TRiple Evolution Simulation
TRES is a numerical framework for simulating hierarchical triple systems with stellar and planetary components. Mass transfer from one star to another and the consequential effect to the orbital dynamics is realized via heuristic recipes. These recipes are combined with three-body dynamics and stellar evolution inluding their mutual influences.
TRES includes the effects of common-envelope evolution, circularized stable mass transfer, tides, gravitational wave emission and up-to-date stellar evolution through SeBa. Other stellar evolution codes such as SSE can also be used. Coming soon: TRES with MESA, transition to N-body calculations (including stellar evolution and dissipative processes) when the system's evolution is not secular anymore.
This document contains the following parts:
TRES-Exo for exoplanet research
TRES makes use of the Astrophysical Multipurpose Software Environment (AMUSE) See https://amusecode.github.io/ for how to install AMUSE. Note that for standard TRES usage, the only necessary community code to install is SeBa.
Thus, after installing the AMUSE pre-requisites, we can simply install the minimal framework and then add SeBa:
pip install [--user] amuse-framework
pip install [--user] amuse-<seba>
After compiling AMUSE, TRES needs to be installed and compiled by means of the Makefile as following:
First, clone the TRES github repository:
git clone https://github.com/amusecode/TRES.git
Then, from the root of the cloned respository compile the Makefile:
cd seculartriple_TPS
make clean
make
Note: If the above line doesn't work, which may be the case for older versions of amuse, try:
(cd seculartriple_TPS)
mv Makefile Makefile_new
mv Makefile_old Makefile
make clean
make
To evolve a single system with the parameters: primary mass M=1.2 Solar mass, secondary mass m=0.5 Solar mass, tertiary mass m=0.6 Solar mass, inner and outer eccentricity e=0.1 & 0.5, inner and outer orbital separation a=200 & 20000 Solar radii, metallicity z=0.001, and time T=10 Myrs, you need to run:
python TRES.py -M 1.2 -m 0.5 -l 0.6 -E 0.1 -e 0.5 -A 200 -a 20000 -z 0.001 -T 10
assuming AMUSE is loaded in your python.
The full list of possible input parameters is: Depreciated (yet still functioning) parameters are given in {}.
parameter unit / default
--M1 {-M} inner_primary_mass in Solar mass
--M2 {-m} inner secondary mass in Solar mass
--M3 {-l} outer mass in Solar mass
--Ain {-A} inner semi major axis in Solar radius
--Aout {-a} outer semi major axis in Solar radius
--Ein {-E} inner eccentricity
--Eout {-e} outer eccentricity
-i, -I relative inclination in rad
--Gin {-G} inner argument of pericenter in rad
--Gout {-g} outer argument of pericenter in rad
--Oin {-O} inner longitude of ascending node in rad
(outer longitude of ascending nodes = inner - pi)
-Z {-z} metallicity default = 0.02 (Solar)
-t, -T end time in Myr
-N, -n integer number asigned to the triple default = 0
-f name of output file default = TRES
-F type of output file (hdf5/txt) default = hdf5
--dir_plots directory for plots for debugging default = "" (current directory)
mode (aka REPORT_DEBUG == True)
--CE which type of modelling for common envelope evolution default = 2
options:
0: alpha-ce + alpha-dce
1: gamma-ce + alpha-dce
2: seba style; combination of gamma-ce, alpha-ce & alpha-dce
Note that in all cases a double common-envelope is calculated using the alpha-ce.
--SN_kick_distr supernova kick distribution default = 10
options:
0: No kick
1: Hobbs, Lorimer, Lyne & Kramer 2005, 360, 974
2: Hobbs, Lorimer, Lyne & Kramer 2005, 360, 974 scaled down for bh by mass
3: Arzoumanian ea 2002, 568, 289
4: Arzoumanian ea 2002, 568, 289 scaled down for bh by mass
5: Hansen & Phinney 1997, 291, 569
6: Hansen & Phinney 1997, 291, 569 scaled down for bh by mass
7: Paczynski 1990, 348, 485
8: Paczynski 1990, 348, 485 scaled down for bh by mass
9: Verbunt, Igoshev & Cator, 2017, 608, 57
10: Verbunt, Igoshev & Cator, 2017, 608, 57 scaled down for bh by mass
--max_CPU_time maximum CPU time allowed (only works in combination with "stop_at_CPU_time")
default = 3600 (seconds)
Additionally, there is a list of stopping conditions that determines whether the simulation of a system should stop at a certain evolutionary phase. By default, these stopping conditions are set to True, which means they are in effect. However, the four specific mass transfer cases (stable, unstable, eccentric stable & eccentric unstable) are set to False by default. Once "--no_stop_at_mass_transfer" is set to False, it is possible to set the specific mass transfer cases to True.
