Classical novae and type I X-ray bursts: challenges for the 21st century

Classical nova explosions and type I X-ray bursts are the most frequent types of thermonuclear stellar explosions in the Galaxy. Both phenomena arise from thermonuclear ignition in the envelopes of accreting compact objects in close binary star systems. Detailed observations of these events have stimulated numerous studies in theoretical astrophysics and experimental nuclear physics. We discuss observational features of these phenomena and theoretical efforts to better understand the energy production and nucleosynthesis in these explosions. We also examine and summarize studies directed at identifying nuclear physics quantities with uncertainties that significantly affect model predictions.


I. INTRODUCTION
"The only true wisdom is in knowing you know nothing." -Socrates The first systematic registry of novae was initiated around 200 BCE by officials of the Chinese imperial court (see Duerbeck 1 for a list of observed novae up to 1604). From the nineteenth century until the 1950s, careful monitoring of the sky with photographic plates led to the discovery of many events. Afterwards and until the 1970s, novae were mainly found through surveys using objective prisms. Since the 1980s, almost all novae have been discovered by amateurs, first using binoculars and later through the analysis of CCD images.
Note that the term nova was originally used to denote all bright, star-like phenomena that suddenly appeared in the night sky and gradually faded with time. It was only in the 1920s and 1930s, through dedicated studies examining the distances to different nova events (distinguishing those of Galactic origin from those at much greater distances) that the distinct terms supernova and nova were introduced to differentiate between the intrinsically brighter supernova events and the dimmer nova events. Several hundred Galactic novae have been discovered to date, with ≈5 events discovered per year. They are characterized by peak luminosities of ≈10 4 -10 5 L ⊙ , light curves of ≈days to months in duration, and mass ejection into the interstellar medium of ≈10 −4 -10 −5 M ⊙ per event. The recurrence time is expected to be ≈10 4 -10 5 years, although the subclass of recurrent novae have recurrence times of only years or decades.
The first X-ray burst was identified in 1975 2 from a previously-known X-ray source, 4U 1820-30. [Note that most X-ray sources are named using letters from the satellites that discovered them (e.g., 4U stands for the 4th catalogue of the satellite Uhuru, the first satellite dedicated to X-ray astronomy), and numbers corresponding to their coordinates in Right Ascension (e.g., 1820 stands for 18h 20min) and Declination (-30 deg) in the sky.
They may also be named after the constellation where they are located and the order of discovery. As a result, a source may have more than one name; e.g., 4U 1820-30 is also known as Sgr X-4.] A similar episode had been observed in 1969 from the source Cen X-4 3 , but the authors related the observed feature to an accretion event and it was not recognized as a new type of source until 1976 4,5 . Cen X-4 is still the nearest-known XRB source (at ≈1 kpc) and has yielded the brightest burst ever recorded (≈50 Crab = 50 × 2.4×10 −8 erg s −1 cm −2 in the 2-10 keV band). Roughly 100 bursting systems have been identified in the Galaxy, with light curves of ≈10 -100 s in duration, recurrence periods of ≈hours to days and similar peak luminosities to those of classical novae. Calculations indicate that radiative winds generated during some bursts may eject material; studies are ongoing to examine the viability of detecting absorption features arising from this material.
Both classical nova explosions (CN) and type I X-ray bursts (XRBs) arise from thermonuclear runaways within the accreted envelopes of compact objects in close binary systems, with orbital periods often less than 15 hours. Generally in a classical nova, H-rich material is transferred from a low mass main sequence or red giant star onto the surface of a white dwarf star. In a type I X-ray burst, a neutron star interacts with a similar low mass companion star; observations are consistent with the accretion of material enriched in H, He or both. Typical accretion rates in these events range from 10 −10 -10 −9 M ⊙ /yr, although the range and implications of different accretion rates (resulting in e.g., stable or marginally stable burning for an accreting neutron star) are still under investigation. As accretion proceeds, the envelope is gradually compressed and becomes degenerate. The temperature of the envelope increases, creating conditions favorable to the ignition of the accreted fuel through nuclear reactions. These reactions, once initiated, drive further reactions, leading to the thermonuclear runaway and the corresponding explosion. Note that the degeneracy of the envelope is lifted as the temperature increases at early times. For example, for the accretion of material with Z/A ≈ 0.5 , degeneracy is lifted at T≈30 MK or ≈300 MK for a white dwarf or neutron star envelope, respectively. The difference between CN and XRBs from the viewpoint of mass ejection arises from how in the latter case the necessary escape velocities are never achieved.
In this article, we will focus on standard models of CN and models of XRBs that occur in envelopes containing substantial H and He. We briefly survey the evolution and state-of-theart of our knowledge of these phenomena. We refer the reader to, e.g., Bode and Evans 6 and José and Hernanz 7 (for CN) and, e.g., Lewin et al. 8 , Strohmayer and Bildsten 9 and Parikh et al. 10 (for XRBs) for more extensive reviews. The framework of this article reflects the approach requested by the editors, namely, to address less what is known, and more what is as yet unknown by discussing questions that still need answering and which methods are the most powerful for doing so. In this vein, we present below four headings regarding needs to better constrain predictions from models of classical novae and type I X-ray bursts. For each heading we provide support and background information as appropriate. We certainly do not claim to have summarized all the varied outstanding problems and challenges that remain for these phenomena. (For example, we do not discuss the unexplained oscillations observed in the light curves of XRBs 9,11,12 or in the soft X-ray light curves from novae [13][14][15] , both of which may be indicative of a confined radiating region.) Nonetheless, the issues discussed below represent major tasks or obstacles that need to be addressed to improve our understanding of these thermonuclear explosions.

