net90

Nuclear network for hydrodynamical simulations. Specially suited for Type Ia SN simulations. It includes 89 nuclear species + electrons.
Electron/positron captures are included only on free protons/neutrons. Temperature is coupled and solved jointly with the nuclear species with an implicit scheme.

Compilation and usage

We provide a makefile that compiles net90 and testnuclear.f90, along with all needed EOS. testnuclear.f90 calls net90 iteratively and mimicking different user-defined scenarios. This is equivalent to the calls to net90 that a hydrodynamic code will do on a single fluid element. The objective of testnuclear.f90 is just to show how net90 should be called and perform toy scenarios. If the objective is to use net90 coupled with a hydrodynamics code, only the folder src/ is needed. To compile simply do make and this will generate an executable runnet90. Only a fortran compiler is needed. Our makefile assumes that gfortran is available.

Calling net90

Only abundance-related magnitudes need to be imported from the main code:
(D) Double precision, (I) Integer, (L) Logical

USE nuclear90_module, only:niso,ye,a,z

• niso (I): nuclear species (=89)
• ye (D): electron abundance
• a[1:niso] (D): array of atomic mass of each species
• z[1:niso] (D): array of atomic number of each species

Then, to call net90:

call net90(tempin,xin,rho,delta,screen,ecapture,tabulated,cv,val1,val2,dUedYein,theta,&
         & tempout,xout,sumtot,nucenergy,k_iter)

INPUT:

• tempin (D): temperature
• xin (D): mass fractions
• rho (D): density (g/cm^3) of the current time-step
• delta (D): time-step in seconds
• screen (L): Activates/deactivates the screening corrections to the rates
• ecapture (L): Activates/deactivates e-/e+ reactions
• tabulated (L): (T) e-/e+ rates interpolating on a table; (F) e-/e+ rates analytically
• cv (D): heat capacity (from EOS)
• val1 (D): (dp/dTemp)*(deltarho/rho**2)
• val2 (D): (dp/dTemp)*(deltarho/rho**2)*Temp
• dUedYein (D): dUe/dYe (from EOS)
• theta (D): Chooses between explicit (0), implicit (1), or mixed. Recommended value is 0.7d0

OUTPUT:

• tempout (D): temperature
• xout (D): mass fractions
• sumtot (D): total mass fraction (=1 if conserved)
• nucenergy (D): total nuclear energy generation rate (erg/s)
• k_iter (I): Total number of Newton-Raphson iterations performed

Description of parameters.in for toy scenarios

• Mass fractions of each species (D)
• Initial_temp (D): initial temperature in K
• Initial_dens (D): initial density in g/cm^3
• Screening (L): Activates/deactivates the screening corrections
• Adiabatic_exp (L): (T) an adiabatic expansion follows after NSE; (F) the process is isochoric
• Isotherm_test (L): (T) temperature is kept constant via an artificially high cv; (F) temperature is updated by net90
• electron_capt (L): Activates/deactivates e-/e+ reactions
• tabul_rates (L): (T) e-/e+ rates interpolating on a table; (F) e-/e+ rates analytically
• Theta (D): Chooses between explicit (0), implicit (1), or mixed. Default value is 0.7d0
• type_eos (I): Selects the EOS. (1) relativistic electrons (Nadyozhin 1974), ions (Bravo & Garcia-Senz 1992), and radiation; (2) helmholtz EOS (Cox & Giuli chapter 24; Timmes & Swesty ApJ 1999)

