AN EXTREMELY DEEP, WIDE-FIELD NEAR-INFRARED SURVEY: BRIGHT GALAXY COUNTS AND LOCAL LARGE SCALE STRUCTURE

We made all the H- and J-band observations (except the CDF-N J band) with the Ultra Low Background Camera (ULBCam) on the UH 2.2 m telescope. The ULBCam NIR imager was the first wide-field infrared camera. It combined four Hawaii2-RG HgCdTe detectors to cover a 17' × 17' field of view (FOV) with a plate scale of 025 per pixel. ULBCam was developed as a prototype for the NIR imager on the James Webb Space Telescope (JWST; Hall et al. 2004).

Our ULBCam observations began in 2003 September. Observations have continued since then totaling over 300 hr of observing through 2008 February. All the data to date have been reduced and are mosaicked into the final images. Average seeing in the final mosaics is ∼1''.

We used a 13-step dither sequence consisting of 45''–90'' shifts between images having exposure times of 30–120 s depending on the background levels. The maximum exposure time of 120 s kept the entire dither sequence less than 30 minutes such that the coadded images from one sequence would represent a relatively constant sky background.

We observed the CDF-N in the K_s-band with the Wide-field Infrared Camera (WIRCam) at the Canada France Hawaii Telescope (CFHT) 3.6 m. We observed a large area (∼0.25 deg²) centered on the field. WIRCam combines four HAWAII2-RG 2k ×  2k detectors that cover a 20' × 20' FOV with a pixel scale of 03. We dithered images to cover the detector gaps and to provide a uniform sensitivity distribution. We performed most of the observations under photometric conditions with seeing from 06  to1''. The final mosaic seeing is ∼09.

Our group made the K_s-band observations in semesters 2006A and 2007A, and we combined these data with public observations of the GOODS-N made with the same instrument by a Canadian group led by Luc Simard in 2006A. Altogether the final K_s image includes ∼40 hr of integration time, making this one of the deepest wide-field K_s-band images ever (5σ limit K_s ∼ 24.8). The K_s-band catalog for this field is given in Barger et al. (2008).

J-band observations with WIRCam were obtained by a group led by Lihwai Lin in 2006A. Our group reduced these public data in 2008. The final mosaic includes ∼9 hr of integration time with mosaic seeing ∼08 and a 5σ limiting magnitude of J ∼ 24.

We observed four of our five fields in K-band with Wide Field Camera (WFCam) on UKIRT (the CDF-N is inaccessible to UKIRT because of declination constraints). WFCam employs four HAWAII2-RG 2k × 2k detectors spaced by 94%. This design, combined with a pixel scale of 04, allows for a coverage of ∼0.77 deg² in a mosaic of four pointings. Average seeing in the final WFCam mosaics is ∼1'' − 12.

We reduced images within each dither set (typically 15–30 minutes in length) using the SIMPLE pipeline. SIMPLE features a robust method for flat fielding in which a sky flat is iteratively derived from dithered night sky images. Application of this method leads to extremely flat images after background subtraction. SIMPLE also corrects for image distortion in a set of dithered images without any prior knowledge about the optics and without the use of an astrometric catalog, which allows for accurate registration of wide-field images.

We applied the following procedures within the SIMPLE pipeline to generate our reduced mosaics: first, we derived a median sky flat and applied it to all frames. We then used the SExtractor package (Bertin & Arnouts 1996) to detect objects in each flattened frame. We masked detected objects to create a new median sky flat and then redid the flat fielding. We subtracted the sky background by fitting a smooth polynomial surface to each masked, flattened frame. We removed the brightest cosmic ray hits with a 5 × 5 pixel spatial sigma filter.

Next, we again used the SExtractor package to measure object positions and fluxes in each flattened, sky-subtracted image. We calculated the first-order derivative of the optical distortion function by measuring the offsets of each object in the dither sequence as a function of location in the image. We obtained absolute astrometry by matching detected objects to a reference catalog. For this purpose, we used the catalogs from the Sloan Digital Sky Survey (SDSS; York et al. 2000) for all fields but Abell 370, where USNO B1.0 was used due to the lack of SDSS coverage. We then warped the reduced exposures to a common tangential sky plane with subpixel accuracy. This projection corrects for both optical distortion and absolute astrometry. Through this process we achieved an rms astrometry error of ∼01–02, except in the A370 field where with the USNO B1.0 catalog we achieve an rms error of ∼05.

