3 Spectra

3.1 Identified lines

The final spectra are shown in Figs. 2-25, grouped by stellar category. The flux scale is normalized to unity at the peak at $\lambda$ 2.293 $\mu$ m, just shortward of the v = 2-0 bandhead. The estimated 1- $\sigma$ noise level is shown by a vertical error bar on the left side. The resolution is $\Delta \lambda =$ 0.0007 $\mu$ m, or R = 3500. At this resolution, the spectra exhibit a rich complexity of absorption features which are predominantly due to the v = 2-0 and 3-1 rovibrational lines of ¹²C¹⁶O, over the wavelength range covered. To aid in identifying individual features in these CO bands, thin vertical lines mark the wavelengths of the P1-P4 and R0-R40 lines of the v = 2-0 band, and R10-R40 of the v = 3-1 band. Also shown as thicker vertical lines are the heads of the v = 2-0, 3-1, and 4-2 bands, and the ¹³C¹⁶O v = 2-0 band. CO line wavelengths were calculated from the molecular constants in Farrenq et al. (1991). Atomic transitions which were detected in the high-resolution spectrum of Arcturus by Hinkle et al. (1995) are marked with lines labelled above the spectrum.

$\begin{figure} \par\includegraphics[angle=-90,width=10cm,clip]{H3202F10.PS}\end{figure}$

Figure 10: Spectrum of W And (M7:p, Mira).

Despite the apparent complexity in Figs. 2-25, close examination of each spectrum shows that almost every feature can be identified with either a single CO line or a blend of lines. The lines from R14 to about R35 in the 2-0 band are clearly resolved, and the R13 line is apparent as an inflection just shortward of the v = 3-1 bandhead. Longward of the 3-1 bandhead, the R-branch lines of the 2-0 and 3-1 bands are alternately blended and resolved. For example, the 2-0 R9 line blends with the 3-1 R33 and R34 lines, and 2-0 R7 with 3-1 R20, producing at this resolution characteristically deep, broadened absorption features. In contrast, the gap between the 2-0 R0 and P1 lines allows for a clear separation of the 3-1 R15 and R16 lines. It is quite possible that some weak absorption is present from lines at energies higher than the bandheads, i.e., >R51. Hinkle et al. (1995) detected up to the 2-0 R99 line in the spectrum of Arcturus, which however has an effective temperature of 4320 K, significantly higher than the stars in our sample. The higher energy lines may contribute weakly but the dominant CO absorption features are those identified in the figures.

$\begin{figure} \par\includegraphics[angle=-90,width=10cm,clip]{H3202F15.PS}\end{figure}$

Figure 15: Spectrum of R And (S6.6, Mira).

$\begin{figure} \par\includegraphics[angle=-90,width=10cm,clip]{H3202F18.PS}\end{figure}$

Figure 18: Spectrum of HV Cas (CVIIe+, Mira).

$\begin{figure} \par\includegraphics[angle=-90,width=10cm,clip]{H3202F22.PS}\end{figure}$

Figure 22: Spectrum of V460 Cyg (C6.3, SRb).

$\begin{figure} \par\includegraphics[angle=-90,width=10cm,clip]{H3202F25.PS}\end{figure}$

Figure 25: Spectrum of AC Her (F2Ibp, RV Tauri variable).

Only a few atomic lines are readily discernible in the spectra. The most obvious are a line of Ti I at $\lambda$ 2.29696 $\mu$ m and a line of Sc I at $\lambda$ 2.29926 $\mu$ m, both of which show up as absorption features on the flank of the v = 2-0 bandhead. A few weak atomic lines are present at the short wavelength edge of the spectra, but other atomic lines, if present, are badly blended with CO lines.

Table 2: CO rovibrational absorption feature intensities (% of continuum).
v = 2-0 v = 3-1 v = 4-2

BH R30^a R14 R0^b BH^c R16 R15 BH^d

Star

(a) Supergiants

SU Per 35 68 64 42 32 56 59 35

S Per 57 67 61 54 45 62 66 53

BI Cyg 37 73 69 46 37 60 64 41

KY Cyg 40 65 61 48 36 56 60 42

NML Cyg 66 79 73 73 60 80 79 70

$\mu$ Cep 44 76 76 54 42 62 69 47

PZ Cas 41 66 61 49 37 56 56 40

TZ Cas 38 70 68 41 32 56 60 33

(b) M giants

W And 30 77 64 38 33 58 61 35

KU And 65 81 81 60 62 72 76 77

T Cas 45 81 74 49 40 66 71 43

IK Tau 68 91 80 65 64 85 89 64

UX Cyg 64 85 78 62 56 75 80 59

(c) S stars

R And 31 72 69 34 31 53 59 36

W Aql 35 68 66 39 35 52 53 38

AD Cyg 27 68 66 40 22 57 56 27

(d) Carbon stars

HV Cas 79 84 84 86 80 89 86 82

V466 Per 50 70 74 56 48 65 63 51

TT Tau 34 65 67 46 35 61 63 41

V Cyg 70 87 84 83 74 90 89 79

V460 Cyg 39 70 73 48 38 59 59 39

RV Cyg 52 73 73 61 50 70 66 57

(e) RV Tauri variables

RV Tau 80 89 92 97 80 99 100 86

AC Her 93 96 95 103 93 102 100 95

^a Blended with v = 2-0 R71; ^b blended with v = 3-1 R17 and ¹³CO v = 2-0 BH
^c blended with v = 2-0 R13; ^d blended with v = 3-1 R12

