dataesr/scientific-paragraphs-categorization huggingface dataset:
ORIGINAL UNEDITED MANUSCRIPT Archive  17  and shown in Fig. 39. The frequency coverage and sensitivity of LiteBIRD allow us to estimate foreground parameters and CMB amplitudes in suitably small sky areas or resolution elements. Thus, the number of non-linear parameters, {β d , T d , β s }, as driven by the resolutions in Table  14 , computed in the f sky = 49% observed sky, is precisely 24,545. The number of Q/U amplitudes contained in the recovered CMB, dust and synchrotron maps is 144,534. Therefore, in total, the component-separation process deals with 169,079 free parameters. This can be compared to the 10 6 -long data vector as formed by the observed Q/U amplitudes in the 22 frequency channels. Table  14 : Values of N side for foreground parameter variations in three different 20 % large regions of the sky.
ORIGINAL UNEDITED MANUSCRIPT this exact methodology will not be applicable to real data sets, a better understanding of foreground morphology, as well as additional observational/theoretical priors on their SEDs, will help us to better define the Galactic masks by the time of the LiteBIRD launch. The angular power spectra of the foreground residuals are estimated using pseudo-C ℓ s corrected for the mask, evaluated using the Healpy Anafast 18  public code. We checked that the power spectra of foreground residuals do not change if they are estimated by the methods such as NaMaster  19  , mainly because foreground E and B modes have similar amplitudes. Figure  38  shows the result of our foreground-cleaning method applied to the multifrequency data set specified in Sect. 5. 2. 2, in the case of Gaussian beam convolution.
ORIGINAL UNEDITED MANUSCRIPT uncertainties are also given. The transfer-function category includes systematic effects due to the uncertainties of the detector time constant and the crosstalk among detectors. Details of each of these items are given in the following sections. Some of the systematic error budget of individual sources can be further divided into the sub-level requirements. One example is the pointing uncertainty, which will be detailed in Sect. 5. 3. 7. 20 e note that the estimated systematic bias is approximately a linear sum of individual systematic effect biases, when those power spectra are much smaller than that of the lensing effect. This is because ∆r is approximately proportional to the square of the error of the systematic effects to first order; the details are given in Sect.
ORIGINAL UNEDITED MANUSCRIPT Table 15: Summary of sources of systematic effects as the top level category. We categorize the systematic effects in the first column. The details of individual categories are shown in the second column. The third column shows the systematic biases on r, except for the cosmic rays, which are supposed to yield an extra noise source. The fourth column describes the sources of systematic effects. The last column shows the types. The type "E" and "R" state the expectation and the requirement, respectively, as described in the text. Note that we assign an error budget of 1 % of the total systematic bias 5. 7 × 10 -6 to individual systematic effects as a nomial error budget in order to account for dozens of potential systematic sources. Details are described in the text.
ORIGINAL UNEDITED MANUSCRIPT systematic effects based on simulated sky maps of the CMB and foregrounds described in Sect. 5. 2. 2. The basic strategy is to obtain a residual sky map that is a difference between the reconstructed sky maps with and without a particular systematic effect, which mitigates the model dependence of the sky maps employed. 5. 3. 2. Formalism of the Errors. This section gives the definition of the bias ∆r and the total error δr. We define a likelihood function L(r) expressed in the multipole domain due to the large sky coverage of the satellite mission. Assuming Gaussian stationary and isotropic fields and hence no coupling between multipoles (which is an approximation in the presence of a mask of the Galactic plane), the likelihood function is given by log L(r) = ℓmax ℓ=ℓmin log P ℓ (r),  (36)  where ℓ min = 2 and ℓ max = 191  22.
We estimate the systematic bias under the condition of the existence of the expected noise N ℓ coming from instrumental and foreground residual uncertainties. The potential systematic bias ∆r is defined as the value giving the maximum of the likelihood function: dL(r) dr r=∆r = 0. ( 40 ) We also define the total error on r, δr, as the value covering 68 % of the area of the total likelihood function: δr 0 L(r)dr ∞ 0 L(r)dr = 0. 68. ( 41 ) ORIGINAL UNEDITED MANUSCRIPT 5. 3. 3. Beam Systematic Effects. Imperfect knowledge of the beam, due to a combination of uncertainties in beam measurements and modeling, are important sources of systematic effects for the measurement of primordial B modes. We model the sky signal p(t, ν, n, ŝ) observed at location n at time t with frequency ν, from a beam centered at location ŝ in the presence of an ideal HWP, without coupling with other optical elements: p(t, ν, n, ŝ) = B ∥ (t, ν, n -ŝ)[I(ν, n) + Q(ν, n) cos 2φ(t, ν) + U (ν, n) sin 2φ(t, ν)] + B ⊥ (t, ν, n -ŝ)[I(ν, n) -Q(ν, n) cos 2φ(t, ν) -U (ν, n) sin 2φ(t, ν)], (42) where φ(t, ν) = 4ρ(t, ν) -2ψ(t, ν), ρ(t, ν) is the HWP rotation position, ψ(t, ν) is the polarizer measurement angle with respect to the axis fixed in the sky, and B ∥ (t, ν, nŝ) and B ⊥ (t, ν, nŝ) are the co-polar and cross-polar beams, respectively.
