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hrdiag.f
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hrdiag.f
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***
SUBROUTINE hrdiag(mass,aj,mt,tm,tn,tscls,lums,GB,zpars,
& r,lum,kw,mc,rc,menv,renv,k2)
*
*
* H-R diagram for population I stars.
* -----------------------------------
*
* Computes the new mass, luminosity, radius & stellar type.
* Input (MASS, AJ, TM, TN, LUMS & TSCLS) supplied by routine STAR.
* Ref: P.P. Eggleton, M.J. Fitchett & C.A. Tout (1989) Ap.J. 347, 998.
*
* Revised 27th March 1995 by C. A. Tout;
* 24th October 1995 to include metallicity;
* 14th November 1996 to include naked helium stars;
* 28th February 1997 to allow accretion induced supernovae.
*
* Revised 5th April 1997 by J. R. Hurley
* to include Z=0.001 as well as Z=0.02, convective overshooting,
* MS hook and more elaborate CHeB
*
implicit none
*
integer kw,kwp
INTEGER ceflag,tflag,ifflag,nsflag,wdflag
COMMON /FLAGS/ ceflag,tflag,ifflag,nsflag,wdflag
*
real*8 mass,aj,mt,tm,tn,tscls(20),lums(10),GB(10),zpars(20)
real*8 r,lum,mc,rc,menv,renv,k2
real*8 mch,mlp,tiny
parameter(mch=1.44d0,mlp=12.d0,tiny=1.0d-14)
real*8 mass0,mt0,mtc
REAL*8 neta,bwind,hewind,mxns
COMMON /VALUE1/ neta,bwind,hewind,mxns
*
real*8 thook,thg,tbagb,tau,tloop,taul,tauh,tau1,tau2,dtau,texp
real*8 lx,ly,dell,alpha,beta,eta
real*8 rx,ry,delr,rzams,rtms,gamma,rmin,taumin,rg
parameter(taumin=5.0d-08)
real*8 mcmax,mcx,mcy,mcbagb,lambda
real*8 am,xx,fac,rdgen,mew,lum0,kap,zeta,ahe,aco
parameter(lum0=7.0d+04,kap=-0.5d0,ahe=4.d0,aco=16.d0)
*
real*8 thookf,tblf
real*8 lalphf,lbetaf,lnetaf,lhookf,lgbtf,lmcgbf,lzhef,lpertf
real*8 rzamsf,rtmsf,ralphf,rbetaf,rgammf,rhookf
real*8 rgbf,rminf,ragbf,rzahbf,rzhef,rhehgf,rhegbf,rpertf
real*8 mctmsf,mcgbtf,mcgbf,mcheif,mcagbf,lzahbf
external thookf,tblf
external lalphf,lbetaf,lnetaf,lhookf,lgbtf,lmcgbf,lzhef,lpertf
external rzamsf,rtmsf,ralphf,rbetaf,rgammf,rhookf
external rgbf,rminf,ragbf,rzahbf,rzhef,rhehgf,rhegbf,rpertf
external mctmsf,mcgbtf,mcgbf,mcheif,mcagbf,lzahbf
*
*
* ---------------------------------------------------------------------
* MASS Stellar mass in solar units (input: old; output: new value).
* AJ Current age in Myr.
* MT Current mass in solar units (used for R).
* TM Main sequence time.
* TN Nuclear burning time.
* TSCLS Time scale for different stages.
* LUMS Characteristic luminosity.
* GB Giant Branch parameters
* ZPARS Parameters for distinguishing various mass intervals.
* R Stellar radius in solar units.
* TE Effective temperature (suppressed).
* KW Classification type (0 - 15).
* MC Core mass.
* ---------------------------------------------------------------------
*
*
* Make evolutionary changes to stars that have not reached KW > 5.
*
mass0 = mass
if(mass0.gt.100.d0) mass = 100.d0
mt0 = mt
if(mt0.gt.100.d0) mt = 100.d0
*
if(kw.gt.6) goto 90
*
tbagb = tscls(2) + tscls(3)
thg = tscls(1) - tm
*
rzams = rzamsf(mass)
rtms = rtmsf(mass)
*
if(aj.lt.tscls(1))then
*
* Either on MS or HG
*
rg = rgbf(mt,lums(3))
*
if(aj.lt.tm)then
*
* Main sequence star.
