-
-
-The MODEST-1 summary paper,
-contains the main conclusion of the workshop.
-
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-
- -download the poster - - |
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-
MODEST-5 will take
-place 11-14 August 2004, and will be hosted by the Department of
-Physics and Astronomy,
| | About - Modest-5Registration -Hotel - reservationsTravel - DirectionsConfirmed - participants |
Immediately after
-the MODEST-5 workshop (16-20 August 2004), a conference on Massive
-Stars in Interacting Binaries is being held north-east of
-
-
-
-MOdeling DEnse STellar systems -
| Working - groups: | -WG1 - | WG2 - | WG3 - | WG4 - | WG5 - | WG6 - | WG7 - | WG8 - | WG9 - | -
| Workshops: | -MODEST-1 - | MODEST-2 - | MODEST-3 - | MODEST-4 - | MODEST-5 - | MODEST-6 - | MODEST-7 - | -
Though neither we nor our projects could possibly be described as -modest, we use the acronym to point out that we want to work with only -MODEST modifications of existing codes, to model dense stellar -systems. So we can read the acronym also as MODifying Existing -STellar codes. - -
While many of us have talked for years about combining `live' -stellar evolution codes directly with N-body simulations, we have now -reached a consensus between various groups about standards and -interfaces, what is needed, and what is doable. On this web site we -will provide up-to-date information about our activities, and pointers -to various projects in progress. - -
In order to participate in ongoing MODEST email discussions, see -the information provided below under LINKS, or go to one of our -working groups. - -
-Though neither we nor our projects can possibly be described as -modest, we use our acronym to point out that we want to work with only -MODEST modifications of existing codes, to model dense stellar -systems. So we can read the acronym also as MODifying Existing -STellar codes. -
-While many of us have talked for years about combining `live' stellar -evolution codes directly with N-body simulations, we have now reached -a consensus between various groups about standards and interfaces, -what is needed, and what is doable. On this web site we will provide -up-to-date information about our activities, and pointers to various -projects in progress. -
-In order to participate in ongoing MODEST email discussions, see the -information provided below under LINKS. - - - -
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-
- -Amsterdam, Dec 16-17, 2002. - |
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-
-Table of contents
-
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-
-One of the goals of our workshop was to specify ways to let existing -computer codes for stellar dynamics (SD) and for stellar evolution (SE) -communicate with minimum modification at either end. In fact, with a -well-defined minimal interface between the two, SD should not care -whether the information obtained results from running an actual SE code, -or from a table look-up or fitting formula. The same holds for SE: -each side should see the other as a black box. Soon, we will also -discuss the role of stellar hydrodynamics (SH), but we'll leave that -out for now, to get started. -
-- -We have just written a toy model version for -the SD-SE interface, following the discussions during the workshop. -In order to test our interface, we constructed a very simple -implementation of both the SD and SE parts of a simulation code. -For SD we simply took two unbound stars on a head-on collision course, -to let them merge into a single star with an unusual composition. -For SE we constructed the following stick-figure version. We would -be grateful to get reactions and suggestions from those of you who -have more experience with SE codes. -
- - -- We approximate each physical quantity Q that describes the state of - a star (mass, radius, Y, Z) with a piece-wise linear function with - one discontinuity, specified by the following six numbers: --Does all this seem reasonable? Are there obvious improvements that -we could make, without making the whole toy model much more complex? -Is anybody aware of toy models resembling this in the literature? --
- t_endms time at which the star leaves the main sequence - t_endrg time at which the star leaves the red giant branch. - f_init value of Q at birth of star (at time t=0) - f_endms value of Q at time t=t_endms - f_endrg value of Q just before time t=t_endrg - f_remnant value of Q just after time t=t_endrg - - ....... f_endrg - /| - / | - / | - / | - ^ / | - | / | - Q / | - _____/.......|...... f_endms - _____----- | - _____-----.......................|...... f_init - |------ f_remnant - +-----------------------+--------+------ 0 - 0 t_endms t_endrg - t --> -- Note that we stick-figure version of stellar evolution mimics - only low-mass stars, while leaving out completely the horizontal - branch part of the evolution. In addition, we will make the - following simplified assumption: t_endrg = 1.1 t_endms. - This leaves us with 17 independent values: one time scale and four - Q values for each of the four Q choices. Here is what we choose, - starting with the three free values mass M, Y_init Y0, Z_init Z0: -- -