action items add these to:
--no_stop_at_mass_transfer avoid stopping the simulation at the onset of mass transfer
--no_stop_at_init_mass_transfer avoid stopping the simulation if there is mass transfer initially
--no_stop_at_outer_mass_transfer avoid stopping the simulation when tertiary initiates mass transfer
methodology is as of yet non-existent
--stop_at_stable_mass_transfer avoid stopping the simulation at the onset of stable mass transfer in the inner binary
--stop_at_unstable_mass_transfer avoid stopping the simulation at the onset of unstable mass transfer in the inner binary (leading to common-envelope evolution)
--stop_at_eccentric_stable_mass_transfer avoid stopping the simulation at the onset of stable mass transfer in the inner binary if the orbit is eccentric
--stop_at_eccentric_unstable_mass_transfer avoid stopping the simulation at the onset of unstable mass transfer in the inner binary if the orbit is eccentric
--no_stop_at_merger avoid stopping the simulation after a merger
--no_stop_at_inner_collision avoid stopping the simulation after a collision in the inner binary
--no_stop_at_outer_collision avoid stopping the simulation after a collision involving the outer star
--no_stop_at_disintegrated avoid stopping after the system disintegrated into seperate systems
--stop_at_semisecular_regime to stop the simulation if the sytem is in the semi secular regime
--stop_at_SN to stop the simulation when a supernova occurs
--stop_at_CPU_time to stop the simulation when the computational time exceeds a given value
If you need to follow the triple evolution for multiple systems with parameters which are already specified you can start TRES multiple times, e.g.
python TRES.py -M 1.2 -m 0.5 -l 0.6 -E 0.1 -e 0.5 -A 200 -a 20000 -z 0.001 -T 10
python TRES.py -M 1.5 -m 1 -l 0.6 -E 0.1 -e 0.5 -A 50 -a 20000 -z 0.001 -T 10
python TRES.py -M 1.5 -m 1 -l 0.05 -E 0.1 -e 0.5 -A 50 -a 20000 -z 0.02 -T 10
This is probably not handy for more than 5 systems. Although this can be added in e.g. a shell or Python script.
A random population can be generated with TPS.py with a Monte Carlo based approach, e.g.
python TPS.py -n 5
python TPS.py -n 10 --M_max 5 --M_min 4 --M_distr 0 --A_max 2000 --A_min 200 --A_distr 2
The full list of options is [default]: Depreciated (yet still functioning) parameters are given in {}.
--M1_max {--M_max} upper limit for the inner primary mass [100 Msun]
--M1_min {--M_min} lower limit for the inner primary mass [0.1 Msun]
--M1_distr {--M_distr} mass function option:
0: "Kroupa", #default
1: "Scalo",
2: "Miller & Scalo",
3: "Salpeter",
4: "Logarithmically flat",
5: "Eggleton",
6: "Kroupa for massive stars M>0.5 powerlaw with exp=-2.3",
--Qin_max {--Q_max} upper limit for the inner mass ratio [1.]
--Qin_min {--Q_min} lower limit for the inner mass ratio [0.]
--Qin_distr {--Q_distr} inner mass ratio option:
0: "Uniform distribution", #default
1: "Kroupa IMF",
2: "Galicher et al. 2016 powerlaw (M^-1.31)", #draws from mass distribution instead of mass ratio distribution,
--Qout_max {--q_max} upper limit for the outer mass ratio [1.]
--Qout_min {--q_min} lower limit for the mass of the outer star [0.]
--Qout_distr {--q_distr} outer mass ratio option:
0: "Uniform distribution", #default
1: "Kroupa IMF",
2: "Galicher et al. 2016 powerlaw (M^-1.31)", #draws from mass distribution instead of mass ratio distribution,
--Ain_max {--A_max} upper limit for the inner semi-major axis [5e6 RSun]
--Ain_min {--A_min} lower limit for the inner semi-major axis [0.5 RSun]
Note that the true minimum separation is also affected by RLOF.
