VLT/NaCo data calibration using binary/cluster

Calibration with HIP 73357

For astrometric calibration of the own VLT/NaCo observations taken in 2011 and 2012, the wide binary system HIP 73357 and the globular cluster 47 Tuc, respectively, were imaged in every observing night. Thereby, the same instrument settings, i.e. filter, camera, read-out and detector mode, and imaging technique as the science targets were used. Furthermore, the public archive was searched for additionally available data yielding 5 extra nights for HIP 73357 and 4 nights for 47 Tuc. In order to monitor possible short term variations in the pixel scale or the detector orientation, and to check for consistency of the overall calibration results, an astrometric calibration of all these data was done.

HIP 73357 is located at a distance of 102.25 pc (van Leeuwen 2007) from the Sun, and both components have spectral types of mid to early A (Houk 1982). Assuming a circular orbit with a radius of about 8.4 arcsec and a total system mass of ∼ 4 M^⊙, the orbital period would be approximately 12 600 yr or shorter if eccentric, respectively. For HIP 73357 precise astrometric measurements with Hipparcos taken in epoch 1991.25 are available, which are listed in Table 5. The time difference between the Hipparcos measurement and the science data epochs is about 20 years. In the case of an circular orbit which is seen edge-on, the separation of the components would change by 2.6 mas/yr or 53 mas in ∼ 20 yr. This

equates to a change of 3.5 pixel for the NaCo S13 camera, which is significantly larger than detection accuracy reachable with available software. In the case of an circular orbit which is viewed pole-on, the position angle (PA) would change by ∼0.03^◦/yr or 0.6^◦ in ∼ 20 yr.

This very simple estimate, and in particular the change in separation over several years, shows that the orbital motion of this calibration binary needs to be taken into account.

Table 5. Hipparcos reference measurement of the NaCo calibration binary Binary Epoch Separation (arcsec) PA^a(deg)

HIP73357 1991.25 8.430±0.028 337.30±0.06

aPosition angle (PA) is measured from North over East to South.

There are 29 astrometric data points taken over the past ∼ 170 yr available for HIP 73357 in the Washington Double Star Catalogue (WDS, Mason et al. 2001). These data points were used to fit the linear change in separation and position angle of the binary component yielding a linear decrease in separation of 0.0018 ± 0.0010 arcsec/yr and a decrease in position angle of 0.0368 ± 0.0055^◦/yr. The corresponding diagrams for separation angle and position alongside the best fits and their one sigma confidence interval are shown in Figure 10. However, WDS does not provide uncertainties for any of the given astrometric data points and hence, the results have to be taken with reservations due to the quite large scatter of the measurements. Also, the observational data, of the position angle, available since 1970 show a lower decrease than the overall result of linear orbital motion fit, indicating that the assumption of a linear orbital motion might be inappropriate. Given the available amount of data points up to date, which cover only about 1.3 % of the entire orbit it is, however, not yet possible to detect significant curvature in the orbital motion.

1850 1900 1950 2000

Figure 10. Astrometric data points for the calibration binary HIP 73357 obtained from the WDS catalogue. The solid red line shows the linear fit to the change of the separation (left) and the position angle (right) over time. The 68% (1σ) confidence interval of the fit is indicated by the dashed red lines.

To determine the pixel scale and the orientation, first the detector positions of the binary components were measured in each individual jitter position in the respective observing night, to account for geometric distortions of the detector. This was done employing the

IDL⁷/starfinderroutine (Diolaiti et al. 2000), which uses a Point Spread Function (PSF) fitting algorithm to detect the sources in an image. For a more detailed description see section 5.1.The separation and position angle on the detector were then calculated for each individual jitter position and the results averaged. Using the calculated rate of change in separation and position angle, the ephemerides of the binary at the time of the science epoch were then extrapolated from the Hipparcos reference measurement. With this result and the measured separation and position angle on the detector in each observing night, pixel scale and detector orientation was calculated for each science epoch. The results for the pixel scale and the detector orientation are listed in Table 6. As can be seen from the data, pixel scale and orientation vary between the epoch, but are consistent within their uncertainties.

Table 6. Astrometric calibration results of HIP 73357 using linear orbit fit of WDS data Observation Epoch Pixel scale Orientation

Calibration with the globular cluster 47 Tucanae

The calibration of science data taken in September 2012 was done using the globular cluster 47 Tuc. The cluster, also known as NGC 104, is located near the Small Magellanic Cloud towards the constellation Tucana at a distance of about 4.7 kpc (Woodley et al. 2012) from the Sun. For this object precise astrometry data are available from the Hubble Space Telescope (HST). There are 4 additional nights with observational data available in the archive, two in December 2011 and 2012, respectively, at which this cluster was observed in the same night as target stars contained in the sample. In Figure 11, the HST/ASC image of 47 Tuc (left) and an image of the same cluster observed with NaCo in 2012 (right) is shown. Therein, the field of view of the NaCo S13 objective in the HST image is indicated by the white rectangle, and the stars employed to extract their position in the NaCo image are marked with circles.

