THE EFFECTS OF THE pep NUCLEAR REACTION AND OTHER IMPROVEMENTS IN THE NUCLEAR REACTION RATE LIBRARY ON SIMULATIONS OF THE CLASSICAL NOVA OUTBURST

The observable consequences of accretion onto white dwarfs (WDs) in close binary stellar systems include the classical nova (CN), symbiotic, and recurrent nova (RN) outbursts, and the possible evolution of the super soft, close binary, X-ray sources (SSS) to Type Ia Supernovae (SNe Ia) explosions (Starrfield et al. 2004). This diversity of phenomena occurs because of differences in the properties of the secondary star, the mass of the WD, the stage of evolution of the binary system (the luminosity of the WD and the rate of mass accretion onto the WD), and the binary characteristics (orbital separation and mass ratio).

A CN explosion occurs in the accreted hydrogen-rich envelope on the low-luminosity WD component of a cataclysmic variable (CV) system. Gas is lost by the secondary star and accreted by the WD. One-dimensional (1D) hydrodynamic studies, which follow the evolution of the material falling onto the WD from a bare core to the explosion, show that the envelope grows in mass until it reaches a temperature and density at its base that is sufficiently high for ignition of the hydrogen-rich fuel to occur. Both observations of the chemical abundances in CN ejecta and theoretical studies of the consequences of the thermonuclear runaway (TNR) in the WD envelope strongly imply that mixing of the accreted matter with core matter occurs at some time during the evolution to the peak of the explosion. How and when the mixing occurs is not yet known (for discussions, see Gehrz et al. 1998, hereafter G1998; Starrfield 2001; Starrfield et al. 2008, hereafter S2008).

If the bottom of the accreted layer is sufficiently degenerate and well mixed with core material, then a TNR occurs and explosively ejects core plus accreted material in a fast CN outburst. The evolution of nuclear burning on the WD and the total amount of mass that it accretes and ejects depends upon: the mass and luminosity of the underlying WD, the rate of mass accretion onto the WD, the chemical composition in the reacting layers (which includes the metallicity of the CV system), the convective history of the envelope, and the outburst history of the system.

The observed levels of enrichment of elements ranging from carbon to sulfur in CNe ejecta confirm that there is significant dredge-up of matter from the core of the underlying WD which enable CNe to contribute to the chemical enrichment of the interstellar medium (ISM). Moreover, extensive studies of CNe with IUE and the resulting abundance determinations reveal the existence of both oxygen–neon–magnesium (ONeMg) WDs and carbon–oxygen (CO) WDs in CN systems (G1998). Therefore, CNe participate in the cycle of Galactic chemical evolution in which dust grains and metal enriched gas in their ejecta, supplementing those of supernovae, AGB stars, and WR stars, are a source of the odd numbered, light and intermediate-mass isotopes (and possibly other elements) in the ISM. Once in the diffuse gas, this material is eventually incorporated into young stars and planetary systems during star formation. CNe are predicted to be the major source of ¹⁵N and ¹⁷O in the Galaxy and may contribute to the abundances of other isotopes such as ⁷Li, ²⁶Al, and ³¹P (José & Hernanz 1998; G1998). Theoretical studies predict that the mean mass returned by a CN outburst to the ISM is ∼2 × 10⁻⁴ M_☉ (G1998). Using the observationally inferred CN rate of 35 ± 11 per year in our Galaxy (Shafter 1997), it follows that CNe introduce ∼7 × 10⁻³ M_☉ yr⁻¹ of processed matter into the ISM. It is likely, however, that this value is a lower limit (G1998). Recent reviews can be found in G1998, Starrfield (2001), and S2008.

Infrared (IR) observations of the epoch of dust grain formation in the expanding shells of CNe have confirmed that some CNe form amorphous carbon grains, SiC grains, hydrocarbons, and oxygen-rich silicate grains in their ejecta (some CNe form all these in the same outburst), suggesting that a fraction of the pre-solar grains recently identified in meteoritic material (Zinner 1998) may come from CNe (G1998; Amari et al. 2001; José et al. 2004; S2008; but see also Nittler & Hoppe 2005).

Finally, and most important to the studies in this paper, the predictions of the 1D hydrodynamic CN simulations are directly affected by the nuclear reactions that both determine the production of the various isotopes and also produce the energy that drives the ejection of the material and the shape of the light curve. In addition, the temperatures reached around the peak of the TNR sample the regimes of nuclear experiments where the cross sections can be measured directly in the laboratory. Moreover, the rates in the libraries can be tested under the same conditions in which they were measured in the laboratory; no extrapolations are necessary. Therefore, over the years we have used a variety of nuclear reaction rate libraries and determined their influence on the properties of the outburst and the resulting nucleosynthesis. In separate papers, we have studied the influence of various nuclear reactions on a subset of the properties of the outburst by post-processing the results of hydrodynamic studies (Parete-Koon et al. 2003; Hix et al. 2000, 2003; Iliadis et al. 2002). Here, we continue this work by computing a new series of evolutionary sequences with a recent nuclear reaction rate library.