We then weighted all projected images by their relative SExtractor object fluxes to correct for variable extinction and combined them to form a dither mosaic. In this combination, we applied a sigma filter to pixels that have the same sky position to further remove faint cosmic rays and artifacts such as reflections inside the optics.

We applied SExtractor a third time to each dither mosaic and scaled the object fluxes into μJys (resulting in an AB zero point of 23.9 for each image) through a comparison with 2MASS (Skrutskie et al. 2006) for point source photometry in each field in the range 14 < JH < 16. This is the range over which 2MASS reports better than signal-to-noise ratio (S/N) =10σ for point sources and our data are well below saturation levels. In the final step, we coadded all reduced dither mosaics into a large final mosaic.

The reduction procedure for the WIRCam data (which is only the CDF-N field) was the same as for the ULBCam data, except for the following details: WIRCam shows significant crosstalk in raw frames between the 32 readout channels. This was removed by subtracting the median of the 32 64 × 2k channels in the object-masked image. This process removed the majority of crosstalk, though weak features persist around the few brightest stars in the field.

We obtained absolute astrometry for the WIRCam frames by matching detected objects to a reference catalog constructed with relatively bright and compact objects in the ACS catalog (Giavalisco et al. 2004; after correcting for the 04 offset between ACS and radio frames) and the SuprimeCam catalog of Capak et al. (2004). The detection limits of 2MASS in the K_s-band only marginally overlap with the linear detection regime of WIRCam, and so rather than using 2MASS, we calibrated WIRCam K_s-band fluxes in each individual reduced frame using our deeper Subaru MOIRCS image as a reference (Barger et al. 2008). In the J band, 2MASS is deeper and we were able to achieve a good calibration for WIRCam frames using 2MASS point sources in the range 14 < J < 16.

Although the WIRCam and ULBCam reduction techniques were similar, the data come from different cameras on different telescopes. As a check for consistency, we compared the final reduced CDF-N J-band WIRCam image with the CDF-N J-band mosaic we generated from the ULBCam data. The result was that for 62 relatively bright stars (14 < J < 16) we found a magnitude offset of J_WIR – J_ULB = 0.003 ± 0.05, and for 691 galaxies at J < 20 we found J_WIR – J_ULB = 0.05 ± 0.05. These small systematics are of the same order of the random errors in the data, and so we consider reduced data from these two cameras to be consistent with one another.

We elected to use the stacked WFCam frames from the Cambridge Astronomical Survey Unit (CASU) pipeline, rather than the micro-dithered raw frames, to take advantage of the existing WFCam reduction pipeline and the "dribbling" algorithm employed by CASU to bring the relatively undersampled (04 per pixel) raw frames to higher effective resolution (02 per pixel). The following is a brief overview of the WFCam data reduction pipeline. Extensive documentation of the pipeline can be found at the CASU-WFCam data processing Web site.⁶

WFCam data are preprocessed in the UKIRT summit pipeline, in which raw frames are corrected for linearity and instrument signature, and then shipped to CASU for further processing. The CASU pipeline includes astrometric alignment, sky background subtraction, and stacking of micro-stepped images. First, dark frames are stacked to generate a master dark which is subtracted from all frames. Next, a flat fielding is performed using a stacked master twilight flat. A sky frame is then generated using a median combination with sigma clipping of a series of dark sky science frames. This is an iterative process including object detection and masking to form the most robust sky background estimation. The resulting sky background is then subtracted from science frames. Individual exposures are both dithered (tens of arcseconds offsets) and micro-stepped (subpixel offsets). The micro-stepping allows for the final step in the pipeline of "dribbling" (similar to drizzling) to stack microstepped raw frames to a finer grid. Processed frames are archived at the WSA.

