Fisker, J L

Hix, W R

Roberts, L F

Smith, M S

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PoS(NIC-IX)202Monte Carlo simulations of Type I X-ray burstnucleosynthesisLuke F. RobertsPhysics Dept., Colorado College14 E. Cache La PoudreColorado Springs, CO 80903, USAW. Raphael HixPhysics Division, Oak Ridge National LaboratoryOak Ridge, TN, 37831-6354, USAMichael Smith∗†Physics Division, Oak Ridge National LaboratoryOak Ridge, TN, 37831-6354, USAE-mail: msmith@mail.phy.ornl.govJacob L. FiskerJoint Institute for Nuclear Astrophysics &Dept. of Physics, Univ. Notre Dame225 Nieuwland HallNotre Dame, IN 46556-5670, USAType I X-ray bursts are recurrent, violent runaway thermonuclear explosions on the surface ofan accreting neutron star in a binary star system, driven by reactions on proton-rich unstablenuclei via the rp-process. Large-scale nucleosynthesis calculations are necessary to determinethe observed X-ray luminosity and the possible production of rare, low-mass p-nuclides in theseoutbursts. We have, for the first time, used a Monte Carlo approach with a post-processing nu-cleosynthesis code to correlate the uncertainties in the (mostly unmeasured) input thermonuclearreaction rates with the uncertainties in the energy generation and synthesized nuclear abundancesthroughout a burst. Preliminary results and future plans for this study will be discussed.International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX25-30 June 2006CERN∗Speaker.†ORNL is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)202Monte Carlo simulations of Type I X-ray burst nucleosynthesis Michael Smith1. Background and MotivationA Type I X-ray burst (XRB) is a violent runaway explosion [1] on the surface of a neutronstar caused by a thermonuclear instability in mass that has been transferred from its solar like com-panion in a binary star system. These outbursts, which can recur hourly, are driven by reactionson proton-rich unstable nuclei via the alpha-p process and rp-process [2, 3]. Large-scale nuclearburning calculations are required to determine the energy generation in XRBs that drives the ob-served X-ray luminosity. Nucleosynthesis calculations can also estimate the possible contributionof these explosions to the abundances of the rare, low-mass p-nuclides such as 74Se, 78Kr, 92,94Mo,and 96,98Ru that are difficult to synthesis in standard p-process scenarios [4].Roughly a thousand different nuclear reactions are thought to occur in XRBs, and almost allinvolve proton-rich unstable nuclei and are unmeasured. XRB nucleosynthesis calculations there-fore rely heavily on reaction rates derived from statistical model calculations of proton capturecross sections. These cross section estimates, in which the contributions from many closely spacednuclear levels are averaged, are appropriate for heavier nuclei (A > 40) at the high peak temper-atures (∼ 1 GK) of XRBs. However, they are not appropriate for reactions through compoundnuclei with lower level densities – such as lighter mass nuclei, or heavier nuclei at lower excitationenergies that contribute to the rate during the lower temperature cooling phase of the burst [5].It is therefore important to improve the determination of input thermonuclear rates for XRBsimulations via measurements or improved modeling. Because of the large number of reactionrates in XRBs, it is crucial to determine which rates to focus on – specifically, which rates havethe largest impact on energy generation (and its related observable, the X-ray luminosity) andon element synthesis. However, because so many reaction rates contribute to the production anddestruction of any given nucleus and to the energy generation in a highly coupled way, traditionalsensitivity analyses where one or a few reaction rates are varied and the others are held constantcannot uncover all of the correlations between input rates and XRB model predictions. Our studyis aimed at developing computation tools – unique for XRB studies – to determine how nuclearreaction rate uncertainties impact understanding of element synthesis and energy generation.2. ApproachOur overall approach involves four parts, the first two of which are completed and published[6, 7, 8]. First, self-consistent 1-dimensional XRB simulations were performed with a code thatcoupled a full thermonuclear reaction network of 298 isotopes to hydrodynamics including dif-fusive heat transport, convection, and general relativity [6, 7]. Second, temperature and densityhistories of descending Langrangian fluid elements in the envelope were traced in time throughoutthe burst [8]. In the third part, the current study, post-processing element synthesis calculationswere performed with these histories, and a methodology devised to determine the reactions crucialfor energy generation and element burning. To do this, we have carried out the first Monte Carlo(MC) element synthesis calculations for an XRB (details below). Finally, the sensitivity of a self-consistent hydrodynamics plus nuclear burning XRB model to reactions deemed important by thepost-processing studies will be investigated in the fourth, future, portion of the project.2PoS(NIC-IX)202Monte Carlo simulations of Type I X-ray burst nucleosynthesis Michael SmithThe Monte Carlo approach, first used in Big Bang studies [10, 11] and then for novae [12, 13],enables the investigation of the input (i.e., reaction rate) sensitivity of highly-coupled systems withmany parameters (i.e., abundances) that are difficult to study with traditional techniques where oneor a few inputs are varied while