MULTI-EPOCH INTERFEROMETRIC STUDY OF MIRA VARIABLES II. Narrowband diameters of R Boo

1. MULTI-EPOCH INTERFEROMETRIC STUDY OF MIRA VARIABLES II. Narrowband diameters of R Boo R. R. Thompson (JPL) M. J. Creech-Eakman (JPL) G. T. van Belle (IPAC/Caltech) American Astronomical Society Meeting 201, Seattle WA 9 Jan 2003

2. Abstract As part of the long-term monitoring of Mira variables at the Palomar Testbed Interferometer, we report high-resolution narrowband angular sizes of the oxygen-rich Mira R Bootis. The dataset spans five pulsation cycles for a total of 1496 25-sec observations), and represents the second study to correlate multi-epoch narrowband interferometric data of Mira variables. When the calibrated visibility data are fit using a uniform disk brightness model, differences are seen in their angular diameters as a function of wavelength within the K band (2.0 - 2.4 m); the source of which are molecular absorptions in or above the photosphere of the oxygen-rich Miras. Using visible photometric data provided by the AFOEV, the continuum minimum size tracks the visual maximum brightness as found in our previous study (Paper I) for the oxygen-rich Mira S Lac. Based on the mean of the continuum angular diameter cycloid, basic stellar parameters are computed for R Boo, with this star showing maximum atmospheric extension with respect to the 2.0 and 2.4 m diameters near phase 0.95. Using the mean value of the fitted cycloids, R Boo has a radius Rmean = 216  40 Rand a mean Teff = 2970  43 K .The dominant source of error in the mean radius is the large uncertainty in the distance to this star. The work performed here was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

3. The Palomar Testbed Interferometer • Maximum projected baselines: N-S 110m, N-W 85m • Resolution range 1.0 - 5.5 mas • 40 cm collecting apertures, K ~ 5 fringe tracking, V ~ 12 angle tracking • Visibilities in H-band (4 chan) and K-band (5 chan) R ~ 22 - 50

4. The Mira variable R Boo (HD 128609) • Chemical type: Oxygen-rich • Spectral type: M3 – M8 IIIe • Pulsation period: P = 224.1 d • Visual magnitude: 7.1 – 12.2 (AFOEV) • K-band magnitude: 2.1 (Gezari et al, 1999) • Mean continuum angular diameter: 3.31  0.02 mas (from 2.2 m cycloid) • Bolometric flux: 28.2  1.6 x 10-8 erg/cm2/s (from photometry longward of 1 m ) • Mean Teff: 2970  43 K • Mean linear radius: 216  40 R

5. Distance Determination The distance to R Boo as quoted herein is a mean value from four independent sources. The large uncertainty in distance results in similar uncertainty in the linear diameter. 500 pc Bowers & Hagen (1984) 570 pc Wyatt & Cahn (1983) 600 pc Jura & Kleinmann (1992) 764 pc Whitelock & Feast (2000), using MK = -7.32 and mK = 2.10 ====== 608  112 pc mean distance (/m = 18%)

6. Narrowband diameter cycloids • Normalized visibilities were fit to a uniformly-bright disk model (UD) diameters () for a projected baseline (B) and wavelength () such that: • Each diameter point in Figure 1 represents a nightly ensemble mean measurement. • No conclusive evidence of departures from circular symmetry found to date.

7. Diameter cycloid best fits Cycloids fit to data are of the form Where a is the amplitude, b is the period(here, set to unity to normalize to 224.1d), is the visual phase,c is the diameter phase offset and d the mean linear offset. Band a c d 2 2.0 m 0.280.05 0.480.02 3.680.03 77 2.2 m 0.390.03 0.520.01 3.310.02 28 2.0 m 0.200.02 0.430.02 4.040.02 21

8. Diameter ratios Both the 2.0 and 2.4 m diameters were normalized to the center channel in the K-band (2.2 m). Figure 2 depicts these quantities, showing the effect of maximum opacity near phase 0.9. This is consistent with that found in the oxygen-rich Mira S Lac (Thompson et al. 2002). The best-fit curves are depicted; however, the 2.0/2.2 ratio data is effected by lower SNR and atmospheric water in the 2.0 m channel.

