The K-Band Intensity Profile of R Leonis Probed by VLTI/VINCI

The K-Band Intensity Proﬁle of R Leonis Probed by VLTI/VINCI

D. Fedele1,2,M.Wittkowski1,F.Paresce1,M.Scholz3,4,P.R.Wood5,and S. Ciroi2

1 European Southern Observatory, Garching bei München, Germany [email protected] 2 Dipartimento di Astronomia, Università di Padova, Italy 3 Institut für Theoretische Astrophysik der Universität Heidelberg, Germany 4 School of Physics, University of Sydney, Australia 5 Research School for Astronomy and Astrophysics, Australian National University, Canberra, Australia

Summary. We present near-infrared K-band interferometric measurements of the Mira star R Leonis obtained in April 2001 and January 2002 with VLTI/VINCI. The April 2001 measurements indicate a center-to-limb intensity variation (CLV) that is clearly different from a uniform disk (UD) intensity profile. We show that these measured visibility values are consistent with predictions from recent self-excited dynamic Mira model atmospheres. We derived high-precision Rosseland diameters for the two epochs and, together with literature estimates of the distance and +50 +50 the bolometric flux, we find linear radii of 350−40 R and 320−40 R and effective temperatures of 2930 ± 270 K and 3080 ± 310 K, respectively.

1 Introduction

Mira stars are cool, low-mass, pulsating variables located on the asympotic giant branch of the Hertzsprung-Russel diagram and that exhibit a conspicous mass-loss. Because of the low temperatures, molecules are present in their extended atmospheres, and dust is formed at larger distances from the star. In this paper, we present a comparison of near-infrared K-band VLTI/VINCI interferometric observations of R Leo with predictions by self-excited dynamic Mira model atmosphere ([10, 23, 13, 14]). R Leo is an oxygen-rich Mira star with spectral type M6e-M8IIIe-M9.5e, a period of 310 days, a V magnitude of 4.4-11.3 ([8]), and a mass-loss rate −7 of ∼ 1 ×10 M/yr ([3, 9]). [20] measured a relatively low dust emission coeﬃcient of 0.23, i.e. the ratio of the total emission of the dust to the total emission of the star in the mid-infrared. We use a parallax value of 8.81 ± 1.00 mas as given by [26], which is the weighted average of the values by [5] and [19]. [27] derived a mean bolometric magnitude mbol=0.65 with total (peak-to-peak) amplitude Δmbol=0.63. 96 Fedele et al. 2Observations

The R Leo interferometric data were obtained on 1 & 3 April 2001 (JD = 2452003, stellar phase φvis =0.08) and on 20 January 2002 (JD = 2452295, φvis =1.02) with the ESO Very Large Telescope Interferometer (VLTI) equipped with the K-band commissioning instrument VINCI ([6]). The VLTI test siderostats were used on stations E0 and G0 forming an unprojected ground baseline length of 16 m. The calibration of the visibility values was performed as described in [25], using a weighted average of all transfer function values obtained during the night. In order to derive eﬀective temperatures from the measured angular radius and the bolometric ﬂux we use the mean bolometric magnitude and its amplitude given by [27].

3Comparisonwithmodels

Our measured R Leo squared visibility amplitudes are shown in Fig. 1 together with a typical model prediction for each epoch based on the P model series by [10, 23, 13, 14]. The P model series is complete self-excited dynamic model atmospheres based on fundamental mode pulsation. For the details of the model calculations, we refer [10]. The parent star of the here considered P series has solar metallicity, luminosity L/L=3470, period 332 days, mass M/M=1.0, radius R/R=241 ([10]). In order to characterize the angular diameter of the fitted CLV, any well-defined reference radius of the model CLV can be used, such as the Rosseland radius or the 1.04 μm continuum radius. Physically most meaningful may be a true continuum radius, such as the 1.04 μm radius, which is not affected by time variable molecular con- tamination (see [10], [15, 13, 14]). In the following, the Rosseland radius is mainly used as reference quantity, as is usual in the literature. The Rosseland angular diameters we found for the two epochs are

