiant (RSG) progenitor, which would result in (near-complete) ejection of the hydrogen-rich envelope with its small binding energy of Here G is the gravitational constant, and M * , M env and R * are respectively the total mass, envelope mass, and radius of the star.Such a near-complete envelope ejection is unlikely for the observed precursors, because (i) the mass of the CSM constrained from the rise time of the subsequent SN is typically ≲ a few M ⊙ and (ii) Type IIn SNe with precursors are not on the luminous end of the entire IIn population (Strotjohann et al. 2021).For the former, the rise times for these SN samples are estimated to be t rise < 25 days (Strotjohann et al. 2021, Table 4), and the timescale of radiative diffusion from the swept-up CSM being shorter than this limits the mass of the CSM as (e.g., Moriya 2015) where we assume a rather large SN shock velocity of v sh = 10 4 km s −1 , c is the speed of light, and κ is the opacity assumed to be constant in time and radius.For the latter, the peak magnitude of SNe with precursors span from −19 to −17 mag (roughly correspoding to 3× 10 42 − 10 43 erg s −1 , Strotjohann et al. 2021;Matsumoto & Metzger 2022a), which agrees with the range seen in typical Type IIn SNe (Kiewe et al. 2012;Ofek et al. 2014b;Nyholm et al. 2020).This indicates that the mass of CSM for SNe with bright precursors should be Figure 1.Schematic picture of our model (not to scale).The SN progenitor in a close binary system with a CO undergoes a mass outburst that creates the dense CSM.This generally results in super-critical accretion of a fraction of the CSM onto the CO, which leads to outflows that boost the energy of the CSM and power the precursor emission.
comparable to those without, and should not be biased towards higher masses.
For Type Ibn/Icn SNe from helium (He)/Wolf-Rayet (WR) stars, light curve modelling of these SNe in general suggests a CSM mass of ∼ 0.01-1 M ⊙ (Maeda & Moriya 2022;Dessart et al. 2022;Wu & Fuller 2022b;Takei et al. 2024).For these stripped progenitors we expect a broad range of masses in their outer helium layers (∼ 0.1-2M ⊙ for solar metallicity; e.g., Yoon et al. 2010;Yoon 2017).Thus for SNe Icn (and some SNe Ibn) complete envelope ejection can still be compatible with observations, though energetically more demanding than partial ejection.
This energetics problem, on the difficulty to produce the observed precursor's energy without significantly modifying the progenitor's structure, can be avoided if the progenitor is more compact than RSGs, such as blue supergiants (luminous blue variables) or He/WR stars.However, even in these cases, a single episode of partial mass ejection struggles to reproduce the bright luminosity of the precursors because of losses to adiabatic expansion, as we show below.
Suppose that the precursor event ejects a CSM of mass M CSM with a velocity v CSM = ηv esc (here η is a param-eter) and is the surface escape velocity.Under the assumption that the energy is sourced from near or inside the base of the envelope 1 , for a partial ejection of the envelope we expect that the bulk CSM velocity is comparable to the surface escape velocity, i.e. η ∼ 1 (Linial et al. 2021).
Similar to SNe (Arnett 1980), as the CSM expands and its optical depth drops, photons in the CSM escape to power the precursor.Its timescale is governed by the 1 There are scenarios for injecting energy close to the surface, such as wave heating in the case of stripped stars (e.g., Fuller & Ro 2018;Leung et al. 2021).However, in this scenario energy injection is continuous (i.e.longer than the dynamical time near surface), and such steady-state energy injection driving a windlike CSM have difficulties to power emission highly exceeding the Eddington luminosity (Quataert et al. 2016;Matsumoto & Metzger 2022a) unless strong velocity gradients develop internal shocks in the wind acceleration region.
diffusion through the expanding CSM, which is The internal and kinetic energy E kin = M CSM v2 CSM /2 are comparable upon the eruption, but until t = t prec,0 the internal energy is converted to kinetic energy by adiabatic expansion and reduced by a factor 2 ϵ rad ≈ (R * /v CSM t prec,0 ) ≤ 1.The luminosity of the precusor is then where For a typical 10 M ⊙ star, the fact that η cannot be much greater than unity limits the luminosity of the eruption to the order of 10 39 erg s −1 , which is much dimmer than the observed precursors with luminosities of 10 40 -10 42 erg s −1 .This scaling in the luminosity is also roughly seen in more detailed light curve modelling.For instance, radiation hydrodynamical simulations of partial envelope ejections find a luminosity of 10 38 -10 39 erg s −1 for the resulting transient (Fuller 2017;Kuriyama & Shigeyama 2020;Tsuna et al. 2023b).A semi-analytical model by Matsumoto & Metzger (2022a) finds that for a RSG of M * = 10M ⊙ , R * = 10 3 R ⊙ , a precursor luminosity of L prec ≈ 10 41 erg s −1 requires an eruption with CSM velocity of ≈ 400-700 km s −1 for M CSM = 0.1-10 M ⊙ (their Figure 4), which corresponds to η ∼ 10.
We can consider two ways to break the limit on the luminosity (equation 5), which is similar to the models proposed for super-luminous SNe (e.g., Moriya et al. 2018b;Gal-Yam 2019;Nicholl 2021).The first possibility is to invoke a pre-existing CSM surrounding the progenitor at the time of the eruption.The collision of the two CSM shells can (re-)convert the kinetic energy into internal energy, effectively raising ϵ rad .This however still requires an energy budget for E kin of at least the radiated energy in the precursors, of 10 47 -10 49 erg (Strotjohann et al. 2021;Jacobson-Galán et al. 2022), which again is disfavored for RSG eruptions.Even for more compact progenitors, the mechanism that can realize this large energy deposition is unclear.Recent models of wave heating find that energy injections of ∼ 10 48 ergs are realized in a limited set of progenitors only during the end stages of nuclear burning (≲ 0.1 yr before core-collapse; Wu & Fuller 2021;Leung et al. 2021), while the precursors are typically seen several months to years before the SN.
The second possibility we explore in the following is a binary with a CO, which acts as a "central engine" to power the light curve.For binaries with sufficiently close separations, the gravitational trapping of a fraction of the CSM by the CO can lead to super-Eddington accretion.As we show below, this accretion can generate outflows that carry energy greatly exceeding the original outburst energy, enhancing the energy budget in equation 5. Thus this scenario is an energetically favorable solution compared to the scenario invoking CSM interaction.

