Compact Source catalogues
Contents
Planck Catalogue of Compact Sources[edit]
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps.
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between 13 August 2009 and 26 November 2010, as described in Planck-2013-XXVIII[1]; it consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between 13 August 2009 and 3 August 2013, as described in Planck-2015-A26[2]; it consists of fifteen lists of sources, one list per channel at 30, 44 and 70 GHz, and two lists per channel at 100, 143, 217, 353, 545 and 857 GHz.
The maps used to produce these catalogues are the 2015 full mission frequency maps (LFI_SkyMap_0??_1024_R2.01_full.fits and HFI_SkyMap_???_2048_R2.00_full.fits).
The are three main differences between the PCCS and the PCCS2:
- the amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data);
- the inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities;
- the division of the catalogues into two sub-catalogues between 100 and 857 GHz, the PCCS2 and the PCCS2E, based on the location of the sources in the sky and on our ability to validate them.
Both the 2013 PCCS and the 2015 PCCS2 can be downloaded from the Planck Legacy Archive.
Detection procedure[edit]
The "Mexican-Hat Wavelet 2" (MHW2) [3][4] is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (called IFCAMEX and HFI-MHW), the results are compatible, at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency matrix multi-filter (MTXF)[5] and Bayesian PowellSnakes (PwS)[6] approaches. Both of these have been used in PCCS and PCCS2 for validation of the results obtained by the MHW2 in total intensity.
In addition, two maximum likelihood methods have been used to perform the analysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density there. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the "filter-fusion" technique [7] and has been applied to WMAP maps [8]. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source Catalogue (Planck-Early-VII[9]). In practice, both of them are methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each.
The detection of the compact sources is done locally on small flat-sky patches to improve the efficiency of the process. The reason for this is that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimized to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centred at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into account the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large-scale diffuse emission and the small-scale noise fluctuation.
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4.
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone.
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag was added to the catalogues for this purpose.
In this version of the Planck catalogue of compact sources, for the 100 to 857-GHz channels, we split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources.
For the lower frequencies, between 30 and 70 GHz, we still use an S/N threshold of 4. Moreover, as will be explained below, we use external catalogues and a multi-frequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic plane and cirrus masks.
Photometry[edit]
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples in total intensity. These additional flux density estimations are based on aperture photometry, PSF fitting, and Gaussian fitting (see Planck-2013-XXVIII[1] for a detailed description of these additional photometry determinations). The native flux density estimation is the only one that is obtained directly from the projected filtered maps, while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Sect. 7.4 of the LFI DPC paper (Planck-2015-A02[10]) and Sect. 3.2 of the HFI DPC paper (Planck-2013-IX[11], with updated discussion in Planck-2015-A07[12]), and can be applied by the user. In polarization we have used two methods to measure the flux densities in the Stokes Q and U maps. One is a maximum likelihood filtering method and the other is aperture photometry.
Validation process[edit]
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be performed with a large number of existing catalogues, whereas the validation of thermal sources is mostly carried out with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.
Internal validation[edit]
The catalogues have been validated through an internal Monte Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry, and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N), and location; while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte Carlo quality assessments by injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 GHz and above, maps from the Full Focal Plane 8 simulations have been used.
External validation[edit]
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy, and flux density accuracy using external data sets, particularly large-area high-frequency radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometry determinations, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, and one additional excercise has been performed. Simultaneous observations of a sample of 61 sources was carried out in the Very Large Array, the Australia Compact Array, and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level.
At higher frequencies, surveys as those with the South Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by Galactic cirrus at high frequencies.
Cautionary notes[edit]
We list here some additional information and warnings for users of the PCCS.
- Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns (Planck-2013-II[13]Planck-2013-VI[14]). Follow-up observations of these sources might show significant differences in flux density compared to the values in the released data products. Although the maps used for the PCCS are based on the sky being covered 2.6 times, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.
- Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see Planck-2013-XIII[15]). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but with a different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.
- Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.
- Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX, and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, (especially in regions of high non-Gaussian background emission), but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds. We have noticed that at the position of some of the brightest sources in polarization there is a small spurious signal related to the complex beams in polarization. This signal can have a small impact on the measurements of the flux densities in Q and/or U. In particular, this spurious signal can affect the polarization position angle in those objects where most of the flux density of the source happens to be in one of the Q or U maps (like in the Crab Nebula). In Planck-2015-A26[2] we discuss an extensive analysis of the Crab Nebula, exploring different ways to remove this effect, but the polarization angles of the other sources in the catalogue have to be used with caution.
- Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in Planck-2013-II[13], Planck-2015-A02[10], Planck-2013-VI[14], andPlanck-2015-A07[12].
- Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium (ISM) features or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters that could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20°, we can use the Revised IRAS-FSC Redshift Catalogue (RIFSCz [16]) to provide a guide to the likely nature of sources. We cross-match the PCCS2 857-GHz catalogue and the PCCS2E 857-GHz catalogue with IRAS sources in the RIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857-GHz catalogue 3094 have plausible IRAS counterparts, while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy sr−1, while the non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy sr−1 and a second peak at about 2.6 MJy sr−1. Both distributions have a long tail, but the non-IRAS-identified tail is much longer. On this basis, sources with SKY BRIGHTNESS > 4 MJy sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8, but many non- matched sources do; these should be treated with caution. The PCCS2E 857-GHz catalogue contains 10 470 sources with |b| > 20°, of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy sr−1, but the non-matched sources have brightnesses extending to > 55 MJy sr−1. Similarly, hardly any of the IRAS-matched sources have CIRRUS N > 8, but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, either inside the filament mask (WHICH ZONE=1), in the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857-GHz sources that do not match an IRAS source and that lie in the region |b| > 20°, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2, and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20°, where 2.47 % is in the filament mask, 23.15 % in the Galactic region, and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20°, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extragalactic sources that are extended at Planck spatial resolution will also meet this criterion.
Planck Catalogue of Sunyaev-Zeldovich Sources[edit]
The Planck Catalogue of Sunyaev-Zeldovich Sources (PSZ) is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in Planck-2013-XXIX[17] and Planck-2015-A27[18]. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (S/N ≥ 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from [19], in the detection approach.
- MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.
- PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.
Planck Catalogue of Galactic Cold Clumps[edit]
The Planck Catalogue of Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in Planck-2015-A28[20]. The sources are extracted with the CoCoCoDeT algorithm (Montier, 2010), using Planck-HFI 857-, 545-, and 353-GHz maps and the 3-THz IRIS map (Miville 2005), an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.
The CoCoCoDeT detection algorithm uses the 3-THz map as a spatial template of a "warm" background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857-, 545-, and 353-GHz maps of the cold residual component map over the full sky. A point source detection algorithm is then applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin from other detections.
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:
- FLUX_QUALITY=1, sources with flux density estimates at S/N > 1 in all bands ;
- FLUX_QUALITY=2, sources with flux density estimates at S/N > 1 only in 857-, 545-, and 353-GHz Planck bands, considered as very cold source candidates ;
- FLUX_QUALITY=3, sources without any reliable flux density estimates, listed as poor candidates.
We also set a flag for the blending between sources, which can be used to quantify the reliability of the aperture photometry processing.
To estimate possible contamination by extragalactic sources we: (1) cross-correlated the positions with catalogues of extragalactic sources; (2) rejected detections with SED (in colour-colour plots) consistent with radio sources; and (3) rejected detections with clear association with extragalactic sources visible in Digitized Sky Survey images. Compared to the original catalogue, these only resulted in a small number of rejections.
Distance estimates, combining seven different methods, have been obtained for 5574 sources, with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for: infrared dark clouds (IRDCs); optical and near-infrared extinction using SDSS and 2MASS data, respectively; association with molecular clouds with known distances; and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.
The derived physical properties of the PGCC sources are: temperature; column density; physical size; mass; density; and luminosity. PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass, and density) covering a large varety of objects, from dense cold cores to large molecular clouds.
The validation of this catalogue has been performed with a Monte Carlo quality assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2 arcmin and 0.8 arcmin for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1σ. This kind of analysis is also very powerful for characterizing the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detections has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.
