PSZSPT: a joint Planck and SPT-SZ cluster catalogue

We present the first cluster catalogue extracted from combined space- (Planck) and ground-based (South Pole Telescope; SPT-SZ) millimeter data. We develop and apply a Matched Multi-Filter (MMF) capable of dealing with the different transfer functions and resolutions of the two datasets. We verified that it produces results consistent with publications from Planck and SPT collaborations when applied on the datasets individually. We also verified that Planck and SPT-SZ cluster fluxes are consistent with each other. When applied blindly to the combined dataset, the MMF generated a catalogue of 419 detections ($S/N>5$), of which 323 are already part of the SPT-SZ or PSZ2 catalogues; 37 are new SZ detections, identified in other catalogues or surveys; and 59 are new unidentified candidates. The MMF takes advantage of the complementarity of the two datasets, Planck being particularly useful for detecting clusters at low redshift ($z<0.3$) while SPT is efficient at finding higher redshift ($z>0.3$) sources. This work represents a proof of concept that blind cluster extraction can be performed on combined, inhomogeneous millimeter datasets acquired from space and ground. This result is of prime importance for planned ground-based cosmic microwave background (CMB) experiments (e.g., Simons Observatory, CMB-S4) and envisaged CMB space missions (e.g., PICO, Backlight) that will detect hundreds of thousands of clusters in the low mass regime ($M_{500} \leqslant 10^{14} M_\odot$), for which the various sources of intra-cluster emission (gas, dust, synchrotron) will be of same order of magnitude and hence require broad ground+space frequency coverage with comparable spatial resolution for adequate separation.


Introduction
Galaxy clusters constitute unique objects to study structure formation in the Universe. Lying at the nodes of the cosmic web, their distribution in mass and redshift is sensitive to cosmological parameters (e.g. Allen et al. 2011, and references therein). They also represent ideal laboratories to understand galaxy formation and evolution (e.g. Voit 2005, and references therein). Progressing in both cosmology and astrophysics with galaxy clusters requires advances in two directions: increasing the number of known clusters and better understanding their physics. The multi-frequency view is now mandatory to achieve these goals.
Clusters are detected in the optical via their member galaxies, in X-ray via Bremsstrahlung emission of the embedded hot ionized gas and, more recently, via the Sunyaev-Zeldovich (SZ, Sunyaev & Zeldovich 1970, 1972 effect. Progress in detecting numerous new clusters has been made in the recent years with the advent of SZ surveys (Staniszewski et al. 2009;Menanteau et al. 2010;Planck Collaboration et al. 2011). The current galaxy cluster catalogues are most often extracted from single experiment data. This is the case for the all-sky Abell (Abell et al. 1989), ROSAT (Böhringer et al. 2000(Böhringer et al. , 2001 and Planck (Planck Collaboration et al. 2011, 2014a, 2016a catalogues.
In order to extract clusters with a low signal-to-noise threshold, hybrid methods have been recently developed to clean the single experiment catalogues from spurious detections. These methods have been successfully applied to X-ray (ROSAT) and SZ (Planck) detections using optical (BOSS, DES, WISE, SDSS) data (e.g. Burenin 2017;Finoguenov et al. 2020;Klein et al. 2019). Another approach to extract new clusters is to use data from different frequency bands jointly. The approach was initially proposed by Maturi (2007), but is difficult to implement in practice because the signals from clusters originate from different physical processes in different frequency bands. It has nevertheless been successfully implemented recently by Tarrío et al. (2016Tarrío et al. ( , 2018Tarrío et al. ( , 2019 for ROSAT and Planck data. A final avenue for extracting low signal-to-noise clusters is to combine different observations in the same frequency band. Aghanim et al. (2019), Madhavacheril et al. (2020) and Naess et al. (2020) followed this path and produced for the first time combined SZ maps from Planck and ACT data, Planck and ACT-Pol data, and Planck and ACT, ACTPol, AdvACT data. These works showed for the first time the significant gain for cluster science when combining space and ground-based data in the ACT footprint. Aghanim et al. (2019) also extracted clusters using a Match Multi-Filter but did not publish the associated catalogue.
Here, we focus on the Planck and SPT-SZ datasets. We propose a practical implementation of a blind Matched Multi-Filter extraction algorithm working on space-and ground-based data jointly, and we publish the associated catalogue: PSZSPT. Crossmatches of the PSZSPT detections and external catalogues are included. We did not use the Planck & SPT-SZ combined maps proposed by Chown et al. (2018) to produce the PSZSPT catalogue because they are not optimized for cluster extraction. We use instead the SPT maps provided in that publication and that we thoroughly test against quantities published with the official SPT-SZ catalogues; only then do we combine them with the public Planck maps.
The study presented here is expected to be important for the forthcoming space-and ground-based experiments. The future CMB experiments will detect low mass clusters (M 500 10 14 M ) for which the SZ signal is expected to be of the same order as the other sources of emission from clusters, in particular radio and infrared emission of galaxies (e.g. Melin et al. 2018). Combining ground-based (ν < 300 GHz) and spacebased (ν > 300 GHz) experiments would help disentangle the various sources of emission [e.g., Simons Observatory (Ade et al. 2019) & Planck or CMB-S4 (Abazajian et al. 2019) & PICO (Hanany et al. 2019) or Backlight (Basu et al. 2019;Delabrouille et al. 2019)].
We first present the two datasets used in our analysis in Sect. 2. We then recall the characteristics of the Matched Multi-Filter in Sect. 3. We apply the Matched Multi-filter on the SPT-SZ and Planck data independently to test the consistency of our results with results published by the two collaborations in Sect. 4. The in-depth work related to Sect. 4 is presented in Appendix A, B and C. In Sect. 5, we test the consistency between the SPT-SZ and the Planck datasets. We detail the construction of the PSZSPT catalogue in Sect. 6 and how we characterize it. We provide a comparison between recovered and published masses in Appendix D. The description of the PSZSPT catalogue is given in Appendix E. Finally, we summarize and discuss our findings, and look to future work in Sect. 7.