II. ARE SPHERICALLY SYMMETRIC MODELS STILL NEEDED?
Different methods and numerical approaches have been used to determine the nucleosynthesis accompanying novae and X-ray bursts. One category of models relies on parameterized one-zone (or multi-zone) calculations (e.g., Refs. [16][17][18][19] for models of CN, and Refs. 20-27 for XRB models). These prescriptions (coined by some authors as 0-D!) relate the thermodynamic history of the compact object's accreted envelope with the time evolution of the temperature and density in a single layer (often the innermost) or multiple envelope layers.
These temperature-density-time profiles are frequently determined by means of semianalytical models or extracted from 1-D hydrodynamic calculations. While representing an extreme oversimplification of the thermodynamic conditions characterizing the envelope, the approach has been extensively used as a way to overcome the otherwise computationally prohibitive calculations that a purely hydrodynamic approach would require. Recently, these techniques have been adopted in sensitivity studies of nucleosynthesis in CN and XRBs to variations in rates of nuclear interactions 28-32 (see Section V).
To date, state-of-the-art nucleosynthesis calculations rely exclusively on 1-D hydrodynamic models (e.g., Refs. [33][34][35][36][37][38] for nucleosynthesis in CN, and Refs. [39][40][41][42][43][44][45] , for nucleosynthesis in XRBs). The underlying assumption in all of these models is, obviously, spherical symmetry. The implication is that the explosion is modeled as occurring uniformly (and simultaneously) over a spherical shell. In sharp contrast, these thermonuclear runaways are expected to originate from point-like ignitions. Clearly, detailed nucleosynthesis models require multidimensional hydrodynamic simulations, but this will only be feasible when sufficient computational power is available to model all relevant details of these explosions (see Section III).

A. Classical novae
Perhaps the first discussion of the physical mechanism powering nova explosions appears in Newton's Principia Mathematica: "So fixed stars, that have been gradually wasted by the light and vapors emitted from them for a long time, may be recruited by comets that fall upon them; and from this fresh supply of new fuel those old stars, acquiring new splendor, may pass for new stars". It is worth noting that the revitalization of an old star through the fresh supply of new fuel (although not by comets!) is at the core of the thermonuclear runaway model, in which mass transfer in a binary system plays the required role.
The underlying physics of the nova phenomenon was exposed, in part, through a number of observational breakthroughs, including: • the first optical spectroscopic analysis of nova T CrB 1866 46 • discovery in 1901 of spectroscopic features at 3869 and 3968Å(later identified as Ne III lines) in the spectra of GK Per 47,48 , suggesting the existence of different nova types (although the first simulations of novae hosting oxygen-neon (ONe) white dwarfs were not performed until the mid-1980s 49 ) • the explanation of the observed spectral features as due to ejection of a shell from a star 50 • the link between the minimum in the DQ Her light curve and episodic dust formation 51 • discovery of the binary nature of DQ Her 52 • systematic studies of novae revealing that binarity is a common property of most cataclysmic variables (novae, in particular [53][54][55][56] While the observational picture was firmly established on the basis of ejection from the surface of a star, explanations of the physics behind the burst were not offered until the middle of the twentieth century. Indeed, its thermonuclear origin was first theorized by Schatzmann 57,58 , although incorrectly interpreted as due to nuclear fusion reactions involving 3 He. Other notable theoretical contributions were made in the late 1950s 59,60 ; attempts to compute the explosion in a hydrodynamic frame were published a decade later [61][62][63] . The idea that CNO enhancement is critical for the energetics of the explosion was first proposed by Starrfield et al. 64,65 . Several groups have analyzed in detail the nucleosynthesis accompanying nova explosions 33,37,66,67 by coupling nuclear reaction networks, containing about a hundred species and a few hundred nuclear interactions, directly to 1-D hydrodynamic models. While these models have been successful in reproducing the gross observational features of nova outbursts (e.g., nucleosynthesis, peak luminosities L peak , light curves), the exact amount of material ejected by the explosion is still a matter of debate. A next generation of models with state-ofthe-art input physics, methods to treat rotation, and better techniques to tackle convective transport (i.e., based on results from 3-D models), will be needed to shed light into these matters.

B. Type I X-ray bursts
The first estimates of the amount of nuclear energy that may be released from the fusion of H-rich material in envelopes accreted by neutron stars were made by Rosenbluth et al. 68 .
The scenario was revisited shortly afterwards in studies 69,70 that revealed that nuclear fusion may trigger thermonuclear runaways. The thermonuclear origin of type I X-ray bursts, resulting from unstable nuclear fusion on the surfaces of neutron stars, was first suggested by Woosley and Taam 71 (for bursts driven through He-burning) and Maraschi and Cavaliere 72 (for bursts driven through H-burning). The mechanism was further defined through a number of increasingly detailed simulations 20,73-82 . The gross observational features of type I XRBs were succesfully reproduced by early studies: using dimensional analysis, Joss 83 and Lamb and Lamb 84 inferred recurrence periods of about 10 000 s, accreted envelope masses of ≈ 10 21 g, and an overall energy release of 10 39 erg per burst (assumed to be driven through He burning). Other estimates of burst properties included peak luminosities L peak ≈ 10 38 erg s −1 , light curve rise times of ≈ 0.1 s, and decay times of ≈ 10 s, on the basis of nuclear energy transport from the deepest envelope layers to the outermost region. Another important observational constraint matched by thermonuclear models of type I XRBs was the so-called α parameter, or ratio of persistent over burst luminosities.