- t_endms = ( 10^4 / M^3 ) Myr - - Q (unit) | Q_init | Q_endms | Q_endrg | Q_remnant - ----------------+----------+-----------+-----------+------------- - mass (Msun) | M | M | M / 2 | M / 4 - radius (Rsun) | M | M | 100 M | 0.01 / M - He fraction Y | Y0 | Y1 | Y2 | Y3 - metallicity Z | Z0 | Z1 | Z2 | Z3 - - where Y1 = minimum(Y0 + 0.1 , 1 - Z1) - Y2 = minimum(Y0 + 0.4 , 1 - Z2) - Y3 = minimum(Y0 + 0.8 , 1 - Z3) - Z1 = Z0 - Z2 = minimum(Z0 + 0.2 , 1) - Z3 = minimum(Z0 + 0.4 , 1) - -- The idea is to let the star lose half of its mass on the red giant - branch due to wind loss; and then again half of its mass in the - instantaneous transition to a white dwarf. For the helium fraction Y - we presume that it increases by 0.1 while on the main sequence, and by - another amount 0.1 on the red giant branch; we then double that number - to get Y = Y0 + 0.4, to account for the mass lost (the newly formed - helium is not lost since it is in the inner regions). After losing - again half the mass, the final Y is concentrated to Y = Y0 + 0.8, but - of course in all cases the total Y+Z cannot exceed unity, hence the - "minimum(,)" operators above. For the metallicity Z we assume that - nothing is generated on the main sequence, and 0.1 on the red giant - branch. -
-As for the interface specification, we will comment on that later. -Below is a sample output of the output from the above model, starting -with a time step of 1 Myr, and letting the time step double each time, -unless the changes in mass, radius, Y, or Z became too large (this is -something that SD could limit through the interface to SE, as we -discussed at the workshop). We imposed the following requirements: -
-
- | delta mass | < 0.1 * mass - | delta radius | < radius - | delta Y | < 0.1 - | delta Z | < 0.1 -- - -
-Output for a one-solar-mass star: - -Age =1.000000000 M = 1.000000000 R = 1.000000000 Y = .2500100000 Z = .2000000000E-01 -Age =3.000000000 M = 1.000000000 R = 1.000000000 Y = .2500300000 Z = .2000000000E-01 -Age =7.000000000 M = 1.000000000 R = 1.000000000 Y = .2500700000 Z = .2000000000E-01 -Age =15.00000000 M = 1.000000000 R = 1.000000000 Y = .2501500000 Z = .2000000000E-01 -Age =31.00000000 M = 1.000000000 R = 1.000000000 Y = .2503100000 Z = .2000000000E-01 -Age =63.00000000 M = 1.000000000 R = 1.000000000 Y = .2506300000 Z = .2000000000E-01 -Age =127.0000000 M = 1.000000000 R = 1.000000000 Y = .2512700000 Z = .2000000000E-01 -Age =255.0000000 M = 1.000000000 R = 1.000000000 Y = .2525500000 Z = .2000000000E-01 -Age =511.0000000 M = 1.000000000 R = 1.000000000 Y = .2551100000 Z = .2000000000E-01 -Age =1023.000000 M = 1.000000000 R = 1.000000000 Y = .2602300000 Z = .2000000000E-01 -Age =2047.000000 M = 1.000000000 R = 1.000000000 Y = .2704700000 Z = .2000000000E-01 -Age =4095.000000 M = 1.000000000 R = 1.000000000 Y = .2909500000 Z = .2000000000E-01 -Age =8191.000000 M = 1.000000000 R = 1.000000000 Y = .3319100000 Z = .2000000000E-01 -Age =10010.10098 M = .9949495117 R = 1.999996680 Y = .3530302930 Z = .2202019531E-01 -Age =10030.30293 M = .9848485352 R = 3.999990040 Y = .3590908789 Z = .2606058594E-01 -Age =10070.70684 M = .9646465820 R = 7.999976758 Y = .3712120508 Z = .3414136719E-01 -Age =10151.51465 M = .9242426758 R = 15.99995020 Y = .3954543945 Z = .5030292969E-01 -Age =10313.13027 M = .8434348633 R = 31.99989707 Y = .4439390820 Z = .8262605469E-01 -Age =10481.81719 M = .7590914062 R = 48.69990156 Y = .4945451563 Z = .1163634375 -Age =10633.63545 M = .6831822754 R = 63.72990947 Y = .5400906348 Z = .1467270898 -Age =10770.27188 M = .6148640625 R = 77.25691563 Y = .5810815625 Z = .1740543750 -Age =10893.24463 M = .5533776855 R = 89.43121826 Y = .6179733887 Z = .1986489258 -Age =10999.99990 M = .5000000488 R = 99.99999033 Y = .6499999707 Z = .2199999805 -Age =11000.00010 M = .2500000000 R = .1000000000E-01 Y = .5800000000 Z = .4200000000 -Age =19192.00010 M = .2500000000 R = .1000000000E-01 Y = .5800000000 Z = .4200000000 - -- -Note the at first the time step doubling was the limiting factor. -Then during the first five steps on the red giant branch, the time step -was constrained by the requirement to at most double the radius. -During the next five steps the constraint was to allow a change in mass -of not more than ten percent. The final step was again constrained by -time step doubling, while the two before were forced to occur at both -sides of the discontinuity at the end of the life of the star. -
-
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-
-
-
-
- Modern star formation theory considers supersonic interstellar
-turbulence, ubiquitously observed in star forming molecular clouds, as
-controlling agent for stellar birth. In this picture, essentially all
-properties of nascent star clusters depend on the interplay between
-gravity the turbulent velocity field. Inefficient, isolated star
-formation will occur in regions which are supported by turbulence
-carrying most of its energy on very small scales. Clusters of stars
-build up in molecular cloud regions where self-gravity overwhelms
-turbulence, either because such regions are compressed by a
-large-scale shock, or because interstellar turbulence is not
-replenished and decays on short timescales. Rich star clusters, thus,
-are expected to form highly-substructured and with dynamical
-interactions between protostars becoming common. This modifies the
-mass accretion rates, leads to mass segregation, and influences the
-resulting IMF, all with important consequences for the subsequent
-evolution of the cluster.
