Millions of Multiples: Detecting and Characterizing Close-Separation Binary Systems in Synoptic Sky Surveys

TLDR: BinaryFinder as discussed by the authors uses point-spread-functions (PSF) ellipticity measurements across wide-field survey images to search for close binaries by using precision measurements of PSF ellipticity across wide field images.

Abstract: The direct detection of binary systems in wide-field surveys is limited by the size of the stars' point-spread-functions (PSFs). A search for elongated objects can find closer companions, but is limited by the precision to which the PSF shape can be calibrated for individual stars. We have developed the BinaryFinder algorithm to search for close binaries by using precision measurements of PSF ellipticity across wide-field survey images. We show that the algorithm is capable of reliably detecting binary systems down to approximately 1/5 of the seeing limit, and can directly measure the systems' position angles, separations and contrast ratios. To verify the algorithm's performance we evaluated 100,000 objects in Palomar Transient Factory (PTF) wide-field-survey data for signs of binarity, and then used the Robo-AO robotic laser adaptive optics system to verify the parameters of 44 high-confidence targets. We show that BinaryFinder correctly predicts the presence of close companions with a <5% false-positive rate, measures the detected binaries' position angles within 2 degrees and separations within 25%, and weakly constrains their contrast ratios. When applied to the full PTF dataset, we estimate that BinaryFinder will discover and characterize ~450,000 physically-associated binary systems with separations <2 arcseconds and magnitudes brighter than R=18. New wide-field synoptic surveys with high sensitivity and sub-arcsecond angular resolution, such as LSST, will allow BinaryFinder to reliably detect millions of very faint binary systems with separations as small as 0.1 arcseconds.

Figures

Figure 6. Ellipticity distributions of 1200 artificial point sources and 1200 randomly chosen PTF objects (top: e1; middle: e2; bottom: e). As can be seen in the histograms, the frequency of the artificial point sources goes to zero for magnitudes of e1 or e2 greater than ≈0.015 or for e greater than ≈0.02. In contrast, the real PTF object distributions have extended tails beyond those ellipticity values.

Figure 7. Ellipticity distributions of the 100,000 PTF targets in the Robo-AO binary discovery target area.

Figure 8. Robo-AO adaptive optics images of the binarity test targets. Each image is 10 by 10 arcsec in size; east is toward the left and the images are rotated by 23.◦5 counterclockwise with respect to a northeast axis. The images are shown with linear scaling with levels selected to best display the binarity (or lack thereof) of each of the targets. The ellipses indicate the predicted binary orientation based on the relative magnitudes of the e1 and e2 parameters; the color indicates confidence level of the predicted companion (red: no companion; yellow: possible companion; green: very likely companion). The order of targets is the same as that of Table 1.

Figure 10. Left: the change in ellipticity with seeing (as a fraction of the magnitude of ellipticity) for the binaries we imaged with Robo-AO. For larger separations, the ellipticity becomes less responsive to the FWHM. Middle: comparison between the separations estimated from PTF data alone and the Robo-AO measured separations; the correlation shows separation measurement at ∼25% precision. Right: comparison between the PTF ellipticity divided by PTF separation, and the Robo-AO measured flux ratio. Although the correlation is weak, there is a significant excess of points toward the lower left, suggesting that the contrast ratio of the binaries can be weakly constrained using PTF data alone.

Figure 1. Partitioning of image (part of PTF data set). The images are 2048 by 4096 pixels with a 1.′′01 pixel size. The red grid divides the image into eight smaller subsections about 800 by 800 pixels in size, each of which will be corrected for anisotropy with a separate polynomial fit. The larger (1200 × 1200) blue square which encloses one of the partitions of the red grid shows the region from which the fit will be derived for that particular partition.

Table 1 Robo-AO Test Targets, Ordered by Increasing PTF-measured Ellipticity

Frequently asked questions

Q1. What have the authors contributed in "C: " ?

