THE ALLEN TELESCOPE ARRAY TWENTY-CENTIMETER SURVEY—A 690 DEG², 12 EPOCH RADIO DATA SET. I. CATALOG AND LONG-DURATION TRANSIENT STATISTICS

RAPID is able to detect and flag RFI on a channel-by-channel basis by looking for channels that often rise above the mean amplitude for all cross-correlations. RAPID also identifies any problem antennas that show signs of corrupted spectra and flags them. It then makes an image of the calibrator, using full multifrequency synthesis (to avoid bandwidth smearing), and iteratively tests for phase and amplitude closure, flags data outside of a certain amplitude range, and makes a new image.

Once all baselines fall within phase rms and closure limits, iteration stops and an image of the calibrator is produced. Baselines that were determined to be bad in the calibrator data are also flagged in the source data. RAPID then makes images of the source fields, and iteratively applies phase self-calibration and amplitude flagging while attempting to maximize the image dynamic range. Once a maximum in dynamic range is achieved, iteration stops—for our images, this results in a median number of CLEAN components per image of 5710, a median rms of 3.56 mJy beam⁻¹ (2.2 times the theoretical rms of 1.6 mJy beam⁻¹), and a median dynamic range of 120. Images were made using natural weighting which gives about a factor of 3 lower noise than uniform weighting for the ATA. Superuniform weighting was also tried, but the results were unsatisfactory, both in terms of image quality and much higher noise than natural weighting.

The data were calibrated using 3C 286. The calibrator flux density was determined to be 14.679 Jy, using the Baars et al. (1977) coefficients. We did not perform a polarization calibration. The ATA produces cross-polarization data, but at the time of this work, the calibration and analysis of the cross-polarization data have not been fully tested. 3C 286 is ∼10% polarized, but since both X and Y polarizations are present in the data, the effect of source polarization on Stokes I flux densities is largely canceled; ignoring polarization calibration will lead to an additional ∼1% uncertainty in flux density. This is negligible compared to other sources of error.

The flagged visibility data, the bandpasses, and the final images were all inspected by eye, but RAPID usually does a sufficiently good job (given optimal input parameters) that little human interaction is required. Where artifacts were visible in the final images, or RFI or other bad data remained in the visibilities, additional manual flagging was performed.

For the 12 good data sets an average of 40.6% of the visibilities were flagged—this includes RFI, the 200 edge channels, and other bad data identified during data reduction. As discussed in Section 3, the ATA was operating at only 39% of its maximum capacity during ATATS, so the fraction of data obtained compared to the technical specifications was 23%. This fraction is now increasing as additional retrofitted feeds are brought online and other technical improvements are made, which will improve the fidelity of future surveys such as PiGSS (Pi GHz Sky Survey; G. C. Bower et al. 2010, in preparation).

The size of the images made for each pointing was 512 × 512 pixels, where each pixel was 35'' × 35''. The data for all 12 epochs for each pointing were included in each image, since the much better (u, v) coverage (Figure 2) provides for much better image fidelity. Not all pointings had good data at all epochs (for example, because of a failed observation, or severe corruption by RFI). Some had bad data at all epochs because they were close to very bright sources—in particular, in the regions surrounding 3C 286 and 3C 295. We included only pointings for which at least 9 out of 12 epochs were good—a total of 243 pointings. The majority of these (218) had good data for all 12 epochs. The coverage of the final mosaic is shown in Figure 3.

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The images were all made with the same sky coordinate for the reference pixel to ensure that the resulting mosaic should have the correct projection geometry. A typical synthesized beam is shown in Figure 4. Since the synthesized beam changes in shape and position angle across the mosaic, it was necessary to use an "average" restoring beam to avoid superposing different beams from neighboring pointings, which creates problems at the catalog creation stage. We examined the beam major and minor axis widths as a function of hour angle (Figure 5), and took the geometric mean of the major and minor axis widths at HA = 0, 150'', as the FWHM of a circular Gaussian which we used as a restoring beam.

