STScI

Fine Guidance Sensor Instrument Handbook for Cycle 14

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Chapter 3: 
FGS Science Guide

3.1 The Unique Capabilities of the FGS
3.2 Position Mode: Precision Astrometry
3.3 Transfer Mode: Binary Stars and Extended Objects
    3.3.1 Observing Binaries: The FGS vs. WFPC2
    3.3.2 Transfer Mode Performance
3.4 Combining FGS Modes: Determining Stellar Masses
3.5 Angular Diameters
3.6 Relative Photometry
3.7 Moving Target Observations
3.8 Summary of FGS Performance
3.9 Special Topics Bibliography
    3.9.1 STScI General Publications
    3.9.2 Position Mode Observations
    3.9.3 Transfer Mode Observations
    3.9.4 Miscellaneous Observations
    3.9.5 Web Resources

This chapter serves as a brief guide to the scientific programs which most effectively exploit the FGS's capabilities. The advantages offered by the FGS are described in this chapter. A representative list of publications making use of FGS science and calibration data is included. Suitable strategies to achieve scientific objectives are outlined in Chapter 4.

3.1 The Unique Capabilities of the FGS

As a science instrument the FGS offers unique capabilities not presently available by other means in space or on the ground. Its unique design and ability to sample large areas of the sky with milliarcescond (mas) accuracy or better gives the FGS advantages over all current or planned interferometers.

The FGS has two observing modes, Position and Transfer mode. In Position mode the FGS measures the relative positions of luminous objects within its Field of View (FOV) with a per-observation accuracy of ~ 1 mas for targets with 3.0 < V < 16.8. Multi-epoch programs can achieve relative astrometric measurements with accuracies approaching to 0.2 mas.

In Transfer mode the FGS is used as a high angular resolution observer, able to detect structure on scales as small as 8 mas. It can measure the separation (with ~1 mas accuracy), position angle, and the relative brightness of the components of a binary system down to ~10 mas for cases where V < 1.5. For systems with a component magnitude difference of 2.0 < m < 4.0, the resolution is limited to 20 mas.

By using a "combined mode" observing strategy, employing both Position mode (for parallax, proper motion, and reflex motion) and Transfer mode (for determination of a binary's visual orbit and relative brightnesses of the components), it is possible to derive the total and fractional masses of a binary system, and thus the mass-luminosity relationship for the components.

Alternatively, if a double lined spectroscopic system is resolvable by the FGS, then the combination of radial velocity data with Transfer mode observations can yield the system's parallax and therefore the physical size of the orbit, along with the absolute mass and luminosity of each component.

In this chapter, we offer a brief discussion of some of the science topics most conducive to investigation with the FGS.

3.2 Position Mode: Precision Astrometry

A Position mode visit consists of sequentially measuring the positions of stars in the FGS FOV while maintaining a fixed HST pointing. This is accomplished by slewing the FGS Instantaneous Field of View (IFOV, see Figure 1.3) from star to star in the reference field. acquiring each in FineLock (fringe tracking) for a short time (2 to 100 sec.). This yields the relative positions of the observed stars to a precision of ~1 milli-arcsecond (mas).

With only three epochs of observations at times of maximum parallax factor (a total of six HST orbits), the FGS can measure an object's relative parallax and proper motion with an accuracy of about 0.5 mas. Several multi-epoch observing programs have resulted in measurements accurate to ~0.2 mas. Unlike techniques which rely upon photometric centroids, the accuracy of FGS measurements are not degraded when observing variable stars or binary systems. And techniques which must accumulate data over several parallactic epochs would have greater difficulty detecting comparably high frequency reflex motions (if present).

Further discussion of how these impacts will affect the observatory and the instruments can be found in a separate Handbook, the HST Two-Gyro Handbook for Cycle 14. See the Two-Gyro Handbook for detailed information. All text in this FGS Handbook assumes three-gyro control.

3.3 Transfer Mode: Binary Stars and Extended Objects

In Transfer mode, the FGS scans its IFOV across a target to generate a time-tagged (40 hz) mapping between the position of the IFOV (in both X and Y) and counts in the four PMTs. These data are used to construct the interferogram, or transfer function, of the target via the relation 

 Sx = (Ax - Bx) / (Ax + Bx)

as described in chapter 2. The data from multiple scans are cross correlated and co-added to obtain a high SNR transfer function.

In essence, Transfer mode observing is conceptually equivalent to sampling an object's PSF with milliarcsecond pixels. This enables the FGS to resolve structure on scales finer than HST's diffraction limit, making it ideal for studying close binary systems and/or extended objects.

The transfer function of a multiple star system is a normalized linear superposition of the S-Curves of the individual stars, with each S-curve scaled and shifted by the relative brightness and angular separation of the components. If the components are widely separated (> ~60 mas), two S-Curves are clearly observed in the transfer function, as illustrated in the left panel of Figure 3.1. Smaller separations result in merged S-Curves with modulation and morphology differing significantly from that of a single star. Figure 4.3 illustrates these points.

