Pulsational Pair-Instability Supernovae

• Pulsational Pair-Instability Supernovae (PPISNe) are episodic eruptive events in very massive stars where pair creation triggers thermonuclear pulses that eject shells without complete disruption.
• Models indicate that PPISNe occur in progenitors with helium-core masses around 35–65 M☉, with pulse energetics and delay times influencing observable transients and circumstellar structures.
• PPISNe play a critical role in limiting the mass of resulting black holes, thereby affecting the distribution in the pair-instability mass gap and influencing gravitational-wave source characteristics.

Searching arXiv for recent and foundational papers on pulsational pair-instability supernovae. Pulsational pair-instability supernovae (PPISNe) are non-terminal eruptive episodes in very massive stars or helium stars whose cores enter the pair-instability regime, undergo one or more thermonuclear pulses, eject shells of matter, and yet remain bound long enough to continue evolving toward a final collapse or, at higher mass, transition to complete pair-instability disruption. Across current modeling, PPISNe occupy the regime between ordinary core collapse and full pair-instability supernovae (PISNe): pair creation softens the equation of state, contraction ignites explosive oxygen burning, and the released energy is sufficient to drive repeated mass ejection but not, initially, to unbind the entire star (Leung et al., 2019). Their significance extends from transient phenomenology—especially shell-collision-powered, hydrogen-poor or hydrogen-rich luminous events—to compact-remnant formation, because PPISN mass loss shapes the upper stellar black-hole spectrum and the lower edge of the pair-instability mass gap (Hendriks et al., 2023).

1. Physical mechanism and regime boundaries

The defining microphysics of PPISNe is electron-positron pair creation in a radiation-pressure-dominated core, commonly represented as

$\gamma + \gamma \rightarrow e^- + e^+ .$

This process removes pressure-supporting photons and softens the equation of state; in the standard description, the instability develops when the effective adiabatic response approaches or falls below the dynamical-stability threshold, often summarized as

$\Gamma < \frac{4}{3}$

or, in global form for stellar-evolution calculations, through a pressure-weighted average $\langle \Gamma_1 \rangle$ approaching $4/3$ (Leung et al., 2019). Contraction then raises the temperature into the explosive oxygen-burning regime, and the resulting thermonuclear flash can reverse collapse and eject mass without necessarily disrupting the star (0710.3314).

The regime boundaries depend on how the progenitor is parameterized. In helium-core language, repeated thermonuclear outbursts have long been associated with helium cores in the range

$$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$

in multidimensional shell-collision studies (Chen et al., 2014), while a broader stellar-evolution survey found PPISN behavior in helium cores $\sim 40$–$62\,M_\odot$, with a $64\,M_\odot$ helium core undergoing complete disruption as a PISN (Leung et al., 2019). In a bare-helium-star grid organized by carbon-oxygen core mass, the transition from no observable surface response to radial expansion and then to true mass ejection is described as: explosions too weak to affect the surface for $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$, large radial expansion for $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$, and mass ejection episodes for $\Gamma < \frac{4}{3}$0 (Renzo et al., 2020). The lowest full disruption in that framework occurs at $\Gamma < \frac{4}{3}$1, with the PISN-to-photodisintegration-collapse transition reappearing above $\Gamma < \frac{4}{3}$2 (Renzo et al., 2020).

A recurring point in the literature is that PPISN and PISN are not distinguished by a different instability mechanism, but by the energetic outcome. In a PISN, explosive burning unbinds the whole star and no remnant remains; in a PPISN, one or more pulses eject matter, the star survives, and later evolution can still culminate in iron-core collapse and black-hole formation (Leung et al., 2019). This distinction is central to both transient classification and remnant-mass predictions.

2. Progenitors, metallicity, rotation, and binary channels

PPISN progenitors can be framed either as very massive main-sequence stars or as stripped helium stars. A systematic evolutionary study found that stars with initial masses $\Gamma < \frac{4}{3}$3–$\Gamma < \frac{4}{3}$4 can enter the pair-instability regime only if metallicity is low enough that winds leave helium cores above $\Gamma < \frac{4}{3}$5; specifically, $\Gamma < \frac{4}{3}$6 is necessary to form He cores massive enough to undergo pulsational pair instability, and metallicities of order $\Gamma < \frac{4}{3}$7 are needed to span the full $\Gamma < \frac{4}{3}$8–$\Gamma < \frac{4}{3}$9 helium-core range (Leung et al., 2019). This metallicity sensitivity arises because wind stripping determines whether the star ever retains a sufficiently massive He or CO core.

