Supernovae, p-process, novae and X-ray bursts

Two kinds of explosion, one common history

Supernovae are the most luminous explosions in the universe after gamma-ray bursts: for a few weeks, a single exploding star can shine as brightly as an entire galaxy of hundreds of billions of stars. Visible light, however, is the minority share of the energy at play: the explosion of a massive star releases $\sim 3 \times 10^{53}$ erg, of which $\sim 99\%$ escapes as neutrinos, $\sim 1\%$ goes into kinetic energy of the ejecta (by definition one foe, $10^{51}$ erg), and less than $1\%$ emerges as electromagnetic radiation. The optical light curve over the following days and months is powered almost entirely by the radioactive decay of a small amount — a few hundredths to tenths of a solar mass — of $^{56}\mathrm{Ni}$ produced in the first seconds of the explosion, which decays in the cascade $^{56}\mathrm{Ni}(\tau_{1/2} = 6{.}1\,\mathrm{d}) \to {}^{56}\mathrm{Co}(\tau_{1/2} = 77\,\mathrm{d}) \to {}^{56}\mathrm{Fe}$ and deposits its gamma rays in the expanding ejecta.

There are two distinct explosion mechanisms, producing superficially similar phenomena but with radically different chemical signatures and timescales. Core-collapse SNe (spectroscopically classified as Type II, Ib, Ic depending on the pre-explosive envelope loss) are the fate of massive stars with $M \gtrsim 8\,M_\odot$: after passing through all the burning phases up to Si (chapter 3) and building an Fe core at $\sim M_{\mathrm{Ch}}$, they lose pressure support, collapse in less than a second, and the released gravitational energy expels the outer layers through a neutrino-mediated hydrodynamic mechanism. Thermonuclear SNe (Type Ia) come instead from the complete disruption of a CO white dwarf in a binary system, in which the accretion of matter or the merger with a second white dwarf triggers a thermonuclear runaway that burns $\sim 1\,M_\odot$ of carbon and oxygen into iron-peak elements in a few seconds. The spectroscopic distinction among the types (presence of H, He, Si lines in the early phases) is summarized in the following table:

The relative Galactic frequencies are $\sim 1$-$2 \times 10^{-2}$ per year for core-collapse SNe and $\sim 3 \times 10^{-3}$ per year for SNe Ia (ratio $\eta_{\mathrm{SN Ia}}/\eta_{\mathrm{CC}} \approx 0{.}2$-$0{.}3$, depending on the SFR and the Hubble type of the galaxy).

The key difference for nucleosynthesis is the $\alpha$-elements/Fe ratio of the ejecta. Core-collapse SNe produce many $\alpha$-elements (O, Mg, Si, S, Ca) — because they come from massive stars that burned up to Si in their inner layers and expel them practically intact — and relatively little iron, with $[\alpha/\mathrm{Fe}]_{\mathrm{CC}} \approx +0{.}4$. SNe Ia produce predominantly iron ($\sim 0{.}6\,M_\odot$ per event) with much smaller amounts of $\alpha$-elements, and have $[\alpha/\mathrm{Fe}]_{\mathrm{Ia}} \approx -0{.}3$. This diversity of chemical signatures, combined with the different timescale of release into the interstellar medium — core-collapse SNe explode a few million years after the formation of the progenitor star, SNe Ia with a median delay time of $\sim 1$ Gyr — is the key to Galactic chemical chronography. In primordial epochs, when only core-collapse SNe have had time to explode, the $[\alpha/\mathrm{Fe}]$ ratio of stars born from the interstellar gas is high and little dispersed; when the SNe Ia come into play ($\Delta t \gtrsim 100$ Myr after the onset of star formation), the ratio descends monotonically. The knee of the $[\alpha/\mathrm{Fe}]$ vs $[\mathrm{Fe/H}]$ curve marks the epoch of the transition, and its precise position is an indicator of the star-formation history of the observed population (chapter 7 for the complete Galactic chemical evolution).

Core-collapse SNe: the mechanism

When the iron core of a massive star exceeds the effective Chandrasekhar limit ($M_{\mathrm{core}} \approx 1{.}4$-$1{.}5\,M_\odot$), nothing can sustain it any longer against its own gravity. The support disappears for two complementary reasons, both active above a critical threshold of central density: electron capture $e^{-} + p \to n + \nu_e$ on the protons of the nuclei removes electron degeneracy pressure and reduces the proton fraction $Y_e$; photodisintegration $\gamma + {}^{56}\mathrm{Fe} \to 13\,{}^{4}\mathrm{He} + 4n$ ($Q = -124$ MeV) absorbs thermal energy from the photon bath to dissociate the most stable nuclei into $\alpha$ particles and free nucleons. Both processes are endothermic: they remove pressure instead of adding it, and the core goes into free fall in less than a second, passing from a sphere ten thousand kilometers in radius to one of ten kilometers — a density exceeding the nuclear density $\rho_{\mathrm{nuc}} \sim 2{.}3 \times 10^{14}$ g/cm$^{3}$. At that point the matter is nuclear-degenerate and incompressible, and the core “bounces”: the repulsion among nucleons produces a hydrodynamic shock that propagates outward at $\sim 30\,000$ km/s.

The bounce shock is not automatically an explosion. It loses energy by photodisintegrating the nuclei it encounters and by emitting neutrinos, and within a few hundred milliseconds it stalls at a radius of order $100$-$200$ km. The problem of core-collapse theory is the problem of reviving this stalled shock. The leading mechanism is delayed neutrino heating: the proto-neutron star radiates roughly $10^{53}$ erg in neutrinos over several seconds, and a small fraction of that flux is absorbed behind the stalled shock, mainly through charged-current interactions on free nucleons. The heated region becomes buoyant, convection grows, and multidimensional instabilities such as the standing accretion shock instability (SASI) increase the dwell time of matter in the heating layer. If heating wins over accretion cooling, the shock is revived and expands through the star.

The complete temporal sequence of a core-collapse SN is then the following. At pre-collapse the star has an Fe core of $\sim 1{.}5\,M_\odot$ surrounded by the onion structure of Si, O, Ne, C, He, H layers (see chapter 3). The onset of collapse at $t = 0$ is triggered by the instability from electron capture and Fe photodisintegration. The free-fall lasts $\sim 100$ ms, with homologous collapse of the inner part of the core and ballistic infall of the outer layer. The core bounce at $t \approx 0{.}1$ s occurs when the central density exceeds $\rho_{\mathrm{nuc}}$. The shock stall at $t \approx 0{.}15$ s arrests the shock at $R \sim 100$-$200$ km. The neutrino reheating at $t \approx 0{.}3$-$1$ s revives the shock through the combination of neutrino transport, convection and SASI. The shock breakout in the following seconds sees the shock cross the Si, O, C and H layers in turn, triggering explosive nucleosynthesis in each (next section). The light curve of the following days and months is powered by the decay $^{56}\mathrm{Ni} \to {}^{56}\mathrm{Co} \to {}^{56}\mathrm{Fe}$, with the characteristic plateau of SNe II-P sustained by the recombination of hydrogen in the extended envelope.

The 3D simulations of the explosion mechanism (Burrows and collaborators at Princeton, Janka and collaborators at Garching, Müller at Monash, Couch at MSU) have converged over the last decade on the fact that the explosion does occur for progenitors over a wide mass range, but with significant dispersion among models in the final energy, in the mass cut (the boundary between expelled matter and matter accreted onto the PNS or the resulting black hole), and in the yields. For progenitors of $M \lesssim 25\,M_\odot$, $M_{\mathrm{cut}} \approx 1{.}4$-$2\,M_\odot$ and the star expels about $90\%$ of its mass; for more massive progenitors, direct fallback to a black hole is possible, with little or zero ejecta — an outcome that varies non-monotonically with the initial mass. The compactness parameter $\xi_{2{.}5} = 2{.}5\,M_\odot / R(M = 2{.}5\,M_\odot)$ at the onset of collapse (O’Connor and Ott 2011) has established itself as an effective predictor of the outcome: for $\xi_{2{.}5} \lesssim 0{.}2$ the explosion typically succeeds, for $\xi > 0{.}3$ it typically fails with direct black-hole formation (a so-called failed SN). The distribution of $\xi$ in solar-metallicity massive stars is irregular as a function of mass, with “islands” of explosion and failure interleaved between $20$ and $40\,M_\odot$ — a prediction testable observationally through the monitoring of nearby massive stars awaiting silent disappearance, like the one already documented in NGC 6946 (Adams et al. 2017). The reference simulation codes are CHIMERA, FLASH, FORNAX, ALCAR, COCONUT, each with different specifications of neutrino transport (Boltzmann vs M1 vs IDSA) and relativistic hydrodynamics.

