EXPLORING THE VARIABLE SKY WITH LINEAR. I. PHOTOMETRIC RECALIBRATION WITH THE SLOAN DIGITAL SKY SURVEY

Variability is an important phenomenon in astrophysical studies of structure and evolution, both stellar and Galactic and extragalactic. Some variable stars, such as RR Lyrae stars, are an excellent tool for studying the Galaxy. Being nearly standard candles (thus making distance determination relatively straightforward) and being intrinsically bright, they are a particularly suitable tracer of Galactic structure (e.g., Sesar et al. 2007, and references therein). Similarly, eclipsing binaries can be used as distance indicators (Guinan et al. 1998), are excellent probes of stellar physics (Prša & Zwitter 2005), and offer a unique method for measuring stellar masses and other parameters as well (e.g., Andersen 1991; Torres et al. 2010).

Despite the importance of variability, the variable optical sky remains largely unexplored and poorly quantified, especially at the faint end (V > 15). To what degree do different variable populations contribute to the overall variability, how are they distributed in magnitude and color, and what are the characteristic timescales and dominant mechanisms of variability are just some of the questions that still remain unanswered. To address these questions, several contemporary projects aimed at regular monitoring of the optical sky were started. The four most prominent wide-area (more than a few thousand deg²) variability surveys in terms of depth and cadence are as follows.

• 1.  
  ROTSE-I (Akerlof et al. 2000) monitored the entire observable sky twice a night from V = 10 to a limit of V = 15.5. The Northern Sky Variability Survey (NSVS; Woźniak et al. 2004) is based on ROTSE-I data and contains light curves for about 14 million objects, with 100–500 measurements per object collected over one year. Typical photometric precision of this data set is about 0.02 mag for sources not limited by photon statistics.
• 2.  
  The All Sky Automated Survey (ASAS; Pojmański 2002) monitors the entire southern and part of the northern sky (δ < +28°) to a limit of V = 14, including about 15 million stars. Typical photometric precision is about 0.05 mag. The third release of the ASAS Catalog of Variable Stars contains close to 50,000 variable stars. About 80% of these are new discoveries (not previously cataloged).
• 3.  
  The Lowell Observatory Near Earth Objects Survey Phase I (LONEOS-I; Miceli et al. 2008) provides photometric data for 1430 deg² of northern sky that has been imaged at least 28 times between 1998 and 2000. The LONEOS-I camera used no bandpass filter and reached a depth of R ∼ 18.5. Typical photometric precision of this data set is about 0.02 mag for sources not limited by photon statistics.
• 4.  
  The Palomar Transient Factory (PTF; Law et al. 2009 and Rau et al. 2009) is an ongoing wide-area, two-band (SDSS-g' and Mould-R filters), deep (R ∼ 20.6, g' ∼ 21.3) survey aimed at systematic exploration of the optical transient sky. As of fall 2011, PTF has observed about 7300 deg² of northern sky at least 30 times in the Mould-R band (∼1800 deg² of sky with more than 100 epochs). Typical photometric precision of this data set is better than 0.01 for sources not limited by photon statistics.

A comprehensive review of past and ongoing variability surveys can be found in Becker et al. (2004).

With hundreds of observations per object, the NSVS and ASAS data sets represent unique resources. Although a number of massive synoptic surveys, such as Pan-STARRS (Kaiser et al. 2002) and LSST (the Large Synoptic Survey Telescope; Ivezić et al. 2008), will significantly improve our knowledge of the variable faint sky, they will not obtain hundreds of observations per object any time soon.

A downside of NSVS, ASAS, LONEOS, and PTF data sets is the lack of precise multi-color photometry, which can provide valuable information about sources in addition to light curve characteristics (Covey et al. 2007). The Sloan Digital Sky Survey (SDSS; York et al. 2000) has obtained five-band photometry for hundreds of millions of stars, but its temporal coverage is very poor. The only region on the sky with more than 10 observations per source is the ∼300 deg² large equatorial region called Stripe 82 (Sesar et al. 2007, and references therein). At the same time, NSVS and ASAS are not deep enough to make efficient use of SDSS photometry. This goal to combine a large-area variability survey providing hundreds of observations with exquisite SDSS photometry was recently made reachable by the LINEAR survey.

