4 Luminosity classification

According to Diaz et al. (1989) and Zhou (1991) the infrared Ca II triplet, and a doublet of Na I can be used for luminosity classification. Unfortunately the lines of the Ca II triplet tend to be blended with Paschen emission lines in the spectra of symbiotic stars and they are also diluted by the emission due to the influence of the hot component, while the strengths of the lines studied are also sensitive to metal abundance. We therefore seek to use other lines.

The measured EWs of all the strong lines of the comparison stars are listed in Table 2 and Table 3. Table 2 lists the data obtained from the spectra taken in France with a 33 Å/mm dispersion. Table 3 lists the corresponding results from observations with a 50 Å/mm dispersion. Due to the blending of the weak lines, only the strongest lines are measured on 50 Å/mm spectra, these being the Ca II triplet and Fe I 8689 Å. There is an approximately 10% systematic deviation between the EWs of the two sets of data, having different dispersions. The continua for measuring the EWs were deduced with the help of the "continuum" program in IRAF, the parameters used in "continuum" being: spline3 function, the order is 1, points with deviations of more than 1$\sigma$ below the continuum are eliminated, while those with 3$\sigma$ above the continuum are eliminated in the spectra of symbiotic stars in order to remove the emission lines. Due to the fact that the different radial velocities of the stars produce different shifts of the lines and that many metal lines fill this band, taking fixed windows to measure EWs will result in large deviations. We must therefore measure the lines one by one carefully. We estimate the deviation in EW to be 10% for the CaII triplet, 15% for Fe I 8689 Å,  20% for Ti I and more than 25% for Na I. The graph of the total EW of Ca II 8542 Å  and Ca II 8662 Å is plotted against spectral type ST in Fig. 3a, where ST is defined so that for G9, ST = -7; for K0, ST = -6, while for K6 and M0, ST = 0. All the 50 Å/mm data in Table 3 are used regardless of whether the same stars are listed in different parts of the table. There are different equivalent widths for stars which have the same spectral type and a different luminosity class. Figure 4 shows that the Ca II of supergiants has the least central residual intensity and the broadest wings among the K2 type standard stars, this being also true for the Fe I 8689 Å and Fe I 8675 Å lines. When ST > 3 (later than M3), the EWs clearly decrease, but still there is difference between those stars having the same spectral type. The central residual intensity of Ca II is also seen to be different (see Fig. 5). Comparing the spectra of T Cr B and of the type I, II and III giants, we can easily conclude that the luminosity class of the cool component of T CrB is III.

   

Table 4: The [TiO] index in the different runs and ST of symbiotic objects

Symbiotic	[TiO]				ST
obs. run	2	3	4	5
YY Her	0.00	0.12			M3.2
CH Cyg	0.67	0.73	0.56		M6.7
CI Cyg	0.31		0.25		M4.4
AG Peg	0.00		0.00		<M3
Z And	0.18				M3.6
T CrB	0.21	0.16			M3.8
V443 Her	0.40	0.37			M4.9
BF Cyg	0.52		0.42		M5.6
UV Aur				0.35	C ??

Figure 3: ST vs. EW. For G9, ST = -7; for K0, ST = -6; for K6 and M0, ST = 0. a) vs. Ca II 8542 Å + 8662 Å; b) vs. Fe I 8689 Å; c) vs. all measured Ti I; d) vs. Na I 8183 Å + 8194 Å

Figure 4: The spectra of K2-type giants

Figure 5: The spectra of T CrB and the comparison giants

Figure 3b is the graph of the EW of Fe I 8689 Å against ST, Fig. 3c is for the total EW of all measured Ti I lines, while Fig. 3d is that for the Na 8183 Å plus Na I 8194 Å lines. The EWs of the Fe I, Ti I and Na I lines are those measured only in the comparison spectra with a 33 Å/mm dispersion, so there are fewer points in the last three graphs. In particular Fe I 8689 Å  is affected by blending in the 50 Å/mm spectra. We find that Fe I 8689 Å is a good luminosity indicator, so is Ti I, but not Na I. Perhaps the measurement deviation of Na I is too large.