Nuclear species included

Corresponding index in the mass fraction array

index	Element	index	Element	index	Element	index	Element	index	Element
1	p	21	26Al	41	39Ca	61	46V	81	59Zn
2	n	22	26Mg	42	37Ar	62	46Ti	82	57Ni
3	4He	23	29P	43	39K	63	49Mn	83	59Cu
4	12C	24	32S	44	38Ca	64	52Fe	84	58Zn
5	16O	25	31S	45	38K	65	51Fe	85	58Cu
6	20Ne	26	29Si	46	38Ar	66	49Cr	86	58Ni
7	21Na	27	31P	47	41Sc	67	51Mn	87	57Co
8	24Mg	28	30S	48	44Ti	68	50Fe	88	59Co
9	23Mg	29	30P	49	43Ti	69	50Mn	89	13N
10	21Ne	30	30Si	50	41Ca	70	50Cr
11	23Na	31	33Cl	51	43Sc	71	53Co
12	22Mg	32	36Ar	52	42Ti	72	56Ni
13	22Na	33	35Ar	53	42Sc	73	55Ni
14	22Ne	34	33S	54	42Ca	74	53Fe
15	25Al	35	35Cl	55	45V	75	55Co
16	28Si	36	34Ar	56	48Cr	76	54Ni
17	27Si	37	34Cl	57	47Cr	77	54Co
18	25Mg	38	34S	58	45Ti	78	54Fe
19	27Al	39	37K	59	47V	79	57Cu
20	26Si	40	40Ca	60	46Cr	80	60Zn

Corresponding index in the reaction rate arrays

index	Reaction	index	Reaction	index	Reaction	index	Reaction
1	12C(12C,a)20Ne 1	46	37K(n,g)38K	91	23Na(p,g)24Mg	136	52Fe(a,g)56Ni
2	12C(16O,a)24Mg	47	37Ar(n,g)38Ar	92	25Mg(p,g)26Al	137	56Ni(a,g)60Zn
3	16O(16O,a)28Si 2	48	40Ca(p,g)41Sc	93	26Al(p,g)27Si	138	20Ne(a,n)23Mg
4	-	49	43Ti(n,g)44Ti	94	26Mg(p,g)27Al	139	24Mg(a,n)27Si
5	a(2a,g)12C 3	50	42Ti(n,g)43Ti	95	27Al(p,g)28Si	140	28Si(a,n)31S
6	12C(a,g)16O	51	40Ca(n,g)41Ca	96	29Si(p,g)30P	141	32S(a,n)35Ar
7	16O(a,g)20Ne	52	42Sc(n,g)43Sc	97	30P(p,g)31S	142	36Ar(a,n)39Ca
8	20Ne(p,g)21Na	53	41Sc(p,g)42Ti	98	30Si(p,g)31P	143	40Ca(a,n)43Ti
9	23Mg(n,g)24Mg	54	41Sc(n,g)42Sc	99	31P(p,g)32S	144	44Ti(a,n)47Cr
10	22Mg(n,g)23Mg	55	41Ca(n,g)42Ca	100	33S(p,g)34Cl	145	48Cr(a,n)51Fe
11	20Ne(n,g)21Ne	56	44Ti(p,g)45V	101	34Cl(p,g)35Ar	146	52Fe(a,n)55Ni
12	22Na(n,g)23Na	57	47Cr(n,g)48Cr	102	34S(p,g)35Cl	147	56Ni(a,n)59Zn
13	21Na(p,g)22Mg	58	46Cr(n,g)47Cr	103	35Cl(p,g)36Ar	148	20Ne(a,p)23Na
14	21Na(n,g)22Na	59	44Ti(n,g)45Ti	104	37Ar(p,g)38K	149	24Mg(a,p)27Al
15	21Ne(n,g)22Ne	60	46V(n,g)47V	105	38K(p,g)39Ca	150	28Si(a,p)31P
16	24Mg(p,g)25Al	61	45V(p,g)46Cr	106	38Ar(p,g)39K	151	32S(a,p)35Cl
17	27Si(n,g)28Si	62	45V(n,g)46V	107	39K(p,g)40Ca	152	36Ar(a,p)39K
18	26Si(n,g)27Si	63	45Ti(n,g)46Ti	108	41Ca(p,g)42Sc	153	40ca(a,p)43Sc
19	24Mg(n,g)25Mg	64	48Cr(p,g)49Mn	109	42Sc(p,g)43Ti	154	44Ti(a,p)47V