The MIT Lincoln Laboratory (MITLL) has operated the Lincoln Near-Earth Asteroid Research (LINEAR) program since 1998 to search for asteroids. The focus of the program is to discover and track near-Earth asteroids (NEAs) larger than 1 km in diameter, but LINEAR has also discovered and tracked many main-belt asteroids and smaller NEAs. Since late 2002, the LINEAR program has maintained an archive of all of its imagery data. This archive now contains approximately 6 million images of the sky, most of which are 5 megapixel images covering 2 deg². The LINEAR image archive contains a unique combination of depth (V < 18), coverage area, and cadence that is potentially useful in exploring a number of time-varying astronomical phenomena.

Since the LINEAR project was focused on astrometric survey, standard stars required for precise photometric calibration were often unavailable. Furthermore, a significant fraction of the data was taken in non-photometric conditions. The main purpose of this paper is to describe photometric recalibration of LINEAR data using stars observed by SDSS as photometric standards. Companion papers are discussed in Section 6.

In Section 2 we describe the LINEAR survey in more detail and discuss recalibration procedures in Section 3. The recalibrated data set is characterized in Section 4 and a preliminary analysis of about 7000 confirmed periodic variables is presented in Section 5. Our results are summarized in Section 6.

2.1. Hardware Characteristics

The LINEAR program operates two telescopes at the Experimental Test Site located within the US Army White Sands Missile Range in central New Mexico at an altitude of 1506 m above sea level and a latitude of 338N. The program uses two essentially identical equatorial-mounted telescopes of the Ground-based Electro-Optical Deep Space Surveillance (GEODSS) type, usually denoted L1 and L2. Each telescope is a folded prime-focus design with a primary mirror diameter of 1.016 m and $f/\#$ of 2.15 (Stokes et al. 2000).

The two telescopes of the LINEAR project are each equipped with a CCD camera developed at MITLL using CCDs developed and manufactured by MITLL for the US Air Force GEODSS system (Burke et al. 1998). These CCID-16 sensors are 5 megapixel (2560 × 1960), back-illuminated, frame-transfer CCDs with fast readout, low dark current, and low read noise. The CCID-16 sensors have eight readout regions (hereafter referred to as cells) and have high quantum efficiency over a broad part of the visible and near-infrared spectrum (with overall solar-weighted quantum efficiency of 65% and peak efficiency of 96% at 620 nm, see Figure 1). The cameras have no spectral filters. The combination of the CCID-16 camera and the 1 m GEODSS telescope produces an instantaneous field of view of 160 × 123 (∼2 deg²), with 225 pixels. In Section 3, the combination of CCID-16 sensors and L1 and L2 telescopes will be referred to as the L1 and L2 setups.

Zoom In Zoom Out Reset image size

For a few months in 2003 (approximately August to November) the camera on the L2 telescope was replaced with a very similar camera containing a smaller format sensor called the CCID-10. This smaller sensor is identical to the CCID-16's in terms of manufacture and processing, readout electronics and settings, spectral quantum efficiency, and pixel size. The only difference between the smaller format camera and the larger format camera is the number of pixels, 1024 × 1024 for the small camera, and the number of readout regions (4 cells). During the four months in 2003 that L2 was operating with the CCID-10 camera, the field of view was about 064 × 064 (∼0.4 deg²). In Section 3, the combination of CCID-10 sensor and L2 telescope will be referred to as the small setup.

2.2. Observing Conditions and Cadence

The telescope site has reasonably dark skies, approaching μ_V = 21 mag arcsec⁻² on the best nights. However, the LINEAR program operates on nights with suboptimal conditions including haze, bright moonlight (to within 3 days of the full moon), scattered clouds, and airglow. LINEAR images are frequently taken under skies as bright as μ_V = 16 mag arcsec⁻². The point-spread function includes unknown contributions from atmospheric seeing and various system contributions (e.g., defocus and dome airflow) and is typically around 5'' FWHM, resulting in slightly undersampled images.

