ev/STARS/TWIN binary stellar-evolution code
Contents
1. 2 3 Creating grids in mass mass ratio and pe riod This is currently broken due to the way output files are opened Apart from computing the model of a single binary or one single star the code can be used to compute grids of models for ranges of initial primary mass mass ratio and orbital period When you want to compute a grid the initial binary parameters SM BMS and PER in init run must be set to negative values to ensure that they don t override the grid values If you want to compute only one model make sure KML KQL KXL 1 See Section 5 2 for more details IO files 3 1 Input files init dat Initialisation file Contains the details of the numerics equations to solve and physics to include while running a stel lar model unit 22 init run Run control file Controls the start and stop conditions for different models in a run One can loop over Mi q uw and P Output from different loops is stored in files with different names or in different directories The file file list gives an overview of which model is stored where unit 23 3 2 Output files As an example I chose the file name file for the model files file outi1 2 Main output file showing what the stars are doing at that moment These files are useful as screen output units po file out Pruned version of the above two files unit 9 To be removed file io12 Contains orbital and mass transfer data from star 1 to be2. du dw Convection artificial mixing Thermohaline mixing Solberg Hoiland mixing Dynamical shear mixing Secular shear mixing Eddington Sweet mixing Goldberg Schubert Fricke mixing 14 The independent variables The independent variables are selected in kp_var in init dat and are also known as id 11 50 ig 11 50 in e g solver In TWIN mode variables 25 to 40 are the same as 1 to 16 but for the companion star while variables 17 to 24 are reserved for binary parameters 1 25 In f a dimensionless quantity closely related to electron degeneracy for the case where electrons are non degenerate and non relativistic f 105p T 2 26 In T logarithmic temperature Kelvins 3 27 X16 fractional abundance by mass of O 4 28 m mass 10 gm 5 29 X1 the abundance of H 6 30 C the gradient of mesh spacing function Q f T m r with respect to mesh point number K C does not vary with K the mesh point number although it varies with time It is in effect an eigenvalue 7 31 In r logarithmic radius 10H cm 8 32 L luminosity 10 erg s Not logged because it may be negative 9 33 X4 the abundance of He 10 34 X12 the abundance of C 11 35 X20 the abundance of Ne For a more sophisticated binary including mass loss magnetic braking rotation uniform but time varying and tidal friction a further 7 variables are stored 12 36 I the moment of inertia of the in
3. RLF1 Relative Roche lobe radius log R Ry RLF2 Relative Roche lobe radius log R Rr DLT Lnu Luminosity due to neutrino losses RA R Alfv n radius Rl MH Total hydrogen mass in the star Mo conv bdries Mass coordinates of convective boundaries 3 pairs logR Log R logL log L Line 5 Horb Orbital angular momentum F1 DF21 BE Lth Luminosity from contraction expansion Bp Poloidal component of the magnetic field MHe Total helium mass in the star Mo semiconv bdries Mass coordinates of semiconvective boundarie 3 pairs k 2 Dimensionless axis of gyration if moment of inertia is cal culated in the code 8 2 Convergence info Iter The first integer displays the number of iterations Err The logarithm of the total error Ferr The residue in the current iteration Fac The factor by which corrections are multiplied before being applied Normally 1 00 but may be smaller if the code has trouble converging Then a list of numbers follows in pairs of an integer and a float e g 79 9 2 There is one pair for each independent variable The integer indicates the mesh point in the star 1 indicates the surface where the largest error for this independent variable occurs and the float indicates the log of the error in that mesh point In practice this means that 199 9 9 is a good thing since 10777 is a very small error 98 3 1 is worrying and when the floats get to 2 0 or large
4. Time step reduced below limit helium left in the core quit BACKUP Time step reduced below limit carbon left in the core quit BACKUP End of MS core hydrogen abundance below limit UC 15 PRINTB Radius exceeds limit PRINTB Convergence to target model reached minimum PRINTB 8 file out 1 2 Note this section is about file out1 and file out2 not file out During a stellar evolution run short summaries of the stellar parameters are written into the files file out1 and file out2 It can be useful to watch this file while the code is running for example by typing tail f file outi This will show the last 10 lines of the file outi file and refresh when file out1 changes exit with Ctrl C The files start with a copy of init dat The rest of the file consists of three different blocks of information Stellar snapshots summaries of the star at a certain model num ber e g its mass age central composition etc Stellar slices detailed summaries of the interior of the star e g P p T etc on every mesh point in the star Convergence info information on the convergence of the set of differential equations for each iteration How often these blocks of information are printed to the file can be set with the parameters KT1 KT5 in init dat 8 1 Stellar snapshots Line 1 M Stellar mass Mo Porb Orbital period days xi Mass transfer rate Mo yr tn Nuclear timescale LH Luminosit
5. sa serete ristas 5 2 Grids of masses and periods 5 6 Rotation and eccentricity 226 6244 5 4 Initial binary parameters hb Termination conditions ae ox 9 m om de 6 file mod bl Header c aa ad ipali xoxo Oz CROR mc 6 2 Blocks of stellar structure 7 file log 8 file out 1 2 Bl Stellarsnapshots essa ene aman 8 2 Convergence inio sa a oeren es 9 file plt 1 2 10 file mdl 1 2 10 1 Header a ea e a a il mmo 10 2 Blocks of stellar structure 11 Creating a ZAMS model 44 46 46 50 52 12 Creating a ZAHB model 13 Variables in SX and PX 14 The independent variables 15 The difference equations 16 The boundary conditions 16 1 Composition 16 2 At the surface K 1 16 3 At the centre K KH 63 64 69 1 Creating your first run 1 1 Obtaining and updating the code To obtain the code use the svn checkout command and address as you received them To update your local version of the code cd into the stars directory and type svn update To update to a spe cific e g the latest stable version use svn update r lt version number gt Don t forget to recompile the code after an update see Sect 1 2 A concise svn howto listing the basic commands can be found here http tiny cc svnhowto 1 2 Compiling the code 1 cd into the directory stars This is the directory that con tains the code subdirectory 2 If you re r
6. together with CT 4 5 1 E1 CT 10 Used for Temperature weight together with CT 7 2 E4 use smooth remesher Switch for the new smooth remesher See also start with rigid rotation in init run false relax loaded model Switch for the new smooth remesher tr 4 3 Time steps KN The number of variables that will be used for determining the next time step KJN 1 KJN 40 The first KN of these identify the variables to be used for determining the next time step see section 14 CT1 The next timestep cannot normally be less than CT1 times present timestep 0 8 0 9 or 1 0 CT2 The next timestep cannot be greater than CT2 times present timestep If both CTI and CT2 are 1 0 then the timestep is constant of course which is useful for constructing a ZAMS by artificial mass gain except that if a model fails to con verge the timestep will be multiplied by CT3 1 1 1 05 or 1 0 CT3 when the solution package fails to converge the code retreats to the second last converged model and continues with the timestep decreased by the factor CT3 0 3 or 0 5 4 4 Convergence KR1 The maximum number of iterations allowed on the first timest 20 KR2 The maximum number of iterations allowed on later timestep 12 If you want to see output when the code is struggeling to converge a model make sure KR2 gt KTS climit Limit changes in variables during iterations 1 0d 1 use_quadratic_predictions Norma
