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Issue
A&A
Volume 682, February 2024
Article Number L22
Number of page(s) 4
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202349002
Published online 23 February 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

In a recent Letter, Chen et al. (2024, hereafter C24) report the appearance of a new Fermi-LAT gamma-ray source consistent in time and position with the supernova (SN) SN 2022jli. In addition to the nuclear-powered gamma-ray emission from the SN, C24 find 12.4 d periodic luminosity variations of the UVOIR emission as the source decays on a ∼250 d timescale, and narrow Hα velocity shifts with a similar 12.4 d period.

C24 point out that all of this evidence is strongly consistent with the SN explosion of a massive star in a binary system with a lower-mass companion. This companion has remained bound despite the explosion, because the anisotropic back-reaction of mass loss in the SN (the “kick”) is suitably directed, as long suggested in models of X-ray binary formation (Flannery & van den Heuvel 1975).

The Hα emission presumably arises as hydrogen stripped from the companion star accretes onto the compact object (black hole or neutron star) formed in the SN. Therefore, SN 2022jli offers a direct view of the birth event of a system that may eventually become a low-mass X-ray binary.

C24 note at least one potential problem with this picture, in that the apparent accretion luminosity of the compact SN remnant is ∼1042 erg s−1, far exceeding the Eddington luminosity of

L Edd ≃ 1.3 × 10 39 m 10 erg s − 1 $$ \begin{aligned} L_{\rm Edd} \simeq 1.3\times 10^{39}\,m_{10}\,\mathrm{erg\,s^{-1}} \end{aligned} $$(1)

for hydrogen-rich accretion, where m10 is the accretor mass M in units of 10 M⊙.

We consider this problem further in this Letter. This leads us to a comprehensive picture of the system, with suggestions for further observations that should offer a stringent test of this picture.

2. Ultraluminous X-ray sources

As C24 note, the apparent discrepancy between the inferred luminosity and the accretor’s Eddington luminosity is already seen in the study of ultraluminous X-ray sources (ULXs), and so we briefly discuss these systems here.

The study of ULXs dates back at least to Fabbiano (1989), who gave a list of 16 off-galactic-centre X-ray sources with luminosities of > 1039 erg s−1, and there are now more than 1800 known systems. There have been a number of models suggested for ULXs (see King et al. 2023 for a review), but the situation is now much clearer (Lasota & King 2023).

Very recently, polarimetric X-ray observations (Veledina et al. 2023) of the X-ray binary Cyg X-3 decisively showed that the behaviour of ULXs results from geometric beaming (more precisely, collimation) of outgoing emission towards the observer, as long suspected (King et al. 2001). In Cyg X-3, the beam robustly inferred from the polarisation measurements has an angular width of 4πb steradians, with b ≃ 1/65, but lies across the line of sight. As a result, the beamed energy is not seen directly; that is, Cyg X-3 is not a ULX but a ULX seen side-on. There are strong arguments (Begelman et al. 2006; Middleton et al. 2021) that the extreme Galactic system SS 433 is another example of this type.

ULX beaming occurs because a potentially super–Eddington mass supply rate is systematically expelled from each radius of the accretion disc by radiation pressure and is progressively reduced to the Eddington value near the accretor. As the accretion energy release at disc radius R is proportional to GMṀ(R)/R, this means that the accretion rate within the disc decreases as Ṁ(R) ∝ R. The total power of the emitted radiation is then ≃ LEdd(1 + ln(Ṁ/ṀEdd)), where Ṁ > ṀEdd is the mass supply rate to the disc from outside (Shakura & Sunyaev 1973), and ṀEdd = LEdd/ηc2, where η ≃ 0.1 is the accretion efficiency (see King 2023b; King et al. 2023 for discussions).

The radiation-pressure-driven outflow from the disc is largely optically thick, except that centrifugal repulsion leaves twin narrow vacuum channels along the accretion disc axis. A luminosity ≃LEdd emitted by the disc eventually finds these channels and escapes to infinity in a narrow double beam (King 2009), while a luminosity of a similar order is emitted from the outer photosphere of the wind (cf., King & Muldrew 2016) but spread over ∼4π steradians.