all others are kept fixed. The basic procedure can be summarizedas follows. First, we simultaneously and independently vary the value of each input reaction ratefor use in a large number of trial simulations. Specifically, we construct the variation of each rateover 50,000 trials to be a log-normal distribution centered on the canonical rate value and with awidth corresponding to the rate uncertainty (estimated or determined from experiment). We use thelog-normal distribution because nuclear reaction rates are manifestly positive: using a Gaussian ornormal distribution of reaction rates can in some cases result in unphysical negative reaction rates.Then, for each MC trial, we run the post-processing element synthesis code with a temperatureand density history from [8] and one of the reaction rate sets. For each trial, we save the ratevariations, final abundances, and energy generation in different burst phases. We also determineif the new rates have significantly altered the burst energy generation compared to the canonicalrun, and therefore violated the self consistency of the post processing calculation; these trials areflagged for further investigation. The distribution of predicted final abundances over the MC trialsenables us to quickly determine abundance uncertainties (90 % confidence limits). Figure 1 showsan example of the distribution of how the final abundance predictions for 74Kr, a decay precursorto the p-nuclide 74Se, are used to determine an abundance uncertainty.We then determine the correlations of abundance and energy generation with rate variations.To do this, the different energy generation phases of the XRB are first automatically determinedby searching for changes in the dominant energy generating reaction in the canonical run. Then,correlations between the input reaction rates and the integration of the energy generation rate overdifferent burst phases are determined. This is followed by determining the correlations between allinput reaction rates and the predictions of all final abundances. The real power of the Monte Carlotechnique is given by these last two calculations: it is the first time that the impact of simultaneousvariation of all input reaction rates has been determined.3. Preliminary Results• Figure 2 shows the positive correlation between the energy generation rate during the phasesleading up to the burst with the rate for the reaction 15O(α,γ)19Ne. This reaction constitutes amajor pathway for processing matter created in the CNO cycle to higher mass nuclei that canact as seed nuclei for the rp-process [9]. The rate with the most significant impact on energygeneration over the entire burst is found to be the triple-alpha reaction rate. The correlation isshown in Figure 3. The rate of the triple-alpha reaction determines if the supply of hydrogenis exhausted in the burst, causing two distinct burning regimes.• Figure 4 shows the anti-correlation between the abundance of 74Kr, a decay precursor tothe p-nuclide 74Se, and the 74Kr(p,γ)75Rb reaction rate. The sensitivity of abundances to anearby capture reaction rate is typical throughout our system. The 74Kr abundance is alsostrongly correlated with the 64Ge decay rate.3PoS(NIC-IX)202Monte Carlo simulations of Type I X-ray burst nucleosynthesis Michael SmithFigure 1: Generation of abundance uncertainties (90 % confidence limits) from Monte Carlo trial results• Some reactions such as 23Al(p,γ)24Si, strongly influence the energy generation as well asthe final synthesized abundances for a wide range of nuclei; other low-mass proton capturereactions were not found to be nearly as important.• Decays of 24Si, 28,30S, 34Ar, 38Ca are strongly correlated with energy generation during dif-ferent burst phases.4. Future WorkWe will repeat our calculations with a new set of improved XRB temperature / density profiles,and then follow this with a detailed study of the sensitivity of a full XRB model with the mostimportant reactions emerging from the Monte Carlo post-processing approach.References[1] S.E. Woosley, R.E. Taam, Nature, 263, 101 (1976).[2] R.K. Wallace, S.E. Woosley, Astrophys. J. Suppl., 45, 389 (1981).[3] S.E. Woosley et al., Astrophys. J. Suppl., 151, 75 (2004).[4] M. Arnould, S. Goriely, Phys. Rept., 384, 1 (2003).[5] T. Rauscher, F.-K. Thielemann, Phys. Rev. C, 56, 1613 (1997).[6] J.L. Fisker et al., Astrophys. J., 608, L61 (2004).[7] J.L. Fisker, E. Brown, M. Liebendorfer, H. Schatz, F.-K. Thielemann, Nucl. Phys. A, 758, 447c (2005).[8] J.L. Fisker et al., Nucl. Phys. A, 752, 604 (2005).[9] J.L. Fisker et al., Astrophys. J., in press (2006).[10] L.M. Krauss, P. Romanelli, Astrophys. J., 358, 47 (1990).4PoS(NIC-IX)202Monte Carlo simulations of Type I X-ray burst nucleosynthesis Michael SmithFigure 2: Positive correlation between energy generation phases with the 15O(α,γ)19Ne reaction rateFigure 3: Regimes of hydrogen exhaustion and non-exhaustion caused by variation in the 4He(2α,γ)12Creaction rate5PoS(NIC-IX)202Monte Carlo simulations of Type I X-ray burst nucleosynthesis Michael SmithFigure 4: Negative correlation between 74Kr abundance and the 74Kr(p,γ)75Rb reaction rate[11] M.S. Smith, L.H. Kawano, R.A. Malaney, Astrophys. J. Suppl., 85, 219 (1993).[12] W.R. Hix, M.S. Smith, A. Mezzacappa, S. Starrfield, D.L. Smith 2003, Nucl. Phys. A 718, 620 (2003).[13] M.S. Smith et al., in Proc. Int. Conf. on Classical Nova Explosions, eds. M. Hernanz & J. Jose,(Melville:AIP) 161 (2003).6

Monte Carlo simulations of Type I X-ray burst nucleosyntheis

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