9. Narrowband vs. synthetic wideband diameters Visibility data from the spectrometer channels can also be used to synthesize a wideband visibility measurement which provides an improved SNR. From Colavita (1999), this is done using a photon-weighted average to the spectrometer visibilities such that and the weighting function is where “cds” represents correlated double sampling.

10. Narrowband vs. synthetic wideband diameters Due to the changing stellar atmospheric opacity in both the 2.0 and the 2.4 m channels (H2O, CO, CO2), wideband diameters tend to overestimate the size of R Boo by as much as 5%. This effect is greatest near phase 0.9, as seen in Figure 3. Minimum differences (NB-WB) are seen just before visual minimum, where R Boo is at its largest linear size.

11. Effective Temperature The bolometric flux was computed from available photometry with  > 1 m. From this value, the effective temperature is calculated using the 2.2 m narrowband angular diameters such that: Maximum Teff occurs just before visual maximum as seen in Figure 4, with a peak-to-peak temperature change of 360 K throughout R Boo’s cycle, and a relative temperature change of Tp-p / Tmean = 12%.

12. Multi-wavelength Diameters Observations of R Boo at both H-band (1.65 m) and K-band (2.2 m) were done only four days from each other (2% of visual phase period) in the 2000 observing season. These data were converted to UD diameters, and are shown in Figure 5. The given K-band shape is representative of the “O1” class (Thompson, 2002), typical of oxygen-rich Miras of early spectral type (M2-M4). Shown for comparison is a figure (Fig 6 herein) from Jacob and Scholz (2002), which represents a theoretical model (“P series”, Rp=241 R, Teff=2860K) from Hofmann, Scholz and Wood (1998) which were transformed to narrowband angular diameters. (The dots/crosses are from Thompson et al. 2002 for the oxygen-rich Mira S Lac.)

13. Comparison with theory From Jacob and Scholz (2002) – dots/crosses are for S Lac (Thompson et al, 2002) at various Rp

14. Discussion The Mira variable R Boo was observed over 5 pulsation periods with the Palomar Testbed Interferometer. This oxygen-rich Mira compares well to another oxygen-rich Mira S Lac in Paper I of the PTI Mira series (Thompson et al, 2002). Maximum atmospheric extension (and hence maximum opacity effects) occurs just before visual maximum, and the multi-wavelength diameters lend themselves well to the “P series” models of Hofmann, Scholz & Wood (1998) and Jacob & Scholz (2002). Departures from circular symmetry were statistically insignificant as evidenced in the use of two PTI baseline orientations. H2O maser emission about R Boo is minimal (Benson & Little-Marenin 1996) as well as SiO and OH masers (refs therein), coinciding with low mass loss (0.1 x 10-6 M / yr, Bowers & Hagen 1984). As suggested by Meixner et al (1997), dusty mass loss during the pre-planetary nebula phase occurs in an axially-symmetric manner.

15. Since departures from circular symmetry have not been detected interferometrically, nor evidence of maser emission in the literature to date, nor a high mass loss rate, it is unlikely R Boo has developed the “superwind” needed to shed its outer atmosphere to create a PPN. Thus, R Boo represents a Mira in its younger stages, with its period around 224 d (mean for oxygen-rich Miras is ~ 325 d), and its effective temperature very close to a theoretical parent star. Photometry obtained from the AFOEV over the 5 pulsation cycles observed at PTI show R Boo to pulsate in a fairly regular manner, as seen in Figure 7. This star also exhibits no evidence to be a symbiotic star (Kenyon & Gallagher 1983) nor a binary system (Blazit et al 1987).

16. The five epochs of PTI observations

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