-
- A full understanding of star cluster evolution needs to take the
-formation processes into account. A complete and comprehensive
-numerical description of star cluster evolution, therefore, requires
-the combination with (or at least input from) realistic gasdynamical
-models of molecular cloud fragmentation and star cluster build-up.
-
-Driver source code in Fortran
-
-Here is the fortran source code for testing the toy model implementation
-described above, with the header file for interface functions.
-This is not meant for distribution; it is still very rough, quickly
-cobbled together to get some results; but if you're interested to look
-under the hood at what we've done, here it is.
-
- subroutine print_star(idstar)
- integer idstar
-#include "modest_star.h"
- write(6,600) getTime(idstar),getMass(idstar),getRadius(idstar),
- $ getY(idstar),getZ(idstar)
- 600 format('Age =',g15.10,' M = ',g15.10,' R = ',g15.10,
- $ ' Y = ',g15.10,' Z = ',g15.10)
- end
-
- program one_star
-#include "modest_star.h"
- integer star
- real*8 dtmax, t
- integer discon_reached, countdown
- real*8 dMmax, dRmax, dYmax, dZmax, new_time
- star = CreateStar(1.0d0,0.25d0,0.02d0)
- dtmax = 1d0
- discon_reached = 0
- t = 0
- countdown = 3
- 100 if (countdown .gt. 0) then
- dMmax = 0.1d0*getMass(star)
- dRmax = 1d0*getRadius(star)
- dYmax = 0.1d0
- dZmax = 0.1d0
- new_time = EvolveStar(star,dtmax,dMmax,dRmax,dYmax,dZmax)
- call print_star(star)
- if ((new_time -t).gt. dtmax - 1d-10) dtmax = dtmax*2
- t = new_time
- if (get_discontinuity_flag(star) .ne. 0) discon_reached = 1
- if (discon_reached .ne. 0 ) then
- countdown = countdown - 1
- endif
- goto 100
- endif
- end
-
-
-
-
-
-
-
-
-modest_star.h
-
-
- real*8 getMass, getRadius, getY, getZ, EvolveStar
- real*8 getTime
- integer CreateStar, get_discontinuity_flag
-
-
-
-Toy model source code in Fortran
-
-Here is the Fortran source code for toy model implementation along
-with the include file for the common block.
-This too is not meant for distribution; it is still very rough, quickly
-cobbled together to get some results; but if you're interested to look
-under the hood at what we've done, here it is.
-
-C------------------------------------------------------------
-C MODEST_STAR.F
-C
-C Piet Hut and Jun Makino
-C Version 0.0 July 1, 2001
-C------------------------------------------------------------
-C
-C Each physical quantity Q that describes the state of a star
-C can be encapsulated as an object of class `stellar_quantity',
-C where Q can stand for mass, radius, etc. Such an object
-C contains the full information about the evolution of Q over
-C the life time of a star. The value of a quantity Q at time t
-C can be obtained by invoking its member function Q.at(t) .
-C
-C In our current toy-model implementation, Q(t) is described by
-C a piece-wise linear function with one discontinuity, specified
-C by the following six numbers:
-C
-C t_endms time at which the star leaves the main sequence
-C t_endrg time at which the star leaves the red giant branch.
-C f_init value of Q at birth of star (at time t=0)
-C f_endms value of Q at time t=t_endms
-C f_endrg value of Q just before time t=t_endrg
-C f_remnant value of Q just after time t=t_endrg
-C
-C ....... f_endrg
-C /|
-C / |
-C / |
-C / |
-C ^ / |
-C | / |
-C Q / |
-C _____/.......|...... f_endms
-C _____----- |
-C _____-----.......................|...... f_init
-C |------ f_remnant
-C +-----------------------+--------+------ 0
-C 0 t_endms t_endrg
-C t -->
-C
-C Note that we stick-figure version of stellar evolution mimics
-C only low-mass stars, while leaving out completely the horizontal
-C branch part of the evolution. In addition, we will make the
-C following simplified assumption: t_endrg = 1.1 t_endms.
-C With no need to specify t_endrg separately, we thus are left
-C with only five independent values.
-C
-
- function interpolate(t0,t1,t,f0,f1)
- real*8 interpolate, t0,t1,t,f0,f1
- interpolate= f0+(f1-f0)*(t-t0)/(t1-t0)
- end
-
- subroutine setup_stellar_quantity(idstar,idfunc,
- $ mstime,f0,f1,f2,f3)
- integer idstar, idfunc
- real*8 mstime, f0,f1,f2,f3
-#include "modest_common.F"
- ttable(1,idfunc,idstar)= mstime
- ttable(2,idfunc,idstar)= mstime*1.1d0
- ftable(1,idfunc,idstar)= f0
- ftable(2,idfunc,idstar)= f1
- ftable(3,idfunc,idstar)= f2
- ftable(4,idfunc,idstar)= f3
- end
-
- function stellar_quantity(idstar,idfunc,t)
- real*8 stellar_quantity,t, value, interpolate
- integer idstar, idfunc
-#include "modest_common.F"
- if (t .lt. ttable(1,idfunc,idstar)) then
- value = interpolate(0d0, ttable(1,idfunc,idstar),
- $ t, ftable(1,idfunc,idstar), ftable(2,idfunc,idstar))
- elseif(t .lt. ttable(2,idfunc,idstar)) then
- value = interpolate(ttable(1,idfunc,idstar),
- $ ttable(2,idfunc,idstar),
- $ t, ftable(2,idfunc,idstar), ftable(3,idfunc,idstar))
- else
- value = ftable(4,idfunc,idstar)
- endif
- stellar_quantity = value
- end
-
-
-
- block data block
-#include "modest_common.F"
- data is_used/nmax*0/
- end
-
- function first_unused_star()
- integer first_unused_star
-#include "modest_common.F"
- integer i
- do i=1,nmax
- if (is_used(i) .eq. 0) then
- first_unused_star = i
- return
- endif
- enddo
- first_unused_star = -1
- end
-
-
-
-
-C FORTRAN:integer CreateStar(M, Y, Z)
-C should be the constructor here...