The authors show that the algorithm is capable of reliably detecting binary systems down to ≈1/5 of the seeing limit, and can directly measure the systems ’ position angles, separations, and contrast ratios. The authors show that BinaryFinder correctly predicts the presence of close companions with a < 11 % false-positive rate, measures the detected binaries ’ position angles within 1◦ to 4◦ ( depending on signal-to-noise ratio and separation ), and separations within 25 %, and weakly constrains their contrast ratios. 

Q2. What was the basic method used to determine the proper motion of the objects?

The basic method was to adopt astrometric uncertainties when given, adopt characteristic numbers when not given (i.e., 200 mas at each epoch for USNO-B1), and then compute a weighted fit for the proper motion. 

Q3. How do the authors measure ellipticities in a CCD?

Undersampled images with FWHMs close to the pixel scale of the CCD cannot accurately measure ellipticities because the ellipticity measurement is then very sensitive to the location of the object relative to the pixel grid. 

Q4. What was the diffraction limit for the target list?

The Robo-AO system provided diffraction-limited resolution (∼0.1 arcsec at these visible wavelengths) for all observed targets, in 1–2 arcsec seeing conditions; the entire target list was observed in a total of only ∼2.5 hr. 

Q5. How many observations do the authors need to obtain an accurate fit of ellipticity with seeing?

The authors require at least 30 separate observations of a target in order for us to obtain an accurate fit of ellipticity with seeing, and the authors also require several hundred sufficiently bright sources within their image for PSF measurement (the last requirement is satisfied by essentially all PTF images). 

Q6. What are the measurements of the ellipticity of the stars in their images?

In order to measure the necessary parameters of all the stars in their images (using Equations (1)–(10)), the authors require centroid coordinates and FWHM measurements of the PSF of each source. 

Q7. How can the authors predict the separation of binary members?

Using the measured relation to predict the Robo-AO measured separation on the basis of PTF data alone confirms that BinaryFinder can measure the binary separations to ∼25% precision. 

Q8. What is the crossover point between single stars and high-confidence binaries?

The crossover point between single stars and high-confidence binaries occurs at the ellipticities predicted by their artificial point source simulations (Section 3), although the >80% binarity fraction of the targets with ellipticities between 0.01 and 0.02, compared to the zero binarity fraction at lower ellipticities, suggests that a less conservative limit could be set for many science programs. 

Q9. How did the authors make the anisotropy dependent on the location of the CCD?

In order to make this anisotropy dependent on the location within the CCD, the authors placed four reference anisotropy kernels at the four corners of their CCD. 

Q10. How many times smaller was the change in the ellipticities of the objects in each?

The authors found that, when using a third degree instead of second degree fit of the p1 and p2 parameters, the resulting change in the corrected ellipticities of the objects in each image was approximately nine times smaller than if the authors used a second degree fit but varied the raw ellipticities and PSF anisotropy parameters by random values consistent with their measurement error. 

Q11. What is the way to correct the ellipticities of high-flux objects?

While applying the algorithm to the PTF images, the authors noticed that the ellipticities of high-flux objects were not corrected accurately to zero using a fit dependent only on x and y object coordinates. 

Q12. What is the way to correct the ellipticities of the regions?

the subset of sources used to create the fits should always extend further than the boundaries of the region being corrected (as shown by the blue square in Figure 1), to ensure that the ellipticities of all sources are corrected based on a fit obtained from sources surrounding them on all sides. 

Q13. What was the average exposure time of the July targets?

The Julytargets, with R.A.s around 13 hr, were observed with 60 s total exposure times in the i-band filter; the August targets (R.A.s of 22–23 hr) used a long-pass filter with a 600 nm cut-on to obtain increased signal compared to a bandpass filter. 

Q14. How many FWHMs do the authors measure for e1 and e2?

When the authors measure the corrected ellipticities of an object across multiple images, the authors measure many values for e1 and e2 at a variety of FWHMs.