The image integration time is allowed to vary over the seasons so that a roughly constant number of search fields fills the available dark time. During the earlier days of the LINEAR program (roughly 1998 to 2006), the integration time was 10–12 s on long winter nights and 3–5 s on short summer nights. In recent years (roughly 2007 to 2009), the integration time was increased to 15–18 s in the winter and 8–13 s in the summer. Under these observing conditions, the magnitude for which the magnitude error is ∼0.2 mag (the 5σ detection limit) is about 18 mag on average.

As shown in Figure 2, the cadence of LINEAR observations (time between revisits of the same patch of sky) is fairly uniform, with a peak at ∼15 minutes and a gap at ∼8 hr. A more detailed description of the LINEAR observing strategy is given in Appendix A.

Zoom In Zoom Out Reset image size

2.3. Photometry and Astrometry Using SExtractor

In this section, we describe the astrometric and photometric recalibration of LINEAR data and quantify the quality of recalibrated data. The recalibration and data quality assessment are done on a field-by-field basis, where a field is defined as part of a LINEAR image observed by a single CCD cell (there are four cells in the small setup and eight cells in the L1 and L2 setups). The only exception to this is the astrometric recalibration, which is done on a image-by-image basis. However, the quality of astrometric recalibration is still assessed on a field-by-field basis.

3.1. Astrometric Recalibration

We recalibrate the preliminary astrometry using the Astrometry.net software (Lang et al. 2010). Astrometry.net uses the x and y (hereafter, pixel) positions of sources extracted by SExtractor and looks for "skymarks" (sets of four stars) that correspond to pre-computed "skymarks" found in the "clean" USNO-B catalog (Barron et al. 2008). Once a skymark is found the code obtains an initial astrometric solution (a transformation from the pixel coordinates into the J2000.0 Equatorial system) in the form of a third-degree polynomial in x and y coordinates. Using this initial astrometric solution, the code looks for additional reference USNO-B stars in the image, and further refines the initial astrometric solution when it finds them.

The quality of recalibrated LINEAR astrometry is estimated by comparing the LINEAR positions with reference USNO-B positions (Figure 3). We find that the recalibrated LINEAR single-epoch coordinates have an rms scatter of ∼06 and are offset ≲ 03 with respect to the USNO-B coordinates. These systematic offsets are independent of pixel positions or the position of the image on the sky and are subtracted from recalibrated LINEAR coordinates. Using a subset of data, we have found that the offsets decrease if Astrometry.net is allowed to search for even more reference USNO-B stars when refining the initial astrometric solution.

Zoom In Zoom Out Reset image size

To find fields with bad astrometry, we calculate the median and rms scatter of astrometric residuals (difference between LINEAR and USNO-B positions) in R.A. and decl. for each field, and tag fields as bad if the median or rms scatter in either coordinate (R.A. or decl.) is greater than 2''. We find that about 7% of all fields have bad astrometry, with the majority of bad fields (∼90%) originating from the L2 setup, and remove them from further processing. Visual inspection of images containing bad fields reveal that bad fields lack several pixel columns, which were most likely dropped due to cell readout problems.

In order to recalibrate the LINEAR photometry, we positionally matched the LINEAR data set to the SDSS Data Release 7 (SDSS DR7; Abazajian et al. 2009) imaging catalog. The SDSS DR7 imaging catalog provides homogeneous and deep (r < 22.5) 1%–2% accurate photometry in five bandpasses (u, g, r, i, and z) of more than 11,000 deg² of the North Galactic Cap, and three stripes in the South Galactic Cap totaling 740 deg². The SDSS positions are accurate to better than 01 per coordinate (rms) for sources with r < 20.5 (Pier et al. 2003), and the morphological information from the images allows reliable star–galaxy separation to r ∼ 21.5 (Lupton et al. 2002).

We match LINEAR sources to SDSS DR7 non-saturated, "primary" objects⁷ using a 3'' radius and find ∼4.8 billion matched pairs (there are 24 million unique SDSS sources included in these pairs). There are ∼1.6 billion LINEAR sources without an SDSS match ("orphans"), and they include observations associated with stars saturated in SDSS (r < 13, ∼60% of orphans), image artifacts (e.g., due to charge bleeding and diffraction spikes), moving objects such as asteroids, and other transients.

