ev/STARS/TWIN binary stellar-evolution code
Contents
1. 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 ein KTH x T DS Dt so you can ignore T DS Dt if you want 1 or 0 KX DX H Dt KX burning rate of 1H so you can ignore the composition change while keeping the energy production 1 or 0 KY The same for He 1 or 0 KZ The same for 2C and O 1 or 0 CALP The mixing length ratio 2 0 CU Along with COS and CPS a convective overshooting parameter 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 o for convective mixing is taken to be CRD times the legitimate rate from mixing length theory except that an approximate multiple of V Val 3 is replaced by the same multiple of V Va Vos where COS a2 Prad V OS 2 5 208 1682 CU logm log P 1 Pras The usual CRD is 107 or 1074 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 semiconvection zone for printout purposes only to be at Vy Va Vos CGR 0 001 CEA A constant energy rate ENC can be added to nuc Etn v An increasing ENC can push a star2. Va n per free electron Voo zg per all electrons e Weonv Convective velocity M I Moment of Inertia q centrifugal gravitational potential Fm Mass flux towards or away from the other star DGOS V Va 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 A0Bsurr between star 1 and 2 FAC2 V FAC1 V Not used Not used Not used Not used RPP Reaction rate pp chain effective 2p 1 2 He4 RPC Reaction rate effective C12 2 p N14 RPNG Reaction rate effective N14 2p gt O16 RPN Reaction rate effective N14 2p gt C12 He4 RPO Reaction rate effective O16 2p N14 He4 RAN Reaction rate effective N14 3 2 He4 gt Ne20 C d5 d log p dL dk LQ advection term for luminosity equation w rotation rate N Brunt V is l frequency squared TODO check this the code suggests it s supposed to be the Richardson number but this may be incorrect 34 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 Dasi mixing coefficient for the dynamical shear instability Dssi mixing coefficient for the secular shear instability ves velocity of Eddington Sweet circulation v counter term for Eddington Sweet circultion p current 47rr p m conversion factor for diffusion coefficients CHECK
3. and perhaps other values 10 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 together with CT 4 5 1 E15 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 true 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 CT1 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 converge 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 timest
4. 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 20 6 file mod This file contains stellar structure output that can be used as input The files file 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 Mi the mass of the primary Mo 2 At time step yr t age of the model yr gt Ww Por the orbital period day oO BMS the total binary mass Mo the orbital eccentricity Prot the rotational period day enc artificial energy term O 0 N QOQ kh the number of mesh points and thus rows in the stellar structure block below 10 kp the total number of models to calculate 11 jmod the current model number 12 jb the number of this star in the binary 1 or 2 13 jin the number of independent variables and thus columns in the stellar structure block below 24 for non TWIN 40 for TWIN 14 jf do or do not overwrite overwrite J and see below Just keep it 0 0 or 2 21 6 2 Blocks of stellar structure E
5. 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 25 Line 4 cM Companion Mass Mo RLF1 Relative Roche lobe radius log R Rof RLF2 Relative Roche lobe radius log R Rof DLT Lnu Luminosity due to neutrino losses RA R Alfv n radius Rx 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 Fl 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 boundaries 3 pairs k 2 Dimensionless axis of gyration if moment of inertia is calculated 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 lar
6. 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 previous 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 replace 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 d 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 parameters 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 ratio 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 19 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 rea
7. but time varying and tidal friction a further 7 variables are stored 12 36 I the moment of inertia of the interior material 10 gm cm 13 37 Prot 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 0 the potential at the surface minus the potential on the L1 surface ergs an eigenvalue 16 40 X14 fractional abundance by mass of 4N 17 Hor the orbital angular momentum 10 gm cm sec an eigenvalue 18 e the eccentricity an eigenvalue 19 the flux of mass towards or away from the other star formerly 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 24 Variable MET related to MENC Var 22 41 X24 fractional abundance by mass of Mg 42 X28 fractional abundance by mass of 7 Si 43 X56 fractional abundance by mass of Fe 44 Total angular momentum 36 15 The 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 Wri