In the following section, we briefly describe both the changes to the NOVA code and the four reaction rate libraries that are used for the calculations reported in this paper. In the following section, we report on the results of our new calculations. We continue, in Section 4, with a discussion of the resulting nucleosynthesis, and end with a summary and discussion.

Over the past few years we have been improving the physics in NOVA and then determining the effects of the improved physics on simulations of the CN outburst (S1998; Starrfield et al. 2000, hereafter S2000; S2008). NOVA is a 1D, Lagrangian, fully implicit, hydrodynamic computer code that incorporates a large nuclear reaction rate network. It is described in detail in S1998, S2000, and references therein. As reported in those papers, we have found that improving the opacities, equations of state, and the nuclear reaction rate library have had important effects on both the energetics and the nucleosynthesis. Similar results have been reported by the Barcelona group (Hernanz & Josè 2000, and references therein). We have continued to explore the effects of improving the reaction rates used in the calculations on the evolution of the CN outburst. In this paper, we compare our earlier studies to new simulations using a reaction rate library of Iliadis which is current as of 2005 August (hereafter I2005). In addition, NOVA is continuously being updated and for the work reported in this paper we have made one major change and numerous minor changes.

The major change is that we no longer use the nuclear reaction network of Weiss & Truran (1990, hereafter WT1990) but have switched to the modern nuclear reaction network of Hix & Thielemann (1999, hereafter HT1999; see also Parete-Koon et al. 2003). While both networks utilize reaction rates in the common REACLIB format and perform their temporal integration using the backward Euler method introduced by Arnett & Truran (1969), two important differences are evident. First, WT1990 implemented a single iteration, semi-implicit backward Euler scheme, which had the advantage of a relatively small and predictable number of matrix solutions, but allowed only heuristic checks that the chosen timestep resulted in a stable or accurate solution. In contrast, HT1999 implemented an iterative, fully implicit scheme, repeating the backward Euler step until convergence is achieved. The iterations provide a measure both of the stability and the accuracy of the solution. Moreover, if convergence does not occur within a reasonable number of iterations, then the timestep is subdivided into smaller intervals until a converged solution can be achieved. Therefore, the fully implicit backward Euler integration can respond to instability or inaccuracy in a way that is impossible with the semi-implicit backward Euler approach. As a result, the fully iterative approach can often safely employ larger timesteps than the semi-implicit approach, obviating the speed advantage of the semi-implicit method's smaller number of matrix solutions per integration step. In addition to the changes in the nuclear reaction network and library, we now use the weak and intermediate screening equations from Graboske et al. (1973) instead of the framework of Salpeter (1954) as described in Cox & Giuli (1968).

Finally, the HT1999 network employs automated linking of reactions in the data set to the species being evolved. This is in contrast to the manual linking employed by WT1990 and many older reaction networks. The automated linking helps to avoid implementation mistakes, as we discovered while performing tests of NOVA in order to understand the source of differences in the results of the simulations between the two versions of the code which used the same reaction rate library but different nuclear reaction networks (plus other differences). We found that while the REACLIB dataset used in prior studies (Politano et al. 1995, hereafter P1995; S1998; S2000), included the pep reaction (p + e⁻ + p → d + ν: Schatzman 1958; Bahcall & May 1969), it was not linked to abundance changes (or the resulting energy generation) in the WT1990 network. While for solar modeling energy generation from the pep reaction is unimportant (but not the neutrino losses: Rolfs & Rodney 1988), in the WD envelope the density can reach, or exceed, values of 10⁴ g cm⁻³ which, in turn, increases the rate of energy generation over the simulations done without the pep reaction included (Starrfield et al. 2007). The increased energy generation reduces the amount of accreted material since the temperature rises faster per gram of accreted material. The effect of changes in the rate of energy generation on simulations of the CN outburst is discussed in detail in S1998. Given a smaller amount of accreted material at the time when the steep temperature rise begins in the TNR, the nuclear burning region is less degenerate and, therefore, the peak temperatures are lower compared to models evolved with the same nuclear reaction rate library used in our previous studies (see the evolution sections below). To the best of our knowledge, none of the previous studies of TNRs in WD envelopes have included this reaction.

Another difference between this work and our previous studies is that we do not initiate nuclear burning until the temperatures have reached nine million degrees in a given mass zone. In our earlier studies, done with the WT network, nuclear burning was initiated at four million degrees. We made this change because the reaction rates in the latest libraries are not fitted to temperatures below about 10 million degrees and, for temperatures of about eight million degrees (and lower), some of the rates begin increasing rapidly and unrealistically. Our test runs found that nine million degrees was a good cut-off value. Fortunately, this has almost no effect on the evolution. We find, for example, that for the sequence done with the Iliadis 2005 reaction rate library at 1.35 M_☉, nuclear burning does not start until the sequence has evolved for 7.1 × 10³ yr (and the accreted material at that time, ∼10⁻⁶ M_☉, has reached down from the surface (mass zone 95) to mass zone 81 (1.1 × 10⁻⁶ M_☉)) compared to the total accretion time of 1.8 × 10⁵ yr (where the accreted material (see Table 2) has reached down to mass zone 63 (2.1 × 10⁻⁵ M_☉)). Therefore, there is no nuclear burning in the accreted material for only ∼4% of the evolution time and, given that the p–p chain is operating at this time, only a small fraction of the total nuclear energy production is neglected.