7. unit 24 zams mod Input structure model for ZAMS models unit 16 zams mas Reading of helper file to find the proper ZAMS model from zams mod unit 197 phys z opacity tables for certain metallicity unit 207 1t2ubv dat Data to compute magnitudes and colours from L Tog unit 217 nucdata dat Data to compute nuclear reactions unit 267 mutate dat Data to do something with merger products unit 63 COtables zx Data to compute opacities unit 41 phvsinfo dat To do unit 42 rates dat To do unit 43 nrates dat To do unit 44 3 4 Temporary files fort 11 is used to create stop the code using the command echo 1 gt fort 11 Output file by unit file out 1 file 1012 file log file out fort 11 zahb mod file last 1 file mod zams mod zams mas phys z It2ubv dat init dat zahb dat nucdata dat file mas file plt1 file mdl1 file nucout1 file nucplt1 file nucmdll COtables z physinfo dat rates dat file list mutate dat 2 14 23 32 34 36 38 40 44 file out2 file last2 init run file plt2 file mdl2 file nucout2 file nucplt2 file nucmdl2 nrates dat 4 init dat The init dat file contains the parameters that are needed to con trol the numerical details of the code the differential equations that need to be solved using which variables and boundary con ditions and which physics nucleosynthesis rotation stellar wind overshooting et cetera The new format post 2005 CVS v
8. best left alone false use_previous_mu Use the previous value of the molecular weight rather than the current value when calculating the effect of thermohaline mixing for numerical stability reasons true off_centre_weight Used to scale the weighting of terms in the dif ference equations A large value means that the weighting is always central a smaller value means that the weighting moves off centre for mesh points where the timestep becomes of the order of the thermal conduction time See Sugimoto 1970 for details 1 0d16 4 5 Accuracy EP 1 3 also known as EPS DEL DHO They determine how the code behaves when the mean modulus change in DH in the latest iteration equals ERR see Writeup section 1 6 EPS The accuracy to which SOLVER is required to solve the equa tions if ERR lt EPS the model has converged 10 9 wanted_eps The desired accuracy The solver will aim for an ac curacy of wanted_eps lt ERR lt EPS This has no effect if wanted_eps lt EPS 1 0d 8 DEL If ERR gt EPS the corrections applied to DH are reduced by the factor DEL ERR 107 DHO Variation in H to compute numerical derivatives 1077 CDC 1 5 CDD is the mean increment r m s wise that you would like in one timestep Different evolutionary phases have different CDD s identified here by name rather than by num ber cdc ms CDD cdc_ms between ZAMS and core hydrogen 0 04 corresponding to the beginning
9. dat see Sect 4 6 2 2 Binary stars When computing the evolution of a binary we can choose whether we want to compute a full model of the secondary or regard it as a point mass which can be useful when dealing with WD NS or BH accretors If we want to compute a detailed model of the secondary we can choose between non simultaneous evolution in which the primary is evolved for KP timesteps before switching to the secondary to catch up in age with the primary and simultaneous evolution also known as TWIN mode in which both components are evolved at the same time and mass transfer is taken into ac count implicitly this is necessary if e g both stars have winds 2 2 1 Primary compact companion point mass Evolving a binary with a point mass is essentially similar to single star mode except that we will set the binary mass BMS and the orbital period PER to the values we want and we make sure that exactly one of CMT or CMS is non zero when using a ver sion of init dat for single star evolution You may want to check whether the equations for orbital evolution and mass transfer are being solved see Sect 4 6 but in principle this is not necessary We also set ISB 1 evolve one star and KTW 1 non simultaneous mode in init dat 2 2 2 Two components non simultaneous This mode was the original way of computing the evolution of a binary the primary is evolved for KP timesteps after which the code switches to the
10. equations in all 16 2 At the surface K 1 6a dM dt CML Mppw r m L B CMJ Mju CMR 1 3 x 10 Lm Ep CMS In R R CMT CMI M 7c Pressure 2 Pras 4 3 Paad g g k 8c Luminosity temperature L racriT 9c gravitational potential 10c d IQ dt the rate of change of angular momentum of the star carried away by stellar wind IMppwl or lost to the orbit by tidal friction Q 27 Prot 11c gravitational potential at the surface 17c dHom dt rate of change of orbital angular momentum including tidal friction which exchanges AM between spin and orbit 18c de dt rate of circularisation due to tidal friction 20c dMp dt sum of the winds from both stars Mg is the binary mass 16 3 At the centre K KH actually one mesh point from the centre 6d m 0 7d L 0 8d r 0 9d 1 0 19d 0 13 CHECK 20 CHECK 25 29 CHECK 777 30 33 CHECK 2x 34 CHECK 35 CHECK 37 CHECK
11. secondary evolves it to the same age as the primary and it keeps alternating between the two This approximates binary evolution sufficiently well for many cases but it will not when the secondary has a non negligible wind or when the secondary fills it s Roche lobe In other words all changes to the orbit are made by the primary and the secondary cannot have any influence on the orbit since if it would this would affect the evolution of a Roche lobe filling primary which has al ready been established in the previous semi cycle During the first semi cycle while evolving the primary data on orbital evolution and mass transfer are stored in file io12 which are then read again during the second semi cycle where the secondary is evolved In order to use this mode set ISB 2 evolve two stars and KTW I non simultaneous mode and make sure you solve equa tions for mass transfer and orbital evolution see Sect 4 6 2 2 8 Two components simultaneous TWIN mode TWIN mode was developed by Peter Eggleton as an improvement of the non simultaneous evolution in the previous section It allows mass loss and mass transfer from the secondary and in particu lar contact binaries at least in principle Both stars are evolved simultaneously and mass transfer is solved implicitly In order to use TWIN mode set ISB 2 evolve two stars and KTW 2 simultaneous mode and make sure you solve all neces sary equations see Sect 4 6
12. used in star 2 in non TWIN binary mode unit 3 file mod Contains a number of complete stellar structure output blocks A block from this file can serve as input for a next model unit 15 file file file file file last1 2 Contains complete structure of last and pre last moc when lucky that can serve as input for a next run units 13 14 list Shows the starting time and path of a run and tables the properties of the different models and the file names or directories in which they are stored unit 50 log Shows how the code was terminated if terminated prop erly unit 8 mas Creation of helper file to find the proper ZAMS model from zams mod unit 297 plt1 2 Contains stellar evolution data one model per line units 31 32 file mdl1 2 Contains a number of complete stellar structure mod file file file 3 3 els one mesh point per line units 33 34 nucout1 2 Main abundances screen output file true uni 35 36 nucplti 2 Contains abundances in stellar evolution models one model per line true units 37 38 nucmdli 2 Contains abundances in stellar structure models one mesh point per line true units 39 40 Data files The files below can be found in the input directory of the instal lation and are used for data input ZAMS opacities etc zahb mod Input structure model for post helium flash models uni 12 zahb dat init dat for post helium flash models