In sources directly identified as ULXs – that is, with apparently highly super-Eddington luminosities –, terrestrial observers lie within the beam. The assumption of isotropic emission then strongly overestimates the total radiation output, as the specific intensity is far higher within the two beams than in the ∼4π steradians outside them. This means that most X-ray binaries with super-Eddington mass-transfer rates do not directly appear as ULXs, as the observer has to be favourably located.

The beaming factor b giving the ratio of the true luminosity ≃LEdd to the apparent (assumed isotropic) luminosity Lsph of a ULX (so that Lsph ≃ (1/b)LEdd) is given by

b ≃ 73 m ˙ 2 , $$ \begin{aligned} b \simeq \frac{73}{\dot{m}^2}, \end{aligned} $$(2)

(King 2009). Here, ṁ ≫ 1 is the ratio of the mass-supply rate at the outer edge of the accretion disc to the value ṀEdd ≃ 10−20 LEdd that would produce the Eddington luminosity. As this process generally involves only electron scattering, the form of Eq. (2) is in practice universal for all the radiation produced deep in the potential well near the disc centre.

The b ∝ ṁ−2 dependence of Eq. (2) arises because conditions close to the accreting compact object always asymptote to the same Eddington flow near the photosphere, regardless of how potentially super-Eddington the mass supply at the outer disc edge is. This same reasoning (King 2009) also predicts a relation

L ∝ T − 4 $$ \begin{aligned} L \propto T^{-4} \end{aligned} $$(3)

for the luminosity Lsph and effective temperature T of beamed blackbody emission. This is observed for “ultrasoft” ULXs, in the form

L 41 ≃ T 6 − 4 $$ \begin{aligned} L_{41} \simeq T_6^{-4} \end{aligned} $$(4)

(Kajava & Poutanen 2009), where L41, T6 are Lsph, T in units of 1041 erg s−1 and 106 K, respectively. The normalisation of this relation fixes the proportionality factor 73 in Eq. (2). We show in Sect. 3 that the ultrasoft component dominates the observed radiation output of SN 2022jli.

3. SN 2022jli and ULXs

We can now see how SN 2022jli can appear with an apparently super-Eddington luminosity of Lsph ≃ 1042 erg s−1. Comparing with Eq. (1) and using Eq. (2) gives

m ˙ = 270 m 10 1 / 2 , $$ \begin{aligned} \dot{m} = \frac{270}{m_{10}^{1/2}}, \end{aligned} $$(5)

which ensures that b ≃ 10−3.

Equation (5) tells us that the companion star currently transfers mass towards the compact accretor at a rate

M ˙ trans ≃ 2.5 × 10 − 5 m 10 1 / 2 M ⊙ yr − 1 . $$ \begin{aligned} \dot{M}_{\rm trans} \simeq 2.5\times 10^{-5}\,m_{10}^{1/2}\,M_{\odot }\,\mathrm{yr}^{-1}. \end{aligned} $$(6)

This very high rate arises because of the violent rearrangement of the binary geometry caused by the SN, which has evidently forced the companion star to overflow its Roche lobe significantly. All but a small part (≃ ṀEdd ∼ 10−7 m10 M⊙ yr−1) of this transfer rate is ultimately ejected to infinity. The SN is also probably responsible for the system’s relatively long current orbital period, as it almost succeeded in unbinding the binary.

An important feature of SN 2022jli is that almost all of its luminosity is emitted in the UVOIR region of the electromagnetic spectrum, rather than in X-rays as one might initially expect. This occurs in ultrasoft ULXs where the mass-transfer rate is particularly high (Kajava & Poutanen 2009), making the optical depth through the outflow very large: all the photons that emerge have undergone many slightly inelastic scatterings. Because of its very soft spectrum, we classify SN 2022jli as an ultrasoft ULX. We see from Eq. (4) that this very soft spectrum is as expected for the inferred value of the apparent luminosity of Lsph ≃ 1042 erg s−1, which gives T ∼ 5 × 105 K1. We can use this value to check that the opacity of the gas outflow is indeed dominated by electron scattering2.