By default contact or semi-detached systems on the ZAMS are removed from the sample.
We recommend to add the command line option --include_circularisation_during_preMS, such that the eccentricity is redrawn (<10x).
--Ain_distr {--A_distr} inner semi-major axis option:
0: "Log Uniform distribution", #default
1: "Constant semi-major axis",
2: "Tokovinin lognormal mu = 10^5d, sigma = 2.3",
3: "Lognormal mu = 10^3.5d, sigma = 2.3",
4: "Rizzuto Lognormal mu = 10^0.95 AU, sigma = 1.35",
5: "Sana et al. 2012",
6: "flat distribution",
7: "Galicher et al. 2016 powerlaw (a^-0.61)", #appropriate for planets
--Aout_max {--a_max} upper limit for the outer semi-major axis [5e6 RSun]
--Aout_min {--a_min} lower limit for the outer semi-major axis [0.5 RSun]
--Aout_distr {--a_distr} outer semi-major axis option:
0: "Log Uniform distribution", #default
1: "Constant semi-major axis",
2: "Tokovinin lognormal mu = 10^5d, sigma = 2.3",
3: "Lognormal mu = 10^3.5d, sigma = 2.3",
4: "Rizzuto Lognormal mu = 10^0.95 AU, sigma = 1.35",
5: "Sana et al. 2012",
6: "flat distribution",
7: "Galicher et al. 2016 powerlaw (a^-0.61)", #appropriate for planets
--Ein_max {--E_max} upper limit for the inner eccentricity [1.]
--Ein_min {--E_min} lower limit for the inner eccentricity [0.]
--Ein_distr {--E_distr} inner eccentricity option:
0: "Thermal", #default
1: "Constant eccentricity",
2: "Sana et al. 2012 e^-0.45", #-> close binaries
3: "Flat distribution",
4: "Powerlaw e^0.5",
5: "Bowler et al. 2020 Beta distribution", #appropriate for planets
--Eout_max {--e_max} upper limit for the outer eccentricity [1.]
--Eout_min {--e_min} lower limit for the outer eccentricity [0.]
--Eout_distr {--e_distr} outer eccentricity option:
0: "Thermal", #default
1: "Constant eccentricity",
2: "Sana et al. 2012 e^-0.45", #-> close binaries
3: "Flat distribution",
4: "Powerlaw e^0.5",
5: "Bowler et al. 2020 Beta distribution", #appropriate for planets
--i_max upper limit for the relative inclination [pi]
--i_min lower limit for the relative inclination [0]
--i_distr relative inclination option:
0: "Circular uniform distribution", #default
1: "Constant inclination",
--Gin_max {--G_max} upper limit for the inner argument of pericenter [pi]
--Gin_min {--G_min} lower limit for the inner argument of pericenter [-pi]
--Gin_distr {--G_distr} inner argument of pericenter option: r
0: "Uniform distribution", #default
1: "Constant argument of pericenter",
--Gout_max {--g_max} upper limit for the outer argument of pericenter [pi]
--Gout_min {--g_min} lower limit for the outer argument of pericenter [-pi]
--Gout_distr {--g_distr} outer argument of pericenter option:
0: "Uniform distribution", #default
1: "Constant argument of pericenter",
--Oin_max {--O_max} upper limit for the inner longitude of ascending node [pi]
--Oin_min {--O_min} lower limit for the inner longitude of ascending node [-pi]
--Oin_distr {--O_distr} inner longitude of ascending node option:
0: "Circular niform distribution",
1: "Constant longitude of ascending nodes", #default
(outer longitude of ascending nodes = inner - pi)
-T or -t binary end time. [13500 Myr]
-Z {-z} metallicity of stars [0.02 (Solar)]
-n number of triples to be simulated [1]
-N number of initial triple [0]
--SN_kick_distr supernova kick distribution default = 10
options:
0: No kick
1: Hobbs, Lorimer, Lyne & Kramer 2005, 360, 974
2: Hobbs, Lorimer, Lyne & Kramer 2005, 360, 974 scaled down for bh
3: Arzoumanian ea 2002, 568, 289
4: Arzoumanian ea 2002, 568, 289 scaled down for bh
5: Hansen & Phinney 1997, 291, 569
6: Hansen & Phinney 1997, 291, 569 scaled down for bh
7: Paczynski 1990, 348, 485
8: Paczynski 1990, 348, 485 scaled down for bh
9: Verbunt, Igoshev & Cator, 2017, 608, 57
10: Verbunt, Igoshev & Cator, 2017, 608, 57 scaled down for bh #default
action items add these to:
--no_stop_at_merger avoid stopping the simulation after a merger
--no_stop_at_inner_collision avoid stopping the simulation after a collision in the inner binary
--no_stop_at_outer_collision avoid stopping the simulation after a collision involving the outer star
--no_stop_at_disintegrated avoid stopping after the system disintegrated into seperate systems
--no_stop_at_mass_transfer avoid stopping the simulation at the onset of mass transfer
--stop_at_semisecular_regime to stop the simulation if the sytem is in the semi secular regime
--stop_at_SN to stop the simulation when a supernova occurs
--stop_at_CPU_time to stop the simulation when the computational time exceeds a given value
In Columba et al. 2023, (A&A, 675A, 156C) we presented an extension for TRES to incorporate exoplanets.
