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project_code.f90
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MODULE VARIABILI
IMPLICIT NONE
REAL*8:: eccitazione, ionizzazione, ricombinazione, ricombinazione_d, free_free,LAMBDA, &
n_h0, n_h1, n_he0, n_he1, n_he2, n_e, n_he, n_h,y, T
CONTAINS
!TASSI DI IONIZZAZIONE
REAL*8 FUNCTION gamma_H0()
gamma_H0=5.85d-11*sqrt(T)/(exp(157809.1d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION gamma_H0
REAL*8 FUNCTION gamma_He0()
gamma_He0=2.38d-11*sqrt(T)/(exp(285335.4d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION gamma_He0
REAL*8 FUNCTION gamma_He1()
gamma_He1=5.68d-12*sqrt(T)/(exp(631515.0d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION gamma_He1
!TASSI DI RICOMBINAZIONE
REAL*8 FUNCTION alpha_H1()
alpha_H1=8.4d-11/(sqrt(T)*(T/1.0d3)**2.0d-1*(1.0d0+(T/1.0d6)**7.0d-1))
END FUNCTION alpha_H1
REAL*8 FUNCTION alpha_d()
alpha_d=1.9d-3*(1.0d0+0.3d0*exp(-94.0d3/T))/((T**1.5d0)*exp(47.0d4/T))
END FUNCTION alpha_d
REAL*8 FUNCTION alpha_He1()
alpha_He1=1.5d-10/(T**0.6353d0)
END FUNCTION alpha_He1
REAL*8 FUNCTION alpha_He2()
alpha_He2=3.36d-10/(sqrt(T)*((T/1.0d3)**0.2d0)*(1.0d0+(T/1.0d6)**0.7d0))
END FUNCTION alpha_He2
!CONTRIBUTI DI RAFFREDDAMENTO [erg/s*cm3]
REAL*8 FUNCTION lambda_ex_H0(n,m)
REAL*8,INTENT(IN):: n, m
lambda_ex_H0=7.50d-19*n*m/(exp(118348.0d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION lambda_ex_H0
REAL*8 FUNCTION lambda_ex_H1(n,m)
REAL*8,INTENT(IN):: n, m
lambda_ex_H1=5.54d-17*n*m/((T**0.397)*exp(473638.0d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION lambda_ex_H1
REAL*8 FUNCTION lambda_ion_H0(n,m)
REAL*8,INTENT(IN):: n, m
lambda_ion_H0=1.27d-21*sqrt(T)*n*m/(exp(157809.1d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION lambda_ion_H0
REAL*8 FUNCTION lambda_ion_He0(n,m)
REAL*8,INTENT(IN):: n, m
lambda_ion_He0=9.38d-22*sqrt(T)*n*m/(exp(285335.4d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION lambda_ion_He0
REAL*8 FUNCTION lambda_ion_He1(n,m)
REAL*8,INTENT(IN):: n, m
lambda_ion_He1=4.95d-22*sqrt(T)*n*m/(exp(631515.0d0/T)*(1.0d0+sqrt(T/1.0d5)))
END FUNCTION lambda_ion_He1
REAL*8 FUNCTION lambda_rec_H1(n,m)
REAL*8,INTENT(IN):: n, m
lambda_rec_H1=8.70d-27*sqrt(T)*n*m/(((T/1.0d3)**0.2d0)*(1.0d0+(T/1.0d6)**0.7d0))
END FUNCTION lambda_rec_H1
REAL*8 FUNCTION lambda_rec_He1(n,m)
REAL*8,INTENT(IN):: n, m
lambda_rec_He1=1.55d-26*(T**0.3647d0)*n*m
END FUNCTION lambda_rec_He1
REAL*8 FUNCTION lambda_rec_He2(n,m)
REAL*8,INTENT(IN):: n, m
lambda_rec_He2=3.48d-26*sqrt(T)*n*m/(((T/1.0d3)**0.2d0)*(1.0d0+(T/1.0d6)**0.7d0))
END FUNCTION lambda_rec_He2
REAL*8 function lambda_drec_He1(n,m)
REAL*8,INTENT(IN):: n, m
lambda_drec_He1=1.24d-13*(1.0d0+0.3d0/exp(94.0d3/T))*n*m/((T**1.5d0)*exp(47.0d4/T))
END FUNCTION lambda_drec_He1
REAL*8 FUNCTION gaunt_ff()
gaunt_ff=1.1d0+0.34d0/exp(((5.5d0-log(T))**2.0)/3.0d0)
