A NEW EXTENSIVE CATALOG OF OPTICALLY VARIABLE ACTIVE GALACTIC NUCLEI IN THE GOODS FIELDS AND A NEW STATISTICAL APPROACH TO VARIABILITY SELECTION*

Carolin Villforth; Anton M. Koekemoer; Norman A. Grogin

doi:10.1088/0004-637X/723/1/737

1. INTRODUCTION

In the last 20 years or so, findings of strong correlations between the black hole masses in the centers of nearby galaxies and the properties of their hosting galaxies (e.g., Ferrarese & Merritt 2000; Graham et al. 2001; Marconi & Hunt 2003; Gebhardt et al. 2000) have moved active galactic nuclei (AGNs) into the center of attention as key players in galaxy evolution.

However, while it is clearly established that AGNs must play a major role in galaxy formation to be able to produce the relation between supermassive black holes and their host galaxies at redshift zero, it is still a mystery when the correlation came into place and through which mechanism. To understand this, one has to understand both the evolution of AGNs and their connection with their hosting galaxies.

While our knowledge of low-redshift AGNs and their correlation with the host is relatively broad, much less is known about high-redshift AGN hosts. Studies of AGN-hosting galaxies seldom reach beyond redshifts of 2. Resolving the host galaxy becomes more and more challenging as the faint hosts are extremely hard to disentangle from the nuclear emission (e.g., Hutchings 2003; Jahnke et al. 2004; Schramm et al. 2008; Villforth et al. 2008). This is due to both the decrease in apparent host galaxy size and surface brightness dimming. Low-luminosity AGNs have a much more favorable core-to-galaxy ratio, making it possible to study the properties of their hosting galaxies up to very high redshifts.

Another open question is the general evolution of AGNs over redshift. It is known that the luminosity function of high-redshift AGNs significantly differs from the one at low redshifts. High-redshift AGNs are on average much brighter than their low-redshift counterparts (Dunlop & Peacock 1990). However, given the fact that almost nothing is known about low-luminosity AGNs at high redshift, this is just the tip of the iceberg and we know little about the shape and normalization of the luminosity function on the faint end.

New studies also imply that high-redshift AGNs might be intrinsically different from their low-redshift counterparts. Jiang et al. (2010) found an interesting sample of dust-free AGNs at high redshift that have no low-redshift counterparts. And Shemmer et al. (2009) found a sample of weak-lined high-redshift AGNs that do not seem to have low-redshifts counterparts. On the other hand, the interesting AGN subclass of BL Lacs, highly variable objects thought to be the beamed counterparts of Fanaroff–Riley I radio galaxies (Urry & Padovani 1995) so far have only been detected at low redshift. The missing high-redshift BL Lacs are still a mystery given their extreme intrinsic brightness (Stocke 2001). Latest theoretical models for the evolution of AGNs imply that the missing BL Lac problem might be due to the fact that certain types of AGNs preferably appear at certain redshifts, with Fanaroff–Riley type I galaxies being extremely rare at high redshifts (Garofalo et al. 2010). Studying low-luminosity AGNs at high redshift might therefore also help in answering the question of what determines the intrinsic properties of AGNs.

It is also still a puzzle how supermassive black holes formed. The fact that AGNs at redshifts greater than 6 are found to host supermassive black holes as large as 10⁹ M_☉ (Jiang et al. 2010) is rather puzzling given the fact that the universe was less than a gigayear old at those redshifts. This poses the question of how and when those black holes were formed. Getting a more complete view of black hole masses at high redshift might help understand how, when, and in which objects mass accumulation took place.

Despite the great interest in this topic, our knowledge about high-redshift AGNs is still limited and almost nothing is known about faint AGNs at high redshifts. To learn more about this topic, we need new complete samples of high-redshift AGNs reaching to much lower luminosities. Deep multi-band surveys offer the possibility to select such samples.

AGNs can be identified in several ways, the most obvious being through spectroscopy. AGNs can either be identified through extremely broad lines or by determining line ratios (Baldwin et al. 1981; Veilleux & Osterbrock 1987). The former has the problem that it only selects the small subset of broad-lined Type I again and misses Type II AGNs as well as weak-lined objects. Both have the problem that spectroscopy is extremely costly especially for faint sources. Therefore, while spectroscopic surveys can play an important role in understanding high-redshift AGNs, carefully selected candidate samples are necessary to make this method efficient.

A commonly used method for AGN selection is through their optical colors. This method was first used by Markarian (1967) who selected objects with excess UV flux and created the first catalog of nearby AGNs. Possibly, the most famous color-selected AGN catalog is the Palomar Green Bright Quasar Catalog (Schmidt & Green 1983, known under the name BQS or PG) in which objects with U − B < −0.44 mag were selected. However, UV excess might also be caused by star formation. Therefore more sophisticated methods are needed to avoid contamination by star-forming galaxies. Warren et al. (1991) designed a multi-color selection method, in which only point-like sources are chosen and stars are rejected by their specific location in a multi-dimensional color space. Similar methods have been used for quasar selection in the Sloan Digital Sky Survey (SDSS; Richards et al. 2002). Such methods are observationally cheap and can easily be applied to big multi-waveband surveys. However, they rely on considerable deviation from a normal stellar-dominated spectral energy distribution (SED). Therefore such methods are not suitable to detect the interesting sample of low-luminosity AGNs in which the galaxy emission dominates the overall SED.

Other ways to select AGNs are through excess radio, X-ray or mid-infrared emission. Radio selection has the downside that it only selects a small sub-sample of AGNs. Only about 10% of all optically selected AGNs show considerable radio emission (Smith & Wright 1980). Radio surveys are also generally shallow or may suffer from confusion due to large apertures. An exception to this rule is the FIRST survey which imaged a large area of the sky using the NRAO Very Large Array, the resolution of this survey is similar to ground-based optical surveys and the depth of the survey exceeds most other radio surveys (Becker et al. 1995). X-ray surveys have similar problems to most radio surveys, the resolution is generally rather poor, causing problems with confusion. Due to the limited size of space-based X-ray telescopes it is also hard to detect faint high-redshift sources (Chandra has a 1.2 m mirror, Weisskopf et al. 2000; the XMM-Newton's effective collecting area corresponds to a mirror size of only about 80 cm, Jansen et al. 2001).

Mid-infrared emission is thought to originate from warm dust in the obscuring dust torus surrounding the AGNs (Sanders et al. 1989). However, also star-forming galaxies such as ultra-luminous infrared galaxies (ULIRGs) show excess mid-infrared emission (Genzel et al. 1998). As star-forming galaxies are especially common at redshifts of around 2 or 3 (see, e.g., Madau et al. 1998; Reddy et al. 2006; Bouwens et al. 2010), mid-infrared selected samples are polluted by star-forming galaxies, especially at higher redshifts. Additionally, at very high redshifts, the universe might have been too young for considerable amounts of dust to be produced. Indeed, some high-redshift AGNs have been shown to be virtually dust free (Jiang et al. 2010).

Given that practically all AGNs vary on all timescales from hours to decades (for a review, see Ulrich et al. 1997), variability can be used as a selection criterion for AGNs (e.g., Sarajedini et al. 2003). Due to light time travel arguments, any variability detected in galaxies on human-observable timescales must originate from the nuclear region. Interestingly, it has also been found that fainter AGNs vary more strongly than their bright counterparts (e.g., Trevese et al. 1994; Cristiani et al. 1996; di Clemente et al. 1996; de Vries et al. 2005; Wold et al. 2007). This makes variability-selected samples especially sensitive to the interesting and otherwise difficult to detect sample of low-luminosity AGNs. Additionally, it has been found that AGNs vary more strongly on shorter wavelength (e.g., di Clemente et al. 1996). This makes variability selection more sensitive at higher redshift in a given optical waveband.

Deep multi-waveband surveys such as the Great Observatories Origins Deep Survey (GOODS; Giavalisco et al. 2004) are very well suited for creating such a variability-selected AGN sample. Data for such surveys are typically taken in several epochs, distributed over several months and are therefore suitable to detect variability on timescales of months. Additionally, extremely deep imaging on a wide range of wavelengths all the way from X-ray to radio gives the possibility to study the broadband multi-wavelength properties of variability-selected AGNs (e.g., Paolillo et al. 2004) as well as their parent population.

Sarajedini et al. (2003) were the first to attempt assembling a variability-selected sample from multi-epoch survey data in the GOODS fields. They used the two-epoch Hubble Deep Field (HDF) V-band data, sampling a time span of five years. They found evidence for nuclear variability in 16 galaxies down to a V-band magnitude of 27.5. Given that this study was performed on only two epochs of data, this was an extremely encouraging result, showing that variability selection can succeed even for sparsely sampled data. The AGNs found by Sarajedini et al. (2003) show redshifts up to 1.8. They were able to show that the variability-selected AGNs cover a wide range of colors and might not have been detected using color–color selection criteria. Based on their sample they derived an AGN luminosity function and found that low-luminosity AGNs are possibly more abundant at high redshifts.

Cohen et al. (2006) published a similar study based on the Hubble Ultra Deep Field (HUDF) i-band data, sampling a time span of about four months. They found about 1% of the sources to show significant variability with photometric redshifts as high as 5.

Klesman & Sarajedini (2007) presented a study of the five epoch V-band data in the GOODS South field. They limited their study to infrared power law and X-ray-selected sources. As much as 26% of their AGN candidate sample showed variability.

Trevese et al. (2008) applied similar method to the Southern inTermediate Redshift ESO Supernova Search (STRESS) data. This survey covers about 5 deg² around the Chandra Deep Field South (CDFS). In contrast to previous studies discussed here, the data were taken with a ground-based telescope. This results in significantly lower resolution, making it harder to detect the variability of a point source against the flux of its hosting galaxy. They applied their method to eight epochs of V-band data taken around CDFS and found 112 out of 5138 objects (about 2% of all sources) to be variable.

Detecting variability from sparsely sampled data is extremely challenging. In general, there are two approaches to variability detection. The first approach is to use well-calibrated and robust statistical estimators such as the χ²-statistics. This approach allows for an effective control of false positive rates as the estimators have known expected distributions for samples of non-variable sources. The downside of such an approach is that one has to rely on the correctness of the error measurements. Given the fact that all kinds of unknown sources of error and systematics might influence aperture photometry, this approach is often avoided. The only statistical estimator for variability selection that does not show this drawback is the analysis of variance (ANOVA; de Diego 2010). It can however only be applied to data with large numbers of data points that are oversampled in the time domain (see, e.g., Villforth et al. 2009; de Diego 2010).

The second approach derives "typical" scatter at a certain magnitude and then declares a certain number of objects that show "significantly more scatter" variable (this approach has been taken by Sarajedini et al. 2003; Cohen et al. 2006; Klesman & Sarajedini 2007; Trevese et al. 2008). While this approach is robust in a sense that the scatter in the "real" data is taken into account, it is lacking a control of false positives and locally differing errors.

In this paper, we will present a method that combines the advantages of both approaches. Our methodology takes into account the observed scatter but uses well-calibrated statistical estimators. We are therefore in full control of expected false positive rates.