3.2. Photometric Recalibration

We model the recalibrated LINEAR magnitudes as

$$\begin{equation} m_{{\rm linear}} = \alpha m_{{\rm instr}} + C(g-i) + Z(x,y), \end{equation} \tag{ 1 }$$

where α measures nonlinearity of SExtractor-supplied instrumental magnitudes m_instr = −2.5log (counts), C is a color-dependent term that accounts for the per-exposure change in the effective central wavelength of the LINEAR bandpass, and Z(x,y) is our model for the field-specific magnitude zero-point dependent on the x–y position in the image, defined as

$$\begin{equation} Z(x,y) = Z_0 + Z_1x + Z_2y + F(x,y), \end{equation} \tag{ 2 }$$

where Z₀, Z₁, and Z₂ vary from field to field, and F(x,y) is the "super flat field" (fixed for each observational setup). Note that the color-independent airmass term (gray extinction) is implicitly included in Z₀.

To recalibrate the LINEAR photometry, we need a catalog of photometric standard stars in the LINEAR photometric (unfiltered) system. Since such a catalog does not exist, we use the SDSS imaging catalog and utilize SDSS gri photometry to derive magnitudes in the LINEAR photometric system.

3.2.1. LINEAR Magnitudes Synthesized from SDSS Photometry

We define LINEAR magnitudes synthesized from the SDSS photometry as

$$\begin{equation} m_{{\rm sdss}} = r + f(g-i), \end{equation} \tag{ 3 }$$

where f(g − i) is some function of g − i and SDSS gri magnitudes are not corrected for the ISM extinction.

We find f(g − i) iteratively by first adopting α = 1.0 in Equation (1), F(x, y) = 0 in Equation (2), and f(g − i) = 0 in Equation (3). For each field, we determine Z₀, Z₁, and Z₂ by minimizing

$$\begin{equation} \chi ^2 = \Sigma [(m_{{\rm linear}}-m_{{\rm sdss}})/\sigma _{{\rm linear}}]^2, \end{equation} \tag{ 4 }$$

where σ_linear is the magnitude error supplied by the SExtractor (errors in m_sdss are assumed to be much smaller than errors in m_linear).

The LINEAR observations of calibration stars must be matched within 2'' to isolated,⁸ unresolved, SDSS objects brighter than r = 17, with 0 < g − i < 2.6. Having Z(x,y) for each field, we calculate m_instr + Z(x, y) − r residuals for all calibration stars, bin the values in g − i bins, and plot the median residuals in Figure 4 for the small, L1, and L2 setups. We plot medians for each setup separately because each setup represents a separate optical, and therefore photometric, system.

Zoom In Zoom Out Reset image size

Even though the three setups are different, their residuals depend similarly on g − i (rms scatter around the mean is 0.01 mag), as indicated by medians plotted in Figure 4. We therefore fit a fourth-degree polynomial to all medians and obtain

$$\begin{eqnarray} f(g-i) &=& 0.0574 + 0.004(g-i) - 0.056 (g-i)^2 \nonumber\\ &&+ 0.052 (g-i)^3 -0.0262(g-i)^4. \end{eqnarray} \tag{ 5 }$$

The transformation from SDSS gri to LINEAR magnitudes, as defined by Equation (3), is then

$$\begin{eqnarray} m_{{\rm sdss}} &=& r + 0.0574 + 0.004(g-i) - 0.056 (g-i)^2 \nonumber\\ &&+ 0.052 (g-i)^3 -0.0262(g-i)^4. \end{eqnarray} \tag{ 6 }$$

This equation effectively turns the SDSS imaging catalog into a catalog of LINEAR photometric standard stars.

