Planck 2013 results. XVII. Gravitational lensing by large-scale structure

Planck 2013 results

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Table 1

Reconstruction bandpower amplitudes and minimum-variance reconstruction for 100, 143, and 217 GHz, computed following Eq. (25).

	Reconstruction bandpower amplitude

L_min–L_max	A^raw - Aⁿ⁰	A ^ps	A ⁿ¹	A ^mc	A ^beam	Â

100 GHz
40–84 ...	(7.883–6.948) ± 0.191	+ 0.005 ± 0.003	+ 0.035 ± 0.003	0.007	±0.011	0.889 ± 0.191	7.297 ± 1.568
85–129 ...	(11.077–9.999) ± 0.197	+ 0.008 ± 0.004	+ 0.040 ± 0.004	–0.010	±0.011	1.040 ± 0.197	6.711 ± 1.272
130–174 ...	(16.360–15.411) ± 0.256	+ 0.014 ± 0.007	+ 0.045 ± 0.004	0.025	±0.011	0.866 ± 0.257	4.294 ± 1.273
175–219 ...	(25.031–23.896) ± 0.337	+ 0.024 ± 0.013	+ 0.057 ± 0.006	0.043	±0.011	1.011 ± 0.337	3.947 ± 1.316
220–264 ...	(36.642–35.881) ± 0.442	+ 0.040 ± 0.021	+ 0.104 ± 0.010	0.009	±0.010	0.607 ± 0.443	1.920 ± 1.400
265–309 ...	(51.002–50.170) ± 0.556	+0.058 ± 0.030	+ 0.205 ± 0.020	–0.076	±0.010	0.645 ± 0.557	1.693 ± 1.462
310–354 ...	(66.348–65.291) ± 0.707	+0.071 ± 0.037	+ 0.304 ± 0.030	–0.010	±0.010	0.692 ± 0.708	1.534 ± 1.571
355–400 ...	(81.994-81.084) ± 0.793	+0.077 ± 0.040	+ 0.332 ± 0.033	–0.121	±0.010	0.621 ± 0.795	1.177 ± 1.507
40–400 ...	(17.725–16.731) ± 0.112	+0.016 ± 0.008	+ 0.062 ± 0.006	0.004	±0.011	0.912 ± 0.113	...
143 GHz
40–84 ....	(3.936-2.841) ± 0.089	+ 0.005 ± 0.002	+ 0.026 ± 0.003	–0.021	±0.004	1.086 ± 0.090	8.917 ± 0.736
85–129 ...	(5.008–4.058) ± 0.090	+ 0.007 ± 0.004	+ 0.032 ± 0.003	−0.016	±0.004	0.928 ± 0.090	5.991 ± 0.582
130–174 ...	(7.076–6.088) ± 0.109	+ 0.012 ± 0.006	+ 0.040 ± 0.004	−0.020	±0.004	0.956 ± 0.109	4.743 ± 0.540
175–219 ...	(10.092–9.207) ± 0.137	+ 0.021 ± 0.010	+ 0.058 ± 0.006	0.013	±0.004	0.793 ± 0.138	3.094 ± 0.538
220–264 ...	(14.254–13.279) ± 0.174	+ 0.032 ± 0.016	+ 0.107 ± 0.011	− 0.010	± 0.004	0.845 ± 0.175	2.671 ± 0.553
265–309 ...	(19.049–18.063) ± 0.211	+ 0.045 ± 0.022	+ 0.191 ± 0.019	0.008	±0.004	0.742 ± 0.213	1.948 ± 0.558
310–354 ...	(24.524–22.862) ± 0.244	+ 0.055 ± 0.026	+ 0.271 ± 0.027	−0.011	±0.004	1.347 ± 0.246	2.988 ± 0.547
355–400 ...	(28.355–27.576) ± 0.273	+ 0.060 ± 0.029	+ 0.298 ± 0.030	−0.006	±0.004	0.427 ± 0.276	0.808 ± 0.524
40–400 ...	(8.403−7.401) ± 0.048	+ 0.016 ± 0.008	+ 0.064 ± 0.006	−0.013	±0.004	0.935 ± 0.050	...
217 GHz
40– 84 ...	(3.884–2.742) ± 0.088	+ 0.003 ± 0.003	+ 0.026 ± 0.003	−0.007	±0.004	1.120 ± 0.088	9.200 ± 0.721