Rotation alters this mapping substantially. In rapidly rotating, very low metallicity progenitors, nearly homogeneous evolution can lower the PPISN threshold to $\langle \Gamma_1 \rangle$0–$\langle \Gamma_1 \rangle$1 on the zero-age main sequence, because rotationally induced mixing builds larger C/O cores for a given initial mass (Chatzopoulos et al., 2012). The resulting first PPISN shells in such models are hydrogen-poor and helium- and oxygen-rich, with shell masses $\langle \Gamma_1 \rangle$2–$\langle \Gamma_1 \rangle$3, kinetic energies $\langle \Gamma_1 \rangle$4–$\langle \Gamma_1 \rangle$5 erg, and characteristic velocities $\langle \Gamma_1 \rangle$6–$\langle \Gamma_1 \rangle$7 (Chatzopoulos et al., 2012). A more recent rotating grid similarly finds that rotation lowers the mass threshold for entering the PPISN regime, but also tends to reduce ejected mass and shell kinetic energy while producing hydrogen-poor, carbon- and oxygen-enriched shells and shorter interpulse delays in some cases (Huynh et al., 28 Jul 2025).

Binary evolution adds further channels. Very close binaries matter because PPISN progenitors with pre-pulse masses $\langle \Gamma_1 \rangle$8 can expand to more than $\langle \Gamma_1 \rangle$9 for $4/3$0–$4/3$1 yr after a pulse, enabling Roche-lobe overflow or common-envelope interaction with a close companion (Marchant et al., 2018). In a different binary pathway, post-main-sequence mergers of two stars that have both formed hydrogen-exhausted cores can produce PPISN or PISN progenitors with significantly more hydrogen than single stars of the same oxygen-rich core mass, potentially yielding hydrogen-rich PPISNe at rates approaching a few in a thousand of all core-collapse supernovae (Vigna-Gómez et al., 2019).

These results imply that PPISN progenitors are not a single stellar class. They include low-metallicity single stars, stripped helium stars, rapidly rotating chemically mixed stars, merger products, and stars in interacting binaries. This diversity is one reason PPISN observables span hydrogen-rich and hydrogen-poor events, different pulse timings, and a broad range of circumstellar structures.

3. Pulses, shell ejection, and circumstellar structure

The pulsational sequence is intrinsically episodic. After a pulse ejects mass, the bound remnant expands, cools, and later recontracts. The delay to the next pulse depends strongly on how far the star was driven from equilibrium and on whether neutrino or photon cooling controls the recovery. In helium-core models, shell launch times relative to final collapse span $4/3$2 yr to $4/3$3 yr (Leung et al., 2019), while in bare helium stars the delays between mass ejection events and the final collapse range from sub-hour to $4/3$4 years (Renzo et al., 2020). This wide timescale range is a defining PPISN feature because it sets both the shell radii and whether shell-shell collisions occur before the terminal collapse.

The amount of pulse-driven mass loss increases with core mass. In the $4/3$5–$4/3$6 helium-core sequence, total ejecta masses are summarized as $4/3$7–$4/3$8 (Leung et al., 2019). In hydrogen-free helium-star grids, the pulse-ejected circumstellar mass spans $4/3$9 (Renzo et al., 2020). These shells are typically launched at a few thousand $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$0 and, under constant-velocity propagation, reach $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$1–$$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$2 cm before core collapse (Renzo et al., 2020). Because first pulses are often faster than later ones but third pulses can overtake second pulses, shell-shell collisions are expected in some multi-pulse cases (Renzo et al., 2020).