8. eet oe bd pe ha he hat Gwe Hehe hee Oe eh eee be bee d 4 6 Equations variables and boundary conditions a oo e e a Ar Biet hat OF state ccc ae o ee PR Ank eR ey ay PEERED OR eRe A AS Murleosyathesls e bacia dok an ee Ea ER we dd ad Se he ee a ee ba eS A 0 A A ea ee 4 10 Stellar structure 4 4 2 04 8608 24440 4b 4 2 bee eee EE HEE ar at en eed Al AL Mas NOSE an an er eek ak A A we ne a EE aa ER Pe a ia bere amp ie a a A AILL Wd mas O ome e A ee eN ee ES JLS Mass TOMES laa cda a ar o a ds eB NET AVS OO ee NAAA init run SI Ripe OP OBERON ood ee aos ERA MLAS ee EERE ae BER REARS ee ee 5 2 Grids of masses and perio 5 3 Rotation and eccentricity 5 4 Initial binary parameters 5 5 Termination conditions file mod 6 1 Header 6 2 Blocks of stellar structure file log EEEN EET in ez Ker Ke Ker er Ke O 00 00 00 00 18 18 18 19 19 20 21 21 22 23 8 file out 1 2 8 1 Stellar snapshots 8 2 Convergence info 9 file plt 1 2 10 file mdl 1 2 10 1 Header 6 ess 10 2 Blocks of stellar structure 11 Creating a ZAMS model 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 24 24 26 27 29 29 31 32 33 36 1 Creating your first run a Obtaining and updating the code To obtain the c
9. 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 fudge for ZAMS models see FUNCS1 0 eos_include_pairproduction Should the equation of state include 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 otherwise they are negligible anyway false 4 8 Nucleosynthesis CH value for initialising X H as a fraction of the total composition 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 12C X Fe 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 13 4 9 Rotation
10. neutrino luminosity Lo 20 Lin luminosity by release of thermal energy Lo 21 Pot rotational period days 22 VK2 K spre with I the moment of inertia 23 Rez Depth of convective envelope R 24 dR Thickness of convective envelope R 25 TET Convective turnover timescale 26 RAF Alfv n radius 27 BP poloidal magnetic field 28 Por orbital period days 29 FLR log R R 1 relative Roche Lobe Radius also called RLF 3Multiply with 1 9891 x 10 to get ergs The reason for this confusing solution is that values of 1040 50 erg don t fit in a single precision variable and that the value may be negative so that a log is no option 27 30 31 32 33 34 35 36 37 38 39 40 41 42 49 56 63 69 75 81 82 83 84 85 86 87 88 89 90 91 92 Fl gure Pr erg M total mass loss Mo yr7 Mina Wind mass loss Mo yr7t Mmt mass transfer rate Mo yr Hor orbital angular momentum 10 g cm s dH rp dt total orbital angular momentum loss rate 10 g cm s dH w dt change in Hor due to gravitational waves 10 g cm s dH dt change in Hop due to wind mass loss 10 g cm s dH dt change in Hor due to spin orbit coupling 10 g cm s dH i dt change in Hspin due to non conservative mass transfer 10 g cm s Meomp Companion mass Mo e orbital ellipticity 48 Surface abundances of 42
11. of CMT or CMS is non zero when using a version 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 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 already 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 1 non simultaneous mode and make sure you solve equations for mass transfer and orbital evolution see Sect 4 6 2 2 3 Two component
12. 91 130 ig 91 130 in e g solver 16 1 Composition la 2a 3a 4a 5a 1b 2b 3b 4b 5b Ont1 2 Xk Xx41 Xy Raue k Mx Mee making 10 such equations in all 16 2 At the surface K 1 6a dM dt CML Mppw r m L Prot CMJ Myxu CMR 1 3 x 107 Lm Eg CMS In R Ry P CMT CMI M 7c Pressure 3 Paas 3 Prad g k 8c Luminosity temperature L racr T 9c gravitational potential 10c d 10 dt the rate of change of angular momentum of the star carried away by stellar wind Mppw or lost to the orbit by tidal friction Q 27 Prot 11c 0 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 dMg dt sum of the winds from both stars Mpg 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 gd 1 0 19d 0 13 CHECK 20 CHECK 25 29 CHECK 30 33 CHECK 2x 34 CHECK 35 CHECK 37 CHECK 38
13. CHECK SSSI RIS TODO TODO 777 CHECK CHECK CHECK CHECK CHECK CHECK CHECK CHECK CHECK du dw Convection artificial mixing Thermohaline mixing Solberg Hoiland mixing Dynamical shear mixing Secular shear mixing Eddington Sweet mixing Goldberg Schubert Fricke mixing 35 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 Inf a dimensionless quantity closely related to electron degeneracy for the case where electrons are non degenerate and non relativistic f 108p 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 1H 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 10 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 2C 11 35 X20 the abundance of Ne For a more sophisticated binary including mass loss magnetic braking rotation uniform