Explosive nucleosynthesis in core-collapse SNe

When the shock crosses the pre-existing layers of the massive star in the seconds after the rebound, it instantaneously heats the matter to very high temperatures and then lets it cool by hydrodynamic expansion. The burnings ignited in these conditions are qualitatively different from the quiescent ones: they last seconds rather than millions of years, operate in a strongly out-of-equilibrium regime, and in some layers reach nuclear statistical equilibrium (NSE) followed by freeze-out — the limit of maximum nuclear assembly. The products include the $^{56}\mathrm{Ni}$ that powers the light curve, the $\alpha$-element loading of the galaxy, and traces of r-process (insufficient for the budget) and of p-process (in the intermediate shells: central part of this chapter).

The structure of explosive nucleosynthesis is organized by the peak temperature reached by the shock, which decreases with radius. In the deep Si layer ($T > 5 \times 10^{9}$ K) complete NSE is reached followed by $\alpha$-rich freeze-out: during the equilibrium phase, the composition is dominated by $\alpha$ particles and free nucleons; during the expansion, the triple-$\alpha$ freezes rapidly into $^{12}\mathrm{C}$, then the subsequent $(\alpha, \gamma)$ captures carry the composition up to the iron peak in the form of $^{56}\mathrm{Ni}$ (favored for $Y_e \approx 0{.}5$). The mass of $^{56}\mathrm{Ni}$ produced is typically $0{.}05$-$0{.}1\,M_\odot$ for standard core-collapse SNe, and reaches $0{.}3$-$0{.}5\,M_\odot$ in the hypernovae associated with long GRBs. In the O/Ne layer ($T \sim 2$-$3 \times 10^{9}$ K) explosive O-burning ignites, producing $^{28}\mathrm{Si}, ^{32}\mathrm{S}, ^{36}\mathrm{Ar}, ^{40}\mathrm{Ca}$; in these same conditions the gamma-process for the p-nuclei also operates (central part of this chapter). In the C/Ne layer ($T \sim 1{.}5 \times 10^{9}$ K) explosive C-burning is activated, producing $^{20}\mathrm{Ne}, ^{24}\mathrm{Mg}, ^{27}\mathrm{Al}$. In the He layer ($T \sim 5 \times 10^{8}$ K) residual explosive He-burning operates, with activation of $^{22}\mathrm{Ne}(\alpha, n){}^{25}\mathrm{Mg}$ providing neutrons for a small s-process tail. The outer H layer ($T < 10^{9}$ K) survives essentially unchanged in composition.

Most of the expelled material therefore preserves the pre-explosive composition of the quiescent onion structure, with four significant explosive additions: the $^{56}\mathrm{Ni}$ produced by the $\alpha$-rich freeze-out of the deepest layer; the p-nuclei produced by the gamma-process in the O/Ne layer; a small amount of r-process from the $\nu$-driven winds (insufficient for the Galactic budget, see chapter 6); and the $^{44}\mathrm{Ti}$ tracer of the $\alpha$-rich freeze-out, revealed through its $\gamma$ line at $1{.}157$ MeV in Cas A by NuSTAR and in SN 1987A by Compton-GRO. The $\nu$-process adds minor but observable contributions to rare nuclei such as $^{11}\mathrm{B}, ^{19}\mathrm{F}, ^{138}\mathrm{La}, ^{180}\mathrm{Ta}^{m}$ — produced by spallation of abundant nuclei through interaction with the neutrino flux — calculated with shell-model $\nu$-nucleus cross sections (Heger et al. 2005) at $\langle E_\nu \rangle \sim 10$-$20$ MeV.

The mean yields integrated over the initial mass function (Salpeter or Kroupa IMF) for stars of $13$-$40\,M_\odot$ at solar metallicity, summarized in Woosley & Heger [Woosley et al. 2002] and refined in Sukhbold et al. (2016) [Sukhbold et al. 2016] , are of order $\langle Y_O \rangle \sim 0{.}8\,M_\odot$, $\langle Y_C \rangle \sim 0{.}06\,M_\odot$, $\langle Y_{Ne} \rangle \sim 0{.}1\,M_\odot$, $\langle Y_{Mg} \rangle \sim 0{.}05\,M_\odot$, $\langle Y_{Si} \rangle \sim 0{.}05\,M_\odot$, $\langle Y_{Fe} \rangle \sim 0{.}07\,M_\odot$ per exploding star. For stars $> 25\,M_\odot$ direct fallback to a black hole can reduce the Fe yield to nearly zero, and the ejecta pattern is dominated by the less processed outer layers. The complete tables for all nuclides, on a dense grid of mass and metallicity, are in Sukhbold-Woosley 2016/2018 (KEPLER), Limongi-Chieffi 2018 (FRANEC, including differential rotation and mass loss), and Pignatari-Herwig 2016 (NuGrid, also calibrated on presolar grains).

An important empirical observation is the $M({}^{56}\mathrm{Ni})$-$E_{\mathrm{kin}}$ correlation: more energetic SNe produce more $^{56}\mathrm{Ni}$, with $M({}^{56}\mathrm{Ni}) \propto E_{\mathrm{kin}}^{0{.}7}$ and dispersion $\sim 0{.}3$ dex. Sub-luminous SNe ($E_{\mathrm{kin}} \sim 10^{50}$ erg, $M({}^{56}\mathrm{Ni}) \sim 10^{-3}\,M_\odot$) are rare but significant — the historical candidate is SN 2008ha — and probably associated with explosions of massive stars with partial fallback or with partially successful failed-SN mechanisms. Hypernovae ($E_{\mathrm{kin}} \sim 10^{52}$ erg, $M({}^{56}\mathrm{Ni}) \gtrsim 0{.}3\,M_\odot$) are, on the contrary, associated with long gamma-ray bursts and with the most massive ($M \gtrsim 30\,M_\odot$), rapidly rotating progenitors, and dominate the Galactic budget of Fe from massive progenitors at ultra-low metallicity.

SNe Ia: the mechanism

Type Ia supernovae come from the complete destruction of a carbon-oxygen white dwarf in a binary system. An isolated white dwarf is stable by definition — the degenerate pressure of the electrons sustains it against gravity in a stationary way — but if it has a stellar companion it can accrete matter or merge with it, and when the effective mass approaches the Chandrasekhar limit ($M_{\mathrm{Ch}} \approx 1{.}4\,M_\odot$ for CO composition) or when the ignition propagates through sub-Chandrasekhar mechanisms, the carbon inside enters a thermonuclear runaway regime. In conditions of electron degeneracy the temperature rises but the pressure does not — the pressure is fixed by the density — and the runaway is uncontrollable: in a few seconds all the carbon and oxygen of the WD are fused into iron-peak elements, the released energy ($\sim 10^{51}$ erg) exceeds the gravitational binding energy ($\sim 5 \times 10^{50}$ erg), and the WD is entirely disintegrated leaving no compact remnant.

The explosion produces $0{.}3$-$0{.}9\,M_\odot$ of $^{56}\mathrm{Ni}$, enough to power a light curve much more luminous than the typical core-collapse SN, and — a fundamental property — standardizable: after empirical corrections for the decline rate of the light curve (the Phillips relation), SNe Ia can be used as “standardizable candles” to measure cosmological distances with $\sim 5\%$ precision. It is through high-redshift SNe Ia that Riess, Schmidt, Perlmutter and collaborators discovered in 1998 the accelerated expansion of the universe, whence the evidence for dark energy — Nobel Prize in Physics 2011.