END FUNCTION gaunt_ff
!cooling function
REAL*8 FUNCTION lambda_ff(n,n1,n2,n3)
REAL*8,INTENT(IN):: n1, n2, n3, n
lambda_ff=1.42d-27*gaunt_ff()*sqrt(T)*(n1+n2+4.0d0*n3)*n
END FUNCTION lambda_ff
SUBROUTINE cooling_function()
REAL*8, DIMENSION(2,2):: matrice1
REAL*8, DIMENSION(2):: cost1, x1
REAL*8,DIMENSION(3,3):: matrice2
REAL*8, DIMENSION(3):: cost2, x2
!2x2!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
matrice1=1.0d0
cost1=0.0d0
matrice1(1,2)=-alpha_H1()/gamma_H0()
cost1(2)=1.0d0
CALL gauss(matrice1,cost1,2,x1)
n_h0=x1(1)
n_h1=x1(2)
!3x3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
matrice2=1.0d0
cost2=0.0d0
matrice2(1,2)=-(alpha_He1()+alpha_d())/gamma_He0()
matrice2(1,3)=0.0d0
matrice2(2,1)=0.0d0
matrice2(2,3)=-alpha_He2()/gamma_He1()
cost2(3)=y
CALL gauss(matrice2,cost2,3,x2)
n_he0=x2(1)
n_he1=x2(2)
n_he2=x2(3)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
n_h0=n_h0*n_h
n_h1=n_h1*n_h
n_he0=n_he0*n_h
n_he1=n_he1*n_h
n_he2=n_he2*n_h
n_e=n_h1+n_he1+2.0d0*n_he2
!contributi al cooling!!!!!!!!!!!!!!!!!!!!!
eccitazione=lambda_ex_H0(n_e,n_h0)+lambda_ex_H1(n_e,n_he1)
ionizzazione=lambda_ion_H0(n_e,n_h0)+lambda_ion_He0(n_e,n_he0)+lambda_ion_He1(n_e,n_he1)
ricombinazione=lambda_rec_H1(n_e,n_h1)+lambda_rec_He1(n_e,n_he1)+lambda_rec_He2(n_e,n_he2)
ricombinazione_d=lambda_drec_He1(n_e,n_he1)
free_free=lambda_ff(n_e,n_h1,n_he1,n_he2)
LAMBDA=eccitazione+ionizzazione+ricombinazione+ricombinazione_d+free_free
END SUBROUTINE cooling_function
END MODULE VARIABILI
SUBROUTINE gauss(matrice,cost,n,x)
INTEGER, INTENT(IN):: n
REAL*8, INTENT(IN):: matrice(n,n), cost(n)
REAL*8, INTENT(OUT):: x(n)
REAL*8:: a(n,n), c(n)
REAL*8:: fakt, summa
INTEGER:: i,j,k,l
a=matrice
c=cost
DO i=1,n-1
DO j=i+1,n
fakt=a(j,i)/a(i,i)
DO k=1,n
a(j,k)=a(j,k)-a(i,k)*fakt
END DO
c(j)=c(j)-c(i)*fakt
END DO
END DO
x(n)=c(n)/a(n,n)
DO i=n-1,1,-1
summa=c(i)
DO j=i+1,n
summa=summa-a(i,j)*x(j)
END DO
x(i)=summa/a(i,i)
END DO
END SUBROUTINE gauss
MODULE INTEGRAZIONE
USE VARIABILI
IMPLICIT NONE
REAL*8, PARAMETER:: passo=1.0d-2 ! costante per calcolare il passo
REAL*8, PARAMETER:: gamma=5.0d0/3.0d0, k=1.380649d-16, mp=1.67262d-24 ! k e mp sono espresse in cgs
REAL*8:: u_0,mu_0,lambda_0,T0,time_0,rho_0
CONTAINS
!DALLA N.B_2
REAL*8 FUNCTION fun(Temp,u)
REAL*8, INTENT(in):: Temp, u
REAL*8:: mu
T=Temp
CALL cooling_function()
mu=(1.0d0+4.0d0*y)/(1.0d0+y+n_e/n_h)
fun=Temp-((gamma-1)*u_0*u*mu*mp/k)
END FUNCTION fun
REAL*8 FUNCTION deriv(Temp,u)
REAL*8, INTENT(in):: Temp, u
REAL*8, PARAMETER:: incr=1.0d-5
!definizione della derivata della funzione fun dato un h=10**-5
deriv=(fun(Temp+incr,u)-fun(Temp,u))/incr
END FUNCTION deriv
SUBROUTINE secante(Temp,u)
IMPLICIT NONE
REAL*8, PARAMETER:: toll=1.0d-6
REAL*8, INTENT(IN):: u
REAL*8, INTENT(INOUT):: Temp
INTEGER:: conta
REAL*8:: delta, T_new
conta=0
DO
conta=conta+1
!formula della secante modificata!!!!!!!