PRECURSORS FROM BINARIES WITH COMPACT OBJECT COMPANIONS
We consider a circular binary system with separation a bin , composed of a CO of mass M • and a massive star of mass M * that undergoes a partial envelope ejection.We restrict the separation to larger than that for Rochelobe overflow to occur, i.e. a bin ≥ 3R * (Eggleton 1983) for mass ratios of M * /M • ≳ 0.3 of interest in this work, which results in non-interacting binaries until the pre-SN outburst (for discussion on interacting binaries see Section 5.3).
We estimate the properties of the energy injection from the CO, and calculate the time-dependent emission from the CSM.The formulations of this model are similar to Kimura et al. (2017), but we newly construct a one-zone light curve model including time-dependent effects of the accretion and ionization of the CSM.The model parameters we employ are summarized in Table 1.The details of each parameter will be described in the following sections.

Accretion Disk Wind from the CO Companion
We assume that the CSM is expanding homologously and has a uniform density profile for simplicity.Hereafter, we define the velocity as that in the rest frame of the star.The CSM has a velocity ranging from v min ≡ χv esc to v max ≡ ξv esc , where the minimal velocity is set by the condition that the CSM reaches the CO without falling back to the progenitor: This definition of χ is approximate as we ignore the gravity from the CO, but for a uniform density profile varying χ would lead to only slight changes in the density for a fixed CSM mass.We treat ξ ≳ 1 as a free parameter not much larger than unity, based on the arguments in Section 2. Given the velocity range, the (uniform) CSM density at time t from the eruption is given by The CSM starts to be accreted when it reaches the CO at at time The gravitational pull of the CO traps the CSM (which is moving approximately homologously at a velocity of a bin /t) within the CO's Bondi radius where we define Equation ( 13) is the orbital velocity of the CO with respect to the star.Note that when the CSM reaches the CO at a bin , the internal energy in the CSM is much smaller than the kinetic energy, and hence the contribution from the sound speed in the CSM to V can be neglected.
As the homologously expanding CSM contains velocity asymmetry of ∼ r B /t due to a velocity difference over the Bondi radius, it carries a specific angular momentum of j ∼ r B (r B /t).This results in a formation of an accretion disk around the CO with outer radius (Shapiro & Lightman 1976) Hence an accretion disk can form outside the CO if r disk > r in , where we adopt r in = 6GM • /c 2 ∼ 9 × 10 6 cm (M • /10M ⊙ ).The accretion rate for t • < t < a bin /v min is given by the Bondi-Hoyle-Lyttleton rate as (Hoyle & Lyttleton 1939;Bondi & Hoyle 1944;Bondi 1952) , where we assumed r B ≪ a bin .Here the Eddington accretion rate is defined by ṀEdd where ϵ sd ∼ 0.1 is the radiative efficiency of a standard disk.
Such accretion should lead to an advection-dominated accretion flow (ADAF, e.g., Ichimaru 1977;Narayan & Yi 1994), where we expect mass outflows of high velocities (e.g., Ohsuga et al. 2005;Jiang et al. 2014;Sadowski et al. 2014;Kitaki et al. 2021).Here we use the ADAF model by Blandford & Begelman (1999) to estimate the luminosity of the disk wind3 that will energize the CSM.In this model most of the accreted material is blown away by the wind, and only a small fraction reaches the compact object.The accretion rate is assumed to be a power-law in radius (from the CO) as Ṁ (r) ∝ r p for a range r in < r < r disk , with r disk defined in equation ( 14).We adopt p = 0.5, which is consistent with the range inferred from simulations and observations of radiatively inefficient accretion flows (0.3 < p < 0.8; Yuan & Narayan 2014).The mass gain of the CO by accretion at r in is Assuming that the wind velocity at each radius is the local escape velocity, the mass-averaged velocity of the wind is obtained from integration over radius as (e.g., Metzger 2012;Tsuna & Kawanaka 2019;Fuller & Lu 2022) The approximation r in ≪ r disk is used only in this section to demonstrate the approximate scaling.The wind kinetic energy luminosity is given as Since the wind luminosity steeply declines with time as V t −2 ∝ t −3 at early times, the total available kinetic energy of the wind to power the precursor is A luminous precursor can be powered if this energy is injected to the CSM at a timescale comparable to the diffusion timescale, analogous to the central engine models proposed for super-luminous SNe (e.g., Kasen & Bildsten 2010; Woosley 2010).

Transients from Wind-CSM Interaction
The disk wind is injected to the rest of the CSM, and we assume that the kinetic energy of the injected wind quickly thermalizes in the CSM (for the validity of this assumption see Kimura et al. 2017).We calculate the dynamics of the CSM and the resulting light curves using the following one-zone model.

Governing Equations
We assume that the opacity in the CSM is uniform and constant, which is justified for the characteristic density of the CSM (e.g., see Figure 3 in Matsumoto & Metzger 2022b) unless significant amounts of dust are formed within the CSM.We can then solve the evolution by the following set of equations (e.g., Section 2.2 of Metzger et al. 2015) where E int is the internal energy, L rad is the radiative luminosity, t diff ≈ 3κM CSM /(4πcR CSM ) is the diffusion timescale in the CSM at time t, and L inj is the rate of energy injection due to the disk wind (with ⟨v wind ⟩ in equation 16) Equation ( 19) is the first law of thermodynamics with PdV work in the first term, and equation ( 21) accounts for the increase of the kinetic energy E kin = 3M CSM v 2 CSM /10 due to PdV work4 .As the wind carries negligible mass compared to the rest of the CSM, we can approximate M CSM as a constant.

