LP 600 SDSS z 0
4.3 Data Reduction and Analysis
Figure 4.2. Images of targets in the Taurus-Auriga regions withr0,i0 andz0 bands mapped to RGB channels. Each image is 3.300×3.300square. The r0, i0 and z0 band images have been square-root scaled from zero to the maximum intensity in the three images. The colors are approximately representative of the spectral energy distribution. Bluer stars are brighter inz0filter. Redder and yellower stars are brighter inr0andi0filters. The images with a prominent central peak are labeled as ‘faint’ in Table 4.2(and correspondingly Table4.3for the Scorpius targets).
Figure 4.3. Images of targets in the Taurus-Auriga regions with r0, i0 and z0 bands mapped to RGB channels. The image size and scaling is same as that of Figure4.2.
Figure 4.4. Images of targets in the Upper Scorpius-Ophiuchus regions with r0, i0 and z0 bands mapped to RGB channels. The image size and scaling is same as that of Figure4.2.
Figure 4.5. Images of targets in the Upper Scorpius-Ophiuchus regions with r0, i0 and z0 bands mapped to RGB channels (continued from Figure4.4).
Figure 4.6. The accuracy ofPYNPOINTas compared toLOCIfor measuring fluxes of simulated planets injected at various distances from the central star in ADI data from the NACO instru- ment at VLT. The three solid lines correspond to measurements recovered byPYNPOINT and the three dashed lines correspond to the same measurements using the LOCIalgo- rithm. It is seen that thePYNPOINTalgorithm, while outperforming theLOCIalgorithm, consistently underestimates the flux by as much as a factor of two. Figure adapted from Figure 5 ofAmara & Quanz(2012).
2007) andPYNPOINT (Amara & Quanz,2012) were developed specifically for accurate PSF subtraction.
Based on literature, we chose to use thePYNPOINTmethod for our data analysis because of its performance in flux measurement compared to LOCI (Figure4.6). Although developed for analysis of ADI data, we were able to adapt the software2 for use with the Robo-AO.
We briefly describe the algorithm used for the PSF fitting.
Overview: The PYNPOINTalgorithm uses a large number of images of targets observed with the same filter closest in time to our sample to create a basis set of PSF shapes. Then
2A preliminary version of thePYNPOINTcode was graciously sent to us by the developers Dr. A. Amara and Dr. S. Quanz for beta testing.
for each image, the secondary target was masked and a PSF estimate was created using a finite number of basis elements. The residuals created by subtracting the PSF estimate from the image was used to estimate the flux of the secondary.
4.3.2.1 Basis Set of PSFs
For each filter (SDSS g’, r’, i’ and z’), I collected a set of about hundred images. I created 300 pixel (6.600) square cutouts centered on the primary star of each target. The central 8 pixel diameter circle was masked to block the central noise peak that might be present in faint images. The data were then read by the PYNPOINT code, normalized and subjected to a principal component analysis (PCA)3. The resulting independent vectors were used as the basis set for PSF estimation.
For thei0 band images, I used a data set of 102 images. The first sixteen basis functions are shown in Figure 4.7.
4.3.2.2 PSF Fitting
In the images where the secondary companion was visually prominent, it was masked with a circular mask to prevent the PSF estimate from fitting the secondary peak. The diameter of the circular mask was chosen to be 0.500, sufficient to block the companion peak and its surrounding halo, if any. However, it is small enough to allow a reasonable estimate of the local PSF shape.
Through trial and error, it was realized that the first 10 basis vectors are sufficient to recreate most of the PSF shape. This constitutes about 10% of the entire set of basis vectors showing that the chosen basis set is quite compact.
Figure 4.8shows the original image for 2MASS 15590208-1844142 (left panel), the PSF estimate (center panel) and the residuals after subtraction (right panel). The color scale in the left and center panels are matched. The color scale for the residuals has been reduced by a factor of ten to increase contrast and show the details of the residual speckles.
We plan measure the aperture flux of the primary star on the PSF estimate and of the secondary in the residual image. In cases where the companion is not visible, we can only calculate the detection limit from the residual. Unfortunately, at the time of writing, this remains a work in progress.
As shown in Figure4.6,Amara & Quanz(2012) calculated the systematic errors in flux estimation by injecting simulated planets in to ADI data from the NACO instrument at the 8-m VLT and comparing the measured fluxes to the original values. They observed that the measured fluxes were consistently lower than the original fluxes of the planets. However, we cannot directly use their estimates of the systematic offset for two reasons: (a) their dataset used ADI for suppressing speckles whereas the Robo-AO dataset does not and (b) the planet-star contrasts tested in their simulations were between 8 to 11 magnitudes which are a much higher contrast than those of the sub-stellar companions we are attempting to study. It is planned to redo the simulations for a sample of Robo-AO PSFs to estimate the systematic errors in our measurements.
3PCA was developed by Karl Pearson in 1901.
Figure 4.7. The basis functions generated from the Robo-AO SDSSi0 band images are shown. The plots correspond to the first sixteen modes seen from left to right and top to bottom.
Each image is 300 pixels (6.600) in size.
Figure 4.8. The original image of 2MASS 15590208-1844142 is shown in the left panel. The center panel is the PSF estimate formed by masking the obvious companion in the left panel.
The color scales of the left and center panels have been matched. The right panel shows the residuals left after subtracting the PSF estimate from the original image. The color scale has been reduced by a factor of 10 to show the residual speckles in higher contrast.
0.6 0.8 1.0 1.2
Wavelength (µm) 5
4 3 2 1 0 1
2MASS 16010519-2227311 2MASS 16025123-2401574
2MASS 16032367-1751422 2MASS 16065436-2416107 2MASS 16090844-2009277
2MASS 16104202-2101319 2MASS 16010519-2227311
Scorpius Targets
0.4 0.6 0.8 1.0
Wavelength (µm) 5
4 3 2 1 0 1
∆Mag (−2.5log10(Fp Fs))
HBC 352
CoKu Tau 3 GH Tau
HP Tau-G2 V710 Tau
HK Tau V928 Tau
UZ Tau
V955 Tau
JH 223 LkHa332-G2
Taurus Targets
Figure 4.9. The flux ratios of widely separated (>100) stars measured using aperture photometry are plotted as a function of wavelength. The y axis is in units of the magnitude difference in each filter.
4.3.3 Aperture Photometry of Widely Separated Systems
While the PSF fitting work was in progress, performed aperture photometry on the targets where the images were widely separated (sep >100). The flux ratios and errors were calcu-
lated in each filter where the companion was visible. Figure 4.9 shows the relative fluxes plotted in magnitude differences as a function of wavelengths.