13. Individual mass loss recipe switches These also turn on recipes when smart mass loss is used although that does store its own set of mass loss options to keep it more modular At the surface M CMT CMS log r ricbe CMI m CMR 1 3x10 CMJ Mina OML L r m Prot LX 2 X if X gt Oand 0 if X lt 0 The equation above is no longer complete as new wind mass loss prescriptions have been added as described in the next subsection See Sect 4 11 1 for a detailed description of the parameters CMR CMJ and CML which deal with wind mass loss and Sect 4 11 2 for the parameters CMT and CMS which describe the mass transfer CMI a constant mass gain loss rate for running up or down the ZAMS yr 0 0 5 0D 9 or 1 0D 6 cmi mode Changes the interpretation of CMI If cmi mode 1 then CMI represents a time scale for exponential mass gain loss M M CMI If cmi mode 2 then CMI rep resents a mass gain loss rate in solar masses per year 1 4 11 1 Wind mass loss smart mass loss Turn on the smart mass loss routine which pick an appropriate recipe depending on the stellar parameters This is an alternative for the De Jager rate and replaces it when smart mass loss is switched on 0 0 off CMR Multiplier for a Reimers like mass loss rate M CMR x M senast 3x10 L 10 00 or 02 10 CMJ Multiplier for the De Jager mass loss rate for luminous stars de Jager et al 1988 0 0 or 1 0 z
14. Peter Eggleton s binary stellar evolution code ev STARS TWIN SVN version User manual Marc van der Sluys Evert Glebbeek Radboud University Nijmegen http stars vandersluys nl June 25 2013 Contents 1 Creating your first run 1 1 Obtaining and updating the code LZ Compiling the code se aast aa L2 R nmmethecode eee ee Se biel id ba A 1A Stopping the pode zo Rx EG Modus operandi Zl MS BR RR b e ERE ERED RS 22 Binary REDE MEE RN 2 2 1 Primary compact companion point mass 2 2 2 Two components non simultaneous 2 2 3 Two components simultaneous TWIN mode 2 3 Creating grids in mass mass ratio and period IO files sl TR ee 22222 eB eee wee we hoe Ce d ook MEE BE ek ed es Re ee ee eA mo ONE lt erca eS ee He KR rcu ad Temporary DEB oie wo ee Pees b Ae SES 35 Output tle ly Umit 2 s q se mad esa ca rras init dat AI LENDER 226 BG oE Ck BOR EEE REDS a2 Meshi Gah an eee eb x 93 we OR ORS 13 Tune eps a aan maersk Ek e dd CONVERGE 2 ew a eb ee RR Xx oce 4 ONE 0 APP 4 6 Equations variables and boundary conditions 4 7 Equation of state ae ae o Rs 48 Nucleosynthesis llle Oo C ow Ql 49 Rotation se ene tad mi c 4 10 Stellar structure 4 11 Mass loss 2 2 2 omo a 4 11 1 Wind mass loss 4 11 2 Mass transfer 00 412 Mbang ce rn etek mek wk hr PCR hd 4 13 Cetet eee xo o ee ee radi 5 init run 5 1 Mode of operation lt
15. Writeup section 1 5 KE1 KE2 The number of first and second order difference equa tions respectively KE3 Subset of KEI that involves 3 rather than 2 adjacent mesh points not yet used keep 0 KBC The number of boundary conditions KEV The number of eigenvalues KEN The number of intermediate functions JH1 JH3 Used for debugging purposes See also Writeup section 1 5 kp_var Determines which and in which order the independent vari ables are used max 40 integers a k a id 11 50 ig 11 50 in e g solver kp_eqn Determines which and in which order the difference equa tions are used max 40 integers a k a id 51 90 ig 51 90 in e g solver kp bc Determines which in which order the boundary conditions are used max 40 integers a k a id 91 130 ig 91 130 in e g solver The same contents as lines 5 11 not currently used See the end of section 1 5 of Writeup 4 7 Equation of state KCL 1 7 also known as KCL KION KAM KOP KCC KNUC KCN KCL Unity includes the Coulomb correction to pressure etc zero suppresses it 1 KION EoS does the ionisation of the first KION elements in the list H He C N O Ne Mg Si Fe No other elements are included KION 5 is about optimal Do not try 9 5 KOP If unity code should use spline interpolation in tables of opacity if zero simple bi linear interpolation 1 KCN If 0 gives standard nuclear network If 1 gives a CNO equilibrium
16. a function of depth and zero below L1 10 gs 1 empty empty empty lt empty gt lt empty gt 40 The same as variables 1 16 but for the secondary in case of a TWIN model otherwise empty since jin above equals 24 in that case d tile log This file contains the exit code with which the Eggleton code ter minated Usuallv the file lists an explanation of these codes at the top of the files but for grids these lines mav lack 2 1 Aa WO N DO N Q A 10 11 12 Requested mesh too large BEGINN No timesteps required STAR12 Finished required timesteps STAR12 Failed backup reduce timestep SOLVER Time step reduced below limit quit BACKUP Star 2 evolving beyond last star 1 model NEXTDT Star 1 stellar radius exceeds Roche lobe radius by limit UC 1 PRINTB Age greater than limit UC 2 PRINTB Carbon burning exceeds limit UC 3 PRINTB Star 2 radius exceeds Roche lobe radius by limit UC 4 PRINTB Close to helium flash UC 5 6 PRINTB Massive gt 1 2M degenerate CO core UC 7 8 PRINTB IM exceeds limit UC 9 PRINTB Impermissible FDT for star 2 NEXTDT Time step reduced below limit hydrogen left in the core quit BACKUP 14 15 16 17 22 32 51 52 53 Funny composition distribution My lt Mye or Mu lt Moo PRINTB Terminated by hand STAR12 ZAHB model didn t converge MAIN Nucleosynthesis didn t converge BEGINN
17. b gt 0 beginning lt 0 end of zone max 3 sets 74 Semi convection zone boundaries msb gt 0 begin ning lt 0 end of zone max 3 sets 80 Nuclear energy production zone Enuc gt Etresh v 10L M boundaries mex gt 0 beginning lt 0 end of zone max 3 sets Qeonv the mass fraction of the convective envelope P central pressure cgs 4 Prot c rotational period in the centre s BE binding energy due to gravitational energy erg 1 Mo 3 BEA binding energy due to internal energy erg 1 Mo BE binding energy due to recombination energy erg 1 Mo 3 BE3 binding energy due to H association energy erg 1 Mo 3 Se specific entropy in core erg g KJ Sr 105k Specific entropy in the convective envelope at T 105K erg g K 1 Rye radius of the helium core Ro 4The latest 2005 version used at NU has STRMDL in column 83 and column 89 as its last column 91 Reo radius of the CO core Ro 92 STRMDL a structure model is stored 1 0 or not 0 0 10 file md1 1 2 The files file mdi1 and file md12 contain stellar structure out put designed for plotting the stellar interiors Each file starts with a line of 3 numbers followed by a number of blocks each of which contains a stellar structure model saved during the evolution of the model star The parameter KT1 determines how often a structure model is saved Each block starts with a line with two numbers T
18. but need e g home user cd run 1s This contains number of subdirectories with different example runs Let s try the second one and copy the contents in order to keep the original cp r 02 single test 02 amp amp cd test 02 amp amp ls The directory contains an example init dat and two example init run files You need one of each to start a run Let s use init run m4 which evolves a 4 Mo star cp init run m4 init run We re all ready to start the code The default syntax is lt path gt ev lt output file base name gt lt metallicity gt lt st directory gt and could be e g codes stars code ev star 02 codes stars which is a little annoying since your code directory is prob ably not going to move around your hard disc a lot Hence step 5 in section 1 2 which allows us to remove the path from the ev command and step 4 with which we can leave out the last command line option altogether Using those steps thus reduces things to ev star 02 The remaining options mean that all my output files will be called star and that I want to use solar metallicity 02 means Z 0 02 Z 0 001 would reduce to 001 etc In fact Z 0 02 is the default option so I could leave it out and run my first model as ev star 1 4 Stopping the code To terminate a running model properly you type echo 1 gt fort 1 in the directory where the code is running Presumably we ll want to replace fort 11 with a proper
