A technique for high-precision CCD photometry with the MASTER-II-Ural telescope of the Kourovka astronomical observatory

maggio 24, 2012  |   AstronomiaNova   |     |   0 Commenti

Burdanov, A.Y.; Krushinsky, V.V.; Popov, A.A.; Avvakumova, E.A.; Punanova, A.F.;

Zalozhnih, I.S.

Kourovka astronomical observatory of the Ural Federal University, Yekaterinburg, Lenina 51, Russia, burdanov.art@gmail.com

Abstract

We present an observational technique and developed post-processing software Astrokit which are used to obtain 2-5 milli-magnitude photometry with the MASTER-II-Ural telescope (40 cm Hamiltonian optical system) of the Kourovka astronomical observatory of the Ural Federal University. Data post-processing includes a correction of brightness variations associated with the variability of the atmospheric transparency and automatic search of variable stars. This precision is sufficient to detect the transits of a short-period giant planet around a solar-type star, to register subtle transit effects and to detect low-amplitude variable stars.

1. Introduction

High-precision time-series stellar photometry is widely used in modern astronomy. It has applications in the study of variable stars, in searching for the new transiting exoplanets and in researching known exoplanetary systems. In each case the observer is interested in obtaining the highest precision of photometry theoretically possible with the current combination of observing technique, telescope and data processing algorithms.

Here we describe noise sources, observational technique and post-processing algorithm to minimize noise contribution to the resulting precision of photometry.

As example we employ observations of known transiting exoplanets HAT-P 10/WASP-11 b and WASP-33 b and open cluster NGC188 obtained in 2011 in the Kourovka observatory on the MASTER-II-Ural telescope. We show that it is possible to reach high precision photometry on short (1-2 hours) and long term (up to several days) time-series observations.

2. Observations

The Kourovka observatory is located on the geographical border between Europe and Asia

(57º N, 60º E) near Yekaterinburg, Russia (see figure 1).

Figure 1: location of the Kourovka observatory

Photometric observations were performed using MASTER-II-Ural robotic telescope (Lipunov, 2010).  MASTER-II-Ural is a part of a global MASTER robotic Net. The telescope consists of a pair of 40 cm Hamilton catadioptric tubes with  the focal length of 100 cm, installed on a equatorial mount (see figure 2).

CCD cameras are Apogee Alta U16M with front-illuminated KODAK KAF-16803 chip with anti-blooming: size of a chip is 4096 x 4096 pixels; pixel size is 9 x 9 μm; CCD gain in e/ADU is 1.3; readout noise in e/pix is 11. Image scale is 1.85 arcsec/pix and field of view is 2º x 2º. The observations are performed simultaneously in two filters (Johnson-Cousins BVRI system), or in two different polarization planes.

Figure 2: MASTER-II-Ural robotic telescope

The observations of open cluster NGC188 (RA2000 = 00h 47m 28s; Dec2000 = +85º 15′ 18”) were made in the period from 11 to 19 March 2011 during 5 nights. Detailed study of this open cluster you can find in the paper of Popov, 2012 (in preparation). The observations of known transiting exoplanets HAT-P 10/WASP-11 b (RA2000 = 03h 09m 28.54s; DEC2000 = +30º 40′ 26.0”) and WASP-33 b (RA2000 = 02h 26m 51.08s; DEC2000 = +37º 33′ 02.5”) were made on the 10 December 2011.

Flat fields for each used filter were obtained from morning twilight sky automatically after every observational night. Dark frames were obtained automatically in the evening before starting the observing run.

3. Sources of noise

To achieve milli-magnitude precision we must pay attention to all sources of noise during observations and data post-processing in order to minimize their effects. We divide noise source  into the 3 groups: object noise, CCD noise and effects of the Earth’s atmosphere.

3.1  Object noise

Noise from the observed object is a Poisson noise. If we want to reach milli-magnitude precision stellar variability σ = 1/√N (where N is the number of photo-electrons collected in the stellar aperture) must be smaller than 1 milli-magnitude. Thus the exposure time of the current object must be adjusted so that more than N = 10^6 photo-electrons in the aperture are registered by CCD. This constraint defines lower limit for the exposure time.

Typical exposure time on the MASTER-II-Ural telescope for stars from V = 8 mag to V = 14 mag is from 5 to 240 sec.

3.2 Noise from CCD

This kind of noise include dark noise (thermal noise), readout noise, effects of CCD’s nonlinearity, pixel-to-pixel and sub-pixel sensitivity variations.