A recurrent modeling issue is that a “pulse” is not uniquely defined. One hydrogen-free survey emphasizes that there is not a one-to-one correspondence between pair-instability-driven ignition and mass ejections: some thermonuclear spikes do not affect the surface, some produce radial expansion without unbinding matter, and only a subset generate observable shell ejection (Renzo et al., 2020). This matters when comparing pulse counts across codes and when linking interior dynamics to observed transients.

The composition of the ejected shells depends on prior stripping and mixing. In stripped helium-core calculations, the pulse-driven circumstellar matter is H-free by construction and evolves from He-rich toward C/O-rich and even Si-bearing ejecta as core mass increases (Leung et al., 2019). Rapidly rotating progenitors also produce hydrogen-poor shells enriched in He/C/O, often strongly oxygen-rich (Chatzopoulos et al., 2012). This composition determines opacity, radiative efficiency, and line formation in later interaction-powered transients.

4. Multidimensional shell collisions and radiative transients

PPISN luminosity is often not powered by the pulse that launches the shell, but by later collisions between shells at large radius. The foundational shell-collision scenario attributes the brightest events to a faster, later ejection overtaking a slower, earlier shell and converting kinetic energy into radiation with high efficiency because the interaction occurs at $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$3–$$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$4 cm rather than near the stellar core (0710.3314). In the widely used $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$5 progenitor, the first pulse ejects $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$6 at $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$7–$$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$8, a second pulse $$35\,M_\odot \lesssim M_{\rm He\,core} \lesssim 65\,M_\odot$$9 years later ejects $\sim 40$0 with $\sim 40$1 erg, and the ensuing collision can radiate $\sim 40$2 erg of light (0710.3314).

Multidimensional hydrodynamics modifies this picture. The first two-dimensional calculations showed that the thin, high-density spikes seen in one-dimensional shell collisions are unstable to Rayleigh–Taylor growth, which truncates the density spike, drives mixing, and smooths the light curve while leaving peak luminosity and duration broadly similar (Chen et al., 2014). In that study, a $\sim 40$3 solar-metallicity star with a $\sim 40$4 helium core undergoes three major outbursts; the dominant second collision yields an estimated peak luminosity

$\sim 40$5

for a bright phase of $\sim 40$6 days, using the analytic shock-power estimate

$\sim 40$7

with $\sim 40$8, $\sim 40$9, and $62\,M_\odot$0 at peak (Chen et al., 2014).

Full multidimensional radiation hydrodynamics reinforces the need for more than 1D shock treatment. The first 2D and 3D radiation-hydrodynamic PPISN simulations found that radiative cooling causes collided shells to evolve into thin, dense structures with hot spots that can enhance the peak luminosity by factors of 2–3, while the light curve peaks at $62\,M_\odot$1–$62\,M_\odot$2 erg s$62\,M_\odot$3 for 50 days and then plateaus at $62\,M_\odot$4–$62\,M_\odot$5 erg s$62\,M_\odot$6 for 200 days, depending on viewing angle (Chen et al., 2019). These calculations also argue that the presence of C and O and absence of Si and Fe in the spectra can uniquely identify the transient as a PPISN shell-collision event (Chen et al., 2019).

The transient zoo potentially connected to shell collisions is broad. Hydrogen-poor PPISN shells from rotating progenitors have been proposed as a route to H-poor circumstellar interaction and some SLSN-I-like events (Chatzopoulos et al., 2012, Huynh et al., 28 Jul 2025), while the original shell-collision model was advanced as an explanation for SN 2006gy (0710.3314). This suggests that PPISNe are better understood as an interaction framework than as a single light-curve template.

5. Observational manifestations and candidate events

Electromagnetic candidates span both hydrogen-rich and hydrogen-poor classes. SN 2006gy was modeled as a PPISN in which shell collisions radiate $62\,M_\odot$7 erg and produce a light curve in good agreement with the observed event, including narrow hydrogen features from slowly moving H-rich material (0710.3314). SN 1961V has been explored with several PPISN subclasses, all with helium-rich ejecta, bulk hydrogenic velocities near $62\,M_\odot$8, total kinetic energies from $62\,M_\odot$9 to $64\,M_\odot$0 erg, and eventual black-hole remnants; in the low-carbon case the preferred progenitor range is $64\,M_\odot$1–$64\,M_\odot$2 on the main sequence with helium-core masses $64\,M_\odot$3–$64\,M_\odot$4 and final black-hole masses $64\,M_\odot$5–$64\,M_\odot$6 (Woosley et al., 2022).