Two main families of scenarios compete for the SN Ia progenitor. In the Single Degenerate (SD) scenario, a CO white dwarf accretes matter from an evolved companion (red giant, main sequence, or He star) through Roche-lobe overflow or wind capture. The WD grows in mass toward $M_{\mathrm{Ch}}$ and ignites when the carbon in the core reaches $T \sim 7 \times 10^{8}$ K and explosive burning is activated in the central region. In the Double Degenerate (DD) scenario, two CO white dwarfs in a tight binary orbit merge through gravitational-wave emission, and the merger leads to an explosive carbon ignition, sometimes sub-Chandrasekhar and sometimes accompanied by complex intermediate phases. Over the last twenty years, the combination of observational constraints — the lack of a recognized companion in the remnants of nearby SNe Ia (SN 1006, SN 1572, SN 1604), the lack of X-ray fluxes from pre-explosive accretion in surveys, the distribution of distances and delay times with respect to star formation — suggests that the majority of normal SNe Ia (the Branch-normal subtype) come from DD scenarios, while peculiar events (SN 91T, SN 91bg) may have SD progenitors or sub-Chandra ignition.

Several explosion models have been proposed and tested against observations. The pure deflagration has the burning front propagate at subsonic speed: it produces much $^{56}\mathrm{Ni}$ but also intermediate products (Si, S) and regions of unburned carbon, and does not reproduce well the spectra of normal SNe Ia. The pure detonation has the front propagate supersonically and burns everything into $^{56}\mathrm{Ni}$: it produces too little Si, S, Ca compared with observations. The favored model for normal SNe Ia is the Delayed Detonation Transition (DDT): an initial deflagration phase that, at a critical density around $\rho \sim 10^{7}$ g/cm$^{3}$, transitions to a detonation and completes the burning. The sub-Chandrasekhar (double detonation) model — re-emerged over the last fifteen years as a realistic candidate — instead envisages an initial detonation of a thin He shell on the surface of the CO WD, which sends a converging shock into the core and triggers a secondary carbon detonation: it reproduces well the light curve and the nucleosynthesis of normal SNe Ia, and also produces p-nuclei in the outer layers of burned He (see the central part of this chapter).

The typical yields of a SN Ia, with the original W7 deflagration model as reference (Iwamoto et al. 1999) and its successors in 3D DDT (Seitenzahl et al. 2013) and sub-Chandra (Shen, Townsley), are $Y_O \sim 0{.}13\,M_\odot$, $Y_{Si} \sim 0{.}15\,M_\odot$, $Y_S \sim 0{.}08\,M_\odot$, $Y_{Ca} \sim 0{.}03\,M_\odot$, $Y_{Fe} \sim 0{.}65\,M_\odot$, with initial $^{56}\mathrm{Ni}$ $\sim 0{.}6\,M_\odot$. The total expelled mass is about $1{.}4\,M_\odot$ for the Chandra models (the entirety of the WD) or $\sim 1{.}0\,M_\odot$ for the sub-Chandra ones (the CO core without the thin He shell). The Mn/Fe ratio is the most sensitive diagnostic for distinguishing the two scenarios: Chandra SNe Ia have high Mn/Fe because the capture $e^{-} + p \to n + \nu_e$ is efficient at $\rho > 10^{9}$ g/cm$^{3}$ and enriches the neutron excess favoring $^{55}\mathrm{Mn}$, while the sub-Chandra models at lower central density produce low Mn/Fe. The most recent 3D-DDT models (Seitenzahl, Townsley, Röpke) produce yields with a dependence on the geometry of the initial ignition and on the number of hotspots, and the Mn/Cr/stable-Ni ratios are diagnostics observable in the integrated spectra of galaxies and in individual metal-poor stars.

Yield tables for galactic evolution

To model the chemical evolution of the Milky Way (chapter 7), one needs tables of mean yields for each type of supernova, integrated over the initial IMF and tabulated as a function of the progenitor metallicity. Several groups around the world produce and maintain these tables, which constitute one of the key inputs of GCE (Galactic Chemical Evolution) models. The main public compilations for core-collapse SNe are Sukhbold-Woosley (2016, 2018), based on the KEPLER code with $\sim 200$ models on a mass grid of $13$-$120\,M_\odot$ at metallicity $Z = 0$-$Z_\odot$; Limongi-Chieffi (2018), based on the FRANEC code and including differential rotation and mass loss; Pignatari-Herwig (2016), based on the NuGrid framework and also calibrated on presolar grains; Nomoto-Kobayashi-Tominaga [Nomoto et al. 2013] , which integrate core-collapse SNe, hypernovae, $\nu$-process and SNe Ia in a consistent GCE pipeline. For the SNe Ia the reference compilations are Iwamoto et al. (1999) for the W7 model, Travaglio et al. (2004) for DDT, and Seitenzahl et al. (2013) for 3D DDT.

The differences among groups in the final yields are significant and depend on specific modeling choices. The Fe yield varies by a factor 2-3 depending on the assumed mass cut and fallback (and in particular on the choice of exploding “by hand” with a piston or a thermal bomb vs self-consistent simulations of the mechanism). The $\alpha$-element yield varies by $\sim 30\%$ depending on the treatment of hydrostatic and explosive C-burning, and in particular on the rate of $^{12}\mathrm{C}(\alpha, \gamma){}^{16}\mathrm{O}$. The yield of neutron-rich species such as $^{22}\mathrm{Ne}, ^{25,26}\mathrm{Mg}$ varies with the initial rotation, because rotational mixing during the main sequence and He-burning redistributes $^{14}\mathrm{N}$ toward the He shells and activates $^{14}\mathrm{N}(\alpha, \gamma){}^{18}\mathrm{F}(\beta^{+}\nu){}^{18}\mathrm{O}(\alpha, \gamma){}^{22}\mathrm{Ne}$ with variable efficiency.

The IMF-integrated yields (Kroupa or Salpeter) per unit stellar generation — the integrated yield $\langle p_X \rangle = \int Y_X(M)\, \xi(M)\, dM$ normalized per solar mass of star formation — are published as tables in Kobayashi, Karakas and Lugaro (2020) [Kobayashi et al. 2020] and are direct input for GCE models. The partition between core-collapse SNe and SNe Ia for the most important elements of Galactic chemical evolution is schematically: O dominated by core-collapse SNe ($> 95\%$); Mg by core-collapse SNe ($\sim 90\%$); Si and Ca a mixed contribution $\sim 50$-$50$; Fe dominated by SNe Ia ($\sim 70\%$) with the rest from core-collapse SNe; Mn dominated by SNe Ia ($> 80\%$); Eu from neutron-star mergers and exotic r-process sites (see chapter 6). The methodological synthesis review of SN nucleosynthesis — both core-collapse and thermonuclear — and of their yields in a Galactic-evolution key is Nomoto, Kobayashi and Tominaga (2013) [Nomoto et al. 2013] in Annual Review of Astronomy and Astrophysics, today the standard reference. The r-process framework after GW170817 and its sites are referred to Thielemann, Eichler, Panov and Wehmeyer (2017) [Thielemann et al. 2017] .

State of the art and prospects

The picture of supernova nucleosynthesis is today consolidated in its main lines. For core-collapse SNe, the self-consistent 3D simulations of the explosion mechanism have reached qualitative convergence on the role of neutrinos and convection, and routinely produce explosions for progenitors over wide mass ranges; quantitative questions remain open on the final energy ($E_{\mathrm{kin}}$ still dispersed by a factor 2 among groups), on the effective mass cut (with direct consequences for the Fe yield), and on the bimodality of the outcome (explosion vs direct fallback to a black hole) as a function of the progenitor compactness. For the SNe Ia, the combination of observational and modeling constraints suggests that the dominant channel for normal SNe is DD or sub-Chandra DD, while the Chandra-mass SD channel is probably subdominant; the exact fraction of each channel and the origin of the peculiar subtypes (SNe Iax, calcium-rich SNe, SNe .Ia) remain to be clarified.