*
mc = 0.d0
tau = aj/tm
thook = thookf(mass)*tscls(1)
zeta = 0.01d0
tau1 = MIN(1.d0,aj/thook)
tau2 = MAX(0.d0,
& MIN(1.d0,(aj-(1.d0-zeta)*thook)/(zeta*thook)))
*
dell = lhookf(mass,zpars(1))
dtau = tau1**2 - tau2**2
alpha = lalphf(mass)
beta = lbetaf(mass)
eta = lnetaf(mass)
lx = LOG10(lums(2)/lums(1))
if(tau.gt.taumin)then
xx = alpha*tau + beta*tau**eta +
& (lx - alpha - beta)*tau**2 - dell*dtau
else
xx = alpha*tau + (lx - alpha)*tau**2 - dell*dtau
endif
lum = lums(1)*10.d0**xx
*
delr = rhookf(mass,zpars(1))
dtau = tau1**3 - tau2**3
alpha = ralphf(mass)
beta = rbetaf(mass)
gamma = rgammf(mass)
rx = LOG10(rtms/rzams)
* Note that the use of taumin is a slightly pedantic attempt to
* avoid floating point underflow. It IS overkill!
if(tau.gt.taumin)then
xx = alpha*tau + beta*tau**10 + gamma*tau**40 +
& (rx - alpha - beta - gamma)*tau**3 - delr*dtau
else
xx = alpha*tau + (rx - alpha)*tau**3 - delr*dtau
endif
r = rzams*10.d0**xx
*
if(mass.lt.(zpars(1)-0.3d0))then
kw = 0
* This following is given by Chris for low mass MS stars which will be
* substantially degenerate. We need the Hydrogen abundance, X, which we
* calculate from Z assuming that the helium abundance, Y, is calculated
* according to Y = 0.24 + 2*Z
rdgen = 0.0258d0*((1.d0+zpars(11))**(5.d0/3.d0))*
& (mass**(-1.d0/3.d0))
r = MAX(rdgen,r)
else
kw = 1
endif
*
else
*
* Star is on the HG
*
mcx = mc
if(mass.le.zpars(2))then
mc = mcgbf(lums(3),GB,lums(6))
elseif(mass.le.zpars(3))then
mc = mcheif(mass,zpars(2),zpars(9))
else
mc = mcheif(mass,zpars(2),zpars(10))
endif
eta = mctmsf(mass)
tau = (aj - tm)/thg
mc = ((1.d0 - tau)*eta + tau)*mc
mc = MAX(mc,mcx)
*
* Test whether core mass has reached total mass.
*
if(mc.ge.mt)then
aj = 0.d0
if(mass.gt.zpars(2))then
*
* Zero-age helium star
*
mc = 0.d0
mass = mt
kw = 7
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
else
*
* Zero-age helium white dwarf.
*
mc = mt
mass = mt
kw = 10
endif
else
lum = lums(2)*(lums(3)/lums(2))**tau
if(mass.le.zpars(3))then
rx = rg
else
* He-ignition and end of HG occur at Rmin
rmin = rminf(mass)
ry = ragbf(mt,lums(4),zpars(2))
rx = MIN(rmin,ry)
if(mass.le.mlp)then
texp = log(mass/mlp)/log(zpars(3)/mlp)
rx = rg
rx = rmin*(rx/rmin)**texp
endif
tau2 = tblf(mass,zpars(2),zpars(3))
if(tau2.lt.tiny) rx = ry
endif
r = rtms*(rx/rtms)**tau
kw = 2
endif
*
endif
*
* Now the GB, CHeB and AGB evolution.
*
elseif(aj.lt.tscls(2))then
*
* Red Giant.
*
kw = 3
lum = lgbtf(aj,GB(1),GB,tscls(4),tscls(5),tscls(6))
if(mass.le.zpars(2))then
* Star has a degenerate He core which grows on the GB
mc = mcgbf(lum,GB,lums(6))
else
* Star has a non-degenerate He core which may grow, but
* only slightly, on the GB
tau = (aj - tscls(1))/(tscls(2) - tscls(1))
mcx = mcheif(mass,zpars(2),zpars(9))
mcy = mcheif(mass,zpars(2),zpars(10))
mc = mcx + (mcy - mcx)*tau
endif
r = rgbf(mt,lum)
rg = r
if(mc.ge.mt)then
aj = 0.d0
if(mass.gt.zpars(2))then
*
* Zero-age helium star
*
mc = 0.d0
mass = mt
kw = 7
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
else
*
* Zero-age helium white dwarf.