For exoplanet research, we have included the following processes and recommend the following settings:
- First things first: tell TRES to include Sub-Stellar Objects by setting the boolean EXCLUDE_SSO to False in TRES.options.py. Amongst other things, this will automatically set the minimum mass of a body to 0.2 Jupiter masses (~0.0002 Solar masses) in stead of 0.0075 Solar masses. Note that our extension is only valid for giant planets, hence the minimum mass of 0.2 Jupiter masses.
- For the dynamical stability of triples, you can which stability criterium is used through the parameter stability_limit_specification in TRES_setup.py. Options applicable to exoplanets are the simple prescription from Petrovich et al. (1), the full prescription from Petrovich et al. (2), Holman's prescription for S-type orbits (3), Holman's prescription for P-type orbits (4).
- energy-limited atmospheric photoevaporation of planets
- initial planetary spin rate as 0.126 the breakup speed (Bryan+2018). This can be adjusted in the function initial_angular_frequency in triple_class.py
Examples
- To evolve a single system (binary star + CBP) that survives for one Hubble time (13.5 Gyr) with the following parameters:
- primary mass: M1 1.04 Msun
- secondary mass: M2 1.00 Msun
- CBP mass: M3 0.011 Msun
- inner binary semimajor axis: Ain 54.6 Rsun
- CBP semimajor axis: Aout 477.8 Rsun
- inner binary eccentricity: Ein 0.67
- CBP eccentricity: Eout 0.15
- relative orbital inclination: i 1.9 (rad)
- simulation time: T 1000 Myr
you can run TRES as:
python TRES.py --M1 1.04 --M2 1. --M3 0.011 --Ain 54.6 --Aout 477.8 --Ein 0.67 --Eout 0.15 -i 1.9 -T 1000 --no_stop_at_mass_transfer
and use the rdc_ py to read the output and print it in readable text format. If you wish to run the complete evolution, use -T 13500 to simulate one Hubble time and you'll obtain a DWD-orbiting CBP ('Magrathea' planet).
- To evolve a single system (binary star + CBP) where the inner binary merges as a DWD around 10 Gyr, you can use the following command:
python TRES.py --M1 1.33 --M2 1.06 --M3 0.0046 --Ain 26.35 --Aout 3012.9 --Ein 0.3 --Eout 0.1 -i 1.7 -T 11000 --no_stop_at_mass_transfer -f 'testRun_2.hdf'
Normally TRES adds the evolution history of individual triples in the TRES.hdf file. Every snapshot represents a moment in the evolution of the triple when something interesting happened, for example one of the star transitions from the main-sequence to the hertzsprung gap, or mass transfer starts or stops.
The python script rdc_TRES.py reduce the TRES hdf output. The full list of available options is [default]:
-f root of the name of the input file [TRES]
-S printing style [0]
-F print all snapshots. By default only the first & last lines are printed.