As shown in the pioneering work of Joss 74 , the key parameters in the modeling of type I X-ray bursts are the mass accretion rate, the neutron star mass and central temperature (which in turn determines the initial surface luminosity of the neutron star) as well as the metallicity of the accreted material. This work confirmed the estimates obtained from previous dimensional analysis studies. Furthermore, it showed that all the accreted fuel is essentially consumed during the burst (processing H-rich material into mostly Fe-peak elements), due to an efficient CNO-breakout, in sharp contrast with the much more limited nuclear activity exhibited by classical novae. As well, most of the energy released during an X-ray burst is emitted as X-rays from the star's photosphere.
Detailed nucleosynthesis studies under the characteristic temperatures and densities reached in neutron star envelopes (with peak values around 10 9 K and 10 6 g cm −3 ) require huge nuclear reaction networks, with hundreds of isotopes and thousands of nuclear interactions. Initially, this was only feasible in the framework of one-zone models 21,[25][26][27] . These pioneering studies revealed that the main nuclear reaction flow is driven by the rp-process (rapid proton-captures and β + -decays), the 3α-reaction, and the αp-process (a sequence of (α, p) and (p, γ) reactions). Only recently has it been possible to use detailed nuclear reaction networks in a purely hydrodynamic framework (1-D -see Refs. [39][40][41] and references therein). The extension of the nuclear activity in XRBs is still a matter of debate, since recent experimental studies 85 have shown difficulties in reaching the SnSbTe-mass region, previously identified as the likely nucleosynthesis endpoint 27 . Additional difficulties in the modeling arose from the discovery of highly magnetized neutron stars (with B ≥ 10 12 G), in which mass accretion from the stellar companion is expected to be funnelled onto the neutron star magnetic poles, enhancing the local accretion rates in those spots by ≈ three orders of magnitude 77 . A number of different ignition regimes for specific ranges of mass accretion rates have been inferred for accretion of solar-like material 20,86 .
General relativistic corrections to calculations performed using a Newtonian framework were first incorporated into models in the 1980s 75,76,79,82 . In short, their effect is a net reduction of the expected peak luminosities and an enhancement of the recurrence times by a factor of 1 + z, with z being the gravitational redshift of the neutron star.
While the modeling of type I XRBs resulting from the combined burning of H and He has been emphasized recently (in part due to the interest of experimentalists in constraining the associated nucleosynthesis), more work needs to be done to explore the nature of superbursts (roughly 1000 times more energetic than type I XRBs, with recurrence times on the order of a year) 87-89 and bursts intermediate in both energy and duration to typical type I XRBs and superbursts 90,91 . Moreover, 1-D models are still needed to resolve possible discrepancies in the extent of the nuclear activity for low-metallicity environments (e.g., Refs. 40,41 ), the possible nuclear origin of double-or multiple-peaked bursts 92,93 , and the possible contribution of type I X-ray bursts to Galactic abundances through radiation-driven winds 73,94-97 .

III. TOWARD MULTIDIMENSIONAL MODELS
The assumption of spherical symmetry has been adopted in the vast majority of models of CN and XRBs, with which gross observable features of these phenomena have been reproduced. It is clear, however, that this assumption excludes details associated with the manner in which a thermonuclear runaway initiates (presumably as a point-like ignition) and propagates. Flames may propagate supersonically (detonations) or subsonically (deflagrations). In both CN and XRBs, burning fronts are expected to propagate subsonically. Such deflagration models are more difficult to compute than detonation models. Indeed, standard compressible hydrodynamics codes usually fail when applied to deflagrations because of the long integration times required. This is a major reason why more multidimensional models of, e.g., Type Ia supernovae 98 (in which at least part of the explosion proceeds as a detonation, according to current models) have been published than of classical novae or type I X-ray bursts.
The first study of localized runaways in degenerate envelopes, involving white dwarfs or neutron stars, was carried out by Shara 99 on the basis of semianalytical models. He suggested that heat transport was too inefficient to spread a localized flame (i.e., the diffusively propagated burning wave may require tens of years to extend along the entire white dwarf surface), and concluded that localized, volcanic-like eruptions were likely to occur. Unfortunately, while this analysis did consider radiative and conductive energy transport, it ignored the major role played by convection on the propagation of the burning front. Indeed, as soon as superadiabatic gradients are established, macroscopic mass elements are exchanged between hotter and cooler regions of the envelope through convective transport. These mass elements ultimately dissolve in the environment, releasing their excess heat. Because of its complexity, the treatment of heat transfer in convective zones is often tackled by means of phenomenological approaches (i.e., mixing-length theory). Unfortunately, convection is a truly multidimensional process that cannot be reliably modeled under the assumption of spherical symmetry.