SPT-SZ
We use the SPT-SZ public maps 1 "SPT Only Data maps" at 95, 150 and 220 GHz. The maps provide a resolution 1.75 arcmin (full width at half maximum FWHM), slightly degraded with respect to the native resolution of 1.6, 1.1 and 1.0 arcmin at 95, 150 and 220 GHz respectively (Bleem et al. 2015b). The other key ingredients for the analysis described in this paper are the filter transfer functions, "SPT Filter Transfer Function", at each frequency and the boundary and point source mask "Mask". All the products are provided at Healpix N side = 8192, which corresponds to a pixel size of about 0.43 arcmin. The frequency responses are not provided in electronic format in the archive. We retrieve them from Fig. 10 of Chown et al. (2018) (long dashed lines in the three panels) using the WebPlotDigitizer 2 . For additional details about the SPT-SZ public data, we refer the reader to the LAMBDA archive webpage given in footnote and to Chown et al. (2018).

Planck
We use the public Planck maps of the High Frequency Instrument covering the six frequencies 100, 143, 217, 353, 545 and 857 GHz. The maps are provided in Galactic coordinates at Healpix resolution N side = 2048, corresponding to a pixel size of about 1.72 arcmin. We upgraded the maps to N side = 8192 by zero padding in harmonic space, and we changed the coordinate system to equatorial to match the SPT-SZ public data. For the analysis, we assume the Planck beams are Gaussian with FWHM of 9.659, 7.220, 4.900, 4.916, 4.675, 4.216 arcmin at 100, 143, 217, 353, 545, 857 GHz respectively as in Planck Collaboration et al. (2016a). The frequency responses are also based on the same reference. We convert the maps to µK, the units of the SPT-SZ maps.

Matched Multi-Filters
We modified the Matched Multi-Filters MMF3 (Melin et al. 2006(Melin et al. , 2012, initially based on Herranz et al. (2002), and developed to extract clusters from the Planck maps for the three data releases (Planck Collaboration et al. 2011, 2014a, 2016a. The MMF3 algorithm works on Planck data with 10 × 10 deg tangential maps. We want to keep the Planck size of the tangential maps, to ease the component separation on large scale, and the SPT-SZ pixel size, to conserve the information at small scale. We therefore divide the six Planck and three SPT-SZ frequency maps covering the SPT footprint into 10×10 deg tangential maps and keep the 0.43 arcmin pixels corresponding to N side = 8192. We filter the resulting maps of 1400 × 1400 pixels with MMF3. These maps contain 4 2 = 16 times more pixels than for the standard Planck analysis and nine frequency maps instead of six, leading to a computationally heavier analysis. We write the nine tangential maps m(x) and decompose them as the cluster component y o t θ s (x) and the noise n(x), corresponding to both instrumental noise and astrophysical components other than the cluster: where y o is the central Compton-y parameter, t θ s (x) is the vector whose i th component is , the tSZ template T θ s convolved by b i (defined hereafter) and modulated by the tSZ frequency spectrum integrated over the frequency response, f ν , in µK units. The integration along the line-of-sight for T θ s is performed out to r = 5R 500 , and θ s is the scale radius, the characteristic scale of the cluster. For Planck, b i is simply the Gaussian beam at frequency ν i assumed to be azimuthally symmetric. For SPT-SZ, b i = B * T i , the convolution of the azimuthally symmetric Gaussian beam B (FWHM=1.75 arcmin) and the filter transfer function T i at frequency ν i . The filter transfer function is not azimuthally symmetric so, in practice, we perform the convolution in allsky Healpix maps at ten locations centered on the ten SPT clusters with the highest signal-to-noise ratio, cut tangential maps centered on b i and average them.
Assuming a pressure profile T θ s , MMF3 obtains the linear estimate of y o with minimum variance: where with and P(k) =< n * (k)n(k) > .
k is the two dimensional spatial frequency. P(k) is the power spectrum matrix of the noise across frequency channels and is estimated directly from the data since the SZ signal is small compared to the other signals. The signal-to-noise (S/N) of the measurement is given by The total integrated flux in the cylinder of radius r = 5R 500 can be estimated as where θ 500 is the angle subtended by R 500 at the cluster redshift. This total flux is then converted to the flux in the sphere of radius r = R 500 , Y 500 , by multiplying Y 5R 500 by the ratio of R 500 0 Melin et al. 2011). t θ s (r) is the three dimensional profile while T θ s (x) is the two dimensional profile i.e. t θ s (r) integrated along the line-of-sight. In the following, we adopt the profile of Arnaud et al. (2010) for t θ s (r), except in Section 5.1 and Appendix B in which we adopt a β-profile to match the SPT-SZ cluster modeling.
We can run MMF3 in unblind or blind mode, i.e., in fixing the position and size of the cluster or in letting position and/or size free. In blind mode, we adopt the size and/or the position that maximize(s) the S/N and refer them(it) as blind size (and blind position). The blind flux is estimated by fixing the filter size to the blind size and the position to the blind position if also left free. The blind mode is further described in Sect. 6.1.

Consistency between public products and results published by the SPT and Planck collaborations
We checked that results obtained with SPT filter transfer functions applied to SPT-SZ maps are consistent with SPT published results. We extracted SPT point sources (Mocanu et al. 2013) in individual frequency maps using the filter transfer functions and we compared our recovered flux to the published flux. Results are presented in Appendix A. The filter functions are accurate for point source flux S < 50 mJy and provide flux biased a few percent high for S > 50 mJy. The simulations created to compute the SPT filter transfer functions do not contain bright point sources (see Sect. 4.1.4 of Chown et al. 2018). We suspect this is the reason for the mis-estimation of bright point source fluxes. We then extracted SPT clusters (Bleem et al. 2015b) using the SPT filter transfer functions and the SPT-SZ maps. Results are shown in Appendix B. SPT cluster flux is recovered without bias for fluxes Y 0.75 SPT < 2 × 10 −4 arcmin 2 , while for Y 0.75 SPT > 2 × 10 −4 arcmin 2 there is a few percent bias to larger fluxes 3 . This bias may come from the filter transfer function, which is biased high for bright sources, as shown above. SPT cluster size is recovered without bias, and SPT S/N is recovered 10% low with respect to results published by the SPT collaboration. We suspect this bias to lower values is due to the poorer resolution of the public SPT maps compared to the native SPT resolution, and possibly to the preprocessing applied by the SPT collaboration to the data for constructing the public SPT Healpix maps. We would expect the bias to disappear if the Matched Multi-Filters were applied to the SPT-SZ data in its native format and resolution.
Finally, we checked the consistency of the Planck cluster properties extracted from the Planck public data to the flux published by the Planck collaboration. Results are presented in Appendix C. We use one of the algorithms developed in the Planck collaboration but we do not expect to find a one-to-one relation between our recovered flux, size and S/N and the quantities published by the Planck collaboration. This is because we upgraded the maps from N side = 2048 to 8192, and we changed the coordinate system from Galactic to equatorial. In particular, the change of coordinates modifies the estimation of the noise power spectrum P(k), introducing some scatter in the recovered quantities with respect to the published values, but no significant bias.
We conclude that our extraction method provide results that are consistent with the results published by both the SPT and Planck collaboration. After these consistency tests between public products and results published by the collaborations, we checked for consistency across the two data sets.