**Table 2:** CO rovibrational absorption feature intensities (% of continuum).
	v = 2-0		v = 3-1		v = 4-2
	BH	R30^a	R14	R0^b		BH^c	R16	R15	BH^d
Star
(a) Supergiants
SU Per	35	68	64	42		32	56	59	35
S Per	57	67	61	54		45	62	66	53
BI Cyg	37	73	69	46		37	60	64	41
KY Cyg	40	65	61	48		36	56	60	42
NML Cyg	66	79	73	73		60	80	79	70
$\mu$ Cep	44	76	76	54		42	62	69	47
PZ Cas	41	66	61	49		37	56	56	40
TZ Cas	38	70	68	41		32	56	60	33
(b) M giants
W And	30	77	64	38		33	58	61	35
KU And	65	81	81	60		62	72	76	77
T Cas	45	81	74	49		40	66	71	43
IK Tau	68	91	80	65		64	85	89	64
UX Cyg	64	85	78	62		56	75	80	59
(c) S stars
R And	31	72	69	34		31	53	59	36
W Aql	35	68	66	39		35	52	53	38
AD Cyg	27	68	66	40		22	57	56	27
(d) Carbon stars
HV Cas	79	84	84	86		80	89	86	82
V466 Per	50	70	74	56		48	65	63	51
TT Tau	34	65	67	46		35	61	63	41
V Cyg	70	87	84	83		74	90	89	79
V460 Cyg	39	70	73	48		38	59	59	39
RV Cyg	52	73	73	61		50	70	66	57
(e) RV Tauri variables
RV Tau	80	89	92	97		80	99	100	86
AC Her	93	96	95	103		93	102	100	95

3.2 Intensities of selected features

The spectra in Figs. 2-25 show broadly similar structure in the CO bands, but there are significant differences from star to star, in the shape and depth of many features. To facilitate comparisons and search for correlations with stellar properties, we list in Table 2 the intensities of selected features, expressed in per cent of the continuum, as measured directly from the spectra. Features tabulated include the following:

(a) v = 2-0 bandhead. The short wavelength limit is at R51 but within one resolution element are blended the R45-R56 lines, which span lower state energies, $E_{\rm low}$ , from 5700 to 8700 K.
(b) v = 2-0 R30. This transition lies at $E_{\rm low}$ = 2565 K, but is nearly coincident in wavelength with the R71 line at $E_{\rm low}$ = 13911 K.
(c) v = 2-0 R14. This line has $E_{\rm low}$ = 581 K. Its wavelength lies between, but is just resolved from, R86 and R87.
(d) v = 2-0 R0. Though one of the more prominent features in most of our spectra, this ground-state line is blended with both the v = 3-1 R17 line ( $E_{\rm low}$ = 3922 K) and the ¹³CO v = 2-0 bandhead ( $E_{\rm low} \approx 7300$ K).
(e) v = 3-1 bandhead. The shape of the bandhead is influenced by the proximity of the 2-0 R12 and R13 lines (with $E_{\rm low}$ = 431 K and 503 K respectively). The bandhead lines have $E_{\rm low} \approx 10\,000$ K.
(f) v = 3-1 R16 and R15. These lines arise from levels with $E_{\rm low} \approx$ 3800 K. They fall between the 2-0 R0 and P1 lines, but are blended with ¹³CO v = 2-0 lines near that bandhead.
(g) v = 4-2 bandhead. Lines near the bandhead have $E_{\rm low} \approx ~$ 13000 K, but are blended with the 3-1 R12 line ( $E_{\rm low} = 3511$ K).

$\begin{figure} \par\includegraphics[angle=-90,width=9cm,clip]{H3202F26.PS}\end{figure}$

Figure 26: Comparison of spectrum of $\mu$ Cep from this paper (resolution R = 3500) (solid line) with that of Wallace & Hinkle (1997) (resolution R = 2700) normalized at the same wavelength (dashed line).

3.3 Comparison with other spectra

The most directly comparable published spectra for any stars in our sample are those of Kleinmann & Hall (1986) and Wallace & Hinkle (1997), who present spectra for 4 stars in common: $\mu$ Cep, SU Per, KY Cyg, and PZ Cas - all M supergiants. (Kleinmann & Hall included $\mu$ Cep and SU Per in their atlas and in fact the same observational data were processed by Wallace & Hinkle 1997.) We have compared our spectra with those of Wallace & Hinkle (1997) and find good agreement, considering the difference in effective resolution. Wallace & Hinkle used the Fourier Transform Spectrometer (FTS) on the NOAO 4-m telescope and presented spectra with an effective frequency resolution of 1.6 cm^-1 after processing, corresponding to R = 2700 or $\Delta \lambda ~=~ 0.00086~\mu$ m at $\lambda 2.32~\mu$ m. At this somewhat lower resolution than ours (R = 3500), the CO bandheads show virtually identical intensities and shapes but the individual rovibrational lines (e.g., 2-0 R14-R30) are less well-resolved, as expected. An example which compares spectra for $\mu$ Cep is shown in Fig. 26. These observations were separated in time by over 12 years, so spectral variability is a possibility, but the main differences can be explained simply by the difference in effective resolution.

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