3.2.2. Super Flat Fields and Nonlinearity of Instrumental Magnitudes

We find the super flat field, F(x,y), iteratively by first adopting α = 1.0 in Equation (1) and F(x, y) = 0 in Equation (2). For each field, we determine Z₀, Z₁, Z₂, and C by minimizing Equation (4) using calibration stars brighter than m_sdss = 17. The super flat-field correction, F(x,y), is then obtained by finding the median of m_linear − m_sdss residuals binned in x–y pixels, and is shown as a color-coded map in Figure 5 (left) for each observational setup. Figure 6 (left) shows the residuals after the subtraction of Figure 5 (left) maps. On average, the median residuals are now smaller than 0.005 mag, compared to ∼0.02–0.03 mag before the correction was made.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To verify our assumption of α = 1.0 (the linearity of instrumental magnitudes), we adopt α = 1.0 in Equation (1), and determine Z₀, Z₁, Z₂, and C by minimizing Equation (4) using calibration stars brighter than m_sdss = 17. We bin m_linear − m_sdss residuals in m_sdss bins, and plot the medians as a function of m_sdss in Figure 7. A strong dependence of residuals on m_sdss would indicate nonlinear (α ≠ 1.0) behavior of instrumental magnitudes. With the exception of a small nonlinearity (<0.02 mag) in the L1 setup for m_sdss < 15, the residuals do not depend on magnitude, indicating that the α = 1.0 assumption is valid.

Zoom In Zoom Out Reset image size

To estimate the magnitude of correction introduced by including the color-dependent term C (accounts for the change in LINEAR bandpass due to varying airmass) in Equation (1), we measure the rms scatter of C(g − i) values obtained from all calibration stars and fields. We find the rms scatter to be ∼0.02 mag, indicating that by correcting for this term the systematic uncertainty in LINEAR photometry is reduced by ∼0.02 mag. On the other hand, the inclusion of the Z₀ term is much more important as it reduces the systematic uncertainty in LINEAR photometry by ∼0.3 mag (the rms scatter of Z₀ values is ∼0.3 mag).

Once the color-dependent term, C, and the zero point, Z(x,y), are obtained for a field, the LINEAR photometry for that field is recalibrated using Equation (1). For "orphan" sources (LINEAR sources not associated with SDSS objects) the color-dependent term is set to C = 0, as g − i colors are not available for these sources. Therefore, the systematic uncertainty in recalibrated photometry is slightly higher for orphans (by ∼0.02 mag).

3.2.3. Checks on Recalibrated Photometry

To quantify the quality of recalibration on a field-to-field basis, we calculate m_linear − m_sdss residuals for calibration stars, and find their median and rms scatter (determined from the interquartile range) for each field. The median of (m_linear − m_sdss) residuals per field is then an estimate of the zero-point error. The distribution of these median offsets, shown in Figure 8, is about 0.01 mag wide and demonstrates the overall quality of recalibrated photometry. About 10% of fields are of low quality (rms scatter in m_linear − m_sdss >0.1 mag), usually due to highly variable cloud coverage. Sources detected in such fields are removed from further consideration.

Zoom In Zoom Out Reset image size

Another useful statistic is the rms scatter of χ values, (m_linear − m_sdss)/σ_linear, in m_sdss bins. This rms scatter should be equal to 1 and should not depend on m_sdss if the SExtractor-supplied magnitude errors (σ_linear) are correct Gaussian errors. As shown in Figure 9, the rms scatter is greater than 1 indicating underestimated σ_linear errors by up to a factor of ∼2.

Zoom In Zoom Out Reset image size

We correct the underestimated magnitude errors by multiplying them by 1.4, 1.85, and 1.65 for the small, L1, and L2 setups, respectively. In the case of the small setup, the factor of 1.4 is only the average value as SExtractor-supplied magnitude errors for that setup seem to depend on magnitude. Therefore, the magnitude errors for the small setup may be slightly overestimated or underestimated depending on the brightness of the source. This is not a major issue as only a small fraction of all LINEAR sources (∼0.1%) originate from the small setup.

The reason for this underestimation of SExtractor-supplied magnitude errors is not clear. Non-inclusion of systematic errors (e.g., due to flat fielding) in σ_linear cannot explain this behavior for L1 and L2 setups. If additive systematic errors were the reason for this underestimation, then (m_linear − m_sdss)/σ_linear should decrease with magnitude because σ_linear is expected to increase with magnitude (see Figure 13). Yet, no such decrease is seen in Figure 9 for L1 and L2 setups.