However, this also means that the outermost mass zones, which have temperatures below nine million degrees until near the peak of the outburst (when the energy and products of nuclear burning are brought to the surface by convection), do not experience nuclear burning during the accretion phase of the outburst. Therefore, when these layers are mixed into the nuclear burning layers near the peak of the outburst they inject a larger amount of unprocessed nuclei into the TNR than found in our earlier simulations. In order to understand the effects of this difference, we redid the earlier calculations with the older reaction rate libraries (see below).

In this paper, we evolve seven different sequences using the same initial conditions but four different reaction rate libraries for each of the two WD masses. We report the results in the tables described in the following section. The first library we use includes the rates from Caughlan & Fowler (1988) and Thielemann et al. (1987, 1988). They were compiled by Thielemann, made available to Truran and Starrfield, and used for the calculations reported in WT1990 and those in Politano et al. (1995, hereafter P1995). The first sequence (labeled P1995A), uses the P1995 library, the WT1990 network, and none of the updates listed in the last section. The second sequence (labeled P1995B) uses the latest version of the NOVA code, the HT1999 network, the P1995 library, but the pep reaction is not included. A comparison of the results from these two sequences shows the results of updating the code. Most of the differences can be attributed to our use of the Graboske et al. (1973) screening in the latest version.

The third sequence (labeled P1995C) is identical to sequence 2 except that it includes the pep reaction and shows how including the pep reaction changes the results of the evolution. The next three sequences are done with three different reaction rate libraries. The second library (labeled S1998) uses an updated reaction rate library which contains new rates calculated, measured, and/or compiled by Thielemann and Wiescher. A discussion of the improvements is provided in S1998. The third library (labeled I2001) is described in Iliadis et al. (2001) and was used for the simulations reported in Starrfield et al. (2001). The fourth library (labeled I2005A) is the 2005 August library of Iliadis and the results of calculations done with this library are given in this paper. We label it "this work" in the plots. These three sequences include the pep reaction. Finally, there is one last sequence (labeled I2005B) which is identical to I2005A except that the pep reaction is not included. Therefore, we can compare sequences P1995B and P1995C and I2005A and I2005B to determine just the effects of including the pep reaction, while sequences P1995C, S1998, I2001, and I2005A show the effects of the different reaction rate libraries on the evolution. In order to prevent confusion, the particular library used for each sequence, the reaction network, and whether or not the pep reaction is included are listed in the comments to Table 2.

References to many of the updated reaction rates used in calculating sequences I2005A and I2005B are given in Table 1 along with some comments on those rates. As required, the ground and isomeric states of ²⁶Al are treated as separate nuclei (Ward & Fowler 1980) and the communication between those states through thermal excitations involving higher lying excited ²⁶Al levels is taken into account. The required γ-ray transition probabilities are adopted from Runkle et al. (2001).

Other changes to NOVA include the use of the analytic fitting formulas of Itoh et al. (1996) for the neutrino energy loss rates from pair ($e^+ + e^- \rightarrow \nu _e + {\bar{\nu }}_e$), photo ($e^{\pm } + \gamma \rightarrow e^{\pm } + \nu + \bar{ \nu }_e$), plasma ($\gamma _{{\rm plasmon}} \rightarrow \nu _e + \bar{ \nu }_e$), bremsstrahlung ($e^-\ +\ A^Z \rightarrow\break e^-\ +\ A^Z\ +\ \nu _e\ +\ \bar{\nu } _e$), and recombination ($e^-_{\rm continuum} \rightarrow e^-_{\rm bound}\ +\ \nu _e\ +\ \bar{ \nu }_e$) processes. As stellar evolution codes generally require derivative information for the Jacobian matrix, our implementation of the Itoh et al. (1996) fitting formulas (available online from cococubed.asu.edu) returns the neutrino loss rate and its first derivatives with respect to temperature, density, $\bar{A}$ (average atomic weight), and $\bar{Z}$ (average charge). Finally, we assume a value of 2 for the mixing length to scale height ratio (l/H_p). There are additional and numerous small changes to NOVA that had minimal effects on the simulations to be described in the following section.

Our initial models are complete 1.25 M_☉ and 1.35 M_☉ WDs discretized into 95 zones. This is the same number used in our previous studies (P1995; S1998; S2000). We assume that the material being accreted from the donor star is of solar (Anders & Grevesse 1989) composition and that it has already mixed with the core material so that the actual accreting composition in this study is 50% solar and 50% ONeMg material. (We use the ONeMg composition of Arnett & Truran 1969.) The use of this composition affects the total amount of accreted mass at the peak of the TNR since it has a higher opacity than if no mixing were assumed (S1998; José et al. 2007). The initial (solar and ONeMg mixed) abundances by mass are given in column 7 of Table 4.