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The ATA primary beam has been measured by various methods, including by off-axis measurement of point sources (MacMahon & Wright 2009, a method known as "hex-7"), by radio holography (Harp et al. 2010), and by comparison of the flux densities of sources visible in two or more ATATS mosaic pointings (C. Hull et al. 2010, in preparation). These measurements give consistent results for the FWHM at 1.4 GHz of 150'. We approximated the primary beam by a Gaussian model. We also experimented with varying the primary beam FWHM value used for mosaicking over a range of values, and found that the canonical value of 150' gave us the most accurate and precise fluxes for the NVSS sources in our data, and so this value was adopted for our analysis. We applied the primary beam correction to the images of each good pointing.

Where the primary beam is well modeled, and where data volumes are small, joint deconvolution (where the entire mosaic is imaged and CLEANed at once) is generally desirable to maximize image fidelity. ATATS uses snapshot observations (where (u, v) coverage is not as good), and the primary beam model used is not as sophisticated, so better quality images can be obtained by imaging of individual fields, and subsequent mosaicking. In any case, the large amount of ATATS data would make joint deconvolution of the entire mosaic difficult without some averaging of the input visibilities (which risks degradation of image quality).

We made a linear mosaic of the 243 individual primary-beam corrected images, masking each outside a radius corresponding to the nominal half-power points (75'), in order to avoid exaggerating the effects of the deviation of the true primary beam from a Gaussian at large distances from the pointing center (in particular, the 10% sidelobes; Harp et al. 2010).

The final image was transformed to a global sinusoid geometry, which has the property that each pixel subtends an equal area on the sky. This is important for an image covering such a large area, since the curvature of the sky introduces distortions. In projections that do not preserve area, the size of the beam would change across the mosaic, resulting in errors in the integrated flux densities reported by the source fitting procedure. If we were not to perform this transformation on the ATATS mosaic, we would bias the flux densities of the sources low by around ∼2% and increase the scatter in the measured flux densities by ∼12% when compared to NVSS.

The rms noise in this final 12 epoch image, which we term the "master mosaic," is 3.94 mJy beam⁻¹. The dynamic range, determined by dividing the peak flux density of the brightest source in our map (4.14 Jy) by the rms noise in a 100 pixel box surrounding this source (23.0 mJy) is 180. The master mosaic covers 689.63 deg² of sky—hence, the mean master mosaic pixel has contributions from 1.73 pixels of the 243 input 12 epoch images, each of which covers 4.91 deg². The master mosaic is shown in Figure 3 and a smaller region, which better shows the individual ATATS sources, is shown in Figure 6.

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The MIRIAD task SFIND was run on the master mosaic. The rms was computed over a box of side 100 pixels and sources above five times the local rms were kept. The resulting SFIND catalog contained 4843 sources. Of these, 197 were poorly fit by SFIND (indicated by asterisks in the SFIND output) and were rejected from the catalog, leaving 4646 sources. Of these, 238 sources were in regions where 10% or more of the pixels in a 1° × 1° box centered on the source were masked (Section 5.1). These sources were also rejected, leaving 4408 sources in the final catalog (Table 2).

By selecting only ATATS sources that match NVSS, we are able to estimate the completeness of the ATATS catalogs; by selecting those that do not match an NVSS source, we are able to identify spurious sources and potential transients. Clearly we wish to reject spurious sources while keeping potential transients and we tweaked the transient detection pipeline to achieve this. We found that the main cause of spurious sources was increased noise at the edges of mosaics, so when looking for transient candidates we reject those which are in fields with a significant fraction (⩾10%) of blanked or masked pixels in a 1° × 1° box centered on the source.

Even without matching the catalogs source by source, we can assess the completeness and reliability of ATATS by plotting the flux density distribution of our catalogs and comparing to NVSS. In order to compare source counts over the same area, we culled sources from the NVSS catalog in regions where ATATS has no data. The resulting culled NVSS catalog, which covers the same area as the ATATS master mosaic, contains 10,729 sources down to a limiting flux density of 10 mJy. We plot source count histograms of the ATATS and culled NVSS catalogs in Figure 10. The two histograms are consistent, within the errors, until the ATATS counts turn over between 40 and 80 mJy.