We present a catalog of 139 variability-selected AGNs from the GOODS North and South field in the Hubble Space Telescope (HST) F850LP band. This is the first variability-selected AGN catalog with a known expected contamination rate. Properties of the variability-selected AGNs will be discussed in an upcoming paper.

Sample selection and data reduction are presented in Section 2. We present and discuss statistical methods for variability selection in Section 3. We present the application of the discussed methods to our data set in Section 4, followed by discussion in Section 5 and summary and conclusions in Section 6.

2. SAMPLE SELECTION AND DATA REDUCTION

For our variability study we select all objects from the GOODS five epoch z-band catalog (Giavalisco et al. 2004) with a signal to noise of 20 or greater. This results in a magnitude limit of about 25–26 in the z/F850LP band. The z band was chosen as it has the deepest imaging of all the space-based optical observations. Another factor in choosing the most appropriate waveband is the fact that AGNs are on average more variable at shorter wavelengths (e.g., di Clemente et al. 1996). For this study, we decided to use the z band as it is considerably deeper than the bluer bands. Additionally, using blue wavebands might increase the influence of star-forming regions, especially at higher redshifts and therefore diminish our detection power. The signal-to-noise cutoff showed to be appropriate for this study as the percentage of variability-selected objects at magnitudes greater than 25 starts to be extremely low. This indicates that the signal to noise at fainter magnitudes is too low to pick up variability.

Data have been taken with the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) aboard HST in the F850LP band. Data reduction is performed using MultiDrizzle (Koekemoer et al. 2002).

Photometry is performed using the NOAO–IRAF³ aperture photometry package daophot. Apertures with four different radii (0 farcs 12, 0 farcs 24, 0 farcs 36, and 0 farcs 72) centered to the catalog positions are used. Different aperture sizes are used to determine the best aperture for this study. Several factors are important when selecting apertures, those are: signal-to-noise ratio (S/N), influence of small changes in point-spread function (PSF) and influences of galaxy light included when detecting variability of a point source against its hosting galaxies. The smallest aperture was chosen because at even lower radii, PSF changes become dominant, the largest was chosen because initial tests showed the S/N to plummet around the value chosen for the largest aperture.

The flux in units of counts per second is derived for all five epochs and all four apertures used. This is done by summing over the aperture and subtracting the sky determined in an annulus with an inner radius of 3'' and a width of 1'' using the NOAO–IRAF sky algorithm "ofilter." This algorithm uses the optimal filtering algorithm and a triangular weighting function employing the histogram of the sky pixels. It is found to yield the least bias in the presence of faint objects in the sky region (H. C. Ferguson 2010, private communication). Flux measurement errors are determined using MultiDrizzle (Koekemoer et al. 2002) weight maps. Inverse variance weight maps are summed over the aperture. These measurement errors include errors introduced by the data reduction process. To check for the correctness of the weight maps, we perform the following test. Blank sky positions are selected and the flux in the blank positions are measured over five epochs. The errors for the sky positions are then determined from the weight maps. No variability is detected using this process. We therefore conclude that the weight maps reflect the errors from the data reduction process correctly. If the weight maps would be incorrect, they would either over- or underestimate the flux measurement errors. As there should be no variability in blank sky positions, this procedure is suitable to determine if the measurement errors derived from the weight maps are correct.

Background subtraction errors are included by quadratically adding the standard error of the mean in the sky ring times the number of pixels in the aperture to the flux error from the weight maps. To account for shot noise, exposure time corrections are determined. To do this, we examine the distributions of the flux measurement errors from the weight maps derived for the objects. As the error determined from the weight maps only includes errors introduced by the data reduction process, the flux error distribution shows three separate peaks, corresponding to areas with four, two, or one pointings per epoch (i.e., longer exposure times correspond to lower errors from the data reduction process). According to the measurement errors determined by the weight maps, the corresponding exposure time is assigned for each object in each epoch. Using this exposure time, we calculate the full standard deviation and variance from shot noise. Standard deviation and variance are scaled to units of counts per second. The standard deviation is calculated as follows:

$\begin{equation} \sigma _{\rm full} = \frac{ \sqrt{(\sigma _{\rm wht} \times t_{\rm exp}) ^ {2} + {\rm flux} \times t_{\rm exp} }}{t_{\rm exp}}, \end{equation} \tag{ 1 }$

where σ_wht is the measurement error from MultDrizzle weight map, flux is the flux in the given aperture and t_exp is the inferred net exposure time.

The scaled variance is calculated as follows:

$\begin{equation} {\rm var}_{\rm full} = \frac{(\sigma _{\rm wht} \times t_{\rm exp}) ^ {2} + {\rm flux} \times t_{\rm exp}}{t_{\rm exp}}. \end{equation} \tag{ 2 }$

Note that we calculate both the standard deviation and the variance scaled to units of counts per second. Due to the fact that the square root is not a linear operator, var = σ² is only valid in units of electrons. Therefore, when fluxes are scaled to counts per second, the corresponding standard deviation and variance have to be calculated separately as var = σ² no longer holds.

3. STATISTICAL METHODS FOR VARIABILITY DETECTION

In this section, we present and discuss different statistical methods suitable for variability detection in sparsely sampled data. These methods are compared to methods previously used in similar studies (Sarajedini et al. 2003; Cohen et al. 2006; Klesman & Sarajedini 2007; Trevese et al. 2008). Statistical calculations are performed using the Python numerical and scientific packages NumPy⁴ and SciPy.⁵ NumPy random number generators are used for all simulations.⁶

For sparsely sampled data, only few statistical methods are suitable for variability detection. In this paper, we test and discuss the χ²-, F-, and C-statistics.

The χ²-statistics is widely used in general model fitting. In variability detection, it is used under the null hypothesis that a flat line fits the data, which corresponds to a null hypothesis that the object is not variable. It is calculated as follows:

$\begin{equation} \chi ^{2} = \sum_{i=1}^n {\displaystyle {(y_{i} - \bar{y})^{2} \over \sigma _{i}^{2}}}, \end{equation} \tag{ 3 }$

where y is the flux, $\bar{y}$ is the mean over all y_i, and σ_i is the measurement error associated with a given flux measurement y_i. This method has the advantage that it associates each flux measurement with its error estimate (as we will see soon, this is not the case for the other two methods). It is therefore well suited if one expects the errors to show significant deviations among epochs.

The F-statistics compares the expected to the observed variance. It is calculated as follows:

$\begin{equation} F = {\displaystyle {{\rm var}_{\rm observed} \over {\rm var}_{\rm expected}}}, \end{equation} \tag{ 4 }$

where var_observed is the variance in the flux measurements and var_expected is the mean of the flux error estimates given as variances. Note that, opposed to the χ²-statistics, the measurements errors are not associated with individual flux measurements. Instead, both the flux measurements and error estimates are considered as samples. The F-statistics should therefore be restricted to cases in which similar errors for each measurement are expected or observed.

The F-statistics is also used in ANOVA. This statistical method is a powerful tool for variability detection in cases in which the time domain is oversampled and many measurements are available. ANOVA does not rely on error measurement but derives the expected variance from sub-samples of the data. It is therefore used in micro-variability studies (de Diego et al. 1998; Villforth et al. 2009) and is shown to have a very high power (where power is defined as one minus the rate of Type II errors or false negatives; de Diego 2010). ANOVA can however not be used in this study due to the small number of data points available.

The C-statistics compares the expected to the observed standard deviation. It is calculated as follows:

$\begin{equation} C = {\displaystyle {\sigma _{\rm observed} \over \sigma _{\rm expected}}}. \end{equation} \tag{ 5 }$

In our case, σ_observed is the observed standard deviation in the fluxes and σ_expected is the mean of the flux error estimates given as standard deviations. Note that this is mathematically not identical to the F-statistics where the variances are compared. From a mathematical standpoint it should be noted that opposed to the variance, the standard deviation is not a linear operator. For example, when adding errors, variances can be added directly while standard deviations cannot. Just as the F-statistics, this method does not relate each measurement to its error and should therefore only be used when similar errors are expected for each epoch.

Previous studies of similar data sets have used other methods. Sarajedini et al. (2003) analyzed two epochs of V-band data of the HDF. They calculated the difference in magnitudes between the two epochs and declared all objects with a deviation three times bigger than the standard deviation of all differences at a given magnitude as variable. They found the distribution of the differences to be close to Gaussian and therefore used two-tailed p-values for a Gaussian distribution to estimate the number of false positives. This method seems very robust, it also provides false positive estimates.

Cohen et al. (2006) analyzed four epochs of data from the HUDF. They compared each of the measurements in the four epochs to the measurements in all other epochs, yielding six measurement pairs per object. They then empirically determined the error distribution for each epoch pair and declared all objects with a difference bigger than 3σ variable for the given epoch pair. Variability is then derived by analyzing the magnitude differences in each of the pairs. This is comparable to the method used by Sarajedini et al. (2003). However, they only had two epochs of data and therefore were limited in their choice of appropriate statistical methods.

The method used by Cohen et al. (2006) has the downside that variability is estimated from six different values and the ultimate selection criterion is rather complex. Determining false positive rates would be possible using simulations, but is not straightforward due to the complex selection criterion used.

A flavor of the C-statistics was used by both Trevese et al. (2008) and Klesman & Sarajedini (2007). In this method, the standard deviation of the measured magnitudes of an individual object is compared to the mean standard deviation of the entire sample under the assumption that most objects are not variable. The two studies differ slightly in the way they calculate the mean error for each object. While Trevese et al. (2008) average over the standard deviations, Klesman & Sarajedini (2007) parameterize variability using a quantity derived from the average of the variances in the magnitudes measured for each epoch. While it is true that var = σ², it should be kept in mind that a square root is not a linear operator. Therefore, var = σ² is only valid in the space of the measurement. This equation is however no longer valid when the measurement is transposed into another space like counts per second (which represents a multiplicative transformation from the original space of the measurements) or magnitude (which is a highly nonlinear transformation).⁷

In those previously mentioned studies, sources that show a scatter of more than e.g., three times the normal scatter are then labeled variables. This method is therefore similar to a C-statistics under the assumption that all objects at a given magnitude have the same errors (i.e., the errors are fully shot-noise dominated and the net exposure times are identical for all objects and epochs).

This method has several problems and caveats. Using this method, it would require extensive simulations to associate the chosen selection criterion (in the example, 3σ) with a significance value. Such simulations have not been performed by the authors. Therefore, no expected false positive rates are available for those studies. This caveat can be important for large samples if they have a high number of false positives, in which case it would adversely impact the statistical significance of the number of detections. The statement that there are 100 variables, technically only means that the 100 most variable objects are listed. The fact that the variability limit is derived from the data also introduces the problem that more variable sources will result in a higher limit, i.e., the detection limit depends on the number of variable sources. This will for example result in an overdetection of variability in faint sources, caused by the fact that this method enforces similar percentage detection rates at every magnitude.