Dark noise and readout noise

Dark noise (thermal noise) is generated in every CCD by the thermal agitation even when no photons are entering the device. Dark noise of typical KODAK front-illuminated chip is about 2 – 4 e/pix/sec at the room temperature (25 ºC). Dark noise decreases twice as temperature lowers for 6 – 6.5 ºC. Our CCD’s dark noise at the typical working temperature (-30 ºC) and with typical exposure time 120 sec is approximateley 10 – 20 e/pix which is negligible for bright objects.

Readout noise is a characteristic of a on-chip amplifier that converts electrons to ADU counts and camera’s electronic. Typical readout noise value of modern CCDs is small and about 10

e/pix and lower.

Calibrating of raw images using master dark frame derived using median combining from a set of initial dark frames takes into account dark noise as well as readout noise.

Effects of CCD’s nonlinearity

CCD’s controller gain is not a constant function of the number of electrons. So the number of ADU counts is not exactly proportional to the number of incident photons. The observer should know the range of counts in ADU where the gain of CCD is a constant function of the number of electrons, i.e. the range of linearity, in order not to introduce additional errors (anti-blooming reduces the range of linear response). This constraint defines upper limit for the exposure time.

Nonlinearity range of Apogee Alta U16M cameras (east and west) installed on the MASTER-II-Ural is from 45 000 to 65 000 ADU counts (see figure 3).

Figure 3: Apogee Alta U16M nonlinearity range

Pixel-to-pixel and sub-pixel sensitivity variations

To correct pixel-to-pixel sensitivity variations we used normalized master flat field frame obtained from the set of initial flat field frames using median combining. While making the FWHM of star’s profile more than 2-3 pixels nullifies sub-pixel sensitivity variations (see Penny, 1996).

3.3  Effects of the Earth’s atmosphere

Effects of the Earth’s atmosphere include: variation of the sky background, fluctuating of atmospheric transparency (extinction) and atmospheric scintillation. Selecting the appropriate filter together with data post-processing algorithm reduces the influence of these effects. In our observations we used V and R filters as they less affected by atmospheric extinction than B filter and by atmospheric emission than I filter. Keeping exposures longer that 10 sec reduces effect of scintillation.

Data post-processing algorithm is described in the next section.

4. Data reduction

Taking into account remarks about sources of noise during observations and selecting the proper filter and exposure time we acquire raw images. On the first stage of data reduction raw images were processed in the IRAF V2.14. package (Tody D. 1986). Processing includes: deleting of the overscan region, subtracting master dark frame, dividing by the normalized master flat field frame. Then astrometric reduction (making proper WCS header) is made using CCSETWCS task of IRAF.

Then the aperture photometry was performed in IRAF/DAOPHOT package using the list of stars obtained from the best frame in the series. The diameter of the aperture is almost equal to the  typical FWHM of the frames but additional photometry is done with the variations of this aperture.

On the second stage output data from IRAF are processed by console application Astrokit which was written in C++ by Krushinsky Vadim and Burdanov Artem. The working algorithm

of this application is discussed in the next section.

Astrokit

As part of the researching program of open clusters, searching for variable stars and study of the known transiting exoplanets the console application Astrokit was written in C ++ for post-processing the results of CCD photometry after IRAF/DAOPHOT package. Application corrects brightness variations associated with the variability of the atmospheric transparency and searches for variable stars. The application allows fast simultaneous processing of large numbers of objects (100 – 10 000 starts on more than 100 images) in an automatic mode.

The program’s structure is shown in figure 4.

Figure 4: schematic diagram of Astrokit

Input data for the program contained in files that are generated by pdump command of  IRAF/DAOPHOT package:

ID – star’s id;

MAG – star’s instrumental magnitude;

MERR – star’s magnitude estimation error;

FLUX – total number of counts excluding sky in the aperture;

AREA – area of the aperture in square pixels;

SUM – total number of counts including sky in the aperture;

NSKY -number of sky pixels used;

MSKY – sky value;

ITIME – exposure time in seconds.

In addition, for the correct operation the program requires a file containing the equatorial coordinates of stars. As an option this file may contain color indexes for each star. Also as an option there is the possibility of using a simple three-point median filtering.

Correction of brightness variations associated with the variability of the atmospheric transparency is based on the modified algorithm described in the work of Everett and Howell, 2001:

1. First, Astrokit recalculates star’s magnitudes and magnitude uncertainties (see Howell, 1993) reported by  IRAF/DAOPHOT for each star (because IRAF calculates them roughly).

2. For each target the ensemble of N stars is formed in the area with radius of 5 arcmin taking into account the magnitude and color index differences between the target and the ensemble stars (this differences may be defined by the user).

