1. LFI systematics and impact on science
Paolo Natoli
Università di Ferrara and INFN
on behalf of the Planck collaboration and of the LFI Data Processing Center
Special credits: L. Colombo, A. Gruppuso, M. Lattanzi, M. Migliaccio, D. Molinari, U. Natale, L. Pagano

2. The Low Frequency Instrument on Planck
LFI was the Low Frequency Instrument on Planck
Radiometric detectors like WMAP, but total power
Frequency range: 30 – 70 GHz
Science Ground Segment in Trieste (INAF-OATs), Italy
Planck built to be a component separation machine, LFI provided the low frequency end
Hard to disentangle systematics impact on science from LFI
But there are interesting exceptions:
Large-angle (low-ell) polarization analysis is one
Analysis pipelines from the two instruments "almost" independent in terms of data content and methodology
Provides nice consistency checks
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

3. Large-angle polarization
Challenging measurement (Jean-Loup Puget's talk)
Of some science importance
Optical depth t is the worst constrained parameter of the six LCDM (14% relative error in Planck legacy)
A full-sky cosmic variance limited measurement of E-mode polarization is still awaited
LiteBIRD: will likely provide this “definitive” measurement at large scales
It will be crucial to get:
Accurate reionization history
Neutrino parameters (esp. masses)
Large-scale anomalies
getting tensor-to-scalar ratio in B-mode reionization peak
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

4. CMB and cosmic reionization
Optical depth to reionization:
Second major change of ionization state of H
Damps temperature and polarization fluctuations inside horizon
Generates new polarization at large angular scales
Sunyaev and Chluba 2006
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

5. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

6. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2013 XV)
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

7. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2013 XV)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2018 V in pr.)
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

8. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2013 XV)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2018 V in pr.)
Planck lowTEB (LFI) (Planck 2015 XIII) 𝜏 = ± 0.023
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

9. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2013 XV)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2018 V in pr.)
Planck lowTEB (LFI) (Planck 2015 XIII) 𝜏 = ± 0.023
Planck lowTEB (LFI) (Planck 2018 V in pr.) 𝜏 = ± 0.020
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

10. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2013 XV)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2018 V in pr.)
Planck lowTEB (LFI) (Planck 2015 XIII) 𝜏 = ± 0.023
Planck lowTEB (LFI) (Planck 2018 V in pr.) 𝜏 = ± 0.020
Planck lowE (HFI) (Planck XLVI) 𝜏 = ± 0.009
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

11. Brief history of t measurements
WMAP 9yrs: 𝜏 = ± (Hinshaw+ 2013)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2013 XV)
WMAP 9yrs + Planck 353 GHz 𝜏 = ± (Planck 2018 V in pr.)
Planck lowTEB (LFI) (Planck 2015 XIII) 𝜏 = ± 0.023
Planck lowTEB (LFI) (Planck 2018 V in pr.) 𝜏 = ± 0.020
Planck lowE (HFI) (Planck XLVI) 𝜏 = ± 0.009
Planck lowE (HFI) (Planck 2018 V in pr.) 𝜏 = ±
WMAP
LFI
HFI
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

12. Foreground mitigation: LFI and HFI
Map-based template fitting procedure to mitigate foreground contamination, using low and high channels as tracers of polarized synchrotron and dust. Same methodology for LFI and HFI
Template cleaning of maps m = [Q, U] for the channels= 70, 100, 143 GHz
353 GHz
30 GHz
30 GHz: tracer of synchrotron emission
353 GHz: tracer of thermal dust emission
Foreground coefficients fitted by minimising, on about 70% of the sky:
Where the rescaled covariance matrix is:
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

13. Pixel-based likelihood modelling
While HFI uses a cross-spectrum based likelihood driven by simulations, LFI uses a map-based formalism
Based on cleaned 70 GHz map
Statistically efficient
Sensitive to full TEB (HFI is EE-only)
Provided CMB signal covariance is adapted, can probe non-isotropic models
But prone to map-level systematics
Requires accurate estimation of the underlying covariance matrix
fSKY = 86%
fSKY = 62.4%
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

14. Correcting for noise mismatch
Estimating the noise covariance matrix is hard:
It is a by-product of the map-making scheme, but exact computation is prohibitive
Have to resort to approximations. This works reasonably well for LFI (less well for HFI)
Still, noise mismatches arise. This can be measured from half-ring half-difference maps, and the noise matrix properly debiased
EE noise bias
BB noise bias
1s shade
HRHD bias
Rescaled noise matrix bias
Original noise matrix bias
L. Colombo
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