We computed the cross-correlation between the PGCC catalogue and the other internal Planck catalogues, i.e., PCCS2, PCCS2E, PSZ, and PHz. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A smaller number of sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting the dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), which require further analysis to elucidate.
The PGCC catalogue also contains 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies that are so close that we can identify individual clumps in them.
References[edit]
- ↑ 1.01.1 Planck 2013 results. XXVIII. The Planck Catalogue of Compact Sources, Planck Collaboration, 2014, A&A, 571, A28.
- ↑ 2.02.1 Planck 2015 results. XXVI. The second Planck catalogue of compact sources, Planck Collaboration, 2016, A&A, 594, A26.
- ↑ The Mexican hat wavelet family: application to point-source detection in cosmic microwave background maps, J. González-Nuevo, F. L. Argüeso, M. López-Caniego, MNRAS, 369, 1603-1610, (2009).
- ↑ Comparison of filters for the detection of point sources in Planck simulations, M. López-Caniego,D. Herranz, J. González-Nuevo, J. L. Sanz, R. B. Barreiro, P. Vielva, F. Argüeso, L. Toffolatti, MNRAS, 370, 2047-2063, (2006).
- ↑ A novel multifrequency technique for the detection of point sources in cosmic microwave background maps, D. Herranz, M. López-Caniego, J. L. Sanz, J. González-Nuevo, MNRAS, 394, 510-520, (2009).
- ↑ A fast Bayesian approach to discrete object detection in astronomical data sets - PowellSnakes I, P. Carvalho, G. Rocha, M. P. Hobson, MNRAS, 393, 681-702, (2009).
- ↑ Detection/estimation of the modulus of a vector. Application to point-source detection in polarization data, F. Argüeso, J. L. Sanz, D. Herranz, M. López-Caniego, J. González-Nuevo, MNRAS, 395, 649, (2009).
- ↑ Polarization of the WMAP Point Sources, M. López-Caniego, M. Massardi, J. González-Nuevo, L. Lanz, D: Herranz, G. De Zotti, J. L. Sanz, F. Argüeso, ApJ, 705, 868, (2009).
- ↑ Planck early results. VII. The Early Release Compact Source Catalogue, Planck Collaboration VII, A&A, 536, A7, (2011).
- ↑ 10.010.1 Planck 2015 results. II. LFI processing, Planck Collaboration, 2016, A&A, 594, A2.
- ↑ Planck 2013 results. IX. HFI spectral response, Planck Collaboration, 2014, A&A, 571, A9.
- ↑ 12.012.1 Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beam processing, Planck Collaboration, 2016, A&A, 594, A7.
- ↑ 13.013.1 Planck 2013 results. II. Low Frequency Instrument data processing, Planck Collaboration, 2014, A&A, 571, A2.
- ↑ 14.014.1 Planck 2013 results. VI. High Frequency Instrument Data Processing, Planck Collaboration, 2014, A&A, 571, A6.
- ↑ Planck 2013 results. XIII. Galactic CO emission, Planck Collaboration, 2014, A&A, 571, A13.
- ↑ The Revised IRAS-FSC Redshift Catalogue (RIFSCz), L. Wang, M. Rowan-Robinson, P. Norberg, S. Heinis, J. Han, MNRAS, 442, 2739, (2014).
- ↑ Planck 2013 results. XXIX. The Planck Catalogue of Sunyaev-Zeldovich sources, Planck Collaboration, 2014, A&A, 571, A29.
- ↑ Planck 2015 results. XXVII. The second Planck catalogue of Sunyaev-Zeldovich sources, Planck Collaboration, 2016, A&A, 594, A27.
- ↑ The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the Y_SZ - M_500 relation, M. Arnaud, G. W. Pratt, R. Piffaretti, H. Böhringer, J. H. Croston, E. Pointecouteau, ApJ, 517, A92, (2010).
- ↑ Planck 2015 results. XXVIII. The Planck catalogue of Galactic cold clumps, Planck Collaboration, 2016, A&A, 594, A28.
(Planck) Low Frequency Instrument
(Planck) High Frequency Instrument
Data Processing Center
Early Release Compact Source Catalog
Full-Width-at-Half-Maximum
Sunyaev-Zel'dovich