Three quantitative questions remain particularly alive. The first is the calibration of the mass cut in core-collapse SN models: the yields of Fe and of the iron-peak elements depend critically on the transition radius between expelled matter and matter swallowed by the PNS, and 1D models must still assume it as a free parameter while waiting for 3D simulations to produce unique and tabulatable predictions. The second is the statistics of hypernovae as a function of metallicity: hypernovae from metal-poor progenitors (with low pre-SN mass loss, high residual rotation) are probably the dominant source of Fe in the ultra-metal-poor stars of the halo, and their relative frequency with respect to standard core-collapse SNe has direct consequences for the abundances observed in EMP stars. The third is the partition among SN Ia channels Chandra/sub-Chandra/SD/DD as a function of metallicity and delay time: the Mn/Fe and Ni/Fe ratios in metal-poor stars offer direct diagnostics, and the high-resolution surveys of the next decade promise to constrain the history quantitatively.

The prospects over 5-10 years include several converging directions. On the theoretical front, the 3D simulations of core-collapse SNe with Boltzmann neutrino transport and full general relativity (Burrows et al., Janka et al., Müller et al.) are beginning to produce self-consistent explosive yields that will replace the “pistoned” 1D explosions of the historical models. On the observational front, Vera Rubin Observatory (LSST) will detect $\sim 10^{6}$ SNe per year, with statistics sufficient to constrain separately the Ia subchannels and the parameters of core-collapse SNe as a function of the progenitor. JWST and the future ELT, GMT, TMT will allow high-resolution spectroscopy of distant SNe and of nearby SN remnants, directly constraining the yields of individual events. Athena, XRISM and the future Lynx will detect the X-ray lines of young SN remnants (Cas A, Tycho, SN 1987A) with resolution sufficient to map the 3D distribution of $^{56}\mathrm{Ni}$, $^{44}\mathrm{Ti}$ and the other explosive tracers. On the multimessenger front, a future Galactic SN (statistically expected $\sim 1$-$2$ times per century, the last in 1987 in the LMC) will be detected simultaneously in neutrinos (Super-K, IceCube, JUNO, DUNE), in gravitational waves (LIGO/Virgo), and — at breakout — in all electromagnetic bands, providing a definitive test of the explosion mechanism and of the yields.

Supernovae are at once the main explosive site of heavy-element nucleosynthesis — alphas, the Fe peak, a large part of the intermediate elements — and the main mechanism of chemical feedback that carries the products of previous stellar generations into the interstellar medium, where they become raw material for the following generations. What remains to be told, in this chapter, are the “orphan” nuclei that neither the s-process nor the r-process produces — the p-nuclei, subject of the central part — and the periodic thermonuclear explosions on white dwarfs and neutron stars in accreting binary systems, the classical novae and the X-ray bursts, subject of the final part. The next chapter is devoted to neutron-star mergers as a combined multimessenger laboratory of r-process nucleosynthesis, GR-MHD hydrodynamics, and the equation of state of ultra-dense matter.

The “orphan” nuclei

On the chart of nuclides, between the proton drip line and the valley of beta stability, there exists a thin strip of stable nuclei that neither the s-process nor the r-process manages to reach. They are about thirty-five isotopes — a small minority of the known stable nuclei — distributed from $^{74}\mathrm{Se}$ to $^{196}\mathrm{Hg}$, and they are collectively called p-nuclei because they are proton-rich with respect to the lightest stable isotope of the same element. Typical examples are $^{92,94}\mathrm{Mo}$, $^{96,98}\mathrm{Ru}$, $^{74}\mathrm{Se}$, $^{102}\mathrm{Pd}$, $^{120}\mathrm{Te}$, $^{144}\mathrm{Sm}$, $^{180}\mathrm{Ta}^{m}$. Their solar abundance is low — typically $10^{-2}$-$10^{-3}$ of the neighboring r or s isotopes — but not zero, and the explanation of their origin is one of the most tormented chapters of quantitative stellar nucleosynthesis.

The structural reason why s and r do not reach them is geometric. The s-process runs along the valley of stability, and any p-nuclide is separated from the s path by at least one stable isotope at lower $Z$ that stops the $\beta^{-}$ cascade — the p-nuclide is “shielded” by its more stable isobar. The r-process populates nuclei at the neutron drip line and transports them toward the valley through multiple $\beta^{-}$ decays: the path never passes through the proton-rich region. To produce the p-nuclei a radically different mechanism is needed, one that starts from an already heavy nucleus and progressively strips neutrons from it: the gamma-process (or p-process in the strict sense), proposed by Woosley and Howard in 1978 and formalized in Arnould and Goriely (2003) [Arnould & Goriely 2003] and in Rauscher et al. (2013) [Rauscher et al. 2013] .

The kinetic picture

The physical condition of the gamma-process is $T \sim (2$-$3) \times 10^{9}$ K, high enough for the Planckian photon bath to contain a significant fraction of photons with $E_\gamma \gtrsim S_n \sim 8$-$10$ MeV, the typical neutron separation energies in heavy nuclei. In these conditions, the photodisintegration reactions $(\gamma, n)$, $(\gamma, p)$, $(\gamma, \alpha)$ become fast on the timescale of seconds and dominate over the inverse captures. Starting from seed nuclei pre-produced by the s-process in the quiescent phases of the star (typical total mass $10^{-3}\,M_\odot$ of Ba, Ce, Nd, Sm, Eu, Gd accumulated in the shell during the AGB or massive-star evolution), the sequence operates in two stages: first the $(\gamma, n)$ cascade strips neutrons from the seed nuclide along its isotopic chain, pushing it toward $S_n \to 0$ (the proton drip line); when the next $(\gamma, n)$ is no longer energetically favored, $(\gamma, p)$ and $(\gamma, \alpha)$ intervene, moving the flow to lower $Z$ and feeding a new vertical chain. The net path on the chart of nuclides is a sequence of vertical segments (at constant $Z$) followed by horizontal deviations (decreasing $Z$), which leaves the stable p-nuclei as final products.

The typical network for the quantitative calculation of the gamma-process contains about $2000$ nuclei and $20\,000$ $(\gamma, X)$ and $(X, \gamma)$ reactions, with the cross sections almost all calculated in the Hauser-Feshbach statistical model. Direct measurements of $(\gamma, n)$, $(\gamma, p)$, $(\gamma, \alpha)$ cross sections at astrophysical energies are difficult — quasi-monochromatic photon beams are available only at a few facilities (HIGS at Duke, NewSUBARU at Spring-8, ELI-NP in Romania) — and for the vast majority of nuclides one resorts to indirect measurements of the inverse reactions $(\alpha, \gamma)$ and $(p, \gamma)$ on stable targets (TRIUMF, ATLAS, GANIL, n_TOF). The reference nucleosynthesis codes for the p-process are NON-SMOKER and TALYS on the nuclear front, NuGrid (Pignatari et al.) [Pignatari et al. 2010] for the complete astrophysical integration in massive stars. Updated nuclear-data compilations are NACRE-II [Xu et al. 2013] and KADoNiS.

In conditions of local dynamic equilibrium (quasi-statistical equilibrium, QSE), the abundance of each p-nuclide is set by the balance between production (the $(\gamma, X)$ cascade from the seed at higher $Z$) and destruction (further photodisintegrations or inverse captures). The yield of a single p-nuclide is therefore sensitive to a handful of key reactions along the production and destruction path: sensitivity analyses (Rapp et al. 2006, Rauscher 2011) have identified about 50 “key” reactions for which a $10\%$ uncertainty in the cross section translates into $> 5\%$ variation in the final yields. It is a dense and strongly coupled network, in which the precision of the astrophysical result is limited by the precision of the laboratory nuclear datum.

The gamma-process in core-collapse supernovae

The historically identified site, and still today the main one for most p-nuclei, is the O/Ne shell during the passage of the shock in a core-collapse supernova (SN II, see the first part of this chapter for the complete hydrodynamics of the explosion). As the shock propagates outward through the pre-existing layers of the massive star, it transiently heats each layer to a temperature proportional to its density: in the O/Ne region, at about $2$-$3 \times 10^{9}$ K, the conditions of temperature and timescale (1-2 seconds of exposure) are optimal for the gamma-process. The s-process pre-enrichment accumulated during the quiescent He- and C-burning phases (see chapter 4, weak component) provides the seed nuclei; the shock activates the photodisintegration; the expelled ejecta carry into the interstellar medium the p-nuclei thus produced.

