The Development of Nuclear Thermometers

As a first step, the hydrodynamic final elemental abundances of the nova models presented in Table3.1were examined for dependence on peak temperature. In order to identify a peak-temperature dependence effectively, it was preferable that any el- emental trends be independent of initial abundance. To this end, the hydrodynamic elemental abundances for the nova models were normalized to the initial abundances of the accreted envelope (see Table3.2) and plotted as a function of mass number Z. These results are shown in Figure3.4. It was determined that certain elements, such as N, Si, P, and S, were overproduced while others, such as O, Na, and Mg, were underproduced. Of these, N, O, Na, Al, P, and S demonstrate significant, monotonic dependence on peak temperature. It must be noted that F, Cl, and Ar also display these trends but their overall abundance in the ejected envelope was expected to be quite low (< 10−5 _{in mass fraction); therefore, these elements would not be useful}

metrics and were not studied further.

Figure 3.4: Final elemental abundances normalized to initial abundances and pre- sented versus atomic number for all four hydrodynamic models. Each nova model is represented by a different color marker. The dotted line represents the point at which the final and initial abundances are equal for a given element. Using this as a guide, it is clear that some elements (O, Na, Mg) are underproduced while others (N, Si, P, S) are overproduced. If production is a monotonic function of temperature, the color sequence of the markers is red, blue, green, black, or the reverse. Originally published inDownenet al.(2013).

on peak temperature were combined to form elemental ratios that preserved this de- pendence. These ratios were designated potential nuclear thermometers as these ra- tios were designed to probe the peak temperature of classical nova explosions. The thermometer candidates are shown versus peak temperature in Figure3.5. Naturally, it is preferable for the ratios to include only elements that are regularly observed spec- troscopically, but four ratios include Na and P, elements that have not been observed in nova ejecta to date and are of limited utility as a result. These ratios are shown

as dotted lines. Of all the candidates, O/S and S/Al demonstrated the most extreme dependence on temperature, varying roughly 3 orders of magnitude over the peak temperature range of the four nova models explored here. The O/P and P/Al values spanned two orders of magnitude, and the remaining ratios increased or decreased by one order of magnitude each.

Figure 3.5: Mass fraction ratios of eight elemental abundances versus temperature. These ratios all demonstrate a dependence on peak temperature of an order of magni- tude or more and are the prime candidates for nova thermometers. Solid lines indicate ratios involving elements that are spectroscopically observed regularly while dotted lines denote elemental ratios with the inclusion of elements that are not generally ob- served. Figure fromDownenet al.(2013).

Of course, the utility of any thermometer would be sharply limited if the uncer- tainty in its value exceeded the already sizable uncertainty present in spectroscopic

uncertainties was investigated. More than 7000 simulations were carried out in order to independently vary the rates of 214 reactions by factors of 0.01, 0.1, 0.2, 0.5, 2, 5, 10, and 100. The final elemental abundances produced with these variations were then linearly interpreted to quantify the effect of the realistic reaction rate uncertainties pro- vided by theSTARLIBlibrary. The results of this probe are given in Figure3.6, which shows eight panels, each displaying a nuclear thermometer and its sensitivity to the STARLIBrate uncertainties graphed as a function of peak temperature. The panels on the left side of the figure pertain to elements that have been observed spectroscop- ically to date while the panels to the right involve nuclear thermometer candidates with at least one element that has not been observed. The solid red line in each panel is the hydrodynamic abundance of the thermometer, and the solid black line is the abundance as given by the post-processing reaction network with the convective mix- ing method that most closely reproduces the hydrodynamic values. The dotted black lines show the range in the thermometer value as a result of theSTARLIBreaction rate uncertainties.

Several conclusions were drawn from the information displayed in this figure. First, there is compelling agreement between the values from the hydrodynamic sim- ulations and the post-processing calculations. These values differ by a factor of 2 or less on average, confirming the hypothesis that post-processing calculations provide a viable method of approximating the results of hydrodynamic simulations for the elements of interest here. In regard to reaction rate uncertainties, the N/O and N/Al thermometers show promise since they have uncertainties of less than 30% and N, O, and Al have all been observed spectroscopically in the past. O/Na and Na/Al have similarly low uncertainties but limited use because sodium has not been successfully observed in the ejecta of neon novae. The utility of the four remaining ratios—O/S, S/Al, O/P, and P/Al—is restricted by substantial reaction rate uncertainty, leading to proportionally large (factor 3–6) uncertainties in their values. These ratios exhibit the

Figure 3.6: Eight nuclear thermometer candidates plotted as functions of peak tem- perature. These elemental ratios all demonstrated a strong, monotonic dependence on peak temperature. The panels to the left only involve elements that have been pre- viously observed in nova ejecta, while the panels to the right include and element (Na or P) that has been searched for but not yet observed. Solid red and black lines indi- cate the ratios given by hydrodynamic and post-processing simulations, respectively, using recommended reaction rates. The dashed black lines represent the uncertainty in the elemental ratios due to reaction rate uncertainty. Broad uncertainty bands, such as the ones present in the lower four panels, indicate the need for improved measure- ments of the primary and secondary sources of uncertainty given in Table3.3. This figure was originally published inDownenet al.(2013).