15. The LFI gain template
Main polarization systematic in low ell LFI comes from calibration, since the presence of polarized foregrounds biases the gain.
At 30 and 44 GHz, where polarized foreground are bright, an iterative scheme allows to mitigate the bias by converging on the foreground template.
In the end, 30 GHz improves much, while 44 GHz cannot be used for low ell cosmology because of other systematics
At 70 GHz diffuse foreground is at a minimum, noise dominates and the iterative scheme does not converge
Still a correction is needed: this comes in the form of a gain template, a by-product of the converged 30 GHz iteration scheme, properly rescaled in amplitude.
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

16. Impact of gain errors
Ignoring the gain template results in about 2 sigma bias on t:
L. Colombo
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

17. Goodness of fit
The cleaned dataset can be selected through goodness-of-fit analysis
a, b from foregrounds, g from systematics
R0.6 R0.8 R1.0 R1.2 R1.8X R2.2X
M. Migliaccio
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

18. Goodness of fit
The cleaned dataset can be selected through goodness-of-fit analysis
a, b from foregrounds, g from systematics
R0.6 R0.8 R1.0 R1.2 R1.8X R2.2X
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

19. Comparison to simulations
How can we tell if we are seeing inadequacy of the foreground cleaning at large sky fraction or residual instrumental systematics (e.g. gain template is not perfect). Simulations help:
Rifare con script di marina? Cosiderare di tohglerla, ci sono cose importanti che non controlliamo
D. Molinari
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

20. Simulation based mask validation
data
Statistics for maximum deviation of Dt across masks
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

21. A joint map from LFI and WMAP
Preliminary
LFI+WMAP
The WMAP low-ell polarization likelihood can be analyzed using a map-based formalism similar for LFI.
Good consistency already at the level of angular power spectrum
This enables use of a joint (weighted-average by pixel) dataset
U. Natale et al. in prep.
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

22. The LFI+WMAP dataset Good consistency across different Galactic masks
Preliminary
Good consistency across different Galactic masks
Dt scatter by mask compared to simulations
U. Natale et al. in prep.
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

23. t from LFI and WMAP from LFI+WMAP Preliminary
Null test is map-based, estimate has ~20% error on t (from low ell only)
Includes TE (and, potentially, BB, TB, EB...)
But from a pixel-based likelihood. Can be used to constrain models for which an EE spectrum-based likelihood (as HFI) in unsuited, e.g.
non-isotropic cosmologies (CMB anomalies)
Cosmological birefringence
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

24. Joint view of existing constraints on t
L. Pagano
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

25. Conclusions and lessons learned
In low ell polarization, LFI has provided constraints based on 70 GHz, used as baseline in 2015 and as consistency in 2018.
Low ell polarization is an hard measurement. The Planck experience shows that systematic errors can arise at the level of data processing, in the interplay between calibration, map-making and component separation
Validation through end-to-end simulations is an extremely important step
Solving problems requires time. LFI could benefit from a well integrated team, thanks to strong links between Science Ground Segment and Science exploitation teams.
Post-legacy analysis is delivering a joint pixel based dataset for LFI and WMAP, competitive in terms of noise and suitable for many non-standard analyses.
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

26. Extra Slides
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

27. Post legacy analysis Preliminary
Several, ongoing post legacy activities on LFI
Timeline reprocessing and improved calibration with component separation interplay is eventual goal: will take some time.
Optimization of the procedure on existing timelines is already yielding results, e.g. in terms of consistency across masking
U. Natale et al, in preparation
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

28. WMAP 9 year dataset
The WMAP large-angle polarization likelihood can be analyzed using a map-based formalism similar for LFI
Using weighted average for Ka, Q and V for CMB
K-band and HFI 353 for synchrotron and dust cleaning
As opposed to LFI 30 GHz and HFI 353 GHz for LFI, with CMB only from 70 GHz
Good consistency already at the level of angular power spectrum
This enables use of a joint (weighted-average by pixel) dataset
Preliminary
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019

29. With and without TE Dt = t(TT+TE+EE) – t(TT+EE)
Paolo Natoli – LFI Systematics and Impact on Science – LiteBIRD Kick Off Meeting - JAXS 1 July 2019