The typical yields are a total mass of p-nuclei ejected of $\sim 10^{-5}$-$10^{-4}\,M_\odot$ for a SN II of $25\,M_\odot$ (Woosley & Weaver 1995, with later updates in Rauscher et al. [Woosley et al. 2002] ), sufficient to reproduce the solar p-process pattern within a factor $\sim 3$ for most nuclides. The signature of the SN II gamma-process is well recognizable in the intermediate and heavy p-nuclei ($A \gtrsim 130$): Sm, Gd, Dy, Er, Yb, Hf, W, Os, Pt and their p-isotopes are produced in proportions close to the solar ratios. A small fraction, of order $\sim 10\%$ of the total, is also produced during the pre-explosive C-burning in the carbon shell, in pre-shock conditions — a contribution that depends sensitively on the rotation velocity and the mass loss of the progenitor star.

The main deficiencies of the SN II gamma-process, recognized since the first complete calculations and still not resolved in standard models, concern the region $A \lesssim 100$. Howard and Meyer (1991) showed that the light p-nuclei — in particular $^{92,94}\mathrm{Mo}$ and $^{96,98}\mathrm{Ru}$ — are produced with relative abundances $\sim 0{.}1$-$0{.}3$ of the required solar value, and the situation has not improved significantly with more recent calculations on denser grids of stellar models. It is the so-called Mo-Ru deficit problem, one of the most discussed open quantitative frictions of nucleosynthesis. The structural reason is that at $Z \sim 42$-$44$, the $(\gamma, \alpha)$ cross sections in the Hauser-Feshbach approximation underestimate the efficiency of the $\alpha$ channel at sub-Coulomb energies, and the s-process seed in massive stars is inefficient in that mass region. The residual uncertainties depend critically on a handful of reactions: $^{96}\mathrm{Ru}(\gamma, \alpha){}^{92}\mathrm{Mo}$, $^{91}\mathrm{Nb}(\gamma, p){}^{90}\mathrm{Zr}$, $^{102}\mathrm{Pd}(\gamma, n){}^{101}\mathrm{Pd}$, $^{120}\mathrm{Te}(\gamma, \alpha){}^{116}\mathrm{Sn}$, whose cross sections are known with $30\%$-$50\%$ uncertainties and whose experimental characterization at TRIUMF, GSI, HIGS, ELI-NP is a priority of the community.

Complementary sites: $\nu$-p, rp, i-process and SNe Ia

The recognition that the SN II gamma-process does not explain the whole p-process pattern — and in particular the Mo-Ru region — has led over the last twenty years to the proposal and characterization of alternative and complementary sites. The consolidated post-2020 picture is that no single site reproduces the whole pattern, and that the Galactic production of p-nuclei is the result of a combination of processes operating in different astrophysical environments.

The $\nu$-p process (Fröhlich, Martínez-Pinedo and collaborators, 2006) operates in the neutrino-driven winds emerging from the proto-neutron star in core-collapse SNe, in the seconds immediately after the rebound. In those conditions, the intense capture $\bar\nu_e + p \to n + e^{+}$ progressively drives the proton fraction $Y_e$ toward marginally proton-rich values ($Y_e \sim 0{.}55$-$0{.}6$); the remaining $\bar\nu_e$ flux keeps converting protons into neutrons at a low but significant rate, and these neutrons are rapidly captured by pre-existing p-rich nuclei in the $\alpha p$ chain, feeding a sequence of proton captures and $(n, p)$ reactions that produces nuclei like $^{64}\mathrm{Ge}$, $^{68}\mathrm{Se}$, $^{72}\mathrm{Kr}$, $^{88}\mathrm{Sr}$, $^{92}\mathrm{Mo}$. The $\nu$-p process reproduces a good part of the p-process pattern up to $A \sim 100$ and in particular contributes significantly to the production of light Mo and Ru, enough — combined with the gamma-process — to partially heal the historical deficit. The sensitivity to the details of neutrino transport ($\nu N$ cross sections, flavor oscillations in the high-density regime) remains significant, and the yields vary by a factor 2-3 among models.

The rp-process (rapid proton capture) operates instead in explosive accretion conditions on neutron stars: Type I X-ray bursts, discussed in detail in the final part of this chapter, are periodic thermonuclear explosions on the atmosphere of accreting NS, with peak temperatures $T \sim 1{.}5 \times 10^{9}$ K and durations of tens of seconds. In these conditions, proton capture $(p, \gamma)$ proceeds rapidly to the proton drip line, crossing waiting points at nuclei such as $^{64}\mathrm{Ge}$, $^{68}\mathrm{Se}$, $^{72}\mathrm{Kr}$, and reaching in favorable cases up to $A \sim 100$ with an end-point at $^{107,108}\mathrm{Te}$ (the SnSbTe cycle). The problem is that the processed matter is typically not expelled into the interstellar medium: it remains on the surface of the NS, buried by subsequent accretion. The rp-process contribution to the Galactic budget of p-nuclei is therefore limited — at most a few percent — even though the local nucleosynthesis is prolific.

The i-process (intermediate neutron capture), proposed by Cowan and Rose in 1977 and the object of a theoretical renaissance over the last decade (Hampel, Stancliffe, Denissenkov, Herwig), operates in the intermediate regime $\tau_n \sim \tau_\beta$ with neutron densities $n_n \sim 10^{13}$-$10^{15}$ cm$^{-3}$ — between the main s and the main r. Candidate sites are the proton ingestion during the He flash in very metal-poor stars of very low mass, some Sakurai’s-object-like stars in which H is ingested into the intershell during the late AGB, and specific accreting systems. Recent models (Hampel et al. 2016 [Hampel et al. 2016] , Denissenkov et al. 2017) suggest that the i-process can contribute significantly to the nucleosynthesis in the region $A = 90$-$140$ in some EMP stars — the so-called CEMP-i — and in particular to the production of some light p-nuclei, although the quantification remains uncertain and dependent on the poorly constrained details of 3D mixing.

Finally, the sub-Chandrasekhar SNe Ia (Travaglio, Rauscher, Röpke and collaborators) — thermonuclear explosions of CO white dwarfs triggered by the detonation of a superficial He shell, below the Chandrasekhar limit — can activate the gamma-process in the outer layers of the ejecta during the detonation, with temperatures $\sim 2 \times 10^{9}$ K. The ratio between s-process seed and temperature is different from that of SNe II, and the SN Ia models reasonably reproduce the abundance of light Mo and Ru, complementing the $\nu$-p contribution. The relative Galactic frequency SN Ia/SN II and the fraction of sub-Chandra (vs Chandra) SNe Ia remain debated, but the post-2020 consensus is that SNe Ia contribute $\sim 30\%$-$50\%$ to the Galactic production of Mo and Ru.

The consolidated picture of the partition among sites can be summarized as follows: light Mo and Ru are produced roughly half-and-half by the $\nu$-p process in SNe II and the gamma-process in sub-Chandrasekhar SNe Ia, with small contributions from rp and from the i-process; Sm, Gd and the heavy p-nuclei ($A > 130$) are produced predominantly by the standard gamma-process in SNe II; Pd, Cd, Sn and the intermediate p-nuclei receive mixed contributions, with possible involvement of the i-process in specific cases. The canonical review of the field is Rauscher et al. (2013) [Rauscher et al. 2013] in Reports on Progress in Physics, complemented by Pignatari et al. [Pignatari et al. 2010] for the massive-star part and by Travaglio et al. (2018) for the SN Ia part.