19. d for single stars but have to be supplied The period should be so large that there is no danger of RLOF see also Sect 2 e g XL 7 0 meaning a period of 10 d KTW 1 for normal non simultaneous operation 2 for TWIN mode where both stars are solved simultaneously See Sect 2 for more detail IP1 the number 13 16 of the file fort 13 fort 16 where the initial model for 1 is to be taken from ZAMS models are on fort 16 IM1 the sequential number of the model required on fort IP1 This is computed automatically from later data if the ZAMS file fort 16 is used so that if IP1 is 16 it doesn t matter what value you give for IM1 but you have to give a value IP2 as IP1 but for 2 IM2 as IMI but for 2 KPT the maximum number of timesteps for each component 2000 to 4000 for fairly complete evolution You may set KPT equal to 1 to indicate that the code should run until one of the termination conditions is met in other words the code will not stop when it reaches a predetermined number of timesteps KP Do approximately KP of xi then enough of 2 to catch up with xi then another KP of x1 etc so that if x2 breaks down before x1 you don t waste a lot of calculation on 1 You will seldom get exactly the number of timesteps that you ask for For single stars KP is set to KPT automatically 5 2 Grids of masses and periods MLI DML KML QLI DQL KQL XLI DXL KXL These three lines contain para
20. e envelope Rx TET Convective turnover timescale RAF Alfv n radius BP poloidal magnetic field Pop orbital period days FLR log R R relative Roche Lobe Radius also called RLF F1 i Dai X Or erg 2 Multiply with 1 9891 x 1033 to get ergs The reason for this confusing solution is that values of 1 040 50 erg don t fit in a single precision variable and that the value may be negative so that a log is no option 31 32 33 34 39 36 37 38 39 40 41 42 49 96 M total mass loss Mo yr Mwina Wind mass loss Mo yr Mat mass transfer rate Mo yr Ho orbital angular momentum 1070 g cm s dH dt total orbital angular momentum loss rate 10 g cm s dH dt change in Hoy due to gravitational waves 10 g cm s7 dHyi dt change in Hom due to wind mass loss 1077 g cm s dH dt change in Hor due to spin orbit coupling 10 g cm s dA dt change in Hspin due to non conservative mass trans fer 10 g cm s Meomp companion mass Mo e orbital ellipticity 48 Surface abundances of 42 H 43 He 44 C 45 N 46 0 AT Ne 48 Mg 55 Tmax abundances of 49 H 50 He 51 C 52 N 53 0 54 Ne 55 Mg 62 Central abundances of 56 H 57 He 58 C 59 N 60 0 61 Ne 62 Mg 63 69 75 81 82 83 84 85 86 8T 88 89 90 68 Convection zone boundaries mc
21. er to create a ZAMS model of certain mass or to ob tain a series of ZAMS models one can use the RMG mass loss gain parameter in the init dat file This parameter gives a mass loss or mass gain that is proportional to the mass of the star The method is as follows e Choose an existing input model with a mass close to the de sired mass e Set the parameter CMI to the desired value usually 4 5 x 107 e Make sure the time step doesn t change CT1 CT2 1 00 e Calculate the factor f with which you want to change the mass to get from the model you have to the model you want If you have 1 00 M and want 1 02 Mo f 1 02 e Calculate the approximate number of steps you need to take for a time step size dtp 10 yr and the CMI above No In f CMI dto e Choose a nice round but at least integer number of steps N No e Calculate the true time step for N steps dt cu e Fill in the values for dt and N in init run e Run the model for N steps and check the final mass in file mc In a dic MI The Fortran program makezams f see website is supposed to do all the above If all goes well you ll end up with the mass slightly off You can give your model the exact mass you want by switching off the wind put the desired mass in init run and run another 10 models or SO If the change in mass is less than expected you may have cho sen your timestep too long so that the code does not converge recalculates
22. ersion contains one parameter either scalar or array per line If a vari able name is used multiple times on multiple lines the last entry will be used This is useful for experimenting with values while keeping the old ones in the file If a variable is not mentioned at all the hard coded default value is used Thus the order of the parameters does not matter but for rea sons of clarity and consistency it is a good practice to keep the order used here 4 1 Output KT 1 4 also known as KT1 KT2 KT3 KTA KT1 Print internal details of every KT1 th model to file out1 2 and file md11 2 20 or 200 KT2 Print internal details at every KT2 th mesh point of the KT1 th model file outi 2 only 1 or 2 KT3 Print KT3 pages of details for every KT1 th model to file oi 1 2 or 3 KT4 Print a five line summary of every KT4 th model to file out1 and save every KT4 th evolution model to file plt1 2 1 2 or 4 KT5 Print a one line summary of each iteration of each model to file out1 2 except for the first KT5 iterations of each model 0 or 2 KSV an output model is stored in file mod fort 15 after ev ery KSV th timestep in a run in the form needed as input for a further run The last model of a run is automatically also stored in file last fort 13 14 5000 KSX 45 The first 15 integers identify the quantities such as log p L X He which are to be printed in columns on the first page of s
23. file name at some point to facil itate running and terminating different versions of the code in the same directory independently 2 Modus operandi The stellar evolution code ev is designed to be a binary evolution code However it can be used to compute the evolution of both single and binary stars and for binaries there are several possible modes to use the code in These modes are set by two parameters in init run ISB 1 or 2 depending on whether we want to evolve one or two stars and KTW 1 or 2 for non simultaneous or non simultaneous binary mode respectively 2 1 Single stars Since ev is a binary evolution code single stars are in effect in a binary Since you don t want to waste your undoubtedly valuable CPU time on computing the secondary we set ISB 1 single star and KTW 1 non TWIN mode I m not sure whether it matters but it seems a safe way to go However here we only tell the code not to compute a model of the secondary It will still exist as a point mass The important thing is that Roche lobes will still be defined and it is important to set the initial orbital period PER in init run to a sufficiently high value to make sure your single star will not fill its Roche lobe In addition I usually set BMS to twice SM to make sure you don t end up with a negative secondary mass Experienced users may want to switch off the equations that govern orbital evolution mass transfer etc in init