If in the area with radius of 5 arcmin around the target there are less than 10 stars that meet the criteria of brightness and color index differences then the radius increases by 5 arcmin and the procedure of ensemble formation starts again. This iterations repeat until more than 10 stars appear in the ensemble that meet entered criteria for the current target or the radius of the area is more than 30 arcmin.

3. A correction to the initial instrumental magnitude of the target on each frame is found by making the mean instrumental magnitude <mj> of the N ensemble stars weighted by their individual uncertainties. The difference between <mi> on each frame and the mean instrumental magnitude of the ensemble stars on all M frames is subtracted from the initial instrumental magnitudes mobs . Thus corrected magnitudes of the target mcor :

mcor ij = mobs ij – (<mj> -  M),

where i – target’s ID; j – number of frame. The error in the correction is then calculated formally from the uncertainties in each individual measurement of the N ensemble stars.

Using a close ensemble of many stars reduces the influence of variations of atmospheric transparency and the contribution of stellar scintillation in the budget of error values (see Kornilov, 2012).

4. On this stage calculation of the corrected magnitude standard deviation for all the reference stars is performed. If standard deviation for any star in the ensemble is more than 2 times exceeds the average for all frames theoretical error of photometry, the star is removed from the ensemble of reference stars and the procedure of brightness correction repeats again but without star with big standard deviation.

5. At this stage searching for variable objects is starting. Searching is made using the algorithm described in Rose, 2007. For each star coefficient RoMS (Robust Median Statistics) is calculated.

RoMS criterion estimates the brightness variations of the object. If it exceeds 1 (but this value can be defined by the user), then the star is suspected to be variable, and additional study of this object is needed. The use of robust median statistics is explained due to it’s greater resistance to random fluctuations. However, this does not give an absolute assurance of the absence of false variables. A lot of the stars suspected to be variable turned out to be constant within the accuracy of our photometry. The final criterion is visual analysis of the light curves, which can be made in the program Vanalyzer, also written in the Kourovka observatory.

6. The output data contain corrected magnitudes for each star on each frame, standard deviation, theoretical error of photometry, number of ensemble stars used to correct each star and radius of area where these ensemble stars were found. 

5. Results

Exoplanets

Light curves of transiting exoplanets HAT-P 10/WASP-11 b and WASP-33 b acquired with the current observing technique and data post-processing algorithm are uploaded to the Exoplanet Transit Database (Poddaný, 2010) and presented below.

Transit of WASP-33 b (V = 8.3 mag) was observed in V filter on the 10 December 2011. The light curve was uploaded to ETD: http://var2.astro.cz/EN/tresca/transit-detail.php?id=1324556030

Duration of the transit is 163.9 +/- 2.9 minutes, transit’s depth is 0.0162 +/- 0.0007 which are defined by ETD algorithms. Standard deviation of a check star is 0.004 mag. Small brightness increase is visible in the middle of the transit.

Light curve of the same transit obtained by our colleagues from the Pulkovo observatory

(St. Petersburg) shows the same increase in the middle of the transit (see figure 6): http://var2.astro.cz/EN/tresca/transit-detail.php?id=1324940687

Figure 5: light curve of WASP-33 b transit in V filter obtained in the Kourovka observatory on the 10 December 2012

Figure 6: light curve of WASP-33 b transit in B filter obtained in the Pulkovo observatory on the 10 December 2012

Thereby we can state that this brightness increase is not a noise but some kind of a subtle transit effect that really happened in the WASP-33 b exoplanetary system and that our precision allows to register such effects.

Transit of HAT-P 10/WASP-11 b (V = 11.89 mag) was observed on the 10 December 2012 in R filter during total lunar eclipse: the first half was observed during total eclipse, the second part during partial eclipse. The transit light curve is presented on the figure 7. Black squares presents raw magnitudes, red dots – magnitudes corrected by Astrokit.

Scattering of the points increases at the end of the transit due to increasing value of sky background and it’s deviation (it was in the end of the lunar eclipse).

Figure 7: light curve of HAT-P 10/WASP-11 b transit in R filter  obtained in the Kourovka observatory on the 10 December 2012

The light curve is also uploaded to the ETD: http://var2.astro.cz/EN/tresca/transit-detail.php?id=1324468836. Duration of the transit is 162.1 +/- 4.6 minutes, transit’s depth is 0.0216 +/- 0.0014 which are defined by ETD algorithms. Standard deviation of a check star is 0.0035 mag.

