Models of Classical Novae with · 2020. 2. 12. · Abstract Classical novae are thermonuclear...

Bachelor degree in Engineering Physics Thesis

Models of Classical Novae with

Author :M. Oriol Abril

Supervisor :Dr. Jordi José

Astronomy and Astrophysics Group

Barcelona, Spain

June 2017

Abstract

Classical novae are thermonuclear runaways at the envelope of a white dwarf due to the pilingup of H-rich accreted material. They have been observed to produce heavy elements during theexplosion, and they may play an important role in galactical abundances of some specific elements.

MESA (Modules for Experiments in Stellar Astrophysics) code has been thoroughly studied forits application to nova explosions. Detailed know-how of nova simulations with MESA has beenachieved, leading the road of future studies using this tool. Its capablities in the field have beentested, demonstrating to reach further than what has been done in previous literature. MESA hasbeen shown to give accurate nucleosynthesis yields for solar-like accreted material without anyfurther postprocessing up to 50 nova bursts.

The dependence of the nova outburst properties with the burst number have been analyzed.However, more simulations are needed in order to extract meaningful conclusions about the roleof the burst number in the properties of novae outbursts.

The key role of the nuclear reaction network has been highlighted, showing that simulationsof consecutive novae outbursts require nuclear reaction networks specifically tested for the work.Many nuclear reaction networks that were thoroughly tested in a single nova explosion have notbeen capable of properly simulating 10 consecutive outbursts. In addition, the sensitivity of someelements like 7Li to the conditions of the simulation has been clearly seen.

The role of convective overshoot mixing as implemented in MESA has also been tested. Ithas been found that, as shown in previous literature, it does account for dredge up. Thus, theabundance profiles show a clear increase in metal content. This at the same time acts as acatalyser of the CNO cycles powering the thermonuclear runaway. We plan to extend this workwith simulations of consecutive novae outbursts implementing convective overshoot.

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Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 Introduction 6

1.1 Classical Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Modules for Experiments in Stellar Astrophysics 7

2.1 MESA outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Physics of MESA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Opacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Nuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Convective overshoot mixing . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Stellar evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.1 Structure and composition equations . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2 Timestep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.3 Mesh control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.4 Mass variation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 MESA output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Methodology 18

3.1 Starting model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Setting up the inlist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Simulating the burst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Nuclear reaction network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Mass loss scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.6 Overshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.7 Processing the output of the simulation . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Results and Discussion 28

4.1 Oxygen-neon white dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1.1 Nuclear reaction networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1.2 Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 Carbon-oxygen white dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Nuclear reaction networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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4.2.2 Mass loss schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.3 Dependence on the burst number . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.4 Convective overshoot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Conclusion and perspectives 41

Appendices 45

A Nuclear reaction network tables 46

A.1 List of reactions included in cno . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

A.2 List of reactions included in ppcno . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

A.3 List of reactions included in nova_ext . . . . . . . . . . . . . . . . . . . . . . . . . 48

A.4 List of reactions included in nova_mod . . . . . . . . . . . . . . . . . . . . . . . . . 49

A.5 List of reactions included in jj_isos . . . . . . . . . . . . . . . . . . . . . . . . . . 51

B Installation guide 58

B.1 Remotely connecting to the server . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

B.1.1 Linux/UNIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

B.1.2 Windows/DOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

B.2 Before MESA installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

B.3 MESA installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

B.4 Analysing MESA output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

C Repositories 60

C.1 pyMESA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

C.1.1 grafics_mesa.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

C.1.2 write_latex.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

C.1.3 AbunMovie.py and PvsNmovie.py . . . . . . . . . . . . . . . . . . . . . . . 63

C.1.4 ejecta.py and plot_compared_ejecta.py . . . . . . . . . . . . . . . . . . . . 63

C.1.5 plot_nova_hist.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

C.1.6 pyMESA libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

C.2 MESAstro-vim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

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List of Figures

1.1 Scheme of the Roche Lobe Overflow . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Regions covered by MESA opacity tables. From Paxton et al. 2011. . . . . . . . . . . 10

2.2 Schematic of some MESA star cell and face variables . . . . . . . . . . . . . . . . . 12

2.3 Illustration of the mesh in both Lagrangian mass and cell inner mass fraction coor-dinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 PGPLOT window appearence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Evolution of a 1M� CO WD using one of the previous versions of the inlist file atan accretion rate Ṁ = 5× 10−8M�/year . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Cumulative number of retries using the same inlist for different accretion rates . . 24

3.4 Mass evolution for Ṁ = 2× 10−10M�/year . . . . . . . . . . . . . . . . . . . . . . 25

4.1 HR diagrams for the different networks . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 Mass evolution of a 1.3M� ONeMg WD . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 Recurrence time and ejected mass versus the burst number . . . . . . . . . . . . . 30

4.4 Metallicity of the ejected material for each burst . . . . . . . . . . . . . . . . . . . 31

4.5 Production factors relative to solar abundances for a 1.3M� ONe WD obtainedwith cno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.6 Production factors relative to solar abundances for a 1.3M� ONe WD obtainedwith nova_ext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.7 Production factors relative to solar abundances for a 1.3M� ONe WD obtainedwith nova_mod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.8 Production factors relative to solar abundances for a 1.3M� ONe WD obtainedwith jj_isos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.9 HR diagram for 20 consecutive novae outbursts using ppcno . . . . . . . . . . . . . 34

4.10 Comparison of the HR diagram obtained with different mass loss schemes for a1.0M� CO WD and ppcno net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.11 Comparison between relevant quantities for different mass loss schemes . . . . . . . 35

4.12 Comparison between recurrence time and ejected mass according to different massloss schemes for a 1.0M� CO WD and ppcno net . . . . . . . . . . . . . . . . . . . 36

4.13 Production factors relative to solar abundances according to the different mass lossschemes for a 1.0M� CO WD and ppcno net . . . . . . . . . . . . . . . . . . . . . 37

4.14 Comparison of mass loss and luminosity between different mass loss schemes . . . 37

4.15 Ejected mass and recurrence time versus burst number . . . . . . . . . . . . . . . . 38

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4.16 Overproduction factors for the 20 consecutive bursts showing no incongruence inthe HR diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.17 Abundance profiles for a 1.0M� CO WD at the onset of the TNR (ppcno net used) 39

4.18 Nuclear power of the different reaction categories . . . . . . . . . . . . . . . . . . . 40

List of Tables

2.1 MESA modules description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

A.1 List of reactions considered in cno_extras_o18_to_mg26_plus_fe56.net . . . . . 46

A.2 List of reactions considered in pp_cno_extras_o18_ne22.net . . . . . . . . . . . . 47

A.3 List of reactions considered in nova_ext.net . . . . . . . . . . . . . . . . . . . . . 48

A.4 List of reactions considered in nova_mod.net . . . . . . . . . . . . . . . . . . . . . 50

A.5 List of reactions considered automatically by MESA when using the isotopes used byJordi José in his thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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1 . Introduction

1.1 Classical Novae

Classical novae are thermonuclear explosions occurring in binary systems, formed by a white dwarfaccreting H-rich material from its companion, either a main sequence or red giant star. The masstransfer streams through the inner Lagrangian point of the system because it is a consequence ofthe companion surpassing the Roche Lobe radius, hence, it starts to lose mass due to Roche LobeOverflow. In fact, the accreted material has angular momentum, which means that accretion isnot spherically symmetric (Figure 1.1).

Figure 1.1: Scheme of the Roche Lobe Overflow. From Pearson Prentice Hall

During the accretion phase, the piling up of material on top of the white dwarf heats theenvelope (compressional heating). This paves the road for the onset of nuclear reactions. If theaccretion rate is low enough, it eventually accumulates under degenerate conditions, leading toa thermonuclear runaway (TNR), a classical nova outburst. For greater accretion rates, steadyburning can be achieved, as the H-rich material is burned at the same rate it is accreted, and foreven greater Ṁ , burning cannot match the accretion, leading to a red-giant-like structure. Thecase of interest of this work, novae explosions, is the most powerful outburst a white dwarf canexperience without being completely disrupted by the process. The ejected mass is of the order of10−4-10−5M� (José et al. 2007). Still, they are quite common phenomenon in the universe. OnlyX-ray bursts are more common, and around 30 ± 10 novae outbursts per year are expected onlyin our galaxy (José et al. 2007).

Therefore, as the white dwarf is not disrupted, all novae are expected to recur, with periodicitiesof the order of 104−105 years1, which makes impossible the observational study of recurrence andits effect on the nova outburst properties for human timescales. This converts simulations of novaeto study the differences (if any) between bursts a basic tool for obtaining observables that coulddepend on the burst number without having to see two consecutive outbursts. One of the maingoals of this work is to simulate many consecutive novae outbursts of the order of 10−100 in orderto study whether there are differences between them, and if there are, which ones.

1Some novae exhibit much shorter periodicities. The recurrent novae subclass is formed by systems for whichmore than 1 nova explosion has actually been seen, with periodicities ranging from 1 to 100 yrs

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2 . Modules for Experiments in StellarAstrophysics

2.1 MESA outline

Modules for Experiments in Stellar Astrophysics (MESA) (Paxton et al. 2011, 2013, 2015, hereafter,MESA papers when referred as a group) is an open source, robust, efficient and thread-safe libraryof Fortran modules with applications in a wide range of stellar astrophysics. Its motivation isto satisfy the demand of a high-fidelity and modern stellar evolution code in the areas of aster-oseismology, nuclear astrophysics, galactic chemical evolution and population synthesis, compactobjects, supernovae, stellar populations, stellar hydrodynamics, and stellar activity. Its particularfeatures and modern techniques as well as the range of both macro- and microphysics taken intoaccount allow MESA to be precise, fast and parallelizable.