14. H 43 He 44 C 45 N 46 0 47 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 68 Convection zone boundaries mcb gt 0 beginning lt 0 end of zone max 3 sets 74 Semi convection zone boundaries msb gt 0 beginning lt 0 end of zone max 3 sets 80 Nuclear energy production zone Enuc gt Etresh 10L M boundaries mex gt 0 beginning lt 0 end of zone max 3 sets Oconv the mass fraction of the convective envelope P central pressure cgs Prot c rotational period in the centre s 4 BEo binding energy due to gravitational energy erg 1 Mo BE binding energy due to internal energy erg 1 Mo BE binding energy due to recombination energy erg 1 Mo BE3 binding energy due to Ha association energy erg 1 Mo Sc specific entropy in core erg g K S105 g Specific entropy in the convective envelope at T 10 K erg g7 K Rye radius of the helium core Ro Rco radius of the CO core Ro STRMDL a structure model is stored 1 0 or not 0 0 4The latest 2005 version used at NU has STRMDL in column 83 and column 89 as its last column 28 10 file mdl 1 2 The files file md11 and file md12 contain stellar structure output designed for plotting the stellar interiors Each file starts with a line of 3 numbers followed by a number of blocks eac
15. 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 o o o eee e ds L2 Compiling the GATE no an eee ae a a AA A e a Ee N Ea EREN OOB ar en a ee ede a RE A RR E ee EG A od EE ed LA Stopping The COLE as are de e ir den tn aes ee Ee AEE EO a ES Modus operandi ZN MAREN oa vene maer ke ADS RGR A derde ge Bede dak A Ee a pie o en a ten es BO eae eee Et hk ee eh a Ee ke A 2 2 1 Primary compact companion point mass ea e 2 2 2 Two components non simultaneous aa c estoa coeno ta traen anaa e PaE 2 2 3 Two components simultaneous TWIN mode oo o e e 2 3 Creating grids in mass mass ratio and period 2 2 ee radka IO files ul OR BBE nr er NAAA Se AME MBR en rn aa eerdere aoe B a B BASES ee Ra ar EW ae eh ed he ee o se en rde ak B de Bn Ge ee Nae ea ee Ge ee we Re S ok Tenors Miles oe nck esa hie ee Gb OGD p BBR A Betere Gee ce ee me we BS do Output ls by mE aora a ed a e ALA ee eh ee nn owe A init dat Ad put a ee o en ee a a Gedo ea eh be Ae an Seb eae bee eta A Mesh CpG oscila bad AA eds db be kek ORES he CS a heen So L3 Timestops nc ae we Se AN dul AOORVEIBENGE 6 aen of aoa NW Sabah eR RASS EES EE Ry eee ee BGs Oe KARA amp A BOLDER bon bn
16. T5 iterations of each model 0 or 2 KSV an output model is stored in file mod fort 15 after every 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 lastx 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 structure 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 interpolation JCH 4 8 initialises composition to uniformity for ZAMS 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 Mc 3 CT 6 Mc 3 M2 3 CT 1 Unused 0 00 CT 2 Used for Luminosity weight 0 00 reasonable values seem to be 0 01 1 0
17. ach block contains the contents of the variable H 24 models for non TWIN models and 40 for TWIN models Columns 1 16 are reserved 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 over all meshpoints in printb the variable Q 1 24 contains the same data as H 1 24 1 or the corresponding variables 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 a oOo gt Ww oO 0 N 0 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 L luminosity Not logged because it may be negative 10 ergs In f a dimensionless quantity closely related to electron degeneracy for the case where electrons are non degenerate and non relativistic f 1089 T 9 In T logarithmic temperature K X16 mass abundance fraction of 160 m mass 10 g X1 mass abundance fraction of H C the gradient of mesh spacing function Q f T m r with respect to mesh point number K EV ln r logarithmic radius 10 cm d X4 mass abundance fraction of He X12 mass abundance fraction of 12C X20 mass abundance fraction of Ne I the moment of inertia of the interior material 10 g cm Prot the rotation period days of the star EV the centrifugal gravitational potentia
18. 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 exponentially on the assigned timescale 1 CET yr until saturating at ENC CEA 1 0E 6 4 11 Mass loss 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 riobe CMI m CMR 1 3x 107 L m Epg CMJ Mix CML L r m Prot X X if X gt 0 and 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 14 CMI a constant mass gain loss rate for running up or down the ZAMS yr7 0 0 5 0D 9 or 1 0D 6 cmi_mode Changes the interpretation of CMI If cmimode 1 then CMI represents a time scale for exponential mass gain loss M M CMD If cmi mode 2 then CMI represents 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 picks an appropriate recipe depending on the stellar param