Among hydrogen-poor events, SN 2016iet is notable because its light curve and spectra require a very massive CO core and a dense hydrogen-poor circumstellar medium, with inferred CSM mass $64\,M_\odot$7 ejected in the final decade before explosion and a progenitor core mass $64\,M_\odot$8, placing it in the PPISN/PISN regime (Gomez et al., 2019). The spectra are dominated by Ca and O with no clear H or He from the SN itself, and the event occurred in a low-metallicity dwarf environment consistent with pair-instability formation channels (Gomez et al., 2019). The authors explicitly note that the observed shell masses and timescales challenge existing PPISN/PISN models, making SN 2016iet a strong but not cleanly explained candidate (Gomez et al., 2019).

At high redshift, shell collisions in a $64\,M_\odot$9 Pop III-like PPISN were predicted to produce superluminous UV transients visible in the near-infrared out to $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$0–20 for wide surveys and to $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$1 for JWST, with a peak bolometric luminosity $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$2 and a luminous duration of $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$3 yr in the rest frame (Whalen et al., 2013). This work treats PPISNe as potential beacons of the first stars rather than only local transient oddities.

There are also multimessenger signatures. Thermal neutrino bursts during pulsations were predicted for helium-core models $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$4–$28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$5, with peak pulse neutrino luminosities around $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$6–$28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$7, mean neutrino energies near $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$8 MeV during pulsation, and potentially detectable event counts in large detectors for sources within $28\,M_\odot < M_{\rm CO} < 30.5\,M_\odot$9 kpc (Leung et al., 2020). Distinctive gravitational-wave signals arise in the final core collapse of PPISN-transition stars, with strong emission in both high-frequency g-mode and low-frequency SASI bands and maximum detection distances up to $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$0 kpc with LIGO and $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$1 kpc with Cosmic Explorer in selected models (Powell et al., 2021).

A recurring observational caveat is that dense circumstellar matter is not unique to PPISN pulses. Envelope pulsations in red-supergiant PISN progenitors can also create dense CSM with mass-loss rates of $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$2–$30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$3, so dense CSM alone does not prove a PPISN origin (Moriya et al., 2014). This is a central interpretive caution in the literature.

6. Final collapse, black holes, and the pair-instability mass gap

PPISNe are central to compact-remnant astrophysics because pulse-driven mass loss limits the final black-hole mass below the pair-instability gap. In helium-core models $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$4–$30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$5, PPISN mass ejection implies an upper black-hole mass of roughly $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$6, more precisely $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$7–$30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$8 in that model set (Leung et al., 2019). A hydrogen-free survey organized by CO core mass finds $30.5\,M_\odot < M_{\rm CO} < 31.4\,M_\odot$9 below the gap, with black holes reappearing only above $\Gamma < \frac{4}{3}$00 once photodisintegration-driven collapse becomes possible for $\Gamma < \frac{4}{3}$01 (Renzo et al., 2020).

The final collapse of PPISN remnants is itself nontrivial. Three-dimensional core-collapse simulations near the lower PPISN boundary show two qualitatively different cases: an $\Gamma < \frac{4}{3}$02 Pop III progenitor experiences a pair-instability pulse coincident with iron-core collapse, revives its shock, and then collapses to a black hole within $\Gamma < \frac{4}{3}$03–$\Gamma < \frac{4}{3}$04 s after bounce depending on the equation of state; a $\Gamma < \frac{4}{3}$05 progenitor had already undergone four pulses $\Gamma < \frac{4}{3}$06 years earlier, lost its H and He envelope, and then proceeds toward a more ordinary stripped-core collapse (Powell et al., 2021). In the $\Gamma < \frac{4}{3}$07 case, the diagnostic energy of the incipient explosion reaches up to $\Gamma < \frac{4}{3}$08 in the SFHx model, but the binding energy of the overlying metal core makes fallback-induced black-hole formation unavoidable, with optimistic lower-limit BH masses $\Gamma < \frac{4}{3}$09–$\Gamma < \frac{4}{3}$10 (Powell et al., 2021).