Accounting for recombination
Initially the CSM is ionized and the adoption of uniform electron scattering opacity for κ is justified.However, as the CSM expands and its photospheric temperature where σ is the Stefan-Boltzmann constant, becomes smaller than the ionization temperature T I , recombination of the CSM sets in.Afterwards, a sharp ionization front develops and recedes within the CSM, with its radius given as R I = (L rad /4πσT 4 I ) 1/2 .In order to calculate the light curve in this regime, the location of the ionization front should be tracked (Popov 1993;Dexter & Kasen 2013;Matsumoto et al. 2016Matsumoto et al. , 2024)).
The radius of the ionization front can be parameterized by the dimensionless variable x i ≡ R I /R CSM (≤ 1), which is 1 when the CSM is fully ionized.Since the outside of R I is transparent, Equation ( 19) is then modified to consider the change of internal energy in the ionized region of volume where ϵ int = E int /V i is the internal energy density.Assuming that the ionized CSM is still optically thick, both the Thomson optical depth and light-crossing time in the ionization region are ∝ x i , so the diffusion time where photons escape is modified to x 2 i t diff .The radiative luminosity is thus modified by a factor x −2 i as which is equated with the luminosity from the ionization front L rad = 4π(x i R CSM ) 2 σT 4 I to obtain Substituting this to equation ( 25), we obtain a differential equation for x i as Note that if the acceleration is negligible and the CSM expands freely with the relation R CSM = v CSM t, we recover the evolution of x i in Dexter & Kasen (2013) (their equation A12; note that their t d differs from our t diff as t diff = t 2 d /t).However the energy injection from the accreting CO can accelerate the CSM via PdV work.The PdV work in equation ( 21) now only comes from the ionized region, but under the one-zone approximation we assume that this pushes the entire CSM with an acceleration given as By solving equations ( 20) and ( 26) -( 29), we can obtain R CSM , L rad , ϵ int , x i and v CSM as a function of t after the recombination starts.

Methods of our light curve model with recombination
Generally, the energy injection raises the precursor luminosity and sustains the ionization of the CSM.One important difference between our situation and existing modeling (Dexter & Kasen 2013;Matsumoto et al. 2024) is that the energy injection is delayed, happening only after the CSM reaches the CO.For the CSM from compact progenitors in tight binaries, this is not a significant effect because the CSM reaches the CO early and energy injection is done well before recombination sets in.In this case the formulation is the same as the modeling of normal type II-P SNe (Popov 1993;Kasen & Woosley 2009).
However, for RSG progenitors the CSM generally recombines before the energy injection.The former timescale is estimated by solving equation ( 28) for L inj = 0 (e.g., Matsumoto et al. 2016): which could be shorter than the latter one t • ≈ 200ξ −1 days (see equation 10).In this case, the recombined CSM is re-ionized by the delayed energy injection and then recombines again at late times.In our one-zone prescription, the sudden energy injection at t = t • to an almost neutral (x i ≪ 1) CSM results in a prompt ionization, due to the last term ∝ L inj /x 3 i in equation ( 28).While this instantaneous ionization essentially comes from our one-zone assumption, we believe that sudden re-ionization probably does occur in nature.This is because the ionization would result from shock heating following the wind-CSM collision, and this occurs over the wind-crossing timescale of the CSM ∼ R CSM /⟨v wind ⟩ which is much faster than the dynamical timescale ∼ R CSM /v CSM .
For energy injection into a neutral CSM (x i ≪ 1), the ionization will proceed as in equation ( 28), and saturates when either x i reaches 1 (full ionization) or dx i /dt = 0.In the latter case, the corresponding degree of ionization is obtained by solving for x i in equation ( 28): Then, the location of the ionization front at saturation is estimated as x i,• = min(1, x sat ).For a reliable calculation of the light curve, we need to smoothly evolve the ionization from the x i just before energy injection to x i,• , and also accurately evolve the equations that control the energy budget (E int , E kin ) of the precursor.
For every time t, we evolve the first set of equations ( 19) -( 22) when the CSM is fully ionized (x i = 1), and when x i < 1 (R I < R CSM ) we evolve the second set of equations ( 20), ( 26) -( 29) that also follow the evolution of x i .We control the timestep of the integration by the equations shown in Appendix A. If the CSM becomes fully ionized during the energy injection, we switch back to solving the equations for x i = 1, with E int = ϵ int (4πR 3 CSM /3) at that time.For the initial conditions at t = 0, we set R CSM,0 = R * , and assume the kinetic and internal energy are equally shared with total energy 3M CSM (ξv esc ) 2 /10, i.e.E kin = E int = 3M CSM (ξv esc ) 2 /20.We set a floor value for x i of 10 −5 , as it increasingly becomes small as the CSM recombines.We verified that enhancing the floor value to 10 −4 and 10 −3 results in almost identical light curves.
There are eight parameters characterizing our binary precursor model, M • , M * , R * , κ, T I , ξ, M CSM , and a bin .For simplicity, in this work we fix ξ = 2 as in Kimura et al. (2017), and consider two values M • = {10, 1.4} M ⊙ representing a BH and NS companion respectively.We discuss the effect of changing ξ in Appendix B, where we find it to not greatly affect the light curves.For the SN progenitor, we consider a RSG and two He star progenitors, with values (M * , R * , κ, T I ) in Table 1.We consider a high-mass He star with a compact radius that is expected to be a typical progenitor of stripped-envelope SNe, and a low-mass He star with mass around 3M ⊙ that expands to a radius of around ∼ 100R ⊙ before core-collapse (e.g., Woosley 2019;Ertl et al. 2020;Laplace et al. 2020;Wu & Fuller 2022b).The values of κ and T I for the two types of progenitors are motivated from singly-ionized hydrogen and helium respectively (e.g., Kleiser & Kasen 2014).We consider a range of values for the remaining free parameters M CSM and a bin , which should greatly vary for each SN progenitor.For M CSM we adopt 0.1M ⊙ ≤ M CSM ≤ 3M ⊙ for RSGs and 0.01M ⊙ ≤ M CSM ≤ 1M ⊙ for He stars (see Section 2).For a bin we consider 3R * ≤ a bin ≤ 30R * for all models, with the upper limit inspired from our finding that beyond this limit most models predict precursors dimmer than those observed (Figure 4).