24. fudge for ZAMS models see FUNCSI 0 eos include pairproduction Should the equation of state includ the effects of pair production This is only important in the very late burning stages of very massive stars Positrons are only calculated if their degeneracy parameter gt 15 0 oth erwise they are negligible anyway false 4 8 Nucleosvnthesis CH value for initialising X H as a fraction of the total composi tion only used for ZAMS models with JCH 4 The default value CH 1 tells the code to use the value provided with the ZAMS model For some lower metallicities and some initial masses M 0 8 Mo the ZAMS model may not converge In such a case setting ML1 to the nearest value for which the ZAMS model converges and SM to the desired mass in init run may help out 1 0 CC CN CO CNE CMG CSI CFE values for initialising X X 95Fe as fractions of the total metallicity Z CZS in input phys z fort 20 only used for ZAMS models with JCH 4 0 176 0 052 0 502 0 092 0 034 0 072 0 072 kr_nucsyn Number of allowed iterations for the nucleosynthesis code 60 4 9 Rotation See also start with rigid rotation in init run rigid rotation Use rigid rotation or differential rotation true 4 10 Stellar structure KTH 1 4 alias KTH KZ KTH ej KTH x T DS Dt so you can ignore T DS Dt if you want 1 or 0 KX DX H Dt KX x burning rate of H so you can ignore
25. function into a smoothed step function see Writeup p 27 0 01 CGW A switch to turn gravitational radiation on and off 0 0 or 1 0 CSO A switch to turn spin orbit coupling on and off 0 0 or 1 0 CMB A multiplication factor to determine the strength of an alter native magnetic braking law currently the one by Rappaport Verbunt amp Joss 1983 0 0 1 0 4 12 Mixing artmix Artificial mixing coefficient cm s Set it to 1 0 to mix the entire star 0 0d0 csmc Semi convection efficiency after Langer 1991 4 0d 2 cdsi Switch for the dynamical shear instability 1 0d0 cshi Switch for the solberg hoiland instability not implemented 1 0d0 cssi Switch for the secular shear instability 1 0d0 cesc Switch for the Eddington sweet circulation 1 0d0 cgsf Switch for the goldreich schubert fricke instability 1 0d0 cfmu Weight of mu gradient in rotational instabilities see Heger s thesis page 36 and Pinsonneault 5 0d 2 cfc Ratio of turbulent viscosity over the diffusion coefficient see Heger s thesis page 35 3 3d 2 convection scheme To do 1 4 13 Cetera enc parachute Emergency energy generation term normally set to 0 This cannot be set from the input file It will be set by remesh if there is no nuclear energy generation in the initial model at all In that case the first iteration s will return LOM 0 0 throughout the star because the thermal energy term is initially 0 as well this i
26. he rest of each block contains typically a few hundred lines each with a few tens of columns 10 1 Header The first line of the file contains three parameters 1 Nmesh number of mesh points in each model the number of rows in each block see the parameter KH2 2 Nyar number of output variables the number of columns in the blocks 3 Dovershoot overshoot parameter COS 7 10 2 Blocks of stellar structure Each block starts with one line with two values 1 Model number for the block of output below 2 t model age yr The first line of each block is followed by an array of data con sisting of Nmesh rows of Nya columns each Hence each row is a mesh point in the stellar model a mass coordinate or radius coor dinate The first row of each block contains data for the centre of the star the last Nmesn th row represents its surface In each row there are Nya columns Each column contains a different physical quantity The quantities in the columns are iP 2 16 17 18 19 20 M mass coordinate Mo R radius coordinate Ro P pressure dyn cm p density g cm T temperature K K Opacity cm g OlogT Vad Glog 5 adiabatic temperature gradient l l Vraa Vaa temperature gradient difference 15 Abundances of 9 H 10 He 11 C 12 N 13 O 14 Ne 15 Mg L total luminosity Lo Eth energy generation due to contraction ca
27. i Ruck Mg Xii XJ X Xia rine 1 H abundance equation 2 FO abundance equation 3 He abundance equation 4 PC abundance equation 5 Ne abundance equation 6 Pressure rotation log Pi log Pe Am k 1 2 7 Radius r rg m 2rpr k41 2 8 Temperature log Ti log Tk VAm k41 2 9 Luminosity Lia Ly m Ei jkaz2z m p lr ME Mk 10 Mass mi m 2m 3m 3 i 44 2 11 Moment of inertia hui Ik 2m r 3 172 12 Surface L potential dia dk Gmm 4rr p cy1 2 13 HN abundance equation 14 1 Mg abundance equation 15 Sum of the abundances is constant 37 X 0 normally used instead of 14 for 7 Mg 16 Equation for artificial mesh dependent energv term MENC 18 Equation for MEA Related to MENC Eq 16 and luminosity 19 Mass transfer rate amp 41 amp CMTx y 26 r m if 0 0 otherwise 22 Equation for MET Related to MENC Eq 16 25 37 CHECK 42 Angular momentum transport 43 Total angular momentum 44 Si abundance equation 45 Fe abundance equation 16 Lhe boundary conditions The boundary conditions are selected in kp bc in init dat and are also known as id 91 130 ig 91 130 in e g solver 16 1 Composition la 2a 3a 4a 5a Ib 2b 3b 4b 5b Ok 1 2 Xk Xii Xy Rouck Mk Mua making 10 such
28. ial Fm Mass flux towards or away from the other star DGOS V V Vos modified Schwarzschild criterion if gt 0 convection but Writeup says not used DLRK Heat transfer due to differential rotation A enth Difference in enthalpy between star 1 and 2 XIK V Abr between star 1 and 2 FAC2 V FACI V Not used Not used Not used Not used RPP Reaction rate pp chain effective 2p 1 2 He4 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 RPC Reaction rate effective C12 2 p N14 RPNG Reaction rate effective N14 2p O16 RPN Reaction rate effective N14 2p C12 4 He4 RPO Reaction rate effective O16 2p N14 He4 RAN Reaction rate effective N14 3 2 He4 Ne20 C dS d log p dL dk LQ advection term for luminosity equation w rotation rate N Brunt Vaisala frequency squared TODO check this the code suggests it s supposed to be the Richardson number but this may be incorrect Dasi mixing coefficient for the dynamical shear instability D mixing coefficient for the secular shear instability ves velocity of Eddington Sweet circulation u counter term for Eddington Sweet circultion p current Arr p 2 m conversion factor for diffusion coefficients CHEC CHECK SSSI RIS TODO TODO 69 70 71 72 73 74 75 76 TT CHECK CHECK CHECK CHECK CHECK CHECK CHECK CHECK CHECK
29. le last1 2 have the same format The file consists of one or more blocks starting with a single line with 13 model properties and followed by a block with one line per mesh point with the independent variables This block contains 24 columns of which only part is used Some of them are eigenvalues and have the same value for every mesh point 6 1 Header The first line of the file contains the 13 numbers 1 2 10 Mi the mass of the primary Mo A t time step yr t age of the model yr Por the orbital period day BMS the total binary mass Mo the orbital eccentricity Prot the rotational period day enc artificial energy term kh the number of mesh points and thus rows in the stellar structure block below kp the total number of models to calculate 11 12 13 14 jmod the current model number jb the number of this star in the binary 1 or 2 jin the number of independent variables and thus columns in the stellar structure block below 24 for non TWIN 40 for TWIN jf do or do not overwrite overwrite J and see below Just keep it 0 0 or 2 6 2 Blocks of stellar structure Each block contains the contents of the variable H 24 models for non TWIN models and 40 for TWIN models Columns 1 16 are re served for the primary 17 25 for binary parameters and 26 40 have the same content as 1 16 but for the secondary in the TWIN case In the loop o