*
mc = mt
mass = mt
kw = 10
endif
endif
*
elseif(aj.lt.tbagb)then
*
* Core helium burning star.
*
if(kw.eq.3.and.mass.le.zpars(2))then
mass = mt
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
aj = tscls(2)
endif
if(mass.le.zpars(2))then
mcx = mcgbf(lums(4),GB,lums(6))
else
mcx = mcheif(mass,zpars(2),zpars(10))
endif
tau = (aj - tscls(2))/tscls(3)
mc = mcx + (mcagbf(mass) - mcx)*tau
*
if(mass.le.zpars(2))then
lx = lums(5)
ly = lums(7)
rx = rzahbf(mt,mc,zpars(2))
rg = rgbf(mt,lx)
rmin = rg*zpars(13)**(mass/zpars(2))
texp = MIN(MAX(0.4d0,rmin/rx),2.5d0)
ry = ragbf(mt,ly,zpars(2))
if(rmin.lt.rx)then
taul = (log(rx/rmin))**(1.d0/3.d0)
else
rmin = rx
taul = 0.d0
endif
tauh = (log(ry/rmin))**(1.d0/3.d0)
tau2 = taul*(tau - 1.d0) + tauh*tau
r = rmin*exp(abs(tau2)**3)
rg = rg + tau*(ry - rg)
lum = lx*(ly/lx)**(tau**texp)
elseif(mass.gt.zpars(3))then
*
* For HM stars He-ignition takes place at Rmin in the HG, and CHeB
* consists of a blue phase (before tloop) and a RG phase (after tloop).
*
tau2 = tblf(mass,zpars(2),zpars(3))
tloop = tscls(2) + tau2*tscls(3)
rmin = rminf(mass)
rg = rgbf(mt,lums(4))
rx = ragbf(mt,lums(4),zpars(2))
rmin = MIN(rmin, rx)
if(mass.le.mlp) then
texp = log(mass/mlp)/log(zpars(3)/mlp)
rx = rg
rx = rmin*(rx/rmin)**texp
else
rx = rmin
end if
texp = MIN(MAX(0.4d0,rmin/rx),2.5d0)
lum = lums(4)*(lums(7)/lums(4))**(tau**texp)
if(aj.lt.tloop)then
ly = lums(4)*(lums(7)/lums(4))**(tau2**texp)
ry = ragbf(mt,ly,zpars(2))
taul = 0.d0
if(ABS(rmin-rx).gt.tiny)then
taul = (log(rx/rmin))**(1.d0/3.d0)
endif
tauh = 0.d0
if(ry.gt.rmin) tauh = (log(ry/rmin))**(1.d0/3.d0)
tau = (aj - tscls(2))/(tau2*tscls(3))
tau2 = taul*(tau - 1.d0) + tauh*tau
r = rmin*exp(abs(tau2)**3)
rg = rg + tau*(ry - rg)
else
r = ragbf(mt,lum,zpars(2))
rg = r
end if
else
*
* For IM stars CHeB consists of a RG phase (before tloop) and a blue
* loop (after tloop).
*
tau2 = 1.d0 - tblf(mass,zpars(2),zpars(3))
tloop = tscls(2) + tau2*tscls(3)
if(aj.lt.tloop)then
tau = (tloop - aj)/(tau2*tscls(3))
lum = lums(5)*(lums(4)/lums(5))**(tau**3)
r = rgbf(mt,lum)
rg = r
else
lx = lums(5)
ly = lums(7)
rx = rgbf(mt,lx)
rmin = rminf(mt)
texp = MIN(MAX(0.4d0,rmin/rx),2.5d0)
ry = ragbf(mt,ly,zpars(2))
if(rmin.lt.rx)then
taul = (log(rx/rmin))**(1.d0/3.d0)
else
rmin = rx
taul = 0.d0
endif
tauh = (log(ry/rmin))**(1.d0/3.d0)
tau = (aj - tloop)/(tscls(3) - (tloop - tscls(2)))
tau2 = taul*(tau - 1.d0) + tauh*tau
r = rmin*exp(abs(tau2)**3)
rg = rx + tau*(ry - rx)
lum = lx*(ly/lx)**(tau**texp)
endif
endif
*
* Test whether core mass exceeds total mass.