There are about 5 billion sources in the recalibrated LINEAR data set. These sources were grouped into clusters using an implementation of the OPTICS algorithm (Ankerst et al. 1999) and a clustering radius of 2''. There are about 25 million clusters with more than 15 observations. SDSS provides morphological classification for 24 million clusters (7 million are resolved and 17 million are unresolved by SDSS), and for 1 million of these clusters there is no SDSS classification (they are slightly outside the SDSS footprint). Clusters with 15 or more sources are hereafter labeled as LINEAR objects or time series. The median number of epochs (observations) per object as a function position and magnitude is shown in Figures 10 and 11. The average number of epochs for objects brighter than 18 mag within ±10° of the ecliptic plane is ∼460, and ∼200 elsewhere.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Clusters with less than 15 sources are not tagged as objects. We have statistically analyzed properties of 385 million sources (∼8% of all LINEAR sources) assigned to such clusters and have found that most of them are very faint (m_linear > 19.5), have very uncertain magnitudes (σ_linear > 0.4 mag), and have high ellipticity (suggestive of cosmic rays and image artifacts). Such clusters and their observations are not included in our database. This also means that the LINEAR database does not include observations of fast moving objects (i.e., objects moving faster than ∼1'' day⁻¹).

In order to enable the discovery of variable objects and to further characterize the LINEAR data set, we have computed various low-order statistics for time series, such as the median recalibrated magnitude (〈m_linear〉), rms scatter (σ), χ² per degree of freedom (χ²_pdf), skewness (γ₁), and kurtosis (γ₂). The cumulative distributions of χ²_pdf for LINEAR objects with more than 30 observations are shown in Figure 12.

Zoom In Zoom Out Reset image size

The median of the χ²_pdf distribution for bright LINEAR objects (14.5 < 〈m_linear〉 < 17) is about 1, indicating that, on average, the uncertainties in LINEAR magnitudes are well determined. For fainter LINEAR objects (17 < 〈m_linear〉 < 18), the median of the χ²_pdf distribution is slightly lower (∼0.7) indicating slightly overestimated photometric errors.

The high-end tail (χ²_pdf > 3) of the cumulative χ²_pdf distribution suggests that ∼5% of bright LINEAR objects exhibit deviations from the mean that are inconsistent with the Gaussian distribution of errors. These objects could be variable or could have unreliable (non-Gaussian) errors. While it is not impossible that some fraction of LINEAR objects are variable (∼1% of sources brighter than r = 20 are variable; see Sesar et al. 2006, and references therein), a fraction of ∼5% seems unlikely. A more likely explanation is spurious variability induced by non-Gaussian errors, caused by blending of sources and unaccounted instrumental defects (e.g., bad pixels).

To estimate the dependence of the median photometric error (Σ) on magnitude, we follow Sesar et al. (2007) and calculate median σ values in 〈m_linear〉 bins. The dependence of median σ on 〈m_linear〉, as shown in Figure 13, can be modeled as a fourth-degree polynomial:

$$\begin{eqnarray} \Sigma (x) &=& 122.995-30.346x+2.8183x^2-0.116893x^3\nonumber\\ &&+0.0018295x^4, \end{eqnarray} \tag{ 7 }$$

where x = m_linear. The smallest photometric errors are at m_linear ∼ 15 (∼0.03 mag) and are limited by systematic errors in calibration. The increase in photometric error at brighter magnitudes is probably due to saturation issues in LINEAR. The photometric error starts to increase rapidly toward fainter magnitudes due to photon noise and reaches ∼0.2 mag at m_linear ∼ 18 (the adopted faint limit).

Zoom In Zoom Out Reset image size

In addition to statistics calculated on light curves, we also calculated time-averaged positions (median and mean R.A. and decl.). To estimate the reliability of time-averaged LINEAR positions, we compared them to SDSS positions in ∼1 deg² pixels on the sky and calculated the median difference in positions for each pixel. We find that, on average, the time-averaged LINEAR positions are within 03 of SDSS positions, with no systematic trends across the sky. The largest median difference (for a ∼1 deg² pixel) is ∼15. While this precision is sufficient for most applications, we still recommend that SDSS positions are used whenever possible to avoid patches where time-averaged LINEAR positions may be less reliable.