Its modularity allows to widen the range of applications, as the modules are not only useful forthe main MESA module star (described in detail in Section 2.3) which implements the 1D stellarevolution but can also be used by other codes, as well as other codes can be brought into MESA.This modularity allows MESA, which is constantly developed, to easily include new functionalitieslike GYRE (Townsend et al. 2013), a set of stellar oscillation codes built on a multiple shootingscheme2.

Each of the modules, either numerical or physical are stored in their own folder inside themain MESA folder. Most of the modules are MESA specific and were developed by MESA team,however, MESA also distributes other packages along with it like PGPLOT3, GYRE2, ADIPLS4(Christensen-Dalsgaard 2008) or CRlibm5. MESA’s own modules are outlined in Table 2.1, andsome of them are detailed in the following Sections 2.2 and 2.3.

Module Use

atm

Physics module. It determines the pressure, temperatureand their partial derivatives at the outermost cell of thestar. This is achieved either from integration, interpolationsfrom atmospheric tables or a third recipe which requires auser specified optical depth τs.

binary

Physics module. Implements the evolution of two completestellar models simultaneously using the star module, ac-counting too for stellar rotation, effects of tidal interactionsand mass exchange between them.

chemPhysics module. Compilation of data and subroutines totreat chemical elements and their isotopes correctly.

colors

Physics module. Uses data from Lejeune et al. 1998, 1997 tointerpolate synthetical magnitudes and colors (i.e. B − V )from the effective temperature Teff , surface gravity log(g)and metal abundance [M/H]6. The approximate coverageof the MESA colors is Teff from 50000K to 2000K, log(g)5.5 to −1.02, [M/H] 1.0 to −5.0.

2https://bitbucket.org/rhdtownsend/gyre/wiki/Home3http://www.astro.caltech.edu/~tjp/pgplot4http://astro.phys.au.dk/~jcd/adipack.n/5http://www.swmath.org/software/12390

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https://bitbucket.org/rhdtownsend/gyre/wiki/Homehttp://www.astro.caltech.edu/~tjp/pgplothttp://astro.phys.au.dk/~jcd/adipack.n/http://www.swmath.org/software/12390

const

Utility containing mathematical and physical constants.Most physical values are taken from CODATA Recom-mended Values of the Fundamental Physical Constants(Mohr et al. 2008), while solar age, mass, radius and lu-minosity are from Bahcall et al. 2005.

eos

Physics module. MESA Equation of State tables. It workswith the natural variables in the Helmholtz free energyformulation ρ and T as independent variables. The ta-bles are based on OPAL EOS tables (Rogers et al. 2002)and extended to lower temperatures using the SCVH tables(Saumon et al. 1995). Outside the region covered by thesetables or for metallicities greater than Z > 0.04, tables fromFrank X Timmes et al. 2000 and Potekhin et al. 2010 areused.

interp_1d Numerical module for 1D interpolation.

interp_2d Numerical module for 2D interpolation.

ionizationPhysics module. Determines the ionization state as a func-tion of T , ρ and free electrons per nucleon (Paquette et al.1986).

kap Physics module. Calculates opacities (Section 2.2.1)

mlt

Physics module. Implements convection through the stan-dard mixing length theory from Cox et al. 1968. Calculatesthe difusion coefficients in order to treat convective mixingas a difussion process. It also has available other optionsto calculate these coefficients, Bohm et al. 1971; Böhm-Vitense 1958; Mihalas 1978 and Henyey et al. 1965

mtxNumerical module. Interface to matrix manipulation rou-tines and linear algebra.

netPhysics module. Creates and manages the nuclear reactionnetwork (Section 2.2.2)

neuPhysics module. Calculates neutrino related energy-lossrates and their derivatives.

numNumerical module. Provides ODEs solvers and a multidi-mensional Newton-Raphson solver for root finding.

package_templateTemplate with the structure and executables to create anew MESA module. Its function is to provide users an easystructure to bring their own codes and modules into MESA.

rates Physiscs module. Detailed in Section 2.2.2.

star 1D Stellar evolution module. Explained in Section 2.3.

utils Miscellaneous.

Table 2.1: MESA modules description

All these MESA modules have the same general structure. Each module has its own directorywith a standard set of subdirectories and scripts. The standard subdirectories for each module aremake, private, public, and test. The test directory has its own make and src directories for

6[M/H] = log(Z/X

Zsun/Xsun)

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the program that tests the module when it is created. The make directory has the makefile for thelibrary and will hold the object files and mod files that are created by the compiler. The publicdirectory has the sources for the interface to the library, while the private directory has sourcesfor the parts of the implementation that are meant for internal use only. For example, if you wantto see what’s available in the eos module, look in eos/public/eos_lib.f for the routines andeos/public/eos_def.f for the data.

The MESA input files relevant to this work are inlists and run_star_extras.f, the two .listfiles, the stellar model and the .net file defining the nuclear reaction network.

The inlist files are the base of a MESA star simulation, because they contain all the informationabout the simulation. They are divided in 3 parts, star job which specifies the type of calculation,the properties of the input model and the sources of EOS, opacities and nuclear rates; controlswhich specifies the options to be applied during the simulation and pgstar which determines theappearance of the live plots during the simulation. The link directs to the page with all theparameters in each part and their default value. These values are also stored in the files in thefolder $MESA_DIR/star/defaults/.

The run_star_extras.f is a complement to the inlist written in Fortran and compiled alongwith MESA star module when executing ./mk. It allows the user to implement simple subroutinesand functions that will run along with MESA and could not be achieved only using the parametersin the inlist file.

The profile_columns.list and history_columns.list files tell MESA which data columns shouldbe stored in the output files. The folder /star/defaults/ contains all possible data columns forprofile and history files and a little explanation of each variable. It also specifies if they are not inS.I. units.

The first lines of a MESA .mod stellar model contain general info about the star like the massin solar units, the model number and star age when ended the run that generated it, the initialmetallicity, the number of cells, the name of the .net file used to generate it or the number of speciesconsidered in the model. Then there is a row for each cell with at least its density, mass, velocity,temperature, luminosity, radius and all mass fraction abundances for each element. Eventually,the last rows contain general information about the previous model.

The nuclear reaction network lists all isotopes and reactions that have to be considered byMESA. Its format will be detailed further in section 3.4.

2.2 Physics of MESA

2.2.1 Opacities

MESA opacity tables are created combining radiative and electron conduction opacity tables. Theelectron opacity tables are taken from Cassisi et al. 2007, which covers the range between −6 <log ρ < 9.75 and 3 < log T < 9. In cases where temperature and density are outside these regions,a fit to the Hubbard et al. 1969 tables (Iben Jr 1975) is used for non-degenerate cores whereasYakovlev et al. 1980 fits are used for degenerate cases.

The radiative opacity tables are based on OPAL (Iglesias et al. 1993) tables, which are extendedsmoothly to J. W. Ferguson et al. 2005 tables at low T and ρ. At high temperature, Comptonscattering dominates the radiative opacity, and therefore, it is then calculated using equationsfrom Buchler et al. 1976. In addition, OP tables (Seaton 2005) can be used in place of OPAL dueto their identical format.

Figure 2.1 shows the range in T and ρ covered by the different opacity tables. Regions insidethe orange lines are covered by tables from previous literature or its blending, in order to smoothtransitions between tables or between tables and algorithms. Black lines indicate the region where

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http://mesa.sourceforge.net/star_job_defaults.htmlhttp://mesa.sourceforge.net/controls_defaults.htmlhttp://mesa.sourceforge.net/pgstar_defaults.html

Figure 2.1: Regions covered by MESA opacity tables. From Paxton et al. 2011.

algorithms are used to calculate the radiative opacity. Above the red dashed line, it is taken intoaccount that the number of e+e− from pair production exceeds the number of e− from ionizednuclei. On the right of the blue dashed line, electron conduction dominates the radiative opacity.The profiles T versus ρ are shown in solid blue lines for different masses indicated in the figure.

2.2.2 Nuclear reactions

The nuclear reactions are implemented between the two modules rates and net. The first mod-ule contains thermonuclear reaction rates from NACRE (Angulo et al. 1999) and JINA Reaclib(Cyburt et al. 2010), with preference given to JINA. In addition, for some specific reactions, otherprescriptions are also available (i.e. 12C(α,γ)16O rate from Kunz et al. 2002).

The net module implements the nuclear reaction networks and contains a set of defined nuclearreaction networks to account for basic burning or more extended events such as hot CNO reactionsor α-capture chains.

2.2.3 Convective overshoot mixing

mlt module treats convection as a time-dependent diffusive process, and therefore, it does notaccount for hydrodynamical instabilities that arise at the borders of convective regions and resultin mixing between the inner layers and the convective region.

To account for this phenomenon, MESA uses an overshoot mixing diffusion coefficient

DOV = Dconv,0 exp(− 2zfλP,0

)(2.1)

where Dconv,0 is the MLT diffusion coefficient that describes the convection near the boundary, zis the distance from the convective region boundary, f is a free parameter that must be calibratedby the user and λP,0 is the pressure scale height.