We use an initial WD luminosity of either ∼3 × 10⁻³L_☉ (1.25 M_☉) or ∼4 × 10⁻³ L_☉ (1.35 M_☉). We use a smaller value for the accretion rate (than in S1998), 1.6 × 10⁻¹⁰ M_☉yr⁻¹, in order to accrete the largest amount of mass possible for a given WD mass. This mass accretion rate is five times lower than the lowest rate used in either S1998 or S2000 and was chosen to maximize the amount of accreted material given the increased energy generation from including the pep reaction. Studies of accretion onto WDs demonstrate that the results of the evolution depend strongly on the initial WD luminosity and mass accretion rate (c.f. Yaron et al. 2005; G1998; S1998; S2000; S2008, and references therein).

The results of our evolutionary calculations are given in Tables 2 through 5. Tables 2 and 3 give the initial conditions and evolutionary results for both WD masses while Tables 4 and 5 give the abundances of the ejected material (by mass) for the eight different simulations done with the pep reaction included. The numerical factor that multiplies the abundances is given in the first column next to the isotope designation. The rows in Tables 2 and 3 are the reaction rate library, the accretion time to the TNR (τ_acc), the accreted mass (M_acc), peak temperature in the TNR (T_peak), peak rate of energy generation during the TNR (_nuc-peak), peak luminosity (L_peak), peak effective temperature (T_eff-peak), ejected mass (M_ej), and the peak expansion velocity after the radii of the surface layers have reached ∼10¹³ cm (V_max). By this time the outer layers are optically thin, have far exceeded the escape velocity at this radius, and there is no doubt that they are escaping.

Table 2. Initial Parameters and Evolutionary Results for 1.25 M_☉ White Dwarfs^a

Sequence:	P1995Ab	P1995Bc	P1995Cd	S1998e	I2001f	I2005Ag	I2005Bh
τacc(105 yr)	5.2	5.0	3.8	3.8	3.8	3.8	5.0
Macc(10−5 M☉)	8.2	8.0	6.0	6.0	6.1	6.1	8.0
Tpeak(106 K)	348	347	321	321	320	320	347
nuc-peak(1017 erg g−1 s−1)	2.8	2.7	2.0	2.1	1.3	1.3	1.8
Lpeak(105 L☉)	4.2	5.7	2.6	2.3	2.0	2.6	5.7
Teff-peak(105 K)	9.1	9.4	8.3	8.6	6.5	6.6	9.4
Mej(10−5 M☉)	5.0	4.8	1.8	1.5	.7	1.5	3.3
Vmax(km s−1)	3563	3681	3081	2860	2772	3143	3761

Notes. ^aThe initial model for all evolutionary sequences had M_WD = 1.25 M_☉, L_WD = 3.2 × 10⁻³ L_☉, T_eff = 1.9 × 10⁴ K, R_WD = 3497 km, and a central temperature of 1.2 × 10⁷ K. ^bPolitano et al. (1995) library: pep reaction not included (Weiss & Truran (1990) network); Anders & Grevesse (1989) solar abundances. ^cPolitano et al. (1995) library: pep reaction not included (Hix & Thielemann (1999) network); Anders & Grevesse (1989) solar abundances. ^dPolitano et al. (1995) library: pep reaction included (Hix & Thielemann (1999) network); Anders & Grevesse (1989) solar abundances. ^eStarrfield et al. (1998) library: pep reaction included (Hix & Thielemann (1999) network); Anders & Grevesse (1989) solar abundances. ^fIliadis et al. (2001) library: pep reaction included (Hix & Thielemann (1999) network); Anders & Grevesse (1989) solar abundances. ^gIliadis 2005 library (this work): pep reaction included (Hix & Thielemann (1999) network); Anders & Grevesse (1989) solar abundances. ^hIliadis 2005 library (this work): pep reaction not included (Hix & Thielemann (1999) network); Anders & Grevesse (1989) solar abundances.

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Table 3. Initial Parameters and Evolutionary Results for 1.35 M_☉ White Dwarfs ^a

Reaction Library:	P1995A	P1995B	P1995C	S1998	I2001	I2005A	I2005B
τacc(105 yr)	2.5	3.6	2.1	2.1	2.1	1.8	3.8
Macc(10−5 M☉)	3.9	5.8	3.3	3.3	3.3	2.8	6.1
Tpeak(106 K)	459	524	413	414	407	392	519
nuc-peak(1017 erg g−1 s−1)	22.8	48.6	8.4	8.6	4.9	4.4	21.8
Lpeak(105 L☉)	8.0	13.4	9.6	8.0	7.3	5.9	10.9
Teff-peak(105 K)	20.0	21.4	13	13	8.8	8.8	18.1
Mej(10−5 M☉)	3.3	4.1	2.3	2.3	2.3	1.7	4.3
Vmax(km s−1)	6050	7452	5239	4755	4787	4513	6599

Note. ^aThe initial model for all evolutionary sequences had M_WD = 1.35 M_☉, L_WD = 4.2 × 10⁻³ L_☉, T_eff = 2.5 × 10⁴ K, R_WD = 2495 km, and a central temperature of 1.2 × 10⁷ K

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As mentioned in the last section, the first three sequences (P1995A, P1995B, and P1995C) employ the P1995 reaction rate library. As shown in Tables 2 and 3, the three different sequences using the P1995 library provide a clear picture both of the impact of the pep reaction as well as the other updates to the NOVA code. Since neither sequence P1995A nor P1995B included the pep reaction, the differences between these two sequences show only the impact of the updates to the NOVA code, which are noticeable but generally small. Most of these differences can be attributed to our use of the Graboske et al. (1973) weak and intermediate screening in this paper and not in earlier papers.