19. d 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 11 in the directory where the code is running Presumably we ll want to replace fort 11 with a proper file name at some point to facilitate 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 c
20. d 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 1111 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 model in years exceeds this number JO 5 2e10 UC 3 LCarb Terminate if Lo 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 Lye gt this number together with UC 6 JO 8 1e3 lower for M 2Mo UC 6 rho Initiate He flash evasion if log pe gt this value 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 pe gt this value together with UC 7 JO 9 6 3 UC 9 mdot Terminate if M gt UC 9 M 7Ku 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 Yeore 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 lt 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
21. dels one model per line true units 37 38 file nucmd11 2 Contains abundances in stellar structure models one mesh point per line true units 39 40 33 Data files The files below can be found in the input directory of the installation and are used for data input ZAMS opacities etc zahb mod Input structure model for post helium flash models unit 12 zahb dat init dat for post helium flash models 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 19 phys z opacity tables for certain metallicity unit 20 1t2ubv dat Data to compute magnitudes and colours from L Tor unit 21 nucdata dat Data to compute nuclear reactions unit 26 mutate dat Data to do something with merger products unit 63 COtables_z Data to compute opacities unit 41 physinfo 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 3 5 Output file by unit COW e file out1 le iol2 le log le out fort 11 ahb mod le last1 le mod zams mod zams mas phys z lt2ubv dat init dat zahb dat nucdata dat file mas file plt1 file mdl1 file nucoutl file nucplt1 file nucmdl1 COtables_z physinfo dat rates dat file list mutate dat Eh Eh th Za N me 2 14 23 44 file out2 file
22. ence 9 15 Abundances of 9 H 10 He 11 C 12 N 13 O 14 Ne 15 Mg 16 L total luminosity Lo 17 etn energy generation due to contraction can be negative erg g7 s7t 18 nuc energy generation by nuclear reactions erg g7 s 19 e energy generation in neutrinos erg g7 s71 20 S specific entropy erg g7 K 1 21 Uint internal energy erg g 4 29 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Reaction rate RPP pp chain effectively 2 p gt gt He4 Reaction rate RPC effectively C12 2 p gt N14 Reaction rate RPNG effectively N14 2 p gt O16 Reaction rate RPN effectively N14 2 p gt C12 He4 Reaction rate RPO effectively O16 2 p N14 He4 Reaction rate RAN effectively N14 3 He4 gt Ne20 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 CHECK Dynamical shear mixing CHECK Secular shear mixing CHECK Eddington Sweet mixing CHECK Goldberg Schubert Fricke mixing 30 11 Creating a ZAMS model Note that this section is about manual meddeling with models you don t need this for norma
23. ep decreased by the factor CT3 0 3 or 0 5 4 4 Convergence KR1 The maximum number of iterations allowed on the first timestep 20 KR2 The maximum number of iterations allowed on later timesteps 12 If you want to see output when the code is struggeling to converge a model make sure KR2 gt KT5 climit Limit changes in variables during iterations 1 0d 1 use_quadratic_predictions Normally the code uses linear extrapolation to predict values for the first iteration on the next timestep Set this switch to true to use quadratic extrapolation which can be slightly more accurate false use_fudge_control obsolete present for backward compatibility 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
24. eters 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 x max eye 10 0 0 or 0 2 1 0 Ubina Tv CMJ Multiplier for the De Jager mass loss rate for luminous stars de Jager et al 1988 0 0 or 1 0 zscaling_mdot Scaling with metallicity applied to De Jager mass loss rate in funcs1 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 641V 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 theory 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 los
25. gest 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 10 is a very small error 98 3 1 is worrying and when the floats get to 2 0 or larger 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 26 9 file plt 1 2 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 JMAD Model number 2 t Age yr At time step yr Ae Ww M stellar mass Mo or Mpe helium core mass Mo Mco carbon oxygen core mass Mo Mone oxygen neon core mass Mo log R stellar radius Ro oO 0 N DD log L stellar luminosity Lo 10 log Teg effective temperature K 11 log T central temperature K 12 log Tmax maximum temperature K 13 log pc central density g cm 14 log PTmax density at T Tmax g cm 15 Upina binding energy of H envelope erg 1 Mo 16 Ly luminosity by hydrogen burning Lo 17 Lye luminosity by helium burning Lo 18 Lo luminosity by carbon burning Lo 19 L