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2.3 Stellar evolution

The main feature of MESA is allowing stellar evolution using all its modules from microphysiscs tomacrophysics. The top level routine for evolving a star is run1_star in $MESA_DIR/star/job/run_star_support.f90. The outline of the subroutine is the following:

Listing 2.1: Subroutine run1_star outline1 call before_evolve2 evolve_loop: do3 call before_step_loop ()4 step_loop: do5 result=star_evolve_step ()6 if (result =="keep_going") result=pick_next_dt ()7 ! pick_next_dt can modify the value of result8 if (result =="keep_going") exit step_loop9 if (result =="redo") result=star_prepare_to_redo ()

10 if (result =="retry") result=star_prepare_to_retry ()11 if (result =="backup") result=star_do1_backup ()12 if result =="terminate" then13 continue_evolve_loop = .false.14 exit step_loop15 end if16 end do step_loop17 ! once we get here , the only options are keep_going or terminate.18 ! redo , retry , or backup must be done inside the step_loop19 call after_step_loop ()20 if result =="terminate" call terminate_normal_evolve_loop ()21 call do_saves ()22 end do evolve_loop23 call after_evolve_loop ()

These subroutines use all the modules detailed in Sections 2.1, 2.2 and the methods detailed inthis section in order to evolve the star. The star module works with one-dimensional, sphericallysymmetrical models by dividing the structure of the star into cells or zones. These zones arenumbered from 1 at the surface towards the center which has the highest number. All coupledequations are solved simultaneously by the Newton solver from num which at the same time usesmatrix routines from mtx.

Cells can have either mass-averaged or defined at the outer border quantities. In order toimprove stability and efficiency, MESA defines the variables as shown in Figure 2.2. Basic variablesdensity ρk, temperature Tk and mass fraction vector Xi,k, being i the identifier of the isotopeare cell averaged quantities whereas mass interior to the face mk, radius rk, luminosity Lk andvelocity vk are boundary variables. In addition, many other variables are calculated at each celland boundary (Figure 2.2).

As it can be seen in Listing 2.1, the last subroutine called in the evolutionary step when therehas been no need for repeating the step or doing a back up is picking the next time step, rightafter selecting the timestep, the preparation of the new step calling before_step_loop sets themesh that will be used during the iteration. The subroutine star_evolve_step contains most ofthe other parts relevant to stellar evolution like mass adjustment or calling the different modulesin order to obtain the model of the star at time t+ dt.

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Figure 2.2: Schematic of some MESA star cell and face variables. From Paxton et al. 2011.

2.3.1 Structure and composition equations

Every iteration, MESA solves the coupled structure equations for pressure Pk, temperature Tk,luminosity Lk, radius rk and mass fractions of all present chemical elements for every cell k usingthe equations detailed in this section. In addition, an extra equation for the velocity vk can beconsidered if the hydrodynamics option is activated (which is not the default option, however, MESAcan swap to hydrodynamics if required). In the case of stellar explosions (novae in particular), itmust be taken into account since material can be ejected from the star at several thousand km/s-1,in dynamical timescales.

To simplify the explanation of the structure equations, all values will be evaluated at t + δtunless stated otherwise.

The density is determined via the mass conservation equation, which is rewritten to improvenumeric stability. That is

ρk =dmk

(4/3)π(r3k − r3k−1)⇒ ln rk =

1

3ln(r3k−1 +

3dmk4πρk

)(2.2)

where dm is the mass of the cell. If hydrodynamics is activated, then the velocity of the face k is

vk = rkd(ln rk)

dt(2.3)

The pressure is set by momentum conservation at the interior of every face.

Pk−1 − Pk = dmk[(

dP

dm

)hydrostatic

+

(dP

dm

)hydrodynamic

]= dmk

[− Gmk

4πr4k− ak

4πr2k

](2.4)

where dmk = (dmk−1 + dmk)/2 and ak is the acceleration, evaluated from the changes in vk.

There are four alternatives to the temperature equation (hydro_eqns.f90 lines 1046-1217), onepurely hydrostatic and 3 hydrodynamic. The standard and hydrostatic form of the temperatureequation is

Tk−1 − Tk = dmk[∇T,k

(dP

dm

)hydrostatic

T k

P x

](2.5)

12

where ∇T,k = d lnT/d lnP af face k from the module mlt (mixing length theory), dmk =0.5(dmk−1 + dmk), T k = (Tk−1dmk + Tkdmk−1)/(dmk−1 + dmk) (the same works with P ) isthe temperature interpolated by mass at face k. The value for dP/dm used in this equationis its hydrostatic value, because mlt module assumes hydrostatic equilibrium (see comment inKippenhahn et al. 1990 chapter 9.1).

In general, and in stars in particular, energy can be transported by three different mechanisms,conduction, convection and radiation. In order to account for these different mechanisms, MESAhas available various alternatives in order to define dP/dm properly independently of the energytransport mechanism. The alternatives are detailed below in order of priority. Text written inthis font makes reference to MESA input parameters from the controls section, and q(k) is themass fraction interior to cell k.

• if q(k) >qmin_freeze_non_radiative_luminosity then

– use Lconv from start of step to get Lrad = L− Lconv,start• else if q(k) ≤qmax_zero_non_radiative_luminosity then

– simply use Lrad = L

• else if option use_dPrad_dm_form_of_T_gradient_eqn selected

– if (∇T < ∇r) then∗ use Lrad = L(∇T/∇r) (Cox et al. 1968)

– else

∗ use Lrad = L

With the resulting Lrad, determine the expected dT/dm by (Kippenhahn et al. 1990)

dPrad/dm = −κLrad/(c area2) (2.6)

where c is the speed of light, area is the surface of face k and κ is the opacity.

The boundary conditions in T and P are given using the atm values for pressure and tem-perature at the surface Ps and Ts. Applying Equations 2.4 and 2.5 to the outermost cell k = 1gives

dPs =Gm1dm18πr41

(2.7)

dTs = dPs∇T,1T1P1

(2.8)

this results in the following implicit boundary conditions, which are solved together with thestructure equation,

lnT1 = ln(Ts + dTs) (2.9)lnP1 = ln(Ps + dPs) (2.10)

Luminosity is calculated using energy conservation

Lk − Lk+1 = dmk(�nuc + �ν,thermal + �grav) (2.11)

where �nuc is the total nuclear reaction energy generation rate (from net) except the neutrino loss,�ν,thermal is the specific thermal neutrino-loss rate (from neu). The term �grav is the rate of changein gravitational energy due to expansion or contraction of the star.

13

Finally, the mass fraction equation for each element Xi,k, where i indicates the element, is

Xi,k −Xi,k(t) = dXburn + dXmix =dXi,kdt

δt+ (Fi,k+1 − Fi,k)δt

dmk(2.12)

being dXi,kdt the rate of change from nuclear reactions (from net) and Fi,k the mass flux of elementi through face k

Fi,k = (Xi,k −Xi,k−1)σk

dmk(2.13)

where σk is the diffusion coefficient obtained after combining standard difussion (from mlt) withconvective overshoot.

Equations 2.2, 2.5, 2.4, 2.11, 2.12 (which is actually one for element) are solved simultaneouslyfor all cells every iteration by the Newton-Raphson method. If chosen, Equation 2.3 is also solvedwith all the other coupled equations.

2.3.2 Timestep

Control of the timestep is a basic part of stellar evolution. Timesteps should be small enough forthe evolution to converge and to ensure a precise calculation but large enough to allow efficientevolution and not require prohibiting computation times. Changes on the timestep should also besmooth enough to prevent propagation of discontinuities but rapid enough to respond to variationsin structure or composition.

The timestep control uses a low-pass filter (Söderlind et al. 2006) to calculate the timestep forthe next iteration using data from the two previous iterations if possible. According to the sourcecode7, the timestep for model i+ 1 is

δti+1 = δtif

([f(νt/νc,i)f(νt/νc,i−1)

δti/δti−1

]1/4)(2.14)

where f(x) = 1 + κ arctan[(x − 1)/κ] with κ = 10 (from file timestep.f90 lines 382-385 and2724-2783). νt is the dt_limit_ratio_target which unless stated otherwise in the inlist is thedefault value 1.0, δti is the timestep used for model i and νc,i is the maximum ratio between allvariables and its soft limits, and between varcontrol and varcontrol_target corresponding tomodel i. νc,i is determined right before applying Equation 2.14. varcontrol is calculated betweenlines 2539 and 2721 of timestep.f90, and is basically an average of the hydrodynamic structurevariables stored in xh.

Thus, the procedure to set δti+1 starts calculating varcontrol, and then enforcing all the softand hard limits. If a variable is inside its soft limit range, its ratio is zero, if it is between the softand hard limit, MESA stores the ratio in order to consider it when setting νc,i and if it is over thehard limit, the iteration is retried directly. Therefore, soft limits will only have an effect if theirratio is greater than varcontrol ratio. Afterwards, the low-pass filter is used (Equation 2.14) andfinally, it is ensured that δt limits are correctly enforced.

2.3.3 Mesh control

The mesh adjustment scheme is called from evolve.f90 every time the subroutine prepare_for_new_step is executed. This calls the subroutines that control the mesh and split or mergeits cells, which are written between adjust_mesh.f90, adjust_mesh_plot.f90, adjust_mesh_split_merge.f90, adjust_mesh_support.f90, mesh_adjust.f90, mesh_plan.f90 and mesh_functions.f90.

7The formula in Paxton et al. 2011, 2013 is slightly different

14

The mesh control is divided into two different stages. The planning stage determines whichcells have to merge or be splitted according to gradient limits on quantities like mass, radius,pressure, temperature, adiabatic gradient, angular velocity, element mass fractions above a giventhreshold or other parameters that can be set to increase the sensitivity in particular regions ofinterest such as convective boundaries or burning regions. In addition, users can specify their ownchecks using other_mesh_functions, file found inside $MESA_DIR/star/other/.