- function CreateStar(m_init, Y_init, Z_init)
- integer CreateStar
- integer idstar
- integer first_unused_star
- real*8 m_init, Y_init, Z_init
- real*8 m,r,z0,z1,z2,z3,y0,y1,y2,y3,mstime
-#include "modest_common.F"
- idstar = first_unused_star()
- if (idstar .lt. 0) then
- CreateStar= -1
- return
- endif
- CreateStar=idstar
- m = m_init
- mstime =1d4 /(m*m*m)
- ms_lifetime(idstar) = mstime
- standard_timestep(idstar) = mstime*1d-5
- call setup_stellar_quantity(idstar,1,
- $ mstime,m,m, m*0.5D0,m*0.25d0)
- r = m
- call setup_stellar_quantity(idstar,2,mstime,
- $ r,r,r*100d0,0.01d0/m)
- z0 = Z_init
- z1 = Z_init
- z2 = min(1.0d0,z0+0.2d0)
- z3 = min(1.0d0,z0+0.4d0)
- call setup_stellar_quantity(idstar,4,mstime,z0,z1,z2,z3)
- y0 = Y_init
- y1 = min(y0+0.1d0,1d0-z1)
- y2 = min(y0+0.4d0,1d0-z2)
- y3 = min(y0+0.8d0,1d0-z3)
- call setup_stellar_quantity(idstar,3,mstime,y0,y1,y2,y3)
- age(idstar) = 0
- discontinuity_flag(idstar) = 0
- end
-
- function EvolveStar(idstar,dtmax,dMmax, dRmax, dYmax, dZmax)
- real*8 EvolveStar
- integer idstar
- real*8 dtmax,dMmax, dRmax, dYmax, dZmax
- real*8 old_age, last_age, max_age
- real*8 m0,r0,y0,z0
- integer dmax_exceeded
- real*8 t0,t1,newt
- real*8 stellar_quantity
-#include "modest_common.F"
- if (discontinuity_flag(idstar) .eq. -1)then
- discontinuity_flag(idstar) = 1
- age(idstar) = age(idstar)
- $ +2*discon_dt*ms_lifetime(idstar)
- EvolveStar = age(idstar)
- return
- endif
- old_age = age(idstar)
- if (discontinuity_flag(idstar) .eq. 1) then
- discontinuity_flag(idstar) =0
- endif
- m0 = stellar_quantity(idstar,1,age)
- r0 = stellar_quantity(idstar,2,age)
- y0 = stellar_quantity(idstar,3,age)
- z0 = stellar_quantity(idstar,4,age)
- last_age = age(idstar)
- max_age = old_age + dtmax
- 100 if (dmax_exceeded(idstar,age(idstar),old_age,
- $ dMmax,dRmax,dYmax,dZmax)
- $ .eq. 0 .and. age(idstar) .lt. max_age) then
- last_age = age(idstar)
- age(idstar) = age(idstar)+standard_timestep(idstar)
- if (age(idstar) .gt. max_age ) age(idstar) = max_age
- goto 100
- endif
- if (dmax_exceeded(idstar,age(idstar),old_age,
- $ dMmax,dRmax,dYmax,dZmax)
- $ .ne. 0) then
- t0 = last_age
- t1 = age(idstar)
- 200 if ((t1-t0) .gt. discon_dt*ms_lifetime(idstar))then
- newt = (t1+t0)/2.0d0
- if(dmax_exceeded(idstar,newt,old_age,
- $ dMmax,dRmax,dYmax,dZmax) .ne. 0) then
- t1 = newt
- else
- t0 = newt
- endif
- goto 200
- endif
- if(dmax_exceeded(idstar,t1,t0,
- $ dMmax,dRmax,dYmax,dZmax) .ne. 0) then
- discontinuity_flag(idstar) = -1
- endif
- age(idstar) = t0
- endif
- EvolveStar = age(idstar)
- end
-
- function dmax_exceeded(idstar, new_age,old_age,
- $ dMmax,dRmax,dYmax,dZmax)
- integer dmax_exceeded,idstar
- real*8 stellar_quantity
- real*8 new_age,old_age,dMmax,dRmax,dYmax,dZmax
- if (abs(stellar_quantity(idstar,1,new_age)
- $ -stellar_quantity(idstar,1,old_age)) .ge. dMmax .or.