Sensitivity to nuclear data and state of the art

The central and recurring problem of the p-process is its sensitivity to a large mass of cross sections of $(\gamma, X)$ reactions on nuclei whose direct experimental characterization is difficult or impossible. The uncertainties in the basic nuclear data propagate in a complicated way onto the calculated final abundances, and the identification of an underproduction of a given p-nuclide in the models can reflect as much a missing site as a poorly constrained nuclear datum — distinguishing between the two hypotheses requires a systematic sensitivity analysis.

The residual uncertainties on the Galactic p-process pattern are dominated by four families of problems. The $(\gamma, \alpha)$ cross sections for intermediate and heavy nuclei ($A > 130$) are constrained at $\sim 30\%$ by the existing data, but for many key p-nuclei they depend on the optical model for $\alpha$ capture at sub-Coulomb energies — the “Coulomb barrier problem” of Hauser-Feshbach calculations, which notoriously underestimate the alpha-channel transitions at low $E_\alpha$ compared with direct measurements where available. The nuclear level densities at high energy, parameterized with back-shifted Fermi gas or with microscopic Hartree-Fock-Bogoliubov calculations, differ by a factor 2 in regions relevant to the p-process. The s-process pre-enrichment in the SN II progenitors — the “load” of seed nuclei accumulated before the explosion — depends sensitively on the rotation, mass loss and mixing of the pre-SN star, and propagates factor-2 uncertainties onto the final p yields. Finally, the details of neutrino transport in the $\nu$-p process environment, particularly the flavor oscillations in the high-density regime, remain a significant source of uncertainty for the Mo-Ru yields.

The experimental prospects over 5-10 years are encouraging on several fronts. The new-generation quasi-monochromatic photon facilities — ELI-NP in Romania, the HIGS upgrade at Duke, and the future new-generation Compton-backscattered $\gamma$ beam planned in China — will allow direct measurements of $(\gamma, n)$ and $(\gamma, \alpha)$ cross sections for dozens of p-nuclei at astrophysical energies, with precision below $10\%$. The new-generation rare-isotope facilities (FRIB, FAIR) will characterize masses and beta rates of proton-rich nuclei along the rp- and $\nu$-p-process paths, reducing the theoretical extrapolations that dominate today. On the astrophysical front, self-consistent 3D simulations of core-collapse SNe with accurate neutrino transport (Burrows, Janka, Foglizzo, Wongwathanarat) are beginning to produce self-consistent quantitative $\nu$-p yields, and the new-generation sub-Chandra SN Ia models (Shen, Townsley, Röpke) will better characterize the expected Mo-Ru statistics. The combination of these fronts promises to bring the residual uncertainties on the p-process yields from the current factor of 3 to a factor $\sim 1{.}5$ within the next decade, and to close quantitatively — if not structurally — the story of the p-process.

The p-process closes — with the last ambiguities that the field has yet to untangle — the picture of the nucleosynthesis of the proton-rich elements. The quiescent burnings of the stellar phases cover from hydrogen to iron; the s-process, in AGB and massive stars, builds about half of the trans-iron elements along the valley of stability; the r-process, in neutron-star mergers and exotic supernovae, builds the other half through the neutron drip line; the p-process, together with its cousins $\nu$-p, rp and i, fills the thin proton-rich strip left orphaned by the other two. The core-collapse supernovae of the previous part provide the site that orchestrates many of these syntheses, where the collapse of the Fe core triggers the shock that crosses the layers and activates gamma-process, $\nu$-p, explosive Si-burning, NSE freeze-out and the production of a large part of the elements we see today in the spectra of stars.

Explosions at the surface

Supernovae are spectacular but rare in the Milky Way — about one per century on average (first part of this chapter) — and dominate the chemical enrichment for many elements but not for all. There are other classes of nuclear explosions, far more frequent but far less powerful per event, that occur at the surface of compact objects — white dwarfs and neutron stars — when a companion star in a binary system transfers matter to them through Roche-lobe overflow or wind capture. These explosions are called classical novae (on CO or ONeMg white dwarfs) and Type I X-ray bursts (on accreting neutron stars), and for nucleosynthesis they matter because they produce specific rare isotopes that no other stellar site produces in significant quantities: $^{15}\mathrm{N}$, $^{17}\mathrm{O}$, $^{22}\mathrm{Na}$, $^{26}\mathrm{Al}$ in novae; proton-rich nuclei up to $A \sim 100$ in X-ray bursts via the rp-process.

The key quantitative differences between novae and XRB are summarized in the following table:

Novae expel matter into the ISM and contribute significantly to the Galactic chemical budget for the isotopes listed above; X-ray bursts probably do not, because the escape velocity from the NS surface is of order $0{.}1\,c$ — far greater than the velocities reached by the post-burst material — and the processed matter remains sequestered on the NS, buried by subsequent accretion. The Galactic contribution of XRB to the chemical budget is therefore limited to at most a few percent of the total p-rich nuclei. The reference reviews are José and Hernanz (2011) [José & Hernanz 2007] for novae and Schatz and Rehm (2006) [Schatz & Rehm 2006] for the XRB; the complete textbook treatment of explosive nucleosynthesis in the accretion regime is in Iliadis (2015) [Iliadis 2015], chapters 5 and 10.

The systematics of novae distinguishes two main families according to the composition of the progenitor white dwarf. CO novae occur on CO white dwarfs of mass $M_{\mathrm{WD}} \sim 0{.}6$-$1{.}0\,M_\odot$ (remnants of low/intermediate-mass AGB, chapter 4); they are more frequent, reach peak $T \sim 2 \times 10^{8}$ K, and their chemical pattern is dominated by the CNO cycles. ONe novae occur on ONeMg white dwarfs of mass $M_{\mathrm{WD}} \sim 1{.}1$-$1{.}3\,M_\odot$ (remnants of Super-AGB); they are rarer, reach peak $T \sim 3 \times 10^{8}$ K, and significantly activate the NeNa and MgAl cycles, producing abundant $^{22}\mathrm{Na}$ and $^{26}\mathrm{Al}$. Typical X-ray bursts are attributed to LMXB systems (Low-Mass X-ray Binaries) in which a NS accretes from a MS or sub-giant companion; examples catalogued with large statistics are GS 1826-238 (the clocked burster, for the exceptional regularity of its bursts), 4U 1820-30, EXO 0748-676. The reference nuclear-hydrodynamic simulation codes are SHIVA (José) for novae, MESA with Denissenkov’s modifications [Denissenkov et al. 2014] , KEPLER, FLASH.

Classical novae: the mechanism

A white dwarf in a tight binary pair with a main-sequence or giant star accretes hydrogen from the companion through Roche-lobe overflow at a typical rate of $\dot M \sim 10^{-10}$-$10^{-9}\,M_\odot/\mathrm{yr}$. The accreted hydrogen layer accumulates on the surface of the WD for thousands or tens of thousands of years, slowly compressing under its own gravity and heating by compression. When the temperature at the base of the layer reaches $T_{\mathrm{base}} \sim 2 \times 10^{7}$ K, the reactions of the CNO cycle ignite; but the material is electron-degenerate and the pressure does not increase significantly with temperature — the standard condition for a thermonuclear runaway. In a few seconds the temperature rises to $\sim 3 \times 10^{8}$ K, the accreted layer expands into an optically thick envelope, and the material is expelled at velocities of $1000$-$4000$ km/s into the circumstellar medium. The star, seen from Earth, “appears” as a nova stella (the historical Latin name, “new star”), shining for a few weeks or months before returning to its background accreting luminosity.