By using point source S-curves from the calibration library one can deconvolve the composite observed transfer function of a binary star into component S-Curves (done by either Fourier Transforms or semi-automated model fitting) to determine the separation, position angle, and relative brightness of the components. If enough epochs of data are available, the time-tagged position angles and angular separations can be used to construct the apparent relative orbit, from which one can derive the parameters P, a, i, and which define the true relative orbit. Note that the semi-major axis is an angular quantity; to convert it to a physical length, one must know the object's distance (which can be obtained from parallax measurements).

3.3.1 Observing Binaries: The FGS vs. WFPC2

The FGS, while capable of very-high angular resolution observations, is not an "imaging" instrument like HST's cameras. However, the ability to sample the S-curve with milli-arcsecond resolution allows the FGS to resolve structure on scales too fine for the cameras. To illustrate, we present a comparison between binary observations with HST's Planetary Camera (PC) and with FGS1r in Figure 3.1. The image at left is a PC snapshot image of the Wolf-Rayet + OB binary WR 146 (Niemela et al. 1998). To the right is a simulated FGS1r "image" of this binary shown at the same scale. With the 0.042" pixels of the PC, the binary pair is clearly resolved. Based on point-spread function (PSF) photometry, Niemela et al. publish a separation of 168  mas for this pair. In comparison, an analysis of the FGS "observation" of the binary yields a separation of 168  mas, a far more accurate result.

Figure 3.1: Comparison: PC Observation v. FGS Observation


 
The figure on the left is from an observation by Niemela et al. (1998) of the WR+OB binary WR 146. They measure an angular separation of 168 mas. The figure on the right is a simulation of an FGS1r observation of the same object. The separation of the stars could be measured to better than 1 mas.
 

Though a vigorous PC (or ACS/HRC) observing strategy involving multiple exposures and image recombination techniques (i.e, "drizzling") might improve the resolution of the binary, the accuracy of the measured separation would not match that achievable with the FGS. In addition, the total exposure time of such a PC program might exceed that of the FGS observation. Most importantly, the FGS can just as easily detect the components and accurately measure their separations for binaries as close as 12  mas, a feat not possible with HST's cameras regardless of the observing strategy.

In Figure 3.2, we show a TinyTIM simulation of a PC image of a 70 mas binary and an FGS observation of the same simulated pair. Note the PC image suggests - by it's shape - that the observed binary is not a point source. However, it would be difficult to determine an accurate component separation or brightness ratio from this image. This is not a problem for the FGS, where both components are easily resolved, and an accurate separation and mass ratio can be determined.

Figure 3.2: Simulated PC Observations v. FGS Observations of a 70mas Binary


 
The figure on the left is a TinyTIM simulation of a PC image of a 70 mas binary composed of stars of nearly equal brightness (no dithering). The figure to the right is an FGS simulation of the same observation. Note that the binary structure is far more obvious in the FGS fringes. The FGS can just as easily resolve binary systems down to 12 mas.
 

3.3.2 Transfer Mode Performance

The most relevant way to express the FGS Transfer mode performance is through its ability to detect and to resolve components of a multiple component system. Figure 3.3 is a plot of the predicted parameter space defined by the separation in milli-arcseconds and the relative brightness of the components of a binary system. The shaded areas are the domains of success in resolving binary systems for both FGS3 and FGS1r. The extension of FGS1r into the smaller separation parameter space is attributed to an optimized S-Curve achieved by proper adjustment of the articulating mirror assembly (see Chapter 2 for more details), and to the fact that its fringes are highly stable in time. (FGS3, by comparison, suffers a persistent random variability of its x-axis fringe which precludes it from reliably studying binary systems with separations less than about 20 mas.) These data originate from simulations and are supported by a special assessment test run aboard the spacecraft in May 1998 as well as GO science data (see Appendix 2 for more details).

Figure 3.3: Comparison of FGS1r and FGS3 Transfer Mode Performance


 

Table 3.1 contains the expected resolution limits for FGS1r. Columns 1 and 2 show the separation and accuracy for a single measurement, column 3 details the relative brightness limit needed to achieve that precision, and the last column is the apparent magnitude of the system. For example, a separation of 10 mas is detectable if the system is ~14 magnitudes or brighter and the magnitude difference of the components (m) is less than 1.0. Likewise, the separation of the components of a V=16.6 binary is measurable to an accuracy of about 2 mas if their separation is greater than ~15 mas and their magnitudes differ by less than 2.


Table 3.1: FGS1r TRANSFER Mode Performance: Binary Star
Minimum
Separation
(mas)
Estimated
Accuracy
(mas)
Maximum Mag
Maximum V
-
1.0
14.0
10a
-
1.0
15.0
15
2
2.0
16.6
20
1
2.5
16.2
20
2
3.0
16.2
50
1
3.5
15.5
1This represents detection of non-singularity. Reliable measurements of the angular separation might not be achievable.

