4 Relations between emission line strengths and spectral class

 

Table 3: Summary of the total number of stars by spectral type showing a particular line in emission for which an EW is measurable. Numbers in brackets refer to the number of stars for which the line is seen in emission, but no measurement of EW is possible (those stars designated as em in Tables 4-8). Only those stars with spectral classifications made in Paper I are listed

Spec. type	No. stars	Br$\gamma$	He I 2.058	He I 2.112	He I 2.161	Mg II	Fe II	Na I
B0	2	1	1	0	0 (1)	0 (1)	0	0 (1)
B0.5	5	2	2 (1)	1	0 (1)	1	0	0 (1)
B1	9	6	5	1	0 (1)	3	1	0
B1.5	8	6	6	0	0 (1)	3	4	0 (1)
B2	5	4	4	0	0 (1)	3	0	0
B2.5	5	5	1	0	0	4	3	0 (1)
B4	4	2	0	0	0	0 (1)	1	0
B5	3	2	0	0	0	0	2	0
B6	3	2	0	0	0	0	1	0
B7	6	6	0	0	0	0	2	0
B8	6	5	0	0	0	0	0	0
B8.5	1	1	0	0	0	0	0	0
B9	1	1	0	0	0	0	0	0
Total	58	43	19 (1)	2	0 (5)	14 (2)	14	0 (4)

4.1 Brackett $\gamma$

Br$\gamma$ is observed in emission in 70 per cent of the stars in the sample. Previous observations of optical H I transitions (e.g. Zorec & Briot 1997) suggest a strong correlation between line strength and stellar temperature; we plot the EW of Br$\gamma$ against the spectral type of the star in Fig. 2. Although a strong linear correlation between spectral type and EW is not present, a general trend of stronger emission from stars of an early spectral type is evident, with no star of spectral type later than B4 having an EW $_{\rm Br{\gamma}} >$10 Å.

There appears to be no correlation between EW $_{\rm Br{\gamma}}$ and luminosity class of the object, although this may be a result of the relatively small number of non main sequence stars observed.

The general trend of stronger Br$\gamma$ emission at earlier spectral types can be understood in the light of the simulations of the infrared spectrum of $\psi$ Per (Marlborough et al. 1997; henceforth MZW97). They show that the strength of Br$\gamma$ is very sensitive to both the changes in disc density and temperature (and the radial gradients of these parameters). For the near infrared Hydrogen lines a decrease in disc temperature in general leads to a decrease in line emission for two reasons. Firstly, the source function of the line (taken to be the Planck function; MZW97) decreases with the disc temperature. Also, the temperature dependant factors in the disc opacity term (Eq. (5) of MZW97) cause the opacity to increase with decreasing temperature for the majority of the disc (see Sect. 6.1). Therefore both effects combine to reduce the line emission from the disc as the temperature decreases. Since the disc temperature is likely to be a function of stellar temperature a reduction in line emission from early to late stars is expected.

A decrease in disc density also leads to a decrease in the strength of the IR emission lines (MZW97). The scatter in Fig. 2 could arise from differences in disc density (or density gradient) between individual stars, although we note that a dependance of disc density (and hence line emission) on spectral type is also possible if the disc formation mechanism is dependant on radiation pressure in some manner.

The stars from groups 2 & 4 (with Br$\gamma$ in absorption) can clearly be distinguished, with the EW of the photospheric profiles being $\sim$equal to those seen for non emission B stars of the same spectral type (HCR96). The same is found for the strengths of the He I 2.058 and 2.112 $\mu$m features of the stars in Group 2. On this basis, despite their prior classification as Be stars we find nothing to distinguish them from field B stars. This raises two possibilities. Firstly it may be that these objects were simply originally misclassified. The second possibility is that since the Be phenomenon is known to be variable, it may simply mean that these particular objects have undergone a phase change from emission ("e'') to non-emission ("non-e''). However in Fig. 3 we plot the distribution of these stars against spectral type. Comparing the distributions of "non-e'' (groups 2 & 5) and "e'' stars with a Kolmogorov-Smirnov (KS) test we find that the the distributions differ at the 3$\sigma$ level. This could imply that these objects are not Be stars in a "non-e'' phase. We will return to this question in Sect. 5.

4.2 Helium I

He I 2.058 $\mu$m emission is confined to the early stars of the sample; being seen in 19 of the 34 stars with spectral types determined in Paper I to be earlier than B2.5 (the dual requirements of a large ionising flux and a dense circumstellar environment required to drive He I 2.058 $\mu$m into emission are likely to be present only in the earliest stars). The relative strength of the He I 2.058 $\mu$m transition is due to the fact that the disc density falls off more rapidly with radius than the stellar radiation density, enabling the disc to remain ionised to large radii. Primarily populated by recombination, He I 2.112 $\mu$m is also only expected to be in emission in the earliest stars, and indeed is only seen in Bd+55 605 (B1V) and Bd+57 681 (B0.5V); in previous studies of hot emission line objects (e.g. Morris et al. 1996) this was absent from all B stars with the exception of the B[e] star S-18. Weak He I 2.161 $\mu$m emission is observed in 3 stars, with possible detections in a further 3, all with a spectral type of B2 or earlier (see Table 4).

