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Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by SZ effect

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Liang Cao (1), Yao-Quan Chu (1) & Li-Zhi Fang (2) ((1)Center for Astrophysics, Univ. of Sci. & Tech. of China, (2) Dept. of Physics, Univ. of Arizona)

Astrophysics · Submitted 3 Mar 2006 · 30 references

Pith's verdict: The f^2-vs-f^4 cross/auto argument is the real contribution; the 4th-order detection itself needs a percentile before I'd trust it.

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arXiv IDastro-ph/0603099 (version 2)
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Citation(2) Dept. of Physics, Liang Cao (1), Univ. of Arizona), Univ. of Sci. & Tech. of China, Yao-Quan Chu (1) & Li-Zhi Fang (2) ((1)Center for Astrophysics. "Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by SZ effect." arXiv:astro-ph/0603099 (2006). https://pith.science/paper/KNIT4EPY
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The paper

The paper claims

The non-Gaussian clustering of 2MASS galaxies is imprinted on the WMAP temperature maps through the Sunyaev–Zel'dovich effect, and this imprint shows up in a fourth-order wavelet cross-correlation even though the WMAP maps alone look…

The reading

The paper sets out to resolve an apparent contradiction: earlier analyses found a Sunyaev–Zel'dovich (SZ) signal by cross-correlating CMB maps with galaxy catalogs, yet the CMB maps themselves show no significant non-Gaussianity. The authors argue that both results are compatible because the SZ signal of the 2MASS galaxies is non-Gaussian but too weak relative to the primary CMB to appear in auto-correlations. They detect it with a fourth-order cross-correlation between wavelet coefficients of the WMAP temperature maps and the densest 2MASS galaxy cells, finding a signal consistent with mock maps built from $\Delta T_{\rm sz}\propto \rho_g^{1.5}$. The mechanism is a factor $f^2$: the SZ-induced non-Gaussian term enters the cross-correlation at order $f^2$ but the auto-correlation only at order $f^4$, where $f\simeq 0.1$ is the ratio of SZ power to CMB fluctuation power on the cluster scale. If correct, the result makes the ratio of auto- to cross-correlations a scale-dependent probe of SZ power.

What carries the argument

The machinery is the discrete wavelet transform (DWT) applied to both the WMAP temperature field and the 2MASS galaxy density field. Wavelet coefficients $\tilde{\epsilon}^T_{j,l}$ and $\tilde{\epsilon}^g_{j,l}$ localize each field in cells of well-defined position and angular scale, allowing cluster-sized cells ($j=8$, $\theta\simeq 0.5^\circ$) to be compared without free linking parameters. The load-bearing identity is the hierarchy of normalized fourth-order correlators: the cross-correlation $C^{2,2}_{j}(0)_{\rm cross}=\langle (\tilde{\epsilon}^T_{j,l})^2(\tilde{\epsilon}^g_{j,l})^2\rangle/(\langle(\tilde{\epsilon}^T_{j,l})^2\rangle\langle(\tilde{\epsilon}^g_{j,l})^2\rangle)$ carries an SZ non-Gaussian term of order $f^2$, while the auto-correlation $C^{2,2}_{j}(0)_{\rm cmb}$ carries the analogous term only at order $f^4$, where $f$ is the ratio of SZ power to CMB fluctuation power. This $f^2$-versus-$f^4$ separation is why the cross-correlation detector succeeds where the auto-correlation detector fails. Mock maps constructed as $\Delta T_{\rm sz}=-f\,\langle(\tilde{\epsilon}^T_{j,l})^2\rangle^{1/2}\langle(\tilde{\epsilon}^{g^\alpha}_{j,l})^2\rangle^{-1/2}\rho_g^\alpha$ with $\alpha\simeq 1.5$ reproduce the observed cross-correlation and calibrate $f\simeq 0.1$.

Extended reading notes

Core claim

The central discovery is that the non-Gaussianity of the 2MASS galaxy field is present in the WMAP temperature maps via the thermal SZ effect, and it is visible only when the CMB field is cross-correlated with the galaxy field. On the cluster scale, $j=8$ ($\simeq 0.5^\circ$), the normalized fourth-order cross-correlation of wavelet coefficients, $C^{2,2}_{j}(|l-l'|)_{\rm cross}$, is elevated above the Gaussian expectation of about $1.03$ at zero lag, matching mock maps in which the SZ decrement is $\Delta T_{\rm sz}\propto \rho_g^{\alpha}$ with $\alpha\simeq 1.5$ and power ratio $f\simeq 0.1$. The same fourth-order statistic applied to WMAP alone shows no signal: the SZ non-Gaussian term is suppressed in the auto-correlation by a factor $f^2$ relative to the cross-correlation, so with $f^2\sim 10^{-2}$ it falls below detectability. The paper therefore claims to have found the non-Gaussian imprint of galaxy clusters on the CMB and to have explained why previous searches of the WMAP maps by themselves came up empty.