- $ abs(stellar_quantity(idstar,2,new_age)
- $ -stellar_quantity(idstar,2,old_age)) .ge. dRmax .or.
- $ abs(stellar_quantity(idstar,3,new_age)
- $ -stellar_quantity(idstar,3,old_age)) .ge. dYmax .or.
- $ abs(stellar_quantity(idstar,4,new_age)
- $ -stellar_quantity(idstar,4,old_age)) .ge. dZmax)then
- dmax_exceeded = 1
- else
- dmax_exceeded = 0
- endif
- end
- function get_discontinuity_flag(idstar)
- integer get_discontinuity_flag, idstar
-#include "modest_common.F"
- get_discontinuity_flag = discontinuity_flag(idstar)
- end
- function DestroyStar(idstar)
- integer DestroyStar
-#include "modest_common.F"
- integer idstar
- if (idstar .lt. 0 .or.
- $ idstar .gt. nmax) then
- DestroyStar = -1
- else
- if (is_used(idstar) .eq. 0) then
- DestroyStar = -1
- else
- DestroyStar = idstar
- is_used(idstar) = 0
- endif
- endif
- end
-
- function getMass(idstar)
- real*8 getMass
- integer idstar
-#include "modest_common.F"
- real*8 stellar_quantity
- getMass = stellar_quantity(idstar,1,age(idstar))
- end
-
- function getRadius(idstar)
- real*8 getRadius
- integer idstar
-#include "modest_common.F"
- real*8 stellar_quantity
- getRadius = stellar_quantity(idstar,2,age(idstar))
- end
-
- function getTime(idstar)
- real*8 getTime
- integer idstar
-#include "modest_common.F"
- getTime = age(idstar)
- end
-
- function getY(idstar)
- real*8 getY
- integer idstar
-#include "modest_common.F"
- real*8 stellar_quantity
- getY = stellar_quantity(idstar,3,age(idstar))
- end
-
-
- function getZ(idstar)
- real*8 getZ
- integer idstar
-#include "modest_common.F"
- real*8 stellar_quantity
- getZ = stellar_quantity(idstar,4,age(idstar))
- end
-
-
-
-
-modest_common.F
-
-
-
-C------------------------------------------------------------
-C MODEST_INC.F
-C
-C Piet Hut and Jun Makino
-C Version 0.0 July 1, 2001
-C------------------------------------------------------------
-C
- integer nmax
- parameter (nmax = 100000)
- integer nfmax
- parameter (nfmax = 4)
- real*8 discon_dt
- parameter (discon_dt = 1d-8)
- real*8 ftable(4,nfmax,nmax), ttable(2,nfmax,nmax)
- real*8 ms_lifetime(nmax)
- real*8 standard_timestep(nmax)
- real*8 discontinuity_time(nmax)
- integer discontinuity_flag(nmax)
- integer is_used(nmax)
- real*8 age(nmax)
-
- common /modest/ftable,ttable,ms_lifetime,standard_timestep,
- $ discontinuity_time, discontinuity_flag, age
-
-
-
-
-
-
-
-Sample output from C++ code
-
-
-Output for a one-solar-mass star:
-
- Age = 1 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 3 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 7 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 15 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 31 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 63 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 127 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 255 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 511 M = 1 R = 1 Y = 0.25 Z = 0.02
- Age = 1023 M = 1 R = 1 Y = 0.26 Z = 0.02
- Age = 2047 M = 1 R = 1 Y = 0.27 Z = 0.02
- Age = 4095 M = 1 R = 1 Y = 0.29 Z = 0.02
- Age = 8191 M = 1 R = 1 Y = 0.33 Z = 0.02
- Age = 10010.1010 M = 0.99494951 R = 1.99999668 Y = 0.35 Z = 0.02
- Age = 10030.3029 M = 0.98484854 R = 3.99999004 Y = 0.35 Z = 0.02
- Age = 10070.7068 M = 0.96464658 R = 7.99997676 Y = 0.37 Z = 0.03
- Age = 10151.5146 M = 0.92424268 R = 15.9999502 Y = 0.39 Z = 0.05
- Age = 10313.1303 M = 0.84343486 R = 31.9998971 Y = 0.44 Z = 0.08
- Age = 10481.8172 M = 0.75909141 R = 48.6999016 Y = 0.49 Z = 0.11
- Age = 10633.6354 M = 0.68318228 R = 63.7299095 Y = 0.54 Z = 0.14
- Age = 10770.2719 M = 0.61486406 R = 77.2569156 Y = 0.58 Z = 0.17
- Age = 10893.2446 M = 0.55337769 R = 89.4312183 Y = 0.61 Z = 0.19
- Age = 10999.9999 M = 0.50000005 R = 99.9999903 Y = 0.64 Z = 0.21
- Age = 11000.0001 M = 0.25 R = 0.01 Y = 0.58 Z = 0.42
- Age = 19192.0001 M = 0.25 R = 0.01 Y = 0.58 Z = 0.42
-
-
-Note the at first the time step doubling was the limiting factor.
-Then during the first five steps on the red giant branch, the time step
-was constrained by the requirement to at most double the radius.
-During the next five steps the constraint was to allow a change in mass
-of not more than ten percent. The final step was again constrained by
-time step doubling, while the two before were forced to occur at both
-sides of the discontinuity at the end of the life of the star.