Consistency between the SPT-SZ and Planck data sets
We checked the consistency between the two data sets by extracting the SPT-SZ clusters in Planck data adopting the SPT cluster modeling and vice versa, i.e., by extracting the Planck clusters in SPT-SZ data adopting the Planck cluster modeling.

SPT-SZ cluster flux in Planck data
We used the full (ξ > 4.5) SPT-SZ published cluster catalogue (Bleem et al. 2015b). For the work described in this Section, we adopted the β-profile for the cluster template with the same parametrization as in the SPT-SZ analysis. We applied MMF3 at the location of the clusters, fixing the size θ c to the value published in the catalogue. The estimated central Compton parameterŷ o is then converted to the integrated flux in a cylinder of radius 0.75 arcmin, Y 0.75 . The flux can be directly compared to the flux given in the published catalogue. Results are shown in Fig. 1. There is a large dispersion between the individual measured fluxes and the published flux (black dots). This is expected because the Planck maps are noisier than the SPT-SZ maps. We averaged the Planck fluxes in SPT-SZ flux bins (red diamonds). The averaged bin flux is generally in good agreement with the SPT-SZ flux. The agreement is very good at large values (Y 0.75 SPT > 2 × 10 −4 arcmin 2 ), and the average Planck flux starts to deviate to lower values with decreasing SPT-SZ flux (Y 0.75 SPT < 2 × 10 −4 arcmin 2 ). We attribute this deviation to the Malmquist bias of the SPT-SZ flux due to the SPT detection threshold. Although Planck is less sensitive than SPT, it is not subject to the selection bias of the SPT sample. We conclude that the SPT cluster flux is consistent with the Planck data.

Planck cluster flux in SPT-SZ data
We used the published Planck catalogue PSZ2 (Planck Collaboration et al. 2016a). We restricted the sample to clusters detected by MMF3 (S /N > 4.5) and used the blind Planck flux and size, i.e., the flux and size given at the maximum of the degeneracy contours provided by the Planck collaboration.We extracted the cluster flux from SPT-SZ maps fixing the position to the Planck blind position and the size to the Planck blind size. The results are given in Fig. 2. The figure shows a large scatter, but no significant bias for Y 500 Planck > 10 −3 arcmin 2 . At lower Planck  fluxes (Y 500 Planck < 10 −3 arcmin 2 ), the SPT-SZ flux deviates towards smaller values. This deviation is likely due to Malmquist bias in the Planck fluxes at the Planck detection threshold. We conclude that the Planck cluster flux is consistent with the SPT-SZ data.
The two data sets being consistent, we now apply the MMF3 algorithm jointly to the Planck and SPT-SZ maps.

The PSZSPT cluster catalogue
We first describe construction of our candidate list using MMF3 in Sect. 6.1. We match our candidates to known clusters in Sect. 6.2. We check for missed SPT and PSZ2 clusters in Sect. 6.3. Finally, we estimate the completeness of our catalogue in Sect. 6.4. The format and fields of the PSZSPT catalogue are given in Appendix E.

Construction of the catalogue
We divide the Planck and SPT-SZ Healpix maps into 52 overlapping tangential maps of 10x10 deg 2 (pixel size = 0.43 arcmin) covering the SPT-SZ footprint, and we run the MMF3 algorithm blindly. The description of the blind MMF3 algorithm is given in Melin et al. (2012);Planck Collaboration et al. (2011, 2014a, 2016a. We briefly recall here its main features and we give the differences with the implementation used for the Planck analyses. The algorithm is run blindly on the individual maps. We fix a detection threshold q thres . We filter each map with a set of 32 logarithmically spaced sizes θ s ranging from 0.8 to 30 arcmin. We look for the maximum in the filtered maps corresponding to our first cluster candidate. We mask it and look for the second maxima. We continue until there are no more remaining maxima above the detection threshold. In doing so, we build a blind catalogue for each tangential map which includes blind positions (corresponding to position of the maxima), blind sizes (corresponding to the sizes maximizing the S/N) and blind fluxes (given by the filter output at the blind positions and for the blind sizes). We proceed similarly for the 52 tangential maps. We then construct a catalogue from the 52 individual catalogues by merging detections with separation less than 2.5 arcmin. We then proceed with a second pass of the algorithm. We divide the Planck and SPT-SZ Healpix maps in tangential maps centered on the first pass detections and run the algorithm again. The second pass allows us to obtain better estimates of the position, size, and flux, and to reject detections with refined S/N lower than q thres .
The Planck and SPT-SZ maps include bright point sources which must be masked to avoid spurious detections. We implement the same methodology for the SPT-SZ and Planck tangential maps. We use a single frequency matched filter for each map and we detect point sources with S /N > 8. For the SPT-SZ data, we mask circular regions of 5 arcmin radius around each point source and reject any SZ detection in a 7.5 arcmin radius. For comparison, Bleem et al. (2020) mask in 4 arcmin radius for S /N > 5 point sources and reject detections within 8 arcmin radius. For the Planck data, we mask in 10 arcmin radius and reject detections in 15 arcmin radius because of the larger beams.
In summary, the differences between this implementation of MMF3 and the implementation used for the official Planck catalogues are: the partial sky coverage (SPT-SZ footprint instead of all-sky), the pixel size of the maps (0.43 arcmin instead of 1.72 arcmin), the orientation of the tangential maps (equatorial pole at north instead of Galactic pole at north), the filter transfer function for the SPT-SZ maps, the merging separation (2.5 arcmin instead of 10 arcmin), the removal of bright point sources (made for SPT-SZ and Planck data on tangential maps instead of all-sky maps for Planck).
We fix the detection threshold q thres to 5 for our joint catalogue. We additionally apply the SPT-SZ boundary mask and the Planck cluster union mask (which keeps the 85% cleanest part of the sky). We thus obtain a catalogue of 419 detections. In Sect. 6.2, we identify our detections with known clusters, and we present the completeness of our catalogue in Sect. 6.4.