We plot the Br$\gamma$ and He I 2.058 $\mu$m EW's for those stars of spectral type B2.5 and earlier in Fig. 4, and find that no linear correlation exists between the two quantities. This lack of correlation is likely due to the extreme sensitivity of the He I 2.058 $\mu$m line to changes in the UV continuum and optical depth. Consequently, beyond being used as an indicator of early (<B2.5) spectral type, this transition is a poor diagnostic for spectral classification. We find that EW $_{\rm HeI} >$EW $_{\rm Br{\gamma}}$ for only three stars out of the 22 stars with both He I 2.058 $\mu$m and Br$\gamma$ in emission. Unfortunately none of the stars were re-examined in Paper I and so only the historical classification of B1-3V is available. We note that in the K band spectra of the Be X-ray binaries (Clark et al. 1999) all of the systems with both Br$\gamma$ and He I 2.058 $\mu$m in emission showed a line ratio in excess of unity; whether this represents a modification of their circumstellar disc by the neutron star present in the systems, or is a function of their early (O9-B0) spectral type is as yet unclear (Clark et al. 1999).

4.3 Magnesium II and Iron II

Mg II and Fe II emission is observed in $\sim$30 per cent of the sample. Mg II emission is likely to be excited via Ly$\beta$ fluorescence (Bowen 1947), and is only seen in stars with spectral types earlier than B4. Assuming both Mg II transitions are optically thin, we would expect a flux ratio of Mg II 2.138:2.144 $\mu$m of $\sim$2.0 due to the greater statistical weight of the 5P_3/2 level (and the same is true if the upper levels are populated via collisional excitation). Comparison of the line ratios in the 14 stars showing Mg II emission (and for which an EW is measurable) shows that EW_2.138> EW_2.141 for 10 stars with an average line ratio of Mg II 2.138:2.144 $\mu$m $\sim$ 1.9 i.e. close to the predicted value for optically thin emission.

Fe II emission is characteristic of moderately warm and dense environments ( $T\sim 5000$ K, $N_{\rm e} \geq 10^9$ cm^-3; Hamann & Simon 1987), both of which are expected to be satisfied in the circumstellar discs of Be stars. Comparison of the EW of the Fe II and Mg II transitions to Br$\gamma$ indicates that while there is no direct correlation between the respective transitions, neither Fe II or Mg II emission is seen in stars with EW $_{\rm Br{\gamma}} <$ 8 Å.

4.4 Sodium I

Two Na I transitions exist at 2.206 & 2.209 $\mu$m. CD-27 11872 has 2 distinct features at these wavelengths that we attribute to Na I emission. Na I emission has previously only been identified in one Be star, HD 34921, the proposed optical counterpart of the X-ray source 1H0521 +37 (Polcaro et al. 1990; Clark et al. 1999 and references therein); we note that CD-27 11872 has been proposed as a candidate Be/X-ray binary by Motch et al. (1997). An echelle spectrum of HD 34921 reveals two narrow (projected velocity <50 km s^-1) emission features suggesting emission at large radii (assuming the lines arise in a Keplerian disc; Clark et al. 1999). Given the low ionisation energy (5.1 eV) of Sodium we might expect it to be fully ionised in the discs of Be stars; the presence of emission features suggests that a region(s) of the circumstellar envelope must be shielded from direct stellar radiation. IRAS $12 - 60~\mu$m fluxes for HD 34921 suggest the presence of cool dust, which could possibly shield the emitting regions in HD 34921 in a manner analogous to B[e] stars. Alternatively, changes in the disc geometry at large radii could produce large enough optical depths to shield the emitting regions from direct stellar radiation.

We find broad emission features at the correct wavelength for Na I emission in 3 stars; BD 12 5132 (BN0.2III), BD+5 3704 (B2.5V) and BD+29 4453 (B1.5V). The apparent width of these features implies a large projected velocity for the emitting regions of the circumstellar envelopes. If we assume that the requirements for the presence of Na I emission (i.e. shielding from direct stellar radiation) can only be fulfilled at large radii where sufficient material exists to prevent ionisation this suggests a radial acceleration of material at such distances. Clearly higher resolution spectra of this region are required before definitive conclusions can be made as to the presence and kinematics of possible Na I emitting regions in the envelopes of these stars.

 

Table 4: Summary of emission features of Group 1 stars; equivalent widths are given in Å, where a positive EW corresponds to emission. em reflects emission in the relevant transition that is to weak to measure (typically <0.2 Å), the addition of a question mark represents an uncertainty as to its presence. The estimated error in the equivalent widths is 20% unless marked with a colon (:) when it is 50%