3.4 Combining FGS Modes: Determining Stellar Masses

Stellar mass determination is essential for many astronomical studies: star formation, stellar evolution, calibrating the mass/luminosity function, determining the incidence of stellar duplicity, and the identification of the low-mass end of the main sequence, for example.

The combination of Position mode and Transfer mode observations is an effective means to derive a full orbital solution of a binary system. Wide-angle astrometry from a multi-epoch Position mode program can be used to measure the parallax, proper motion and reflex motion of a binary system. High angular resolution Transfer mode observations can be used to determine the relative orbit and differential photometry of the components. Figure 3.4 illustrates the benefit of this technique as applied to the low mass binary system Wolf 1062 (Benedict et al. 2001). The small inner orbit of the primary star was determined from Position mode measurements of the primary's position relative to reference field stars. The large orbit of the secondary low mass companion was derived from Transfer mode observations of the binary, which at each epoch yields the system separation and position angle. Combining these data allows one to locate the system barycenter and thereby compute the relative mass of each component. And with the parallax known (from the Position mode data), the total system mass, and hence the mass of each component, can be determined.

Further discussion of how these impacts will affect the observatory and the instruments can be found in a separate Handbook, the HST Two-Gyro Handbook for Cycle 14. See the Two-Gyro Handbook for detailed information. All text in this FGS Handbook assumes three-gyro control.

Figure 3.4: Relative Orbit of the Low-Mass Binary System Wolf 1062 AB


 
Figure 3.4 shows the orbits of the components of Wolf 1062 about the system's barycenter. This has been determined from both Transfer mode observations, which yield the relative orbit, and Position mode observations, which map the orbit of the primary relative to reference stars distributed about the FGS FOV (in effect establishing the inertial reference frame). Note that the Position mode data also yield the system's parallax and proper motion.
 

3.5 Angular Diameters

The FGS has been used (Lattanzi et al. 1997) to determine the angular diameters of non-point sources. The example given in Figure 3.5 shows the Transfer Function of a Mira-type variable superposed on the S-Curve of a point source (both observed with FGS3). The extended source - a disk of 78 mas - is clearly distinguishable from a point source. In addition to stellar discs, other objects which might be (or have been) resolved by the FGS include galactic nuclei, asteroids, and planetary moons.

Figure 3.5: Mira-type variable with a resolved circumstellar disk


 

3.6 Relative Photometry

While observing in Position mode, FGS3 serendipitously observed the outburst of a flare on the nearby star Proxima Centauri (Figure 3.6, see Benedict et al. 1998). The FGS has also been used to measure the relative flux of a star during an occultation of that star by the Neptunian moon Triton (Figure 3.7), and the data were subsequently used to examine the thermal structure of Triton's atmosphere (see Elliot et al. 1998 and Elliot et al. 2000).

The absolute FGS photometric response of FGS 3 has been stable at the 2% level over the past eight years (L. Reed, BFGoodrich). FGS1r is expected to be as stable or better. For relative photometry on time scales of orbits, the FGS has been shown to be stable at the 1 milli-magnitude level, thus affording an opportunity for 0.1-0.2% time series photometry.

Figure 3.6: Flare Outburst of Proxima Centauri as Observed with FGS3


 
Figure 3.7: Triton Occultation of the Star TR180 as Observed by FGS 3


 

3.7 Moving Target Observations

The FGS is suitable for the observation of solar system objects in both Position and Transfer modes. The technique to acquire the data is not as straightforward as standard HST moving target observations, but in cases where the target is not moving too rapidly, the observation is certainly feasible. We note that the FGS has been used in previous Cycles to observe Main Belt asteroids, both in Position mode and in Transfer mode. More detail on moving target observations can be found in Chapter 4.

3.8 Summary of FGS Performance

In Position mode, the FGS offers capabilities not achievable by other HST instrument or by the current generation of ground-based interferometers. These capabilities include:

Similarly, the FGS Transfer mode offers:

Additionally, mixed-mode observations - employing both Position mode and Transfer mode - allow the user to combine parallax, proper motion, and relative orbit information to derive the true orbit of a multiple-star system and a determination of stellar masses.

The FGS's two observing modes make it possible for the instrument to resolve structure in objects too faint for other interferometers and on scales too small for any imaging device, while simultaneously measuring the distance to that object. It is anticipated the FGS will be the sole occupant of this niche until the arrival of the long baseline interferometer in space, such as the Space Interferometry Mission (SIM), expected to launch in 2009.

3.9 Special Topics Bibliography

3.9.1 STScI General Publications

3.9.2 Position Mode Observations

3.9.3 Transfer Mode Observations

3.9.4 Miscellaneous Observations

3.9.5 Web Resources

Many additional documents, including Instrument Science Reports and ST Analysis Newsletters are available through the FGS web page: 

 http://www.stsci.edu/hst/fgs/
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