Identification of known clusters
We follow the methodology of Tarrío et al. (2019) to identify clusters in our joint catalogue. We first identify clusters in the SPT-SZ catalogue (Bleem et al. 2015b) (Sect. 6.2.1) and in the PSZ2 catalogue (Planck Collaboration et al. 2016a) (Sect. 6.2.2). We then cross match the catalogue with other relevant catalogues in the SPT-SZ footprint (Sect. 6.2.3): the Meta catalogue of Xray Clusters MCXC (Piffaretti et al. 2011), the Meta catalogue of SZ Clusters MCSZ 4 , the ComPRASS catalogue (Tarrío et al. 2019), the Abell catalogue (Abell et al. 1989) and the cluster catalogue from the Blanco Cluster Survey (Bleem et al. 2015a). We finally use SIMBAD and NED (Sect. 6.2.4). We present the unidentified detections in Sect. 6.2.5.

SPT-SZ catalogue
First, we match each of the 419 blind detections to the closest cluster of the SPT-SZ cluster catalogue. We then separate the detections in two sets: the detections matched to a SPT-SZ cluster with an estimated mass M 500 and redshift z, and the detections matched to a SPT-SZ detection without an estimated mass.
We plot the first set in the θ/θ 500 versus θ plane where θ is the distance between the blind candidate and the closest SPT-SZ cluster and θ 500 is the angular radius corresponding to the published SPT-SZ mass M 500 and redshift z. The result is given in Fig. 3, which shows two clouds of detections: the detections which can be matched to an SPT-SZ cluster in the lower left corner and the detections which cannot be matched in the upper right corner. We define a detection as being matched to an SPT-SZ cluster if θ < 2 arcmin, or θ/θ 500 < 1 and θ < 10 arcmin. We label it as rank=1. These detections correspond to the white region. We also define a detection as being not matched to a SPT-SZ cluster if θ > 10 arcmin corresponding to the dark grey regions. We note it as rank=0. We then define the light grey region (θ/θ 500 > 1 and 2 arcmin < θ < 10 arcmin) as the possibly matched clusters (rank=2).
For the second set without an estimated mass, we associate clusters (rank=1) if θ < 2 arcmin and we do not associate clusters (rank=0) if θ > 10 arcmin. The detections with 2 arcmin < θ < 10 arcmin are set as possibly associated (rank=2). The association is shown in Fig. 4. Note that there is no rank=2 detection of this category (light grey area) for the matching with the SPT catalogue.
Finally, we check for detections matched or possibly matched (rank=1 or rank=2) to the same SPT-SZ cluster, and we keep only the closest associated detection, giving priority to rank=1 over rank=2. We degrade the other multiple associations from rank=1 or rank=2 to rank=3. They are marked as crosses in Fig. 3. There are no rank=3 detections in Fig. 4.
As a final test, we estimate the mass for rank=1 associations using the cluster redshift z and a X-ray prior on the Y − M scaling relation (see Planck Collaboration et al. 2014aCollaboration et al. , 2016aTarrío et al. 2019). We plot it against the published SPT-SZ mass after recalibrating it by a factor 0.8 to account for our mass definition, as was done in Tarrío et al. (2019) and as implemented in the MCSZ catalogue. The result is shown in Fig. 5. The agreement between the two masses is good. We discuss further this figure, including outliers, in Appendix D.

PSZ2 catalogue
We apply the same methodology to the PSZ2 cluster catalogue. The matching with PSZ2 clusters with mass M 500 and redshift z is shown in Fig. 6, and the matching with clusters without masses is shown in Fig. 7. Given the larger beam size of Planck we change the limits for association. We define a detection as being matched to a PSZ2 cluster if θ < 5 arcmin, or θ/θ 500 < 1 and θ < 20 arcmin (white region in Fig. 6, rank=1). A detection with θ > 20 arcmin (dark grey region, rank=0) is considered as being not matched, and the detection with θ/θ 500 > 1 and 5 arcmin < θ < 20 arcmin (light grey region, rank=2) is considered as being possibly matched.
The association with PSZ2 clusters without a published mass is shown in Fig. 7 with the same color coding of the regions for  matched, not matched and possibly matched detections. We also discard double matching as we did for SPT-SZ (rank=3).
As for the SPT-SZ matching, we estimate the mass for rank=1 associations and plot them against the published PSZ2 masses in Fig. 8. The agreement is also good. We discuss further this figure, including outliers and the systematic underestimation of the PSZ2 mass, in Appendix D.
Among the 419 joint detections, we found 112 matched to PSZ2 clusters (rank=1) and 1 possibly matched to PSZ2 clusters (rank=2). Finally, 82 detections are matched or possibly matched to a SPT-SZ and a PSZ2 cluster at the same time. At this stage, we thus have 419-292-113+82=96 detections which are not matched or possibly matched to a cluster from the SPT-SZ or the PSZ2 catalogue.

Other catalogues
After the matching with the SPT-SZ and the PSZ2 catalogues, we proceed with the same methodology for the MCSZ Meta cat-   (Table 4 and 5 of Abell et al. 1989), and the Blanco Cosmology Survey (BCS, Bleem et al. 2015a). For the matching procedure, we adopt the same values as for the PSZ2 for all these catalogues (5 and 20 arcmin), except for the SPT clusters in the MCSZ for consistency with Sect. 6.2.1, for which we adopt the SPT-SZ values (2 and 10 arcmin).
Among the 96 detections which are not matched or possibly matched to a SPT-SZ or a PSZ2 cluster, These matched detections are mainly at low (z < 0.1) and intermediate (z ∼ 0.3) redshift, or have no published redshift. Some of them are in common between the catalogues. After this new set of associations, 71 detections among the 96 remain unmatched. Among these 71 detections, three are rank=3 detections (for which we broke a rank=1 and rank=2 association) and the 68 others are not classified.