Object	He I	Fe II	He I	Mg II	Mg II	He I	Br$\gamma$	Na I
name	2.058	2.089	2.113	2.138	2.144	2.161	2.166	2.206/9
CD-28 14778	3.4	0	0	1.4	0.9	em	24.0	0
CD-27 11872	4.5	0	0	1.2	0.7	em	12.7	em
BD-13 893	8.7	0	0	0	0	0	6.1	0
BD-12 5132	4.3	0	0	em	em	em?	7.2	em
BD-1 3834	0.9	0	-0.4	0.7	0.5	0	10.5	0
BD+1 1005	8.8:	0	0	0	0	em?	5.2	0
BD+4 1002	3.2	0	-0.9	0	0	0	1.2	0
BD+5 3704	0	0	-1.5	0	0	0	1.0:	em
BD+29 4453	1.1	0.5	0	0.8	0.7	0	16.9	em
BD+31 4018	1.6	0	0	0	0	0	9.2	0
BD+36 3946	3.9	0	0	0	0	0	5.8	0
BD+40 1213	1.5	0	0	0.5	0	0	21.0	0
BD+42 1376	0.5:	0	-0.6	0	0	0	1.8:	0
BD+45 3879	3.2	0.2	0	0.8	0.8	0	10.6	0
BD+47 3985	2.2:	0	-1.1	0.8	0.8	0	8.9	0
BD+55 605	8.5	0	1.3	0.3	0	em	8.6	0
BD+55 552	-1.9	0	0	0	0	0	1.6	0
BD+56 469	1.0:	0	-1.6	0	0	0	1.3	0
BD+56 473	2.0:	0	0	1.0:	0.4	0	4.2	0
BD+56 478	9.0	0.1	0	0	0	em?	8.7	0
BD+56 484	3.5	0.8:	0	0.9	0	0	16.9	0
BD+56 511	-0.5:	0	-0.9	0	0	0	3.7:	0
BD+56 573	0.8:	1.0:	0	0.9	0	0	15.4	0
BD+57 681	6.7:	0	1.2:	0	0	0	4.6	0
BD+58 2320	3.4	0	0	0	0	0	7.2	0

 

Table 5: Summary of emission features of Group 2 stars. See Table 4 for explanation

Object	He I	Fe II	He I	Mg II	Mg II	Br$\gamma$
name	2.058	2.089	2.112	2.138	2.144	2.166
CD -25 12642	0	0	-1.3	0	0	-3.9
BD+20 4449	0	0	-1.1	0	0	-5.0
BD+23 1148	0	0	-1.2	0	0	-4.0
BD+25 4083	0	0	-1.5	0	0	-4.1
BD+27 797	em	0	0	0	0	-6.5
BD+27 850	0	0	-1.2	0	0	-7.3
BD+28 3598	-0.8	0	-1.2	0	0	-2.7
BD+29 3842	0.9	0	-1.5	0	0	-3.3
BD+37 3856	0	0	-1.2	0	0	-6.2
BD+45 933	0	0	-1.0	0	0	-5.4
BD+56 493	0	0	-1.1	0	0	-5.5

 

Table 6: Summary of emission features of Group 3 stars. See Table 4 for explanation

Object	He I	Fe II	He I	Mg II	Mg II	Br$\gamma$
name	2.058	2.089	2.112	2.138	2.144	2.166
BD-8 929	0	0	0	em	em	8.1
BD+42 4538	0	0.8	0	0.1:	0.6	21.7
BD+47 183	0	0.3	0	0.5	0.3	17.7
BD+47 857	0	1.4	0	em	em	17.0
BD+47 939	0	0.2	0	0.3	0.6	13.6

 

Table 7: Summary of emission features of Group 4 stars. See Table 4 for explanation

Object	He I	Fe II	He I	Mg II	Mg II	Br$\gamma$
name	2.058	2.089	2.112	2.138	2.144	2.166
BD-19 5036	0	0	0	0	0	-6.9
BD+17 4087	0	0	0	0	0	-6.1
BD+19 578	0	0	0	0	0	-4.3
BD+27 797	0	0	0	0	0	-6.5
BD+30 3227	0	0	0	0	0	-4.8

 

Table 8: Summary of emission features of Group 5 stars. See Table 4 for explanation

Object	He I	Fe II	He I	Mg II	Mg II	Br$\gamma$
name	2.058	2.089	2.112	2.138	2.144	2.166
CD-27 16010	0	0	0	0	0	-3.4
CD-27 13183	0	0	0	0	0	0.1
BD-20 5381	0	0	0	0	0	9.3
BD-5 1710	0	0	0	0	0	3.4
BD-2 5328	0	0	0	0	0	2.9
BD-0 3543	0	0	0	0	0	0.7
BD-0 1468	0	0.8	0	0	0	8.7
BD+0 1203	0	0	0	0	0	7.1
BD+2 3815	0	0.4	0	0	0	4.6
BD+21 4695	0	0.4	0	0	0	-2.4
BD+27 3411	0	0	0	0	0	-1.8
BD+37 675	0	0.9:	0	0	0	6.8
BD+43 1048	0	0	0	0	0	3.3
BD+46 275	0	0	0	0	0	-1.4
BD+49 614	0	0.2	0	0	0	2.5
BD+50 825	0	0	0	0	0	3.3
BD+50 3430	0	0	0	0	0	3.8
BD+51 3091	0	0	0	0	0	-4.2
BD+53 2599	0	0	0	0	0	-1.9
BD+55 2411	0	0	0	0	0	-3.1
BD+58 554	0	0	0	0	0	6.5