2 Observations and data reduction

2.1 Instrument and observing method

The observations were made with the Steward Observatory 1.54 m telescope on Mt. Bigelow, Arizona (elevation 2510 m) on 1993 October 5 and 6 and 1994 Sep. 12 and 13. The spectrometer was at the Cassegrain focus of the f/45 infrared-optimized chopping secondary.

The spectrometer, described by Williams et al. (1993), has a 120 arcsec long slit which illuminates a liquid nitrogen cooled grating. The grating used was ruled at 600 l/mm blazed for $\lambda 2.5~\mu$m. The detector was a NICMOS3 $256 \times 256$ HgCdTe array. The resolution at $\lambda 2.3~\mu$m with this grating is $\Delta \lambda = 0.0007$ $\mu$m, or $R \equiv \lambda / \Delta \lambda = 3500$with a slit width of 1.8 arcsec, which was used for most of the data presented. During the second observing period, a 3.6 arcsec slit was used to allow adequate guiding. (As a result the resolution was degraded to $R \approx$ 2500 for a few stars as noted below.) The grating setting used gave a wavelength range from 2.28 to 2.36 $\mu$m.

Observations were made by moving the telescope so as to place the star at six positions along the slit. The detector was read out for each position and the separate frames were differenced to subtract the sky and yield two independent spectra of the star. Integration times per exposure ranged from 0.5 s to 30 s, depending on the stellar magnitude.

Standard stars, selected mainly from the Bright Star Catalog, were dwarfs within a few degrees of the target stars, and with spectral types between early F and late B. Wallace & Hinkle (1997) have shown that dwarfs with spectral types from B3 to F5 have essentially featureless spectra in the wavelength range 2.2-2.4 $\mu$m when observed at $R \approx$ 3000. Standard and program stars were almost always observed in pairs at nearly identical airmasses, in an "ABBA" sequence, i.e., two pairs per observation. Integration time on the standard stars was typically 30 s per exposure. No absolute photometry was attempted in either observing period. Wavelength calibration was determined to first order with exposures of a NeKr lamp, and refined by an iterative procedure of line identification described below.

 

Table 1: Stellar properties and log of observations.

	Spec.	Var.				Obs.	Light	Standard Star		Int.
Star	Type	Class	Period	K	$\dot M_{\rm gas}$	Datea	Phase	Name	Sp.type	time	RMS
			(d)	(mag)	($M_{\odot}$ y-1)		(cycles)			(s)
(a) Supergiants
SU Per	M3.5Iab	SRc	470	1.50	...	236	--	HR 870	F7IV	24	0.037
S Per	M3Iae	SRc	--	1.31	1.4e-6f	236	--	HR 870	F7IV	24	0.037
BI Cyg	M4	Lc?	--	0.58b	...	236	--	HR 7769	A2V	24	0.034
KY Cyg	M3.5Ia	Lb	--	0.28	...	237	--	HR 7784	A1V	24	0.048
NML Cyg	M4.5-M7.9	...	--	0.62	...	237	--	HR 8028	A1V	24	0.033
$\mu$ Cep	M2Iae	SRc	--	-1.88b	9.1e-8f	236	--	HR 8357	B6V	12	(0.03)
PZ Cas	M3Ia	SRa	--	0.98	8.3e-6f	236	--	HR 9019	A0V	24	0.030
TZ Cas	M2Iab	Lc	--	1.95b	...	236	--	HR 9019	A0V	24	0.037
(b) M giants
W And	M7:p	M	396.71	0.88	...	236	0.31	HR 670	A1V	24	0.027
KU And	M9	M	750:	2.52	9.6e-6g	638	...	HR 76	A0V	60	0.017
T Cas	M7e	M	445.0	-0.97	5.1e-7h	638	0.41	HR 96	B9IV	6	0.016
IK Tau	M6me	M	500:	-1.24	3.8e-6g	638	...	HR 1137	A0V	18	0.016
UX Cyg	M5	M	561.24	1.97c	3.2e-6h	639	0.56	SAO 70289	F0V	36	0.012
(c) S stars
R And	S6.6	M	408.97	0.34	1.0e-6g	236	0.00	HR 63	A2V	24	0.031
W Aql	S4.9	M	490.16	0.84	6.5e-6i	236	0.67	HR 7366	A9V	24	(0.03)
AD Cyg	S5.8	Lb	--	1.24	2.5e-8i	237	--	HR 7887	F0V	24	0.035
(d) Carbon stars
HV Cas	CVIIe+	M	527	2.32	...	236	0.1	HR 343	A7V	24	0.038
V466 Per	N0. V	SR	--	1.01	...	236	--	HR 1160	B8V	24	0.025
TT Tau	C5II	SRb	166.5	1.05	...	237	--	HR 1554	F2IV	24	0.053
V Cyg	C7.4e	M	421.27	0.82	2.6e-6h	236	0.34	HR 7958	A3V	24	0.032
V460 Cyg	C6.3	SRbj	--	0.23	1.1e-6h	237	--	HR 8307	A0V	24	0.039
RV Cyg	C6.4II	SRb	300:	0.36	1.7e-6h	237	--	HR 8307	A0V	24	0.034
(e) RV Tauri variables
RV Tau	G2 Iaed	RVb	78.698	5.0e	...	638	0.55	HR 1554	F2IV	360	0.007
AC Her	F2Ibpd	RVa	75.4619	5.5e	...	639	0.30	SAO 103879	A0V	360	0.009