T_new=Temp-fun(Temp,u)/deriv(Temp,u)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
delta=abs(T_new-Temp)
IF (delta<toll) THEN
EXIT
ELSE IF (T_new<1.0d4) THEN
Temp=1.0d4
EXIT
ELSE IF (conta>100) THEN
PRINT*, "la convergenza non è stata raggiunta (secante)."
STOP
END IF
Temp=T_new
END DO
END SUBROUTINE secante
SUBROUTINE dydx(u,f,Temp)
REAL*8, INTENT(IN):: u
REAL*8, INTENT(INOUT):: Temp
REAL*8, INTENT(OUT)::f
REAL*8:: rho, mu
T=Temp
CALL cooling_function()
mu=(1.0d0+4.0d0*y)/(1.0d0+y+n_e/n_h)
rho=mu*(n_h+y*n_h+n_e)*mp
f=-rho_0*LAMBDA/(rho*lambda_0)
END SUBROUTINE dydx
SUBROUTINE Runge_Kutta_2(h,u_old,u_new,Temp)
REAL*8, INTENT(IN)::h, u_old
REAL*8, INTENT(INOUT):: Temp
REAL*8, INTENT(OUT):: u_new
REAL*8, PARAMETER:: b_2=2.0d0/3.0d0 ! <-- metodo di Ralston per minimizzare l'errore di troncamento
REAL*8:: k1,k2,a_11,c_1,b_1
a_11=1.0d0/(2.0d0*b_2)
c_1=a_11
b_1=1.0d0-b_2
CALL dydx(u_old,k1,Temp)
u_new=u_old+(3.0d0/4.0d0)*h*k1
Temp=Temp+(3.0d0/4.0d0)*h
CALL dydx(u_new,k2,Temp)
u_new=u_old+h*(b_1*k1+b_2*k2) !<-- formula finale della secante
!per ottenere la temperatura al tempo t+dt
CALL secante(Temp,u_new)
END SUBROUTINE Runge_Kutta_2
END MODULE INTEGRAZIONE
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PROGRAM PROGETTO_2
USE VARIABILI
USE INTEGRAZIONE
IMPLICIT NONE
REAL*8::X,T_step,h
REAL*8:: u,u_tilde,rho,mu,t_cool,time,Temp
CHARACTER(30):: file_name
CHARACTER(5):: str
INTEGER::i,j
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!STATO DI IONIZZAZIONE E FUNZIONE DI COOLING PER X00.76 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PRINT*, "inizio il calcolo delle diverse densità e della funzione di cooling per X=0.76"
PRINT*, " "
OPEN(1,file="densità_relative.dat")
OPEN(2,file="cooling_function_X0.76.dat")
WRITE(1,'(a13,5a18)') "Log10(T[°K])","n_H0/n_htot","n_H+/n_htot", &
"n_He0/n_Hetot","n_He+/n_Hetot","n_He++/n_Hetot"
WRITE(2,'(a12,a15,a21,2a20,a18,a25)') "Log10(T[°K])","eccitazione", &
"ionizzazione","ricombinazione","ric_dielettrica","free_free","totale [erg/s*cm**3]"
X=0.76d0
y=(1-X)/(4*X)
n_h=1.d0
n_he=y
T_step=(log10(1.0d8)-log10(1.0d4))/200 ! rappresenta il passo da mantenere
DO i=0,200
T=10.0d0**(4.0d0+T_step*i)
CALL cooling_function()
WRITE(1,'(f8.5,4x,5f18.11)') log10(T),n_h0,n_h1, &
n_he0/n_he,n_he1/n_he,n_he2/n_he
WRITE(2,'(f8.5,6f20.10)') log10(T),log10(eccitazione),log10(ionizzazione), &
log10(ricombinazione),log10(ricombinazione_d),log10(free_free),log10(lambda)
END DO
CLOSE(1)