*
if(mc.ge.mt)then
*
* Evolved MS naked helium star.
*
kw = 7
xx = (aj - tscls(2))/tscls(3)
mass = mt
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
aj = xx*tm
else
kw = 4
endif
*
else
*
* Asymptotic Red Giant.
*
* On the AGB the He core mass remains constant until at Ltp it
* is caught by the C core mass and they grow together.
*
mcbagb = mcagbf(mass)
mcx = mcgbtf(tbagb,GB(8),GB,tscls(7),tscls(8),tscls(9))
mcmax = MAX(MAX(mch,0.773d0*mcbagb-0.35d0),1.05d0*mcx)
*
if(aj.lt.tscls(13))then
mcx = mcgbtf(aj,GB(8),GB,tscls(7),tscls(8),tscls(9))
mc = mcbagb
lum = lmcgbf(mcx,GB)
if(mt.le.mc)then
*
* Evolved naked helium star as the envelope is lost but the
* star has not completed its interior burning. The star becomes
* a post-HeMS star.
*
kw = 9
mt = mc
mass = mt
mc = mcx
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
if(mc.le.GB(7))then
aj = tscls(4) - (1.d0/((GB(5)-1.d0)*GB(8)*GB(4)))*
& (mc**(1.d0-GB(5)))
else
aj = tscls(5) - (1.d0/((GB(6)-1.d0)*GB(8)*GB(3)))*
& (mc**(1.d0-GB(6)))
endif
aj = MAX(aj,tm)
goto 90
else
kw = 5
endif
else
kw = 6
mc = mcgbtf(aj,GB(2),GB,tscls(10),tscls(11),tscls(12))
lum = lmcgbf(mc,GB)
*
* Approximate 3rd Dredge-up on AGB by limiting Mc.
*
lambda = MIN(0.9d0,0.3d0+0.001d0*mass**5)
tau = tscls(13)
mcx = mcgbtf(tau,GB(2),GB,tscls(10),tscls(11),tscls(12))
mcy = mc
mc = mc - lambda*(mcy-mcx)
mcx = mc
mcmax = MIN(mt,mcmax)
endif
r = ragbf(mt,lum,zpars(2))
rg = r
*
* Mc,x represents the C core mass and we now test whether it
* exceeds either the total mass or the maximum allowed core mass.
*
if(mcmax-mcx.lt.tiny)then
aj = 0.d0
mc = mcmax
if(mc.lt.mch)then
if(ifflag.ge.1)then
*
* Invoke WD IFMR from HPE, 1995, MNRAS, 272, 800.
*
if(zpars(14).ge.1.0d-08)then
mc = MIN(0.36d0+0.104d0*mass,0.58d0+0.061d0*mass)
mc = MAX(0.54d0+0.042d0*mass,mc)
if(mass.lt.1.d0) mc = 0.46d0
else
mc = MIN(0.29d0+0.178d0*mass,0.65d0+0.062d0*mass)
mc = MAX(0.54d0+0.073d0*mass,mc)
endif
mc = MIN(mch,mc)
endif
*
mt = mc
if(mcbagb.lt.1.6d0)then
*
* Zero-age Carbon/Oxygen White Dwarf
*
kw = 11
else
*
* Zero-age Oxygen/Neon White Dwarf
*
kw = 12
endif
mass = mt
*
else
if(mcbagb.lt.1.6d0)then
*
* Star is not massive enough to ignite C burning.
* so no remnant is left after the SN
*
kw = 15
aj = 0.d0
mt = 0.d0
lum = 1.0d-10
r = 1.0d-10
else
if(nsflag.eq.0)then
mt = 1.17d0 + 0.09d0*mc
elseif(nsflag.ge.1)then
*
* Use NS/BH mass given by Belczynski et al. 2002, ApJ, 572, 407.