Example Light Curves
Figure 2 depicts the evolution of luminosities and the CSM velocities for different parameter sets and progenitors, in the case of a BH companion of M • = 10 M ⊙ .The left panels show the light curves (solid curves) and corresponding wind (injection) luminosity L wind (dotted curves).For RSG-BH binaries (top panel) and our fiducial parameters of M CSM = 0.1 M ⊙ and a bin = 5 R * (≈ 4 × 10 14 cm), the CSM completely recombines ≈ 50 days after the ejection.The CSM starts to accrete onto the CO at t • ≈ 100 days, which triggers a powerful disk wind and energy injection until ≈ 250 days.Since the diffusion timescale is almost comparable to the energy injection time t • , the resulting light curve traces the injected L wind .Therefore, the light curve shows two distinct components: an early injection-free part and a later part due to energy injection.It should be noted that the former corresponds to the precursor emission from a single star, and its luminosity ∼ 10 39 erg s −1 is consistent with our luminosity limit in equation ( 5).As shown in the middle panel, once the energy injection starts the CSM is accelerated until recombination sets in.
Inspecting the dependence of the light curve on the parameters a bin and M CSM , a more massive CSM (gray curve) increases the diffusion time (equation 4) and wind luminosity (equation 17).Since t • is independent of the CSM mass, the longer diffusion time makes (i) the light  1).Dotted lines show the wind (injection) luminosity L wind for each parameter, and dashed lines show the injection-free cases, i.e., a single star progenitor.The points show the light curves of eight well-observed SN precursor samples: SN 2019zrk (Fransson et al. 2022), 2006jc (Pastorello et al. 2007), 2019uo (Strotjohann et al. 2021), and others from Matsumoto & Metzger 2022a.For SN 2006jc and 2019uo, the precursors are observed ≈ 2 yr and ≈ 300 day before the SNe, respectively.For the data points, the times of SN explosions are set so that the points are roughly aligned with our light curves.The post-peak part of the SN light curve are in small empty circles, to distinguish with the precursor emission (large filled circles) we aim to reproduce.The horizontal dash-dotted lines show our luminosity limit for the single star case (equation 5).The right panels show the observed CSM velocities of these events by Strotjohann et al. (2021) (SN 2019zrk andSN 2019uo); Foley et al. (2007) (SN 2006jc); Matsumoto & Metzger (2022a) and references therein (others).Note that in the center panel the blue line is overlapped with the gray line; while larger MCSM gives larger L wind , the increased inertia results in an acceleration independent of MCSM.curve broader and deviate from L wind , and (ii) delays the recombination which results in higher CSM velocity.A larger binary separation (orange curve) simply delays the energy injection, which leads to smaller L wind and makes the light curve almost identical to the evolution of L wind .Therefore, in this regime the duration and luminosity of the precursor are given by where we used V = ξv esc and t = t • to estimtate the luminosity.
For the compact He star models, energy injection generally happens before recombination in the CSM completes.In particular for the high-mass He star models (middle panels) the injection timescale of t • ≈ 0.1−1 day is shorter than the diffusion timescale of t prec,0 ≈ 10 day.Therefore the evolution is practically the same as the CSM ejected with an initial radius of a bin and energy of E wind .Before the recombination, the luminosity is given by where we used equation ( 5) but replacing E kin , R * , and v esc with E wind , a bin , and v acc ≡ 10E wind /3M CSM (the CSM velocity after the acceleration), respectively.Note that the normalization of the escape velocity is different from the case of RSG progenitors.Interestingly the luminosity is independent of the CSM mass and binary separation, as roughly seen in our results.By using this luminosity, the onset time of the recombination is estimated by During the recombination, the light curve is described by the Popov model (Popov 1993), which gives the duration and luminosity (Matsumoto et al. 2016(Matsumoto et al. , 2024) ) t prec,2 ≈ 7 5/14 t 2/7 i t 5/7 prec,0 Here, again we replaced v CSM in t prec,0 with v acc .In particular, the duration weakly depends on the parameters.
When recombination sets in (seen as the small kinks in the light curves), the light curve temporarily rises and then steeply drops.This is due to the rapid recession of the ionization front, which quickly reduces the diffusion time and initially enhances the luminosity.We do not expect that this will always happen in reality, as the detailed evolution of the ionization front will depend on the density profile of the CSM.
A sample of six well-observed precursors of SN II (taken from Matsumoto & Metzger 2022a;Fransson et al. 2022) and two precursors of SN Ibn (Pastorello et al. 2007;Strotjohann et al. 2021) are plotted as colored dots.For the case of a BH companion, the range of luminosity observed in these precursors (∼10 40 -10 42 erg s −1 ) is well reproduced by the range in binary separation, given a CSM mass typical for these SNe.In particular, we find that qualitative properties of these precursor light curves could be dictated by two timescales, the beginning of energy injection t • and diffusion timescale t prec,0 (see below for a more quantitative discussion).While the smooth light curve of SN 2020tlf may indicate t prec,0 ≲ t • , the other precursors have longer diffusion timescales.However, we note that the detailed morphology of the light curve can depend on the CSM profile, especially when the diffusion timescale in the CSM is shorter than the wind duration.Thus we do not attempt to make a detailed fit of the light curves here, and leave this to a future numerical study that considers a realistic density/velocity profile of the ejected CSM.
Figure 3 depicts the results for the NS companion case, where the same calculations are done but for a reduced M • = 1.4 M ⊙ .While the qualitative properties are the same as the BH case, the precursor is dimmer and CSM acceleration is weaker due to the smaller Bondi accretion rate.In this case, the low-mass He star model can reproduce the observed luminosity of SN Ibn precursors.
Comparison of our model to the observed precursors for both SN IIn and Ibn shows that the eruption of the envelope should have occurred around a year to a few years prior to core-collapse.For typical massive stars of 10M ⊙ ≲ M * ≲ 30M ⊙ this corresponds to the oxygen/neon burning stages (Woosley et al. 2002), which may be more promising than the other burning stages for some scenarios of envelope ejection (e.g., Wu & Fuller 2021).