Since SDSS is about 4 mag deeper than LINEAR, it can be used to estimate the completeness of the LINEAR object catalog (i.e., LINEAR object catalog is a subset of the SDSS object catalog). To estimate the completeness of the LINEAR object catalog, in Figure 14 we plot the fraction of SDSS objects matched to LINEAR objects as a function of m_sdss (LINEAR magnitude synthesized from SDSS photometry; see Equation (6)). For this purpose, we use SDSS and LINEAR objects with 0 < g − i < 2.5 (color range where Equation (6) is valid), 170° < R.A. < 220°, and $15\mbox{$^\circ $}< {\rm {\rm decl.}} < 65\mbox{$^\circ $}$. As shown in Figure 14, the LINEAR object catalog is more than 90% complete for m_sdss < 19. This estimate may be a bit misleading as the criterion for object creation is having at least 15 detections. Even faint objects (18 < m_sdss < 19.5) are likely to be detected at least 15 times out of an average of 200 observations (see Figure 11), if the observing conditions are better than average (e.g, due to better seeing and darker skies).

Zoom In Zoom Out Reset image size

We have examined a small subset of objects with χ²_pdf > 3 (∼5000) and identified a subset of periodically variable stars. We confirmed expectation from the preceding section that only a few percent of the χ²_pdf > 3 subsample are convincing cases of periodic variability. As an illustration of the quality of LINEAR light curves at the bright (〈m_linear〉 ∼ 15) and faint (〈m_linear〉 ∼ 17) ends, we show their period-folded light curves in Figure 15. The main strength of the LINEAR survey is easily discernible in these plots: even at the faint end, the light curve features are well defined, thanks to dense LINEAR sampling.

Zoom In Zoom Out Reset image size

To exploit the full potential of the LINEAR photometric database, an automated selection and classification of variable objects is desirable. This desideratum is not easy to accomplish because the fraction of spurious objects with χ²_pdf > 3 is an order of magnitude larger than the fraction of truly variable objects. In order to enable the deployment of automated selection and classification methods, we have undertaken an extensive program of visual light curve classification. Details of this program are described in a companion paper (L. Palaversa et al. 2011, in preparation, hereafter Paper II) and here we only provide a brief description of the variable candidate selection and their distribution in various color–color diagrams.

In the first step, we define a flux-limited sample of objects with 14.5 < 〈m_linear〉 < 17 and select about 200,000 light curves with χ²_pdf > 3 and σ > 0.1 mag (σ is the rms scatter in the light curve). We limit classification to objects exhibiting periodic variability and use phased light curves for visual inspection. The periods are determined using the Supersmoother algorithm (Reimann 1994). In total, about 7000 LINEAR objects (3.5% out of 200,000) were visually confirmed as periodic variables, with about two-thirds classified as RR Lyrae type ab stars and eclipsing binary stars of all types. The remaining 1/3 include SX Phoenicis and Delta Scuti stars, long-period variables, as well as possible RR Lyrae type ab and eclipsing binary stars with less certain classification. The distributions of classified objects in the SDSS u − g versus g − r color–color diagram is shown in Figure 16.

Zoom In Zoom Out Reset image size

The differences between the distributions of all sources and those of the confirmed variable subsample demonstrate that the latter are robustly classified (i.e., the classification is not random). The most obvious difference is a much higher fraction of RR Lyrae stars in the classified sample (u − g ∼ 1.15, g − r < 0.3). The eclipsing binary systems of all types dominate the visually classified sample in the main stellar locus region. There seems to be a hint for the median period of eclipsing binaries becoming longer for bluer stars. The distribution of eclipsing stars is offset from the distribution of all stars in the direction perpendicular to the stellar locus (offset to upper left). There is also a lack of variable (eclipsing) systems of the late-K and early-M spectral type. These results are discussed in more detail in Paper II.

In this work, we have described astrometric and photometric recalibration of data obtained by the asteroid survey LINEAR. The public access to the recalibrated LINEAR data set will be provided through the SkyDOT Web site (http://skydot.lanl.gov). A description of various cataloged parameters that are available in this database is given in Appendix B.

