OBSERVATIONS OF BINARY STARS WITH THE DIFFERENTIAL SPECKLE SURVEY INSTRUMENT. II. HIPPARCOS STARS OBSERVED IN 2010 JANUARY AND JUNE

Our method for measuring the pixel scale and orientation relative to celestial coordinates is essentially the same as described in Paper I. Briefly, we continue to use a slit mask that we can mount to the tertiary mirror baffle support structure in order to obtain a precise measurement of the pixel scale. When the mask is on the telescope, we take a speckle observation of a bright unresolved star. The slits of the mask (which are in the converging beam but may be effectively mapped back to the aperture plane) give rise to a sequence of linear features in the power spectrum of the speckle observation, with spacing directly related to the spacing of slit pairs on the mask. When combined with the telescope focal length, mounting surface position relative to the image plane, and the wavelength of the observation, the features can be used to provide the scale. Horch et al. (1999) provide more detailed information on this method.

We have found it important to rotate the Nasmyth port of the telescope to various angles during our mask calibrations in order to fully map out the dependence of the pixel scale on position angle that was discussed in Paper I. This is due to a small surface misalignment within the instrument and is visible in the back port of the DSSI optics package. We have again used the model of a tilted surface to calibrate and remove this effect in that channel; no misalignment was detected in the side port of the instrument. Another important consideration in the determination of our final scale values for this paper is the use of calibration stars with a wide variety of color; for the two runs discussed here, four sequences of mask files were taken, two in January and two in June, where the stars chosen ranged in spectral type from B6III to K3Iab. The color of the star changes the effective wavelength of the observation slightly, so that without a range of color, a systematic error in the pixel scale can result. Based on our mask results, we find that the side port has a scale of 21.766 ± 0.028 mas pixel⁻¹. The value for the back port is similar, but varies slightly with position angle due to the surface misalignment. It nonetheless has a similar percentage error to that of the side port, i.e., ∼0.13%. Since the astrometry presented in the next section is the average of both channels, we suggest that the uncertainty due to the scale calibration is 0.13%$/\sqrt{2} = 0.09$%.

We use sequences of short exposure (1 s) images of reasonably bright targets to establish the detector orientation. Between two successive exposures, the telescope is offset in a given direction by a small amount (typically 5 arcsec). By determining the centroid of the star in each of these frames and noting the change between exposures, it is possible to determine both the scale and the orientation, although we do not use the scale values in general because the mask results are typically of much higher precision. (Nonetheless, there were no major discrepancies between the two methods for the data presented here.) Offset images are generally taken each night and the results averaged. We did not find any significant change between the January and June runs, so that the final numbers used were the average values of both runs. The position angle offset of celestial coordinates relative to the pixel axes in the side port of the instrument was −538 ± 028, while in the back port, the figure obtained was +515 ± 018. Since our final position angles discussed in the next section are the average of both channels, we estimate that the uncertainty due to our offset measurements may be obtained by adding these two results in quadrature and dividing by two, yielding an orientation uncertainty of ∼017.

Our observing routine and reduction method also remain the same as discussed in Paper I. In all of the work presented here, the side port of DSSI was fitted with the 692 nm filter, the back port was fitted with the 562 nm filter, and our red–green dichroic was used. The filter transmission curves of these optics appear in Paper I; the full width at half-maximum of the transmission is 40 nm for both filters. Insofar as it is possible, we try to group our targets together on the sky and observe them in sequence, together with a bright point source calibrator. Unlike the results discussed in Paper I, however, the galvanometer mirrors were held stationary during the observation since the EMCCDs were read out fast enough to maintain good speckle coherence. The typical observation is a sequence of 1000 speckle 128 × 128 pixel subframes centered on the object, with a frame-integration time of 40 ms. Other frame times from 30 to 60 ms were tried, but 40 ms appears to give the highest signal-to-noise ratio for typical observing conditions at WIYN.

Our reduction method continues to be Fourier based, where we compute the average spatial frequency power spectrum for each observation, deconvolve the speckle transfer function by dividing by the power spectrum of the point source, and then compute a weighted least-squares fit of a fringe pattern to a masked version of the resulting function. (The mask sets to zero pixels in the Fourier plane that have low signal-to-noise ratio and low-frequency values judged to be in the seeing disk.) In order to determine the quadrant of the companion star, we compute a reconstructed image via bispectral analysis (e.g., Lohmann et al. 1983).