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The NVSS histogram truncates abruptly at 10 mJy due to the cut we impose on the catalog. This is well above the 99% completeness limit of the NVSS, 3.4 mJy, so the NVSS counts may be considered a measure of the true source counts for this region of sky. The ATATS histogram is marginally higher than that for NVSS for the bins between 320 and 1280 mJy, and marginally lower for the bins between 40 and 160 mJy (above the points where the source counts turn over). This is to be expected since the poorer resolution of ATATS will tend to combine the flux of multi-component NVSS sources into a single brighter ATATS source, and occasionally to detect extended flux resolved out by NVSS. This should only affect a small number of sources though, so the effect on the histogram is not large.

The ratio of the ATATS to NVSS histograms can also be interpreted as the efficiency with which we would detect transient sources of a given brightness, or as a measure of the survey completeness. We plot the ratio of the two histograms, which we denote by C, in Figure 10. We can see that ATATS is >90% complete down to around 40 mJy, or approximately ten times the rms noise in the master mosaic, below which the completeness falls off rapidly. The shift of some sources into higher flux bins due to the resolution mismatch results in some bins with computed C>1. So, some of the sources "missing" at S ≳ 40 mJy are in fact detected, but with higher flux density, and the 90% completeness value may be considered a lower limit. Matching of individual ATATS sources to NVSS and the subsequent examination of postage stamp images (Section 5.4) also support the conclusion that 90% is a conservative value.

As shown in Figure 6, which plots a region of the master mosaic, with NVSS sources brighter than 20 mJy overlaid, there is an excellent match between the two surveys, although counterparts to some of the faintest sources above the NVSS cut are sometimes marginal or non-detections in ATATS.

We are also able to estimate completeness by adding simulated sources to the ATATS mosaic. We took the flux densities of the 10,729 sources in the culled NVSS catalog, assigned them to random positions within the ATATS mosaic, and created simulated Gaussian sources with FWHM 150'' at these positions. We then ran SFIND using the same parameters as used for the generation of the science catalog (Section 4.4). The resultant catalog contains both the real sources detected in ATATS and those of the simulated sources that were recovered by SFIND. In order to determine our ability to accurately recover the input flux densities, we searched for the closest ATATS source (within a maximum radius of 75'') to the input positions of the simulated NVSS sources. The resulting flux–flux diagram is shown in Figure 11. This exercise is similar to the matching of the real NVSS catalog with the ATATS catalog, as seen in Figure 7, modulo the fact that adding simulated sources increases the number of detections in the SFIND catalog from 4843 to 9404 (which will increase source confusion somewhat); that resolution effects apply to the match with NVSS, but not to the retrieval of simulated sources; and that intrinsic source variability will result in changed fluxes in Figure 7, whereas no such effect should be seen in Figure 11.

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We also searched for ATATS sources within 75'' of NVSS sources within the region where we have good ATATS data. This provides a similar (and consistent) estimate of completeness to the ratio of the ATATS and NVSS histograms in Figure 10. Ninety-three percent of NVSS sources brighter than 40 mJy are detected by ATATS, as are 97% of sources brighter than 120 mJy. The remaining 3% of sources without a match in the ATATS catalog are in fact clearly visible in the mosaic images, but are not present in the ATATS catalog due to poor fits or failed deblending (Section 5.4).

To determine the positional accuracy of ATATS versus NVSS (which has an intrinsic positional accuracy typically ≲3''), we plot the offsets in R.A. and decl., and a histogram of the magnitude of the offset between ATATS and NVSS positions (Figure 12). A 120'' match radius was used for these plots, but as can be seen, the majority of the matches fall within a radius corresponding to the ATA synthesized beam (∼75''), the value adopted for the match radius in our analysis.

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The median offset of the ATATS position from the NVSS position is (ΔR.A., Δdecl.) = (14, 098), and the rms scatter in the positional offsets is (σ_R.A., σ_decl.) = (204, 147).

As shown in Figure 6, the positional accuracy is sufficient in most cases to provide a clear match between ATATS and NVSS sources, although in some cases a single ATATS source is associated with multiple NVSS sources due to the differing resolutions of the two surveys.