Table 3.3. Uncertainty Sources of Neon Nova Abundance Predictions

Ratio Rangea Primary Source Secondary Source

Reaction Uncertaintyb _{Reaction Uncertainty}b

N/O 13.4 16_O(p,γ)17_{F 1.16} 13_N(p,γ)14_{O 1.06}

N/Al 5.59 20_Ne(p,γ)21_{Na 1.29} 13_N(p,γ)14_{O 1.18}

O/S 332 30_P(p,γ)31_{S 3.36} 28_Si(p,γ)29_{P 1.09}

S/Al 529 30_P(p,γ)31_{S 4.62} 28_Si(p,γ)29_{P 1.12}

O/Na 10.8 16O(p,γ)17F 1.16 20Ne(p,γ)21Na 1.12

Na/Al 6.83 23_Na(p,γ)24_{Mg 1.19} 20_Ne(p,γ)21_{Na 1.10}

O/P 541 30_P(p,γ)31_{S 6.44} 16_O(p,γ)17_{F 1.26}

P/Al 216 30_P(p,γ)31_{S 6.53} 20_Ne(p,γ)21_{Na 1.22}

Note. — This table was originally published inDownenet al.(2013).

a_{Factor variation of final elemental abundance ratio over range of nova models}

explored in present work, obtained from the solid black lines shown in Figure3.6.

b_{Factor uncertainty of final elemental abundance (mass fraction) ratio, caused by}

varying rate of individual reaction within its current uncertainty.

measurement of currently uncertain nuclear reactions, phosphorus would also need to be determined in observational spectra in order for the O/P and P/Al thermome- ter candidates to be applied. It was concluded that N/O, N/Al, O/S, and S/Al were viable nova thermometers in light of these considerations.

In order to guide efforts to further reduce the reaction rate uncertainty, the re- actions acting as the primary and secondary sources of uncertainty for each nuclear thermometer were identified. This information is presented in Table 3.3. The first column lists the nuclear thermometer candidates where the first four entries only include elements that have been observed in the past, and the last four entries in- volve elements that have not been previously observed. The second column provides the range in value of each ratio over the entire peak temperature range as produced by the post-processing calculations. This value indicates the strength of a given ratio’s

dependence on temperature and, therefore, its utility, irrespective of sensitivity to re- action rate uncertainty. The next two columns (columns 3 and 4) display the primary sources of uncertainty in the potential nova thermometers with the uncertain reaction to the left and its uncertainty at nova temperatures to the right. The final two columns (columns 5 and 6) provide the secondary sources of uncertainty in the same format.

A variety of information was extracted from Table3.3. First, the secondary sources of uncertainty only result in abundance ratio variations of 30% or less, which has rela- tively little effect when the substantial uncertainties in the spectroscopically observed abundances are considered (see Table 1.2). Secondly, the ratios involving P and S— namely, O/S, S/Al, O/P, and P/Al—demonstrate the most potent dependence on temperature. The third and, perhaps, most significant conclusion is that one reac- tion, 30_P(p,γ)31_{S, bears nearly sole responsibility for the reaction rate uncertainty of}

the ratios including P and S. However, the importance of this rate to the production of sulfur and heavier elements is well-known (Jos´eet al.,2001;Parikhet al.,2011, among

others). 30_{P is a short-lived nuclide (t}

1/2 = 2.498 minutes, Basunia, 2010), meaning

that direct studies of30_P(p,γ)31_{S can only be conducted at radioactive beam facilities.}

However, a sufficiently intense30_{P beam has not been produced to date, so only lim-}

ited data from indirect studies (seeDohertyet al.,2012;Parikhet al.,2011;Wredeet al., 2009) is available. For a recent review on the status of this measurement, seeWrede

(2014). As a result, the 30P(p,γ)31S rate included in the_STARLIB library was adopted

from the Hauser-Feshbach statistical model estimates of Rauscher and Thielemann

(2000) with an assumed factor of 10 uncertainty in the classical nova temperature range. This rate is in agreement with the Parikh et al. (2011) rate, and its factor 20

uncertainty, determined using a Monte Carlo approach (Parikhet al., 2008). In short,

any improvement to the30_P(p,γ)31_{S rate uncertainty would significantly increase the}

viability of the P and S nuclear thermometers presented, and these results provide added motivation for the continuing efforts to experimentally measure this reaction.