Additionally, using this method gives little control over the correctness of the error measurements. While the method takes into account the real scatter of the data, it cannot determine if the measured errors are correct. Therefore, PSF changes or location-dependent errors will remain unnoticed using this method. Apprehensions concerning erroneous error estimates seem very realistic given the complexity of the errors that can be introduced in the data reduction process and the known complexity of space-based PSFs.

On a side note, using magnitudes for variability detection seems to be very common. However, errors in magnitude space will be both non-Gaussian and asymmetric, while being close to Gaussian in flux space. When using common statistical estimators, this can cause problems as most statistical methods explicitly or inexplicitly assume Gaussian errors.

3.1. Calibrating Statistical Methods

To compare the different methods, the p-values for the different estimators need to be calibrated. p-values are values assigned to a given value of an estimator (in our case, χ², F, and C). The p-value for a given value of the estimator is the probability that a value as "extreme" occurs from random data. Two different p-values exist and they should not be confused.

Two-tailed p-values give the probability that a value derived from random data is further away from the center of the distribution than the given value or values. Two-tailed p-values are symmetric for symmetric distributions. For asymmetric distributions, they are defined such that each tail contains the same probability.

One-tailed p-values give the probability that a value derived from random data is bigger than the given value. It can be derived for all distributions, including asymmetric ones.

Whether one- or two-tailed p-values should be used depends on the variability statistics used. For distributions in which both tails represent extreme variability (for example, if deviations from catalog magnitudes are given), two-tailed p-values should be used. For distributions in which one tail represents extreme variability while the other tail represents low variability, the one-tailed p-values should be used (for example, when using the χ²-statistics where low values indicate low variability and high values represent high variability).

The p-value associated with the value at which objects are considered variable is equal to the significance. The significance determines the number of false positives or Type I errors. It will also influence the power of the test. The power describes the percentage of real variables detected variable, and therefore is related to the number of false negatives (Type II errors). Choosing a very strict significance limit will result in a low power. On the other hand, choosing a very loose significance limit will result in a higher power. Therefore, when comparing different methods one has to be sure to compare them at the same significance.

Some authors use 3σ or 5σ to describe the significance levels used in their studies, defining objects that deviate from the commonly observed scatter by more than 3σ/5σ as variable. This is consistent in itself but often wrongly related to p-values. For example, relating 3σ to a significance level of 99.7% is wrong in the concept of variability detection as this is the two-tailed p-value for the Gaussian distribution. As discussed above, using two-tailed p-values is correct only for certain statistics. And this still leaves aside the fact that the distribution is likely not Gaussian and therefore the association between the σ values and the p-values for Gaussians does not hold.

The p-values for the three statistics used in this study at different significance levels are shown in Table 1.

Table 1. One-tailed p-values for Estimators χ², F, and C

Estimator	p = 95%	p = 99%	p = 99.9%	p = 99.99%
χ²	9.48	13.26	18.46	23.41
F	1.89	2.65	3.69	4.70
C	1.38	1.63	1.92	2.17

Note. p-values are given for light curves with five data points at different significance values.

Download table as: ASCII Typeset image

3.2. Testing the Power of Different Statistical Tests

Using the p-values derived in the previous section, the power of the different statistical tests can be determined. Mock variable light curves are created, randomized, and the statistical estimators are derived. Detection rates are then calculated. Three different types of mock variable data sets are studied.

1.
Noise. The flux for each data points is drawn from a normal distribution with a range of standard deviations σ_var.
2.
Slope. The underlying theoretical light curve is a simple linear trend with a range of slopes, each data point is randomized with a standard deviation of σ_o.
3.
Burst. The underlying light curve is completely uniform with only a single outlier with a range of differences between base and peak value, each data point is randomized with a standard deviation of σ_o.

A measurement error of σ_o is assigned to all flux values. A range of "variability strengths" V is studied for all mock light curve classes. The variability strengths V are defined as follows for the different mock light curve classes.

1.
Noise. $V = {\displaystyle {\sigma _{\rm var} \over \sigma _{o}}}$ .
2.
Slope. $V = {\displaystyle {\max ({\rm light\ curve})-\min ({\rm light\ curve}) \over \sigma _{o}}}$ .
3.
Burst. $V = {\displaystyle {{\rm peak\ value} - {\rm base\ value} \over \sigma _{o}}}$ .

The power of the different statistical tests (i.e., the detection rate) at a given significance is then derived for the different types of light curves for a range of variability strengths. The detection rates for three methods show only minimal deviations that are consistent with error expected from the fact that we only use two decimals and therefore our p-values are not completely accurate. The results are shown in Table 2.

Table 2. Detection Power (in %) for Different Mock Light Curves at a Significance Level of 99.9%

V	Slope	Burst	Noise
0.5	0.11	0.17	0.00
1.0	0.20	0.35	0.14
1.5	0.40	0.97	8.33
2.0	0.82	2.46	32.96
2.5	1.59	5.74	56.55
3.0	2.94	12.14	72.53
3.5	5.57	22.62	82.59
4.0	9.65	37.15	88.45
4.5	15.57	53.80	92.12
5.0	23.64	69.91	94.70
5.5	33.32	82.97	96.32
6.0	45.39	91.74	97.23
6.5	56.99	96.60	97.93
7.0	68.56	98.81	98.40
7.5	78.35	99.62	98.83
8.0	85.97	99.92	99.05
8.5	91.90	99.98	99.28
9.0	95.63	99.99	99.38
9.5	97.88	100.00	99.54

Note. V is the strength of the variability as defined in the text.

Download table as: ASCII Typeset image

3.3. Testing Robustness of the Tests

As we have shown, the three different statistical tests have equal power for "perfect" data. However, real data is hardly perfect. Therefore, we will determine how robust the statistical tests are in presence of deviations from the perfect simulated data.

In the previously presented test, the flux measurement errors (meaning the standard deviation or variance) are measured accurately. However, this is not expected for real data. Errors are measured in a similar way to fluxes and this process introduces measurement errors also into the error measurement. Therefore, it is of interest to see how different tests perform for "erroneous" error measurements. For our mock data, that means that the flux measurement errors will also be drawn from a normal distribution with a certain width. The width of this distribution will give the "defectiveness" of the error measurements.

When rerunning the tests using "erroneous" errors we find that the different tests differ in their detection power. The χ²-statistics now shows the highest detection power, the C-statistics shows the second highest power, and the F-statistics shows the lowest power. Results for the detection power with "erroneous" errors are shown in Table 4, located in Appendix A.

We therefore conclude that the χ²-statistics should be used in cases in which the errors show strong deviations between the different epochs. The C-statistics is to be preferred over the F-statistics due to its greater power under the influence of erroneous error measurements. We will therefore only use the C- and χ²-statistics for our study.

3.4. Estimating the Influences of Sparse Sampling

Additionally, it is of interest to understand the detection power for AGN light curves. To determine the detection power, we create mock AGN light curves using the method introduced by Timmer & Koenig (1995). This method randomizes both the phase and the amplitude of the Fourier transform. In other methods, only the phase is randomized and therefore only a subset of all possible light curves is simulated (Timmer & Koenig 1995).

Ten-thousand mock AGN light curves are created. We simulate light curves 10 times longer than the sampling timescale to include the red-noise leak (see, e.g., Vaughan et al. 2003, for a discussion of the red-noise leak), five data points are drawn from the mock light curves with sampling similar to the GOODS five epoch time sampling. The data are then randomized with a range of errors and data are analyzed using the three statistical estimator discussed.

As a measure of the variability strength, we give the ratio between the assigned flux measurement errors and the median spread in the analyzed light curves in percent. With changes on a timescale of years of typically around 1 mag in AGN light curves, a common error of 0.1 mag would result in a signal strength of about 3, resulting in a detection probability of about 78% at 95% significance. Detection probabilities for other typical errors and variability strengths can be derived from Table 3.

Table 3. Detection Power (in %) for Mock AGN Light Curves for Different Significance Levels and Different Errors in % as Defined in the Text

Error (%)	Power (95%)	Power (99%)	Power (99.9%)
0.11	100.00	100.00	100.00
0.23	100.00	99.97	99.97
0.34	99.97	99.97	99.95
0.45	99.95	99.95	99.93
0.57	99.93	99.92	99.83
0.68	99.92	99.82	99.52
0.79	99.82	99.53	99.29
0.91	99.56	99.32	98.87
1.02	99.44	99.02	98.25
1.13	99.22	98.73	97.40
2.27	91.99	87.42	81.46
3.40	78.12	69.34	60.51
4.54	63.25	53.08	42.69
5.67	49.47	38.72	28.92
6.81	37.74	27.84	18.82
7.94	28.81	19.34	11.81
9.08	21.23	13.33	7.32
10.21	15.58	8.86	4.11
11.35	10.92	5.49	2.13
12.48	7.80	3.32	1.21
13.62	5.24	1.93	0.53
14.75	3.36	1.18	0.28
15.89	2.09	0.61	0.13
17.02	1.43	0.35	0.03
18.16	0.88	0.20	0.00
19.29	0.43	0.07	0.00
20.43	0.33	0.02	0.00
21.56	0.19	0.00	0.00

Download table as: ASCII Typeset image

4. RESULTS

4.1. Zero-point Calibration

First, we check for possible zero-point offset between epochs. We analyze offset in the zero point for bright, point-like objects. Zero-point offsets are derived for aperture corrections (i.e., the correction applied to determine the entire flux of the object instead of the flux in the aperture) and inter-epoch zero-point drifts. This is done by calculating the mean offset between the measured magnitude and catalog magnitude for bright, point-like objects. The zero-point drifts for the large apertures are very mild, indicating changes below 0.01%. This implies that the photometric calibration is extremely accurate, the differences are within the error of the estimator used.

For the smallest aperture (0 farcs 12 radius) however, the fitting indicates inter-epoch changes on the level of ∼1%. We therefore correct the fluxes and errors with the derived zero-point offsets for the 0 farcs 12 aperture and compare the number of detections with and without the correction applied. The number of variables increases when correcting for zero-point drifts indicating that either the error of the fitting routine is dominating or that changes in the PSF are location dependent. Therefore, we test for possible problems with PSF instabilities in the next subsection.

While we could simply use the biggest aperture to avoid such problems, this is not the optimal solution. Big apertures can result in both low S/Ns and lower detection rates for faint AGNs due to high contribution from the hosting galaxy. Therefore, we will try to assess which aperture is optimal for this study.

4.2. PSF Stability

Using TinyTim (Krist 1995), we test possible influences of defocusing over the field of view and changes in the PSF shape to get an estimate of the errors expected from PSF changes.

First, images are checked for possible changes in the apparent position between the different epochs. Objects show decentering between different epochs only on sub-pixel scales, as this is comparable to the accuracy of the centering algorithm, no decentering is assumed between epochs.