The sudden loss of mass from the star that exploded as a SN, leaving only a compact remnant accretor, must make the binary extremely eccentric; indeed it is only the asymmetric kick which holds the binary together, keeping the eccentricity e below unity. The high eccentricity is also the reason why the binary transfers mass at all, as otherwise the effective Roche lobe (see Eq. (11) below) is too large for the companion star to fill it. We demonstrate below that for a solar-type star to fill the lobe, we need 1 − e ≲ 0.045 or e ≳ 0.95.

For such extreme eccentricities (actually e ≳ 0.97, King 2023a; Miniutti et al. 2023), the viscous timescale in the accretion disc is shorter than the binary period of P = 12.4 days. The observed light curve therefore reflects the periodic bursts of mass transfer as the companion star passes through the binary pericentre: each burst is largely accreted by the black hole or neutron star before the next occurs 12.4 days later.

The stability of the light curve also suggests that the accretor (black hole or neutron star) is relatively fixed near the centre of mass of the system, with its radiation beam oriented stably towards us. This must mean that the companion star has a significantly lower mass than the accretor. SN 2022jli therefore represents the birth event of a low-mass X-ray binary (LMXB).

The asymmetric nature of the SN kick also makes it very likely that the spin axis of the accreting black hole or neutron star is misaligned with respect to the binary orbit. Viscous torques caused by the resulting precession (e.g. Lense–Thirring) then cause the central accretion disc to be warped into the spin plane. Since SN 2022jli appears as a ULX, this plane is orthogonal to the line of sight along the vacuum funnels through the outflow. The binary orbital plane is misaligned with respect to this axis, and so we observe periodic Doppler shifts resulting from its orbital motion.

4. The evolution of SN 2022jli

The new eccentric binary LMXB that SN 2022jli created must evolve very rapidly because of its high mass-transfer rate Eq. (6) caused by the violent effect of the SN explosion. This is far larger than effects such as orbital angular momentum loss, and implies a typical current evolution timescale of

t evol ∼ M 2 − M ˙ 2 ∼ 10 5 yr , $$ \begin{aligned} t_{\rm evol} \sim \frac{M_2}{-\dot{M}_2} \sim 10^5\,\mathrm{yr}, \end{aligned} $$(7)

where M2 ∼ 1 M⊙ is the companion mass. The binary angular momentum J is

J = M 1 M 2 ( Ga M ) 1 / 2 ( 1 − e 2 ) 1 / 2 , $$ \begin{aligned} J = M_1M_2\left(\frac{Ga}{M}\right)^{1/2}(1 - e^2)^{1/2}, \end{aligned} $$(8)

where M1 is the compact object mass, M = M1 + M2 is the total binary mass, and a is the binary separation. During the evolution, we have Ṁ2 < 0, Ṁ1 ≃ 0, and Ṁ = Ṁ2. In the current phase, we can neglect systemic angular momentum loss and eccentricity evolution, and so logarithmic differentiation of Eq. (8) gives

a ˙ a ≃ − 2 M ˙ 2 M 2 > 0 . $$ \begin{aligned} \frac{\dot{a}}{a} \simeq - \frac{2\dot{M}_2}{M_2} > 0. \end{aligned} $$(9)

The binary expands because mass is being transferred closer to the centre of mass while conserving total angular momentum. This expansion must significantly reduce the mass-transfer rate and therefore also the accretion luminosity once the increase in separation Δa becomes of order the atmospheric scale height of the companion star3. This is

H = k T 2 R 2 2 G M 2 μ m H ∼ 5 × 10 7 cm , $$ \begin{aligned} H = \frac{kT_2R_2^2}{GM_2\mu m_{\rm H}} \sim 5\times 10^7\,\mathrm{cm}, \end{aligned} $$(10)

where we have taken solar values for the surface temperature T2 and radius R2 (μ and mH are respectively the mean molecular and hydrogen mass). For a star filling the modified Roche lobe for a binary of eccentricity e, we have

R 2 a ≃ 0.46 ( M 2 M 1 ) 1 / 3 ( 1 − e ) , $$ \begin{aligned} \frac{R_2}{a} \simeq 0.46\left(\frac{M_2}{M_1}\right)^{1/3}(1 - e), \end{aligned} $$(11)

and again assuming M2 ∼ 1 M⊙, M1 ∼ 10 M2, and R2 ∼ R⊙, we find a ≃ 3 × 1012 cm. Comparing with Eq. (10) gives H ≲ 10−5a. From Eq. (9) in the form of Δa/a ∼ −2ΔM2/M2, this shows that the initial mass-transfer rate of the binary must decrease on a timescale of ≲1 yr as Δa ∼ H. This is evidently the origin of the observed luminosity decay over ∼250 days.