Parameter Exploration of Light Curves
We next conduct a parameter study to understand the expected range of light curve properties by the model parameters (M CSM , a bin ).We logarithmically sample the range of M CSM and a bin in Table 1 by ten points, resulting in a total of 100 parameter sets for each progenitor model.We focus on the light curve from t = t • , and define the precursor duration as the timescale over which 10% to 90% of the total radiated energy is radiated away.In other words, we solve for t 10 , t 90 from and then define the duration and luminosity of the precursor respectively as We show the dependence of these light curve properties on (M CSM , a bin ) in Figure 4.For the RSG-BH models, a wide range of luminosity (10 39 -10 42 erg s −1 ) and timescale (month to years) are found with varying M CSM and a bin .For a fixed CSM mass, increasing a bin always makes the precursors dimmer and longer.This is because the energy injection is delayed, and the more tenuous CSM gives a lower Bondi accretion rate.
On the other hand, increasing M CSM basically results in brighter and longer precursors, except for large a bin where the duration becomes nearly independent of M CSM .This behavior is understood by comparing the diffusion and energy injection timescales.As we discussed in the previous section, for smaller a bin , the energy injection happens before the radiative diffusion plays a role, and the light curve is practically the same as that described by Popov (1993) In the opposite limit, the precursor basically traces the wind luminosity and hence we have t prec ∝ a bin (equation 32) independent of M CSM , and L prec ∝ M CSM a −2 bin (equation 33).The boundary between these two limits can be obtained by comparing t prec,0 and a bin /ξv esc : Combining this relation with equations ( 36) and ( 37), the boundary on which t prec,0 = t • holds, is given by where we show the dependence on the recombination temperature explicitly.We plot this boundary in Fig- ure 4, which roughly captures the transition of two cases.
For the case of a NS companion, the resulting duration and luminosity are basically the same as the BH case, but the luminosity is reduced by an order of magnitude (note L prec,1 ∝ M • , and L prec,2 ∝ M 11/14 • ).At large a bin where the radiated luminosity traces the wind luminosity, the duration only weakly increases as a bin increases.This is because the accretion disk formation is delayed for a NS companion until the CSM velocity at the Bondi radius, V ≈ a bin /t, becomes small enough so that r disk > r in is satisfied.
The He star models generally predict shorter durations of weeks to months, with the high mass models generally resulting in dimmer and faster light curves when the parameters are fixed.This is because for a fixed a bin /R * , the high-mass models with smallest R * have the shortest accretion time scales, and lose most of the injected internal energy into adiabatic expansion before it can be radiated.
In Figure 4 we also show a more detailed comparison with the observed Type IIn and Ibn precursors in the luminosity-duration phase space.We note that the observed duration gives only a lower limit on the possible intrinsic duration, because when the SN explosion occurs, precursors are outshined by the SN radiation.While the RSG-BH models reproduce the range of precursor luminosities, the RSG-NS models can reproduce only the dimmer precursors of L prec ≲ 10 41 erg s −1 .The parameters of the precursors for the He star models are found to cluster in a narrower range of 10 40 -10 42 erg s −1 , with timescales from weeks to months.These roughly overlap with the two precursors observed for type Ibn SNe, with SN 2006jc (SN 2019uo) better reproduced by the HeHighMass-BH (HeLowMass-NS) model.

Velocity of Accelerated CSM
Figure 5 shows the final velocity of the precursor ejecta as a function of (M CSM , a bin ).For the RSG-BH models, the final velocities generally agree with CSM velocities observed in SN IIn, from 100 km s −1 to ∼ 10 3 km s −1 (Kiewe et al. 2012;Taddia et al. 2013).It is noteworthy that this is reproduced even for RSG progenitors which are generally expected to have slow CSM velocities.
However, a direct comparison to the observed CSM velocities on an event-by-event basis is not straightforward.For instance, broad emission lines of 1000 − 3000 km s −1 are observed in SN 2010mc, but broad wings are not solely due to fast CSM, and can also be created by Thomson scattering in the CSM if the CSM is optically thick (e.g., Chugai 2001;Huang & Chevalier 2018;Ishii et al. 2024).Furthermore, for the CSM velocities measured after explosion (2010mc, 2016bdu, 2019zrk, 2020tlf), they have additional contributions from radiative acceleration by the bright SN emission (Chevalier & Irwin 2011;Kochanek 2019;Tsuna et al. 2023a).
For SN 2009ip, multiple velocity features are observed during the outburst, from 800-1400 km s −1 typical for CSM in SN IIn, but also with a broad ∼ 10 4 km s −1 absorption feature (Pastorello et al. 2013;Margutti et al. 2014).Similar coexistence of slow components (600-1000 km s −1 ) and fast emission line wings (2600-6000 km s −1 ) are observed in SN 2015bh during the outburst phase (Elias-Rosa et al. 2016).While the slow component can be explained by our model, the fast part cannot.It could be explained if we are directly observing the accretion disk wind as well as the CSM (equation 16; see also Tsebrenko & Soker 2013).Multi-dimensional simulations would help understand the observability of such fast outflows.
For SN Ibn, the observed CSM velocities are typically of the order of ∼ 10 3 km s −1 .For compact He stars this can be easily achieved, as the CSM can be close to this velocity even without energy injection.On the other hand, for the low-mass extended He star models, significant energy injection is needed to accelerate the CSM to the observed values.This would require either a small orbital separation or a BH companion, but the latter may be in tension with observations for some SN Ibn, as it predicts bright precursors (Figure 4).Radiative acceleration may also bring the CSM velocity of the low-mass He star models closer to the observed values.Due to its slower velocity, the precursor CSM for these models is likely to be more confined at the time of SN, and will receive significant acceleration by the subsequent SN radiation (e.g., Figure 6 of Tsuna et al. 2023a).
While the HeHighMass-BH and HeLowMass-NS models predict similar precursor luminosities that are consistent with the observed ones, the final velocities of the CSM are quite different.As shown in Figure 5, the former would lead to CSM velocities of a few 1000 km s −1 , while the latter would have velocities less than 1000 km s −1 for the most of the parameter space.These are consistent with the measured velocities of SN 2006jc (2000-3000 km s −1 ; Foley et al. 2007) and SN 2019uo (550-1000 km s −1 ; Strotjohann et al. 2021) respectively.This implies that the precursors of SN Ibn may be a mixture of two binary populations, low-mass (a few M ⊙ ) He stars with NS companions and more massive He stars with BH companions.