Two-dimensional general-relativistic collapse calculations of PPISN progenitors with ZAMS masses $\Gamma < \frac{4}{3}$11, $\Gamma < \frac{4}{3}$12, and $\Gamma < \frac{4}{3}$13 likewise find that black-hole formation occurs within $\Gamma < \frac{4}{3}$14–$\Gamma < \frac{4}{3}$15 ms after bounce in all cases, with neutrino heating reviving the shock in all but the rapidly rotating $\Gamma < \frac{4}{3}$16 model (Rahman et al., 2021). In the shock-reviving models, the explosion energy reaches maxima around $\Gamma < \frac{4}{3}$17 erg, but after black-hole formation the neutrino luminosities drop steeply, the neutrino-heated matter is swallowed, and the explosion energies decrease to zero within a few seconds (Rahman et al., 2021). Only a weak outgoing shock or sonic pulse remains, potentially ejecting at most $\Gamma < \frac{4}{3}$18–$\Gamma < \frac{4}{3}$19 from the outer layers, leaving final BH masses close to $\Gamma < \frac{4}{3}$20–$\Gamma < \frac{4}{3}$21 (Rahman et al., 2021).

These collapse studies reinforce a broader point already evident in evolutionary calculations: PPISN mass loss and final fallback both contribute to the clustering of stellar-origin black holes below the upper mass gap. They also indicate that some PPISN remnants may experience transient shock revival without producing a successful supernova in the ordinary sense.

7. Current debates and open problems

One active debate concerns whether the $\Gamma < \frac{4}{3}$22 feature inferred in gravitational-wave primary-mass distributions is a PPISN signature. A recent cosmological binary-population study concludes that it is unlikely: in a fiducial physically motivated PPISN model, the pile-up appears at $\Gamma < \frac{4}{3}$23–$\Gamma < \frac{4}{3}$24, not $\Gamma < \frac{4}{3}$25, and reproducing the observed feature would require shifting the PPISN CO-core range downward by $\Gamma < \frac{4}{3}$26, in tension with state-of-the-art stellar models and likely with the observed rate of hydrogen-less super-luminous supernovae (Hendriks et al., 2023). Conversely, shifting the PPISN range upward in line with more recent stellar models predicts a third black-hole mass peak near $\Gamma < \frac{4}{3}$27 (Hendriks et al., 2023). This suggests that the location of the PPISN-induced mass pile-up is not observationally settled.

A second uncertainty is microphysical. Relativistic Coulomb screening in pair-rich plasmas slightly modifies pulse morphology, collapse timing, and ejecta composition, but changes the maximum PPISN black-hole mass by only about $\Gamma < \frac{4}{3}$28 at the high-mass end and does not significantly alter the pair-instability mass gap within current model uncertainties (Famiano et al., 2021). This suggests that PPISN outcomes are somewhat sensitive to thermonuclear microphysics, though not enough, in current calculations, to erase the remnant-mass signatures.

A third issue is dimensionality. One-dimensional stellar-evolution and radiation-transport models remain indispensable for parameter surveys, but multidimensional fluid instabilities, radiative cooling, mixing, and geometry all alter shell-collision structure and emergent light curves (Chen et al., 2014, Chen et al., 2019). This suggests that some sharp temporal structure in older 1D PPISN light curves may be numerical rather than physical. A plausible implication is that transient classifications tied too tightly to 1D shell morphology may be unstable as multidimensional modeling improves.

Finally, progenitor uncertainty remains large. Mass loss, metallicity, rotation, binary stripping, mergers, envelope retention, and pulse timing all shift the mapping from initial mass to $\Gamma < \frac{4}{3}$29, $\Gamma < \frac{4}{3}$30, ejecta composition, and remnant mass (Leung et al., 2019, Chatzopoulos et al., 2012, Vigna-Gómez et al., 2019). For that reason, PPISNe are best regarded not as a single explosion model, but as a regime of pair-instability-driven stellar evolution that generates a family of eruptions, circumstellar structures, and collapse outcomes.