First, an astrometric reference catalogue was created from the HST image. Therefore, the star positions were extracted using GAIA (Graphical Astronomy and Image Analysis Tool, Draper 2000) and the included SExtractor⁸ (Soruce-Extractor, Bertin and Arnouts 1996)

7IDL (Interactive Data Language) is a commercial plotting, image processing, programming, and graphical user interface (GUI) development language distributed by the Research Systems Inc., Boulder CO.

8SExtractor is an image processing software which contains automated techniques that detects, de-blends, measures and classifies sources from astronomical images.

Figure 11. HST/ASC image of 47 Tuc (left) used as reference for astrometric calibration taken on 2002-07-24 with the F 250 W wide band filter in the ultra-violet, and exemplary VLT/NaCo K s band image (right) of the same cluster taken on 2012-09-19 with the S13 camera. The field of view of the NaCo S13 example image is indicated by the white rectangle (left image), and the stars used for calibration are marked with white circles (right image).

Table 7. Astrometric calibration results of the globular cluster 47 Tuc Observation Epoch Pixel scale Orientation

date (year) (mas/pixel) (deg)

2010-12-24 2010.979 13.265±0.020 0.642±0.087 2010-12-25 2010.982 13.271±0.016 0.599±0.069 2012-09-19 2012.717 13.273±0.011 0.679±0.046 2012-12-04 2012.925 13.267±0.011 0.572±0.049 2012-12-05 2012.928 13.262±0.014 0.615±0.062

therein. The same was done for all NaCo images of 47 Tuc. Then, the obtained NaCo catalogues were matched with the reference catalogue using a written PYTHON routine, and the pixel scales and detector orientations were computed from the found matches.

Additionally, sigma clipping was applied to exclude those results with significantly different pixel scales and orientations, which are most likely caused by stars with high proper motion and hence, larger deviations between the measured positions in the HST and NaCo images, respectively. The results are summarized in Table 7.

The comparison of the results of both calibration methods shows differences in the esti-mated pixel scales, and in particular in the found detector orientations. As mentioned, one reason can be the inaccurate assumption of a linear model for the orbital motion.

The use of a cluster, in general, is more appropriate for calibration purposes, due to the amount of stars that can be used for the position matching and hence, higher precision of the estimated pixel scale and rotation of the detector. For that reason, 47 Tuc was used for a more precise calibration of the available HIP 73357 data, and thus more precise and

updated ephemerides of the binary.

There are 3 nights available in the NaCo archive where HIP 73357 and 47 Tuc were ob-served in the same night; two of them taken with the S13 objective and one with S27, respectively. These nights were used to correct the discrepancies in pixel scale and ori-entation of the detector. Therefore, the detector was first calibrated using the 47 Tuc and the afore described procedure. The computed results are listed in Table 8, column 2 and 3. With the obtained calibration for each of the three observing nights, separation and the position angle of HIP 73357 could be measured in the respective epoch yielding the ephemerides listed in Table 8, column 4 and 5. With the new computed ephemerides

Table 8. Recalculated ephemerides of the calibration binary HIP 73357

47 Tuc HIP 73357

Observation Pixel scale Orientation Separation PA^a

date (mas/pixel) (deg) (arcsec) (deg)

2009-08-07/08 13.290±0.014 0.384±0.059 8.454±0.010 336.94±0.06 2010-08-18/19 27.070±0.012 0.523±0.027 8.445±0.006 337.05±0.03 2011-06-02/03 13.278±0.014 0.513±0.061 8.451±0.009 336.87±0.06

aPosition angle (PA) is measured from N over E to S.

and the Hipparcos reference measurement of epoch 1991.25, the linear orbit motion of HIP 73357 was then re-estimated. For HIP 73357 the result is an increase in separation of 0.0011 ± 0.0003 arcsec/yr and a decrease of the position angle of 0.018 ± 0.005^◦/yr. The pixel scales and detector orientations for the available science epochs were re-calculated using these values. The final results for pixel scale and detector orientation, applied to the respective science data in this thesis, are listed in Table 9. In Figure 12, the pixel scale

Table 9. Final astrometric calibration results

data of the two calibration methods alongside the re-calculated results for HIP 73357 are plotted. Although consistent within their uncertainties, the results of the linear orbital mo-tion fit using the available WDS data points, shown as black dots, deviate significant from

the calibration result obtained using the globular cluster 47 Tuc shown as red squares. The re-calculated results for the calibration binary shown as black diamonds still vary slightly between the epochs. However, they now are consistent with the more precise calibration results determined from the globular cluster 47 Tuc.

2007 2008 2009 2010 2011 2012 2013

Observing epoch (years) 13.10

13.15 13.20 13.25 13.30 13.35

Pixel scale (mas/pixel)

47Tuc

HIP73357 (WDS cal.) HIP73357 (47Tuc re-cal.)

Figure 12. Summary plot of derived NaCo S13 pixel scales for the science epochs versus time.

The pixel scales calculated from the linear orbit fit of the WDS data are shown as black dots. The red squares indicate the derived pixel scales using the 47 Tuc cluster, and the corrected results of HIP 73357 using new calculated ephemerides from 47 Tuc calibrated data are plotted as blue diamonds.