We retrieved the stacked frames from the WSA and applied the post-stacking steps of the SIMPLE pipeline described above to perform additional background subtraction and spatial sigma filtering to get rid of any residuals from the initial reduction. We obtained absolute astrometry by matching detected objects in each stacked frame to a reference catalog. We then warped the reduced stacks to a common tangential sky plane with subpixel accuracy to correct for both optical distortion and absolute astrometry. Through this process, we achieved an rms astrometry error of ∼01–02, except in the Abell 370 field where with the USNO B1.0 catalog we achieve an rms error of ∼05.

Our CLANS field overlaps with the UKIDSS Deep Extragalactic Survey (DXS), and as such we retrieved the public DR3 data from the WSA and added it to our final CLANS K-band mosaic. The UKIDSS DXS observations employed a very similar approach to our observations and could be combined directly with our data using the same reduction techniques.

Finally, we applied SExtractor to each dither mosaic and scaled the object fluxes into μJys (resulting in an AB zero point of 23.9 for each image) through a comparison with 2MASS (Skrutskie et al. 2006) for point source photometry in each field in the range 14 < K_s < 16. In the final step, we coadded all reduced dither mosaics into a large final mosaic.

Regarding the calibration of our WFCam data using 2MASS, the WFCam K filter is a classical K filter with a central wavelength of ∼2.2 μm, while the 2MASS K_s filter has a central wavelength of ∼2.16 μm. The difference between photometry for stars in these two filters can be empirically quantified, as is done in the generation of UKIDSS catalogs, where 2MASS K_s is used to calibrate WFCam K data via the following relation: $K_{{\rm WFCam}} = K_{s,\rm {2MASS}} + 0.01(J_{{\rm 2MASS}}-K_{s,\rm {2MASS}})$.

We use the above UKIDSS empirical relation to calibrate our WFCam data using 2MASS. However, for the analysis in this paper we wish to compare our WFCam K-band galaxy counts with 2MASS K_s-band counts. The K_s − K magnitude difference for galaxies is different than that of stars and depends both on the shape of the galaxy's SED and its redshift. To explore the possible systematic and random errors associated with generating K_s-band galaxy counts from K-band data, we employed two methods.

First, we used the Bruzual & Charlot (2003) template SEDs for a wide range of stellar population ages. We find that out to a redshift of ∼2.5, the magnitude difference K_s − K has a median value of ∼−0.1 with rms variability of ±0.05. The difference is slightly larger (∼−0.15 ± 0.05) at the lowest redshifts. Second, we compared magnitudes from our own photometry of bright galaxies in our four WFCam fields (described in Section 4) to 2MASS magnitudes for the same objects. We find a K_s − K difference of ∼−0.15 ± 0.1 between 2MASS and our magnitudes, in good agreement with the low-redshift estimation using the Bruzual & Charlot (2003) templates described above. Thus, in our galaxy counts and analysis, we adopt a zero-point offset to our K-band data of −0.15 mag to bring the counts in line with the 2MASS K_s band.

In the case of our WFCam K-band fields, we did not have photometry from ULBCam or WIRCam to compare with directly as a check on the different reduction methods. We did, however, check our photometry against the UKIDSS catalogs in the CLANS field where we overlap and found a magnitude offset for 564 bright (15 <  K <  18) stars and galaxies of K_UKIDSS − K = 0.03 ± 0.05 which, again, is of the same order as the random errors in the data. In addition, the fact that our K-band photometry when compared with 2MASS K_s is in agreement with the predictions from simulations using the Bruzual & Charlot (2003) templates suggests the reductions have performed as expected.

We used a combination of morphology and color to separate stars from galaxies for our galaxy counts. Our methods include use of the SExtractor "CLASS_STAR" parameter, the ratio of semimajor to semiminor axes of objects, and J − K_s color to separate stars from galaxies. We honed our methods on a group of spectroscopically identified stars and galaxies in the GOODS-N (a subfield of the CDF-N). This involved the use of J- and K_s-band catalogs from this study and the GOODS-N redshift catalog from Barger et al. (2008). Finally, as an independent test of our methods, in four of our five fields (all but A370) where we overlap with the SDSS, we compared our classified stars having JHK_s <  19 with the morphological classifications for these objects in the SDSS catalogs. The results of these methods are discussed below. Our final star counts generated using these methods are shown in Figure 2.