CLOSE(2)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!FUNZIONE DI COOLING per X=1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PRINT*, "calcolo la funzione di cooling per X=1"
PRINT*, ""
OPEN(3,file="cooling_function_X1.0.dat")
WRITE(3,'(a12,a15,a21,2a20,a18,a25)') "Log10(T[°K])","eccitazione", &
"ionizzazione","ricombinazione","ric_dielettrica","free_free","totale [erg/s*cm**3]"
X=1.0d0
y=(1-X)/(4*X)
DO i=0,200
T=10.0d0**(4.0d0+T_step*i)
CALL cooling_function()
WRITE(3,'(f8.5,6f20.10)') log10(T),log10(eccitazione),log10(ionizzazione), &
log10(ricombinazione),ricombinazione_d,log10(free_free),log10(lambda)
END DO
CLOSE(3)
PRINT*, 'i risultati del primo e secondo step sono stati salvati nei file'
PRINT*, 'densità_relative.dat'
PRINT*, 'cooling_function_X0.76.dat'
PRINT*, 'cooling_function_X1.0.dat'
PRINT*, ''
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!INTEGRAZIONE DELLA ODE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PRINT*, "procedo con la risoluzione della ODE per l'evoluzione temporale"
PRINT*, ''
X=0.76d0
y=(1-X)/(4*X)
!IL CICLO INTEGRERÀ IL SISTEMA PER 3 DIVERSE DENSITÀ DI IDROGENO
DO i=1,3
IF(i==1) THEN
n_h=0.1d0
str='_n0.1'
ELSE IF(i==2) THEN
n_h=1.d0
str='_n1.0'
ELSE
n_h=10.0d0
str='_n_10'
END IF
n_he=n_h*y
T0=1.d6
Temp=T0
T=T0
CALL cooling_function()
!Adimensionalizzazione delle variabili!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!queste sono le condizioni iniziali del sistema
lambda_0=LAMBDA
mu_0=(1.0d0+4.0d0*y)/(1.0d0+y+n_e/n_h)
rho_0=mu_0*(n_h+n_he+n_e)*mp
u_0=k*Temp/((gamma-1.0d0)*mu_0*mp)
time_0=u_0*rho_0/lambda_0
u_tilde=1.0d0 !<-- u/u_0
time=0.0d0
h=passo !<-- il time-step iniziale che verrà modificato man mano nell'integrazione
t_cool=0.0d0 !<-- che cambierà durante l'integrazione
file_name='Temp_evolution'//str //'.dat'
OPEN(10,file=file_name)
WRITE(10,"(a18,a20)") "Log10(t/t_cooling)", "Log10(T[°K])"
!integriamo fino a 10 volte il tempo di cooling iniziale(time_0)
DO WHILE(time<time_0*10.0d0)
CALL Runge_Kutta_2(h,u_tilde,u,Temp)
WRITE(10,"(f14.7,f20.7)") log10(time/time_0), log10(Temp)
mu=(1.0d0+4.0d0*y)/(1.0d0+y+n_e/n_h) !<--peso molecolare e densità si evolvono poiche dipendenti da T
rho=mu*(n_h+n_he+n_e)*mp
!N.B_3
t_cool=u*u_0*rho/LAMBDA
h=passo*t_cool/time_0
time=time+h*time_0
!N.B_1
IF (Temp==1.d4) THEN
u_tilde=((1.d0/(gamma-1.d0))*((k*Temp)/(mu*mp)))/u_0
ELSE
u_tilde=u
END IF
END DO
CLOSE(10)
END DO
PRINT*, "integrazione terminata, i risultati ottenuti sono stati salvati nei file:"
PRINT*, 'Temp_evolution_n0.1.dat'
PRINT*, 'Temp_evolution_n1.0.dat'
PRINT*, 'Temp_evolution_n_10.dat'
END PROGRAM PROGETTO_2