All these mesh functions evaluate the relative change between cells and weight it using themesh_delta_coef parameter. All the cells where the weighted change is larger than the limits setare marked for splitting whereas the cells that have too small changes are marked for merging. Ifthe weighted changes of consecutive cells are all below the merging limit, all contiguous cells wouldbe merged into one single cell. This could give rise to numerical diffusion because when merging5 consecutive cells, the fifth may have a different composition than the first one. Therefore, thereare mechanisms to prevent it (i.e. limits to size difference between adjacent cells). In addition,the number of cells merged every iteration is a little percentage of the total, which alone shouldalready prevent numerical diffusion.

When the change between two cells is over the limit and they are marked for splitting, MESAchecks which one is bigger and marks this one for splitting. After every cell merge or split, a checkfor relative size difference is performed in order to ensure that no cell is mesh_max_allowed_ratiobigger than its neighbours.

The adjustment stage applies the remesh plan and sets the new values for the basic variables.Whenever possible, physical considerations are taken into account when recalculating the val-ues, such as conservation of mass when calculating the new density, energy conservation for thetemperature or angular momentum conservation for the angular velocity.

For cells being merged, the abundance of the different elements are set to the mass averagedabundances from the parent cells, whereas for cells being split, the neighbouring cells are used tolinearly interpolate the abundances at any point of the cell. Then the slopes are corrected so thatthe sum of the mass fraction always is 1 and eventually these functions are integrated to obtainthe new abundances.

2.3.4 Mass variation scheme

Modifying the mass of a star requires to accurately compute the state of the newly added materialin case of accretion or of the inner layers that become the new surface in case of mass ejection.For an accretion rate Ṁ at a cell with lagrangian mass coordinate m (the interior mass) there aretwo relevant timescales, the thermal time τth = (M −m)CpT/L where M is the total mass of thestar, Cp the specific heat at constant pressure, T the temperature and L the luminosity of the starand the time to accrete this same layer τacc ' (M −m)/Ṁ .

Near the surface, L� CpTṀ meaning that τth � τacc, giving the accreted material sufficienttime to relax to the thermal equilibrium imposed by L. Even when L is solely due to compressionsuch as the case of a cold WD (where L ∼ CpTbṀ being Tb the temperature at the boundary of thedegenerated core) the temperarute fulfills T � Tb, thus, not breaking the τth � τacc inequality.

That also means that the thermal state of the accreted material can be neglected and directlyassume the material arrives with the same entropy as the surface of the star, because it will reachthis value in the τth fast timescale.

The mass gain or mass loss in MESA is implemented in two steps, first the δM is calculatedusing the mass gain or mass loss from the mass change Ṁin (which is an input parameter) andthe mass loss from the winds subroutines. Afterwards, the mass of each cell is adjusted withoutmodifying the number of cells. In this work, two different mass loss approaches relevant to novaehave been considered. Both winds are activated by setting their scaling factor to η > 0.

15

Super Eddington Wind

Super Eddington Wind is triggered by a threshold luminosity LEdd, assuming that exceding LEddtriggers the mass loss, which is determined once triggered by:

ṀEdd = −2ηEddL− LEddv2esc

(2.15)

where ηEdd is the Super Eddington Wind scaling factor, set to ηEdd = 1 for all simulations on thesework with this wind activated, vesc =

√2GM/R, L the luminosity of the star and LEdd = 4GcMκ ,

being G the gravitation constant, c the speed of light, M the mass of the star and κ the Rosselandmean opacity at the surface.

Roche Lobe Overflow

The mass loss via Roche Lobe Overflow takes place only when certain conditions specified in theinlist file are fulfilled. The name of the inlist file parameters is indicated using this font. Thereare three conditions, L > Lrlo =rlo_wind_min_L which defaults to 10−6L�, R > Rrlo =rlo_wind_roche_lobe_radius which defaults to 0.4R�, and Teff < Teff ,rlo =rlo_wind_max_Teffwhich defaults to 1099 K. The equation giving the mass loss rate is:

Ṁrlo = −Ṁrlo,0ηrlo exp(R−RrloHrlo

)(2.16)

where Ṁrlo,0 is the base Roche Lobe Overflow mass transfer, ηrlo is the scaling factor (also set toηrlo = 1 for all simulations with Roche Lobe Overflow activated), Rrlo is the Roche Lobe Radiusand Hrlo is the wind scale height, both in R� units.

In addition, when Roche Lobe Overflow is activated, there are two other relevant parametersthat modify the mass change, roche_lobe_xfer_full_on = φon and roche_lobe_xfer_full_off= φoff. Then, for accretion (Ṁin > 0), when Ṁrlo = 0 (i.e. when the conditions on luminosity orradius are not fulfilled), the applied mass change becomes Ṁ = φxferṀin:

• φrlo < φon ⇒ φxfer = 1• φon < φrlo < φoff ⇒ φxfer = 12

(1− cos(π φoff−φrloφoff−φon )

)• φrlo > φoff ⇒ φxfer = 0

where φrlo = R/Rrlo.

Cell mass adjustment

Once δM = Ṁdt has been defined, the mass contained in each zone or cell must be adjustedaccordingly or the outermost zones removed from the model. Since 2015, MESA implements thefirst approach in the following way.

The two diferent timescales fulfilling τth � τacc imply that the outer layers T (q) varies reallyslowly and therefore it is easier to work with the q coordinate (mass fraction interior to thecell). Thus, the code divides the mesh in three regions (Figure 2.3), an inner region where timederivatives can be estimated in the form (∂/∂t)m simply using a same-cell difference, an outerregion where the same procedure can be applied to (∂/∂t)q and an intermediate region where theyare interpolated from the locations in q or m at the start of the step to the regions with the samecoordinate value at the end of the step.

Figure 2.3 shows a simplification of the mesh model of an accreting star during a time evolutionstep. The vertical lines show the cell boundaries, which in a real MESA simulation would be of theorder of 103. As the figure shows, there can be many cells containing the accreted material.

16

Figure 2.3: Illustration of the mesh in both Lagrangian mass and cell inner mass fraction coordi-nates. From Paxton et al. 2015.

2.4 MESA output

MESA returns its output in different types of file, history and profile .data files and it also allowsto save the star model at the end of the run as .mod, format which can be used to start a newsimulation from the model.

The history.data and profile.data files have the same format, a header with general informationabout the run and the model; and the body, which contains the values from the columns specifiedin history_columns.list and profile_columns.list separated by spaces. In addition to the valuesspecified in the .list files, extra information can be added to the file using the run_star_extras.f.

17

3 . Methodology

This work is based on MESA simulations, which were compared between them and compared withprevious results from other works. Therefore, explaining the details of the simulations is reallyimportant to understand the work and what are the simulations actually doing. This section aimsto explain how are MESA simulations set and which parameters and assumptions they considered.

3.1 Starting model

The starting model is the initial point of the simulation, therefore, it must be thoroughly checkedin order to simulate the desired phenomenon, consecutive novae bursts. MESA has the capabilityof evolving stars in nearly all stages of their live and particularly from the pre main sequenceprotostar to a cooling white dwarf. However, learning how to do this is not trivial and and out ofthe scope of this work. Thus, only two models have been used, a 1M� CO WD from Wolf et al.2013 and a 1.3M� ONe WD from P. A. Denissenkov et al. 2012b.

3.2 Setting up the inlist

In MESA, the inlist file is the one containing all the parameters of the run. Due to MESA’s wide rangeof aplication, its list of input parameters is also really wide, making really difficult to know alloptions MESA has available. Therefore, most of the parameters could not be tested nor its effect inour simulations could be studied, in which case, either the default MESA value or values from otherworks were used. We started from inlists used for similar goals: P. A. Denissenkov et al. 2012b,Wolf et al. 2013 and the two inlists based in these works present in the test_suite as nova andwd2 respectively. These two last inlists, were a little simplified from the published work but hadall parameter names actualized to the current release 9575. Eventually, an inlist suitable to ourcalculations could be achieved (Listings 3.1. 3.2 and 3.3) that worked for the input parametersrelevant to this work: accretion rates, initial models and nuclear reaction networks.

Listing 3.1: Inlist file: star_job1 &star_job2 ! Set this to false if you want to skip the initial terminal output3 show_log_description_at_start = .false.4 ! Choose which initial model to load5 load_saved_model = .true.6 saved_model_name = ’wd2.mod ’7 ! Choose the .net file containing the specifications of the nuclear ←↩

reaction network8 change_initial_net = .true.9 new_net_name = ’pp_cno_extras_o18_ne22.net ’

10 auto_extend_net = .false.11 ! Print on terminal the list of isotopes and reactions of the nuclear ←↩

reaction network at the start of the run12 show_net_species_info = .true.13 show_net_reactions_info = .true.14 ! Save model at end of run, useful to continue the calculations ←↩

afterwards15 save_model_when_terminate = .true.16 save_model_filename = ’final.mod ’

18

17 ! change whether MESA evolves a (radial) velocity variable, v, defined←↩at cell boundaries (activates the hydrodynamics option)

18 change_v_flag = .true.19 new_v_flag = .true.20 ! Restart age and model number count21 set_initial_age = .true.22 initial_age = 0 ! in years23 set_initial_model_number = .true.24 initial_model_number = 02526 set_tau_factor = .true.27 set_to_this_tau_factor = 3028 ! Show PGPLOT plots on the fly29 pgstar_flag = .true.30 / ! end of star_job namelist

The star job section of the inlist details the parameters, input files and other parameters set upat the start of the run that define the job to execute (along with some other parameters from thecontrols section). The initial star model is specified here, as well as the nuclear reaction networkand whether or not to save the final model. It is not recommended to set auto_extend_net to trueunless it is a user defined one, because many of the predefined nets contain a specifically thoughtlist of isotopes and reactions and also specify which reactions should not be included. This lastpart in particular, could give problems when extending the net.