Load-bearing premise

The entire calculation rests on modeling the SZ signal of a 2MASS cluster as $\Delta T_{\rm sz}\propto \rho_g^{\alpha}$ with $\alpha\simeq 1.5$, and on setting that signal to zero outside the selected dense galaxy cells; if the hot gas is more extended or differently distributed than the galaxies, the inferred SZ power $f$ and the claimed non-Gaussian cross-correlation could be misattributed.

Editorial extensions

If this is right

  • The non-detection of non-Gaussianity in WMAP alone is not evidence against SZ contamination; high-order auto-correlations are expected to look Gaussian even when the SZ signal is present.
  • The ratio $C^{2,2}_{j}(0)_{\rm cmb}/C^{2,2}_{j}(0)_{\rm cross}$ at a given scale estimates $f^2$, the squared ratio of SZ power to CMB fluctuation power, giving a scale-by-scale probe of SZ power.
  • The 500 densest 2MASS wavelet clusters contaminate roughly 0.4% to 1% of the WMAP sky at the level of about $-15\pm 10\,\mu$K, corresponding to a Compton $y\simeq (3.7\pm 2.4)\times 10^{-6}$.
  • With higher-resolution CMB maps, the same cross-correlation detector should reveal whether the SZ-induced non-Gaussianity grows stronger or changes shape on smaller angular scales.
  • The DWT-based cluster identification makes the CMB–galaxy comparison parameter-free, since the cluster cells, scales, and shapes are fixed by the wavelet basis rather than by a linking length.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The suppression hierarchy likely generalizes to any secondary CMB component that is uncorrelated with the primary CMB: cross-correlating higher-order statistics with a tracer can expose it even when its auto-correlation is buried under cosmic variance.
  • Because the mock sets the SZ signal to zero outside the selected cells, the inferred $f\simeq 0.1$ is probably a lower bound; the signal seen one cell away hints at a broader gas distribution, which would raise the true SZ power.
  • Extending the same wavelet cross-correlation to galaxies split by redshift, or to X-ray selected clusters, would test where along the line of sight the SZ signal originates and whether the $f^2$ ratio is stable across scales.
Original abstract

We study the SZ-effect-induced non-Gaussianity in the cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features as the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalog we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the 4^{th} order cross correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the 4^{th} order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high order auto-correlation of the WMAP. This is because the SZ signals in the auto-correlations of the WMAP data generally is weaker than the WMAP-2MASS cross correlations by a factor f^2, which is the ratio between the powers of SZ effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high order auto-correlations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of SZ effect on various scales.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,424 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.20 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.61 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the SZ-effect-induced non-Gaussianity in the cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features as the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalog we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the 4^{th} order cross correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the 4^{th} order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high order auto-correlation of the WMAP. This is because the SZ signals in the auto-correlations of the WMAP data generally is weaker than the WMAP-2MASS cross correlations by a factor f^2, which is the ratio between the powers of SZ effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high order auto-correlations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of SZ effect on various scales.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the SZ-effect-induced non-Gaussianity in the cosmic microwave background (CMB) fluctuation maps. contribution 0.94 0.89 0.06 asserted 0.51
s1 If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features as the galaxy and cluster fields. background 0.94 0.08 0.07 hedged possibility 0.52
s2 Using the WMAP data and 2MASS galaxy catalog we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. result 0.81 0.95 0.64 asserted 1.00
s3 The signature of non-Gaussianity can be seen with the 4^{th} order cross correlation between the wavelet variables of the WMAP maps and 2MASS clusters. result 0.79 0.89 0.23 asserted 0.95
s4 The intensity of the 4^{th} order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. result 0.97 0.95 0.36 hedged possibility 0.60
s5 We also show that this non-Gaussianity can not be seen by the high order auto-correlation of the WMAP. result 1.00 0.93 0.12 asserted 1.00
s6 This is because the SZ signals in the auto-correlations of the WMAP data generally is weaker than the WMAP-2MASS cross correlations by a factor f^2, which is the ratio between the powers of SZ effect map and the CMB fluctuations on the scale considered. interpretation 0.97 0.59 0.08 asserted 0.99
s7 Therefore, the ratio of high order auto-correlations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of SZ effect on various scales. interpretation 0.85 0.43 0.57 asserted 0.68