To test for possible errors due to changes in the PSF, PSFs for 64 ACS WFC positions with filter F850LP are created. Defocusing is introduced with values between −5 and +5 μm in steps of 1. These values describe the movement of the secondary mirror with respect to the primary, where 0 corresponds to the telescope being in focus. Those values are typical focus changes due to "breathing" of the HST spacecraft (di Nino et al. 2008). Both an E galaxy template and a QSO template are used for the objects spectral shape, but no difference show in the resulting PSFs. Aperture photometry is then performed on each image with the same aperture sizes used for the data. From this measurement, typical errors due to both changes of the position of the object on the chip and the focus can be estimated. For the smallest aperture (0 farcs 12), typical values for PSF changes expected are ∼1%, dropping to ∼0.25% for the 0 farcs 24 aperture, ∼0.15% for the 0 farcs 36 aperture, and ∼0.1% for the 0 farcs 72 aperture.

Note that there is a known red halo in the ACS WFC for the F850LP filter which is not included in TinyTim (Sirianni et al. 2005). This might slightly alter our results, making the possible changes due to defocusing and changes over the field of view smaller. False variability due to the changes in the red halo are only expected if spectral changes occur. In case the spectral shape changes, the object is intrinsically variable. Therefore, the red halo might cause true variability to be boosted, but no excess false variability is expected to be introduced due to this effect.

Given the expected errors due to PSF changes, we will first asses if PSF instabilities induce false variability for small apertures in the data. Figure 1 shows the detection rates for point-like and extended objects over the aperture radius used. As we can see, the detection rate for point-like objects is generally significantly larger than for extended objects. This indicates that point-like objects are intrinsically more variable than extended objects. This is expected given the fact that most high-luminosity AGNs would appear point-like due to the fact that the AGN significantly outshines the galaxy.

**Figure 1.** Percentage of object-detected variables, separated into point-like (red pentagons) and extended (blue circles) objects. Detections are performed using C-Statistics for four different aperture radii.
Download figure:
Standard image High-resolution image

However, the detection rate for stars is significantly higher at the two smallest apertures, indicating that PSF changes induce false variability. Figure 2 shows a comparison between the observed estimator distributions of point-like and extended sources. The shape of the distribution differs strongly for the two smallest apertures. For the two biggest apertures however, the distributions agree well. This indicates that PSF changes will not affect those apertures.

**Figure 2.** Observed distribution for variability estimator C for point-like (red dashed line) and extended (green dash-dotted line) objects. Objects are divided into classes according to their stellarity measure ClassStar at a value of 0.5.
Download figure:
Standard image High-resolution image

On the other hand, for the purpose of studying variable AGNs, it should be noted that making the aperture bigger will start to drown the variability in the host galaxy light. This is due to the fact that bigger apertures will include more emission from the hosting galaxy. Therefore, the smallest possible aperture should be used. As the two smallest apertures show signs of variability due to PSF errors, we use an aperture with a radius of 0 farcs 36.

4.3. Re-calibration of Statistical Estimators

The photometric errors of ACS have been studied excessively (Sirianni et al. 2005). However, given the extreme importance of exact error measurements in this study and the general complexity of photometric errors, we will check and if necessary correct the error measurements derived. To check the quality of our measurement errors (σ_full as defined in the text), we compare the distributions of measured χ² and C to the theoretical distributions. It is assumed that most objects are not variable and therefore the observed distribution should follow the theoretical distribution.

We find that the observed distributions for our measurements with an aperture radius of 0 farcs 12 agree rather well with the theoretical distributions (Figure 3), inspite of the PSF problems. Using bigger apertures, the distributions start to deviate from the theoretical ones, showing a flatter tail toward higher values than expected (Figure 3). This indicates that either the shot noise or the background contribution are underestimated. This will result in excess false positives. However, as we have discussed in the last paragraph, aperture radii of 0 farcs 36 should be used to avoid false positives due to PSF changes.

**Figure 3.** Comparison between observed and theoretical χ² distribution for four different aperture radii. Upper panel: theoretical distribution (red dashed line) and observed distributions (solid line histograms). Lower panel: difference between theoretical and observed distributions. Only objects with detections in five epochs are included.
Download figure:
Standard image High-resolution image

To check more closely for possible problems in the error determination, we compare the variability estimator distributions to the theoretically expected distributions for different object magnitudes. We find that the distributions shift to higher values at higher fluxes for all apertures (see Figure 4 for an aperture radius of 0 farcs 12 and left panel of Figure 5 for an aperture radius of 0 farcs 36). This could be related to an underestimation of shot-noise errors or other factors. To correct for this problem, which could cause an overdetection of variability in bright sources, we decide to include a flux-dependent factor in the variability estimators. To derive this factor, we use the C-statistics. When applying a correction to the estimator, the error estimates are changed for all five epochs. This means that a correction is applied to the sample of errors. This is more compatible with the C than the χ²-statistics. Therefore, from now on the C-statistics will be used.

**Figure 4.** Comparison between theoretical and observed χ² distributions for a 012 aperture in different flux bins. Upper panel: theoretical distribution (red dashed line) and observed distribution (solid line histograms). The inset plot shows the histogram of catalog fluxes, the vertical lines denote the left limit flux of the histogram of the given color. Lower panel: difference between theoretical and observed distributions for same flux bins as in the upper panel.
Download figure:
Standard image High-resolution image

farcs — **Figure 4.** Comparison between theoretical and observed χ² distributions for a 012 aperture in different flux bins. Upper panel: theoretical distribution (red dashed line) and observed distribution (solid line histograms). The inset plot shows the histogram of catalog fluxes, the vertical lines denote the left limit flux of the histogram of the given color. Lower panel: difference between theoretical and observed distributions for same flux bins as in the upper panel.
Download figure:
Standard image High-resolution image

**Figure 5.** C-distribution (036 aperture) for four different flux bins before (left) and after (right) the flux-correction is applied. The solid-line histograms show the histograms for the different flux bins; the dashed red line shows the theoretical distribution. Lower panels show the differences between the theoretical and observed distributions. For the meaning of the histogram colors, see legend and inset plot in Figure 4.
Download figure:
Standard image High-resolution image

To derive the correction factor, we divide the sample into seven flux bins. A histogram of the test statistics is then calculated for each bin and a gaussian is fitted to determine the peak position of the distribution. This estimate for the distribution peak is then plotted against both the mean and the median of fluxes in each bin (see Figure 6). A clear trend for the peak to move to higher values at higher fluxes is visible. As the increase is presumably due to an underestimated flux error, a square root function with a y-axis offset is fitted to the data. The correction is then applied to the data by normalizing the test statistics with the value derived. From the definition of the C-statistics, we can see that this can also be interpreted as a correction applied to the error estimates.

**Figure 6.** Determining the flux-dependent error corrections for the observed C-distribution. Shown is the observed peak of the C-distribution vs. the mean (red "+" symbols) and median (blue "×" symbols) flux in each bin. The best fit to the data is shown as a dashed red line for the mean and a blue dotted line for the median. The big plot shows the data for low fluxes, the small inset shows the same data for the entire flux range. The axes labels for the inset plot are identical to the big plot.
Download figure:
Standard image High-resolution image

The flux-corrected C-distributions are shown in the right panel of Figure 5. As we can see that the distributions now agree well with the theoretical distributions. There are small deviations, but those indicate that the correction produced a slight overshoot, resulting in an overcorrection for very low C values. This could possibly cause an increase in the number of false negatives. However, as the deviations are only apparent in the left tail of the distribution, the possible effects of this overcorrection should be minimal. Using the flux-corrected 0 farcs 36 C value gives us 173 variable sources out of 11931 total sources at a significance level of 99.9%.

4.4. Clustering of Variable Sources: Testing for Locally Underestimated Errors

Next, we will determine if location-dependent errors or strongly location-dependent changes in the PSF have been underestimated. Extreme clustering of variable sources might indicate such problems. These kind of problems could be very hard to pick up using the previously described test as they would potentially affect only a small percentage of sources.

The spatial distribution of the variable objects in the GOODS North and South field is shown in Figures 7 and 8. At first visual inspection, a clear clustering at a few distinct locations is visible, especially in the GOODS North field. We inspect these areas by eye and find that those objects are located very close to bright stars that show clear diffraction spikes. The light curves show heavy outliers in some epochs. Indeed, visual inspection shows that diffraction spikes are present close to the centers of these objects. We reject the 18 objects affected by this problem, dropping our number of variables from 173 to 155.

**Figure 7.** Location of the variable (big red stars) and non-variable (small black dots) objects in the GOODS North field. Objects that have been rejected due to influences of nearby bright stars are plotted as small blue circles. Only objects with detections in all five epochs are included.
Download figure:
Standard image High-resolution image

**Figure 8.** Location of the variable (big red stars) and non-variable (small black dots) objects in the GOODS South field. Objects that have been rejected due to influences of nearby bright stars are plotted as small blue circles. Only objects with detections in all five epochs are included.
Download figure:
Standard image High-resolution image

However, there might still be more subtle clustering caused by underestimated location-dependent errors that is not picked up by eyeball inspection. Therefore, we calculate the distance to the nearest variable neighbor for all variables in the North and South field. We then create a mock variable catalog by randomly selecting the same number of sources for each field. Only objects with detections in five epochs are used for the selection. The distance to the nearest neighbor is also calculated for the mock catalogs.

The distributions of nearest neighbor distances for the variable and mock variable catalogs are then compared using a two-sample Kolmogorov–Smirnov test. In case the variable sources would be extensively clustered, the p-values should be small, indicating that the samples are not drawn from the same parent population.

We create 100,000 mock catalogs for each of the fields. Kolmogorov–Smirnov tests are then performed for the variable sample against each of the mock samples and against a master distribution created by merging all mock distributions. The p-values for the North field range from 0.02% to >99.9% with a mean of 36% and a median of 30%. Comparing the distribution for the variables to the master distribution gives a p-value of 28%. The p-values for the South field range from 10⁻⁴ to >99.9% with a mean of 32% and a median of 28%. Comparison with the master distribution gives a p-value of 20%. This shows that no excess clustering is found after rejecting objects affected by diffraction spikes. This finding indicates that location-dependent errors are well accounted for.

Auto or two-point correlation functions might be more appropriate to study possible clustering, but as our test with nearest neighbor distances does not show any abnormalities, this easy test should be enough to check for problems with location-dependent errors or PSF changes. Additionally, weak "real" clustering in our variability sample might be present. We will therefore not further explore this topic.

4.5. Rejection of Saturated Objects, Stars, and Supernovae

At this point, our catalog is only a catalog of variable objects, we are however interested in variable AGNs. To produce a catalog of variable AGNs, we need to reject saturated objects, stars and supernovae.

Figure 9 shows the location of the variable sources in a magnitude–stellarity plot. As a measure of stellarity, we use the SExtractor parameter ClassStar provided in the GOODS catalog (Dickinson et al. 2003). Objects with high stellarity can have two potential problems. They could be saturated or the nonlinear range of the chip could be reached, in both cases, false variability is expected.

To flag possible saturated objects or those in the nonlinear regime, we determine at which magnitude the objects start to enter the nonlinear regime. Therefore, the object flux is compared to the objects peak flux for all point-like sources and the turnover point is marked. This happens at 18th magnitude. All objects showing a peak flux higher than the turnover point or are brighter than 18th magnitude and point like are therefore rejected from our sample. None of our detected variable objects is in this regime. All bright stars were rejected before due to extremely high error bars, caused by the saturation or diffraction spikes.