With the electron-multiplying gain function enabled, individual photons striking the EMCCD usually generate a signal large enough to clearly see above the read noise. Thus, the device has extremely low effective read noise while maintaining quantum efficiency above 90% through most of the visible spectrum. Although the dynamic range of the device is small in this configuration, the necessity to take short frames in speckle imaging renders this deficiency insignificant. The result is that the limiting magnitude of speckle observations is much fainter than with either low-noise CCDs, which suffer in comparison due to a higher read noise, or microchannel-plate-based devices such as intensified-CCDs (ICCDs), which typically have lower quantum efficiencies.

Tokovinin and his collaborators have made early and extremely effective use of EMCCDs in speckle observations (Tokovinin & Cantarutti 2008; Tokovinin et al. 2010). These papers have clearly shown the potential of these new devices in speckle imaging, leading to their acquisition by both our team and the speckle collaboration working at the Special Astrophysical Observatory 6 m Telescope (e.g., Docobo et al. 2010), among others. In our case, making the change to EMCCDs has been the deciding factor in the use of DSSI in the substantial ground-based follow-up work for Kepler and CoRoT, as the deeper limiting magnitude has made their targets accessible for the first time using speckle imaging at WIYN. While that theme will be developed further in a future paper that details those observations (S. B. Howell et al. 2011, in preparation), it is appropriate here to make a brief study of the detection capability for binary star work in general.

Figure 1(a) shows the magnitude difference obtained as a function of separation for all objects successfully resolved during the January and June runs (and tabulated in the next section). Figure 1(b) shows the same magnitude differences, but plotted as a function of V magnitude of the object. Both figures look very similar to diagrams of this nature that we have previously constructed (see, e.g., Figure 1 of Horch et al. 2010). For example, when plotted against separation, systems with a magnitude difference as large as approximately 5 can be detected through a wide range of separation, with decreasing sensitivity at small separations (<0.2 arcsec), down to a maximum Δm of approximately 3.5 at the diffraction limit. When plotted against V magnitude, systems with magnitude differences as large as 5 are detected at least as faint V = 10, with an apparent decrease as the V magnitude becomes fainter. However, most of the targets observed here are drawn from the Hipparcos Catalogue (ESA 1997), and this downturn is dominated by the apparent-magnitude distribution of those stars, few of which are fainter than magnitude 12. Furthermore, while nothing fainter than a V magnitude of 14 had been successfully detected at WIYN with our previous imaging detectors, Figure 1(b) shows two objects beyond that limit, namely WDS 20367+4021 = NML 2AB = WR 147 (V = 14.9) and WDS 14125+1636 = WSI 117 = LP 439-387 (V = 15.7). It is worth stating that these magnitudes appear to be somewhat uncertain; Niemela et al. (1998) quote magnitudes of the components of NML 2AB as 13.86 and 16.02 based on Hubble Space Telescope Wide Field Planetary Camera 2 images and therefore a system magnitude of 13.72. On the other hand, the Washington Double Star (WDS) Catalog has magnitudes of 15.0 and 17.2, resulting in a system magnitude of 14.87. The latter agrees well with what appears in the SIMBAD database,⁷ namely 14.89. In the case of WSI 117, while both the SIMBAD database and the WDS agree on a system magnitude of approximately 15.7, the count rate obtained during our observations was somewhat higher than what would be expected for a star of that magnitude (though our astrometry agrees well with that appearing in the WDS, up to a quadrant flip of the secondary).

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To demonstrate the data quality for faint targets, we show our standard reconstructed images for WSI 117 and NML 2AB in Figure 2, both in the 562 nm and the 692 nm filters. Comparing the images for WSI 117, the secondary appears brighter relative to the primary star in the 562 nm filter, indicating that the companion is bluer than the primary. On the other hand, for NML 2AB, the secondary is detected only in the 692 nm image, with a magnitude difference of over 2.0. This indicates that the companion is almost certainly much redder than the primary. (The 5σ detection limit at the relevant separation as defined in Section 3.3 for the 562 nm observation is approximately 4.5 mag.) The four images together indicate that, even at magnitudes fainter than 14, relatively good image quality can be obtained. Despite some uncertainty in the magnitudes of these objects, we conclude that the detection of companions is probably possible to at least 16th magnitude and possibly fainter, under good observing conditions.