Possible Formation Channels and Rates
So far we have discussed a phenomenological model of a mass ejection in close binaries, and demonstrated that they can reproduce the energetics of observed precursors.Here we outline the binary channels that produce these systems, and roughly estimate their rates.
Our channel requires a massive star in a binary with a compact object, at a separation of ∼3-30 R * at the time of core-collapse.Population synthesis predicts that the outcome of massive binary systems are nearly equally split among stellar merger, envelope stripping and noninteracting binaries (Sana et al. 2012).For the latter two channels, the binary can become unbound following the core-collapse of the first object, due to the natal kick of the CO.While the fraction is very sensitive to the magnitude of natal kicks, population synthesis calculations find a binary survival fraction of 14 +20 −10 %, with comparable amounts of NS and BH remnants (Renzo et al. 2019, Figure 4).The surviving binaries with NS companions are weighted towards close separations and massive secondaries, due to NSs typically having larger kicks and (SN) ejecta masses than BHs.From Figure D1 in Renzo et al. (2019), the separation just before the first corecollapse has a bimodal distribution, with the first peak at a few 100 R ⊙ (a few 10% of the whole) and a broader second peak at 10 3 -10 4 R ⊙ (∼ 50%).From the orbital velocity in equation ( 13), we expect that surviving binaries with NSs are largely biased towards separations in the first peak, while those with BHs populate both the first and second peaks with comparable numbers.
We therefore expect that roughly 1 -10% of corecollapse SNe can arise in the presence of a CO companion.This fraction is divided into hydrogen-rich progenitors (our RSG-CO models in most cases) and stripped-  2021) with 5 or more unbinned detections in multiple bands (green stars).The SN IIn precursors have been shining until core collapse, so their durations are lower limits.The dashed orange line is the binding energy (equation 1) for the RSG model, and the horizontal dash-dotted lines are the luminosity limit for single stars (equation 5).The solid blue line in the left panel represents the boundary on which tprec,0 = t• holds (equation 41).Below (above) the line, the light curve is described by the wind luminosity (Popov model;Popov 1993).
envelope progenitors (our He star-CO models), which is further complicated by various binary interaction processes (and their uncertainties) preceding the second core-collapse.While we cannot predict the relative fractions and their expected binary separations without in-depth population synthesis calculations, we expect that for most surviving binaries the pre-SN secondary will reside close to the CO, since it is likely to expand to a similar size to that of the primary during its post-main sequence evolution.The binaries populating the first peak in separation would interact due to the expansion and (if they avoid merger) likely become He star-NS/BH binaries with separations of a few 100 R ⊙ or less, while those in the second peak would typically become detached RSG-BH binaries with separations ≲ 10 4 R ⊙ , i.e. less than a few 10 R * .The separation is further favored to be close for stripped progenitors, which are usually stripped by the CO companion.Another population synthesis estimate finds that the number of stripped-envelope SNe with CO companions is ∼ 1% (Zapartas et al. 2017), which is roughly consistent with this assumption.
As discussed below, the precursor rate is expected to be ∼ 1% of core-collapse SNe for bright IIn precursors, and ∼ 0.1% for Ibn precursors.Hence, our scenario can plausibly reproduce the observed precursors if pre-SN outbursts or enhanced pre-SN mass loss is relatively common, with a fraction of at least ≳ 10%.For RSG progenitors the common presence of confined dense CSM in Type II SNe may support this (Morozova et al. 2018;Förster et al. 2018;Bruch et al. 2021Bruch et al. , 2023)), although there are alternative possibilities to explain the dense CSM (Dessart et al. 2017;Kochanek 2019;Soker 2021; see also Davies et al. 2022).
We note that for SN 2006jc, a point source was detected several years after the SN, whose spectral energy distribution is most consistent with a companion star of the SN progenitor (Maund et al. 2016;Sun et al. 2020).As the inferred stellar mass for the surviving companion (≲ 12 M ⊙ ) rules out a luminous blue variable, these works conclude that it is indeed the progenitor that made the precursor outburst, and not the companion.If our scenario for the precursor is correct, this may imply that the progenitor of SN 2006jc was in a hierarchical triple system, with the surviving companion star as the outer tertiary.