Developed technique is also used on the other MASTER Net telescopes. Light curve of the WASP-12 b (V = 11.69 mag) transit in R filter observed in Tunka (52° N, 103° E) on the 16 March 2012 by Kirill Ivanov in very good atmospheric conditions and without the Moon is presented below:

Figure 8: light curve of WASP-12 b transit in R filter obtained using MASTER-II-Tunka telescope on the 16 March 2012

ETD link: http://var2.astro.cz/EN/tresca/transit-detail.php?id=1335164469. Duration of the transit is 176.1 +/- 2.2 minutes, transit’s depth is 0.0179 +/- 0.0012 which are defined by ETD algorithms. Standard deviation of a check star is 0.003 mag.

Open cluster NGC188

A photometric study of variable stars in the field of old open cluster NGC188 is performed using Astrokit application and discussed in details in the mentioned paper of Popov, 2012. Here we will concern only the use of data reduction algorithm.

Observations were carried out in two bands R and I for 5513 stars up to R = 17 mag. Despite the fact that NGC188 is a well-studied cluster we discovered 18 new variables among several hundreds of false-positives that were in output of Astrokit (about 10% of all stars). Photometry for 5513 stars in the range of magnitudes from 11 to 17 with a corresponding accuracy from 0.004 to 0.05 mag (in band R) was carried out in field of 90×90 arcmin.

The standard deviation versus the magnitude (left) and RoMS versus the magnitude (right) for the R band are presented below in the figure 9. Red squares are variable stars.

Standard deviation itself is not a good criterion for searching variable stars unlike RoMS criterion. Standard deviations of variable stars are not always vastly differs from standard deviations of constant stars. But RoMS criterion allows to extract variable stars more confidently.

Figure 9: the dependence of the standard deviation (left) and RoMS (right) for the R band

Several phase curves of new periodic variable stars are shown on the figure 10.

Figure 10: the light curves of periodic variable stars. Black circles are band R, red triangles are band I.

dI indicates a shift of magnitude in band I

6. Conslusion

We described noise sources that make contribution to the overall photometric accuracy and observational and data post-processing techniques to minimize their effects. Console application Astrokit that was developed in the Kourovka observatory of the Ural Federal University for post-processing the results of CCD photometry after IRAF/DAOPHOT package corrects brightness variations associated with the variability of the atmospheric transparency and searches for variable stars. The application allows fast simultaneous processing of large numbers of objects (100 – 10 000 stars on more that 100 images) in an automatic mode.

As examples observations of known transiting exoplanets HAT-P 10/WASP-11 b and WASP-33 b and open cluster NGC188 obtained in 2011 in the Kourovka observatory using MASTER-II-Ural telescope were presented. Acquired precision is sufficient to detect the transits of a short-period giant planet around a solar-type star, to register subtle transit effects and detect low-amplitude variable stars.

Burdanov Artem: research-assistant of the Kourovka Observatory since 2010. Research interests: exoplanetary science, high-precision photometry.

Krushinsky Vadim: head of the department of the astronomical engineering of the Kourovka Observatory. Research interests: optical systems, astronomical engineering.

Popov Alexander: principal engineer of the Kourovka Observatory since 2008. Research interests: variable stars, star clusters, high-precision photometry.

Avvakumova Ekaterina: principal engineer of the Kourovka Observatory since 2004. Research interests: close binary systems, stars of early spectral classes, eclipsing variables.

Punanova Anna: research-assistant of the Kourovka Observatory since 2010. Research interests: high-resolution spectroscopy, stellar evolution.

Zalozhnih Ivan: research-engineer of the Kourovka Observatory since 2009.  Research interests: astronomical software development.

References

Everett, M. E., & Howell, S. B. 2001, PASP, 113, 1428

Howell, S. B. 1993, in Stellar Photometry – Current Techniques and Future Developments,         ed. C. Butler & I. Elliot (Cambridge: Cam- bridge Univ. Press), 318

Kornilov V., G., 2012, in preparation

Lipunov, V., Kornilov, V., Gorbovskoy, E., et al., 2010, Advances in Astronomy, 2010

Penny, A. J., Leese, R., 1996, Astronomical Data Analysis Software and Systems V, ASP   Conference Series, Vol. 101

Poddaný, S., Brát, L., Pejcha, O., 2010, New Astronomy, Vol. 15, Issue 3, 297–301

Popov, A., Krushinsky, V., Avvakumova, E., et al., 2012, Open European Journal on Variable     Stars, in preparation

Rose, M. B., & Hintz, E. G., 2007, AJ, 134, 2067

Tody, D., 1986, procspie, 627, 733









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