*
if(mc.lt.2.5d0)then
mcx = 0.161767d0*mc + 1.067055d0
else
mcx = 0.314154d0*mc + 0.686088d0
endif
if(mc.le.5.d0)then
mt = mcx
elseif(mc.lt.7.6d0)then
mt = mcx + (mc - 5.d0)*(mt - mcx)/2.6d0
endif
endif
mc = mt
if(mt.le.mxns)then
*
* Zero-age Neutron star
*
kw = 13
else
*
* Zero-age Black hole
*
kw = 14
endif
endif
endif
endif
*
endif
*
90 continue
*
if(kw.ge.7.and.kw.le.9)then
*
* Naked Helium Star
*
rzams = rzhef(mt)
rx = rzams
if(aj.lt.tm)then
*
* Main Sequence
*
kw = 7
tau = aj/tm
am = MAX(0.d0,0.85d0-0.08d0*mass)
lum = lums(1)*(1.d0+0.45d0*tau+am*tau**2)
am = MAX(0.d0,0.4d0-0.22d0*LOG10(mt))
r = rx*(1.d0+am*(tau-tau**6))
rg = rx
* Star has no core mass and hence no memory of its past
* which is why we subject mass and mt to mass loss for
* this phase.
mc = 0.d0
if(mt.lt.zpars(10)) kw = 10
else
*
* Helium Shell Burning
*
kw = 8
lum = lgbtf(aj,GB(8),GB,tscls(4),tscls(5),tscls(6))
r = rhehgf(mt,lum,rx,lums(2))
rg = rhegbf(lum)
if(r.ge.rg)then
kw = 9
r = rg
endif
mc = mcgbf(lum,GB,lums(6))
mtc = MIN(mt,1.45d0*mt-0.31d0)
mcmax = MIN(mtc,MAX(mch,0.773d0*mass-0.35d0))
if(mcmax-mc.lt.tiny)then
aj = 0.d0
mc = mcmax
if(mc.lt.mch)then
if(mass.lt.1.6d0)then
*
* Zero-age Carbon/Oxygen White Dwarf
*
mt = MAX(mc,(mc+0.31d0)/1.45d0)
kw = 11
else
*
* Zero-age Oxygen/Neon White Dwarf
*
mt = mc
kw = 12
endif
mass = mt
else
if(mass.lt.1.6d0)then
*
* Star is not massive enough to ignite C burning.
* so no remnant is left after the SN
*
kw = 15
aj = 0.d0
mt = 0.d0
lum = 1.0d-10
r = 1.0d-10
else
if(nsflag.eq.0)then
mt = 1.17d0 + 0.09d0*mc
elseif(nsflag.ge.1)then
if(mc.lt.2.5d0)then
mcx = 0.161767d0*mc + 1.067055d0
else
mcx = 0.314154d0*mc + 0.686088d0
endif
if(mc.le.5.d0)then
mt = mcx
elseif(mc.lt.7.6d0)then
mt = mcx + (mc - 5.d0)*(mt - mcx)/2.6d0
endif
endif
mc = mt
if(mt.le.mxns)then
*
* Zero-age Neutron star
*
kw = 13
else
*
* Zero-age Black hole
*
kw = 14
endif
endif
endif
endif
endif
endif
*
if(kw.ge.10.and.kw.le.12)then
*
* White dwarf.
*
mc = mt
if(mc.ge.mch)then
*
* Accretion induced supernova with no remnant
* unless WD is ONe in which case we assume a NS
* of minimum mass is the remnant.
*
if(kw.eq.12)then
kw = 13
aj = 0.d0
mt = 1.3d0
else
kw = 15
aj = 0.d0
mt = 0.d0
lum = 1.0d-10
r = 1.0d-10
endif
else
*
if(kw.eq.10)then
xx = ahe
else
xx = aco
endif
*
if(wdflag.eq.0)then
*
* Mestel cooling
*
lum = 635.d0*mt*zpars(14)/(xx*(aj+0.1d0))**1.4d0
*
elseif(wdflag.ge.1)then
*
* modified-Mestel cooling
*
if(aj.lt.9000.0)then
lum = 300.d0*mt*zpars(14)/(xx*(aj+0.1d0))**1.18d0
else
fac = (9000.1d0*xx)**5.3d0
lum = 300.d0*fac*mt*zpars(14)/(xx*(aj+0.1d0))**6.48d0
endif
*
endif
*
r = 0.0115d0*SQRT(MAX(1.48204d-06,(mch/mt)**(2.d0/3.d0)
& - (mt/mch)**(2.d0/3.d0)))
r = MIN(0.1d0,r)
if(mt.lt.0.0005d0) r = 0.09d0
if(mt.lt.0.000005d0) r = 0.009d0
*
endif
endif
*
if(kw.eq.13)then
*
* Neutron Star.