Implications for Other Observations
For the RSG-BH progenitors, we may find the progenitors of these systems in Gaia when they are in their main-sequence (MS) phase.Assuming a circular orbit, The HeHighMass-NS model has a negligibly small acceleration for the entire parameter space (see also Figure 3), while other models predict larger acceleration for smaller a bin and larger MCSM.
the orbital period is ≈ 3.9 yr a bin 10 14 cm 3/2 Since these progenitors will be non-interacting before the precursor, we may expect that the orbital period has not greatly changed from the first BH formation.
The required orbital separations of a ≲ a few ×10 14 cm for powering bright precursors of L prec ≳ 10 41 erg s −1 overlap with the binary periods up to which Gaia can detect their astrometric motions, of ≲ 10 years (e.g., Shikauchi et al. 2022;El-Badry et al. 2023a).Theoretical calculations also predict that such detached OB-BH binaries with long periods are more common than interacting ones seen as X-ray binaries (e.g., Langer et al. 2020;Janssens et al. 2022).
We estimate the number of such systems in the Milky Way, assuming that they explain the observed precursors of Type IIn SNe.Adopting a bright precursor fraction in SN IIn of f prec = 5-69% (Strotjohann et al. 2021) 5 , SN IIn fraction among core-collapse SNe of f IIn = 5% (Cold & Hjorth 2023), MW core-collapse SN rate of R SN,MW ≈ 1.6 per century (Rozwadowska et al. 2021), and assumed lifetime of the MS star t MS ∼ 5 Myr after the companion becomes a BH, we expect such MS-BH binaries in the Milky Way.The value of t MS is assumed to be roughly half of the typical lifetime of a BH progenitor ∼ 10 Myr (e.g., Woosley et al. 2002), but should greatly vary for each binary system.Population synthesis models predict that there are ∼ 10 4 -10 5 detached BH binaries in the Milky Way that have period within 10 years accessible by Gaia, with a good fraction of those with longer periods of years (Shikauchi et al. 2023; see also Chawla et al. 2022;Rodriguez et al. 2024).The mass of the luminous star is typically ∼ 1 M ⊙ , with massive ones of ≳ 8 M ⊙ comprising typically only ∼ (1-few)% depending on binary population synthesis models.Thus the number of RSG-BH binary systems are estimated to be of the order of 100 -1000, which roughly agrees with that estimated from the SN IIn precursor rate although both still contain large uncertainties.Ongoing observations by Gaia can lead to a better constraint on our scenario, as longperiod binary systems with BHs are starting to be discovered (El-Badry et al. 2023a,b;Tanikawa et al. 2023;Chakrabarti et al. 2023).
For precursors from He stars that are progenitors of SNe Ibn, the event rates are less certain as we have only a few detections.For the case of HeHighMass-BH models that may explain the SN Ibn precursors, we may compare the precursor event rates to the NS-BH merger rate.For these binaries with separations of our interest, these two can be linked because the merger timescale by gravitational wave (GW) emission (Peters 1964)  2021), while they obtain an upper limit of < 31% for precursors brighter than -13 mag.This translates to an event rate of ∼ 100 Gpc −3 yr −1 or an upper limit of ≲ 300 Gpc −3 yr −1 , assuming a SN Ibn fraction of 1% among all corecollapse SNe (Pastorello et al. 2008;Maeda & Moriya 2022).This event rate is similar to the NS-BH merger rate of 130 +112 −69 Gpc −3 yr −1 , inferred from the GW detections of two NS-BH mergers by the LIGO-Virgo-KAGRA collaboration (Abbott et al. 2021).
The Ibn precursor rate is uncertain, as it could be increased relative to the CO merger rate because it can operate in binaries with periods too long to merge via GWs.However, it could be suppressed relative to the CO merger rate if pre-SN outbursts are uncommon.Although we do not claim that these kinds of binaries are the sole channel for NS-BH mergers, this approximate agreement may motivate further investigations of the connection between these peculiar optical transients and formation of binary compact objects.
Finally, there is a handful of known high-mass X-ray binaries hosting BHs (Remillard & McClintock 2006), and recently a few detached binaries with a massive Otype star and a putative BH companion have been identified (HD130298, Mahy et al. 2022;VFTS 243, Shenar et al. 2022).These binaries have rather tight orbits with periods of ≲ 10 days, and they may lead to He star-BH binaries if the O-stars lose their hydrogen-rich envelopes through future binary interactions.

Possible Caveats and Future Avenues of our Model
We have restricted our model to the case of CSM created from outbursts, which has the advantage of both the CSM mass and velocity being well-defined.However, there are other mechanisms to lift material to larger radii, such as a steady-state wind (e.g., Yoon & Cantiello 2010;Moriya 2014;Quataert et al. 2016), or envelope inflation through energy injection and/or intense shell burning (e.g., Soker 2013;Smith & Arnett 2014;Fuller & Ro 2018;Ouchi & Maeda 2019;Wu & Fuller 2022a,b) resulting in rapid mass transfer.This more gradual mass expulsion from the star can result in a steady-state energy injection from the CO, and lead to precursors more long-lasting than what we have simulated here.It would be useful future work to extend our precursor model to such cases.
In this work we have not considered interacting binaries that are undergoing Roche-Lobe overflow.If the mass transfer rate is sufficiently high, both the matter undergoing mass transfer and the circum-binary matter can complicate the accretion onto the CO and the dynamics of the precursor-generated CSM.The precursor CSM will collide with this pre-existing matter, which may make the precursor even brighter.Even in cases where the pre-existing matter has much less mass than the precursor CSM and are dynamically unimportant, the precursor is still brighter due to the tighter separation.For example, the HeLowMass-NS model with M CSM = 0.1 M ⊙ and a bin = 2.2R * (approximately the Roche limit) predicts a precursor ∼ 40% brighter than that with the same M CSM and a bin = 3R * .
Two major multi-dimensional effects are not captured in our one-zone light curve modeling.First, as energy injection starts soon after the fastest end of the CSM reaches the CO, the CSM is initially heated not from the center but from the outside.This may affect the initial evolution of the CSM, while the effect may be smaller at late times.Second, we do not consider the detailed angular dependence of the energy injection due to disk wind.In our work, the angle subtended by the wind is somewhat idealized like Kimura et al. (2017), i.e. wide enough so that it can heat the entire CSM, but not too wide such that feedback would prevent the CSM from accreting onto the CO.These effects are important caveats that should be investigated in multi-dimensional hydrodynamical simulations.
Related to these multi-dimensional effects, if a powerful disk wind or a relativistic jet hypothetically launched from the CO emerges from the CSM, it may produce radio/X-ray precursors of SN explosions.This is analogous to a model where accretion of a SN ejecta by a very close CO companion can potentially power a gammaray burst jet and a high-energy transient (e.g., Rueda & Ruffini 2012;Fryer et al. 2014).Detecting such signals would be a smoking gun signature of our model.We plan to study their detectability in future work.
We have focused on the putative progenitors of Type IIn/II-P and Ibn SNe where precursors were observed, but there is a diversity in SNe and the structures of their progenitors.An example we have not considered is Type IIb SNe, whose progenitors are believed to have a lowmass hydrogen layer of ∼ 0.1 M ⊙ outside the helium core (e.g., Claeys et al. 2011;Yoon et al. 2017).For these progenitors, a partial envelope ejection of M CSM < 0.1 M ⊙ is not capable of powering a bright precursor of ≳ 10 41 erg s −1 like the ones observed (except for the tightest separations; Figure 4), whereas a complete envelope ejection would likely make the terminal SN identified as Type Ib (or IIn when CSM interaction happens) instead of Type IIb.Thus we expect bright precursors of SN IIb to be much less likely than SN IIn/II-P, which is consistent with the observations so far.