In fact Jaschek & Jaschek (1987) pointed out that Fe I 8689/Fe I 8675 is a luminosity indicator for M-type stars. Due to the lack of metal abundance determinations for most symbiotic stars, it is much better to use the ratio of these lines to determine the luminosity class. Their closeness in wavelength minimizes moreover effects due to varying contributions at different wavelengths of residual continuum emission of the hot compoment. This ratio vs. ST is shown in Fig. 6; however we only find that it is a luminosity indicator for K-type stars. The ratio Ca II 8662 to Fe I 8675 against ST is shown in Fig. 7, it being also an indicator for K-type stars. Nevertheless we must be cautious to use it because of the chemical anomalies of some stars such as those of many symbiotic stars (Smith et al. 1996, 1997; Pereira 1995). Another reason is that CaII 8662 Å of a symbiotic star may be diluted by the emission due to the presence of the hot star.

The EWs of the symbiotic stars with 33 Å/mm spectra taken in 1993 are listed in Table 5; the EW value followed by a B character means that the line is blended with some visible emission, while a negative EW value means that the line is in emission. The data for the 50 Å/mm dispersion spectra are listed in Table 6. We observed most symbiotic stars twice and the EWs of the atomic lines do not vary greatly. However the Ca II triplets of some symbiotic stars vary dramatically, presumably due to emission produced by the presence of the hot companion. Therefore, Fe I 8689 Å is the best luminosity indicator for symbiotic objects as long as one can assume solar abundances for metals, while the ratio indicator Fe I 8689/Fe I 8675 is a better luminosity indicator, usable for K-type symbiotic cool components.

Figure 8 is the normalized spectrum of AG Dra. The Ca II triplet lines are blended with the Paschen emission lines of hydrogen and possibly some Ca II emission due to the presence of the hot component. If we assume that P13, P14, P15, P16, P17 have the same EW, then the EW of Ca II with the Paschen lines minus the average EW of P14 and P17 is the real EW of Ca II. The EWs of Ca II and Fe I are much less than those of type III giants. The very detailed stellar atmosphere analysis of Smith et al. (1996) shows that AG Dra is a metal-poor giant, ([Fe/H] = -1.3, log(g) = 1.6, $T_{{\rm eff}}$ = 4300 K). Therefore, it is more suitable to use the ratio luminosity indicator to determine its luminosity class. Fe I 8689/Fe I 8675 and CaII 8662/Fe I 8675 are 1.12 and 6.38 respectively for AG Dra. From Fig. 6 AG Dra is classified as a supergiant (the spectral type of AG Dra is supposed to be K0-K3). The effect of the metal abundance must be considered, when using the latter indicator, if the star is very metal-poor. The low metal abundance results in a lower electron pressure and more ions (Saha formula). For the very metal-poor star AG Dra, Ca II 8662/Fe I 8675 should then be larger than for stars with a normal metal abundance, if only simple Saha equation effects are taken in account. In addition we must also take into account Smith's result, that [Ca/Fe] = 0.21. The ratio Ca II 8662 Å/Fe I 8675 Å of this star would be less than 6.38, if that abundance ratio were normal. Comparing with Fig. 7, we obtain in fact the result that the lines have a ratio characteristic of a Ib or a II giant. The result obtained by the latter indicator is not certain, as Ca II 8662 Å may be diluted by the emission due to the presence of the hot stellar component. However AG Dra may still also have a larger luminosity and a larger radius than a normal giant, and indeed Smith et al. (1996) admit that their determination of the physical parameters of the cool component is not completely precise. Physically it would be easier to understand the processes of AG Dra if it were larger than a normal giant (Huang et al. 1994). The minimum distance of 1 kpc from HIPPARCOS observations found by Viotti et al. (1997) is unfortunately not decisive, as the maximum M_v near 1.0 is compatible with the cool component being a class III giant.