^a JD2449000+; ^b Josselin et al. (2000); ^c Feast & Whitelock (2000); ^d Oudmaijer et al. (1995); ^e Gezari et al. (1999); ^f Josselin
et al. (2000); ^g Neri et al. (1998); ^h Loup et al. (1993); ⁱ Bieging & Latter (1994); ^j Jørgensen et al. (2000).

2.2 Source list

Stars were selected to provide a representative sample of M supergiants and AGB stars of M, S, and C spectral types. Two RV Tauri variables, a class believed to be in a post-AGB evolutionary stage, were also observed. In total, we observed 8 M supergiants, 5 M giants, 3 S stars, 6 carbon stars, and 2 RV Tauri variables. Their properties are summarized in Table 1. Spectral types are from the SIMBAD database, except as noted. Variability class and period are from the General Catalog of Variable Stars (GCVS - Kholopov et al. 1985). K-band magnitudes were from the Two Micron Sky Survey (Neugebauer & Leighton 1969) except as noted. Most of these objects are strongly variable in the visual, but at K-band the variability is much less, typically <1 mag in total range. The gas mass loss rates in column 6 were determined from model fits to observations of the CO J = 1-0 and/or 2-1 mm-wavelength transitions, taken from the literature as noted. For the Miras with well-determined periods, the phase of the light cycle for the observation is given in Col. 8. The period and reference date were taken from GCVS, and we follow the (somewhat inconsistent) convention used there that zero phase is at maximum visual light for the Miras, but is at the deeper minimum in the cycle for the RV Tauri variables. The standard stars, listed in Col. 9, all have spectral types consistent with a nearly featureless spectrum in the observed wavelength range at R = 3500.

The integration time in Col. 11 is the total for all target star exposures averaged into the final spectra. The last column lists an estimate of the rms noise level of the final spectrum. Because almost the entire spectral range covered is filled with absorption features for these stars, it is not possible to calculate a noise level in a region of line-free continuum. Instead, we calculated the ratio spectrum of the difference over the sum of the two observations of a given star in the ABBA sequence, for both the standard and the target, and computed the rms values across these ratio spectra. The rms in Table 1 is then the root-sum-squared of the rms values for standard and target stars, since the final spectrum is the ratio of the target star spectrum divided by the standard spectrum, expressed in terms of the normalized flux. Typical values of the rms noise are in the range 1-3% of the continuum.

2.3 Data reduction

The data were reduced with the IRAF software package. Individual exposures (usually 6) were shifted and combined to produce a single two-dimensional spectrum. Flat-fielding was done with a dark current-corrected dome flat. A one-dimensional spectrum was produced with the IRAF aperture extraction tasks, for both the program and standard stars. Finally, the program star spectra were divided by the corresponding standard star spectra to remove telluric features.