As for excluding stars, we have to take into account that both stars and AGNs can appear point like. High-luminosity AGNs can be more than 100 times brighter than their hosting galaxy. Therefore, they appear point like even if the host galaxy could theoretically be resolved. Therefore, we will not reject point-like objects per se.

However, we correlate our data set with other catalogs to exclude stars. 15 objects in our variable catalog turned out to be red stars and are therefore rejected from the variable AGN catalog. They are given in the final table but are flagged as stars. More of our variability-selected objects might be stars, but we are confident that we were able to flag the majority of stars.

Supernovae are the only other objects that show variability on the sampled timescale. Therefore, we correlated our data with supernovae identified by Riess et al. (2004). This study identified supernovae from the five epoch GOODS data. We found that one supernova from Riess et al. (2004) is identified in this study as variable. This supernova (2003XX) went off in the very center of an elliptical galaxy. The light curve of this object indeed shows a singly outlier. This object is therefore rejected from the final variable AGN catalog. It is however listed in the variable table and flagged.

4.6. Variable AGN Catalog

Now that we have determined a reliable variability estimator and rejected objects influenced by diffraction spikes, saturated objects, stars, and supernovae, we can go ahead and asses the properties of the final variable AGN sample.

Figure 10 shows the flux-corrected C for a 0 farcs 36 aperture versus the object magnitude for the final sample. Variability is detected down to magnitudes as faint as 25.5, with the faintest object being clearly detected with a significance of 99.99%. All of the variable sources brighter than 18th magnitude are galaxies. At fainter magnitudes, both point-like and extended objects show in our variability sample, the most variable objects tend to be point like.

To assess if the signal-to-noise limit used in our data is too strict, the detection rate for the faintest sources is derived. For magnitudes >25, the detection rate is close to the expected false positive rate. This indicates that a lower signal-to-noise limit would only result in more false positives and not more "real" detections.

With 11,931 objects with five epoch detections in our catalog, false positive detections might pose a serious problem. To get an estimate for the expected false positives contamination, we conservatively assume that all objects are non-variable and calculate the number of false positives at a given significance.

For a significance of 95% we expect as many as 596 false positives. Even at a significance at 99%, the number of expected false positives is still very high (119). Only for a significance of 99.9% does the number of expected false positives drop to 12. At a significance level of 99.99%, we expect only a single false positive, making a catalog with such a strict selection criteria "clean" from false positives.

To see how this affects real data, we show the number of raw and false positive corrected detections in a number of magnitude bins (Figure 11). False positive corrections are applied by assuming that all objects are non-variable and subtracting the expected number of false positives from the number of detections. We see that false positives pose a very serious problem at all significance levels lower than 99.9%. Thus, this very strict limit should be used when determining the variable object catalog.

However, lower significance levels can be used when trying to estimate the number of variable objects in the field for statistical arguments. If one is not interested in knowing the individual objects that show variability but just the number of variable object in a given sub-sample, slack significance levels can be useful as they reduce the number of false negatives. This becomes evident when looking at Figure 11, there is a big number of false negatives at a 99.9% significance level.

To estimate the true number of variables, we use a relaxed significance level of 95%, this gives us 1072 "variable" objects, given the expected number of false positive (596) at this significance, we are left with 476 "true" variable objects, from those, we subtract the 18 objects found to show false variability due to spikes from bright objects. According to our findings, about 3.8% of all objects are variable. This however, does not account for contamination due to stars. In our final 99.9% significance catalog with 155 entries, 15 objects are stars. More objects might turn out to be stars, but could not be identified as such. Therefore, at least 10% of all variable objects identified in this study turn out to be stars. Assuming that 10% of all variable objects are stars, we derive that about 3.4% of all objects in our sample are variable AGNs. (Note that the percentage of stars might depend on the magnitude and therefore our assumption of a fixed rate of stars might not be correct.)

For the catalog, a significance level of 99.9% will be used. The final sample of variables therefore contains 155 objects, with catalog z magnitudes between 16.45 and 25.5. As mentioned above, the conservatively estimated number of false positives is 12, resolution in an expected catalog contamination of about 7.7%. Out of these 155 variable objects, 15 are identified as stars and one object is a supernova, leaving 139 variable AGNs.

Additionally, a "clean" sub-catalog with a selection criterion of 99.99% is provided. This catalog contains 93 objects and has only one expected false positive entry. This sub-catalog contains 10 stars and one supernovae, leaving 82 AGNs.

Both final catalogs are shown in Table 5. A flag in the table indicated if the objects belongs to the "normal" (99.9% significance) or "clean" (99.99% significance) catalog. The entire catalog will be made available at Vizier.⁸

4.7. Variability Strength

Additionally, we derive the intrinsic variability for the variability-selected sample. The observed variability can be written as

$\begin{equation} \sigma _{\rm observed} = \sqrt{\langle \sigma \rangle ^{2} + \sigma _{\rm intrinsic}^{2}}, \end{equation} \tag{ 6 }$

where σ is the measurement error. This gives the percentage variability V:

$\begin{equation} V = {\displaystyle {\sigma _{\rm intrinsic} \over \langle \mbox{flux} \rangle }} = {\displaystyle {\sqrt{\sigma _{\rm observed}^{2} - \langle \sigma \rangle ^{2}} \over \langle \mbox{flux} \rangle }}. \end{equation} \tag{ 7 }$

The percentage variability V for all objects in our variable sample is shown in Figure 12. Naturally, there is a lower envelope to the variability strength that is rising to lower luminosity objects, caused by the fact that the S/N is worse for lower luminosities, making it impossible to detect very subtle variability. V for all variable objects is also shown in the catalog table (Table 5).

To asses the detection limit, we fit a lower envelope to the data. The data is fit well by the following third-order polynomial:

$\begin{equation} V = 0.036 \times {\rm mag}^{3} -1.504 \times {\rm mag}^{2} + 15.993 \times {\rm mag} -1.644. \end{equation} \tag{ 8 }$

This equation holds for magnitudes >21, for lower magnitudes, a lower detection limit of about 1% variability strength is found.

5. DISCUSSION

5.1. Properties of Variability-selected AGN Candidates

All variability-selected objects are matched to the GOODS spectroscopic data (Vanzella et al. 2008; Popesso et al. 2009). Redshifts, flags, and absolute magnitudes of those objects are included in Table 5. Twenty-eight out of 155 objects can be matched to the spectroscopic data. Out of those 28 objects, 5 have been identified as stars. For three objects, no spectroscopic redshift could be derived. The remaining 20 objects have redshifts between 0.045 and 3.7. Amongst those are five broad-lined AGNs, with redshifts of 0.74, 0.84, 1.23, 1.61, and 2.80. With absolute rest-frame z-band magnitudes ranging between −22.57 and −24.31, all spectroscopically identified AGNs in our sample are rather faint. One spectroscopically identified object has an inferred absolute magnitude of −12.8, indicating that the redshift identification might be faulty. However the redshift estimation is based on a single line and might therefore not be correct. Practically, all sources show extremely strong line emission, indicating either high star formation rates or AGN activity.

All variability-selected objects are visually inspected. Forty-one objects are unresolved, out of those 15 are identified as stars, leaving 26 unresolved AGN candidates. Eighteen objects have a dominant core and show faint extended emission. Nine objects show clear signs of interaction, either in the merger stage or showing tidal tails. Sixteen objects are elliptical galaxies and four show clear disk structure. Forty-one are resolved, but no morphology can be determined. Those are mostly faint objects of small size. One object (J033241.87-274651.1) has been identified by Straughn et al. (2006) as a tadpole galaxies. Those interesting objects are believed to be galaxies in an early stage of merging (Straughn et al. 2006). However, this particular object is a rather extreme example of this object class as it shows much less substructure than most tadpole galaxies. It looks similar to a strong lensed galaxy. However, there are no clusters nearby.

Finally, seven objects show complex structures. Those galaxies either have multiple cores or are clearly extended with no clear center. Note that objects with multiple centers might be wrongly identified as variables due to PSF changes. This can happen even in cases in which the aperture is big enough to avoid false variability due to PSF changes for single-center objects. However, one of those complex sources (J033228.30-274403.6) is detected in X-rays. This object is also a B-band dropout, indicating redshifts around 2–3. Given that hot cluster gas emission is not detectable at such high redshifts, this indicates that there is indeed an AGN in this object. Therefore, complex objects will be included in the final catalog.

5.2. Comparison with Other Variable AGN Catalogs in the GOODS Field

Now that we have presented our variability-selected AGN catalog and the estimated occurrence of variability, we would like to compare our sample to other samples derived in a similar way in the same field.

Sarajedini et al. (2003) studied HDF data and found 16 variability-selected AGNs, none of those is found to be variable in our sample. They performed their study in the V band, which should pick up different types of variability than our z-band study (di Clemente et al. 1996). Additionally, they are covering a timespan of five years while our observations span only about a year. This will result in higher sensitivity for the detection of more luminous AGNs (e.g., Trevese et al. 1994; Wold et al. 2007). Sarajedini et al. (2003) used the HDF data, therefore the field is much smaller than ours but the data are deeper. All in all, their data are very different from ours, therefore, the missing overlap is somewhat expected.

Cohen et al. (2006) studied i-band HUDF data and found 45 "best variable candidates." The i band used by Cohen et al. (2006) is only slightly bluer than the z band used in this study. Therefore, the wavelength dependence of AGNs variability between those bands should be negligible. However, they covered a timespan of only about four months, opposed to about a year in this study. This makes their study less sensitive to variability on timescales of months and longer. The area covered by Cohen et al. (2006) is much smaller than ours, but their data are significantly deeper. Out of the 45 variable objects identified by Cohen et al. (2006), two are found in our catalog as variable. However, the objects found variable by Cohen et al. (2006) are mostly fainter than 25th magnitude and the two objects that are found in both catalogs are amongst the brightest in the Cohen catalog. Given that their data is much deeper, it is expected that little overlap is found between their and our sample.

Klesman & Sarajedini (2007) studied a sample of 112 X-ray and infrared-selected AGN candidates they selected from the GOODS V-band five epoch catalog. Twenty-nine of those objects showed variability. They used the V-band data as AGN variability is found to be stronger at bluer wavelengths (see, e.g., di Clemente et al. 1996). On the other hand, the z-band data used in this study are deeper than the V-band data used by Klesman & Sarajedini (2007). The time coverage for the Klesman & Sarajedini (2007) is practically identical to the one in this study. Their sample was drawn just from the GOODS South field and was also restricted to AGN candidates that were preselected, thus also accounting for the difference in sample size.

Out of the 29 variables from the Klesman & Sarajedini (2007) sample, 13 are detected variable in our study, 12 of those are in our clean catalog, two objects are too faint to be included in our sample, and two objects have been rejected due to suspiciously high error bars. Two objects have been detected variable in our study but not by Klesman & Sarajedini (2007). All other objects are not detected variable in both studies. This is a rather promising overlap.