Whether or not to show the PGPLOT window during the run must also be set here, but thepgstar section is reread every iteration, allowing the user to redefine the number and appearanceof plots in the window, and even the number of windows.

Listing 3.2: Inlist file: controls1 &controls2 ! Initial parameters, if a model is loaded they are not used3 initial_mass = 1.04 initial_z = 0.02d05 ! Type2 opacities for extra C/O during and after He burning6 use_Type2_opacities = .true.7 Zbase = 0.02d0 ! gives the metal abundances previous to any CO ←↩

enhancement8 !----------------!9 ! Accretion rate !

10 !----------------!11 mass_change = 2d-1012 !-------------------!13 ! Mass loss schemes !14 !-------------------!15 ! Roche Lobe Overflow16 rlo_scaling_factor = 1 ! uncomment to use Roche Lobe Overflow17 ! Roche Lobe Overflow Wolf et al 2013 parameters18 rlo_wind_min_L = 1d-6 ! only on when L > this limit. (Lsun)19 rlo_wind_max_Teff = 1d99 ! only on when Teff < this limit.20 rlo_wind_roche_lobe_radius = 100 ! only on when R > this (Rsun)21 rlo_wind_base_mdot = 1d-8 ! base rate of mass loss when R = roche ←↩

lobe radius (Msun/year)22 rlo_wind_scale_height = 1d-2 ! determines exponential growth rate ←↩

of mass loss (Rsun)23 roche_lobe_xfer_full_on = 0.5d0 ! full accretion when R/RL = this25 ! Super Eddington Wind, we use Ledd averaged over mass to optical ←↩

19

depth tau = 10026 super_eddington_scaling_factor = 1 ! parameter for mass loss driven←↩

by super Eddington luminosity27 super_eddington_wind_Ledd_factor = 1 ! multiply Ledd by this factor←↩

when computing super Eddington wind28 ! Convection treatment29 MLT_option = ’Cox’30 mixing_length_alpha = 231 ! Use Ledoux criterion for convection and semiconvection32 use_Ledoux_criterion = .true.33 alpha_semiconvection = 1d-334 thermohaline_coeff = 1d335 ! Overshooting36 ! Non -burning region37 overshoot_f0_below_nonburn_shell = 0.001 ! The switch from ←↩

convective mixing to overshooting happens at a distance f0*Hp ←↩into the convection zone

38 overshoot_f_below_nonburn_shell = 0.005 ! Thus, the "new_f" ←↩corresponds to f0+f_old when comparing to older versions of ←↩MESA. In this case, the value used if f_nova from Denissenkov ←↩2012

39 ! Hydrogen40 overshoot_f_below_burn_h_shell = 0.00541 overshoot_f0_below_burn_h_shell = 0.00142 ! Helium43 overshoot_f0_below_burn_he_shell = 0.00144 overshoot_f_below_burn_he_shell = 0.00545 ! Metals46 overshoot_f_below_burn_z_shell = 0.00547 overshoot_f0_below_burn_z_shell = 0.00148 ! Simulation termination criteria49 logQ_limit = 100 ! Stop if logQ at any zone is larger than this. ←↩

logQ = logRho - 2*logT + 1250 gamma_center_limit = 1000 ! gamma is the plasma interaction ←↩

parameter. Stop when the center value of gamma exceeds this ←↩limit

51 min_timestep_limit = 1d-1252 ! Output management53 log_directory = ’LOGS’54 max_num_profile_models = 500055 photo_interval = 5056 profile_interval = 557 history_interval = 258 terminal_interval = 559 write_header_frequency = 1060 ! Mesh control61 mesh_delta_coeff = 0.362 max_allowed_nz = 2000063 xa_function_species (1) = ’h1’ ! name of nuclide as defined in ←↩

chem_def64 xa_function_weight (1) = 2065 xa_function_param (1) = 1d-666 xa_function_species (2) = ’he4’ ! name of nuclide as defined in ←↩

chem_def67 xa_function_weight (2) = 2068 xa_function_param (2) = 1d-269 ! Timestep control70 varcontrol_target = 2d-4

20

71 delta_lgL_H_limit = 0.05 ! limit for magnitude of change in lgL_H72 delta_lgL_H_hard_limit = 0.5 ! limit for magnitude of change in ←↩

lgL_H73 lgL_H_burn_min = 1.5 ! ignore changes in lgL_H if value is less ←↩

than this74 delta_lgL_He_limit = 0.1 ! limit for magnitude of change in lgL_He75 delta_lgL_He_hard_limit = 1 ! limit for magnitude of change in ←↩

lgL_He76 lgL_He_burn_min = 2.5 ! ignore changes in lgL_He if value is less ←↩

than this77 delta_lgRho_limit = 1 ! limit for magnitude of max change in log10 ←↩

density at any point78 delta_lgRho_hard_limit = -179 delta_lgL_limit = 0.180 delta_lgL_hard_limit = 0.1581 delta_lgT_limit = 0.582 delta_lgT_hard_limit = 183 delta_lgTeff_limit = 0.1084 delta_lgTeff_hard_limit = 0.3085 ! these params provide the option to turn off mass change when have ←↩

small timesteps.86 ! mass change doesn’t do much in such cases except make convergence ←↩

harder.87 mass_change_full_on_dt = 1d-6 ! (seconds)88 mass_change_full_off_dt = 1d-6 ! (seconds)89 ! Nuclear reaction network90 net_logTcut_lo = 5.3d0 ! Strong rates are zero logT < logTcut_lo91 net_logTcut_lim = 5.4d0 ! Strong rates cutoff smoothly for logT < ←↩

logTcut_lim92 ! Composition of the accreted material93 accrete_same_as_surface = .false.94 accretion_h1 = 0.7000 ! Estimate Nomoto 200795 accretion_h2 = 096 accretion_he3 = 0.292910D -0497 accretion_he4 = 0.279971 ! Estimated Nomoto 200798 accretion_zfracs = 1 ! Anders & Grevesse 198999 ! atm module

100 which_atm_option = ’grey_and_kap ’101 / ! end of controls namelist

The initial parameters are not used because the star model is loaded in the star job instead ofbeing created by MESA at the start of the run, but these values are the ones that will be printedon the command line at the start of the run. Therefore, for consistency, they are kept here andmodified according to the model.

The Type2 opacities block specifies the use of the Type2 opacities tables from OPAL thatconsider Carbon and Oxygen enrichment (Iglesias et al. 1993). Type2 tables are for a given X,Zbase, dXC, and dXO, being dXC and dXO the non-negative enrichments in Carbon and Oxygenrespectively and Zbase the metallicity before CO enrichment, which must be specified.

Two mass loss schemes were taken into account, Super Eddington Wind and Roche LobeOverflow, whose parameters are set here in the inlist. In Section 3.5 three options and theircombinations are compared, the main options are Super Eddington Wind which would meancommenting all Roche Lobe Overflow parameters, default Roche Lobe Overflow, commentingeverything except rlo_scaling_factor = 1 and Wolf Roche Lobe Overflow, commenting onlythe two Super Eddington Wind commands.

The convection treatment is the default one but using Ledoux criterion and parameters taken

21

from Wolf et al. 2013 instead of P. A. Denissenkov et al. 2012b.

Overshooting due to convection instabilities is modelled using the only option available in MESAto account for dredge up, and using parameters from P. A. Denissenkov et al. 2012a. There areno inlists available from this work, and there is only a reference to fnova = 0.004 as overshootingparameter. Since then, many MESA releases have come, and now only one parameter is not enough8,as the boundary of the convection zone is ill defined in the exponential overshoot model, whichmotivated the introduction of a new free parameter f0 in addition to the already existent freeparameter of the model f . As outlined in the comments, the switch from convective mixing toovershooting happens at a distance f0λp,0 into the convection zone, which means that the f valuesfrom before the introduction of f0 must be changed to fnew = f0 + fold.

After the overshooting parameters there are some limits to force the termination of MESA ifsurpassed. All references set limits to these three quantities.

Output management indicates how many profiles can be written at most, value after whichMESA will start overwriting existing profiles. It is highly recommended to set this value to apositive value, and not to −1 (which would be no limit on the number of profiles) in order toavoid collapsing the disk space. Therefore, all other values about output periodicity should be setkeeping in mind how many models should the simulation last and how many space is available.

Mesh control parameters define the density of the grid used by MESA. The delta coeff basicallyallows the user to easily increase or decrease the number of zones in the model. Decreasing thiscoefficient by half will roughly double the number of zones. The relation is not exact due to theother factors affecting the mesh size, like xa_function_[species,wheight or param](:) thatconstrains the concentration gradient in the specified elements, increasing the number of zones ifsurpassed.

The timestep controls specify soft and hard limits on different quantities rellevant to the clas-sical novae in order to guarantee a smooth evolution of their values.

In order to speed up the computation time, certain nuclear reactions are neglected below agiven temperature. Right before being neglected, MESA has the option of a smooth transitionbetween the full off value below which they are completely neglected ant the full on value overwhich all of them are considered.

Finally, the composition of the solar-like accreted material is detailed. The comand accretion_zfracs has some integers assigned to different compilations of solar abundances, the one used isAnders et al. 1989 which is number 1.