The corresponding ratios for TX CVn are 1.02 and 6.10 respectively, giving a luminosity class for the cool component of this system of II or Ib from Fig. 6 and Fig. 7, taking into consideration that the spectral type for TX CVn is K5.3 according to Kenyon & Fernandez-Castro (1987). The same uncertainty exists for this object as for AG Dra concerning conclusions obtained from Fig. 7, because of emission due to the presence of the hot component. Kenyon & Garcia (1989) determined orbital solutions for this binary. They suggest that the components are a K5 III + a B9 shell star, the orbital period being 199 days. However they admit that there are quite many uncertainties. According to them the hot component is not a normal B9 star, but could rather be a white dwarf, undergoing a hydrogen shell flash. The cool component could, using their conditions for the orbit, be in addition up to almost 50 times brighter than a K5 III giant, without necessarily exceeding the size of its orbit. The exact limit for the cool component not to be larger than its Roche lobe clearly depends on the masses assumed for each stellar component.

Finally, it must also be pointed out that the ratio indicator of luminosity is not very sure because of the small number of standard stars. The present ratio indicators are moreover suitable only for K-type stars.

The luminosity classes of the other symbiotic stars are determined from the EW of Fe I 8689 Å,  Ti I and Ca II. F I 8689 Å plays the key role. We compare the central residual intensities and the wings of Fe I 8689 Å  and the Ca II triplet of the symbiotic stars with the standard stars. The spectral types of most symbiotic stars are taken from Table 4; those of AG Peg and EG And being taken as M3.0 and M2.4 (Kenyon & Fernandez-Castro 1987). The lines of the symbiotic stars are usually similar to those of a giant or a little weaker, except that Ca II of some symbiotic stars is in emission. The results of luminosity classification for the symbiotic stars are given in the last column of Table 6. The visual comparison gives the final result, and Fe I 8689 Å has an important role, except for AG Dra and TX CVn where the ratio criteria are used.

Figure 6: ST vs. Fe I 8689 Å/Fe I 8675 Å

Figure 7: ST vs. Ca II 8662 Å/Fe I 8675 Å

Figure 8: The normalized spectrum of AG Dra

   

Table 5: The data of 1993

Symbiotic star	EW(CaII)		EW(FeI)		EW(TiI)
$\lambda\lambda$(Å)	8542	8662	8675	8689	8364	8378	8382	8379	8412
AG Dra	3.11 B	2.17 B	0.34	0.38	0.18	0.18	0.37	0.13	0.11
YY Her	-0.74 B	-0.43 B	0.47	0.52	0.41	0.24	0.39	0.19	0.27
CH Cyg	0.76	1.32	0.30	0.41	0.37	0.32	0.44	0.36	0.27
TX CVn	3.26	2.50	0.41	0.42	0.35	0.24	0.45	0.19	0.34
CI Cyg	1.82	2.33	0.49	0.59	0.55	0.44	0.58	0.31	0.37
AG Peg	3.79	2.65	0.31	0.43	0.48	0.31	0.60	0.30	0.29
Z And	1.28 B	1.22 B	0.43	0.52	0.53	0.37	0.60	0.31	0.33
T CrB	3.14	3.19	0.49	0.69	0.53	0.38	0.64	0.35	0.43
V443 Her	0.64 B	1.30 B	0.42	0.50	0.53	0.41	0.59	0.42	0.28
BF Cyg	1.38 B	1.55 B	0.42	0.51	0.61	0.42	0.59	0.41	0.45

   

Table 6: The data of the 50 Å/mm spectra

Date	1996, 5, 29-30			1997, 7, 13
Symbiotic star	EW(CaII)	EW(CaII)	EW(FeI)	EW(CaII)	EW(CaII)	EW(FeI)	LC
$\lambda\lambda$(Å)	8542	8662	8689	8542	8662	8689
AG Dra	2.46 B	1.85 B	0.38				Ib or II
YY Her	2.28	1.72	0.35				IIIb
CH Cyg	1.26	1.34	0.40	1.15	1.37	0.32	III
TX CVn	3.06	2.16	0.40				II or Ib
CI Cyg				1.54	1.37	0.58	III or IIIa
AG Peg				2.75	1.98	0.59	III
Z And				-1.86 B	-1.86 B	0.66	III
T CrB	2.79	2.15	0.45				III
V443 Her	0.91	1.25	0.32				III
BF Cyg				1.56 B	1.69 B	0.56	III
EG And*	3.76	2.82	0.40				III

* EG And was only observed on 7/11/97.