The differences might be due to several reasons. The different waveband used might play a role since variability is stronger at shorter wavelengths (di Clemente et al. 1996). Additionally, we used a larger aperture than Klesman & Sarajedini (2007), which we chose in order to reduce PSF-related variability to less than 0.15%. Finally, the variability detection for our z-band selected sample becomes limited beyond about z ∼ 25, although a direct comparison with the V-band sample would also need to include differences in variability amplitude and color terms between the two bands.

Trevese et al. (2008) selected variable AGNs from the two year Southern inTermediate Redshift ESO Supernova Search (STRESS) data. Data were taken about every three months over a timespan of two years. Therefore, Trevese et al. (2008) not only cover double the time span covered in this study, they also have more data points available, making it more likely to detect variability. They used V-band data taken with the ground-based ESO/MPI 2.2 m telescope at ESO, La Silla (Chile). With a seeing of about 1'', their resolution is about 10 times poorer than that in all other studies discussed here (Sarajedini et al. 2003; Klesman & Sarajedini 2007; Cohen et al. 2006; this study). The poorer resolution makes Trevese et al. (2008) less sensitive to low-luminosity AGNs with clearly extended host galaxies. The area covered in their study is about six times larger than one GOODS field and therefore about three times larger than our entire field.

From the 112 variable objects found by Trevese et al. (2008), only 17 are also in the GOODS footprint. Out of those, three have been detected variable in our study, six objects did not have detections in all epochs, five are not variable in our study, two objects were too faint for our signal-to-noise cutoff, and one object would have been labeled saturated in our study. Given the big differences between their and our study, such a small overlap is expected.

6. SUMMARY AND CONCLUSIONS

In this paper, we have presented and discussed different statistical methods that can be used to detect variable sources in large samples. Results have been applied to the GOODS North and South five epoch z-band data.

All three statistical methods tested (C, F, χ²) show equal powers for mock data, however, in cases in which the error determinations are erroneous, χ² shows the highest power, followed by C and F. We have presented a robust statistical method for detecting variable objects from sparsely sampled data. Our method makes it possible to control the number of false positives and to test and correct for possible problems in the error determination.

We present a final catalog of 155 variable objects, selected with a 99.9% significance value. Out of those 155 objects, 15 are identified as stars and one objects is a supernova, leaving 139 variability-selected AGN candidates. The AGN candidates have magnitudes between 16.5 and 25.5 mag in the z band. The catalog has a expected false positive contamination of 12 objects, corresponding to a contamination of 7.7% in the entire variable catalog. Additionally, we present a "clean catalog" with a significance of 99.99%. This catalog contains 93 objects and 82 AGN candidates. It is expected to contain only a single false positive, corresponding to a contamination rate of about 1%. Detection rates at lower significance levels indicate that in total about 3.5% of objects are variable AGNs. This is higher than the variables rates claimed in previous studies (Sarajedini et al. 2003; Cohen et al. 2006; Klesman & Sarajedini 2007).

Twenty variability-selected AGNs have spectroscopic redshifts. The redshifts of those objects lie between 0.045 and 3.7. Amongst the 20 objects with optical spectra are five broad-lined AGNs, with redshifts between 0.7 and 2.8. With absolute magnitudes ranging between −22.57 and −24.31, all spectroscopically identified AGNs in our sample are rather faint. This shows that this method is indeed suitable for detecting low-luminosity AGNs up to very high redshifts.

Compared to other variability selected catalogs published so far, our GOODS catalog is larger than the one published by Sarajedini et al. (2003) on the Hubble Deep Field which covers a much smaller area, but goes deeper. Similarly, compared to Cohen et al. (2006), who covered the Hubble Ultra Deep Field, our sample also covers a larger area with about three times more sources, but is less deep. Since we study both GOODS fields and don't limit our sample to a preselected AGN catalog, our sample is also larger than that of Klesman & Sarajedini (2007), and our chosen aperture size reduces our susceptibility to false positives. Our area covered is smaller than the one in Trevese et al. (2008), and they also have a better time sampling. However, their ground-based data has poorer resolution, making it much less sensitive to the interesting sample of low-luminosity AGNs. Finally, our study, along with that of Sarajedini et al. (2003), are the only ones that provide estimates for false positive rates.

We have therefore presented a new extensive catalog of variability-selected AGNs in the GOODS fields. Our catalog contains interesting low-luminosity AGNs that cannot be detected using commonly used selection techniques. This makes our catalog an interesting probe for the poorly understood population of high-redshift low-luminosity AGNs.

Given the formidable multi-wavelength coverage of both GOODS fields and the availability of both photometric and spectroscopic redshifts, this sample can give unique insights into the properties of AGNs up to high redshifts and open the window to a sample of previously undetected low-luminosity high-redshift AGNs.

The multi-wavelength properties and parent population of our variability-selected AGN sample will be presented in an upcoming paper.

We thank the anonymous referee for helpful comments. Partial support for this work was provided by NASA through grant HST-GO-09935.01-A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. We acknowledge the help and support from H. Ferguson in providing advice on running the goodsphot script, which uses daophot to carry out photometry on the images. We acknowledge M. Paolillo for helpful discussions, and Vicki Sarajedini for helpful comments and a thorough reading of the paper.

APPENDIX A: RESULTS OF STATISTICAL SIMULATIONS

Results for the detection power with "erroneous" errors are shown in Table 4.

Table 4. Detection Power (in %) for Different Mock Light Curves at a Significance of 99.9% with "Erroneous" Errors

Statistical Method	Signal Strength	Slope 5%	Slope 25%	Burst 5%	Burst 25%	Noise 5%	Noise 25%
F	0.5	0.13	0.22	0.15	0.25	0.00	0.00
C	0.5	0.14	0.26	0.15	0.34	0.00	0.00
χ²	0.5	0.14	1.05	0.17	1.18	0.00	0.01
F	1.0	0.20	0.34	0.37	0.56	0.11	0.18
C	1.0	0.20	0.43	0.37	0.69	0.11	0.23
χ²	1.0	0.22	1.32	0.40	1.92	0.12	0.97
F	1.5	0.40	0.59	0.98	1.21	8.72	8.75
C	1.5	0.41	0.76	0.99	1.47	8.80	9.68
χ²	1.5	0.45	2.03	1.04	3.49	8.94	13.52
F	2.0	0.80	0.98	2.43	2.92	32.92	32.17
C	2.0	0.81	1.20	2.47	3.43	33.07	33.80
χ²	2.0	0.87	2.98	2.61	6.50	33.31	38.29
F	2.5	1.60	1.95	5.71	6.29	56.23	54.96
C	2.5	1.62	2.33	5.79	7.23	56.36	56.57
χ²	2.5	1.70	4.76	5.99	11.62	56.50	59.90
F	3.0	3.05	3.55	12.16	12.57	72.62	71.01
C	3.0	3.10	4.17	12.29	14.14	72.73	72.22
χ²	3.0	3.20	7.47	12.57	19.65	72.82	74.52
F	3.5	5.56	6.19	22.90	22.13	82.45	81.42
C	3.5	5.63	7.08	23.10	24.23	82.53	82.31
χ²	3.5	5.77	11.36	23.34	30.04	82.59	83.83
F	4.0	9.50	9.74	36.92	35.31	88.55	87.62
C	4.0	9.62	11.11	37.19	37.92	88.59	88.24
χ²	4.0	9.88	16.40	37.45	43.16	88.65	89.31
F	4.5	15.58	15.65	53.77	50.89	92.46	91.50
C	4.5	15.73	17.30	54.06	53.67	92.50	91.94
χ²	4.5	16.00	23.46	54.14	57.53	92.51	92.64
F	5.0	23.68	23.12	69.73	66.09	94.58	94.18
C	5.0	23.86	25.31	69.96	68.56	94.60	94.50
χ²	5.0	24.18	31.94	69.95	70.40	94.66	94.99
F	5.5	33.49	31.93	82.58	79.40	96.24	95.81
C	5.5	33.73	34.54	82.75	81.21	96.26	96.04
χ²	5.5	34.25	41.10	82.72	81.52	96.29	96.39
F	6.0	45.00	42.66	91.52	88.97	97.27	97.02
C	6.0	45.26	45.37	91.61	90.22	97.28	97.19
χ²	6.0	45.61	51.54	91.48	89.66	97.28	97.44
F	6.5	56.66	53.90	96.50	94.88	97.96	97.79
C	6.5	56.93	56.63	96.54	95.57	97.97	97.90
χ²	6.5	57.28	61.89	96.48	94.89	97.96	98.07
F	7.0	68.09	64.65	98.72	97.92	98.39	98.33
C	7.0	68.33	67.20	98.74	98.21	98.40	98.42
χ²	7.0	68.55	71.43	98.72	97.72	98.40	98.54
F	7.5	78.02	74.83	99.66	99.27	98.77	98.69
C	7.5	78.20	76.94	99.67	99.39	98.77	98.78
χ²	7.5	78.31	79.91	99.64	99.10	98.77	98.90
F	8.0	85.96	82.80	99.92	99.78	99.08	98.94
C	8.0	86.11	84.43	99.93	99.82	99.08	99.01
χ²	8.0	86.16	86.35	99.92	99.67	99.08	99.09
F	8.5	91.73	89.12	99.98	99.95	99.25	99.18
C	8.5	91.82	90.28	99.98	99.96	99.26	99.22
χ²	8.5	91.81	91.57	99.98	99.91	99.25	99.31
F	9.0	95.46	93.57	100.00	99.99	99.40	99.35
C	9.0	95.52	94.37	100.00	99.99	99.40	99.38
χ²	9.0	95.52	94.99	100.00	99.97	99.41	99.45
F	9.5	97.70	96.39	100.00	100.00	99.48	99.44
C	9.5	97.72	96.87	100.00	100.00	99.48	99.47
χ²	9.5	97.75	97.22	100.00	100.00	99.49	99.52

Notes. Variability strength V is identical to the one used in Table 2 and defined in the text. Results are given for an error in the error measurement of 5% and 25%.

Download table as: ASCII Typeset image

APPENDIX B: VARIABLE OBJECT CATALOG

Variable object catalogs are described in Table 5.