As noted in Section 5.1, simulated sources inserted into the image and then recovered in the catalog give a measure of the intrinsic scatter due to measurement error and confusion. When the ATATS catalog is compared to NVSS, additional scatter is partly due to intrinsic variability, which we attempt to quantify here. Figure 13 shows the same data as in Figures 7 and 11 (for sources between 0 and 1 Jy), this time on a single plot to aid comparison. Points inserted from the simulated catalog have the same resolution as ATATS and do not cluster, unlike when comparing to NVSS, which has higher resolution and multi-component sources. As a result, the ATATS–NVSS match has some points (in the lower right quadrant of Figure 13) that are due to the ATA detecting a single object that is resolved by NVSS into several fainter components. Such sources are not present in the match to the simulated catalog. Even in the simulated catalog, however, an inserted source can still be matched erroneously to a nearby ATA source; these are the red points in Figure 13 scattered well below the main cloud of points. So even when the resolutions are matched and sources do not vary with time (the red points), there is still quite a lot of scatter just caused by measurement error and confusion. Clearly, though, there is some additional spread in the black points, which is at least in part due to the variability of the sources.

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We use the measured flux densities, $S_{m_i}$, and comparison flux densities, $S_{c_i}$ to compute the Pearson product-moment correlation coefficient,

$$\begin{equation} r = \frac{\sum _{i=1}^n (S_{m_i}- \bar{S}_{m}) (S_{c_i}- \bar{S}_{c})}{\sqrt{\sum _{i=1}^n (S_{m_i}- \bar{S}_{m})^2} \sqrt{\sum _{i=1}^n(S_{c_i}- \bar{S}_{c})^2}}, \end{equation} \tag{ 1 }$$

for the sources shown in Figures 7 (ATATS near NVSS positions), 8 (NVSS near ATATS positions), and 11 (simulated source retrieval); the values are r = 0.863, 0.969, and 0.973, respectively. When we smooth the NVSS catalog (as in Figure 9), the correlation is even better (r = 0.985), but we cannot apply this smoothing to the simulated catalog because the sources there have random positions. A clue to the additional scatter introduced by source variability is given by the comparison of r for NVSS near ATATS and for the retrieval of simulated sources, which shows that measurement uncertainties dominate.

We can examine this in more detail by computing the scatter in the points for the two samples. We define the fractional variability of each data point,

$$\begin{equation} V_i = \frac{2 \times (S_{m_i}- S_{c_i})}{S_{m_i}+ S_{c_i}}, \end{equation} \tag{ 2 }$$

and in Figure 14, we plot a histogram in V_i for the ATATS–NVSS match (for the sample as a whole, and split into subsamples of sources with S_ATATS ⩽ 100 mJy and S_ATATS>100 mJy). The central peak of the histogram is narrower for the bright sources, showing that their fractional variability is lower. All the histograms show the asymmetry toward high V_i due to the mismatch of bright ATATS and fainter NVSS sources discussed above. To obtain a measure of the true variability, we wish to quantify the scatter in V_i without being biased by these mismatched outliers, so we choose to measure the interquartile range of V_i, as opposed to the standard deviation. We compute the interquartile range, IQR_V, in 26 flux density bins, with bin edges selected to place an equal number (188) of data points, $S_{m_i}$, in each bin.

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By examining the change in IQR_V as a function of flux density, we can quantify the spread of the points in the flux–flux plots. As well as computing IQR_V for the ATATS–NVSS match, we compute the same statistic comparing the measured flux densities, $S_{m_i}$, to the inserted simulated catalog values, $S_{c_i}$. We plot IQR_V for the two samples in Figure 15. Although there is quite a large amount of scatter in the points, we can see that generally the ATATS–NVSS match tends to show a little more variability than the simulated catalog, as discussed above, especially above ∼300 mJy, where the reliability of the retrieval of simulated sources improves, but the scatter in the match to NVSS is higher. Some resolution effects undoubtedly remain, but at least some of this additional variability is presumably intrinsic. The fractional variability generally decreases toward higher flux densities (with the exception of the brightest bin, where the mismatched sensitivities and resolutions appear to dominate).

