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Prototypical Operations Support Tools for NASA Interferometer Missions: Applications to Studies of Binary Stars Using the Palomar Testbed Interferometer Next: Correction of Systematic Errors in Differential Photometry
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Bambery, R. & Backus, C. 2001, in ASP Conf. Ser., Vol. 238, Astronomical Data Analysis Software and Systems X, eds. F. R. Harnden, Jr., F. A. Primini, & H. E. Payne (San Francisco: ASP), 369

Prototypical Operations Support Tools for NASA Interferometer Missions: Applications to Studies of Binary Stars Using the Palomar Testbed Interferometer

Raymond J. Bambery and Charles Backus
Jet Propulsion Laboratory, Caltech, Pasadena CA 91109

Abstract:

The Palomar Testbed Interferometer (PTI) is a 110-meter baseline K-Band infrared interferometer located at Palomar Mountain, California. In 1999 an effort was started to provide more observer-friendly observation planning and monitoring tools, such as might be used in NASA interferometer missions. This session illustrates how these prototype tools aid in the observation of spectroscopic binary stars. Animations, using IDL, show how the measured visibilities relate to the positions of the secondary star during its orbital period.

1. Introduction

The Palomar Testbed Interferometer (PTI) is a two-element infrared interferometer located at Palomar Mountain, San Diego County, California (Colavita 1999). Although it has 3 telescopes, only two of them (1-baseline) can be used at one time. PTI was developed as a proof-of-concept for three NASA optical and infrared interferometers: the Keck Interferometer (a ground-based visible and infrared interferometer), the StarLight Mission (a space-based formation-flying visible wavelength interferometer) and the Space Interferometry Mission (a space-based visible astrometric interferometer). In spite of its testbed origins, PTI is a fully-functional astronomical interferometer capable of performing scientific investigations. From 1997-98 an off-line suite of routines performed analyses on spectroscopic binaries, stellar diameters and atmospheric modeling. In 1999 an effort was undertaken to prototype mission operations support tools at PTI. This session illustrates how these prototype tools aid in the observation of spectroscopic binary stars.

2. PTI Data

2.1. Astrometric Precision

PTI has a fringe spacing of $\sim$ 5.0milliarcseconds (mas) in the K-Band infrared (2.0-2.4 microns) for its 110-meter North-South baseline. By comparison, the Hubble Space Telescope WFPC-2 camera has a pixel size of $\sim$ 46mas and a point spread function at Full-Width Half-Maximum of 50mas (Figure 1).

**Figure:** PTI resolution compared to HST.
$\begin{figure} \epsscale{0.8} \plotone{D-13-01a.eps} \end{figure}$

2.2. PTI Observables

In its simplest operating mode PTI yields unphased visibility (actually visibility squared), which is the fringe contrast of an observed brightness distribution on the sky normalized to [0:1]. As described by Boden (1999) the Visibility modulus, V, for a single star in a uniform disk model is:

$\begin{displaymath} V = 2 J_1 (\pi B\theta /\lambda) / (\pi B \theta / \lambda) \end{displaymath}$

(1)

where

is the first order Bessel function, B is the Projected baseline vector magnitude at the star position, in meters, $\theta$ is the apparent angular diameter of star, in radians, and $\lambda$ is the center-band wavelength, in meters. Visibility is related to the angular size of the star. When the size is point-like relative to the fringe spacing then the visibility approaches unity, but as the size approaches the fringe spacing ( $\sim$ 5.0mas) the visibility approaches zero.

Double star visibility squared in a narrow pass-band is:

$\begin{displaymath} V^2 = V_1^2 + V_2^2 r^2 + 2r V_1 V_2 \cos (2 \pi {\bf B} \cdot {\bf s}/ \lambda) / (1 + r)^2 \end{displaymath}$

(2)

where $V_{1}$ and $V_{2}$ are visibility moduli for each component, r is the brightness ratio between primary and secondary, B is the projected baseline vector at the star position, and s is the primary-secondary angular separation vector on plane of sky. Since the angular separation of the two stars in the spectroscopic binary is greater than the fringe spacing, visibility goes to a maximum when the centers of the two stars lie on fringe maxima (multiples of the fringe spacing). Visibility goes to a minimum when the center of the secondary star lies on a fringe minimum. (The center of the primary star is always on a fringe maximum.)

Delay line jitter, the measured movement of the delay position of the central fringe (measured in nanometers) over the duration of the integration time, is converted to phase error in radians. Jitter provides a measure of both the instrument and atmospheric stability for each observation and yields the formal errors in the visibility calculation. Observations on each target are accompanied by measurement of calibrator targets, whose angular sizes are computed from astrophysical models. Visibilities from the calibrators are used to determine the system (instrumental and atmospheric) response for a nightly run.

2.3. Observation Program

During 1999 $\alpha$ -Andromedae, a B8 IVmnp spectroscopic binary, was observed on 7 nights over 75 days of $\alpha$ -Andromedae's 96.7-day period. Using the visibilities and baseline orientation from observations at PTI, combined with the radial velocity semi-amplitudes, K1 and K2 from Ryabchicova (1999), allowed monitoring of the orbital motion of the secondary star.

3. Tools

For the years 1997-98, PTI science observers used software developed by the instrument engineers to monitor their nightly runs. However, this software only manages the current target observation and has no ability to recall earlier observations. The night observer would run an off-line batch process to display the earlier observations to note trends in the instrument performance or seeing conditions. In 1999, an effort was started to provide more observer-friendly observation planning and monitoring tools. For example, a science analysis routine was modified to provide a real time monitoring tool, rtvis. The output of rtvis is read by a Java tool that continually monitors instrument output as the data is collected.

**Figure:** PTI Night 261: (a) visibility vs. time, (b) jitter vs. time.
$\begin{figure} \epsscale{1.0} \plotone{D-13-01b.eps} \end{figure}$

Figures 2a and 2b show two of the diagnostics that summarize the results of an observation. Figure 2a shows a typical night (Night 261 in 1999) for the variation of visibility of $\alpha$ -Andromedae over $\sim$ 2 hours. Figure 2b shows the corresponding jitter value for the same period. Note that PTI is queue-scheduled for a number of different observers and the figures show these other observations. The values for $\alpha$ -Andromedae (HDC358) and its calibrators HDC1404 and HDC166 are circled in both figures. Note the variation of visibility as the secondary star passes through a fringe maximum and minimum. An IDL animation was created from this data, radial velocity data and orbital parameters. Figure 3 is one frame from that animation and shows the orbit of the secondary around the primary. The width of the arrows extending downward from each star through the fringe pattern indicates the relative contribution of each star to the total visibility. The two lower panels show the visibility values on the left and the baseline orientation on the right. During the animation the values for each observation are highlighted on these panels.

Acknowledgments

The research described in this article was carried out by the Jet Propulsion Laboratory, California, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. A special thanks to Dr. Andrew F. Boden of Caltech's Interferometry Science Center for numerous and valuable discussions, comments, and clarifications of interferometric observations of binary stars at PTI.

**Figure:** PTI Observations vs. Orbit of $\alpha$ -Andromedae.
$\begin{figure} \epsscale{0.6} \plotone{D-13-01c.eps} \end{figure}$

References

Boden, A., et al. 1999, ApJ, 515, 356

Colavita, M., et al. 1999, ApJ, 510, 505

Ryabchicova, T., Malanuschenko, V., & Adelman, S. 1999, A&A, 351, 963

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