26. h 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 The 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 consisting of Nmesh rows of Nya columns each Hence each row is a mesh point in the stellar model a mass coordinate or radius coordinate The first row of each block contains data for the centre of the star the last Nmesh th row represents its surface In each row there are Nyar columns Each column contains a different physical quantity The quantities in the columns are 1 M mass coordinate Mo 2 R radius coordinate Ro P pressure dyn cm Ae Ww p density g cm 5 T temperature K 6 k opacity em g 4 T Vad BF adiabatic temperature gradient 8 Vrad Vaa temperature gradient differ
27. ints 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 centre 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 4 degeneracy parameter 2 P Pressure p Mass density Ae Ww T Temperature 5 k Opacity 6 Vaa Adiabatic temperature gradient i 5 a a dlog T 7 V True temperature gradient dlog P 8 Vraa Vaa Difference between the radiative and adiabatic V s 9 M Mass 10 H Hydrogen abundance 11 Het Helium abundance 12 C1 Carbon abundance 13 N Nitrogen abundance 14 O Oxygen abundance 15 Ne Neon abundance 16 Mg Magnesium abundance 17 R Radius 18 L Luminosity 19 Ein Thermal energy generation rate 20 Enuc Nuclear energy generation rate 21 E Energy loss rate in neutrinos 22 dM Shell mass 23 Diffusion coefficient for thermohaline mixing 24 HT ress Homology invar 25 Unom rep Homology invar 26 Vrom E Homology invar 27 U Internal energy 28 S Entropy 33 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 L Leaa Luminosity relative to Eddington Weonv X l Weony Convective velocity l mixing length u Mean molecular weight wt
28. l erg Qs the potential at the surface minus the potential on the L1 surface EV erg X14 mass abundance fraction of 14N Hor the orbital angular momentum EV 10 gm cm s 1 e the orbital eccentricity EV F the flux of mass towards or away from the other star a function of depth and zero below L1 10 gs lt empty gt lt empty gt lt empty gt 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 22 7 This file contains the exit code with which the Eggleton code terminated Usually the file lists an explanation of file log these codes at the top of the files but for grids these lines may lack 2 1 0 o A QA A A WwW N 11 12 14 15 16 17 22 32 51 52 53 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 2Mo degenerate CO core UC 7 8 PRINTB M exceeds limit UC 9 PRINTB Impermi
29. l operation of the code e g to change the ZAMS mass of a model for that see the section init run If you want to create a ZAMS series see the example run 01 in the directory run 01 zams In order to create a ZAMS model of certain mass or to obtain 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 desired mass e Set the parameter CMI to the desired value usually 5 x 1079 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 Mo and want 1 02 Mo f 1 02 e Calculate the approximate number of steps you need to take for a time step size dty 10 yr and the CMI above No cura e Choose a nice round but at least integer number of steps N No e Calculate the true time step for N steps dt at N 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 mod 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 anothe
30. 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 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 alternative 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 16 4 13 Cetera enc parachute Emergency energy generation term
31. 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 control the numerical details of the code the differ ential equations that need to be solved using which variables and boundary conditions and which physics nucle osynthesis rotation stellar wind overshooting et cetera The new format post 2005 CVS version contains one parameter either scalar or array per line If a variable 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 reasons 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 KT4 KT1 Print internal details of every KT1 th model to file out1 2 and file mdl1 2 20 or 200 KT2 Print internal details at every KT2 th mesh point of the KT1 th model file out1 2 only 1 or 2 KT3 Print KT3 pages of details for every KT1 th model to file out1 2 1 2 or 3 KT4 Print a five line summary of every KT4 th model to file out1 2 and save every KT4 th evolution model to file plti 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 K