30. lly the code uses linear ex trapolation to predict values for the first iteration on the next timestep Set this switch to true to use quadratic extrapo lation which can be slightly more accurate false use_fudge_control obsolete present for backward compatibil ity Used to switch certain fudges on and off as needed Now unused true allow extension unused present for backward compatibility Allow the code to do a few extra iterations if it is close to converging when it runs out of iterations A better approach is to set a convergence window false allow underrelaxation Allow the code to suppress the diffusion terms in the composition equations and then switch them on slowly as the code iterates false allow overrelaxation Allow the code to magnify the diffusion terms in the composition equations and then relax them to their normal value as the code iterates false allow egenrelaxation Allow the code to fall back to the energy generation rate from the previous timestep and then smoothly transition to its current value as the code iterates false allow mdotrelaxation Allow the code to suppress mass loss from stellar winds or RLOF and switch it on smoothly as the code iterates false allow avmurelaxation Together with use previous mu determine whether the current or the previous value of the mean molec ular weight should be used to estimate the effect of thermo haline mixing Normallv
31. meters for 3 nested loops mass mass ratio and initial period to be run through Each loop has starting value increment number of cases 1 more than the number of increments e The first outer loop is logio mass solar units starting at MLI increasing by steps of DML to MLI KML 1 DML e The second loop is logio mass ratio in sense larger smaller korsa at QLI increasing by steps of DQL to QLI KQL 1 DQL e The third inner loop is X logig orbital period period necessary for x1 to fill its Roche lobe when still on the ZAMS starting at XL1 increasing by steps of DXL to XLI KXL 21 DXE e If you want to compute only one model single or binary set KML KQL KXL 1 When a grid is computed the initial binary parameters SM BMS and PER must be set to negative values to ensure that they don t override the grid values 5 3 Rotation and eccentricity ROT KR EX ROT KR KR 1 Po for each star rotational breakup period 10ROT PERC breakup or RLOF at ZAMS KR 2 Po for each star max 1 05 rotational breakup period orbital period 10ROT PERC breakup or RLOF at ZAMS KR gt 3 set Prot P4 almost synchronous rotation EX the initial eccentricity 5 4 Initial binary parameters SM DTY AGE PER BMS ECC P ENC JMX a k a AX 1 8 JMX The AX s are optional replacements for the values of SM ENC that the code would normally pick up in fort IP1 from some pre
32. model in years exceeds this number JO 5 2e10 UC 3 LCarb Terminate if Lc gt this number JO 6 100 UC 4 rlf2 Terminate if FLR RLF Sect 9 nr 29 of star 2 exceeds this number JO 7 0 2 UC 5 LHe Initiate He flash evasion if Lu gt this number to gether with UC 6 JO 8 1e3 lower for M 2M UC 6 rho Initiate He flash evasion if log pe gt this value 2 together with UC 5 JO 8 5 3 UC 7 MCO Terminate if degenerate CO core exceeds this mass together with UC 8 JO 9 1 2 UC 8 14 UC 8 rho Terminate if log p gt this value 2 together with UC 7 JO 9 6 3 UC 9 mdot Terminate if M gt UC 9 M Tku JO 10 3e2 UC 10 XHe Change eps next number if the core Helium abundance drops below this number 0 15 UC 11 eps If Yoore lt XHe previous number set EPS to this number Do not use keep this number 1e 6 1e 6 UC 12 dtmin Terminate if At dtmin in seconds 1e6 UC 13 sm8 The total mass the post He flash model should get can also be used manually 1e3 UC 14 vmh8 The He core mass he post He flash model should get can also be used manually 1e3 UC 15 21 UC 15 XH If gt 0 terminate if the core H abundance drops below this value you can e g stop at the TAMS JO 51 0 0 UC 16 21 Unused 6 hle mod This file contains stellar structure output that can be used as input The files fi
33. n be negative erg g 77 Enuc energy generation by nuclear reactions erg g7 s Ep energy generation in neutrinos erg g s S specific entropy lere ov K 1 21 22 23 24 25 26 21 28 29 30 3l 32 33 34 35 36 3T 38 Ui internal energy erg g Reaction rate RPP pp chain effectively 2 p gt i He4 Reaction rate RPC effectively C12 2 p gt N14 Reaction rate RPNG effectively N14 2 p O16 Reaction rate RPN effectively N14 2 p C12 He4 Reaction rate RPO effectively O16 2 p gt N14 He4 Reaction rate RAN effectively N14 2 He4 Ne20 6 8 u mean molecular weight amu Mixing coefficient for thermohaline mixing or unused Mixing coefficient for convective mixing convective velocity x mixing length dlogT dlog P True temperature gradient w rotation rate CHECK CHECK du CHECK dw CHECK Convection artificial mixing CHECK Thermohaline mixing CHECK Solberg Hoiland mixing 39 40 41 42 CHECK Dynamical shear mixing CHECK Secular shear mixing CHECK Eddington Sweet mixing CHECK Goldberg Schubert Fricke mixing 11 Creating a ZAMS model Note that this section is about manual meddeling with models you don t need this for normal operation of the code e g to change the ZAMS mass of a model for that see the section init run 1 you want to create a ZAMS series see the example run 01 in the directory run Ol zams In ord
34. of the hook in stars above 1 2M 0 04 or 0 01 cdc_ems CDD cdc_ms cdc_ems between the beginning of the hook and hydrogen exhaustion The purpose is to reduce the timestep so that the hook is properly resolved 0 15 or 1 0 cdc_hg CDD cdc_ms cdc hg between core hydrogen ex haustion and the base of the giant branch The intention is to increase the timestep during the Hertzsprung gap 3 0 or 1 0 cdc_ldup CDD cdc_ms cdc_ldup during first dredgeup 1DUP on the giant branch 0 10 or 1 0 cdc_hec CDD cdc_ms cdc_hec for evolution during core He burning 0 0625 or 0 25 ede hes CDD ede ms ede hes for further evolution until the He shell nearly catches up with the H shell 0 25 or 1 0 cdc dbish CDD ede ms ede dblsh for double shell burni The intention is to either make the timestep large and skip over the thermal pulsing phase if gt 1 or to cut back the timestep and resolve the thermal pulses if lt 1 1 0 or 4 0 ede rlof CDD CDD ede rlof to reduce the timestep if the system is moving closer to Roche lobe overflow RLOF The criterion is that the star is close to filling its Roche lobe and expanding 0 05 or 1 0 cdc rlof reduce CDD CDD cdc rlof reduce to keep the timestep smaller while the svstem detaches after RLOF The criterion is that the star is close to filling its Roche lobe and shrinking 0 25 or 1 0 4 6 Equations variables and boundary condi tions See also
35. one of two versions of MT by RLOF CMS amp CMT are alternatives set one of them to zero 0 0 or 1 0D 2 1 0D2 for stars of increasing mass For contact binaries CMT is preferred or even mandatory CMS one of two versions of MT by RLOF CMS amp CMT are alternatives set one to zero 0 0 or 1 0D0 1 0D4 A too high value can crash the model at the onset of MT Use CMT for contact binaries cmtel Eddington limited accretion factor depends on the stellar parameters 0 0d0 or 1 0d0 cmtwl Angular momentum limited accretion factor depends on the stellar parameters 0 0d0 or 1 0d0 ccac Switch for composition accretion 0 0d0 cgrs Switch for gravitational settling 0 0d0 CPA partial accretion the fraction of one star s wind that is accreted by the other 0 0 CBR bipolar re emission the fraction of material accreted by a star that is ejected in bipolar jets Needed for CVs LMXBs 0 0 CSU spin up specifically of the gainer due to accretion CSU is the specific angular momentum AM relative to orbital OAM taken out of the orbit by material leaving the L1 point acquiring AM due to Coriolis force and landing on the other star so OAM is converted to gainer s internal AM Does not seem to work properly yet 0 0 CSD spin down the same process also spins down the loser I suppose though not by as much Does not seem to work properly yet 0 0 CDF this is used to convert a step
