Astrophysical implications of the models

Perhaps the most significant result of the model calculations is the fact that (for both models) the primary as well as the secondary components of MT Ser are very close to filling their respective Roche lobes.

In the subsequent discussion we will compare model predictions - considering Models 1.1, 2.2.1 and 2.2.2 - concerning the system luminosity and the distance to MT Ser to corresponding literature results, mainly based on studies of the planetary nebula. To do so, however, assumptions concerning the component masses are required. For all models, three mass values are considered: Two values which generously embrace the possible mass range which might be realized in MT Ser, and a plausible intermediate one. They will be referred to as the high (H) and low (L) mass limit, and the intermediate (I) mass, respectively. The adopted mass values are listed in Table 6.

In Model 1 we expect the primary component to be a hot sub-dwarf. It will probably evolve into a white dwarf without substantial further mass loss. Therefore, it must not have more than the Chandrasekhar mass (1.43 M_o), while the lower mass limit is given by the low mass cut-off of the white dwarf mass distribution which we place at 0.2 M_o to be on the safe side. As intermediate mass a value of 0.6 M_o is adopted, close to the peak of the white dwarf mass distribution. Together with the mass ratio of 0.92 (see Table 3) the component masses as listed in Table 6 result.

Table: Stellar parameters derived from model calculations
Model 1.1 Model 2.2.1 Model 2.2.2

H I L H I L H I L

primary star mass (M_o) 1.43 0.6 0.2 1.43 0.6 0.2 1.43 0.6 0.4

secondary star mass (M_o) 1.31 0.55 0.18 1.43 0.6 0.2 0.72 0.30 0.2

component separation (R_o) 1.38 1.03 0.71 2.22 1.66 1.15 2.02 1.51 1.32

primary star radius (R_o) 0.62 0.46 0.32 1.00 0.75 0.52 1.05 0.78 0.68

secondary star radius (R_o) 0.58 0.44 0.30 1.00 0.75 0.52 0.78 0.58 0.51

log g (cm s^-2) (primary star) 5.01 4.89 4.73 4.59 4.46 4.31 4.55 4.43 4.37

log g (cm s^-2) (secondary star) 5.02 4.90 4.73 4.59 4.46 4.31 4.51 4.38 4.32

system luminosity (10³ L_o) (T₁=50000 K) 2.14 1.20 0.57 9.42 5.28 2.51 8.37 4.68 3.58

system luminosity (10³ L_o) (T₁=35000 K) 0.44 0.25 0.12 2.24 1.31 0.61 2.00 1.13 0.86

M_B (T₁=50000 K) 0.34 0.97 1.77 -1.38 -0.75 0.06 -1.22 -0.60 -0.30

M_B (T₁=35000 K) 1.06 1.68 2.48 -0.80 -0.22 0.61 -0.66 -0.03 0.26

distance (kpc) (T₁=50000 K; A_B=2.28) 5.9 4.9 3.0 13.0 9.7 6.7 12.0 9.0 7.8

distance (kpc) (T₁=50000 K; A_B=1.09) 10.1 7.6 5.2 22.4 16.8 11.6 20.9 15.7 13.6

distance (kpc) (T₁=35000 K; A_B=2.28) 4.2 3.2 2.2 9.9 7.6 5.2 9.3 6.9 6.1

distance (kpc) (T₁=35000 K; A_B=1.09) 7.3 5.5 3.9 17.2 13.1 9.0 16.0 12.0 10.5

**Table:** Stellar parameters derived from model calculations
	Model 1.1		Model 2.2.1	Model 2.2.2
	H	I	L	H	I	L	H	I	L
primary star mass (M_o)	1.43	0.6	0.2	1.43	0.6	0.2	1.43	0.6	0.4
secondary star mass (M_o)	1.31	0.55	0.18	1.43	0.6	0.2	0.72	0.30	0.2
component separation (R_o)	1.38	1.03	0.71	2.22	1.66	1.15	2.02	1.51	1.32
primary star radius (R_o)	0.62	0.46	0.32	1.00	0.75	0.52	1.05	0.78	0.68
secondary star radius (R_o)	0.58	0.44	0.30	1.00	0.75	0.52	0.78	0.58	0.51
log g (cm s^-2) (primary star)	5.01	4.89	4.73	4.59	4.46	4.31	4.55	4.43	4.37
log g (cm s^-2) (secondary star)	5.02	4.90	4.73	4.59	4.46	4.31	4.51	4.38	4.32
system luminosity (10³ L_o) (T₁=50000 K)	2.14	1.20	0.57	9.42	5.28	2.51	8.37	4.68	3.58
system luminosity (10³ L_o) (T₁=35000 K)	0.44	0.25	0.12	2.24	1.31	0.61	2.00	1.13	0.86
M_B (T₁=50000 K)	0.34	0.97	1.77	-1.38	-0.75	0.06	-1.22	-0.60	-0.30
M_B (T₁=35000 K)	1.06	1.68	2.48	-0.80	-0.22	0.61	-0.66	-0.03	0.26
distance (kpc) (T₁=50000 K; A_B=2.28)	5.9	4.9	3.0	13.0	9.7	6.7	12.0	9.0	7.8
distance (kpc) (T₁=50000 K; A_B=1.09)	10.1	7.6	5.2	22.4	16.8	11.6	20.9	15.7	13.6
distance (kpc) (T₁=35000 K; A_B=2.28)	4.2	3.2	2.2	9.9	7.6	5.2	9.3	6.9	6.1
distance (kpc) (T₁=35000 K; A_B=1.09)	7.3	5.5	3.9	17.2	13.1	9.0	16.0	12.0	10.5

Within Model 2 both components are hot sub-dwarfs which are expected to become white dwarfs. Therefore, for Model 2.2.1 (q=1) the above values of 1.43 M_o, 0.6 M_o, and 0.2 M_o for the H, I, and L cases, respectively, are adopted for both stars, while for Model 2.2.2 (q=0.5) the additional contraint applies that none of the components may have a mass above or below the permitted range for a white dwarf. As intermediate mass case it is assumed that the primary component has a mass corresponding to the peak of the white dwarf mass distribution (0.6 M_o).