Table 5. First Part of Variable Object Catalog

ID	R.A. (J2000)	Decl. (J2000)	mag (z)	CS	C	V (%)	Catalog	Comment	z	M_abs
J033203.00-274213.6	53.01248	−27.7037872	25.14	0.09	2.55	28.23	Clean	Resolved	...	...
J033203.01-274544.7	53.0125331	−27.7624232	24.90	0.02	2.05	22.05	Normal	Resolved	...	...
J033203.26-274530.3	53.013574	−27.7584257	22.70	0.03	2.15	3.99	Normal	Resolved	...	...
J033204.41-274635.5	53.018367	−27.7765167	21.14	0.98	3.92	2.20	Clean	Unresolved	...	...
J033205.11-274317.5	53.021302	−27.7215411	21.91	0.98	4.30	3.72	Clean	Unresolved	...	...
J033205.40-274429.2	53.0224983	−27.7414518	22.97	0.03	2.47	7.86	Clean	Disk Galaxy	None	...
J033208.68-274508.0	53.036184	−27.7522317	22.70	0.03	1.98	5.01	Normal	Resolved	1.2964^L	−22.11
J033209.57-274634.9	53.0398585	-27.7763722	22.97	0.03	2.03	4.04	Normal	Elliptical	...	...
J033209.58-274241.8	53.0399142	−27.7116218	23.39	0.03	2.05	5.38	Normal	Elliptical	...	...
J033209.80-274308.6	53.0408277	−27.7190613	23.12	0.03	1.93	5.85	Normal	Interacting system	2.3021^S	−23.20
J033210.52-274628.9	53.0438334	−27.7747007	23.85	0.03	2.10	9.06	Normal	Resolved	...	...
J033210.91-274414.9^KS	53.0454704	−27.7374846	22.37	0.93	4.69	6.02	Clean	Elliptical	1.6082^L	−23.01
J033211.02-274919.8	53.045918	-27.8221721	23.45	0.03	2.15	9.70	Normal	Interacting system	1.9431^L	−23.42
J033212.16-274408.8	53.0506774	−27.7357915	24.79	0.03	2.29	22.17	Clean	Resolved	...	...
J033213.21-274715.7	53.0550544	−27.7876915	24.09	0.03	2.28	13.89	Clean	Resolved	...	...
J033213.34-274210.5	53.0555659	−27.7029202	23.84	0.99	2.34	7.71	Clean	Unresolved	...	...
J033215.16-274754.6	53.0631513	−27.7985117	22.98	0.98	2.07	3.32	Normal	Unresolved	...	...
J033215.93-275329.3	53.0663591	−27.8914797	19.86	0.92	2.15	0.69	Normal	Star^a	0.0000^S	...
J033216.34-274851.7	53.0681031	-27.8143745	21.98	0.98	2.65	2.37	Clean	Unresolved	...	...
J033216.87-274916.7	53.0702817	−27.8212937	23.40	0.98	2.43	5.88	Clean	Unresolved	0.0000^L	...
J033217.06-274921.9	53.0710682	-27.8227401	19.20	0.03	2.03	0.93	Normal	Interacting system	0.3375^S	−22.06
J033217.14-274303.3^KS,T	53.0714326	−27.7175864	20.57	0.03	3.14	1.44	Clean	Elliptical	...	...
J033217.72-274703.0	53.0738469	−27.7841607	23.59	0.03	1.99	6.18	Normal	Interacting system	...	...
J033218.24-275241.4^KS	53.0760024	−27.8781606	24.28	0.99	2.15	9.61	Normal	Unresolved	2.8049^S	−22.57
J033218.70-275149.3	53.0778965	-27.8637054	21.74	0.03	2.20	3.04	Clean	Disk galaxy	0.4568^S	−20.55
J033218.81-274908.5	53.0783542	-27.8190409	23.90	0.03	2.55	14.44	Clean	Complex	...	...
J033218.84-274529.2	53.078519	−27.7581146	18.78	0.03	2.44	0.97	Clean	Elliptical	...	...
J033219.81-275300.9	53.0825539	−27.8835727	24.46	0.03	1.95	11.16	Normal	Resolved	3.7072^S	−23.12
J033219.86-274110.0	53.0827492	−27.686119	23.37	0.00	2.07	8.80	Normal	Interacting system	None	...
J033220.80-275144.5	53.0866794	−27.8623513	21.22	0.98	2.91	1.71	Clean	Star	...	...
J033221.52-274358.7	53.0896509	−27.732984	21.00	0.97	1.95	0.99	Normal	Star^b	...	...
J033222.82-274518.4	53.0950956	−27.7550986	23.22	0.03	1.92	5.70	Normal	Resolved	...	...
J033223.53-274707.5	53.0980434	−27.785425	23.23	0.03	2.00	7.25	Normal	Interacting system	...	...
J033224.23-274129.5	53.1009433	−27.691518	25.01	0.00	1.96	21.51	Normal	Complex	...	...
J033224.54-274010.4	53.1022685	−27.6695645	21.88	0.03	1.95	2.54	Normal	Interacting system	...	...
J033224.80-274617.9	53.1033449	−27.7716431	23.06	0.03	2.69	7.15	Clean	Resolved	...	...
J033225.10-274403.2	53.1045636	−27.7342138	17.75	0.03	2.73	0.75	Clean	Elliptical	...	...
J033225.15-274933.3	53.1048118	−27.8259053	21.61	0.99	2.56	1.73	Clean	Star^a	0.0000^S	...
J033225.99-274142.9	53.1082952	−27.6952603	24.54	0.03	1.95	14.06	Normal	Resolved	0.0459^S	−12.18
J033226.40-275532.4	53.109991	-27.9256529	24.32	0.00	2.21	25.29	Clean	Complex	...	...
J033226.49-274035.5^KS,T	53.1103938	−27.6765399	19.60	0.93	13.45	4.35	Clean	Core + spiral structure	0.5404^L	−22.87
J033227.01-274105.0^KS	53.1125287	−27.6847238	19.00	0.93	3.97	1.00	Clean	Core + extended emission	0.7423^S	−24.31
J033227.18-274416.5	53.113269	−27.73791	19.37	0.03	2.26	0.89	Clean	Elliptical	...	...
J033227.51-275612.4	53.114644	−27.9367764	24.04	0.03	4.18	20.42	Clean	Resolved	0.6630^S	−18.97
J033227.86-275335.6	53.1160832	-27.8932186	21.84	0.98	5.00	2.44	Clean	Star^c	...	...
J033227.87-275335.9	53.1161233	-27.8933035	21.63	0.99	2.30	1.08	Clean	Star^c	...	...
J033228.30-274403.6	53.1179209	−27.7343234	23.76	0.00	2.25	28.74	Clean	Complex	...	...
J033228.45-274203.8	53.118527	−27.7010451	24.23	0.99	2.08	9.44	Normal	Unresolved	...	...
J033229.88-274424.4^KS	53.1244949	−27.7401248	16.45	0.03	2.23	1.09	Clean	Disk galaxy	...	...
J033229.98-274529.9^KS	53.1249148	−27.7583013	21.06	0.93	4.38	2.62	Clean	Core + extended emission	1.2091^S	−23.55
J033229.99-274404.8	53.1249588	−27.7346753	16.84	0.03	2.32	0.84	Clean	Disk Galaxy	0.0746^S	−20.81
J033230.06-274523.5^KS	53.1252547	-27.756535	21.81	0.25	2.47	3.20	Clean	Resolved	...	...
J033230.22-274504.6^KS	53.1258995	−27.7512749	21.50	0.92	5.39	4.07	Clean	Core + extended emission	...	...
J033230.36-275133.2	53.1264805	−27.8592312	25.01	0.03	2.09	22.48	Normal	Resolved	...	...
J033231.80-275110.4	53.1324925	−27.8528853	21.03	0.98	6.58	2.99	Clean	Unresolved	...	...
J033231.82-275110.6	53.1325905	−27.8529435	21.06	0.99	5.74	2.50	Clean	Star^b	...	...
J033231.94-274531.3	53.1330882	−27.7587052	21.11	0.99	2.15	1.16	Normal	Star^d	...	...
J033232.04-274523.9	53.1334996	−27.7566329	23.45	0.03	1.97	6.95	Normal	Interacting system	...	...
J033232.12-275636.8	53.1338346	−27.9435593	21.04	0.99	1.97	1.02	Normal	Star^e	...	...
J033232.32-274316.4	53.1346778	−27.7212189	22.11	0.98	2.24	2.16	Clean	Unresolved	...	...
J033232.49-275044.0	53.1353687	−27.8455431	23.42	0.03	2.12	8.15	Normal	Disk galaxy	...	...
J033232.61-275316.7	53.1358826	−27.8879636	22.93	0.03	2.32	5.00	Clean	Interacting system	0.9873^S	−21.14
J033232.67-274944.6	53.1361117	−27.829048	18.29	0.03	2.95	0.83	Clean	Elliptical	...	...
J033233.68-274035.6	53.1403383	−27.6765489	24.94	0.02	2.59	24.37	Clean	Resolved	...	...
J033235.38-274704.3	53.1474321	−27.7845155	25.21	0.04	1.97	20.68	Normal	Resolved	...	...
J033236.92-275308.4	53.1538193	−27.885679	24.41	0.03	1.95	11.75	Normal	Resolved	...	...
J033237.16-274128.2	53.1548456	−27.6911768	23.36	0.03	2.49	7.93	Clean	Resolved	...	...
J033237.93-274609.1^C	53.1580245	−27.769192	19.96	0.93	4.37	1.51	Clean	Unresolved	0.086^f	−18.02
J033238.12-273944.8^KS	53.1588307	−27.6624444	20.43	0.92	13.09	5.39	Clean	Core + extemded emission	0.8376^S	−23.20
J033238.89-275406.7	53.1620545	−27.9018501	24.49	0.03	1.99	18.00	Normal	Resolved	...	...
J033239.09-274601.8^C,KS	53.1628593	−27.7671602	20.96	0.94	7.88	4.39	Clean	Core + extended emission	...	...
J033239.47-275300.5	53.1644567	−27.8834689	20.54	0.03	2.01	1.23	Normal	Elliptical	...	...
J033240.27-274949.7	53.1678017	-27.830481	24.69	0.02	1.99	17.90	Normal	Complex	None	...
J033240.89-275449.2	53.1703678	−27.9136643	25.14	0.02	2.01	17.08	Normal	Resolved	...	...
J033241.05-275234.1	53.1710547	−27.8761468	20.72	0.97	2.71	1.08	Clean	Star^a	0.0000^S	...
J033241.87-274651.1	53.1744478	−27.7808655	23.35	0.01	2.01	12.07	Normal	Tadpole galaxy^g	...	...
J033242.61-275453.8	53.1775348	−27.9149453	20.82	0.99	2.64	1.25	Clean	Star^a	0.0000^S	...
J033243.24-274914.2^KS,T	53.1801493	−27.8206046	22.49	0.93	9.56	12.41	Clean	Core + extended emission	0.2145^T	−17.66
J033243.93-274351.1	53.1830401	−27.7308524	24.26	0.04	2.00	9.75	Normal	Resolved	...	...
J033244.10-275212.9	53.1837535	−27.8702564	20.88	0.94	2.33	0.90	Clean	Star^b	...	...
J033245.02-275207.7	53.1875887	−27.8688155	22.57	0.03	4.45	7.33	Clean	Disk galaxy	...	...
J033246.37-274912.8	53.1932061	−27.8202112	21.94	0.03	2.08	2.07	Normal	Elliptical	0.6830^S	−21.15
J033246.39-274820.1	53.1932909	-27.8055737	21.16	0.97	2.59	1.45	Clean	Star^h	...	...
J033247.53-275159.9	53.1980298	−27.8666421	21.01	0.99	2.11	0.95	Normal	Star	...	...
J033247.98-274855.7	53.1999289	−27.8154702	20.56	0.04	2.61	1.33	Clean	Elliptical	0.2340^S	−19.79
J033251.22-275418.3	53.2134115	-27.905076	24.25	0.03	1.95	13.30	Normal	Resolved	...	...
J033252.88-275119.8^KS	53.2203537	−27.8555099	21.84	0.12	2.93	4.23	Clean	Disk galaxy	1.2283^S	−22.81
J033253.44-275001.4	53.2226606	-27.8337103	24.44	0.00	1.96	15.49	Normal	Complex	...	...
J123553.12+621037.5	188.9713311	62.1770907	21.26	0.93	5.71	4.78	Clean	Interacting system	...	...
J123556.88+621117.3	188.9870032	62.1881435	20.23	0.92	6.41	2.34	Clean	Unresolved	...	...
J123557.62+621024.7	188.9900912	62.1735292	22.62	0.94	4.55	6.53	Clean	Core + extended emission	...	...
J123603.82+621039.3	189.0159143	62.1775909	24.48	0.00	2.60	21.88	Clean	Interacting system	...	...
J123605.75+621356.1	189.0239559	62.2322631	20.82	0.99	4.01	1.93	Clean	Unresolved	...	...
J123606.47+621506.4	189.0269558	62.2517698	21.42	0.89	1.98	1.28	Normal	Core + extended emission	...	...
J123612.61+621238.4	189.0525622	62.2106579	20.18	0.89	3.11	1.05	Clean	Core + extended emission	...	...
J123617.99+621635.3	189.0749736	62.2764767	20.18	0.87	9.25	4.21	Clean	Core + extended emission	...	...
J123619.57+620715.2	189.0815546	62.1208771	25.14	0.02	2.04	22.65	Normal	Resolved	...	...
J123621.26+621640.4	189.0885649	62.2778893	21.57	0.03	1.94	1.88	Normal	Interacting system	...	...
J123622.94+621527.0	189.095583	62.2574929	20.27	0.90	4.52	1.70	Clean	Core + extended emission	...	...
J123627.48+621406.4	189.1144932	62.2351164	25.22	0.04	2.25	25.05	Clean	Resolved	...	...
J123627.98+621508.1	189.1165918	62.2522625	21.86	0.03	1.94	2.33	Normal	Interacting system	...	...
J123629.44+621513.3	189.1226602	62.2536973	23.70	0.98	1.97	5.83	Normal	Unresolved	...	...
J123629.68+621734.7	189.1236482	62.2929798	22.45	0.98	2.27	2.73	Clean	Unresolved	...	...
J123631.68+620848.7	189.1320148	62.1468517	22.56	0.03	2.14	3.24	Normal	Elliptical	...	...
J123631.70+620752.3	189.1320712	62.1311963	24.12	0.03	2.19	9.17	Clean	Resolved	...	...
J123632.50+620701.7	189.1354166	62.1171419	25.37	0.82	2.03	20.07	Normal	Resolved	...	...
J123633.23+620834.9	189.1384756	62.1430369	21.08	0.03	5.24	3.87	Clean	Interacting system	...	...
J123636.51+620806.4	189.1521369	62.1350985	22.29	0.03	2.06	3.24	Normal	Elliptical	...	...
J123637.85+620724.1	189.1576928	62.1233725	22.21	0.00	1.94	5.06	Normal	Complex	...	...
J123641.44+620730.4	189.1726778	62.1251072	22.62	0.00	1.94	5.58	Normal	Disk galaxy	...	...
J123648.32+621250.1	189.2013266	62.2139299	20.39	0.93	2.93	1.02	Clean	Core + extended emission	...	...
J123650.44+620749.7	189.2101509	62.1304753	23.62	0.03	1.98	6.34	Normal	Resolved	...	...
J123650.75+621439.9	189.2114589	62.2444226	23.73	0.03	2.13	9.86	Normal	Disk galaxy	...	...
J123651.32+621751.2	189.2138382	62.2975491	24.46	0.03	1.98	13.91	Normal	Resolved	...	...
J123652.44+620959.9	189.2185084	62.1666296	22.44	0.98	2.23	2.58	Clean	Unresolved	...	...
J123654.99+621635.1	189.2291393	62.2764217	25.46	0.97	2.31	22.23	Clean	Unresolved	...	...
J123655.90+620828.3	189.2329249	62.1411947	21.01	0.99	2.85	1.49	Clean	Unresolved	...	...
J123656.51+620837.7	189.2354508	62.1438079	20.75	0.99	3.38	1.56	Clean	Unresolved	...	...
J123656.91+621950.3	189.2371093	62.330639	21.61	0.03	2.07	2.67	Normal	Disk galaxy	...	...
J123700.71+621854.4	189.2529566	62.3151155	23.58	0.03	2.20	9.72	Clean	Interacting system	...	...
J123700.88+621129.5	189.2536832	62.1915322	20.32	0.97	3.40	1.22	Clean	Starⁱ	...	...
J123701.55+622103.9	189.2564508	62.3510871	23.02	0.06	2.04	3.85	Normal	Elliptical	...	...
J123702.09+621737.8	189.2586984	62.2938331	20.43	0.99	2.02	0.79	Normal	Unresolved	...	...
J123702.72+621543.9	189.2613473	62.2621972	19.41	0.03	2.18	0.91	Clean	Disk galaxy	...	...
J123704.80+621455.2	189.2699968	62.2486665	20.99	0.98	2.79	1.44	Clean	Unresolved	...	...
J123705.48+621526.8	189.2728214	62.257434	24.62	0.03	2.16	14.31	Normal	Resolved	...	...
J123706.25+622136.9	189.2760529	62.3602611	20.90	0.90	10.05	8.36	Clean	Disk galaxy	...	...
J123706.87+621702.5	189.2786271	62.2840158	19.86	0.92	3.81	1.27	Clean	Core + extended emission	1.0200^j	−24.29
J123706.93+621429.9	189.2788629	62.2416441	20.70	0.98	2.77	1.24	Clean	Unresolved	...	...
J123707.49+622148.1	189.2812076	62.3633707	22.03	0.92	3.75	3.83	Clean	Elliptical	...	...
J123708.35+621105.8	189.284812	62.184941	23.47	0.03	2.00	6.04	Normal	Resolved	...	...
J123708.65+621051.5	189.286038	62.1809766	20.67	0.03	2.03	1.91	Normal	Interacting system	...	...
J123716.68+621733.6	189.3194798	62.2926732	22.12	0.72	2.97	3.74	Clean	Elliptical	...	...
J123717.79+622034.2	189.3241356	62.3428338	23.91	0.00	1.94	26.94	Normal	Resolved	...	...
J123717.82+621130.5	189.3242369	62.1918003	24.28	0.17	2.19	10.70	Clean	Resolved	...	...
J123719.47+621320.4	189.3311376	62.2223455	20.79	0.96	2.56	1.20	Clean	Core + extended emission	...	...
J123720.16+621518.9	189.3339866	62.2552618	20.16	0.88	6.72	2.39	Clean	Core + extended emission	...	...
J123723.70+621200.3	189.3487632	62.2000936	24.82	0.00	1.97	21.53	Normal	Resolved	...	...
J123723.72+622113.3	189.3488236	62.3537049	23.62	0.98	2.30	6.61	Clean	Unresolved	...	...
J123724.77+622103.0	189.3531954	62.3508303	23.80	0.00	1.96	14.08	Normal	Resolved	...	...
J123728.43+622044.8	189.3684533	62.3457887	22.69	0.02	2.24	7.50	Clean	Resolved	...	...
J123728.95+621127.8	189.3706346	62.1910553	21.75	0.03	6.06	6.20	Clean	Supernova^k	...	...
J123729.58+621557.8	189.3732355	62.2660663	19.91	0.85	2.12	0.60	Normal	Core + extended emission	...	...
J123732.41+621751.4	189.3850213	62.2976196	24.58	0.03	2.55	17.65	Clean	Resolved	...	...
J123736.11+621619.1	189.4004397	62.2719614	24.07	0.03	2.91	15.16	Clean	Resolved	...	...
J123736.59+621632.7	189.4024445	62.2757619	25.03	0.03	3.09	37.46	Clean	Resolved	...	...
J123738.83+622024.0	189.4117843	62.3399951	20.20	0.96	3.41	1.24	Clean	Core + extended emission	...	...
J123740.64+622007.9	189.4193208	62.3355268	22.60	0.03	2.50	5.41	Clean	Disk galaxy	...	...
J123741.21+621925.2	189.4217126	62.3236767	21.04	0.98	2.84	1.50	Clean	Unresolved	...	...
J123741.38+621540.2	189.4224198	62.2611689	25.19	0.02	2.11	20.13	Normal	Resolved	...	...
J123742.12+621903.0	189.425516	62.3174941	24.48	0.04	3.43	29.44	Clean	Resolved	...	...
J123742.53+621812.2	189.4272043	62.3033909	21.31	0.98	5.40	3.36	Clean	Unresolved	...	...
J123746.85+621624.2	189.4452252	62.2733875	21.94	0.98	2.27	1.96	Clean	Unresolved	...	...
J123749.58+621346.6	189.4565982	62.2296055	24.56	0.98	2.49	14.73	Clean	Unresolved	...	...
J123754.25+621853.0	189.47606	62.3147251	24.84	0.02	2.21	20.84	Clean	Resolved	...	...