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The fact that two data files are taken simultaneously in DSSI observations provides an important internal check on our derived astrometry. By comparing the results in both channels (which should yield the same value), we can easily characterize the repeatability of our position angle and separation measures. In Figure 3, we show the residuals obtained in both parameters as a function of the average separation. There is very good agreement between the two channels. In position angle, we find a mean difference of 003 ± 004 with a standard deviation of 075 ± 003. As seen in Figure 3(a), this scatter in position angle increases for small separations, as expected for a constant linear measurement uncertainty. If one considers the range of separations from 0.2 to 0.8 arcsec, then the standard deviation obtained in position angle is reduced to 044 ± 002.

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Figure 3(b) shows a nearly constant scatter in the separation residuals regardless of the system separation; we find a mean difference in separation measures between the two channels of −0.01 ±  0.11 mas with a standard deviation of 2.13 ±  0.08 mas. If one computes the expected scatter in position angle based on this figure (assuming the same linear measurement uncertainty in the direction orthogonal to separation), one obtains approximately 012/ρ, where ρ is measured in arcseconds. In the interval ρ = 0.2 to 0.8 arcsec, the predicted range of σ(Δθ) is 06–015 using this formula. We therefore claim that our scatter of 044 over this interval in separation is consistent with the scatter in separation residuals.

There are five objects in Table 1 which were observed on two different occasions. These are WDS 11008 + 3913 = YSC 5, WDS 13157 +  5424 = HDS 1858, WDS 13514 +  2620 = YSC 50, WDS 17077 +  0722 = YSC 62, and WDS 19178 +  5950 = HDS 2729, which span a range in V magnitude from 5.07 to 14.02. We have computed the standard deviation of the differences between the two measures and find values of 033 ± 010 in position angle and 1.4 ± 0.4 mas in separation. Because the astrometry from both channels has already been combined in these measures, we would expect them to be smaller than the previous results by a factor of $\sqrt{2}$. If one converts the position angle standard deviation to a linear measurement standard deviation using the average separation of the five objects, one obtains 1.8 mas. Then averaging this with the 1.4 mas result for separation (since they represent independent, i.e., orthogonal, coordinates), we obtain 1.6 mas, which is very close to $2.13/\sqrt{2} = 1.51$ mas. Finally, we note that both this comparison and the previous one involve independent measures drawn from a distribution of width σ, which should be approximately the same in both cases. When forming the subtraction between two such measures, the resulting distribution will have a width $\sqrt{2} \cdot \sigma$. For this reason, our final repeatability estimate for a single observation appearing in Table 1 is approximately 1.5 mas divided by $\sqrt{2}$ or in other words about 1.1 mas.

Repeatability of measurements between the two channels is not the same as measurement precision of the observational program overall; the latter can be affected by factors such as the long-term run-to-run stability and accuracy of the pixel scale and orientation calibrations, seeing variation, zenith angle variation, small instrumental changes brought about by mounting, dismounting, and other handling of the instrument, diurnal temperature variations at the observatory, systematic errors in data reduction when comparing to other speckle observers, and other factors. In general, the true measurement precision of the program will be larger than the repeatability results. To investigate the true measurement accuracy and precision for the current data set, we have compiled the list of objects from Table 1 that have Grade 1 or Grade 2 orbits in the Sixth Orbit Catalog of Hartkopf et al. (2001a). The objects and the original orbit references are shown in Table 3. Since these orbits are the highest quality that currently exist, representing the work of several different observing teams in most cases, they are the best way to judge true measurement accuracy, albeit in a preliminary fashion given that only two observing runs are represented in this paper. They can also give some indication of the true measurement precision, if the uncertainties in the orbits are accounted for in the process. Figure 4 shows the results of these comparisons. In these two plots, the orbits of highest quality, as judged by the uncertainty in the ephemeris position at the time of the observation, are shown as filled circles. We calculate this by taking the published uncertainties in the orbital elements and performing an error propagation to the position angle and separation for a given observation date. Specifically, for the position angle comparison, the filled circles are systems where the derived uncertainty in the position angle was 20 or less, and for the separation comparison, the derived uncertainty is 2 mas or less. We find that for these highest quality comparisons, the mean position angle residual is −009 ± 025 with a standard deviation of 056 ± 018 while for the separation residuals, the mean value is −1.26 ± 1.67 mas with a standard deviation of 3.33 ± 1.18 mas. The separation values are clearly affected by the data point for STF 1728 at a separation of approximately 0.6 arcsec. We note that although the orbit used was that of Mason et al. (2006) and has therefore been relatively recently recalculated, our point is off by nearly the same magnitude and in the same direction as that of Mason et al. (2009). If this point is excluded (which admittedly leaves only three other high-quality comparisons), then the mean value shrinks to 0.37 ± 0.50 mas with a standard deviation of 0.86 ± 0.35 mas. This latter figure by itself is smaller than the average uncertainty derived from the orbital ephemerides (1.23 mas). While this is not yet a large enough sample to draw any hard conclusions, there is no evidence at this point for any significant deviations from published high-quality orbits. Furthermore, a true measurement precision of between 1 and 2 mas would seem to be a reasonable guess given that the orbits themselves contribute a significant portion of the errors obtained here.