You can also select specific types of triples. For these a single extra line is added on the first occasion the requirements are met. Options are:
--st1 stellar type of inner binary primary star [-1]
--st2 stellar type of inner binary secondary star [-1]
--st3 stellar type of outer star [-1]
--btin binary type of inner binary [-1]
--btout binary type of outer binary [-1]
--trt triple type [-1]
or if you prefer to specify these in string format:
--st1str stellar type of inner binary primary star [all]
--st2str stellar type of inner binary secondary star [all]
--st3str stellar type of outer star [all]
--btinstr binary type of inner binary [all]
--btoutstr binary type of outer binary [all]
--trtstr triple type [all]
Which parameters are printed and in which style can be adjusted to your liking in the function rdc(). Currently there are 3 options settable on the command line via -S (print_style):
0 Selected parameters are printed in a human readible way
1 Full - all possible parameters are printed (sys.exit after first snapshot)
2 TRES standard - selected parameters
3 TRES standard - selected parameters, csv format
For option 2: 6 lines are printed for every snapshot. The columns represent:
General information on the system:
Line 1: snapshot number, triple number, time, relative_inclination, dynamical_instability, kozai_type, error_flag_secular, CPU_time
Orbital information (inner binary | outer binary) :
Line 2: 'bs:', binary type, semimajoraxis, eccentricity, argument_of_pericenter, longitude_of_ascending_node
| binary type, semimajoraxis, eccentricity, argument_of_pericenter, longitude_of_ascending_node
Stellar information (primary | secondary | tertiary)
Line 3: 'st:', is_donor, stellar_type, mass, spin_angular_frequency, radius, core mass
| is_donor, stellar_type, mass, spin_angular_frequency, radius, core mass
| is_donor, stellar_type, mass, spin_angular_frequency, radius, core mass
For option 0: One line is printed for every snapshot with the parameters in the same order as above (excluding the snapshot number). The units are Solar Mass, Solar radius, Myr.
The stellar types in TRES follow the standard terminology of AMUSE:
0 lm_ms deeply or fully convective low mass MS star
1 ms Main Sequence star
2 hg Hertzsprung Gap
3 rgb First Giant Branch
4 cheb Core Helium Burning
5 eagb Early Asymptotic Giant Branch
6 tpagb Thermally Pulsating Asymptotic Giant Branch (not used in SeBa -> labelled as 5)
7 hems Main Sequence Naked Helium star
8 hehg Hertzsprung Gap Naked Helium star
9 hergb Giant Branch Naked Helium star
10 hewd Helium White Dwarf
11 cowd Carbon/Oxygen White Dwarf
12 onewd Oxygen/Neon White Dwarf
13 ns Neutron Star
14 bh Black Hole
15 sn Massless Supernova
16 unknown Unknown stellar type
17 prems Pre-main-sequence Star
18 planet Planet
19 bd Brown Dwarf
When selecting for stellar type, you can also use the following strings for combinations of startypes:
agb eagb, tpagb [5,6]
heg hehg, hergb [8,9]
wd hewd, cowd, onewd [10,11,12]
Note that stellar type 0, 6 & 8 are not used in SeBa. All main-sequence stars are stellar type 1, all AGB stars have the label stellar type 5 (both EAGB as TPAGB stars), and both helium hertzsprung gap stars as helium giants are labelled with stellar type 9.
The binary type is a classification for a specific orbit, e.g. the inner or the outer orbit of a triple. The following options exist:
-1 all
0 unknown
1 merger
2 disintegrated
3 dynamical_instability
4 detached
5 contact
6 collision
7 semisecular
8 rlof
9 stable_mass_transfer
10 common_envelope
11 common_envelope_energy_balance (i.e. alpha-CE)
12 common_envelope_angular_momentum_balance (i.e. gamma-CE)
13 double_common_envelope
And similarly for the triple as a whole:
-1 all
0 hierarchical
1 dynamical_instability
2 semisecular_regime (currently not in use)
3 error_flag_secular
Do you want to rerun a system in your datafile? No need to copy all the parameters, simply run rdc_TRES.py with two extra parameters:
--print_init to print initial conditions for re-running
-l the line number of the first line in your hdf datafile where the system appears
where the stars are on the zero-age main-sequence.
For example: rdc_TRES.py -f TRES.hdf --print_init -l 0. This will return something like:
amuse TRES.py -M 1.3 -m 0.5 -l 0.5 -A 200.0 -a 20000.0 -E 0.1 -e 0.5 -G 0.1 -g 0.5 -I 1.3962634016
For more advanced tips, see the README in the developer-folder.
See the following publication: Toonen et al 2016 for more details on TRES in general. See Columba et al 2023 for more details on TRES-Exo.