Listing 3.3: Inlist file: pgstar1 &pgstar2 Grid8_win_flag = .true.3 Grid8_win_width = 74 Summary_Burn_xaxis_name = ’logxq ’5 Summary_Burn_xaxis_reversed = .true.6 Summary_Burn_xmin = -147 Summary_Burn_xmax = -38 Abundance_xaxis_name = ’logxq’9 Abundance_xaxis_reversed = .true.

10 Abundance_xmin = -1411 Abundance_xmax = -312 / ! end of pgstar namelist

Listing 3.3 shows an example of pgstar parameters that create a plot like the one in Figure 3.1.8For more information about f and f0 see https://sourceforge.net/p/mesa/mailman/message/34305621/. The

old MESA releases did not start at the boundary either but at a distance fλp,0, which caused confusion and drovepeople to think no f0 was used

22

https://sourceforge.net/p/mesa/mailman/message/34305621/

As explained before, the pgstar section of the inlist can be changed during the run with the onlydrawback that when changing the number of displayed windows, MESA pauses until the enter keyis pressed in the terminal were it is being executed.

Figure 3.1: PGPLOT window appearence

In order to achieve this inlist and all the set of parameters, different pieces had to be testedand fixed one by one. Due to the length of the simulations, the time available to conduct thisfinal degree thesis was the main reason to stop testing parameters further. The first part consistedin managing to simulate the whole burst, then the effect of the nuclear network was studied,afterwards the role of the mass loss scheme and finally simulating the mixing between the metalrich WD material and the accreted envelope via convective overshoot at the base of the zonesshowing convection.

3.3 Simulating the burst

For reasons unknown, special effort had to be made to simulate low accretion rate novae (i.e.∼ 10−10M�/year). The first inlist tried, adapted from the test_suite wd2, was originally thoughtfor accretion rates ∼ 10−8M�/year, at the verge of steady burning. For these conditions, MESA wasable to simulate recurrent novae using that set of parameters (Figure 3.2) but it dit not convergefor lower accretion rates.

The simulations for Ṁ ∼ 10−8M�/year were quite fast and required between 1000-10000 stepsto simulate many consecutive novae (Figure 3.3a shows the iteration number (which corresponds tothe column model_number in MESA profile .data files) and number of retries of the same simulationshown in Figure 3.2). For Ṁ ∼ 10−10M�/year MESA reached without significant problems the

23

0 500 1000 1500 2000 2500Star age (years)

1.00001

1.00002

1.00003

1.00004

1.00005

1.00006

1.00007

1.00008

1.00009

Star

mas

s (M

⊙)

(a) Mass evolution

0 500 1000 1500 2000 2500Star age (years)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

log(L)

(L⊙)

(b) Luminosity

Figure 3.2: Evolution of a 1M� CO WD using one of the previous versions of the inlist file at anaccretion rate Ṁ = 5× 10−8M�/year

start of the nova burst and at a reasonable age (Figure 3.4), but afterwards, it increased endlesslythe number of retries (Figure 3.3b) without significantly evolving the star.

0 500 1000 1500 2000 2500 3000Model number

0

50

100

150

200

250

300

350

Numbe

r of retrie

s

(a) Ṁ = 5× 10−8M�/year

0 20000 40000 60000 80000 100000 120000Model number

0

5000

10000

15000

20000

25000

30000

Numbe

r or retrie

s

(b) Ṁ = 2× 10−10M�/year

Figure 3.3: Cumulative number of retries using the same inlist for different accretion rates

The inlist was thought for recurrent novae near the steady burning region, where Figure3.2 actually seems to converge to, so it was eventually discarded and a new inlist was rewrit-ten from scratch based on inlist_ne_nova9. inlist_ne_nova came along and relied on itsrun_star_extras.f, to which no major changes were done. It implemented some checks afterevery iteration and a new termination code based on the burst number. For the termination code,the subroutine checks the luminosity of the star; L > Lburst = 104L� indicates the start of theburst, and L < Lbetween = 103L� its end, increasing the burst number until the maximum burstnumber allowed for the run.

Eventually, either some of the many changes in the inlist or the use of the run_star_extras.fallowed to simulate bursts with low accretion rates, which meant moving forward to check otherrelevant inlist parameters.

9Available at http://www.astro.uvic.ca/~dpa/MESA_NuGrid_Tutorial.html

24

http://www.astro.uvic.ca/~dpa/MESA_NuGrid_Tutorial.html

320000 325000 330000 335000 340000 345000Star age (years)

1.0000780

1.0000785

1.0000790

1.0000795

1.0000800

1.0000805

1.0000810St

ar m

ass (M

⊙)

Figure 3.4: Mass evolution for Ṁ = 2× 10−10M�/year

3.4 Nuclear reaction network

The selection of the nuclear reaction network is a crucial part of an stellar evolution and a nu-cleosynthesis simulation, and must not be overlooked. Previous literature does also pay specialattention to the nuclear reaction networks used by always specifying which .net file was used.

The .net file which contains all the information about the network in MESA Thus, the net andrates modules use the isotopes and reactions listed there and the rate info MESA already haseither from JINA or NACRE. Listing 3.4 is a template of a .net file. In a net file, MESA allows tointroduce other nets, to add or remove isotopes or reactions or using add_isos_and_reactionsto directly add the listed isotopes and all reactions MESA has available linking them.

Listing 3.4: Template of a MESA.net file1 include ’basic.net ’ ! Include already defined net2 add_isos( ! add specific isotopes3 c124 n145 o166 )78 ! Add or remove specific reactions9 add_reactions(

10 rpp_to_he3 ! p(p e+nu)h2(p g)he311 rpep_to_he3 ! p(e-p nu)h2(p g)he312 r_he3_he3_to_h1_h1_he4 ! he3(he3 2p)he413 )1415 remove_reactions(16 rne20gp_to_o1617 )

25

1819 add_isos_and_reactions(20 neut21 h 1 2 ! It allows to specify an element and all its desired ←↩

isotopes without repeating the element name22 he 3 423 )

There are mainly 3 nets used in previous literature:

• cno_extras_o18_to_mg26_plus_fe56.net (Wolf et al. 2013) which contains a net with 1H,3–4He, 12–13C, 13–15N, 14–18O, 17–19F, 18–20,22Ne, 22,24,26Mg and 56Fe (24 different isotopes)and 75 nuclear reactions (Table A.1). Hereafter cno.

• pp_cno_extras_o18_ne22.net (Rukeya et al. 2017) which contains a net with 1–2H, 3–4He,7Li, 7Be, 8B, 12–13C, 13–15N, 14–18O, 17–19F, 18–20,22Ne and 22,24Mg (26 different isotopes)and 81 nuclear reactions (Table A.2). This net is only used for CO white dwarfs. Hereafterppcno.

• nova_ext.net (P. A. Denissenkov et al. 2012b) which contains a net with 1H, 3–4He, 7Li,7Be, 8,11B, 12–14C, 13–15N, 14–18O, 17–19F, 18–22Ne, 20–23Na, 21–26Mg, 23–27Al and 24–30Si(48 different isotopes) and 121 nuclear reactions (Table A.3). Hereafter nova_ext.

All three reaction networks yield extremely similar results for the first burst, however, aftersome bursts, probably due to accumulation of errors, the results become incoherent. The HRdiagram clearly shows that there is something off with the simulation. There are more problemswith ONe WD than with CO WD, because for CO WD, a relatively simple net (but obviouslywell chosen) shows a better behaviour for 10 bursts than any of the studied options for ONe WD.Therefore, some changes were performed to the reaction networks, creating two more networks.

• nova_mod.net which contains the same isotopes as nova_ext (48 isotopes) and all the 245nuclear reactions MESA has available between them (Table A.4). Hereafter nova_mod.

• jj_isos.net which contains species n, 1–3H, 3–4He, 6–7Li, 7,9Be, 8,10–11B, 9,11–14C, 12–15N,13–19O, 17–19F, 18–22Ne, 20–25Na, 21–28Mg, 22–28Al, 26–30Si, 28–33P, 29–37S, 31–38Cl, 33–39Ar,36–39K and 39–40Ca (99 different isotopes) and all the 999 nuclear reactions MESA has avail-able between them (Table A.5). Hereafter jj_isos.

3.5 Mass loss scheme

The net ppcno was used to compare different mass loss schemes available in MESA, specifically themost relevant ones when studying classical novae, Super Eddington Wind and Roche Lobe Over-flow. The inlists available from P. A. Denissenkov et al. 2012b only considered Super EddingtonWinds, and Wolf et al. 2013 considered either one or the other in order to compare them. In thiswork, variations between these different schemes have been implemented and run. Wolf et al. 2013uses a set of parameters for the Roche Lobe Overflow which differ significantly from MESA defaultones.

Therefore, five combinations have been considered: only Super Eddigngton Wind (edd), onlyRoche Lobe Overflow using the default parameters (rloD), only Roche Lobe Overflow using Wolfet al. 2013 parameters which did not converge (probably due to the fact that the Roche LobeRadius considered in their work is 100R�, which seems too large to account for all the mass lostduring a novae event, MESA default value is 0.4R�), Super Eddigngton Wind and default RocheLobe Overflow (rloD+edd) and finally Super Eddigngton Wind and Wolf et al. 2013 Roche LobeOverflow (rloW+edd).

26

3.6 Overshooting

Finally, simulations trying to mimic the convective instability overshooting (Casanova et al. 2010,2011) at the bottom of convection regions are being conducted with only one set of parametersas shown in Listing 3.2. In order to obtain the same results as P. A. Denissenkov et al. 2014simulating the dredge up, the parameter f0 should be refined until simulations are able to reproduceexperimental results or 3D simulations in case observations were not available.

