[mesa-users] Notation of mathematical formular in MESA

Byeong-Chan Park pbc1918 at gmail.com
Wed Sep 21 14:02:45 EDT 2016


Dear mesa users.

I tried to display a nuclear reaction rate of triple alpha reaction with
respect to temperature shown in below reference, but it was not well
matched up with a nuclear reaction rates graph in published paper. I think
I misunderstand mathematical formular of the reaction rate.

I though that

>          ! a0 T9i23 exp_cr(-a1 T9i13 - (T9*a2)^2)
>          !     * (1 + b0 T9 + b1 T92 + b2 T93 + b3 T94 + b4 T95)
>          ! + c0 T9i32 exp_cr(-c1/T9)
>          ! + d0 T9i32 exp_cr(-d1/T9)
>          ! + e0 T9^e1 exp_cr(-e2/T9)

is

and

>          call rnacre_rev(tf, &  ! a0 T932 exp_cr(-a1/T9)

is

of course, unit of the "T" is giga kelvin. But this formular shows large
difference in order of magnitude as compared with the triple alpha
reaction rate based on nacre displayed in a published paper.

What's wrong?


Best regards
Park


Reference (from rates directory in mesa):
>       subroutine rate_tripalf_nacre(tf, temp, fr, rr)
>          type (T_Factors), pointer :: tf
>          real(dp), intent(in) :: temp
>          real(dp), intent(out) :: fr, rr
>          real(dp) :: r2abe, rbeac, bb, term, rev
>          ! he4(a, g)be8
>          ! a0 T9i23 exp_cr(-a1 T9i13 - (T9*a2)^2)
>          !     * (1 + b0 T9 + b1 T92 + b2 T93 + b3 T94 + b4 T95)
>          ! + c0 T9i32 exp_cr(-c1/T9)
>          ! + d0 T9i32 exp_cr(-d1/T9)
>          ! + e0 T9^e1 exp_cr(-e2/T9)
>
>          if (tf% t9 < lowT9_cutoff) then
>             fr = 0; rr = 0; return
>          end if
>
>          call rnacre(tf,  &
>                2.43d9, 13.490d0, 1d0/0.15d0, & ! a0, a1, a2
>                74.5d0, 0d0, 0d0, 0d0, 0d0, & ! b0, b1, b2, b3, b4
>                6.09d5, 1.054d0, &  ! c0, c1
>                0d0, 0d0, & ! d0, d1
>                0d0, 0d0, 0d0, & ! e0, e1, e2
>                r2abe)
>         ! be8(a, g)c12
>          ! a0 T9i23 exp_cr(-a1 T9i13 - (T9*a2)^2)
>          !     * (1 + b0 T9 + b1 T92 + b2 T93 + b3 T94 + b4 T95)
>          ! + c0 T9i32 exp_cr(-c1/T9)
>          ! + d0 T9i32 exp_cr(-d1/T9)
>          ! + e0 T9^e1 exp_cr(-e2/T9)
>          call rnacre(tf,  &
>                2.76d7, 23.570d0, 1d0/0.4d0, & ! a0, a1, a2
>                5.47d0, 326d0, 0d0, 0d0, 0d0, & ! b0, b1, b2, b3, b4
>                130.7d0, 3.338d0, &  ! c0, c1
>                2.51d4, 20.307d0, & ! d0, d1
>                0d0, 0d0, 0d0, & ! e0, e1, e2
>                rbeac)
>          if (tf% T9 <= 0.03d0) then
>             bb    = 3.07d-16*(1 - 29.1d0*(tf% T9) + 1308d0*(tf% T92))
>             if (bb < 0) then
>                bb = 0
>             end if
>          else
>             bb    = 3.44d-16*(1 +     0.0158d0*pow_cr(tf% T9,-0.65d0))
>          end if
>          term    = r2abe * rbeac * bb
>          call rnacre_rev(tf, &  ! a0 T932 exp_cr(-a1/T9)
>             2.003d20, 84.415d0, &  ! a0, a1
>             rev)
>          fr    = term
>          rr    = rev * term
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