In contrast, much larger differences are seen when sequence P1995B is compared to P1995C which does include the pep reaction but is otherwise identical. This conclusion is reinforced by comparing sequences I2005A and I2005B (both calculated with the latest library (I2005) and current version of NOVA) since I2005A includes the pep reaction and it is not included in I2005B. Tables 2 (1.25 M_☉) and 3 (1.35 M_☉) show that for both WD masses the largest change in the results of the evolution occurs with the inclusion of the pep reaction. If we compare rows P1995B and P1995C or rows I2005A or I2005B, then the increase in energy production from adding the pep reaction to the network results in a significant decrease in both accretion time and accreted mass. Because there is less accreted mass on the WD at the time of the TNR, all the peak values are smaller. However, the effects are much more important for the 1.35 M_☉ evolution than for the 1.25 M_☉ evolution. This is because the density is higher in the more massive WD at the beginning of the TNR and, therefore, the pep reaction provides more energy ( ∼ ρ²). Interestingly enough, the peak temperatures reached in the two 1.35 M_☉ simulations without the pep reaction (P1995B and I2005B) exceed 5 × 10⁸ K which is sufficiently high for CNO breakout (the ¹⁴O(α,γ) and ¹⁵O(α,γ) reactions) to occur (see below). Unfortunately, evolution without the necessary physics of the pep reaction included is not realistic and we will have to look elsewhere for initial conditions that produce sufficiently high temperatures for breakout.

If we compare the results for the four sequences with the pep reaction included (P1995C, S1998, I2001, I2005A), we see that changes in the nuclear reaction rate library produce differences in ejected mass and peak luminosity for both the 1.25 M_☉ and 1.35 M_☉ evolutionary sequences. The results of the evolutionary sequences show that because the WD mass is larger and the radius is smaller for 1.35 M_☉, the mass zones where the TNR occurs reach higher densities and higher peak temperatures than do the sequences at lower WD mass (Starrfield 1989; S2008; Yaron et al. 2005). At 1.35 M_☉ the sequence done with the latest reaction rate library (I2005A) accretes and ejects the lowest amount of mass moving at the lowest ejection velocities. In addition, the peak luminosity and effective temperature is lowest for the calculation done with this library. The amount of ejected mass and the ejection velocities are in disagreement with the observations (S2008).

Table 2 shows that only about 25% of the accreted material is ejected in the explosive phase of the outburst at 1.25 M_☉ and Table 3 shows about 60% of the accreted material is ejected at 1.35 M_☉. This is a common feature of our 1D hydrodynamic simulations (G1998; S2008). The material that is not ejected returns to quasistatic equilibrium on the WD and stays luminous and hot with radii exceeding 10⁹cm. X-ray studies of this phase of evolution for a CN in outburst indicate that we are observing a hot, luminous stellar atmosphere (Petz et al. 2005; Ness et al. 2007) just as in the Super Soft X-ray Binaries such as CAL 83 (Kahabka & van den Heuvel 1997; Lanz et al. 2005). The predicted time required to burn the remaining envelope material and return the CN to quiescence can exceed 100 yr (Starrfield 1989) which is not observed (Orio 2004). It has been proposed that the remaining material is ejected via radiation pressure driven mass loss on short timescales (Starrfield 1979; MacDonald et al. 1985; Starrfield et al. 1991). Nevertheless, some of the accreted envelope may actually be burnt to helium enriched material and become part of the material ejected in the next CN outburst (Krautter et al. 1996). However, the amount of accreted material that is not ejected suggests that it is insufficient to counteract the amount of WD core mass lost in the outburst. As a result, the WD is losing mass as a result of the CN outburst and CNe cannot be the progenitors of supernovae of Type Ia.

Figure 1 shows the variation of temperature with time for the zone where peak conditions in the TNR occur in the 1.25 M_☉ evolutionary sequences. In this figure and all other figures we plot only the four simulations done with the pep reaction included. The specific evolutionary sequence is identified on the plot and in the caption. The reference to the nuclear reaction rate library used for that calculation is given in the caption for Figure 1 and indicated on the figure. The designation "this work" refers to the I2005A sequence as described in the tables and discussed earlier. The time coordinate is chosen to clearly show the rise and decline time of each evolutionary sequence. Interestingly enough, the rise time and peak temperature are nearly the same for all four sequences at 1.25 M_☉.

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Figure 2 shows the same plot for the sequences at 1.35 M_☉. Here we see differences between the four simulations. Peak temperature drops from about 413 million degrees to 392 million degrees and peak nuclear energy generation drops by about a factor of 2 from the oldest library to the newest library (8.4 × 10¹⁷ erg g⁻¹ s⁻¹ to 4.4 × 10¹⁷ erg g⁻¹ s⁻¹). The temperature declines more rapidly for the sequence (P1995C) computed with the oldest reaction library (P1995) because there was a larger release of nuclear energy throughout the evolution so that the overlying zones expanded more rapidly and the nuclear burning region cooled more rapidly than in the other sequences. In contrast, the newest library, showing the smallest expansion velocities, cools slowly. There is a factor of two difference in the time coordinate used for Figures 1 and 2 because the simulations at 1.35 M_☉ evolve much more rapidly near the peak of the TNR than those at 1.25 M_☉. This is a direct result of the higher gravity and higher degeneracy in the nuclear burning region of the more massive WDs.