The preliminary astrometry produced by the survey has been recalibrated using the Astrometry.net software and USNO-B catalog as the reference astrometric catalog. The precision (rms scatter) of single-epoch-recalibrated LINEAR coordinates is ∼06 with respect to the reference (USNO-B) astrometric catalog. The precision of time-averaged LINEAR coordinates is ∼03 with respect to SDSS positions.

In order to recalibrate the LINEAR photometry, we positionally matched the LINEAR data set to the SDSS DR7 imaging catalog and used SDSS as a catalog of photometric standard stars. LINEAR instrumental magnitudes were corrected for changes in the LINEAR bandpass (due to varying airmass) and for zero-point variations across the CCD (due to imperfect flat fielding). These corrected LINEAR magnitudes were then offset on a per-LINEAR field basis to match the SDSS magnitude zero-point system. In general, the recalibrated LINEAR magnitudes (m_linear) behave linearly, with the exception of a small nonlinearity (<0.02 mag) in the L1 setup at magnitudes brighter than 15 mag.

We find the average uncertainty in recalibrated LINEAR magnitudes to be ∼0.03 mag at the bright end (m_linear ∼ 15, the systematic uncertainty) and ∼0.2 mag at the faint end (m_linear ∼ 18, the adopted faint limit for the survey). The SExtractor-supplied magnitude errors were found to be underestimated by 40%–85%, independent of magnitude, and were subsequently corrected for this behavior using multiplicative factors.

There are about 5 billion photometric measurements in the recalibrated LINEAR data set. The sources detected in each observation were grouped into clusters (time series or objects) using a clustering radius of 2''. There are about 25 million clusters with at least 15 observations (7 million resolved and 17 million unresolved by SDSS, the rest without morphological classification). The median number of epochs (observations) per object brighter than 18 mag and within ±10° of the ecliptic plane is ∼460, and ∼200 elsewhere. The completeness of the LINEAR object catalog (relative to the SDSS imaging catalog) was estimated to be better than 90% for sources brighter than 19 mag.

LINEAR data set represents a major new resource for studying the variability of faint optical sources. With an average of 200 observations per object, LINEAR data provide time domain information for the brightest four magnitudes of the SDSS survey. At the same time, LINEAR significantly extends the deepest similar wide-area variability survey, the Northern Sky Variability Survey, by 3 mag.

In order to help automated discovery of variable objects, we have computed various low-order statistics for time series (median recalibrated magnitude, rms scatter, χ² per degree of freedom, skewness, and kurtosis). The χ²_pdf distribution for bright LINEAR objects (brighter than 17 mag) is centered at ∼1 (indicating that, on average, the uncertainties in LINEAR magnitudes are well determined), and has a long high-end (χ²_pdf > 3) tail. About 5% of LINEAR objects have χ²_pdf > 3; in a sample with Gaussian errors, less than 0.01% of objects are expected to have χ²_pdf > 3. This high-end tail is populated by truly variable objects, but is most likely dominated by spuriously variable objects with unreliable (non-Gaussian) errors (caused by, for example, unaccounted instrumental defects such as bad pixels or by blended sources).

Since the fraction of spurious variable objects is at least a few times greater than the fraction of truly variable objects, we have undertaken an extensive program of visual light curve classification in order to enable future deployment of automated methods. Details of this program are described in a companion paper (L. Palaversa et al. 2011, in preparation).

B. Sesar thanks NSF grant AST-0908139 to J. G. Cohen and NSF grant AST-1009987 to S. R. Kulkarni for partial support. Ž.I. acknowledges support by NSF grants AST-0707901 and AST-1008784 to the University of Washington, by NSF grant AST-0551161 to LSST for design and development activity, and by the Croatian National Science Foundation grant O-1548-2009. Partial support for this work was provided by NASA through a contract issued by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. The LINEAR program is sponsored by the National Aeronautics and Space Administration (NRA Nos. NNH09ZDA001N, 09-NEOO09-0010) and the United States Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government. This research made use of tools provided by Astrometry.net.