SIMBAD and NED
We search for counterparts in SIMBAD and NED for the remaining 71 detections which are not matched to any of the clusters in the studied catalogues. We set the search radius to 20 arcmin for the two databases and we look for galaxy cluster type objects. We did not find a cluster in the search radius for 45 detections. We set rank=0 (meaning unidentified) for these 45 detections.
For the other 71-45=26 detections, we found three obvious bright and large clusters (ACO 3667, ACO S 1063 and ACO 3911) close to the three rank=3 detections confirming that these three detections are multiple (therefore false) detections produced by the algorithm. We also found 9 SPT clusters not included in the cluster catalogue provided with Bleem et al. (2015b): 8 are excluded from the official SPT catalogue because they are close to a bright point source (Table 3 of Bleem et al. 2015b), one is in Saro et al. (2015), but not in Bleem et al. (2015b). We set rank=1 for these 9 detections. The remaining 26-3-9=14 detections are not obviously matched to the clusters found in the search radius because the counterparts are at distance greater than 7 arcmin. We thus set rank=0 (unidentified) for these 14 detections.

Unidentified detections
We look for the spatial distribution of the 59 unidentified detections in the SPT footprint. We found no specific pattern which could indicate a problem with the extraction algorithm related to possible systematics in the maps, except in a specific location on the edge of the SPT footprint. This location is displayed in Fig. 9. The figure shows the local variance of the instrumental SPT-SZ noise at 150 GHz as the half map difference ∆HM squared filtered by a 10 arcmin FWHM Gaussian beam G minus the square of the filtered half map difference: The black triangle on the right of the image is outside the SPT footprint. There is a clear separation between the top and bottom of the image with the upper part of the image being less noisy than the bottom part (factor 2.5 between the variances of the two parts). This noise difference is due to different integration times or instrumental sensitivities around this location. The detections are displayed as discs. The black/white are identified/unidentified detections. A cluster of unidentified detections is visible in the bottom part. The MMF algorithm estimates the noise on the full map. It is thus possible that the noise is not correctly estimated in this specific patch due to the inhomogeneity of the SPT-SZ instrumental noise. However, there are four detections identified with known clusters in this patch, two of them being in the top part and the other two in the bottom part. We thus do not flag unidentified detections in this patch.
In the first line of Fig. 10, we summarize the number of PSZSPT detections according to their rank. In the other lines, we provide the number of rank=1 and rank=2 detections associated to external catalogues that we considered in this article. Note that the total number exceeds 348+9=357 (numbers given in the first line) because the external catalogues share some common objects.

Missed SPT and PSZ2 clusters
We now investigate the SPT and PSZ2 clusters in the SPT-SZ footprint with signal-to-noise greater than five which are not in the PSZSPT catalogue. The official SPT catalogue contains 677/409 detections with signal-to-noise ξ > 4.5/5. After the Chown et al. (2018) mask is applied, 379 detections with ξ > 5 remain. We additionally apply the Planck union mask which leaves 376 ξ > 5 detections in the SPT catalogue. We found 292 matches in Sect. 6.2 between the full SPT catalogue (ξ > 4.5) and the PSZSPT catalogue. This reduces to 268 matches with SPT detections at ξ > 5 in the Chown et al. (2018) and Planck union masks. Thus 376-268=108 SPT detections at ξ > 5 are unmatched with PSZSPT detections. Seven of them are in the point source mask built by our extraction algorithm (Sect. 6.1). Among the remaining 101, four have ξ > 7 and 82 have assigned redshift  Other lines: Number of rank=1 and rank=2 detections associated to external catalogues. and mass. We plot the SPT detections having redshift and mass in Fig. 11 as small blue dots. We over-plot the 82 unmatched detections with large black crosses. We add large black circles on the four high ξ > 7 clusters (they all have a redshift).
We apply the same methodology to the PSZ2 detections. 107 PSZ2 detections with S /N > 5 are in the Chown et al. (2018) and PSZ2 union masks. Among the 113 matches found in Sect. 6.2, 91 have S /N > 5. This leaves 107-91=16 PSZ2 detections unmatched. Five of them are in the point source mask built by our extraction algorithm (Sect. 6.1). Among the remaining 11, one have S /N > 7 and six have assigned redshift and mass. We plot the PSZ2 clusters with redshift and mass as large red dots in Fig. 11. We over-plot the six unmatched detections with large black crosses and the cluster with S /N > 7 with a large black circle. Note that we have applied a 0.8 recalibrating factor on the SPT mass as in Fig. 5. When combining SPT-SZ and Planck, the S /N of the detections is expected to be, on average, greater than the S /N on the individual experiments. However, due to estimation errors, there is a scatter around the expected value, which makes some of the clusters, especially those close to the limit, to down-scatter below the PSZSPT detection threshold. Additionally, we have shown in Appendix B that our extracted S /N on SPT-SZ maps is on average 10% lower than the signal-to-noise ratio ξ published by the SPT collaboration. For these reasons, we expected to miss several SPT-SZ clusters close to ξ = 5, and also a small number of higher signal-to-noise clusters.
The majority of the unmatched candidates (indicated by the black crosses) are indeed at the detection limit of the SPT and Planck catalogues. Thus they may have been missed because of noise fluctuations in the filtered maps. There are, however, four SPT detections and one Planck detection (large black circles) with signal-to-noise greater than seven. Three of the SPT clusters have S /N < 5 in the filtered maps after the first pass and are thus not detected by the joint algorithm. The last SPT cluster has S /N ∼ 8.1 in the filtered maps after the first pass. It is thus detected in the first pass of the algorithm but is not included in the catalogue after the second pass because it is located close to the edge of the SPT-SZ footprint and the noise power spectrum is not estimated properly after the cluster re-centering so the detection is rejected. The PSZ2 undetected cluster has S /N ∼ 5.5 after the first pass of the algorithm but it does not pass the threshold after the re-centering of the second pass (S /N ∼ 4.6) and is thus not included in the catalogue.