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The CLASS_STAR parameter is an output of SExtractor to describe whether a given object looks like a point source or an extended source. The CLASS_STAR output contains a value between 0 (extended object) and 1 (point source) and is assigned by SExtractor to each object detected in the image. CLASS_STAR can be used to separate stars from galaxies at bright magnitudes, but the accuracy of this parameter breaks down at fainter magnitudes. Where that breakdown occurs depends on the depth of the field and the SEEING_FWHM input parameter (see Table 2).

The SEEING_FWHM input parameter is provided to SExtractor by the user to describe the average point source full width at half-maximum (FWHM) in the image. This parameter is critical for SExtractor to accurately identify stars with its output parameter CLASS_STAR.

We determined the optimal value for the SEEING_FWHM input parameter by first running SExtractor on an image to determine the FWHM of point sources in the image (using an initial guess at the image seeing for the input SEEING_FWHM). We then took the median FWHM for selected point sources (CLASS_STAR >0.95) as the final input value for the SEEING_FWHM parameter. Values calculated in this way for the SEEING_FWHM parameter in each field are listed in Table 3.

We found that on occasion for bright galaxies, the CLASS_STAR parameter misidentified galaxies as stars that were clearly galaxies by eye (2 out of 125 galaxies at K_s < 19 in the GOODS-N catalog). We resolved this issue by constraining the ratio of semimajor to semiminor axis for stars (a/b ⩽ 1.3).

Using the star identification criteria of CLASS_STAR >0.7 for JK_s < 17.5 and CLASS_STAR >0.9 and a/b ⩽ 1.3 for $17.5\,{<}\,{{\it {\it JK}}_s}\,{<}\,19$, we correctly identified 100% of stars for JK_s < 19 from the spectroscopic sample of Barger et al. (2008).

To extend our star–galaxy separation to fainter magnitudes, we used a combination of the SExtractor CLASS_STAR parameter and the J − K_s color of objects. We determined that a color cut of J − K_s < 0.1 and CLASS_STAR >0.95 for 19 < JK_s < 24 accurately identified >90% of stars while only misclassifying <1% of galaxies as stars. Because galaxies dominate the counts at these faint magnitudes, the combination of these effects introduces less than 1% error in the counts in the range 19 < JK_s < 24. These results are displayed in Figure 3 where the K_s-band magnitude is plotted against the J − K_s color for the Barger et al. (2008) sample. Blue stars show correctly identified stars, red circles show correctly identified galaxies, and purple stars and green circles show misclassified stars and galaxies, respectively.

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In our fields that overlap with SDSS (all but A370), we were able to perform a check on our bright (JHK_s <  19) star selection by cross-correlating with objects classified morphologically as point sources in SDSS. We looked at two things in this analysis. First, we searched for objects that we identified as stars which were classified as extended objects in SDSS. Second, we searched for objects that we found to be galaxies that were classified as point sources in SDSS.

For JHK_s <  17.5, we found that none of our galaxies were listed as point sources in SDSS. However, a handful (5–15) of our stars in each field were listed as extended sources in SDSS. We first investigated this discrepancy by eye and found that many of these objects were clearly point sources in our images identifiable by their diffraction spikes. This is perhaps due to the fact that our images are much deeper than SDSS, or these are late-type stars that are brighter in the NIR than in the optical. Other sources appeared to be close binary point sources in our images, perhaps unresolved by the SDSS. Given that the majority of discrepant point sources appear to be misclassifications in the SDSS, we conclude that we have done a robust job of star–galaxy separation for JHK_s <  17.5.

In the range 17.5 <  JHK_s <  19, we found >90% agreement between objects we classified as stars and point sources identified by SDSS, as well as for objects we classified as galaxies and their SDSS counterparts. To investigate discrepant sources, we employed g'(SDSS) −J versus J − K_s color–color diagrams. The utility of such diagrams for separating stars and galaxies is shown in Figure 4 using the Barger et al. (2008) sample as an example, where SDSS counterparts are found for 131 stars and 647 galaxies. Using this sample, we determined that a color cut of g' − J>6.5 × (J − K_s) + 1.8 was appropriate for selecting the vast majority of stars.