36. r something is really wrong It is usually a good idea to scroll up and look whether earlier blocks exist and if so to see whether the same variables are causing the problems there sometimes one variable starts causing problems and then drags along others 9 file plt11 2j This file contains stellar evolutionary properties for one structure model per line The first line contains the number of columns in the output block The block currently contains 81 columns with the following contents 1 2 10 11 12 13 14 JMAD Model number t Age yr At time step yr M stellar mass Mo Mge helium core mass Mo Mco carbon oxygen core mass Mo Mone oxygen neon core mass Mo log R stellar radius Ro log L stellar luminosity Lo log T g effective temperature K log T central temperature JK log Tmax maximum temperature JK log pe central density g cm log PTmax density at T Tmax g em 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Ubina binding energy of H envelope erg 1 Mo Ly luminosity by hydrogen burning Lo Lye luminosity by helium burning Lo Lo luminosity by carbon burning Lo L neutrino luminosity Lo Len luminosity by release of thermal energy Lo Pot rotational period days VK2 K We with J the moment of inertia Rez Depth 2 of convective envelope R dRez Thickness 2 of convectiv
37. s a numerical fudge to re move the resulting singularity This term will be set to L M constant energy generation throughout the star and will be reduced to 0 by printb 0 0 5 Init run The init run file contains parameters that control how to start and stop the run You have to decide on each of four options each giving two alternatives The options are a single stars or binary stars b new i e starting from scratch ZAMS or old e g starting from the end of a previous run c independent evolution normal mode or simultaneous evolu tion TWIN mode of the components d a one model or grid run A grid means several runs one after the other but simultaneous using the massively par allel version not described here with the three parameters of primary mass mass ratio and orbital period being cycled through One shot means what it says Not all 16 possibilities make sense e g if you are doing TWIN evolution you won t want single stars Many but not all of the remaining possibilities should be viable 5 1 Mode of operation ISB KTW IP1 IM1 IP2 IM2 KPT KP ISB evolve one or two stars ISB 1 implies only one star should be computed in detail ISB 2 evolves both components of a binary For single stars you may still use the outer first cycle for masses The inner 2 cycles are automatically set to do only one case each The mass ratio and the period are of course virtually ignore
38. scaling mdot Scaling with metallicity applied to De Jager mass loss rate in funcsi 0 8 CMV Multiplier for the Vink mass loss rate CMK Multiplier for the Kudritzki 2002 mass loss rate CMNL Multiplier for the Nugis amp Lamers mass loss rate for Wolf Rayet stars CMRR Multiplier for the real Reimers mass loss rate CMVW Multiplier for the Vasiliadis amp Wood 1993ApJ 413 641 mass loss rate superwind for late AGB stars CMSC Multiplier for the Schr der amp Cuntz mass loss rate CMW Multiplier for the Wachter et al 2002A amp A 384 452W mass loss rate superwind for late AGB stars CMAL Multiplier for Achmad amp Lamers the mass loss rate for A supergiants cphotontire Switch to include photon tiring 0 0 CML A mass loss rate as obtained from a simplistic dynamo the ory 0 0 or 1 0 CHL A factor multiplying the rate of ang mom loss associated with the rate of mass loss according to the same dynamo model 0 0 or 1 0 cmdotrot_hlw Multiplier for rotationally enhanced mass loss rate by Heger Langer amp Woosely Set at most one of these cmdotrot mm Multiplier for rotationally enhanced mass loss rate by Maeder amp Meynet Set at most one of these CTF A factor multiplying an expression for the rate of tidal fric tion 0 0 or 0 01 CLT A coefficient used in the estimation of heat flux between com ponents in contact It does not really work yet or does it 4 11 2 Mass transfer CMT
39. terior material 107 gm c 13 37 P the rotation period days of the star here taken to be independent of depth so that it is an eigenvalue like C above 14 38 the centrifugal gravitational potential ergs 15 39 the potential at the surface minus the potential on the L1 surface ergs an eigenvalue 16 40 X14 fractional abundance by mass of HN 17 Hop the orbital angular momentum 109 gm cm sec an eigenvalue 18 e the eccentricity an eigenvalue 19 the flux of mass towards or away from the other star for merly F 10 gm sec a function of depth but zero below the L1 surface 20 Mg the total mass of the binary depleted by wind in either or both stars but not by mass transfer between the stars An eigenvalue 22 Variable MENC for artificial mesh dependent energy term 23 Variable MEA related to MENC Var 22 and luminosity idda 24 Variable MET related to MENC Var 22 41 X24 fractional abundance by mass of Mg 42 X28 fractional abundance by mass of 78Si 43 X56 fractional abundance by mass of Fe 44 Total angular momentum 15 he difference equations The difference equations are selected in kp eqn in init dat and are also known as id 51 90 ig 51 90 in e g solver See also the Writeup Section 1 5 p 9 for more explanation 1 5 13 14 44 45 Abundance equations Oy Ar Xy ey as X Ari X
40. the composition change while keeping the energy production 1 or 0 KY The same for He 1 or 0 KZ The same for PZC and 90 1 or Q CALP The mixing length ratio 2 0 CU Along with COS and CPS a convective overshooting param eter see CRD 0 1 COS A convective overshooting parameter for H burning cores see CRD Zero implies no overshooting 0 12 CPS as COS but for He burning cores 0 12 CRD The diffusion coefficient c for convective mixing is taken to be CRD times the legitimate rate from mixing length the ory except that an approximate multiple of IV V ar a6 E replaced by the same multiple of IV Va Vos where COS 2 5 206 1682 CU logm log P 1 P The usual CRD is 107 or 1074 Vos CXB Defines the boundary of a core to be at X 1H or X He CXB for printout and envelope binding energy 0 15 CGR Defines the boundary between a convection zone and a semi convection zone for printout purposes only to be at V V 4 Vos CGR 0 001 CEA A constant energy rate ENC can be added to nue Een v An increasing ENC can push a star back from the ZAMS to the Hayashi track CEA and CET determine how ENC changes with time 1 0E2 CET The equation for the growth of ENC with time is dENC dt ENCxCETx 1 ENC CEA so that ENC increases ex ponentially on the assigned timescale 1 CET yr until sat urating at ENC CEA 1 0E 6 4 11 Mass loss
41. the model with a smaller timestep and continues with this smaller timestep since it is not allowed to change 12 Creating a ZAHB model In order to create a ZAHB model for instance because the format of the input files has changed or because you want a different metal licity you can use the following recipe Most of the work is actually already done by test run 07 However or lower metallicities you will need a more massive ZAMS star and it may be harder to get a low mass ZAHB star e Evolve a 2 25 M star until it starts core helium burning Do not allow the helium to be consumed KY 0 This is done in run 07a e Start mass loss until the star is down to about 0 4Mc This step is covered by run 07b e Put the starting model and an appropriate init dat file in input zahb lt Z gt mod where Z is the metallicity 02 for Z 0 02 etc e Test the result for a 1 0 Mo model run 03 e If the code can produce the ZAHB model but it cannot con tinue the evolution on the HB error code 16 the problem may be a too small desired number of models see the param eter kp in the first i e header line of the structure model in input zahb lt Z gt mod 13 Variables in SX and PX These quantities are calculated in printb and stored in the vari ables SX and PX In the loop over all meshpoints SX J IKK is the previous value of PX J from the previous mesh point IKK runs from 1 to NM the number of meshpoints or from the cen