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We take the ATATS and smoothed NVSS flux densities (as plotted in Figure 9) and plot their ratio as a function of the ATATS flux density in Figure 16. Again we see that the scatter around the 1:1 line increases toward the fainter ATATS flux densities, suggestive of increased fractional variability for fainter sources. As discussed in Section 5, an asymmetry in the point cloud can be seen, most obviously at flux densities fainter than the ATATS completeness limit (to the left of the dotted lines in Figure 16). Above the completeness limit the point cloud is more symmetric about the 1:1 line, although there are still more outliers that appeared to get brighter from NVSS to ATATS than those that appeared to get fainter.

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We also plot in Figure 16 the median flux density ratio in bins of 0.25 dex in S_ATATS. For sources brighter than the completeness limit, the median ratio of S_ATATS/S_NVSS is 0.97 ± 0.10. This suggests that ATATS marginally underestimates the fluxes of NVSS sources. This may be due to a combination of the differing survey resolutions, the accuracy of the overall flux density calibration, and the CLEAN bias (Condon et al. 1998). However, we do not expect the CLEAN bias to be the dominant effect. The beam sidelobes are <10% of the main lobe (Figure 4), the RAPID software is designed not to CLEAN too deeply, and the combination of 12 snapshot observations into the master mosaic means that the (u, v) coverage is relatively good (Figure 2).

Some of the sources in Figure 13 that exhibit more variability than the simulated (non-variable) sources are likely real variables, especially those that are significantly brighter in NVSS than in ATATS (because the resolution effects discussed above tend to increase scatter toward the lower right of the 1:1 line in this plot rather than toward the upper left). Some sources that appear highly variable turn out not to be on closer inspection, however, so we carefully examined the most extreme cases.

We examined postage stamps from the ATATS mosaic and from NVSS for the 67 sources brighter than the ATATS completeness limit which have measured fluxes a factor of 2 or more different (either brighter or fainter) from their flux densities as measured from the smoothed NVSS catalog. We judged that only six of the sources were relatively compact and isolated in both NVSS and ATATS, and may therefore have varied by a factor of 2 or more in the 15 yr between epochs. These sources are marked by squares in Figure 16. Postage stamps for these sources are shown in Figure 17. The remaining 61 candidates had complex morphologies or near neighbors (Figure 18). These are most likely cases where multiple NVSS sources were not deblended successfully by the lower-resolution ATATS (see Section 5.4), although we cannot rule out that some may really be highly variable—however, as stated in Section 5, we would expect such variations, if real, to be symmetrically distributed about the 1:1 line.

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We plot the highly variable source candidates on the plot of flux ratio versus flux density in Figure 16. As can be seen, no highly variable sources are seen to get fainter from NVSS to ATATS, suggesting that most apparently highly variable sources appear so because of resolution effects. Of the six good candidates, two were brighter than S_NVSS = 40 mJy (i.e., to the right of the slanted dotted line in Figure 16). A search of the NASA Extragalactic Database shows that the five brightest sources of the six are known QSOs or radio galaxies (Table 3). We judge that the faintest source is also likely a QSO (although not previously classified as such) due to its compact radio morphology and variable radio flux.

By combining the data from all 12 epochs to make the master mosaic, we should gain a factor of 3.5 in rms sensitivity (which scales as the square root of the observing time), but in practice we gain somewhat more in image fidelity due to the poor (u, v) coverage of the individual snapshots. However, this comes at the expense of sensitivity to short duration transients. A transient with a characteristic timescale much shorter than the several days between ATATS epochs, and hence which appears only in a single epoch, will have a flux density in the master mosaic a factor of ∼12 less than in the image made from the epoch in which it occurred. So we expect that by comparing catalogs generated from the 12 single-epoch images, we will detect any such transients with ∼3.5 times better signal-to-noise ratio than we are able to detect by comparing the master mosaic and NVSS. The analysis of the constraints on transients and variability from epoch to epoch will be the subject of a forthcoming paper (S. Croft et al. 2010b, in preparation). For transients with characteristic timescales longer than the 81 days between epochs 1 and 12, but shorter than the ∼15 yr between NVSS and ATATS, the master mosaic catalog compared to NVSS (as discussed in this paper) provides the best sensitivity.