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As this is the first large data set that we have obtained with the two EMCCDs, it is our first opportunity to investigate the photometric precision of these devices in the context of speckle imaging. In previous papers (e.g., Horch et al. 2004), we have discussed the utility of considering where the secondary star lies within the isoplanatic patch of the primary star in order to determine if the photometry derived from a given speckle observation can be judged to be relatively free of speckle decorrelation effects. To that end, one can compute the ratio

$$\begin{equation} q = \frac{\rho }{\delta \omega } \propto \rho \omega, \end{equation} \tag{ 1 }$$

where ρ is the separation of the two stars in arcseconds, δω is the size of the isoplanatic angle, and ω is the seeing. (The isoplanatic angle is known to be inversely proportional to the seeing.) This relationship determines the separation as a fraction of the isoplanatic patch size. Defining q' = ρω in arcseconds squared, we can then plot the difference between the observed magnitude difference from our observations and the magnitude difference appearing in the Hipparcos Catalogue as a function of q'. This is shown in Figure 5(a) for all observations in the 550 nm filter appearing in Table 1 and having an uncertainty in the Hipparcos magnitude difference of less than 0.3 mag. The graph shows the typical trend that we have observed at WIYN before: a difference that is relatively flat for low values of q', under 0.6 arcsec squared, but a tendency for points to lie above zero at larger values of q', meaning that the speckle magnitude difference is larger than that of Hipparcos. This is consistent with decorrelation between primary and secondary speckle patterns. In addition, the effective field of view with the EMCCDs is smaller than that of the CCDs previously used (∼2.8 × 2.8 arcsec with the EMCCDs versus ∼3.7 × 3.7 arcsec with the CCDs), which means that it is possible that in poor seeing and/or at large separations, image cropping will cause some loss of light from the primary, secondary, or both. Depending on the centering of the object within the detector subarray, it is possible to obtain either a larger or a smaller magnitude difference than that of the object due to this effect. However, at low values of q', we expect that image cropping is a small effect, as is speckle decorrelation. For these reasons, we have not reported magnitude differences in Table 1 if the q' value for the observation is above 0.6 arcsec squared.

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Another factor complicating the situation in Figure 5(a) however is the color difference between the Hipparcos H_p filter and the 562 nm filter of DSSI. Even though both filters are reasonably close to the Johnson V-band filter in center wavelength, the 562 nm filter is much narrower and slightly redder than the H_p filter. To minimize these differences, we consider a subsample of the data which has a B − V less than +0.6 and also have an uncertainty in ΔH_p of less than 0.10 mag. In Figure 5(a), these are drawn as filled circles. These points show a much tighter clustering in the figure. They have a mean value of 0.03 ± 0.02 and the standard deviation is 0.098 ± 0.012 mag. Given that the average uncertainty in ΔH_p for these points is 0.051 mag, we may subtract this number in quadrature from the 0.098 mag result to arrive at an estimate of the single-measurement precision for our observations, $\sqrt{0.098^2 - 0.051^2} = 0.084$ mag. This same subset of objects is plotted in Figure 5(b) with the ΔH_p value as a function of our measured Δm at 562 nm. The mean line of the data lies very close to the y = x line.