3.7 Processing the output of the simulation

The output of the simulation was analyzed using the codes detailed in Appendix C, basicallyejecta.py, plot_compared_ejecta.py and plot_nova_hist.py, which use functions defined inthe pyMESA*.py files and matplotlib (Hunter 2007) as plotting library. The first two codes dealwith the profile.data files whereas the third one with the history.data file. In the profiles, MESAonly returns information on the WD, which is the evolving star, and gives no direct informationabout the ejected material.

The script ejecta.py reads the history.data file in order to find the mass loss interval andwhich model numbers correspond to each mass loss interval, in order to avoid loading profileswhere there is no mass loss and accelerate the code. Afterwards, it reads the profile.data filescorresponding to the mass loss interval and check how many cells have a speed greater than theescape velocity, which are the ejected cells. All mass fractions from these cells are ponderated withtheir cell mass and added into a single value per burst in order to obtain the composition of theejected material for each burst. During the process, it also calculates the maximum tamperatureof the WD during the loss of mass, and the minimum and maximum velocities of escaping cells.All the data is saved in a .dat and a .txt file in order to avoid having to execute ejecta.py again.

plot_compared_ejecta.py plots the data resulting from ejecta.py either from a single runor more of them in order to compare. It generates overproduction plots compared to solar fractionsfrom Anders et al. 1989 (all overproduction plots in this work have been generated with plot_compared_ejecta.py), and also, Tmax, speed range of the ejected material and metallicity of theejected material for each burst.

plot_nova_hist.py plots the relevant quantities stored in the history.data file, star massevolution, luminosity, recurrence time, ejected mass, Teff and two HR diagrams, one with onecolor for each history.data file and another with one color for each burst number and a specificlinestyle for each history.data.

27

4 . Results and Discussion

4.1 Oxygen-neon white dwarfs

4.1.1 Nuclear reaction networks

Oxygen-neon (ONe) white dwarfs (WD) were simulated with 4 different nuclear reaction networksfor Ṁ = 2× 10−10M�/year while trying to find a net that could simulate up to 10 bursts withoutpresenting problems. Even though none of the studied nets gave the desired results, due to thetime requirement of the simulations, no more networks nor modifications of the existing ones (i.e.checking reaction by reaction like P. A. Denissenkov et al. 2012a; P. Denissenkov et al. 2013) couldbe studied. However, results seem to indicate that the effect of the problematic bursts could betreated simply as an outlier, not affecting the bursts after it.

The simulation with the cno net, was the first to be conducted, and only up to 4 bursts. As itpresented the incongruencies at the third burst (Figure 4.1a), no more efforts were dedicated tothis net. The simulation with nova_ext presented the incongruencies at the seventh burst (Figure4.1b), nova_mod at the tenth (Figure 4.1c) and surprisingly, jj_isos at the seventh and tenthbursts (Figure 4.1d).

4.55.05.56.06.57.0log(Teff) (K)

−2

0

2

4

6

8

log(L)

(L⊙)

burst num 1burst num 2burst num 3burst num 4

(a) cno

4.55.05.56.06.57.0log(Teff) (K)

−2

0

2

4

6

8

log(L)

(L⊙)

burst num 1burst num 2burst num 3burst num 4burst num 5burst num 6burst num 7burst num 8burst num 9burst num 10

(b) nova_ext

4.55.05.56.06.57.0log(Teff) (K)

−2

0

2

4

6

8

log(L)

(L⊙)


(c) nova_mod

4.55.05.56.06.57.0log(Teff) (K)

−2

0

2

4

6

8

log(L)

(L⊙)


(d) jj_isos

Figure 4.1: HR diagrams for the different networks. Each burst is represented using a differentcolor to show which burst number does not correspond to a proper nova explosion

28

Thus, simply considering larger reaction networks improved the reliability of the calculationsfrom cno to nova_ext and then to nova_mod but that stopped to be true for jj_isos which isby far the most complete but does not represent any improvement over the two nova nets. Manyconsiderations must be taken into account in order to properly understand this phenomenon. Thetwo nova nova nets are a set of reactions picked by hand, and thoroughly checked for a single novaoutburst. The only difference between the two of them is that nova_mod contains all reactionslisted in nova_ext and some more were added. jj_isos is automatically created by MESA fromthe list of isotopes given to it.

Therefore, there are probably nuclear reactions present in nova_ext, nova_mod or in the nuclearreaction list used in José et al. 1998 that are not included in jj_isos, in particular, all bridgereactions (i.e. 19F(n,γ)20F(β−)20Ne) will not be included because the intermediate isotope is notincluded in the isotope list. In addition, the reactions available to be included using the methodadd_isos_and_reactios are not explained in any of the MESA papers and it is not the whole MESAdatabase, because as seen in Tables A.1 and A.2, MESA has available rates for bridge reactions.

Therefore, in order to study more in depth the role of the nuclear reaction networks, nuclearreactions present in nova nets should be checked in order to see whether all of them are included injj_isos and the relevance of these missing reactions similarly to what was done in some previousworks (P. A. Denissenkov et al. 2012a; P. Denissenkov et al. 2013).

This results make clear that testing the nuclear reaction network for a single nova outburstis not enough (because all the used nets except jj_isos had been tested in these conditions),and that the complexity and range of these networks must be at least of the order of nova_mod.Therefore, a possible follow up of the work reported in this thesis is to perform a thorough analysisof the nuclear reaction network, identifying key reactions within MESA, and extend the analysis toONe novae.

Figure 4.2 shows the mass evolution of the ONe WD showing all the bursts. It can be clearlyseen that all the networks give extremely similar results. All of them also agree on the fact thatwhite dwarfs accreting solar composition material slowly win mass when convective overshootingis not considered.

0 50000 100000 150000 200000 250000 300000Star age (years)

0.000088

0.000089

0.000090

0.000091

0.000092

0.000093

0.000094

0.000095

0.000096

Star

mas

s (M

⊙)

+1.2999cnonova_extnova_modjj_isos

Figure 4.2: Mass evolution of a 1.3M� ONeMg WD

29

The total ejected mass and recurrence time have also been calculated when solar compositionis accreted (Figure 4.3). The bursts that presented incongruencies in the HR diagram are patentin the ejected mass plot, but afterwards, the values seem to return to the proper values as theyrejoin the results of the nets that still have not shown problems. Even though the number ofbursts is only ten, a clear but weak dependency over the burst number can be seen, encouragingmore work towards this area.

28000

29000

30000

Recu

rrenc

e tim

e(y

ears

)

cnonova_extnova_modjj_isos

2 4 6 8 10Burst number

0.00000475

0.00000500

0.00000525

0.00000550

0.00000575

0.00000600

Ejec

ted

mas

s (M

⊙)

Figure 4.3: Recurrence time and ejected mass versus the burst number. The recurrence time isplotted at half integers to clarify its value is defined between two bursts

4.1.2 Nucleosynthesis

Diffusion and standard convection 1D models do not present overshooting, therefore, the mixingbetween the accreted material and the ONe rich material from the outer layers of the WD was nottaken into account during these simualtions. Thus, the metallicity of the ejected material is of theorder of solar metallicity, which was also observed in previous works, where the accreted materialhad solar material instead of being a premixed composition between solar abundances and WDmaterial (P. A. Denissenkov et al. 2014; José et al. 1998). As the nucelar reaction network arenot complete enough to properly simulate ten consecutive bursts, no nucleosynthesys results havebeen obtained in this work for ONe WD. However, overproduction plots are shown in Figures4.5-4.8 in order to show the effect of overly simplified nuclear networks.

In addition, this figures also show which elements have larger variations between bursts, iden-tifying them as the most sensitive to incorrect nuclear reactions. Thus, they lead the road toidentify missing reactions.

30

2 4 6 8 10Burst number

0.0192

0.0194

0.0196

0.0198

0.0200

0.0202

0.0204

0.0206

0.0208

Metallicity

cnonova_extnova_modjj_isos

Figure 4.4: Metallicity of the ejected material for each burst

0 5 10 15 20 25 30Atomic mass number

10−10

10−8

10−6

10−4

10−2

100

102

Mas

s fra

c io

n/So

lar m

ass f

rac

ion

Mg

F

H

C

ONe

FeN

He

Burs num 1Burs num 2Burs num 3Burs num 4

Figure 4.5: Production factors relative to solar abundances for a 1.3M� ONe WD obtained withcno

31


10−10

10−8

10−6

10−4

10−2

100

102Mass fracti n/S

lar m

ass fracti n Mg

B

F

Al

H

C

Ne

O

N

Si

Na

Li

He

Burst num 1Burst num 2Burst num 3Burst num 4Burst num 5Burst num 6Burst num 7Burst num 8Burst num 9Burst num 10

Figure 4.6: Production factors relative to solar abundances for a 1.3M� ONe WD obtained withnova_ext


10−10

10−8

10−6

10−4

10−2

100

102

Mass fracti n/S

lar m

ass fracti n Mg

B

F

Al

H

C

Ne

O

N

Si

Na

Li

He

Burst num 1Burst num 2Burst num 3Burst num 4Burst num 5Burst num 6Burst num 7Burst num 8Burst num 9Burst num 10

Figure 4.7: Production factors relative to solar abundances for a 1.3M� ONe WD obtained withnova_mod

32

0 5 10 15 20 25 30 35 40Atomic ass nu ber

10−10

10−8

10−6

10−4

10−2

100

102

Mass fraction/Solar ass fraction

Be

Mg

B

Cl

AlNe

Ca

F

C

O

N

PSi

Ar

Na

Li

S

H

K

He

Burst nu 1Burst nu 2Burst nu 3Burst nu 4Burst nu 5Burst nu 6Burst nu 7Burst nu 8Burst nu 9Burst nu 10

Figure 4.8: Production factors relative to solar abundances for a 1.3M� ONe WD obtained withjj_isos

33

4.2 Carbon-oxygen white dwarfs

4.2.1 Nuclear reaction networks

One of the simplest networks available for CO WD, ppcno is capable of simulating 20 burstswithout any incongruence (Figure 4.9), thus, simulations were performed using this net, and nofurther effort was dedicated to nuclear reaction network comparisons.