The temporal sequence of a classical nova unfolds in seven distinct phases. The slow accretion phase sees the progressive accumulation of a total mass $\sim 10^{-5}\,M_\odot$ in $10^{4}$-$10^{5}$ years (the recurrence time of the system). During the compression and heating, the base of the layer compresses under its own gravity and $T_{\mathrm{base}}$ rises to $\sim 2 \times 10^{7}$ K. The CNO ignition starts with the reactions $^{12}\mathrm{C}(p,\gamma)^{13}\mathrm{N}$ and $^{14}\mathrm{N}(p,\gamma)^{15}\mathrm{O}$; the presence of pre-existing $^{12}\mathrm{C}$ and $^{14}\mathrm{N}$ as CNO catalysts is essential, and the mixing of the WD into the accreted substrate via Kelvin-Helmholtz instabilities provides extra CNO seeds that significantly amplify the rate — observationally confirmed by the mass fraction $X_{\mathrm{CNO}} \sim 0{.}2$-$0{.}5$ measured in nova ejecta, against $\sim 0{.}01$ of solar material. The Hot CNO phase ($T > 5 \times 10^{7}$ K) sees the lifetimes of the unstable isotopes $^{13}\mathrm{N}$, $^{14}\mathrm{O}$, $^{15}\mathrm{O}$ become comparable to or shorter than the characteristic times of the subsequent $(p, \gamma)$ reactions: the cycle enters the beta-limited regime, in which the rate of the CNO cycle is limited by the half-life $\tau_{1/2}(^{15}\mathrm{O}) = 122$ s and stabilizes, becoming independent of T. The convective runaway is activated on timescales of a few seconds: convection transports energy from the hot point (the base) to the cold point (the surface), and $T_{\mathrm{base}}$ reaches the peak $\sim 3 \times 10^{8}$ K in $\sim 100$ s. During the outburst, the envelope expands beyond the Roche limit of the system and the matter is expelled at $v \sim 1000$-$4000$ km/s into the circumstellar medium. Finally, during the post-burst evolution the nuclear pumping ceases, the expelled layer cools and thins, and the star returns to the accreting state awaiting the next nova. The mass expelled per event is $\sim 10^{-5}$-$10^{-4}\,M_\odot$, rich in peculiar nucleosynthetic products.

The key nuclear reactions of the hot CNO and of the secondary cycles active in novae are well characterized. The Hot CNO is dominated by the chain $^{12}\mathrm{C}(p,\gamma)^{13}\mathrm{N}(\beta^{+}\nu)^{13}\mathrm{C}(p,\gamma)^{14}\mathrm{N}$ limited by $^{14}\mathrm{N}(p,\gamma)^{15}\mathrm{O}$ in the beta-limited regime. The CNO breakout at $T > 4 \times 10^{8}$ K sees $^{15}\mathrm{O}(\alpha,\gamma)^{19}\mathrm{Ne}$ break the CNO cycle, carrying the flow to $^{19}\mathrm{F}$, $^{22}\mathrm{Na}$ and beyond; it is active mainly in ONe novae. The NeNa cycle $^{20}\mathrm{Ne}(p,\gamma)^{21}\mathrm{Na}(\beta^{+}\nu)^{21}\mathrm{Ne}(p,\gamma)^{22}\mathrm{Na}$ produces abundant $^{22}\mathrm{Na}$, observationally traceable. The MgAl cycle $^{24}\mathrm{Mg}(p,\gamma)^{25}\mathrm{Al}(\beta^{+}\nu)^{25}\mathrm{Mg}(p,\gamma)^{26}\mathrm{Al}$ produces $^{26}\mathrm{Al}$ in significant quantities in the ONe novae. The SiP chain $^{30}\mathrm{P}(p,\gamma)^{31}\mathrm{S}$ is active in the extreme ONe regime. The typical yields per event and their observational significance are summarized in the following table:

The cross sections critical for nova yields include $^{18}\mathrm{F}(p,\alpha)^{15}\mathrm{O}$, $^{18}\mathrm{F}(p,\gamma)^{19}\mathrm{Ne}$, $^{25}\mathrm{Al}(p,\gamma)^{26}\mathrm{Si}$, $^{30}\mathrm{P}(p,\gamma)^{31}\mathrm{S}$. Direct measurements in underground laboratories (LUNA at Gran Sasso, n_TOF at CERN, JUNA at Jinping, DRAGON at TRIUMF) have reduced the rate uncertainties to $10$-$20\%$ for most of these reactions — a precision sufficient to constrain the nova yields quantitatively with synthesis uncertainties of $30\%$ for the individual isotopes.

Nova yields and Galactic impact

Novae are frequent — about 30 per year in the Milky Way, with a rate that varies by a factor 2-3 with the ambient metallicity and with the mean mass of the progenitor WDs — and although the mass expelled per event is small, integrated over the Hubble time they contribute significantly to the Galactic budget of some specific isotopes. They are the dominant source of $^{15}\mathrm{N}$, the almost exclusive site of $^{17}\mathrm{O}$, and an important source of post-BBN $^{7}\mathrm{Li}$ and of living Galactic $^{26}\mathrm{Al}$. The estimated partition between novae and other sites for the key isotopes is approximately: $^{15}\mathrm{N}$ about $50\%$ from novae (the rest from core-collapse SNe via the $\nu$-process); $^{17}\mathrm{O}$ about $100\%$ from novae (almost exclusive site); $^{26}\mathrm{Al}$ $20$-$50\%$ from novae (the rest from Wolf-Rayet stars, intermediate-mass AGB, and core-collapse SNe); post-BBN $^{7}\mathrm{Li}$ $\sim 50\%$ from novae, with the remaining contributions from GCR spallation (chapter 2), AGB HBB (chapter 4) and the $\nu$-process.

The most direct observational confirmation of the nova mechanism comes from the detection of $^{7}\mathrm{Be}$ — which decays into $^{7}\mathrm{Li}$ via electron capture with $\tau_{1/2} = 53$ d — in the spectra of Nova Cygni 2013 (Tajitsu et al. 2015) and of V959 Mon (Izzo et al. 2018). The spectroscopic detection of the $^{7}\mathrm{Be}$ II absorption line at $\lambda 313{.}1$ nm and $\lambda 313{.}0$ nm in the expanding ejecta directly confirms the beryllium transport mechanism of Cameron-Fowler hypothesized decades ago: in a nova explosion, the accreted $^{3}\mathrm{He}$ produces $^{7}\mathrm{Be}$ via $^{3}\mathrm{He}(\alpha,\gamma)^{7}\mathrm{Be}$ at $T \sim 10^{8}$ K at the base of the envelope, and the rapid convection transports $^{7}\mathrm{Be}$ toward the cold surface where it later decays into $^{7}\mathrm{Li}$ — preserved from further mixing. The $\gamma$-ray detection of the $^{26}\mathrm{Al}$ decay (the $1{.}809\,\mathrm{MeV}$ line) by INTEGRAL/SPI provides an integrated Galactic flux of $\sim 4 \times 10^{-4}$ ph/cm$^{2}$/s, corresponding to a total mass of living $^{26}\mathrm{Al}$ in the Galaxy of $\sim 2\,M_\odot$ — of which the nova contribution is estimated at $0{.}3$-$1\,M_\odot$, an important but not dominant fraction of the total.

The main uncertainties in the nova yields are progressively reduced by modeling progress. The mass accreted before ignition depends on the accretion rate, the WD mass and the WD equation of state, with factor 2-3 variations that notably change the expelled mass. The WD-substrate mixing ratio controls how much C and O of the WD enters the accreted layer, and therefore how much CNO seed is available for proton capture; recent MHD models (Casanova et al. 2011, José, Denissenkov [Denissenkov et al. 2014] ) indicate active mixing via Kelvin-Helmholtz instabilities during the pre-burst phase, reducing the uncertainty on the final CNO yields. The cross sections of the key reactions listed above remain a source of uncertainty at $10$-$20\%$, being reduced by the new LUNA-MV, JUNA, DRAGON programs. The 3D simulations of novae (Casanova et al. 2011, José-Casanova 2018) show that the explosion is not spherically symmetric and that the ejecta have a “clumpy” structure with composition dispersion $\sim 30\%$ among different clumps, but the mean composition of the ejecta is similar to that of the 1D models — a result that justifies the continued use of 1D models for the predictions of integrated Galactic yield.