42. tre to the surface of the star In the same loop the variable Q 1 24 contains the values of H 1 24 1 for mesh point I see Sect 6 1 2 10 11 12 13 yw degeneracy parameter P Pressure p Mass density T Temperature ki Opacity A OlogT Vaa Adiabatic temperature gradient rs 2 F dlogT V True temperature gradient iba P Vraa Vaa Difference between the radiative and adiabatic V s M Mass H Hydrogen abundance He Helium abundance CH Carbon abundance NH Nitrogen abundance 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 39 O 6 Oxygen abundance Ne Neon abundance Mg Magnesium abundance R Radius L Luminosity Ein Thermal energy generation rate Enuc Nuclear energy generation rate E Energy loss rate in neutrinos dM Shell mass Diffusion coefficient for thermohaline mixing n dlogp el deer Homology invar _ dlog R Unom Tog P Homology invar Viem oe M Homology invar U Internal energy S Entropy L Leaa Luminosity relative to Eddington Weonv X l Weonv Convective velocity l mixing length u Mean molecular weight wt 33 34 35 36 3T 38 39 40 41 42 43 44 45 46 47 48 49 50 Ve per free electron Ve 0 F per all electrons Weonv Convective velocity M I Moment of Inertia centrifugal gravitational potent
43. tructure details for every KT1 th model The next two lots of 15 relate to the optional further pages See section 13 4 2 Mesh spacing KH2 The number of mesh points you want if this differs from KH the code should interpolate in the given model to produce a new one but you must also set JCH to gt 2 to implement this change 199 JCH If JCH gt 1 the REMESH initialises the model in various ways JCH 1 Does nothing JCH 2 Initialises some new variables for instance the mass JCH 3 2 constructs new mesh spacing by interpo lation JCH 4 3 initialises composition to uniformity for ZAMQ At least in some cases JMX in init run must be 0 if JCH gt 1 in order for the first model to converge CT 1 10 coefficients used in the mesh spacing function Q Q CT 4 log P CT 5 log P CT 9 CT 7 log T CT 7 log T CT 10 CT 3 log 1 R CT 8 log CT 6 MES CT 6 M2 M29 CT 1 Unused 0 00 CT 2 Used for Luminosity weight 0 00 reasonable values seem to be 0 01 1 0 and perhaps other values CT 3 Used for Radius weight together with CT 8 0 05 CT 4 Used for Pressure weight together with CT 5 10 0 05 CT 5 Used for Pressure weight together with CT 4 10 0 15 CT 6 Used for Mass weight 0 02 CT 7 Used for Temperature weight together with CT 10 0 45 CT 8 Used for Radius weight together with CT 3 1 E 4 CT 9 Used for Pressure weight
44. unning on a computer cluster you probably want to link the executable statically To do this edit the file CMakeLists txt and set the option WANT_STATIC to on 3 Configure and compile starting from the directory stars Use CMake type cmake version to see whether CMake is installed If you updated the code and build already exists and com pilation doesn t work you should type make clean before step 3b If the code still doesn t compile do rm rf build before step 3a Note that at step 3b CMake chooses a com piler To overrule this execute e g FC gfortran cmake instead Step 3c may produce some remarks and should pro duce the binary executable code ev 4 It is very useful to set the environment variable to the path of the stars directory e g export evpath home user codes stars This line should probably go into your m bashrc Check with echo evpath 5 It is very useful to put ev in your path You could do one of these a PATH PATH echo evpath code to add the di rectory where ev sits to your path Again you should add this to your bashrc b cp code ev bin if bin is in your path 1 3 Running the code Change this to using stars_standard instead 1 I assume you re still in the stars directory T m assuming you re using bash If you re using csh replace export a b with setenv a b and m bashrc with cshrc Some compilers e g gfortran don t accept
45. ver all meshpoints in printb the variable Q 1 24 contains the same data as H 1 24 1 or the corresponding vari ables for the secondary in a TWIN model for each mesh point I Each line represents a mesh point the first one usually the surface of the star The eigenvalues are marked with EV The columns are 1 In f a dimensionless quantity closely related to electron de generacy for the case where electrons are non degenerate and non relativistic f 108p TH 2 In T logarithmic temperature K 3 X16 mass abundance fraction of O og 4 m mass 1 5 X1 mass abundance fraction of H 6 C the gradient of mesh spacing function Q f T m r with respect to mesh point number K EV 7 In r logarithmic radius 10 cm 8 L luminosity Not logged because it may be negative 10 erg 9 X4 mass abundance fraction of He 10 X12 mass abundance fraction of 12C 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 X20 mass abundance fraction of Ne I the moment of inertia of the interior material 10 g cm Pot the rotation period days of the star EV the centrifugal gravitational potential erg os the potential at the surface minus the potential on the LI surface EV erg X14 mass abundance fraction of 14N Ho the orbital angular momentum EV 10 gm cm s e the orbital eccentricity EV F the flux of mass towards or away from the other star
46. vious run or from the ZAMS library fort 16 JMX similarly is an optional replacement for JMOD They are only applied if they are non negative Thus you can re place only one or several SM Primary mass Mo DTY Time step yr AGE Model age yr PER Orbital period d or fraction of break up BMS Total binary mass Mo ECC Orbital eccentricity P Spin period of the primary Id ENC Artificial energy rate see CEA and CET JMX New model number JMOD Set to 1 to keep unchanged to 0 to set the mass of a ZAMS model using the loop pa rameters ML1 QL1 above ignoring SM when using IP1 2 16 True and to any positive value to start counting models at that value For grids looping over primary mass and mass ra tio you must set JMX to 0 In some cases when restarting an evolved model you seem to have to set JMX to gt 0 START_WITH_RIGID_ROTATION Can be TRUE or FALSE 5 5 Termination conditions UC The last three lines are a set of 21 criteria UC 1 21 to determine when the run is to be ended e g when the age is greater than 2 x 10 yr or when some special procedure should be initiated e g the He flash evasion You ll have to read the end of printb f to figure them out completely In many cases the code is stopped by changing the termination code JO UC 1 7 UC 1 rifl Terminate if FLR RLF Sect 9 nr 29 of star 1 exceeds this number JO 4 0 1 UC 2 age Terminate if the age of the
47. y by Hydrogen burning P cr McHe Mass of Helium core CXH Central H Abundance CXHe Central He abundance CXC Central C abundance CXN Central N abundance CXO Central O abundance CXNe Central Ne Abundance CXMg Central Mg abundance Cpsi Central value of the electron degeneracy parameter Crho Log Central density CT Log Central Temperature Line 2 dty Time step yr Prot Rotational period days zet Mass loss rate other than Roche lobe overflow e g wind Mo a tKh Kelvin Helmholtz timescale LHe Luminosity due to helium burning RCZ McCO Mass of CO core TXH H abundance at Tmax TXHe He abundance at Tmax TXC C abundance at Tmax T XN N abundance at Tmax T XO O abundance at Tmax TXNe Ne abundance at Tmax TXMg Mg abundance at Tmax Tpsi Value of the electron degeneracy parameter at Tmax Trho log Tmax TT log rho at Tmax Line 3 age Stellar age yr ecc Orbital eccentricity mdt Mass loss Mo yr tET Envelope Turnover timescale of the convective envelope LCO Luminosity due to Carbon Oxveen burnine DRCZ McNe Mass of Neon Core SXH Surface abundance of H SXHe Surface abundance of He SXC Surface abundance of C SXN Surface abundance of N SXO Surface abundance of O SXNe Surface abundance of Ne SXMg Surface abundance of Mg Spsi Surface value of the electron degeneracy parameter Srho Log Surface density ST Log Surface Temperature Line 4 cM Companion Mass Mo
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