The importance of multidimensional effects in explosions occurring in thin stellar shells was revisited by Fryxell and Woosley 100 . The study concluded that the most likely scenario involves runaways propagated by small-scale turbulence in a deflagrative (subsonic) regime, leading to the horizontal spread of the front at typical velocities of v def ∼ 10 4 cm s −1 (for CN) and v def ∼ 5 × 10 6 cm s −1 (for XRBs).
The first attempts to address the importance of multidimensional effects on nova explosions in a truly hydrodynamic framework were performed by Shankar et al. 101 thin slice of the star, 0.1π rad, was considered). These new simulations showed that the thermonuclear runaway initiates as a myriad of irregular, localized eruptions that appear close to the envelope base, each surviving for only a few seconds. Turbulent diffusion efficiently dissipates any local burning around the core, and hence the flame must eventually spread along the entire envelope. Large convective eddies, extending up to 2/3 of the envelope height (with typical velocities v conv ∼ 10 7 cm s −1 ) were found. The core-envelope interface appears to be convectively unstable, with CO-rich material being efficiently dredged-up from the outermost white dwarf layers. This mechanism allows for metallicity enhancement of the envelope through Kelvin-Helmholtz instabilities, at levels that agree with observations (∼ 20 − 30%, by mass 106 ). Moreover, the simulations revealed that despite the differences found in the convective flow patterns in 1-D and 2-D models, the expansion and progress of the 2-D burning front towards the outer envelope quickly becomes almost spherically symmetric, even though the initial burning process was not. stable eddies, which led to more limited dredge-up and mixing episodes. Such discrepancies were even more striking in 3-D simulations 108 , in which the limited dredge-up of core material translated into maximum envelope velocities that were a factor ∼ 100 smaller than the corresponding escape velocity; presumably, no mass ejection resulted. The controversy was carefully analyzed by Glasner et al. 109 who concluded that the early stages of the explosion, when the evolution is quasistatic, are extremely sensitive to the adopted outer boundary conditions.
Confirmation of the feasibility of the core-envelope mixing scenario was provided by a set of independent 2-D simulations 110,111 performed with the Eulerian code FLASH. These models showed that Kelvin-Helmholtz instabilities can naturally lead to self-enrichment of the accreted envelope with core material, at levels that agree with observations. Two dimensional prescriptions for convection are, however, unrealistic 112 . Indeed, the conservation of vorticity imposed by a 2-D geometry forces the small convective cells to merge into large eddies, with a size comparable to the pressure scale height of the enve-lope. In contrast, these eddies will become unstable and break up in 3-D (in fully developed turbulent convection), transferring their energy to progressively smaller scales 113,114 . These smaller structures, vortices and filaments, will undergo a similar fate down to approximately the Kolmogorov scale. A pioneering 3-D simulation of mixing at the core-envelope interface during nova explosions 115 has shown hints of the nature of the highly fragmented, chemically enriched and inhomogeneous nova shells observed in high-resolution spectra. This, as predicted in the Kolmogorov theory of turbulence, has been interpreted as a relic of the hydrodynamic instabilities that develop during the initial ejection stage. Although such inhomogeneous patterns inferred from the ejecta have usually been assumed to result from uncertainties in the observational techniques, they may represent a real signature of the turbulence generated during the thermonuclear runaway.
For X-ray bursts, only preliminary 2-D simulations of specific aspects of the explosions (such as flame propagation 116 or the early convective stages preceding ignition 117 ) have been conducted to date. Attempts to overcome the difficulties associated with multidimensional modeling have included the filtering of acoustic waves. This allows for larger time steps since, in this approximation, this quantity is now determined by the fluid velocity rather than by the speed of sound. Several such "low-Mach number" codes have been developed in recent years [116][117][118] . It is not clear why more emphasis has been placed on the multidimensional modeling of novae rather than X-ray bursts. We do note that some of the groups that performed pioneering multidimensional nova simulations (based in e.g., Arizona, Garching, and Chicago) eventually shifted towards the modeling of Type Ia supernovae. Only two groups (based in Jerusalem and Barcelona) are currently involved with multidimensional nova models, while only one (based in Stony Brook) is actively developing 2-D XRB simulations.
All of these multidimensional simulations are extremely time-consuming. As a result, they rely only on very simplified nuclear reaction networks (typically containing about a dozen species). Furthermore, simulations have followed the evolution of a nova over only a very small fraction of the overall time associated with the event (e.g., ∼ 1000 s near the peak temperature, to be compared with the duration of the accretion stage for a nova outburst, ∼ 10 5 yr). Hence, no reliable nucleosynthesis predictions can be made using current multidimensional models. Finally, the use of Eulerian frameworks do not allow one to follow the progress of the explosion once it reaches dynamic stages, as material would be artificially lost through the edges of the computational domain. A 3-D implicit ALE hydrodynamic code would be best suited to overcome this limitation.

IV. WHEN STELLAR EXPLOSIONS HATE THEORISTS:
OBSERVATIONAL CONSTRAINTS

A. Absorption features in X-ray bursts
The potential contribution of XRBs to Galactic abundances (e.g., of the light p-nuclei often assumed to represent the composition of the entire envelope. In (multi-zone) hydrodynamic simulations, however, the abundances of many species, including these p-nuclei, decrease by more than an order of magntiude relative to their values in the innermost layers because of limited convective transport 41 . Unfortunately it is material from these outermost layers that are most likely to be ejected by any radiation-driven winds. The predicted overproduction factors in these outer regions are several orders of magnitude smaller than those required to account for the origin of Galactic light p-nuclei 41,120 , in contrast with the results reported from one-zone calculations 27 . As such, according to current models, XRBs are unlikely to be dominant contributors to the Galactic abundances of p-nuclei.