X-ray bursts and the rp-process

A neutron star in an LMXB binary system accretes hydrogen and helium from its main-sequence or sub-giant companion. The NS surface sits under an enormous gravitational field — about $10^{14}$ cm/s$^{2}$, a billion times the Earth’s gravity, with escape velocity $\sim 0{.}1\,c$ — and the accreted material rapidly compresses into a very thin layer ($\sim 10$ m thick) of density $\sim 10^{5}$-$10^{6}$ g/cm$^{3}$. When the layer reaches a critical mass $\sim 10^{-12}$-$10^{-11}\,M_\odot$, the thermonuclear burning of H and He ignites explosively: in a few seconds all the accreted matter is fused through a rapid chain of proton captures, the rp-process (rapid proton capture). The processed matter is not expelled into the interstellar medium — the escape velocity is too large compared with the convective velocities reached during the burst — but the phenomenon is observed as a brief flash of thermal X-rays with effective temperature $T_{\mathrm{bb}} \sim 1$-$2$ keV: the classic Type I X-ray burst, distinct from Type II bursts which have a non-thermonuclear, accretive origin.

The temporal sequence of a Type I XRB unfolds in six phases. During the accretion, matter (fractions $X \sim 0{.}7$, $Y \sim 0{.}3$, small $Z$) is deposited onto the NS at a rate $\dot M \sim 10^{-9}$-$10^{-8}\,M_\odot/\mathrm{yr}$, forming a progressively thicker surface layer. During the compression, the accreted layer grows for hours-days and the $T$ at the base reaches $\sim 10^{8}$ K. The ignition starts when at $T \sim 5 \times 10^{8}$ K the $3\alpha$ runaway activates on the pre-existing He, instantaneously releasing $\sim 10^{19}$ erg/g — energy sufficient to drive the rapid ignition of the residual H. The H/He burning via rp-process proceeds at the peak temperature $T \sim 1$-$2 \times 10^{9}$ K: the rapid chain of proton captures $(p,\gamma)$ progresses toward p-rich nuclei in the band $A = 60$-$100$, with waiting points at specific nuclei. The $\beta^{+}$ decay and cooling over $\sim 10$-$100$ s let the layer stabilize; the processed matter remains on the NS and, under subsequent accretion, is compressed further into deep layers of the neutron crust. After hours-days of accretion, the cycle repeats (recurrence).

The rp-process (rapid proton capture), formally proposed by Wallace and Woosley in 1981, operates through the schematic sequence

$$(A, Z) \xrightarrow{(p, \gamma)} (A+1, Z+1) \xrightarrow{\beta^{+}\nu} (A+1, Z) \xrightarrow{(p, \gamma)} \dots$$

The net flow proceeds along the proton drip line, with waiting points at nuclei with $\beta^{+}$ lifetimes of order seconds: $^{64}\mathrm{Ge}$, $^{68}\mathrm{Se}$, $^{72}\mathrm{Kr}$, $^{76}\mathrm{Sr}$. At these waiting points, the next proton capture $(p, \gamma)$ is blocked by an unfavorable Q-value and a wait for $\beta^{+}$ decay sets in — analogously to the r-process waiting points of chapter 6 but in the proton-rich regime. The parallel $\alpha p$-process — sequences of $(\alpha, p)$ reactions — bypasses some waiting points and accelerates the net flow in specific regions. The termination of the rp-process is the so-called SnSbTe cycle: the final path reaches $^{107}\mathrm{Te}$ (which $\alpha$-decays) or $^{105}\mathrm{Sn}$ (which emits protons), and the path does not extend beyond $A \approx 110$. The critical cross sections include $^{15}\mathrm{O}(\alpha,\gamma)^{19}\mathrm{Ne}$, $^{59}\mathrm{Cu}(p,\gamma)^{60}\mathrm{Zn}$, $^{61}\mathrm{Ga}(p,\gamma)^{62}\mathrm{Ge}$, $^{65}\mathrm{As}(p,\gamma)^{66}\mathrm{Se}$; recent measurements via inverse $(\gamma, p)$ reactions in storage rings (GSI), Coulomb breakup (NSCL/FRIB) and indirect ANC methods have significantly reduced the uncertainties. The final composition of the post-burst layer (Schatz, Cyburt, Parikh et al.) is characterized by enrichment in $^{56}\mathrm{Ni}$, $^{60}\mathrm{Zn}$, $^{64}\mathrm{Ge}$, $^{72}\mathrm{Kr}$, $^{96}\mathrm{Pd}$, $^{100}\mathrm{Sn}$, a $^{12}\mathrm{C}$ abundance reduced practically to zero, and the absence of $\alpha$-rich residues (all $\alpha$ consumed in the rp-process).

Implications and prospects

Novae and X-ray bursts offer unique windows onto nuclear processes in extreme conditions — temperatures of hundreds of millions to billions of kelvin, explosive reactions proceeding in seconds, strongly compressible degenerate matter — and are natural laboratories for studying reactions difficult to measure in conventional laboratories, in particular the rp-process which proceeds via nuclei with sub-second lifetimes far from the valley of stability. For Galactic nucleosynthesis, novae are the specific source of some rare but observable isotopes (in particular $^{15}\mathrm{N}$, $^{17}\mathrm{O}$, $^{22}\mathrm{Na}$, $^{26}\mathrm{Al}$); X-ray bursts are interesting more for the nuclear physics of the nuclei at the proton drip line than for their chemical impact, because the processed matter does not propagate into space.

Three development fronts are particularly active over the next five years. The first is the direct measurement of the key reactions of the hot CNO and of the rp-process with radioactive beams at new-generation facilities: $^{18}\mathrm{F}(p,\alpha)^{15}\mathrm{O}$, $^{30}\mathrm{P}(p,\gamma)^{31}\mathrm{S}$, $^{65}\mathrm{As}(p,\gamma)^{66}\mathrm{Se}$ with the RIB facilities FRIB (MSU), RIBF (RIKEN), GANIL-SPIRAL2. The second is the development of 3D nova models with self-consistent MHD simulations of accretion, WD-substrate mixing and eruption, with resolution adequate to capture the Kelvin-Helmholtz instability and to confirm/falsify the mixing predictions of the 1D models. The third is the systematic characterization of nova-type presolar grains identifiable in meteorites by their isotopic anomalies — high $^{20}\mathrm{Ne}/^{22}\mathrm{Ne}$, $^{15}\mathrm{N}/^{14}\mathrm{N}$, $^{22}\mathrm{Na}$; the catalog of Amari, Hoppe and collaborators today counts $\sim 100$ candidate grains with a nova signature, and the updated methodological review is Hoppe et al. (2017) [Hoppe et al. 2017] (chapter 4 for the complete treatment of presolar grains as laboratories of individual stellar nucleosynthesis).

Recent observational constraints on novae include several directions. The infrared spectroscopy of novae by JWST has allowed the identification of the CO band at $4{.}7\,\mu\mathrm{m}$ in the ejecta, with a direct measurement of the $^{12}\mathrm{C}/^{13}\mathrm{C}$ ratio showing values $\sim 1$-$10$ (against the solar 89) — direct confirmation of the hot CNO regime. The $\gamma$-ray search for $^{22}\mathrm{Na}$ ($1{.}275$ MeV) from individual novae has produced stringent upper limits from INTEGRAL and CGRO, with single-event detection expected as a priority target of COSI (launching 2027) and of the subsequent MeV observatories. The measurements of light-element abundances in old nova nebulae (FK Ser, GK Per, V603 Aql, and other ancient remnants) confirm the presence of Li, Mg and Al with peculiar isotopic compositions attributable to the hot CNO/NeNa/MgAl pattern. For the X-ray bursts, the detailed observations of the clocked bursters (in particular GS 1826-238) with NICER in X-ray timing have constrained the burst light curve and spectra to $\sim 5\%$ precision, confirming the general rp-process models but indicating residual uncertainties on the key mid-rp-process cross sections ($^{59}\mathrm{Cu}(p,\gamma)$ and $^{61}\mathrm{Ga}(p,\gamma)$) that require further direct measurements.

Classical novae and X-ray bursts close the sequence of thermonuclear explosive sites treated in this chapter: together with the core-collapse SNe and the SNe Ia (first part of this chapter), they cover the regime of stellar explosions in which thermonuclear burning is the primary source of nucleosynthesis. What remains to be addressed is the complementary class of explosive sites in which the decisive factor is extreme neutron capture in matter expelled by colliding compact objects — the neutron-star mergers and the r-process — subject of the next chapter.