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We plotted objects we identified as stars, but whose SDSS counterparts were classified as extended on the g'JK_s plane and found that the majority matched the color criterion for stars defined above. Those that did not meet the criterion typically had very high SExtractor CLASS_STAR parameters in our catalogs and, as such, are likely candidates to be late-type M and L dwarf stars.

Finally, we plotted objects that we identified as galaxies but whose SDSS counterparts were classified as point sources on the g'JK_s plane. We found a minority of these objects did, in fact, meet the g'JK_s color criterion for stars. In this case, we flagged these objects as stars in our catalogs. Stars identified in this way through comparison with the SDSS were very few in number and only affect the galaxy counts in the 17.5 <  JHK_s <  19 range on the ∼0%–3% level.

The SDSS does not cover our A370 field, so we do not have the opportunity to compare our star–galaxy separation with an independent optical morphology classification like we have done for the other fields. Based on our comparison with the SDSS in other fields, we expect that stars we may have missed in the A370 field could contribute to an excess on the few percent level to counts in the 17.5 <  JHK_s <  19 range.

As seen in Figure 3, there are stars that will be missed by our color cut in J − K_s. These will tend to be M and L dwarf stars because they are redder than the rest of the main-sequence population (T dwarfs, in fact, have J − K_s < 0 like typical main sequence stars). However, we would expect to identify the majority of M and L dwarfs as stars based on morphology alone for K_s < 19 (as demonstrated above), corresponding to distances of out to ∼100 pc. Beyond this we would miss these faint dwarf stars in our star removal.

The space density of M and L dwarfs is poorly constrained at large heliocentric distances, but Stanway et al. (2008) and Pirzkal et al. (2009) have shown that M and L dwarfs may exist in large numbers out to several kpc into the Galactic halo. The star counts for M dwarfs from these two groups roughly agree and appear flat out to very faint magnitudes at levels of ∼100–200 mag⁻¹ deg².

In our galaxy counts, assuming the worst case scenario, this could represent a 15% systematic error in the brightest bin (K_s = 19–20), for which we require J − K_s < 0.1. Assuming flat star counts for these late-type dwarf stars, this error would drop to <10% at K_s = 20.5 and <5% at K_s = 21.5. The focus of this paper is the bright galaxy counts for which we believe our star–galaxy separation is robust, but we alert the reader that the counts remain uncorrected for late-type dwarf stars fainter than JHK_s =  19.

We downloaded the entire 2MASS extended source catalog (XSC) and 2MASS-6x XSC from the NASA/IPAC Infrared Science Archive.⁷ We constructed 2MASS galaxy counts from the catalog over an area of ∼20, 000 deg² representing the entire 2MASS XSC for Galactic latitude |b|> 30 (2π Steradians). We limited this 2MASS sample to JHK_s <  15.5 to stay within the all sky catalog's completeness limits. We excluded known 2MASS Galactic extended sources from the counts using the Galactic extended source catalog available at NASA/IPAC Web site. As shown in Figure 6, galaxy counts from 2MASS from 11th to 15th magnitude are sampling M* galaxies in the local universe at distances of ∼50–350 Mpc.

We also constructed galaxy counts from the 2MASS-6x (Beichman et al. 2003) catalog of extended sources in the ∼25 deg² centered on the Lockman Hole area of low galactic H i column density (Lockman et al. 1986). These data represent 25 deg² where 2MASS observed six times as long as the all sky catalog exposure times, thus making the 2MASS-6x catalog roughly 1 mag deeper in J, H, and K_s. We were able to further "deepen" the 2MASS-6x Lockman Hole catalog because our deep data in the CLANS and CLASXS fields overlaps 100% with the 2MASS-6x Lockman Hole. As such, we were able to measure completeness in the 2MASS-6x catalog, and correct the counts to JHK_s =  16.75. Thus, we use the 2MASS and 2MASS-6x catalogs to firmly establish average galaxy counts on the bright end. The average 2MASS galaxy counts for |b|>30° are shown in Figure 7.