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The evolution of the total nuclear energy generation in the nuclear burning layers (in solar units: L/L_☉) as a function of time for each mass is shown in Figures 3 (1.25 M_☉) and 4 (1.35 M_☉). The time coordinates are the same as those used in Figures 1 and 2, respectively. Again, there is hardly any difference at the lower WD mass but at 1.35 M_☉ the peak for the calculation done with the latest library is definitely lower than seen in the earlier libraries.

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Figures 5 and 6 show the variation of the effective temperature (T_eff) with time as the layers begin their expansion. We plot the results with the same time coordinates as in Figures 1 and 2 and these plots show how rapidly the energy and β⁺-unstable nuclei reach and heat the surface layers. Note that peak T_eff occurs when the WD radius is still small and earlier in the evolution than when peak luminosity occurs. The large amplitude oscillations seen in the sequences using the older libraries, and not in that from the latest library, are caused by the intense and rapid heating of the surface layers. They expand, cool, collapse back onto the surface, and expand again. The outer layers are still deep within the gravitational potential well of the WD (since hardly any expansion has occurred at the time of the oscillations) and so the "quasi"-period is that of the free-fall time for the underlying WD. After a few seconds the outer layers are expanding sufficiently rapidly, have cooled, and the oscillations cease. They are not present in the sequence using the latest library because surface heating is less important. The outburst evolves more gradually and the star has started to expand by the time that the β⁺-unstable nuclei reach the surface. This can also be seen in Figure 7 (1.35 M_☉) which shows the velocity of the surface layers as a function of time around the time-of-peak temperature in the nuclear burning region.

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Figures 8 and 9 show the variation with time of the surface luminosity (for the first 11 hr of the TNR) for each of the two WD masses. The intense heat from the β⁺-unstable nuclei causes the luminosity to become super-Eddington and the layers begin expanding. However, they are still deep within the potential well of the WD and oscillate for a few seconds. In contrast, the sequence done with the latest library does not become as luminous and the initial oscillations exhibit a much smaller amplitude. These figures imply that if we could observe a CN sufficiently early in the outburst, then it would be super-Eddington and emitting soft X-rays. However, by the time a CN is typically discovered its luminosity has declined to below Eddington. In contrast to this result, however, the IUE observations of LMC 1991 showed that it was super-Eddington for more than 10 days (Schwarz et al. 2001), a result that is not predicted by any existing CN simulations (S2008).

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The initial spike (at a time of about 100 s) is caused by a slowing of the expansion as the energy produced by the β⁺-decays decreases. After this time, expansion and cooling of the outer layers causes the opacity to increase and radiation pressure then accelerates the layers outward. The continuous flow of heat from the interior, combined with the increase in opacity, causes another increase in luminosity until the peak is reached.

In this section, we present the predicted ejecta abundances for the four sequences at each WD mass done with the pep reaction included. Because it is a necessary piece of the p–p reaction chain, calculations done without it included in the reaction network are not realistic and we do not report the abundance results for the three sequences done without the pep reaction at each WD mass. However, we do provide two plots which show the effects on the abundances of not including the pep reaction and discuss them below. The results for each nucleus in our nuclear reaction network are given as mass fraction in Table 4 (1.25 M_☉) and Table 5 (1.35 M_☉). The factor multiplying each isotope can be found just to the right of the isotopic designation. Note that the right-hand column in Table 4 is the initial abundance of the given nucleus (we do not repeat this column in Table 5).

In order to more clearly show which nuclei are produced by CNe explosions, in Figures 10 and 11 we plot the stable, ejected nuclei divided by the Anders & Grevesse (1989) solar abundances. In both figures the x-axis is the atomic mass number. The y-axis is the logarithmic ratio of the ejecta abundance divided by the solar abundance of the same nucleus. The most abundant isotope of a given element is marked by an asterisk and isotopes of the same element are connected by solid lines and labeled by the given element. These plots are patterned after similar plots in Timmes et al. (1995). They show for both WD masses that we predict that ¹⁵N, ¹⁷O, and ³¹P are overproduced by a factor of 10⁴ in CNe ejecta. There are other nuclei that are overproduced by factors of a thousand and could be important for CN nucleosynthesis. In Figures 12 (1.25 M_☉) and 13 (1.35 M_☉), we show the ratio of the ejected abundances for the simulation (I2005A) done with the pep reaction (using the I2005 reaction rate library) compared to a simulation (I2005B) done without the pep reaction (also using the I2005 library). The plot style is the same as for Figures 10 and 11 as described above except that the y-axis is linear and not logarithmic.