32. locks 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 Luminosity 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 24 Line 2 dty Time step yr Prot Rotational period days zet Mass loss rate other than Roche lobe overflow e g wind Mo yr tKh Kelvin Helmholtz timescale LHe Luminosity due to helium burning RCZ MeCO Mass of CO core TXH H abundance at Tmax TXHe He abundance at Tmax TXC C abundance at Tmax TXN N abundance at Tmax TXO O abundance at Tmax TX Ne 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 Oxygen burning DRCZ McNe Mass of Neon Core SXH Surface abundance of H SXHe Surface abundance of He SXC Surface abundance of
33. mes 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 out1 2 Main output file showing what the stars are doing at that moment These files are useful as screen output units 1 2 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 be 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 last1 2 Contains complete structure of last and pre last model when lucky that can serve as input for a next run units 13 14 file 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 file log Shows how the code was terminated if terminated properly unit 8 file mas Creation of helper file to find the proper ZAMS model from zams mod unit 29 file plt1 2 Contains stellar evolution data one model per line units 31 32 file md11 2 Contains a number of complete stellar structure models one mesh point per line units 33 34 file nucout1 2 Main abundances screen output file true units 35 36 file nucp1t1 2 Contains abundances in stellar evolution mo
34. 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 is a numerical fudge to remove 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 17 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 evolution 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 parallel 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
35. ode 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 specific 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 1 2 Compiling the code cd into the directory stars This is the directory that contains the code subdirectory If you re running 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 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 compilation 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 compiler To overrule this execute e g FC gfortran cmake instead Step 3c may produce some remarks and should produce the binary executable code ev 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 bashrc Check with echo evpath It is very u
36. ode 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 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 account 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
37. 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 ignored 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 107 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 IM1 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 1 then enough of 2 to catch up with 1 then another KP of x1 etc so that if 2 breaks down before x1 y
38. ou 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 ML1 DML KML QL1 DQL KQL XL1 DXL KXL These three lines contain parameters 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 ML1 KML 1 DML 18 e The second loop is logio mass ratio in sense larger smaller starting at QL1 increasing by steps of DQL to QL1 KQL 1 DQL e The third inner loop is X logio orbital period period necessary for 1 to fill its Roche lobe when still on the ZAMS starting at XL1 increasing by steps of DXL to XL1 KXL 1 DXL 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 Pot for each star rotational breakup period 10R0T PERC breakup or RLOF at ZAMS KR 2 Pt for each star max 1 05 rotational breakup period orbital period 10ROT PERC breakup or RLOF at ZAMS KR gt 3 set Prot Porp
39. r 10 models or so If the change in mass is less than expected you may have chosen your timestep too long so that the code does not converge recalculates the model with a smaller timestep and continues with this smaller timestep since it is not allowed to change 31 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 metallicity 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 Evolve a 2 25Mo 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 4Mo 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 Test the result for a 1 0 Mo model run 03 If the code can produce the ZAHB model but it cannot continue the evolution on the HB error code 16 the problem may be a too small desired number of models see the parameter kp in the first i e header line of the structure model in input zahb lt Z gt mod 32 13 Variables in SX and PX These quantities are calculated in printb and stored in the variables SX and PX In the loop over all meshpo
40. r 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 evolution ary phases have different CDD s identified here by name rather than by number cdc_ms CDD cdc_ms between ZAMS and core hydrogen 0 04 corresponding to the beginning 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 ede hg CDD cdc_ms ede hg between core hydrogen exhaustion 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_dblsh CDD cdc_ms cdc_dblsh for double shell burning 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 cdc_rlof CDD CDD edc_rlof to reduce the timestep if the system is moving closer to Roche lobe overflow RLOF The criterion i