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The solid lines in Figure 7 show an error-weighted least-squares fit to the data. In the left panels the counts are shown in the standard N versus magnitude form, and in the right panels the counts are shown divided through by a normalized Euclidean model. For this global average of galaxy counts in J, H, and K_s we find α = 0.59, 0.59, and 0.63(∼ ±0.01 in all three bands), respectively. These values are all 0.01–0.02 above the Euclidean prediction, representing a possible galaxy space density increase toward fainter magnitudes of 7%–15% over the magnitude range sampled.

Next, we extracted 2MASS counts for areas of ∼25 deg² centered on each of our fields. In Figure 8, we show our raw counts (red diamonds) for JHK_s <  17.5 plotted with 2MASS counts (black asterisks) from each of these 25 deg² subfields. The dashed lines show an error-weighted least-squares fit to the data. In the CLANS and CLASXS fields we include our counts extracted from the 2MASS-6x survey (green triangles), because these two fields lie within the 2MASS-6x Lockman Hole. The counts have been divided through by a normalized Euclidean model (α = 0.6). The calculated slopes are tabulated in the plots. We note that in many cases fitting to only the data points from this study would yield a much steeper slope than that obtained with the inclusion of 2MASS. In this measurement of the local slope at our field positions, we find a mix of values ranging from sub-Euclidean to super-Euclidean. We note that the most sub-Euclidean slopes are found in our fields near the supergalactic equator (CLANS and CLASXS). We return to this point in Section 6.2.

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In Figure 9, we show the error-weighted average of our counts (red squares) alongside the error-weighted average of the 2MASS counts (black diamonds) extracted from the 25 deg² subfields centered on our fields (for a total of 125 deg²), as well as the counts from the 2MASS-6x Lockman Hole (green triangles). Again, we fit the slope with an error-weighted least-squares method and the slopes are listed in the plots. We find that, on average, when combined with 2MASS, our counts yield a Euclidean slope within our error bars of ±0.01. We note that taken on their own, our counts in both the H- and K_s bands would appear super-Euclidean. This is likely due simply to a lack of bright objects in the fields (HK_s ∼ 15), leading to large random errors in the brightest bin.

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We now consider the implications of our bright galaxy counts in terms of local large scale structure. The most striking feature in the local large scale structure is the supergalactic Plane discovered by de Vaucouleurs 1953. The plane is roughly perpendicular to our Galactic plane. In Figure 8, we find that in the CLANS and CLASXS fields, the slope appears distinctly sub-Euclidean, whereas in the other three fields the slopes are closer to the Euclidean prediction. This is interesting because the CLANS and CLASXS fields are of nearly equatorial supergalactic latitude (−18 and −39, respectively; see Table 1). In fact, all of our fields are at relatively low absolute supergalactic latitude (average $|\rm {SGB}|\sim 10^\circ$), with A370 being the furthest off the plane at −257.

The fields of Huang et al. (1997), where a strong super-Euclidean slope was found in the K_s band, span absolute supergalactic latitudes from $10<\rm {SGB}<54$ with an average of subgiant branch ($\rm {SGB}) \sim 30^\circ$. As a verification of the Huang et al. (1997) result, we did another comparison in which we extracted 2MASS galaxies from patches of 25 deg² centered on the Huang et al. (1997) fields. First, however, we extracted 2MASS counts from the actual areas of the Huang et al. (1997) fields and found a zero-point offset of −0.3 to their counts. We show this in Figure 10. We applied this offset to their counts before proceeding with the comparison to the larger (25 deg²) fields.

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We plot the zero-point-adjusted counts from Huang et al. (1997) with the average of 2MASS counts over the larger surrounding areas in Figure 11. We calculate a slope of α = 0.67 for the combined data set. This value is slightly smaller than that found using just the Huang et al. (1997) data points (α = 0.69), but still distinctly super-Euclidean. Over the magnitude range sampled, this would still represent roughly a factor of 2 increase in the space density of galaxies as found by Huang et al. (1997).