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The initial abundance of ¹H is 0.365. (This value is half the solar abundance of Anders & Grevesse (1989).) The hydrogen abundance in the ejected gases for the 1.25 M_☉ I2005A sequence has declined to ∼ 0.31. This decline of ∼ 0.05 in mass fraction results in a total energy production from proton captures of ∼4 × 10⁴⁶ erg which agrees with the values typically quoted for observed CN explosions (Starrfield 1989; G1998; S2008). Interestingly, the ejecta abundance of ⁴He decreases slightly as the reaction rate library is improved and the smallest increase occurs in the calculations done with the two most recent libraries. A ⁴He ejecta abundance of 0.16 is far smaller than the values typically quoted for observed CN ejecta (G1998 and references therein). We therefore support the speculation of Krautter et al. (1996; see also S1998; S2000) that the large amount of helium observed in CN ejecta implies (1) that most of the ejected helium was mixed up from the outer layers of the WD by the TNR, and (2) that it was actually produced in previous CN outbursts and subsequent nuclear burning on the WD.

Turning to the more massive nuclei, the abundances of ¹²C and ¹³C drop by about a factor of 2 from the oldest to the newest reaction rate libraries while ¹⁴N increases by about a factor of 2 and ¹⁵N declines by slightly less than a factor of 2. Note that the abundance of ¹⁵N far exceeds that of ¹⁴N and it is likely that the nitrogen observed in CN ejecta is mostly ¹⁵N rather than ¹⁴N. Therefore our speculation about helium may also hold true for nitrogen. The observed nitrogen is probably ¹⁵N produced in previous outbursts, mixed into the newly accreted material, and then ejected during the current CN outburst.

Similarly, ¹⁶O declines by about 30% while ¹⁷O increases by more than a factor of 2. In fact, ¹⁷O is the most abundant of the CNO nuclei in the ejecta and the abundances of ¹⁵N and ¹⁷O exceed those of the even-numbered isotopes. Finally, the C/O ratio in the ejecta drops from about 30% to about 8% from the earliest to the latest library. Other interesting nuclei at this WD mass are ¹⁸O which drops about a factor of 10 as the library is improved, ²²Na whose abundance remains virtually unchanged as the library is improved, ²⁴Mg which drops a factor of 3 and is severely depleted from its initial abundance, and both ²⁶Al and ²⁷Al which drop by about a factor of 2 in abundance.

We also find that most of the higher mass nuclei (⁴⁰Ca is the most massive nucleus in our network) are all produced by the TNR in the outburst (see Table 4). Interestingly, the abundances of ²⁸Si, ²⁹Si, and ³⁰Si are largest in the calculations done with the latest library while the abundances of ³³S, ³⁴S, and ³⁵Cl decrease in the latest library. Finally, ³⁶Ar is depleted by the outburst (its final abundance is less than the initial abundance) in all sequences except P1995C.

The ejecta abundance results for TNRs on 1.35 M_☉ WDs are given in Table 5 for the same reaction rate libraries used in the study at lower WD mass. Hydrogen is depleted by a larger amount at this WD mass than for the 1.25 M_☉ sequences resulting in a total energy production from proton captures of ∼3 × 10⁴⁶ erg. This value is smaller than in the lower mass sequence because the 1.35 M_☉ sequences accrete less mass. As in the sequences at 1.25 M_☉, the helium abundance in the ejecta is small compared to the observed helium abundances in CN ejecta and the results at this WD mass also support our prediction that the accreted material mixed with the outer layers of the WD at some time during the outburst. We emphasize, in addition, that the large helium abundances observed in recurrent novae such as U Sco or V394 CrA imply that mixing with the WD has occurred in these systems even if the total CNO abundances in their ejecta are not dramatically enriched over solar (Shore et al. 1991).

Examining the behavior of the individual abundances, we see that ¹²C and ¹³C are virtually unchanged by the updated reaction rates. In contrast, the abundance of ¹⁴N nearly doubles and that of ¹⁵N decreases by a factor of 2 going from the earliest to the latest reaction rate library. ¹⁶O doubles in abundance while ¹⁷O grows by a factor of 60 and becomes the most abundant of the CNO nuclei in the ejecta. For this WD mass and the latest library, the C/O ratio is 0.12. The abundance of ¹⁸O declines by nearly a factor of 5 and the abundances of ¹⁸F and ¹⁹F also decline by large factors in the sequence done with the latest library.

The initial abundance of ²⁰Ne in all four sequences is 0.25 (see Table 4) so that it is depleted by a smaller amount in the calculations done with the latest library. The abundance of ²²Na decreases with the library update and ²⁴Mg is severely depleted by the TNR. In fact, all the Mg isotopes are depleted in the calculations done with the latest library. In contrast, the ejecta abundance of ²⁶Al is unchanged by the changes in the reaction rates while the abundance of ²⁷Al drops by a factor of 2. We also find, contrary to a conclusion in Politano et al. (1995), that the amount of ²⁶Al ejected is virtually independent of WD mass.

All the Si isotopes (²⁸Si, ²⁹Si, and ³⁰Si) are enriched in the calculations done with the latest library, and ²⁹Si and ³⁰Si are more abundant in the 1.35 M_☉ simulations than the 1.25 M_☉ simulations. Other nuclei whose abundances are largest in the calculations done with the latest library are ³¹P and ³²S. These nuclei are also more abundant at the higher WD mass. In addition, while the ejecta abundance of ³³S does not depend on the reaction rate library, it is nearly 30 times more abundant in the calculations done with the more massive WD. Finally, we note that while the ejecta abundances of ³⁴S, ³⁵Cl, ³⁶Ar, and ⁴⁰Ca have all declined as the reaction rate library has been improved, we predict that they will be produced in a nova TNR since their final abundances exceed the initial abundances.