-Driver source code in C++
-
-Here is the C++ source code for testing the toy model implementation
-described above.
-This is not meant for distribution; it is still very rough, quickly
-cobbled together to get some results; but if you're interested to look
-under the hood at what we've done, here it is.
-
-
-#include <iostream>
-#include <cmath>
-#include <cstdlib>
-#include "modest_star.H"
-using namespace std;
-
-void print_star(modest_star star)
-{
- cout.precision(10);
- cout << " Age = " << star.getTime()
- << " M = " << star.getMass()
- << " R = " << star.getRadius()
- << " Y = " << star.getY()
- << " Z = " << star.getZ() << endl;
-}
-
-
-
-int main()
-{
- modest_star star = modest_star(1,0.25,0.02);
- double dtmax = 1;
- int discon_reached = 0;
- double t = 0;
- int countdown = 3;
- while(countdown>0){
- double dMmax = 0.1*star.getMass();
- double dRmax = 1*star.getRadius();
- double dYmax = 0.1;
- double dZmax = 0.1;
- double new_time = star.EvolveStar(dtmax,dMmax,dRmax,dYmax,dZmax);
- print_star(star);
- if ((new_time -t)> dtmax - 1e-10) dtmax *= 2;
- t = new_time;
- if (star.get_discontinuity_flag()) discon_reached = 1;
- if (discon_reached)countdown --;
- }
-}
-
-
-
-
-
-
-
-Toy model source code in C++(modest_star.H)
-
-Here is the C++ source code for toy model implementation (as a header
-file containing class definitions).
-This too is not meant for distribution; it is still very rough, quickly
-cobbled together to get some results; but if you're interested to look
-under the hood at what we've done, here it is.
-
-//
-// Each physical quantity Q that describes the state of a star
-// can be encapsulated as an object of class `stellar_quantity',
-// where Q can stand for mass, radius, etc. Such an object
-// contains the full information about the evolution of Q over
-// the life time of a star. The value of a quantity Q at time t
-// can be obtained by invoking its member function Q.at(t) .
-//
-// In our current toy-model implementation, Q(t) is described by
-// a piece-wise linear function with one discontinuity, specified
-// by the following six numbers:
-//
-// t_endms time at which the star leaves the main sequence
-// t_endrg time at which the star leaves the red giant branch.
-// f_init value of Q at birth of star (at time t=0)
-// f_endms value of Q at time t=t_endms
-// f_endrg value of Q just before time t=t_endrg
-// f_remnant value of Q just after time t=t_endrg
-//
-// ....... f_endrg
-// /|
-// / |
-// / |
-// / |
-// ^ / |
-// | / |
-// Q / |
-// _____/.......|...... f_endms
-// _____----- |
-// _____-----.......................|...... f_init
-// |------ f_remnant
-// +-----------------------+--------+------ 0
-// 0 t_endms t_endrg
-// t -->
-//
-// Note that we stick-figure version of stellar evolution mimics
-// only low-mass stars, while leaving out completely the horizontal
-// branch part of the evolution. In addition, we will make the
-// following simplified assumption: t_endrg = 1.1 t_endms.
-// With no need to specify t_endrg separately, we thus are left
-// with only five independent values.
-
-class stellar_quantity
-{
-private:
- double t_endms, t_endrg;
- double f_init, f_endms, f_endrg, f_remnant;
- double interpolate(double t0,
- double t1,
- double t,
- double f0,
- double f1)
- {
- return f0+(f1-f0)*(t-t0)/(t1-t0);
- }
-public:
- stellar_quantity(double ms_lifetime=0,
- double f0=0,
- double f1=0,
- double f2=0,
- double f3=0)
- {
- t_endms = ms_lifetime;
- t_endrg = ms_lifetime*1.1;
- f_init = f0;
- f_endms = f1;
- f_endrg = f2;
- f_remnant = f3;
- }
- double at(double t)
- {
- if (t < t_endms)
- return interpolate(0.0, t_endms, t, f_init, f_endms);
- if (t < t_endrg)
- return interpolate(t_endms,t_endrg, t, f_endms,f_endrg);
- return f_remnant;
- }
- double discontinuity_time()
- {
- return t_endrg;
- }
-};
-
-double discon_dt = 1e-8;
-
-class modest_star
-{
-private:
- stellar_quantity mass, radius, Y, Z;
- double ms_lifetime;
- double discontinuity_time;
- int discontinuity_flag; // Should be enum...
- // for now, -1= just before discontinuity
- // +1= just after discontinuity
- // 0= no discontinuity
- double age;
- double standard_timestep;
- double m0,r0,y0,z0,dmmax,drmax,dymax,dzmax;
- int dmax_exceeded(double age)
- {
- return ( (fabs(mass.at(age)-m0)>=dmmax)||
- (fabs(radius.at(age)-r0)>=drmax)||
- (fabs(Y.at(age)-y0)>=dymax)||
- (fabs(Z.at(age)-z0)>=dzmax));
- }
-
-public:
- // FORTRAN:integer CreateStar(M, Y, Z)
- // should be the constructor here...