The detection of absorption lines in the neutron star atmosphere seems to be the most Recent, more encouraging results include the observation, albeit with limited spectral resolution, of absorption edges from Fe-peak elements in photospheric radius "superexpansion" bursts 131 . Higher spectral resolution observations of these superexpansion bursts (e.g., with Chandra 132 or XMM-Newton 127 , though an exposure time of ≈ 500 ks may be necessary) would be of great interest.

B. Isotopic abundances from nova explosions
Spectroscopic studies of classical nova explosions provide elemental abundances which can be used to constrain predictions of nucleosynthesis in nova models 33,[133][134][135] . Measurements of the relative abundances of different isotopes in nova ejecta could further improve model constraints; these could be provided through measurements of presolar grains or through detections of γ-rays from the decay of radioisotopes produced during the explosion.
Classical novae are Galactic dust factories, as revealed by infrared and ultraviolet observations 106 . The first to realize the importance of dust to constrain nova models were Clayton and Hoyle 136 , who pointed out a number of isotopic signatures that should characterize grains condensed in nova ejecta (e.g., large overproduction of 13,14 C, 18 O, 22 Na, 26 Al or 30 Si relative to solar values). Since then, efforts to identify candidate grains from novae have focused mainly on searching for low 20 Ne/ 22 Ne ratios. This is because noble gases such as Ne do not easily condense into grains; hence, excesses of 22 Ne could be attributed to in situ decay of 22 Na that had been trapped in the grain.
In 2001 the first set of presolar SiC and graphite grains with isotopic compositions similar to nova model predictions were measured, after isolation from the Murchison and Acfer 094 meteorites 137,138 . These grains were characterized by low 12 C/ 13 C and 14 N/ 15 N ratios, a high 30 Si/ 28 Si ratio, and close-to-solar 29 Si/ 28 Si values (high 26 Al/ 27 Al and 22 Ne/ 20 Ne ratios were also observed for some of these grains). The composition of these grains, however, was only consistent with diluted abundances from model predictions. That is, mixing between nova ejecta predictions and more than ten times close-to-solar material prior to grain formation was required to match the grain composition. Such mixing may result from the interaction between the ejecta and the accretion disk, or even with the outer layers of the secondary star.
Calculations to test such scenarios are currently in progress (Figueira et al., in preparation).
Later, concerns about the nova paternity of these grains were raised 139 after the identification of three other SiC grains from the Murchison meteorite with similar trends (in particular, low 12 C/ 13 C and 14 N/ 15 N ratios) but additional features (such as non-solar Ti isotopic ratios).
As such, a supernova origin for these grains cannot be excluded 139,140 . The issue is far from being settled since models suggest that rare, more violent nova outbursts in which the nuclear activity may extend beyond calcium can be obtained in very-low metallicity systems 141 or during mass-transfer episodes at low rates 142 .
grains whose composition can be qualitatively matched by nova models have also been identified 143,144 . Overall, only a handful of candidate grains from novae have been isolated.
As such, the implications derived from such analyses are not statistically sound. A larger number of grains of putative nova origin would be very valuable.
Isotopic abundances may also be provided through the detection of predicted γ-ray features from radioisotopes produced in novae [145][146][147][148][149]  between an enhancement factor applied to a rate X and the corresponding change in the yield of a species Y may be deduced). Obviously, results from these types of sensitivity studies are most clearly interpreted when rates are varied by well-defined, temperature-dependent, experimentally-based uncertainties. While this situation may hold for most reaction rates comprising networks coupled to standard models of classical nova explosions (as well as for, e.g., Big Bang nucleosynthesis), it certainly does not apply to networks needed for detailed nucleosynthesis predictions from type I X-ray bursts (especially for ignition conditions where an extended rp process is predicted). Nonetheless, variation of theoretical rates in the network provides guidance to experimentalists as to where resources are best focused, as well as insight into the level of dependence of model predictions on the method used to determine theoretical rates. Suitable variation factors for theoretical rates may be adopted to account for possible discrepancies between predictions of rates from different codes. For example, while these rates are often stated to be reliable, on average, to a factor of ≈ 2, significantly larger deviations have been observed when comparing (i) statistical model rates to experimental rates (up to a factor of ≈ 100 in some cases) and (ii) statistical model rates for a common reaction determined with different codes (up to an order of magnitude) 10 .
As well, different libraries of theoretical rates may be used to test the effects on model predictions of systematic differences (or improvements) in predicted rates.
In this section we review studies that have either identified nuclear physics quantities of interest for predictions from models of classical novae and type I XRBs, or examined the impact of specific measurements on model predictions. We do not discuss experimental or theoretical results that have not been demonstrated to significantly affect model predictions.
On this note, we encourage all relevant studies to test and report the impact of the obtained results in the framework of an astrophysical model whenever possible. have also been performed to examine e.g., the production of the radioisotopes 18 F, 22 Na and We review the impact of the most influential reactions identified in these sensitivity studies below. (Note that nuclear masses and weak interaction rates seem to be sufficiently well known for current nova models.) Often, though not always, an article on a relevant experiment explores the impact of the outstanding uncertainty in a rate using some model. We also include below some of these particular results with significant impact on nucleosynthesis predictions from models.