In Horch et al. (2010), a further data cut of 1.0 < ΔH_p < 4.0 was applied when comparing Hipparcos magnitude differences with speckle measures. The rationale for omitting large magnitude differences (>4.0 mag) was that the uncertainty in magnitude difference can be expected to increase that end of the diagram and thus an aberrant point might bias the mean value obtained. On the other hand, at small magnitude difference, the argument was made that a systematic error can be expected since a negative magnitude difference is normally reported as a positive value with a quadrant flip. While we are in agreement with the quadrant determined by Hipparcos for the five cases with ΔH_p less than 0.5 mag here, the lack of intervening data in one case (HIP 13637, ΔH_p = 0.13) and disagreement in quadrant assignment between observers in another case (HIP 8019, ΔH_p = 0.20) make it impossible to determine the proper quadrants with certainty at present. If the data cut 1.0 < ΔH_p < 4.0 is applied to the current data set, then the mean Δm(562 nm) − ΔH_p residual is reduced to 0.00 ± 0.02 with σ = 0.088 mag. Again using the average uncertainty in ΔH_p for these points, which is 0.053 mag in this case, we may subtract that in quadrature from the σ value to obtain a measurement precision estimate of 0.070 mag.

One may also use the five objects observed twice to estimate the photometric measurement precision. By computing the standard deviation of the difference between the magnitude differences in each filter, we obtain σ(Δm₁ − Δm₂) = 0.11 ± 0.03. However, this is the subtraction of two measures drawn from the same distribution, hence the single-measurement uncertainty is 0.11 divided by $\sqrt{2}$, in other words, 0.08 ± 0.02. Overall, we conclude that (1) if any systematic difference exists between our data and those of Hipparcos, that difference is less than 3 ± 2 hundredths of a magnitude and (2) our photometric measurement precision for a single observation is 0.08 mag or less for magnitude differences less than 4. We hope to refine these conclusions with future data.

Table 2 contains 130 cases where a secondary was not detected in an observation judged to be high in quality. As previously discussed, we compute reconstructed images via bispectral analysis of all observations that we take. For an observation where a component is found, that image is then used to make the quadrant determination before completing the analysis by fitting the object's average spatial frequency power spectrum with a fringe pattern. However, with the EMCCDs, these reconstructed images are often extremely high in quality and can be used to set limits on the brightness of a possible companion, that is, to answer the question of how bright the companion could be and still fail to be detected.

In this regard, we note the excellent work of Tokovinin et al. (2010), who were also working with an EMCCD and discussed the detectability of companions. We follow that work to a certain extent and obtain comparable results, but because we work with reconstructed images and not autocorrelation functions as they did, our method is not exactly the same. In our case, we consider every local maximum in the reconstructed image as a potential stellar signal and compute the implied magnitude difference in each case. One may then plot these magnitude differences as a function of separation from the central star and compute the standard deviation of these values within bins of separation. We choose bins centered at 0.2, 0.4, 0.6, 0.8, and 1.0 arcsec from the primary star with a full width of 0.1 arcsec, corresponding to annuli centered on the primary star on the image plane. We then define the 5σ detection limit as the magnitude difference corresponding to the mean peak value in the bin plus five times the standard deviation of these peak values.

Reconstructed images also have local minima, usually with a value less than zero, since any background is in effect removed in the process of reconstructing the image. We studied the statistical properties of these values as well, finding that the distribution of minima is the mirror image of the distribution of maxima: the mean value is usually close to the negative of the mean value for positive peaks, and the standard deviations are usually similar. Therefore, to calculate the best possible value for the 5σ detection limit, we have averaged the value obtained from both maxima and minima. To illustrate these distributions, we have shown a sample result in Figure 6. We show the magnitude difference corresponding to each maximum and minimum in the image (taking the absolute value of the minima prior to computing their magnitude differences). Also shown in these plots is a cubic spline interpolation of the 5σ detection limit from 0.2 to 1.0 arcsec. Below 0.2 arcsec, the magnitude differences obtained tend to be significantly smaller than above this value (and there are fewer peaks to work with); this same behavior was also noted in Tokovinin et al. (2010) and is presumably related to the well-known decrease in signal-to-noise ratio in the high-frequency portion of the power spectrum in speckle observing. For the 5σ detection limits appearing in Table 2, the value at 0.2 arcsec is given.

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