This is a very rare case where the very high mass-transfer rate (caused here by the SN explosion) makes the Roche lobe move through a stellar scale height on a timescale so short that it is observable. This means that the observed mass-transfer rate is close to the (changing) evolutionary mean. In general, this condition does not hold, and observed changes in mass-transfer rates are completely unrelated to the evolutionary mean (see King & Lasota 2021 and references therein).

5. Evolution to a low-mass X-ray binary

This rapid decay of the impulsive mass transfer resulting from the destabilising effect of the SN explosion will soon cause the system to detach. This opens various possible routes to the system’s probable endpoint as a LMXB.

Systemic angular momentum loss (AML) will tend to reverse the current decaying orbital expansion. However, at the current (and lengthening) 12.4 d binary period, the gravitational radiation timescale exceeds a Hubble time, even given the likely high orbital eccentricity, and so this form of AML is unlikely to restart mass transfer. The other possible AML process is magnetic stellar wind braking of the companion star spin, which is transmitted to the orbit via tides. Current treatments only consider the case of circular binaries, and so again estimates are problematic.

Regardless of these AML effects, a likely upper limit to the timescale for reaching the LMXB state is the main sequence lifetime of the companion star. If AML has not yet shrunk the binary and restarted mass transfer by the time that the companion leaves the main sequence, the nuclear evolution of the companion will drive mass transfer instead, and the system will become a relatively long-period (days–years) LMXB.

6. A possible observational test

The ideas of this Letter are in principle open to an observational test. From Kepler’s law, the expansion of the system driven by the current very rapid mass transfer implies a rate of period increase of

P ˙ P = 3 a ˙ 2 a − M ˙ 2 M ∼ 10 − 5 yr − 1 , $$ \begin{aligned} \frac{\dot{P}}{P} = \frac{3\dot{a}}{2a} - \frac{\dot{M}}{2M} \sim 10^{-5}\, \mathrm{yr}^{-1}, \end{aligned} $$(12)

which implies

P ˙ ∼ 3 × 10 − 7 s s − 1 . $$ \begin{aligned} \dot{P} \sim 3 \times 10^{-7} \mathrm{s\, s}^{-1}. \end{aligned} $$(13)

This gives a direct test of the deduced mass-transfer value Eq. (6), but may be difficult to measure as the system fades on the current short timescale.

7. Conclusion

Most of the distinctive features of SN 2022jli come from the violent disturbance to the binary geometry caused by the sudden mass loss in the SN explosion. The ultraluminous nature of the current accretion onto the newborn compact component allows us to quantify the resulting mass-transfer rate and its effects on the binary. Unusually, these include changes in the binary separation comparable to the density scale height of the donor star on observable timescales, with consequent effects on the mass-transfer rate, as detailed in Sect. 6.

1

We note that although Eq. (4) formally predicts that the blackbody emission would eventually appear in medium-energy X-rays – i.e. with T6 = 10 – during the final fast luminosity decay, but the luminosity would then only be ∼1037 erg s−1, making this effectively unobservable.

2

We stress that Eq. (4) applies only to sources being supplied with mass at a strongly super-Eddington rate. The peak X-ray luminosity of the famous hyperluminous source HLX-1 in the galaxy ESO 243–49 is > 1042 erg s−1 (Farrell et al. 2009), but the mass of its black hole is presumably > 104 M⊙, and so it is fed mass at a near-Eddington rate (Godet et al. 2012). This system may be a long-period quasi-periodic eruption (QPE) source (King 2022; Webb et al. 2023), where a star (in practice a white dwarf) that has narrowly avoided complete tidal disruption by the black hole periodically fills its tidal lobe at the pericentre of an extremely eccentric orbit about the black hole (Godet et al. 2014; King 2022).

3

We note that a main sequence star does not expand on adiabatic mass loss unless its mass is low, i.e. ≲0.3 M⊙.

Acknowledgments

We thank the anonymous referee and the Editor of the paper for perceptive and helpful comments.

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