A. Sensitivity studies for classical nova explosions
Thermonuclear reaction rates with demonstrated impact on nova model predictions:   166 found that the calculated 18 F abundance varied by a factor of ≈ 300 when comparing results using their low and high 18 F+p rates (at 0.2 GK, the ratio of the high to low rate was about one and two orders of magnitude for the (p, γ) and (p, α) rates, respectively). When individually varied by the adopted uncertainties (a maximum of a factor of 15 and a factor of 30 for the (p, γ) and (p, α) rates, respectively, over T peak = 0.1 − 0.4 GK) in the postprocessing studies of Iliadis et al. 28 , the final calculated abundances of 16 O, 17 O and post-processing study conducted with a Monte Carlo approach to rate variations, the 18 F(p, α) reaction is given in a prioritized list of reactions that affect the production of the radioisotope 18 F 168, 169 . Using a multi-zone post-processing approach 160 , Bardayan et al. 174 and Kozub et al. 175 reported that roughly twice as much 18 F was produced when using a (p, α) rate ≈ 1.5 − 2 times lower and ≈ 5 times lower, respectively, than that of Coc et al. 166 at nova temperatures. Chae et al. 176 , also using a multi-zone approach, found that the amount of 18 F produced varies by roughly a factor of two when (p, α) rates differing by roughly a factor of ≈ 10 are used (see also Adekola et al. 177 ). Laird et al. 178 , using a 1-D hydrodynamic model, found that 18 F production varies by roughly a factor of two when two (p, α) rates differing by roughly a factor of two (at 0.2 GK) are used.
Coc et al. 165 , using a semi-analytical approach (a "compromise" between hydrodynamic and one-zone calculations), found that the final abundance of the radioisotope 22 Na increased by a factor of ≈ 1.5 when their 21 Na(p, γ) rate was reduced by a factor of 10, and increased by a factor of ≈ 1.5 − 3 (depending on the white dwarf mass) when their 21 Na(p, γ) rate was reduced by a factor of 100. Using a 1-D hydrodynamic model, José et al. 167 also found that 22 Na production increased by factors of ≈ 1.5 − 3 (depending on the white dwarf mass) when their rate was reduced by a factor of 100.
When individually varied by the adopted uncertainty (a factor of 100) in the postprocessing studies of Iliadis et al. 28 , the final calculated abundances of 21 Ne, 22 Na and 22 Ne varied by at least a factor of two. In a one-zone post-processing study conducted with a Monte Carlo approach to rate variations, the 21 Na(p, γ) reaction is given in a prioritized list of reactions that affect the production of 22 Na 168, 169 . Using a 1-D hydrodynamic model, Bishop et al. 179 and Davids et al. 180 found that 22 Na production decreased by about 20% when results using two rates differing by a factor of ≈ 5 (at 0.2 GK) were compared.
Coc et al., using a semi-analytical approach 165 , compared the yield of 22 Na obtained using different 22 Na(p, γ) rates. Reduced rates by a factor of ≈ 10 or ≈ 50 at 0.2 GK increased the 22 Na yield by a factor of ≈ 10 or ≈ 40, respectively, in their models.
Using a 1-D hydrodynamic model, José et al. 167 found that 22 Na production increased by a factor of ≈ 3 when comparing results using rates that differed by more than one order of magnitude for T > 0.1 GK. In a one-zone post-processing study conducted with a Monte Carlo approach to rate variations, the 22 Na(p, γ) reaction is first in a prioritized list of reactions that affect the production of 22 Na 168,169 . Jenkins et al. 181 and Sallaska et al. 159 compared yields from hydrodynamic models using two 22 Na(p, γ) rates differing by a factor of ≈ 10 and a factor of ≈ 3 (both at 0.2 GK), respectively; they found that the 22 Na yield varied by a factor of ≈ 3 and ≈ 2, respectively. in their (p, α)/(p, γ) rate ratio was ≈ 30%, while that from NACRE 161 was a factor of ≈ 3 (with similar central value). This led to improved constraints on the production of isotopes between 22 Na and 29 Si; e.g., the uncertainty in the production of 26 Al was reduced from a factor of ≈ 3 to ≈ 20%.  Al(p, γ) rate) in the post-processing studies of Iliadis et al. 28 , the 26g Al(p, γ) and 26m Al(p, γ) rates affected the final calculated abundances of 26 Al and 26 Mg, respectively, by at least a factor of two. In a one-zone post-processing study conducted with a Monte Carlo approach to rate variations, the general 26 Al(p, γ) reaction is given in a prioritized list of reactions that affect the production of 26 Al 168,169 . Ruiz et al. 186 remeasured the strength of the 188 keV resonance in 26g Al(p, γ) and found it to be ≈ 2/3 of the previously assumed value 165,167 . Using a 1-D hydrodynamic model, they compared results using two rates that differed by ≈ 20% over nova temperatures and found a variation in the 26 Al yield of about 20%.   28,169,191,192 . Some nova models that explore quite extreme, rare scenarios (low accretion rates 142 or accretion of extremely metal-poor material 141 ) have been published in recent years. It may be interesting to explore the role of nuclear uncertainties in these models, for completeness.