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Gardner et al. (1993) found a super-Euclidean bright counts slope of α = 0.67 in their survey of a collection of fields totaling ∼10 deg² at an average absolute SGB of ∼25. Väisänen et al. (2000) found a sub-Euclidean slope at bright magnitudes in the K_s-band at high supergalactic latitude ($\rm {SGB}=40$), but this can likely be explained by the fact that they had three Abell clusters in their fields (A2168 at z = 0.06; A2211 at z = 0.15; and A2213 at z = 0.15), which likely dominate their galaxy counts at bright magnitudes. The effect of just one galaxy cluster in a similar sized field can be observed in our data in Figure 1, where the A370 (z = 0.37) counts show a large excess in the range 17 <  JHK_s <  19. The three lower redshift clusters in the Väisänen et al. (2000) fields would produce large excesses at brighter magnitudes, and indeed they find their counts to be in excess over all other published studies at bright magnitudes.

Thus, from the evidence above, it seems that a large fraction of the variability in the slope and absolute numbers between different bright counts studies can be attributed to nearby large scale structure, be it individual galaxy clusters or local superstructure. When individual nearby galaxy clusters are avoided, there appears to be evidence for the slope of bright galaxy counts to be related to supergalactic latitude.

To investigate this further, we calculated the bright counts slope in 2MASS as a function of position on the sky by dividing the |b|>30 catalog into slices in supergalactic latitude ranging in area from ∼500 to 2500 deg² each. As a result, we obtained slope measurements in J, H, and K_s for $-60<\rm {SGB}<60$. We plot the average 2MASS slope as a function of SGB in Figure 12. In this figure, the Euclidean slope prediction has been subtracted from the measured values such that the dashed horizontal line represents the expectation for a Euclidean slope in all three bands. J band is represented in blue, H band in black, and K_s band in red. The error in the slope measurements is ∼0.01 in all cases. We note that the similarity in slope measurements between bands suggests that our slope determinations are robust.

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In Figure 12, the only distinctly sub-Euclidean slopes are found near the supergalactic equator, consistent with results from our CLANS and CLASXS fields, with all other latitudes appearing to be super-Euclidean. At high northern supergalactic latitudes we find that slopes exceeding the Euclidean prediction by >0.05, such as those found by Huang et al. (1997) and Gardner et al. (1993), are typical. One interpretation of these results would be that near the supergalactic plane, the very brightest counts are populated with an excess of sources causing the slope to drop, and above the plane a relative paucity of nearby sources above the plane causing the slope to steepen. The southern supergalactic latitudes do not display the same sharp rise to super-Euclidean as in the north. The magnitude range sampled in these counts is 10.5 <  JHK_s <  15.5, which means that the brightest magnitude bin is centered on typical galaxies at a distance of ∼50 Mpc. This means that toward high northern SGB, where slopes are ∼0.1 above the Euclidean prediction, the space density of galaxies at a distance of 50 Mpc could be low by roughly a factor of 2 compared to the space density of 250–350 Mpc distant. In the southern supergalactic cap, the slopes are not as steep (∼0.03 above Euclidean), but still represent a possible underdensity of ∼25% at 50 Mpc relative to 250–350 Mpc.

Next we took a broad average of 2MASS counts in and out of the supergalactic plane. In Table 7, we give the measured average slope for galaxy counts in the supergalactic plane ($|\rm {SGB}|< 10$) and out of the plane. We find that on average the counts in the plane are sub-Euclidean, consistent with what we found in Figure 12. The slope out of the plane is steeper by some Δα ∼ 0.02–0.06 in both the northern and southern supergalactic caps, and super-Euclidean on average. Thus, the expected variability in the 2MASS bright counts slope is ∼±0.04 due only to the very largest local structure.

Table 7. 2MASS Galaxy Counts Slope Over the Galactic Caps, the Supergalactic Equator, and the Supergalactic Caps

Region	J Slopea	H Slopea	Ks Slopea
Gal. |b|>30°	0.59	0.59	0.63
$|\rm {SGB}|<10^\circ$	0.55	0.57	0.59
SGB <−10°	0.60	0.59	0.63
SGB >10°	0.61	0.61	0.65
$|\rm {SGB}|>10^\circ$	0.61	0.60	0.64

Note. ^aErrors in fitted slopes are ∼0.01 in all cases.