To look for such transients, we matched the final ATATS catalog of 4408 sources with the culled NVSS catalog (Section 5.1) of 10,729 sources, once again with a 75'' match radius. We found that 4333 of the ATATS sources had a match in NVSS. Of the remaining 75 sources without an NVSS match, 39 are above 40 mJy, the ATATS 90% completeness limit. We examined postage stamp images for these 39 sources (from the ATATS mosaic and from NVSS) and concluded that none were real transient sources. In the majority of cases, these were sources which consisted of multiple NVSS sources (usually as part of a double source—presumably a radio galaxy) which were not successfully deblended by ATATS. Examples of some of these sources are shown in Figure 19.

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NVSS is complete to a much fainter flux density limit than ATATS, so we can be more confident that an ATATS source without an NVSS counterpart is a transient than we could be confident that an NVSS source of similar brightness without an ATATS counterpart is a transient. Nevertheless, we searched for NVSS sources within the ATATS field without an ATATS counterpart. We limited ourselves to the 978 NVSS sources brighter than S_NVSS = 120 mJy (i.e., three times the measured ATATS 90% completeness limit) where ATATS is over 97% complete (Section 5.1). We examined postage stamp images of the 26 NVSS sources brighter than this limit with no ATA counterpart. All are sources with complex morphologies, and in each case it is clear from the images that the NVSS source does in fact have a counterpart in ATATS. Although comparing the catalogs using a 75'' match radius results in only 97% completeness, the fact that fewer than 1 out of 978 NVSS sources brighter than 120 mJy are truly missed by ATATS when the morphologies of complex sources are examined means that we can be >99.9% confident that no real 120 mJy sources were undetected in the ATATS images.

We can use the lack of transients seen when comparing ATATS to NVSS to place constraints on the population of transient sources brighter than ∼40 mJy. We see no sources in ATATS without a counterpart in NVSS (after visual inspection of the 39 candidates without a match within 75''). Poisson statistics give the probability

$$\begin{equation} P(n) = \frac{e^{-r}r^n}{n!} \end{equation} \tag{ 3 }$$

of detecting n transients given that r transients are expected over the survey area. Poisson 2σ confidence intervals correspond to P(n) = 1 − 0.95 = 0.05, and given that we detect n = 0 sources in the field, we derive a 2σ upper limit on the transient rate of r = −ln 0.05 = 3 sources in the 690 deg² survey, or 0.004 deg⁻².

Figure 20 shows the constraints on transient rates from some of the surveys discussed in Section 2, compared to the constraint from the comparison of ATATS and NVSS. It is hard to reconcile the steeply falling source counts suggested by the Gal-Yam et al. (2006) and ATATS results with the detections of nine transients brighter than 1 Jy reported by Matsumura et al. (2009) unless these transients make up a different population with a very steep cutoff below 1 Jy. The ATATS 2σ upper limit is marginally consistent with the M09 results above 1 Jy, but if the Matsumura et al. transients have flat or rising source counts toward fluxes <1 Jy we would expect to see them in ATATS. However, it should be noted that the characteristic timescale of the transients reported by Matsumura et al. is minutes to days, whereas our averaging of 12 ATATS epochs means that transients with durations shorter than a few days (i.e., those which might be present in a single ATATS epoch but not in the other 11) will have their mean flux densities reduced by a factor of 12 (and signal-to-noise by a factor of 3.5) relative to the single-epoch values. Nevertheless, if there are transients that reach average flux densities brighter than 12 times our completeness limit (i.e., ∼500 mJy and above) for at least 1 minute (the integration time for each individual ATATS epoch), they should appear as sources at least as bright as the completeness limit (i.e., averaged down by up to a factor of 12 if undetected at other epochs) in the master mosaic. No such sources are seen.

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We will examine transient statistics from the images and catalogs from individual epochs in S. Croft et al. (2010b, in preparation).