20	26Al(n,g)27Al	65	51Fe(n,g)52Fe	110	42Ca(p,g)43Sc	155	48Cr(a,p)51Mn
21	25Al(p,g)26Si	66	50Fe(n,g)51Fe	111	43Sc(p,g)44Ti	156	52Fe(a,p)55Co
22	25Al(n,g)26Al	67	48Cr(n,g)49Cr	112	45Ti(p,g)46V	157	56Ni(a,p)59Cu
23	25Mg(n,g)26Mg	68	50Mn(n,g)51Mn	113	46V(p,g)47Cr	158	54Fe(a,p)57Co
24	28Si(p,g)29P	69	49Mn(p,g)50Fe	114	46Ti(p,g)47V	159	57Co(n,g)58Co
25	31S(n,g)32S	70	49Mn(n,g)50Mn	115	47V(p,g)48Cr	160	12C(p,g)13N
26	30S(n,g)31S	71	49Cr(n,g)50Cr	116	49Cr(p,g)50Mn	161	13N(a,p)16O
27	28Si(n,g)29Si	72	52Fe(p,g)53Co	117	50Mn(p,g)51Fe	-	p(e-,nu)n 4
28	30P(n,g)31P	73	55Ni(n,g)56Ni	118	50Cr(p,g)51Mn	-	n(e+,anu)p 4
29	29P(p,g)30S	74	54Ni(n,g)55Ni	119	51Mn(p,g)52Fe
30	29P(n,g)30P	75	52Fe(n,g)53Fe	120	53Fe(p,g)54Co
31	29Si(n,g)30Si	76	54Co(n,g)55Co	121	54Co(p,g)55Ni
32	32S(p,g)33Cl	77	53Co(p,g)54Ni	122	54Fe(p,g)55Co
33	35Ar(n,g)36Ar	78	53Co(n,g)54Co	123	55Co(p,g)56Ni
34	34Ar(n,g)35Ar	79	53Fe(n,g)54Fe	124	57Ni(p,g)58Cu
35	32S(n,g)33S	80	56Ni(p,g)57Cu	125	58Cu(p,g)59Zn
36	34Cl(n,g)35Cl	81	59Zn(n,g)60Zn	126	58Ni(p,g)59Cu
37	33Cl(p,g)34Ar	82	58Zn(n,g)59Zn	127	59Cu(p,g)60Zn
38	33Cl(n,g)34Cl	83	56Ni(n,g)57Ni	128	20Ne(a,g)24Mg
39	33S(n,g)34S	84	58Cu(n,g)59Cu	129	24Mg(a,g)28Si
40	36Ar(p,g)37K	85	57Cu(p,g)58Zn	130	28Si(a,g)32S
41	39Ca(n,g)40Ca	86	57Cu(n,g)58Cu	131	32S(a,g)36Ar
42	38Ca(n,g)39Ca	87	57Ni(n,g)58Ni	132	36Ar(a,g)40ca
43	36Ar(n,g)37Ar	88	21Ne(p,g)22Na	133	40ca(a,g)44Ti
44	38K(n,g)39K	89	22Na(p,g)23Mg	134	44Ti(a,g)48Cr
45	37K(p,g)38Ca	90	22Ne(p,g)23Na	135	48Cr(a,g)52Fe

References

• Garcia-Senz, Cabezon, Reichert, Sanz, Escartin, Psaltis, Arcones, Thielemann; (2024) Upcoming
• Sanz, Cabezon, Garcia-Senz; NIC-XVI, 260 (2022)
• Cabezon, Garcia-Senz, Bravo; ApJS 151 (2004)
• Garcia-Senz, Cabezon; NPA, 718 (2003)

Authors (in alphabetical order)

Ruben M. Cabezon: (sciCORE) University of Basel
Domingo Garcia-Senz: Polytechnic University of Catalonia
Axel Sanz: Polytechnic University of Catalonia

Footnotes

1. This reaction is split into two branches: 50% 12C(12C,a)20Ne, 50% 12C(12C,p)23Na ↩

2. This reaction is split into two branches: 40% 16O(16O,a)28Si, 60% 16O(16O,p)31P ↩

3. The triple alpha reaction is calculated in two steps via 8Be ↩

4. electron and positron reactions are stored independently, hence they don't have an associated index ↩ ↩²