- modest_star(double m_init, double Y_init, double Z_init){
- double m = m_init;
- ms_lifetime = 1e4 /(m*m*m);
- standard_timestep = ms_lifetime*1e-5;
- mass = stellar_quantity(ms_lifetime,m,m, m*0.5,m*0.25);
- double r = m;// simple linear mass-radius relation
- // in Msol-Rsol units
- radius = stellar_quantity(ms_lifetime,r,r,r*100,0.01/m);
- double z0 = Z_init;
- double z1 = Z_init;
- double z2 = fmin(1,z0+0.2);
- double z3 = fmin(1,z0+0.4);
- Z = stellar_quantity(ms_lifetime,z0,z1,z2,z3);
- double y0 = Y_init;
- double y1 = fmin(y0+0.1,1-z1);
- double y2 = fmin(y0+0.4,1-z2);
- double y3 = fmin(y0+0.8,1-z3);
- Y = stellar_quantity(ms_lifetime,y0,y1,y2,y3);
- age = 0;
- discontinuity_flag = 0;
- }
- // FORTRAN:real*8 EvolveStar(id, dtmax, dMmax, dRmax, dYmax, dZmax)
- //
- // Sample implementation for checking dMmax etc.
- // return time to the accuracy of discon_dt
-
- double EvolveStar(double dtmax,
- double dMmax,
- double dRmax,
- double dYmax,
- double dZmax )
- {
- if (discontinuity_flag == -1){
- discontinuity_flag = 1;
- age += 2*discon_dt*ms_lifetime;
- return age;
- }
- double old_age = age;
- if (discontinuity_flag == 1)discontinuity_flag =0;
- m0 = mass.at(age);
- r0 = radius.at(age);
- y0 = Y.at(age);
- z0 = Z.at(age);
- dmmax = dMmax;
- drmax = dRmax;
- dymax = dYmax;
- dzmax = dZmax;
- double last_age = age;
- double max_age = old_age + dtmax;
- while((!dmax_exceeded(age))
- &&(age < max_age)) {
- last_age = age;
- age += standard_timestep;
- if (age > max_age ) age = max_age;
- }
- if (dmax_exceeded(age)){
- double t0 = last_age;
- double t1 = age;
- while ((t1-t0)>discon_dt*ms_lifetime){
- double newt = (t1+t0)/2;
- if(dmax_exceeded(newt)){
- t1 = newt;
- }else{
- t0 = newt;
- }
- }
- if(fabs(mass.at(t1)-mass.at(t0))>dMmax ||
- fabs(radius.at(t1)-radius.at(t0))>dRmax ||
- fabs(Y.at(t1)-Y.at(t0))>dYmax ||
- fabs(Z.at(t1)-Z.at(t0))>dZmax ){
- discontinuity_flag = -1;
- }
- age = t0;
-
- }
- return age;
- }
- int get_discontinuity_flag()
- {
- return discontinuity_flag;
- }
-
- // integer DestroyStar(id) --- replaced by default destructor
-
- // real*8 getMass(id)
- double getMass()
- {
- return mass.at(age);
- }
-
- // real*8 getRadius(id)
- double getRadius()
- {
- return radius.at(age);
- }
- // real*8 getTime(id)
- double getTime()
- {
- return age;
- }
- // real*8 getY(id)
- double getY()
- {
- return Y.at(age);
- }
- // real*8 getZ(id)
- double getZ()
- {
- return Z.at(age);
- }
-};
-
-
-
diff --git a/modest-save/modest_wg1.html b/modest-save/modest_wg1.html
deleted file mode 100755
index 9eef5a1..0000000
--- a/modest-save/modest_wg1.html
+++ /dev/null
@@ -1,77 +0,0 @@
-
-
-
-MODEST Working Group 1:
-
-Star Formation
-
-
-
-
-
-
-In order to follow the evolution of a dense stellar system, one has to
-know (or choose) the initial conditions of that system. Traditionally,
-the starting points have been Plummer or King models, i.e. systems
-which include only zero-age main sequence stars evenly distributed
-throughout the cluster, and no gas, star formation, or proto-stellar
-disks. However, we know that most of these assumptions are at best
-simple and at worst downright wrong.
-
-
-
-
| Contact: | -Ralf Klessen | -
| Web site: | -WG1 | -
-
-
-Stars in clusters evolve, and this evolution provides a crucial
-feedback on the evolution of the cluster as a whole - through mass
-loss, interaction, and collisions between stars. Conversely, the
-dynamical cluster environment strongly modifies the evolution of many
-of its members, and the often exotic stars that result can be an
-important diagnostic of the (hydro)dynamical processes that take
-place.
-
- Our challenge is to model the evolution of any star that can be
-present in a dense cluster, whether single, binary or a member of a
-higher-order multiple. This includes non-canonical stars that result
-from stellar mergers and collisions. We thus require a stellar
-evolution code that can run autonomously from an arbitrary initial
-configuration to the end of a star's nuclear and thermal
-evolution. The code should be sufficiently fast so as not grind a
-cluster simulation to a halt. Above all, it should be robust and give
-a meaningful result under any conceivable circumstance.
-
-
-
-
| Contact: | -Onno Pols - |
| Web site: | -WG2 | -
-
-
-Dynamics of (globular) star clusters, galaxies and galactic nuclei;
-galaxies in the young universe. Study of the effects of rotation, mass
-segregation, primordial binaries and central massive objects on the
-evolution of dense stellar systems. Using Direct N-body Simulations,
-anisotropic gaseous models, direct solutions of the Fokker-Planck
-equation and Monte Carlo methods to simulate numerically the effects
-of stellar evolution, a realistic mass spectrum, galactic tidal fields
-on the evolution of dense young or globular star clusters.