Notes. Columns: ID: IAU object identification; R.A. (J2000): Right Ascension (Julian Year 2000); Decl. (J2000): declination (Julian Year 2000); mag (z): SExtractor z-band magnitude; CS: stellarity (1 is point like, 0 is extended); C: flux-corrected C for 0 farcs 36 aperture; V (%): variability strength in percent; Catalog: Normal (99.9% insignificance) or Clean (99.99% significance); Comment: morphology or classification, references for classifications are given; z: spectroscopic redshift if available and flag (secure (S), likely (L), tentative (T)), "None" if spectroscopy is available but no redshift was found. Unless otherwise noted, all spectroscopic redshifts are from Popesso et al. (2009); M_abs: absolute magnitude in observed frame z (only for objects with spectroscopic redshift > 0). Objects that have been detected in other studies are marked by superscripts in the ID column: Cohen et al. (2006): C, Klesman & Sarajedini (2007): KS, Trevese et al. (2008): T. ^aPopesso et al. 2009. ^bWolf et al. 2008. ^cGroenewegen et al. 2002. ^dSantini et al. 2009. ^eHatziminaoglou et al. 2002. ^fSzokoly et al. 2004. ^gStraughn et al. 2006. ^hTaylor et al. 2009. ⁱMendez & Guzman 1998. ^jHornschemeier et al. 2001. ^kRiess et al. 2004.

Download table as: ASCIITypeset images: 1 2 3

A NEW EXTENSIVE CATALOG OF OPTICALLY VARIABLE ACTIVE GALACTIC NUCLEI IN THE GOODS FIELDS AND A NEW STATISTICAL APPROACH TO VARIABILITY SELECTION^*

Article metrics

Permissions

Author affiliations

Dates

ABSTRACT

1. INTRODUCTION

2. SAMPLE SELECTION AND DATA REDUCTION