In summary, most of the nuclear physics uncertainties for models of novae have been identified and addressed by experiments. In particular, significant recent progress has been made towards better determining the rates of the 18 F(p,α) 15 O 178,193-197 , 25 Al(p,γ) 26 Si 184,185,[198][199][200][201] and 30 P(p,γ) 31 S 189,202-204 reactions, often stated as dominant contributors to remaining uncertainties in nova nucleosynthesis 7,205 . Nevertheless, a comprehensive sensitivity study using a hydrodynamic model with current rate uncertainties 163,164,206 should be performed to end the debate of whether studies based solely on post-processing treatments are fully reliable.

B. Sensitivity studies for type I X-ray bursts
For models of type I XRBs with parameters (e.g., accretion rate, composition of accreted material) chosen to favour nucleosynthesis that eventually proceeds via the rp process, detailed results from a comprehensive sensitivity study have only been reported in Parikh et al. 31,32 . Post-processing of temperature-density-time trajectories from single zones (sampling parameter space in peak temperature, burst duration and composition of accreted material) was used with both the individual variation of ≈ 3500 rates and the simultaneous variation of all rates using a Monte Carlo method (see also Roberts et al. 30 for preliminary results from a post-processing sensitivity study using a Monte Carlo method for rate variations).
Reactions influencing the predicted nucleosynthesis, as identified using the two methods, were generally in excellent agreement 31 . (We note that studies have shown that, at least for one-zone models, there appears to be a strong correlation between the sensitivity of the burst ashes and the sensitivity of the light curve to individual rates 207,208 .) Furthermore, reaction Q-values (and hence, nuclear masses) with uncertainties sufficiently large to significantly impact predicted yields were identified (see also Brown et al. 209 and Fleckenstein 210 for important masses identified through one-zone models). Knowledge of these masses is critical to understanding the (p,γ)-(γ,p) reaction rate equilibria that develop at waiting points along the rp process and the subsequent evolution of abundances beyond these nuclei 119,209,211 .
Weak interaction rates as determined in the laboratory were also varied in this study, by both experimental uncertainties (which had no impact on final yields 31 ) and larger factors.
Although this approach can also probe the influence of a particular nuclear physics uncertainty on the predicted nuclear energy generation rate E gen during a burst, it is usually not sufficient to examine in detail the impact on predictions of the chief observable, the XRB light curve. This is because these one-zone studies neglect crucial hydrodynamic effects such as convection and the finite diffusion time for energy to escape from the accreted envelope.
Furthermore, the post-processing approach is not self-consistent; that is, the thermodynamic history employed is independent of changes in the nuclear energy generation rate due to a rate variation.
Further progress has been made through (i) calibrating a one-zone model to a 1-D hydrodynamic model by adjusting ignition conditions until the light curve and final ashes agree as much as possible, (ii) identifying reaction rates (through the individual variation approach) to which the calibrated one-zone model shows the greatest sensitivity, followed by (iii) considering these rate variations in a 1-D hydrodynamic model to assess the impact on light curves. Preliminary and partial results from such studies have been reported 29,207,208 . The impact of different rate libraries 25,119,206 , different sets of proton separation energies (calculated using different compilations of masses) 209,210,212,213 , different network sizes 22,26 , and variations in groups of weak interaction rates 39 has also been explored.
We summarize the impact of the most influential rates and masses from these sensitivity studies below. We also include below results from limited investigations of the impact of individual reaction rate uncertainties (e.g., from explorations of the impact of a new rate calculated following an experiment) on predictions from 1-D hydrodynamic or one-zone models coupled to large networks.
Nuclear physics quantities with demonstrated impact on XRB model predictions: a. Thermonuclear reaction rates When individually varied by the adopted uncertainty (a factor of 10) in the postprocessing studies of Parikh et al. 31 , the 14 O(α, p) rate led to significant variations (by greater that 5%) in the nuclear energy generation rate E gen during a burst. Hu et al. 214 , also using a one-zone post-processing model, also found significant changes to the profile of E gen vs time when comparing two rates that differed by factors of 2 − 36 over 0.1 − 2 GK. The use of two other rates that differed by a factor of ≈ 5 at 0.35 GK and less than 10% at 1 GK led to essentially identical E gen profiles in that study.