4.254.504.755.005.255.505.75log(Teff) (K)

−2

−1

0

1

2

3

4

log(L)

(L⊙)

30-4040-50

Figure 4.9: HR diagram for 20 consecutive novae outbursts using ppcno. Bursts going from 30thto 50th.

4.2.2 Mass loss schemes

The results obtained with each scheme are quite different, except for rloW+edd which yieldsexactly the same as only Super Eddington Wind. This effect is probably for the same reason itdid not converge when used alone, the huge Roche Lobe Radius considered, making the mass lostwith these schemes negligible. In general, rloD+edd looks like an average between the two pureschemes (Figure 4.10).

All quantities have reasonable values and do no differ much between the different schemes. Themetallicity is basically solar metallicity, which is what should be expected because no overshootingis being taken into account, and MESA standard diffusion and convection models do not implementit. Figure 4.12 shows the ejected mass and the recurrence time. In this figure, the burst havingthe different HR trajectory towards larger luminosity and effective temperature can be identified.

Finally, nucleosynthesis analysis of the ejected material does also show a good agreementexcept for 7Li (Figure 4.13). Note that in most cases, only two lines differ from the other results,which correspond with the two bursts that show a different trajectory in the HR diagram, onefor rloD+edd and the other for edd (which as detailed before is exactly the same as rloW+eddand therefore, data corresponding to edd cannot be seen in any plot becaure it is overlapped byrloW+edd data).

34

Figure 4.10: Comparison of the HR diagram obtained with different mass loss schemes for a 1.0M�CO WD and ppcno net

(a) Luminosity evolution (b) Maximum temperature during themass ejection phase

(c) Maximim and minimum velocities ofthe ejected cells (d) Metallicity of the ejected material

Figure 4.11: Comparison between relevant quantities for different mass loss schemes for a 1.0M�CO WD and ppcno net

35

Figure 4.12: Comparison between recurrence time and ejected mass according to different massloss schemes for a 1.0M� CO WD and ppcno net

Note that the only 7Li yield with a mass fraction greater than 10−10 for rloD+edd and eddis the one corresponding to the problematic burst, while all other results are lower than 10−10and differ less than an order of magnitude between them. On the other hand, for rloD the resultsbetween different bursts range from one yield ∼ 10−9 and the remaining 9 are between 10−7−10−5.That is a difference of 4-5 orders of magnitude in the resulting yields depending on the mass lossscheme.

The explanation of this phenomenon is not clear nor straightforward. The most probableexplanation is that the parameters used for the Roche Lobe Overflow have not been properlychosen. However, to be sure, the luminosity and mass evolution for all three rellevant schemes(Figure 4.14) have been compared for the first burst. Significant differences in the duration of theluminosity peak have been observed even though the mass loss in really similar.

7Li is easily destroyed above 2 × 106 K, and the peak temperatures reached in novae arelarger than that (Figure 4.11b). Therefore, if the mass loss mechanism affects the duration of theluminosity peak by increasing it 2 years, significant differences could be observed in temperatureprofiles and duration of the peak temperatures. Thus, more work and further simulations shouldbe dedicated to study the effect of the mass loss scheme. Observations capable of distinguishingthe Roche Lobe radius in order to study the relation between its value and the duration of thenovae would also be really useful.

4.2.3 Dependence on the burst number

All results obtained for CO WD show that, for solar-like accreted material and no overshoot, mostof the properties of the white dwarf do not vary with the burst number. Figure 4.15 shows theejected mass and recurrence time for 50 consecutive bursts. The value is not exactly the same forall bursts, but there is no observable trend. Therefore, the initial properties of the model which inprinciple could afffect the result do not play any role other than specifying the mass of the WD,its temperature and its composition, as proved by the similar properties of the nova outbursts

36

0 5 10 15 20 25Atomic mass number

10−12

10−10

10−8

10−6

10−4

10−2

100

102

Mass fracti n/S

lar m

ass fracti n

Mg

F

HC

NeO

N

Li

He

eddrl Dedd+rl Dedd+rl W

Figure 4.13: Production factors relative to solar abundances according to the different mass lossschemes for a 1.0M� CO WD and ppcno net

335346.4 335346.6 335346.8 335347.0Star age (years)

1.00001

1.00002

1.00003

1.00004

1.00005

1.00006

1.00007

1.00008

Star

mas

s (M

⊙)

rloDrloD+eddedd

(a) Mass loss interval of the first burst

46 48 50 52 54 56 58 60 62Star age (years) +3.353e5

0

1

2

3

4

log(L)

(L⊙)

rloDrloD+eddedd

(b) Luminosity peak of the first burst

Figure 4.14: Comparison of mass loss and luminosity between different mass loss schemes for a1.0M� CO WD and ppcno net

obtained after a long series of explosions.

Figure 4.16 shows the overproduction factors for burst numbers between 30 and 50, and it isimpossible to distinguish the 20 superimposed lines for most elements. The elements produced arecoherent with expected values from solar-like accreted material. Even the somewhat noticeablevariations found for oxygen are smaller compared to variations induced by uncertainties in thecorresponding nuclear reaction rates, for synthesis and destruction of this species.

37

325000

330000

335000

340000

Recu

rrenc

e tim

e(yea

rs)

00-1010-2020-3030-4040-50

0 10 20 30 40 50Burst number

6.20e-05

6.40e-05

6.60e-05

6.80e-05

Ejec

ted mas

s (M

⊙)

Figure 4.15: Ejected mass and recurrence time versus burst number

0 5 10 15 20 25Atomic ma number

10−1510−13

10−1110−9

10−7

10−510−3

10−1

101103

Ma

fraction/So

lar m

a f

raction

Mg

F

HC

NeON

Li

He

30-4040-50

Figure 4.16: Overproduction factors for the 20 consecutive bursts showing no incongruence in theHR diagram.

4.2.4 Convective overshoot

Implementing the convective overshoot implies using a smaller mesh_delta_coeff, and thus, thesimulations are slowed drastically, not only the time spent per iteration increases around a factor3, but also many more iterations are needed. Therefore, tests that include convective overshoothave only been initiated in the framework of this thesis. Figure 4.17 shows the profile of the WDat the onset of the burst (when the star has lowest effective temperature and luminosity) for thecases without convective overshoot and with convective overshoot. Axis have been fixed at exactlythe same scale, in order to allow direct comparation.

As expected, it can be clearly seen that the metallicity is larger for models with convectiveovershoot, due to the enrichment of the envelope from material of the outer CO degenerate core.This dredge up also eliminates the 4He shell that was formed between the H-rich envelope formed

38

−12−10−8−6−4log10 (1− q)

10−4

10−3

10−2

10−1

100A

bund

ance

h1h1h1

he4he4he4

c12

c12c12

c13

n13n13 n14

n14n14

n15

n15

o14

o14o15

o15

o16

o16o16

o17o17

f17

f17f18f18

ne20ne20ne20

ne22ne22ne22

mg24mg24mg24

age 3.3535e+05 yrs Model 427

(a) No convective overshoot

−12−10−8−6−4log10 (1− q)

10−4

10−3

10−2

10−1

100

Abu

ndan

ce

h1h1h1

he4he4he4

c12

c12c12

c13

c13

n13n13

n14

n14n14

n15

n15

o14

o14 o15o15

o16

o16o16

o17o17f17

f17

f18

ne20ne20ne20

ne22ne22ne22mg22mg22

mg24mg24mg24

age 3.3629e+05 yrs Model 1430

(b) Convective overshoot

Figure 4.17: Abundance profiles for a 1.0M� CO WD at the onset of the TNR (ppcno net used)

from the accreted material and the CO core.

In addition to these two general effects, every difference in the abundance profile of all elementsis also relevant because they modify the properties of the TNR. Let’s take 12C mass fraction, its

39

minimum at the border of the degenerate core is one order of magnitude larger when convectiveovershoot is implemented. Thus, CNO generated nuclear power will be significantly larger andfollowing it, convective overshoot will also incrase. This will lead, as expected, to significantlylarger abundances of elements which are part of CNO cycles. However, there is also an observableenrichment in 20Ne, and 22Mg only has abundances larger than 10−4 when convective overshootis considered.

As the TNR is driven by CNO cycles, the larger number of CNO elements acts as catalizer forH burning, increasing the energy produced via nuclear reactions (Figure 4.18) and thus, shouldlead to the expected increase in the violence of the explosion.

The abundances at the outermost layers, where the TNR still has not arrived and the abun-dances at the center are the same in both cases.

−12−11−10−9−8−7−6−5−4−3log(1 − q)

100

102

104

106

108

1010

1012

1014

1016

Nucle

ar p

ower

(erg

s/g/

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Models of Classical Novae with · 2020. 2. 12. · Abstract Classical novae are thermonuclear...

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