The effects of including the pep reaction on ejecta abundances are shown in Figures 12 and 13 in which we plot the ratio of the ejecta abundance of the sequence with the pep reaction included divided by the abundance from the equivalent sequence with the pep reaction not included. Figure 12 shows that most nuclei have a higher abundance in the 1.25 M_☉ sequence with no pep. This is also true for the 1.35 M_☉ WD sequence with the notable exception of the carbon isotopes, ¹⁴N, ²⁰Ne, ²¹Ne, and ³²S. These results are as expected since the sequence at 1.35 M_☉ reaches to higher temperatures.

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Finally, given the high temperatures attained in the 1.35 M_☉ sequence without the pep reaction included, we checked to determine if breakout had occurred. We found that the total CNO abundances decreased from their initial values in both sequences (using the latest reaction library only). As expected, the sequence done without the pep reaction showed the most depletion but for neither mass was it sufficiently large to be observable.

In this paper, we examined the consequences of improving the nuclear reaction rate library on our simulations of TNRs on 1.25 M_☉ and 1.35 M_☉ ONeMg WDs. We found that the changes in the rates affected predictions of both the nucleosynthesis and the observable features of the evolution such as peak luminosity, peak effective temperature, ejected mass, and ejecta velocities. A major change to our previous calculations, that affects virtually all features of the predicted outburst, has been the inclusion of the pep reaction in the p–p chain. This reaction is important during the accretion phase of the evolution because the density of the accreting material quickly reaches values of ∼10⁴ g cm⁻³. This high density increases the nuclear energy generation over studies done with the pep reaction absent. The increased energy generation reduces the time to reach the TNR and, thereby, the amount of accreted material and as a result the peak values of temperature and energy generation are smaller than we have found in our previous studies.

If we examine the abundance predictions for the four 1.25 M_☉ sequences done with the pep reaction included, we see that the differences caused by improving the reaction rate library are that the abundance of ¹²C declines by about a factor of 2 (all abundances are given in mass fraction), ¹⁴N increases by almost a factor of 2, and ¹⁶O declines by about a factor of 1.5. Both ¹²C and ¹³C are depleted in the latest sequence (compared to the P1995 library) as is ¹⁵N while ¹⁷O is enriched in the calculation done with the latest reaction rate library. In addition, in all four sequences the ejected oxygen exceeds carbon as found in our earlier studies. This result continues to be puzzling in light of the production of carbon-rich dust grains in CN ejecta (G1998). It is possible that the carbon dust grain forming CNe occur on lower mass CO WDs which never develop sufficiently hot nuclear burning temperatures to deplete the carbon as compared to oxygen. As we examine the more massive nuclei at 1.25 M_☉, we see that ²⁶Al and ²⁷Al are depleted in the simulations done with the latest library while ³²S is enhanced. Interestingly, the abundance of ²²Na increased with the sequences done with the libraries intermediate in time but then decreased to a value nearly equal to that in the earliest library.

The effects of changing the nuclear reaction library are also apparent for the sequences at 1.35 M_☉. Both ¹²C and ¹³C drop in abundance while ¹⁴N, ¹⁶O, and ¹⁷O increase in abundance. We find that while the ejecta abundance of ²²Na is lowest in simulations done with the I2005 library, it is still a factor of about 5 more abundant at 1.35 M_☉ than at 1.25 M_☉. The abundance of ²⁶Al is unchanged while that of ²⁷Al declined by about a factor of 2. In addition, the abundance of ²⁶Al is roughly constant from one WD mass to the other while the abundance of ²²Na declined by about a factor of 2 as the WD mass increased. This is not what we reported in earlier studies (done without the pep reaction) using older libraries where we found that the abundance of ²⁶Al declined as the WD mass increased. Finally, we note that the abundance of ³²S is largest for the latest library at 1.35 M_☉. In fact, it reaches 4% of the ejected material.

In summary, the nucleosynthesis predictions from our simulations show significant impact from improvements in the reaction rates over the past 15 or so years. Observable features of the models, such as the variation of the effective temperature and luminosity with time, and also the mass ejected, exhibit a notable influence from changes in these rates because of their dependence on heating from the decays of nucleosynthesis products that have been mixed into the outer layers.

We thank L. Bildsten, A. Champagne, R. Gehrz, J. Krautter, H. Schatz, D. Townsley, J. Truran, and C. E. Woodward for interesting discussions. We are grateful to the anonymous referee whose comments improved the presentation of this paper. S.S. thanks J. Aufdenberg and ORNL for generous allotments of computer time. C.I. is supported in part by the U.S. Department of Energy under Contract No. DE-FG02-97ER41041. W.R.H. has been partly supported by the National Science Foundation under contracts PHY-0244783 and AST-0653376. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725. S. Starrfield acknowledges partial support from NSF and NASA grants to ASU.