In a post-processing study conducted with a Monte Carlo approach to rate variations 30 , the 15 O(α, γ) reaction rate is stated to affect the nuclear energy generation rate during early stages of the burst. When individually varied by a factor of 3 or 10 in the post-processing studies of Parikh et al. 31 , the 15 O(α, γ) rate led to significant variations (by greater that 5%) in the nuclear energy generation rate E gen during a burst. • 18 Ne(α, p) 21 Na When individually varied by a factor of 3 or 10 in the post-processing studies of Parikh et al. 31 , the 18 Ne(α, p) rate led to significant variations in the nuclear energy generation rate E gen during a burst (by greater that 5%, see also Groombridge et al. 218 ); variation of the rate by a factor of 10 also significantly changed the final yields of at least three species by at least a factor of two. When varied by a factor of 100 in a one-zone model "calibrated" to reproduce results from a 1-D hydrodynamic code 207  • 23 Al(p, γ) 24 Si In a post-processing study conducted with a Monte Carlo approach to rate variations 30 , the 23 Al(p, γ) reaction rate is stated to strongly influence E gen and the nucleosynthesis during the burst. When individually varied by a factor of 10 in the post-processing studies of Parikh et al. 31 , the 23 Al(p, γ) rate led to significant variations (by greater that 5%) in the nuclear energy generation rate E gen during a burst. When varied by a factor of 100 in a one-zone model "calibrated" to reproduce results from a 1-D hydrodynamic code and later by a temperature-dependent uncertainty in a 1-D hydrodynamic model 207,208 , the rate of this reaction led to significant changes in the predicted light curve. b. Nuclear masses To constrain models of type I XRBs, nuclear masses are desired to a precision of better than ≈ 50 keV 32,211 . Through studies with a one-zone model, Brown et al. 209 identified species along the path of the rp process for which a more precise mass would better constrain their calculations: 61 Ga, 62 Ge, 64 Ge, 65 As, 66 Se, 68 Se, 69 Br, 70 Kr, 72 Kr, 73 Rb, and 74 Sr. Later, following post-processing sensitivity studies in which mass measurements needed to better constrain reaction Q-values were examined, Parikh et al. 32 encouraged measurements of the masses of 26 P, 27 S, 43 V, 46 Mn, 47 Mn, 51 Co, 56 Cu, 62 Ge, 65 As, 66 Se, 69 Br, 70 Kr, 84 Nb, 85 Mo, 86 Tc, 87 Tc, 89 Ru, 90 Rh, 96 Ag, 97 Cd, 99 In, 103 Sn, 106 Sb, and 107 Sb, and more precise measurements of the masses of 31 Cl, 45 Cr, and 61 Ga, 71 Br, 83 Nb, and 86 Mo. Fleckenstein 210 , using a one-zone XRB model, assessed the role of uncertainties in masses of species in the region A = 80 − 105, and identified the most influential masses as 94 Ag, 93 Pd, 91 Rh, 94 Pd, 80 Zr, 95 Ag, 90 Ru, 99 In, 98 Cd, 91 Ru, 103 Sn, and 100 In.
Of the above masses, according to the 2012 Atomic Mass Evaluation 223 , experimental determinations of the masses of 26 P, 27 S, 46 Mn, 56 Cu, 62 Ge, 66 Se, 70 Kr, 73 Rb, 74 Sr, 84 Nb, 86 Tc, 89 Ru, 90 Rh, 97 Cd, 99 In, 94 Ag, 93 Pd, 91 Rh, and 95 Ag are still needed. In addition, the experimentally-known masses of 31 Cl, 61 Ga, 65 As, 80 Zr, 83 Nb, 96 Ag, 100 In and 103 Sn may be needed to better precision. We note that the impact on predictions from XRB models coupled to large networks has been examined for recent measurements of particular  21 Na rates (see above). Moreover, since "stellar" (temperature-and densitydependent) weak interaction rates should ideally be used rather than "laboratory" rates, we encourage the development of improved, consistent treatments for calculating stellar weak interaction rates for all isotopes in a typical XRB network. (Following a few recent measurements 120,241 , we note that "laboratory" weak interaction rates are available for most species involved in XRBs; as well, beta-delayed proton decay seems to have little influence

VI. OUTLOOK
When feasible, modelers should work to evolve multidimensional hydrodynamic model calculations of both classical nova explosions and type I X-ray bursts from the accretion stage through the explosion and ejection (for novae) stages. From the point of view of the associated nucleosynthesis, however, the limited nuclear networks coupled to these computationally-demanding simulations assures the endurance of results from 1-D models for now.
We have attempted to summarize reactions and nuclear masses that have been identified in previous studies as having uncertainties that significantly affect model predictions of classical novae and type I X-ray bursts. Nevertheless, new comprehensive sensitivity studies are needed, ideally using 1-D hydrodynamic models coupled to updated networks with current nuclear physics uncertainties. These studies should also focus upon resolving possible discrepancies observed between current XRB models, such as the impact of uncertainties in the 15 O(α, γ) or 18 Ne(α, p) rates on predicted light curves or discerning the exact role of the metallicity of the accreted material on observable predictions. Detailed calculations using, e.g., sufficiently large numbers of type I X-ray bursts to ensure convergence of the calculations, would help to shed light on these issues. In the meantime, experimentalists should build further upon recent accomplishments to fully characterize the rates of reactions such as 18 F(p, α), 23 Mg(p, γ), 25 Al(p, γ) and 30 P(p, γ) for nova explosions and 14 O(α, p), 15 O(α, γ), 22 Mg(α, p), 23 Al(p, γ), 30 S(α, p), 59 Cu(p, γ) and 65 As(p, γ) for XRBs. Consistent treatments for calculating stellar weak rates for all isotopes in a typical XRB network are also needed.
New observatories, such as the recently-launched NuSTAR 248 and proposed LOFT 249 missions, hold promise for the identification of absorption features from XRBs. Such results could provide a needed direct constraint on nucleosynthesis in these environments. As well, prospects for the ejection of nuclear-processed material by radiation-driven winds from XRBs still need to be evaluated through detailed models. For novae, UV observations had often been used in the past to determine abundances of ejected material, and the WSO-UV 250 project will help to further advance such studies. High resolution X-ray spectra of nova ejecta have been obtained by e.g., Chandra 132 and XMM-Newton 127 , however improvements in expanding atmosphere models are necessary before abundances can be reliably extracted from these spectra.