CONCLUSION
We studied the emission from pre-SN outbursts from massive stars with a CO companion, aiming to reproduce the observed bright precursors of interacting SNe.We model the super-Eddington accretion of (a fraction of) the ejected CSM onto the CO, and the resulting energy injection into the CSM by the disk wind launched from the CO.We considered SN progenitors consisting of a RSG, a high-mass compact He star, and a low-mass extended He star (with parameters in Table 1), each with a 10 M ⊙ BH or a 1.4 M ⊙ NS companion.
We constructed a one-zone light curve model including time-dependent energy injection, emission and acceleration of the CSM.We find that binary systems with separations of 3-30 times the stellar radii can generally reproduce both the luminosity and duration of the observed precursors, as well as the velocity of the CSM inferred from spectroscopy.
For the RSG model motivated for precursors of hydrogen-rich (Type II) SNe, a BH companion leads to precursors with broad ranges of luminosity 10 39 -10 42 erg s −1 and durations of months to years.We find that this can successfully explain the observed precursors, for a realistic range of CSM masses in Type II SNe corresponding to outburst energies only of the order of 10 46 -10 47 ergs.The case of NS companions can explain dimmer precursors of ≲ 10 41 erg s −1 which are observed in a fraction of Type IIn SNe (Strotjohann et al. 2021) but not the brightest ones approaching ∼ 10 42 erg s −1 .
For the He star models motivated for Type Ibn SNe, the luminosity and duration of the precursors also agree with the two observed precursors of SN 2006jc and 2019uo.From the precursor luminosity, timescale, and the CSM velocity observed in the SN phase, we conclude that the progenitor of SN 2006jc is likely a compact (Wolf Rayet-like) He star with a BH companion, whereas that of SN 2019uo is likely an inflated He star with a NS companion.This may indicate a diverse progenitor channel for Type Ibn SNe, in addition to the claim that a fraction of these SNe may not be from massive stars (Hosseinzadeh et al. 2019).
We find that the predicted event rates of our model roughly agree with the observed precursor rates, if enhanced mass-loss is relatively common months to years before core-collapse.However, we urge a more in-depth population synthesis study for rate predictions, as future observations will likely narrow down the uncertainty in the observed rate.Moreover we point out a possible link between the systems powering the precursors and CO binary systems observable by Gaia and gravitationalwave detectors, which can also be investigated by such population synthesis studies.
In the era of the Rubin Observatory (Ivezić et al. 2019), the number of SN precursors we can detect is expected to dramatically increase, and we may also be able to probe deeper into the dimmer end of the precursor population (e.g., Tsuna et al. 2023b;Strotjohann et al. 2024).We expect that our framework would be helpful to characterize the origin and diversity of such precursors 7 .and denser.Thus we expect the energy injection by the disk wind to start later, and be shorter duration with higher power.
Figure 6 shows the dependence of the precursor light curves and final CSM velocities on ξ.We focused on the case for the BH companion, and adopted the same parameter sets as in Figure 2. As expected, for a fixed (a bin , M CSM ) we see that for ξ = 1.4 the precursor light curve rises at a later time than ξ = 2, have a slightly brighter peak luminosity, and have a slightly faster final CSM velocity.However these quantities are very similar for the two cases of ξ, with differences typically within a few 10%.
We note that the precursor duration can become quite different for extended stars with large a bin , as shown for the case of a bin = 15R * for the top-left panel.This is because the precursor duration in this parameter region (typically 100s of days) is governed by the duration of the disk wind (equation 32), rather than the diffusion timescale of the CSM.However since no precursors are observed for much longer than 100 days, we expect this finding to not affect the discussion on the comparison of our model with the observed precursors in Section 4.

Figure 2 .
Figure2.Light curves and CSM velocities for a few parameter sets of (a bin , MCSM), for the case of a 10M⊙ BH companion (other parameters are in Table1).Dotted lines show the wind (injection) luminosity L wind for each parameter, and dashed lines show the injection-free cases, i.e., a single star progenitor.The points show the light curves of eight well-observed SN precursor samples: SN 2019zrk(Fransson et al. 2022), 2006jc (Pastorello et al. 2007), 2019uo(Strotjohann et al. 2021), and others from Matsumoto & Metzger 2022a.For SN 2006jc and 2019uo, the precursors are observed ≈ 2 yr and ≈ 300 day before the SNe, respectively.For the data points, the times of SN explosions are set so that the points are roughly aligned with our light curves.The post-peak part of the SN light curve are in small empty circles, to distinguish with the precursor emission (large filled circles) we aim to reproduce.The horizontal dash-dotted lines show our luminosity limit for the single star case (equation 5).The right panels show the observed CSM velocities of these events byStrotjohann et al. (2021) (SN 2019zrk and  SN 2019uo);Foley et al. (2007) (SN 2006jc);Matsumoto & Metzger (2022a) and references therein (others).Note that in the center panel the blue line is overlapped with the gray line; while larger MCSM gives larger L wind , the increased inertia results in an acceleration independent of MCSM.

Figure 3 .
Figure 3. Same as Figure 2, but for the case of a 1.4M⊙ NS companion.

Figure 4 .
Figure 4. Light curve properties of our precursor models (dots), compared with the observed well-sampled precursors in Figure 2 (red stars) and selected well-sampled events of Strotjohann et al. (2021) with 5 or more unbinned detections in multiple bands (green stars).The SN IIn precursors have been shining until core collapse, so their durations are lower limits.The dashed orange line is the binding energy (equation 1) for the RSG model, and the horizontal dash-dotted lines are the luminosity limit for single stars (equation 5).The solid blue line in the left panel represents the boundary on which tprec,0 = t• holds (equation 41).Below (above) the line, the light curve is described by the wind luminosity(Popov model;Popov 1993).

Figure 5 .
Figure5.Final velocity of the precursor CSM as a function of a bin and MCSM.The HeHighMass-NS model has a negligibly small acceleration for the entire parameter space (see also Figure3), while other models predict larger acceleration for smaller a bin and larger MCSM.

Table 1 .
Parameters adopted in our precursor model.Values shown in only one column are common to all three systems.
44)is less than a Hubble time for separations of a bin ≲ 10 R ⊙ (M BH /10M ⊙ ) 1/2 , and for compact stellar radii R * ≲ (a few) R ⊙ expected in masLaplace et al. 2020)Yoon et al. 2010; Woosley 2019;Laplace et al. 2020)6 .We infer the bright precursor fraction of Type Ibn SNe to be ∼ 10% since one precursor was detected out of 11 targets inStrotjohann et al. (