What kind of paper the classifier reports this is: empirical study 0.94 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Cross correlation hT(|l − l ′ |) [eq.(8)] between the WMAP maps of W (top) and Q (bottom) bands and top 500 2MASS DWT clusters on scale j = 8. The angular scale of |l − l ′ | is |l − l ′ |123.88/2 8 degree. method if the mean size of the friend-of-friend identified clusters is the same as that of DWT clusters. The scale of DWT variables is well defined, and therefore, it is parameter-free. On the other hand, the friend-of-friend algorithm needs the so-called link parameter. These parameters may introduce uncertainty in the correlation analysis. Moreover, The clusters iden￾tifie
Figure 2. Cross correlation hT(|l − l ′ |)i [eq.(8)] between mock sample A and top 500 2MASS DWT clusters on scale j = 8. The angular scale of |l − l ′ | is |l − l ′ |123.88/2 8 degree. from 104 to 106−7 K. Nevertheless, the relation between the mean temperature and mass density of the gas can be approximated as a polytropic relation Te ∝ ρ α−1 g , where α is about 1.5 (He et al. 2004). Thus, we have ∆Tsz(x) ∝ ρ α g (x). Therefore, to mimic the thermal SZ effect, it would be reasonable to assume ∆Tsz(x) = −f h(˜ǫ T j,l ) 2 i 1/2 h(˜ǫ gα j,l ) 2i 1/2 ρ α g (x), (10) where ǫ˜ T j,l and ǫ˜ gα…
Figure 3. Cross correlation hT(|l − l ′ |)i [eq.(8)] between mock sample B and top 500 2MASS DWT clusters on scale j = 8. The angular scale of |l − l ′ | is |l − l ′ |123.88/2 8 degree. also in their nearby cells, we have sample of Mock B. The cross correlation between mock sample B and 2MASS DWT clusters are shown in Fig.3, which does show a tail of ∆T (|l −l ′ |). We see that the sample of f = 0.1 is also basically the same as observation. The term ∆Tsecond(x) of eq.(9) comes from the ISW and mi￾crowave point sources. The ISW effect is mainly from potential with linear evolution. The ISW…
Figure 5. C 2,2 j (|l − l ′ |), vs |l − l ′ | at j = (j, j) = (8, 8) for 2MASS galaxy samples of north (solid) and south (dashed). h(˜ǫ Tcmb j,l ) 2 (˜ǫ g j,l ′ ) 2 i h(˜ǫ T j,l ) 2ih(˜ǫ g j,l ′ ) 2i + f 2 h(˜ǫ gα j,l ) 2 (˜ǫ g j,l ′ ) 2 i h(˜ǫ gα j,l ) 2ih(˜ǫ g j,l ′ ) 2i Since there is no correlation between primeval CMB map and galaxies, we have h(˜ǫ Tcmb j,l ) 2 (˜ǫ g j,l ′ ) 2 i = h(˜ǫ Tcmb j,l ) 2 ih(˜ǫ g j,l ′ ) 2 i. Therefore, the first term on the right hand side of eq.(15) is always ∼ 1. It is irrelevant to the non-Gaussian features. The non-Gaussian signal fully comes from the…
Figure 7. C 2,2 j (|l − l ′ |)cmb vs. |l − l ′ | for W (top) and Q (bottom) bands of WMAP data. The mock samples of A and B are also shown. The error bars are the 90% range of 100 simulation samples. 5 CONCLUSION With the DWT clusters of 2MASS sample, we confirmed the pre￾vious results of the SZ effect of 2MASS galaxies on the WMAP data (Myers et al. 2004; Afshordi et al. 2004). For the foreground cleaned WMAP maps of W and Q bands, there are about 0.4-1% area of the maps is contaminated by the SZ effect of 2MASS DWT clusters with the Compton parameter y = (3.7 ± 2.4) × 10−6 . With moc

Showing 5 of the paper's 7 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/0603099 by the authors.

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