Completeness
In this section, we adopt the Planck Collaboration et al. semi-analytically the completeness of the joint and individual surveys. We assume that the noise of the maps is Gaussian after filtering with the matched multi-filters. Thus, the completeness can be expressed as a erf function of the cluster size θ 500 , the cluster flux Y 500 , the detection threshold q (set to 5 in this work) and the position on the sky (ra,dec). We express the completeness as a function of redshift z and mass M 500 , adopting the Y 500 − M 500 and θ 500 − M 500 relations from Eq. 7 and Eq. 9 in Planck Collaboration et al. (2014b). We then integrate the result over the sky coverage of SPT-SZ.
The resulting completeness is shown in the left panel of Fig. 12 for the three catalogues: Planck+SPT-SZ, Planck, SPT-SZ. The completeness of the joint catalogue Planck+SPT-SZ is driven by SPT-SZ at redshift z > 0.5 and by Planck at z < 0.1. This is expected because SPT-SZ has less instrumental noise and a better resolution than Planck, leading to better efficiency at detecting high-z clusters. On the other hand, the SPT scanning strategy smoothes the large angular scales, which prevents the detection of very low-z clusters. Planck, as a satellite, is not affected by this effect and can detect the low redshift clusters. Both surveys contribute to the intermediate redshift range 0.1 < z < 0.5.
We expect the unidentified detections to populate mainly this specific range. (1 − b) is the "mass bias factor" which relates the true mass M 500 to the XMM-Newton like mass M 500,X = (1 − b)M 500 . The scaling laws from Eq. 7 and Eq. 9 in Planck Collaboration et al. (2014b) are based on XMM-Newton masses, and we decide to leave this parameter free in this left panel to aid comparison with other works.
From the completeness, we can predict the expected cluster counts from a given mass function. We choose the Tinker et al.  Table 1) on an extended dataset. The predicted redshift distribution is given in the right panel of Fig. 12 for the SPT-SZ footprint.
As expected from the completeness, the overall Planck+SPT-SZ cluster count (thick red line) is dominated by the SPT-SZ dataset, except at very low redshift where Planck provides the information. The predicted total number of clusters is 413/302/111 for Planck+SPT-SZ/SPT-SZ/Planck respectively, in very good agreement with the number of detections given in Sect. 6.1. The union catalogue of the individual Planck and SPT-SZ catalogues is shown as the thin red line for comparison with the joint catalogue. We provide these predicted cluster numbers as a consistency check between the cluster counts of our joint catalogue and the Planck Collaboration et al. (2018) CMB cosmology. Constraining cosmological parameters from this joint catalogue is beyond the scope of this work.

Summary, discussion and future work
We performed for the first time a SZ cluster extraction using space (Planck) and ground-based (SPT) data jointly, and provided the associated PSZSPT catalogue of 419 sources at S /N > 5.
For this purpose, we modified the MMF3 algorithm initially developed for Planck data to make it compatible with ground based data. The main difficulties are the inclusion of the transfer function of the SPT survey, and the handling of the high resolution ground-based and low resolution space data at the same time, which required the use of small (0.43 arcmin) pixels on large (10 × 10 deg 2 ) tangential maps. In the process of building the joint catalogue, we thoroughly characterized the SPT public maps (transfer function, point source and cluster photometry) with respect to the SPT official catalogues (Sect. 4, Appendix A and B). We found a good agreement between quantities extracted with our tools and the official SPT catalogues. However, the signal-to-noise ratio of our SPT extractions is 10% lower than the published values. We attribute this to the poorer than native resolution of the public SPT Healpix maps, together with the possibility that some pre-processing was applied to the raw data before the construction of the public Healpix maps. Our extraction method would thus be more efficient could it be applied on the original SPT maps. We also checked that our new extraction method provides results consistent with Planck publications (Sect. 4, Appendix C). We then showed that the Planck and SPT data provide consistent flux measurements for SPT and Planck clusters respectively (Sect. 5).
We cross-matched the PSZSPT catalogue with other cluster catalogues in the SPT-SZ footprint. We checked for remaining unidentified detections in SIMBAD and NED. 292(113) detections are matched or possibly matched to SPT-SZ(PSZ2) detections respectively with 82 being common to the two catalogues. We identified 25 detections with clusters in catalogues other than SPT-SZ and PSZ2, and 12 additional detections using SIMBAD and NED. Finally, we could not identify counterparts for the remaining 59 detections which need to be validated by future external follow-ups (Sect. 6.2).
We finally estimated the completeness of the PSZSPT catalogue and checked that the extracted counts are consistent with the standard ΛCDM model when adopting the Planck cluster modeling and scaling laws (Sect. 6.4). The PSZSPT catalogue is described in Appendix E and a complete version is available in electronic format.
The gain in number counts from the joint catalogue with respect to the union of the space and ground-based catalogue is moderate as shown in Fig. 12 (difference between the red thin and thick lines). The majority of new detections are expected to be in the redshift range [0.1,0.6] around the location where the Planck and SPT-SZ completenesses cross. The most interesting application of the space and ground based joint cluster analyses with current data sets may thus be astrophysical studies, and in particular cluster profiles, the space(ground-based) data providing the large(small) scale information respectively. We leave this work to a future article.
This first proof of concept of joint cluster extraction with space and ground-based data opens the path to other possible catalogues when new data will be publicly available, for example Planck & ACT  or Planck & SPT-ECS (Bleem et al. 2020). But the approach would be most useful in the case of the longer term ground-based Simons Observatory (Ade et al. 2019) or CMB-S4 (Abazajian et al. 2019) and proposed space mission such as PICO (Hanany et al. 2019) or Backlight (Basu et al. 2019;Delabrouille et al. 2019) which have resolutions matching between space and ground (1 arcmin FWHM at 300 GHz) and cover together a large frequency range from a few tens of GHz to the THz. The space+ground approach will be crucial to disentangle the various emissions in clusters: the different SZ effects and the radio and infrared emission of galaxies hosted by clusters. physics Science Archive Center (HEASARC). HEASARC/LAMBDA is a service of the Astrophysics Science Division at the NASA Goddard Space Flight Center. We also used the HEALPix software (Górski et al. 2005) available at https://healpix.sourceforge.io and the WebPlotDigitizer by Ankit Rohatgi. This research has also made use of the M2C Galaxy Cluster Database, constructed as part of the ERC project M2C (The Most Massive Clusters across cosmic time, ERC-Adv grant No. 340519), the SIMBAD database operated at CDS, Strasbourg, France (Wenger et al. 2000), and the NASA/IPAC Extragalactic Database (NED), which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. J.-B. Melin thanks Monique Arnaud for constructive discussions which helped to improve this article and for suggesting the acronym PSZSPT. He also warmly thanks the high school students Julie Hebert, Aubin Mayer, Hugo Levandowski and Anaëlle Meurant who helped him search the PSZSPT locations in the SIMBAD and NED databases. A portion of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