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We next divided the 2MASS |b|>30 sky into 844 patches of ∼25 deg² each. We measured the slope of the galaxy counts from 11 <  JHK_s  <  15 for each and found an rms variability in the slope of ∼0.1. Inside distances of ∼250 Mpc, 2MASS is 1–2 mag deeper than M* and, as such, is measuring a fairly complete sample of the local luminosity function. This implies our 25 deg² patches are sampling structure on size scales of ∼20 Mpc and find rather strong variability.

To test for the angular size over which all local large scale apart from the supergalactic plane could be sufficiently averaged out, we divided up the 2MASS |b|>30 sky into increasingly larger subfields and measured the rms variability in the measured slope across all subfields. Figure 13 shows the result of this exercise for subfields ranging from ∼25 to 10, 000 deg². We find that when averaging over subfields larger than ∼1000 deg², the rms variability between all subfields is of the same order of that induced by the supergalactic plane alone, and as such, all other local large scale structure has been sufficiently averaged out. In the 2MASS sample, this suggests that effects of local large scale structure have been sufficiently averaged out over scales of ∼150 Mpc.

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Based on the analysis above, we conclude that the local supergalactic plane is overdense by 10%–15% compared to regions at distances of ∼250–350 Mpc, while the voids just above and below the plane are underdense by up to a factor of 2 relative to similarly distant regions.

Cold Dark Matter simulations such as the Millennium Run (Springel et al. 2005) predict that the largest structures in the universe should be ⩽100 Mpc in extent. Observed large scale structures, most notably the Sloan Great Wall (Gott et al. 2005), demonstrate the existence of structure on scales much larger than simulations predict. Consensus has not yet been reached on whether a structure like the Sloan Great Wall represents an extreme nonlinearity in the matter distribution of the universe, or if inhomogeneities on several hundred Mpc scales are typical. Two recent analyses of the distribution of matter in the SDSS DR6 data set (Sarkar et al. 2009; Kitaura et al. 2009) demonstrate the current range of interpretation of observations, in which Sarkar et al. (2009) arrive at a scale of homogeneity of 70 Mpc and Kitaura et al. (2009) claim to have discovered a new large void 150 Mpc in diameter. Clearly the typical size of large scale structure still depends on how one interprets the data. In our analysis, we find that averaging galaxy counts over areas on the sky spanning ∼150 Mpc sufficiently smooths out local structure. However, in the same data, the super-Euclidean slopes above and below the supergalactic plane suggest that the local space density of galaxies may be low by 25%–100% compared to regions a few hundred Mpc away, which would suggest that local structure exists on much larger scales than 150 Mpc.

We employ the UKIDSS survey to investigate the possibility that the entire 2MASS volume resides in a relatively underdense region that is ⩾250 Mpc in radius, as suggested by Huang et al. (1997). The expectation if this were the case would be a steepening of the galaxy counts slope in the range 15 <  JHK_s <  17, as, in fact, is seen in the Huang et al. (1997) sample when compared with 2MASS.

As a test for a large void, we employ the UKIDSS (Lawrence et al. 2007) third data release (DR3; S. Warren et al. 2010, in preparation) Large Area Survey (LAS), which has recently become public. The DR3 LAS covers several hundred degrees of sky within the SDSS footprint to depths of JHK_s ∼  19. We selected three large subfields totaling ∼135 deg² in the UKIDSS LAS. We downloaded catalogs from the WSA, and the range in celestial coordinates and SGB for these subfields are given in Table 8. We selected the fields to span a wide range of SGB above and below the supergalactic plane.

We cross-correlated the UKIDSS catalogs with their SDSS counterparts and removed stars from the catalogs via the SDSS classifier and g'JK color–color diagrams in a similar manner to what is described in Section 5.1. A comparison between the slope of the 2MASS counts and the UKIDSS counts for the three subfields is shown in Figure 14. 2MASS counts are shown in black diamonds and UKIDSS counts in red asterisks. The dashed and solid lines show error-weighted least-squares fits to the 2MASS and UKIDSS counts, respectively. The slopes for each fit are listed in the plots, and the associated errors in the fitted slopes are ∼±0.01 in all cases.

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The result is that for these three subfields, we do not observe a steepening of the slope at magnitudes beyond the 2MASS limits. In fact, in the majority of cases in Figure 14, the slope appears to be decreasing into the fainter magnitudes of the UKIDSS survey.