-
-| Contact: | -Rainer Spurzem - |
| Web site: | -WG3 | -
-
-
-Collisions between stars in dense stellar systems are thought to
-produce tell-tale `stellar exotica,' i.e. stars with a peculiar
-structure and evolution, like blue stragglers or very massive
-stars. They also influence the overall dynamics by changing the
-number, masses and orbits of stars. In galactic nuclei, collisional
-mass loss contributes to the feeding of massive black holes. Our goals
-are to understand and describe stellar collisions through
-hydrodynamical simulations and (semi)analytical calculations and to
-develop numerical methods to incorporate that knowledge into stellar
-dynamical models.
-
-| Contact: | -Marc Freitag - |
| Web site: | -WG4 | -
-
-
-We have developed extensive software environments and simulation codes
-to model star clusters. Now is time to get feedback from observers,
-so that we can present our increasingly realistic data in a way that
-is most useful for direct comparison with observations. At the same
-time we can give feedback to observers, indicating what would be most
-useful for us, to learn from new observations. And of course, in this
-process, we would like to compare notes with other theoreticians as
-well.
-
-| Contact: | -Simon Portegies - Zwart | -
| Web site: | -WG5 | -
-
-
-The data structures used in the codes are important in order for
-different modules to properly exchange and interpret as much
-of their information as possible.
-The current activity is on defining a framework
-so we agree on nomenclature and contents of the data, as depicted
-in the figure to the right. We don't need to come up with
-a FITS like standard, although something like that would be nice
-(the new
-VOTable
-comes to mind here).
-
-| Contact: | -Peter Teuben - |
| Web site: | -WG6, see - also - Theory in a Virtual Observatory pages for examples. - | -
-
-
-The evolution of dense stellar systems is such a complicated problem
-that no exact solutions and few exact constraints are known.
-Therefore the reliability of simulations can best be checked by
-cross-validation. The aim of this working group is to compare results
-from different simulation methods on a small suite of well specified
-test problems. The results can be used to check that a new code is
-working correctly, or that approximate methods give results consistent
-with more elaborate methods.
-
-| Contact: | -Douglas Heggie - |
| Web site: | -WG7 | -
-
-
-There are a great many papers and a number of books concerning stellar
-clusters. The motivation of this working group is to produce and
-maintain a relatively concise list of references intended as a
-starting point for researchers new to the field (eg new grad
-students). We list books, review papers and conference proceedings as
-appropriate.
-
-| Contact: | -Melvyn Davies - |
| Web site: | -WG8 | -
-
-
-In recent years, theoretical models of dense stellar systems have
-become increasingly sophisticated. It is now possible to develop
-realistic N-body models with up to many tens of thousands of stars;
-the evolution of binaries and single stars in dense environments can
-be followed as the cluster evolves as a whole and all of the models
-can be tested extensively against the observations.
-
-- -On the observational side,the advent of space telescopes and of -ground-based 10-m size telescopes, have provided a huge amount of -data, spanning the range of wavelengths from radio to X-rays. The -development of astrometrical techniques, and the availability of -multifiber high resolution spectrographs allows astrometry and -observational kinematics, with radial velocities and proper motions, -both from the ground and with HST, measured for up to 10,000 stars per -cluster. Large-field imaging cameras now routinely provide photometric -data for up to a few hundred thousands stars per cluster. HST and -interferometric techniques provide a deep view in the very center of -dense stellar systems. A complete inventory of kinematic and -photometric properties, from X-ray to near-infrared, of all luminous -stars from the very center to the outskirts of clusters and nearby -galaxies is now a reality. And an increasing number of catalogs of -kinematic and photometric data are now available on the Web. There is -a significant progress in the determination of geometrical distances -to globular clusters, which will provide a solid foundation for the -calibration of their ages and an important step in the distance -ladder, both with a significant impact in cosmology. And finally, -there has been a great deal of progress in the understanding of -extragalactic globular cluster systems, with a complex variety of -luminosities, masses, ages, metallicities, and dynamical evolution, -and their role in galaxy formation. - -
-
-It is now time to directly compare the output of the models with the
-observation, and MODEST is the ideal framework to do it. This working
-group is intended to collect the most up-to-date observational data,
-to help develop observational projects to provide input parameters,
-and to test the more and more realistic models developed within
-MODEST.
-
-
-
-
| Contact: | -Giampaolo Piotto - |
| Web site: | -WG9 | - -
-Though neither we nor our projects can possibly be described as -modest, we use our acronym to point out that we want to work with only -MODEST modifications of existing codes, to model dense stellar -systems. So we can read the acronym also as MODifying Existing -STellar codes. -
-While many of us have talked for years about combining `live' stellar -evolution codes directly with N-body simulations, we have now reached -a consensus between various groups about standards and interfaces, -what is needed, and what is doable. On this web site we will provide -up-to-date information about our activities, and pointers to various -projects in progress. -
-In order to participate in ongoing MODEST email discussions, see the -information provided below under LINKS. - - - -
-