ΘRoss(April 2001, phase 0.08) = 28.5 ± 0.4 mas and ΘRoss(January 2002, phase 1.02) = 26.2 ± 0.8mas. The Rosseland angular diameter at the variability phase closer to the maximum (1.02) is smaller by ∼ 8 % than that at variability phase 0.08. This is consistent with pulsation models (see, e.g. [13] and [14]). Together with the adopted values for π and fbol, these angular diameters for April 2001 and +50 +50 January 2002 correspond to linear radii of 350−40 R and 320−40 R,andto eﬀective temperatures of 2930 ± 270 K and 3080 ± 310 K, respectively.

4 Conclusions

We have compared VLTI/VINCI observations of the Mira star R Leonis to recent self-excited dynamic models. We ﬁnd that these model CLVs for the R Leo Intensity proﬁle probed by VINCI 97

1.0 1.0 R Leo, Apr. 2001 R Leo, Jan. 2002 0.8 UD 0.8 UD P22 P30 0.6 0.6

0.4 0.4

0.2 0.2

Squared visibility amplitude 0.0 Squared visibility amplitude 0.0 0 10 20 30 40 50 0 10 20 30 40 50 Spatial frequency B/λ (1/arcsec) Spatial frequency B/λ (1/arcsec) 0 0 0.14 0.14 R Leo, Apr. 2001 R Leo, Jan. 2002 0.12 UD 0.12 UD 0.10 P22 0.10 P30 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 Squared visibility amplitude 0.00 Squared visibility amplitude 0.00 30 32 34 36 38 30 32 34 36 38 Spatial frequency B/λ (1/arcsec) Spatial frequency B/λ (1/arcsec) 0 0

P22 P30 1.5 R = 1.10 R 1.5 R = 1.03 R 50% p 50% p R = 1.32 R R = 1.13 R Ross p Ross p R = 1.26 R R = 1.14 R 1.0 Cont p 1.0 Cont p SiO maser ring radii Cotton et al. (2004) Rel. Intensity Rel. Intensity 0.5 0.5

0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 R/R R/R p p

Fig. 1. (Top) Measured R Leo squared visibility amplitudes obtained in April 2001 and January 2002, together with the well fitting P22 and P30 models predictions. For comparison, the UD curve is shown as well. (Bottom) CLV prediction from the P22 and P30 model corresponding to the model visibility curves above. The thin lines denote the monochromatic CLVs while the thick line denotes the CLV averaged over the VINCI sensitivity function. Indicated are also the Rosseland radius, the 1.04μm true continuum radius, as well as the radius at which the filter-averaged CLV drops by 50%. The mean SiO maser ring radii measured by [2] close in time to our April 2001 data are indicated by the arrows. phases of our observations are consistent with our measurements. The corre- spondence of our obtained linear radii with model radii of the fundamental mode pulsation models used is in agreement with the general recent conclusions that Mira stars pulsate in fundamental mode. Two recent works ([28] and [17]) show accordance with predictions by the P-model series and clear deviation from UD profile for post-maximum observations of o Cet and R Leo. It is remarkable that the two stars appear to show similar CLVs, in agreement with the P model series, while their lightcurves and variability amplitudes are different. These findings increase our confidence in these dynamic Mira star models, which are often used to transform broad-band filter-specific UD diameters into more meaningful Rosseland or continuum diameters. More de- tailed observations are desirable in the future in order to better constrain the models. Such observations should probe the CLV at a larger range of spatial 98 Fedele et al. frequencies. In addition, measurements with high spectral resolution in both true continuum and certain molecular bands with AMBER will be useful in order to separate line-forming and continuum-forming layers. Moreover, monitoring of the observed CLVs in time over several cycles with a resolution of ∼ 10% of the variability period are desirable in order to investigate the strong model-predicted CLV variations with variability phase and cycle.

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