# Presentation: 273334

## 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***

## 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 R****mean**** = 216 ******** 40 R******** ****and a mean T****eff ****= 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. ***

## 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**

## 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/cm****2****/s (from photometry longward of 1 ********m )**
**Mean T****eff****: 2970 ******** 43 K**
**Mean linear radius: 216 ******** 40 R******** **

## 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**
**	****	****M****K**** = -7.32 and m****K**** = 2.10**
**======**
**608 ******** 112 pc   mean distance (********/m = 18%)**

## 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. **

## 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**

## 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.**

## 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.**

## Narrowband vs. synthetic wideband diameters

**Due to the changing stellar atmospheric opacity in both the 2.0 and the 2.4 ********m channels (H****2****O, CO, CO****2****), *****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.**

## 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 T****eff**** 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 ********T****p-p**** / T****mean**** = 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”, R****p****=241 R********, T****eff****=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.)**

## Comparison with theory

***From Jacob and Scholz (2002) – dots/crosses are for S Lac (Thompson et al, 2002) at various R******p***

## 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. H****2****O 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.**

**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).**

## The five epochs of PTI observations

## References

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**Blazit, Bonneau & Foy, 1987, A+AS, 71, 57**
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**Gezari et al, 1999, “Catalog of Infrared Observations”, 5****th**** edition (available on CDSweb.u-strasborg.fr)**
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**Jacob & Scholz, MNRAS, 336, 1377**
**Jura & Kleinmann, 1992, ApJS, 79, 105**
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***The authors gratefully acknowledge Kevin Rykoski and Jean Mueller of Palomar Observatory for their efforts in obtaining much of the data herein.***