41. s 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 particular 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 necessary equations see Sect 4 6 2 3 Creating grids in mass mass ratio and period 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 3 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 stellar 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 MI and P Output from different loops is stored in files with different na
42. s rate by Maeder amp Meynet Set at most one of these CTF A factor multiplying an expression for the rate of tidal friction 0 0 or 0 01 CLT A coefficient used in the estimation of heat flux between components in contact It does not really work yet or does it 15 4 11 2 Mass transfer CMT 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 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
43. s that the star is close to filling its Roche lobe and expanding 0 05 or 1 0 ede rlof reduce CDD CDD cdc_rlof_reduce to keep the timestep smaller while the system detaches after RLOF The criterion is that the star is close to filling its Roche lobe and shrinking 0 25 or 1 0 12 4 6 Equations variables and boundary conditions See also Writeup section 1 5 KE1 KE2 The number of first and second order difference equations respectively KE3 Subset of KE1 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 KFN 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 variables 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 equations are used max 40 integers a k a id 51 90 ig 51 90 in e g solver kp_be 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
44. seful to put ev in your path You could do one of these a PATH PATH echo evpath code to add the directory 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 2 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 3 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 4 cp init runm4 init run 1 m assuming you re using bash If you re using csh replace export a b with setenv a b and bashre with cshre 2Some compilers e g gfortran don t accept but need e g home user 5 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 stars 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 probably 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 comman
45. ssible FDT for star 2 NEXTDT Time step reduced below limit hydrogen left in the core quit BACKUP Funny composition distribution My lt Mye or Mye lt Mco PRINTB Terminated by hand STAR12 ZAHB model didn t converge MAIN Nucleosynthesis didn t converge BEGINN 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 23 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 outl This will show the last 10 lines of the file out1 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 number 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 b
46. teup Section 1 5 p 9 for more explanation G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 22 5 13 14 44 45 Abundance equations O 1 2LXx41 Xx Origa Kr Kri Xk Rue Arrr Xx ri 4 1H abundance equation 160 abundance equation 4He abundance equation 12C abundance equation 20Ne abundance equation Pressure rotation log Px 1 log Pk Am k 41 2 Radius r rg m 2mpr x41 2 Temperature log Tk 1 logT VAm x 1 2 Luminosity Ligt Ly M Er xy1 2 ME mx m Ea k rie Mass mA m 2m 3m1 3 4172 Moment of inertia 41 lx 2m 1r 3 x41 2 Surface Li potential dier dx Gmm 4rrtp k 1 2 MN abundance equation 24Mg abundance equation Sum of the abundances is constant gt X 0 normally used instead of 14 for Mg Equation for artificial mesh dependent energy term MENC Equation for MEA Related to MENC Eq 16 and luminosity Mass transfer rate Ex 1 amp CMTx 2 s r m x 1 2 if d gt 0 0 otherwise Equation for MET Related to MENC Eq 16 25 37 CHECK 22 42 43 44 45 Angular momentum transport Total angular momentum 288i abundance equation 56Fe abundance equation 37 Xx Xx 1 Mx 1 16 The boundary conditions The boundary conditions are selected in kp_bc in init dat and are also known as id
47. the code iterates false 11 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 determines whether the current or the previous value of the mean molecular weight should be used to estimate the effect of thermohaline mixing Normally 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 difference 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 equations if ERR lt EPS the model has converged 1079 wanted_eps The desired accuracy The solver will aim for an accuracy 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 facto
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