*
mc = mt
if(mc.gt.mxns)then
*
* Accretion induced Black Hole?
*
kw = 14
aj = 0.d0
else
lum = 0.02d0*(mt**0.67d0)/(MAX(aj,0.1d0))**2
r = 1.4d-05
endif
endif
*
if(kw.eq.14)then
*
* Black hole
*
mc = mt
lum = 1.0d-10
r = 4.24d-06*mt
endif
*
* Calculate the core radius and the luminosity and radius of the
* remnant that the star will become.
*
tau = 0.d0
if(kw.le.1.or.kw.eq.7)then
rc = 0.d0
elseif(kw.le.3)then
if(mass.gt.zpars(2))then
lx = lzhef(mc)
rx = rzhef(mc)
rc = rx
else
if(wdflag.eq.0)then
lx = 635.d0*mc*zpars(14)/((ahe*0.1d0)**1.4d0)
elseif(wdflag.ge.1)then
lx = 300.d0*mc*zpars(14)/((ahe*0.1d0)**1.18d0)
endif
rx = 0.0115d0*SQRT(MAX(1.48204d-06,
& (mch/mc)**(2.d0/3.d0)-(mc/mch)**(2.d0/3.d0)))
rc = 5.d0*rx
endif
elseif(kw.eq.4)then
tau = (aj - tscls(2))/tscls(3)
kwp = 7
CALL star(kwp,mc,mc,tm,tn,tscls,lums,GB,zpars)
am = MAX(0.d0,0.85d0-0.08d0*mc)
lx = lums(1)*(1.d0+0.45d0*tau+am*tau**2)
rx = rzhef(mc)
am = MAX(0.d0,0.4d0-0.22d0*LOG10(mc))
rx = rx*(1.d0+am*(tau-tau**6))
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
rc = rx
elseif(kw.eq.5)then
kwp = 9
if(tn.gt.tbagb) tau = 3.d0*(aj-tbagb)/(tn-tbagb)
CALL star(kwp,mc,mc,tm,tn,tscls,lums,GB,zpars)
lx = lmcgbf(mcx,GB)
if(tau.lt.1.d0) lx = lums(2)*(lx/lums(2))**tau
rx = rzhef(mc)
rx = MIN(rhehgf(mc,lx,rx,lums(2)),rhegbf(lx))
CALL star(kw,mass,mt,tm,tn,tscls,lums,GB,zpars)
rc = rx
elseif(kw.le.9)then
if(wdflag.eq.0)then
lx = 635.d0*mc*zpars(14)/((aco*0.1d0)**1.4d0)
elseif(wdflag.ge.1)then
lx = 300.d0*mc*zpars(14)/((aco*0.1d0)**1.18d0)
endif
rx = 0.0115d0*SQRT(MAX(1.48204d-06,
& (mch/mc)**(2.d0/3.d0) - (mc/mch)**(2.d0/3.d0)))
rc = 5.d0*rx
else
rc = r
menv = 1.0d-10
renv = 1.0d-10
k2 = 0.21d0
endif
*
* Perturb the luminosity and radius due to small envelope mass.
*
if(kw.ge.2.and.kw.le.9.and.kw.ne.7)then
mew = ((mt-mc)/mt)*MIN(5.d0,MAX(1.2d0,(lum/lum0)**kap))
if(kw.ge.8) mew = ((mtc-mc)/mtc)*5.d0
if(mew.lt.1.d0)then
xx = lpertf(mt,mew)
lum = lx*(lum/lx)**xx
if(r.le.rx)then
xx = 0.d0
else
xx = rpertf(mt,mew,r,rx)
endif
r = rx*(r/rx)**xx
endif
rc = MIN(rc,r)
endif
*
* Calculate mass and radius of convective envelope, and envelope
* gyration radius.
*
if(kw.lt.10)then
CALL mrenv(kw,mass,mt,mc,lum,r,rc,aj,tm,lums(2),lums(3),
& lums(4),rzams,rtms,rg,menv,renv,k2)
endif
*
if(mass.gt.99.99d0)then
mass = mass0
endif
if(mt.gt.99.99d0)then
mt = mt0
endif
*
return
end
***