85–129 ...	(4.817–3.866) ± 0.088	+ 0.005 ± 0.005	+ 0.032 ± 0.003	−0.012	±0.004	0.927 ± 0.089	5.982 ± 0.572
130–174 ...	(6.601–5.788) ± 0.103	+ 0.007 ± 0.009	+ 0.040 ± 0.004	−0.000	±0.004	0.766 ± 0.103	3.800 ± 0.512
175–219 ...	(9.544–8.637) ± 0.131	+ 0.012 ± 0.014	+ 0.058 ± 0.006	0.012	±0.004	0.824 ± 0.132	3.217 ± 0.516
220–264 ...	(13.409–12.317) ± 0.162	+ 0.018 ± 0.021	+ 0.103 ± 0.010	0.004	±0.004	0.967 ± 0.163	3.057 ± 0.516
265–309 ...	(17.825–16.583) ± 0.202	+ 0.025 ± 0.028	+ 0.179 ± 0.018	−0.003	±0.004	1.041 ± 0.204	2.733 ± 0.536
310–354 ...	(22.391–20.915) ± 0.227	+ 0.030 ± 0.034	+ 0.251 ± 0.025	−0.014	±0.004	1.210 ± 0.231	2.683 ± 0.513
355–400 ...	(26.119–25.068) ± 0.265	+ 0.032 ± 0.037	+ 0.279 ± 0.028	−0.026	±0.004	0.766 ± 0.269	1.451 ± 0.510
40–400 ...	(8.122–7.111) ± 0.046	+ 0.009 ± 0.011	+ 0.064 ± 0.006	−0.004	±0.004	0.942 ± 0.048	...
MV
40– 84 ...	(3.297–2.170) ± 0.073	+ 0.006 ± 0.003	+ 0.026 ± 0.003	−0.011	±0.003	1.105 ± 0.073	9.077 ± 0.601
85–129 ...	(4.062–3.062) ± 0.074	+ 0.009 ± 0.004	+ 0.032 ± 0.003	−0.014	±0.003	0.972 ± 0.074	6.276 ± 0.476
130–174 ...	(5.480–4.542) ± 0.084	+ 0.015 ± 0.007	+ 0.040 ± 0.004	−0.012	±0.003	0.895 ± 0.085	4.442 ± 0.420
175–219 ...	(7.616–6.758) ± 0.103	+ 0.024 ± 0.011	+ 0.058 ± 0.006	0.009	±0.003	0.766 ± 0.104	2.992 ± 0.406
220–264 ...	(10.587–9.576) ± 0.131	+ 0.036 ± 0.017	+ 0.101 ± 0.010	−0.003	±0.003	0.876 ± 0.133	2.771 ± 0.419
265–309 ...	(14.004–12.903) ± 0.156	+ 0.048 ± 0.022	+ 0.175 ± 0.017	0.000	±0.003	0.878 ± 0.158	2.304 ± 0.415
310–354 ...	(17.677–16.285) ± 0.181	+ 0.057 ± 0.026	+ 0.246 ± 0.025	−0.009	±0.003	1.099 ± 0.185	2.438 ± 0.409
355–400 ...	(20.647–19.583) ± 0.208	+ 0.061 ± 0.028	+ 0.274 ± 0.027	−0.024	±0.003	0.753 ± 0.212	1.427 ± 0.401
40–400 ...	(6.788–5.768) ± 0.039	+ 0.020 ± 0.009	+ 0.066 ± 0.007	−0.009	±0.003	0.943 ± 0.040	...

Notes. The overall amplitude A is evaluated as Â = A^raw − Aⁿ⁰ − A^ps − Aⁿ¹ − A^mc. The bands are wide enough that the correlation of the measurement uncertainty between bins is negligible, as discussed in Appendix D; however, most of the systematic errors are significantly correlated between bands. The final column lists the physical bandpower estimates and their errors obtained by scaling flat averages of across each bin in our fiducial ΛCDM model by the given Â value.

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