Appendix A: Characterization of the SPT-SZ filter transfer function
The SPT-SZ filter transfer function is provided with the public data for each SPT frequency. We tested it by comparing point source fluxes extracted from the public data (using the provided transfer function) and the fluxes published for the same sources by the SPT collaboration. In practice, we adopted the positions of the point sources in the 2013 catalogue (Mocanu et al. 2013) and extracted their flux using a single frequency matched filter applied to the public data. We use the SPT-SZ frequency responses given in Fig. 10 of Chown et al. (2018) (long-dashed lines). Results are presented in Figure A.1 for the three SPT channels.
We restricted the extraction to sources with published SPT flux above 1 mJy. The left-hand column shows our extracted flux as a function of published SPT flux for the 95 (top figure), 150 (middle) and 220 (bottom) GHz channels. There is global agreement between the two. The right-hand column shows the ratio of the two fluxes versus the SPT flux. Blue diamonds are weighted averages of the individual measurements (red dots). We see that in fact our fluxes are systematically over-estimated, in particular for flux S above 50 mJy (indicated by the vertical dotted blue line) for the three SPT frequencies. The overestimation is about 5% with respect to the published values. For fluxes below 50 mJy, there is no significant over-estimation in the 95 GHz channel, but there remains an over-estimation for the 150 and 220 GHz channels, although less significant than for point sources with fluxes above 50 mJy.
To investigate the origin of this effect, we stacked the SPT-SZ maps at the locations of the bright (S>50 mJy) and faint (S<50 mJy) point sources separately. We then compared the two stacks to the beam convolved by the filter transfer function. Figure A.2 presents the results for the 150 GHz sources. The lefthand column gives the two stacks (S<50 mJy top, S>50 mJy bottom). The middle column shows the beam convolved by the filter transfer function (duplicated top and bottom). The righthand column shows the difference of the first two columns. The stack of the faint sources displays the same pattern as the beam convolved with the filter transfer function, but the stack of the bright sources does not. This result confirms that the beam convolved by the filter transfer function does not correctly model the shape of the bright (S>50 mJy) point sources in the data. A similar analysis of the 95 GHz and 220 GHz channels leads to the same conclusion, with different patterns in the stacks of point sources with flux above and below 50 mJy: The stacks of sources with fluxes below 50 mJy show a pattern identical to the beams convolved by the filter transfert functions, while the stacks of sources with fluxes above 50 mJy do not. The simulations created to compute the SPT filter transfer functions do not contain bright point sources (see Sect. 4.1.4 of Chown et al. 2018). We suspect this is the reason for the mis-estimation of bright point source fluxes.
The fact that bright sources are not well modeled by the beam convolved by the filter transfer function is the most probable explanation for the over-estimation of the SZ flux of bright clusters (Y 0.75 SPT > 2×10 −4 arcmin 2 ) in the SPT-SZ data with respect to the published SPT values. This issue is described in Appendix B and illustrated in Fig. B.3.

Appendix B: SPT-SZ photometry
We re-extracted the flux and size of the SPT-SZ clusters, fixing the position to the coordinates provided in the SPT cluster cata-logue (Bleem et al. 2015b). The goal is to check the consistency between our photometry (i.e., flux and size estimation) and the photometry from the SPT collaboration. We adopted the cluster modeling of the SPT collaboration: β profile of size θ c ranging from 0.25 to 3 arcmin in steps of 0.25 and β = 1 fixed. We allowed the filter size to vary in the aforementioned range and, for each cluster, we kept the size that maximizes the signal-to-noise. We then extracted the cluster flux for this specific size. Figure B.1 compares our extracted signal-to-noise (maximum across filter scales) to the signal-to-noise published by the SPT collaboration, ξ. The left-hand panel shows that our signalto-noise ratio is in global agreement with the published SPT signal-to-noise, although systematically lower. The right-hand panel shows the ratio of the two signal-to-noise values. Our S/N is on average 0.9 times ξ for ξ > 5. We suspect this factor comes from the lower resolution of the public maps (1.75 arcmin for the three SPT channels) with respect to the native SPT resolution (1.6, 1.1, 1.0 arcmin for 95, 150 and 220 GHz respectively), and possibly to the preprocessing applied by the SPT collaboration to the data when constructing the public Healpix maps. If our method were applied to the original SPT data set at native resolution, we expect the ratio of the S/N values to attain unity on average, and consequently the joint extraction to be more efficient. Figure B.2 compares our recovered blind size to the size published by the SPT collaboration. Each histogram corresponds to clusters with the same size θ c determined by the SPT collaboration. Our recovered sizes (red histograms) show no significant deviation from the size published by the SPT collaboration (vertical black line). The thick dashed vertical blue line shows the median of our recovered sizes, which is in good agreement with the SPT size. Figure B.3 compares our blind SZ flux to the flux published by the SPT collaboration. The left panel shows that there is a good agreement between the two flux values at low flux (Y 0.75 SPT < 2 × 10 −4 arcmin 2 ), but that our blind flux is systematically over-estimated at high flux (Y 0.75 SPT > 2 × 10 −4 arcmin 2 ). The right panel shows the ratio of the two flux values: the over-estimation is about 10% for Y 0.75 SPT > 2 × 10 −4 arcmin 2 . Since the cluster size is correctly estimated, as shown in Figure B.2, we attribute this over-estimation to inadequate modeling of bright sources by the filter transfer function provided by the SPT collaboration, as discussed in Appendix A.