Most of the stars were observed at two spectrometer grating settings, offset by either 0.5 or 1.5 resolution elements. This was done to ensure that the full resolution was achieved, since the spacing of the detector elements produced just $\Delta \lambda /2$ sampling of the spectrum. To combine the spectra taken at two grating settings, the telluric-corrected spectra of the program stars were interpolated onto a finer grid in $\lambda$, then cross-correlated to determine the exact shift in pixels between the two grating settings. One spectrum was shifted with respect to the other by regridding with the offset determined by cross-correlation, and the two spectra were summed. Finally, the summed spectrum was multiplied by a normalized 10000 K blackbody spectrum to correct for the slope introduced in dividing by the standard star. At $\lambda$2.3 $\mu$m, the difference in slope between a 7500 K and a 15000 K blackbody is negligibly small across the observed band, so a 10000 K spectrum, appropriate to an A0V star, was adopted.

2.4 Wavelength calibration and line identification

An initial estimate of the dispersion functions of the measured spectra was made from exposures of a neon-krypton lamp. These were not taken at grating settings identical to all those used for the stars, however, and the location of the star on the slit introduced a zero-point offset in the dispersion function, so it was necessary to use an iterative line identification procedure to determine an accurate wavelength calibration for each target star spectrum. As noted in the introduction, the CO rovibrational bands are potentially useful diagnostic probes of cool stellar atmospheres because the lines arise from a very wide range of energy levels but are confined to a relatively small range in wavelength. The small spectral range means, however, that many lines are blended or even almost perfectly coincide, especially for wavelengths longward of the CO 3-1 bandhead. These properties are illustrated in Fig. 1, which shows the lower state energy of the CO 2-0, 3-1, and 4-2 bands and the ¹³CO 2-0 band, over the range of wavelengths covered in the spectra presented here. Wavelengths and energy levels were calculated from the molecular data of Farrenq et al. (1991). Shortward of the 3-1 bandhead, the lines are resolved at $\Delta \lambda = 0.0007~\mu$m up to about R30. Longward of the 3-1 bandhead, the lower R- and P-branch lines of the 2-0 band are in some cases blended and in others just resolved from the R-branch lines of the 3-1 band.

Figure 1: Energy levels of CO 1st-overtone bands in the wavelength range observed. Lower-state energies expressed in temperature units, E/k, are plotted versus wavelength for the 2-0, 3-1, and 4-2 bands of 12C16O and for the 2-0 band of 13C16O. Selected transitions are labelled. Horizontal bar at lower left shows resolution, $\Delta \lambda$, of the spectra.

These spectral characteristics of the CO bands led us to an iterative procedure to refine the wavelength calibration and to identify as many spectral features as possible. First, the 2-0 and 3-1 bandheads are usually readily identified. The 3-1 head, however, is blended with the 2-0 R12 line, but the R14 line lies shortward of the 3-1 head just enough to be well resolved at R = 3500. Higher R-branch lines up to about R31 are well-separated, so we used the 2-0 R14 and R26 lines, and the 2-0 bandhead wavelengths. On the longward side, the 2-0 R0 line, blended with the ¹³CO 2-0 bandhead was always recognizable and usually the 4-2 bandhead (but blended with 3-1 R12). These identifications were used to derive a dispersion function from a 3-segment linear spline fit with IRAF. Because the bandheads are blended and have shapes which should depend on the properties of the stellar atmospheres, we made a second iteration using only lines that were unblended at $\Delta \lambda = 0.0007~\mu$m, or that were coincident with another line. The second pass lines included 2-0 band R6, R7, R8, and R14 through R31; 3-1 band R15, R16, and R21; 2-0 P4 blended with 3-1 R10; and the 2-0 bandhead. Typical scatter about the fitted dispersion function was < $0.0002~\mu$m peak-to-peak or an rms scatter of <$10 \%$ of a resolution element.

Figure 2: Spectrum of SU Per (spectral type M3.5Iab, variability class SRc). CO lines up to R40 are identified at the bottom, with bandheads as thick vertical lines. Atomic lines from Hinkle et al. (1995) are indicated at the top.

Figure 3: Spectrum of S Per (M3Iab, SRc).

Some of the atomic lines which Hinkle et al. (1995) detected in their high resolution spectrum of Arcturus are also evident in our spectra. These lines are heavily blended with CO lines except at the edge of the spectra shortward of the 2-0 bandhead, where the noise level increases, so no atomic lines were used in the fits to determine the dispersion functions.