Appendix C: Planck photometry
We re-extracted the flux and size of Planck clusters, fixing the position to the coordinates provided in the PSZ2 catalogue (Planck Collaboration et al. 2016a) in order to check the consistency between our photometry (i.e., flux and size estimation) and the photometry published by the Planck collaboration. We restricted the PSZ2 cluster catalogue to MMF3-only clusters, since our extraction method is derived from it, and we focus only on the clusters in the SPT footprint. The differences are not expected to be negligible, because we work with upgraded Planck maps (N side = 8192) instead of native Planck maps (N side = 2048) and we changed the coordinate system from Galactic to equatorial to match the SPT-SZ public data. This changes the estimation of the noise power spectrum, P(k). In addition, we did not use the refined point source masking procedure used by the Planck collaboration (Sect. 3.1 of Planck Collaboration et al. 2016a), but detected the point sources above S /N > 8 with single frequency matched filters in individual channel maps There is overall agreement between our recovered fluxes and the values published by the SPT collaboration. Right column: Zoom-in on the ratio between the two flux measurements as a function of SPT flux. Blue diamonds are weighted averages. Thick bars display 68% statistical errors, and thin bars show 68% errors obtained by bootstrap. Despite the global agreement in the log-log plane shown in the left column, the ratio is significantly greater than unity, in particular at large flux (S>50 mJy) for the three SPT frequencies. We indicate this 50 mJy limit by the vertical blue dotted lines in the three panels. and masked them with a ten-arcmin radius disc, which is simpler and computationally faster.  In particular, the stack does not show the negative tails before and after the central maximum in right ascension, which can be seen in black in the middle image. This difference in the patterns can be seen in the difference image as the horizontal trail.
Fig. C.3 shows results for the flux measurements. As for the sizes, the global agreement is good except for some specific clusters. They correspond to clusters that we marked with the red crosses in Fig. C.2. Due to the low S/N of some detections, the size is poorly determined, which directly translates into a bad recovery of the integrated flux.  (Bleem et al. 2015b). Despite overall agreement, our S/N is systematically lower than the signal-to-noise published by the SPT collaboration. Right: Ratio of the two signal-to-noise values as a function of the signal-to-noise published by the SPT collaboration. Our S/N is on average 0.9 times ξ for ξ > 5. Red dots are individual clusters. Blue diamonds are weighted averages. Thick error bars display 68% statistical errors, and thin error bars show 68% errors obtained by bootstrap.
In summary, the outliers may originate from flux contamination due to close-by point sources and/or to miss-match of the masses already present in the published SPT-SZ and PSZ2 catalogues. This mass miss-match in the original catalogues can also be due to point source contamination or specific issues from the datasets (e.g. flux estimation of nearby clusters such as SPT-CLJ2313-4243 and SPT-CLJ0431-6126 in the SPT data may be difficult).
Appendix D.2: Joint versus published mass for PSZ2 clusters Fig. 8 shows a small underestimation of the joint mass with respect to the published PSZ2 mass. We investigate if this trend is visible for detections matching PSZ2-only or for detections matching both SPT-SZ and PSZ2 clusters. We mark in Fig. D.2 detections matching both SPT-SZ and PSZ2 clusters with red crosses: they show the same trend as detections matching PSZ2only clusters. We also mark the SPT-SZ and PSZ2 clusters in This underestimation of the joint mass with respect to published mass is very likely due to the underestimation of the SPT flux with respect to Planck flux when using the XMM-Newton prior to determine the filter size instead of the blind size. The joint mass is determined using the XMM-Newton prior. When using this prior to estimated PSZ2 cluster masses in the SPT-SZ data, the SPT flux are systematically smaller than the Planck flux as shown in Fig. D.4. The consequence of a smaller SPT flux is a smaller joint flux so a smaller mass.
In all the figures of Appendix D, the published SPT masses has been recalibrated by 0.8 to account for our mass definition.

Appendix E: Description of the PSZSPT catalogue
The PSZSPT catalogue contains 419 detections. For each detection, we provide the following fields, partially shown in Table E.1. A complete version of the catalogue is provided in electronic format.
-NAME: Name of the candidate, PSZSPT Jxxxx+yyyy -RAJ2000: Right ascension (J2000) in degrees -DEJ2000: Declination (J2000) in degrees -GLON: Galactic longitude in degrees -GLAT: Galactic latitude in degrees -SNR: Signal-to-noise ratio obtained with the best filter size -RANK: Rank of the candidate (0=unidentified; 1=identified; 2=possibly identified; 3=multiple detection) -Z: Redshift of the candidate -Z_REF: Origin of the redshift -M500: Estimated cluster mass in solar masses -M500_INF: Lower bound of 68% confidence interval on the estimated cluster mass in solar masses -M500_SUP: Upper bound of 68% confidence interval on the estimated cluster mass in solar masses -SPT: Name of the SPT (Bleem et al. 2015b) (Tarrío et al. 2019) cluster matched to the candidate -ABELL: Name of the Abell (Abell et al. 1989) cluster matched to the candidate -BCS: Name of the BCS (Bleem et al. 2015a) cluster matched to the candidate -SIMBAD: Name of the SIMBAD counterpart found in a 20 arcmin radius disc around the candidate -NED: Name of the NED counterpart found in a 20 arcmin radius disc around the candidate -NOTES: Notes on specific candidates   (Bleem et al. 2015b). There is good agreement at low flux, but our flux is systematically over-estimated at high values (Y 0.75 SPT > 2 × 10 −4 arcmin 2 ). Right: Ratio of the two flux values as a function of the flux published by the SPT collaboration. Our flux is in good agreement for Y 0.75 SPT < 2 × 10 −4 arcmin 2 , but is on average 1.1 times Y 0.75 SPT for Y 0.75 SPT > 2 × 10 −4 arcmin 2 . Red dots are individual clusters. Blue diamonds are weighted averages. Thick error bars display 68% statistical errors, and thin error bars show 68% errors obtained by bootstrap. ). There is overall agreement, but also a large scatter between the two measurements due to upgraded pixel size, change of coordinate system and change in the point-source masking procedure. Right: Ratio of the two signal-to-noise values as a function of the signal-to-noise published by the Planck collaboration. Red dots are individual clusters. Blue diamonds are weighted averages. Thick error bars display 68% statistical errors, and thin error bars show 68% errors obtained by bootstrap. There is overall agreement, but some clusters show deviations larger than a factor of two. They are marked with a red cross. The dotted black line delineates the deviation by a factor of two. Right: Ratio of the two size values as a function of the signal-to-noise ratio published by the Planck collaboration. The deviating clusters are mainly located at the lower S/N, for which the blind size estimation is uncertain. There is overall agreement, but some clusters show deviations from the equality line. They correspond to clusters having blind sizes deviating by more than a factor of two from the values published by the Planck collaboration and are marked as red crosses (see also Fig. C.2). Right: Ratio of the two flux values as a function of the flux published by the Planck collaboration. The ratio is consistent with unity. Blue diamonds are weighted averages. Thick error bars display 68% statistical errors, and thin error bars show 68% errors obtained by bootstrap.   We also marked three outliers with a blue circle and upward and downward triangles.  This is the same figure as Fig. 2 except that we used the XMM-Newton prior to fix the filter size instead of the blind PSZ2 size, both for the Planck fluxes (x-axis) and SPT fluxes (y-axis).