Description of Simulations. For this study, we employ the beam-convolved sky maps generated by TOAST described in Sect. 5. 2. 2. In order to set the requirements on the farsidelobe beam calibration, we have considered the beam convolution in the angle ranges 5 • < θ < 10 • , 10 • < θ < 15 • , and 15 • < θ < 90 • , where θ is the angle with respect to the 89/156 ORIGINAL UNEDITED MANUSCRIPT main lobe peak. This convolution has been performed for all sets of co-added foreground maps. We do not include noise in the input simulated maps because we are interested in the estimation of the requirements in terms of a bias on r (∆r) for the beam systematic effects. The time-ordered data (TOD) are simulated for the 22 nominal frequency bands of LiteBIRD. A subset of detectors for each frequency band is considered, instead of the full focal plane.
The selected detectors are well spread across the arrays so that we can assume that the results are representative of the full focal plane, and therefore a global rescaling of the results is applied at the end. LiteBIRD's scanning strategy with nominal parameters of the IMo (see Sect. 5. 1) is simulated and a full-sky convolution of the beams is performed. Input simulated reference beams are calculated using GRASP software with a simplified optical model, i. e. , no multiple reflections have been included in the beam model. GRASP beams have been simulated at the central frequency for each band, neglecting the color effects and hence the differential effects on various sky components. We will describe the possible systematic effects that are not accounted for in the model above in the last paragraph of this subsection.
ORIGINAL UNEDITED MANUSCRIPT Table  16 : Beam perturbation requirements for each frequency channel and each of the three angle ranges of the beam perturbations giving ∆r = 1. 9 × 10 -5 /66, fixing the other perturbations for the other frequency channels and angle ranges to 0. Units are dB for δB lim and σ cal 0. 25 □ , and dBi for δR lim. The indicated values of angles in the first row, providing the typical range in which the beam is perturbed, are such that 95 % of the perturbed beam power for a typical CMB channel is within this range (the value varies from channel to channel as the beam shape varies). This explains why the upper bound for the last window is only 50 • while the window extends to 90 • as the beam drops above 50-60 • , depending on the channel. The calculated values of the required precision σ cal 0.
ORIGINAL UNEDITED MANUSCRIPT that we calibrate the whole area of the beam for all the frequency channels with a constant precision σ cal 0. 25 □ , we have evaluated the desired precision is -56. 90 dB to have requirements equivalent to what is presented in Table  16. The total contribution of ∆r has been estimated with handred realizations by simultaneously varying individual α values with a uniform distribution in the range [max(-1, -√ 3α lim ); √ 3α lim ], with α lim calculated from Table  16. The √ 3 factor is to keep the same variance α 2 lim as the gaussian distribution used for Table  16  to derive requirements. We find the systematic bias resulting from the above assumptions to be ∆r = 2. 2 × 10 -5. We want to stress several important limitations of this analysis. Firstly, one of the key assumptions is that the scanning strategy induces enough symmetrization of the beam so that many calibration measurements can be averaged for large θ and that the beam systematic effects are then dominated by uncertainties in the transfer function.
ORIGINAL UNEDITED MANUSCRIPT to values close to those in the GRASP simulation. The typical values are 1. 7 • from the mainlobe center for the position, 0. 6 • for FWHM and -20 dB with respect to the main lobe for the height. We repeat a similar analysis by changing the ring position, width, and height, and find that a ±20 % variation from the nominal values corresponds to ∆r = 5. 7 × 10 -6. In summary, we require a calibration accuracy of better than 10 % for the near sidelobe in order to have a systematic bias ∆r < 5. 7 × 10 -6.
ORIGINAL UNEDITED MANUSCRIPT systematic errors and requiring a deglitching process. For LiteBIRD, we will use a different detector technology and expect that the outcome of cosmic-ray effects may differ from that of Planck -HFI. In order to predict and characterize the potential effects of cosmic-ray glitches, two studies have been conducted: one is to use actual laboratory measurements to estimate the response of the detectors to energetic particle impacts by irradiating the detectors with alpha particles, γ-rays, or cosmic-ray muons; and the second is to realize an end-to-end simulation to evaluate the propagation of cosmic-ray effects. The former is described in Sect. 4. 4. 2 (see also Ref. [222] ). Here we describe details for the latter approach (see also Refs. [297, 298] ). For LiteBIRD, we will employ TES arrays on a 10-inch silicon wafer.
ORIGINAL UNEDITED MANUSCRIPT with respect to the optical axis of the HWP; and R(2ψ) is the rotation matrix for Stokes parameters. The HWP Mueller matrix M is written in the frame of the HWP. The Mueller matrix of the HWP has been calculated using the electromagnetic wave propagation simulation tool rigorous coupled-wave analysis (RCWA) assuming a nine-layer HWP with pyramidal ARC optimized for LFT. 23 In an electromagnetic simulation, we find that the Mueller matrix can be expanded into three components consisting of the constant one (0f), one modulated with an angular frequency twice that of the HWP rotation (2f), and one with 4 times that frequency (4f). Each element of the matrix M ij for a given incident angle Θ is decomposed into sine waves with respect to the angle ρψ, and only the first three terms are shown to be significant: M ij (Θ, ρ -ψ) = M (0f) ij (Θ) + M (2f) ij (Θ) cos(2ρ -2ψ + ϕ (2f ) ij ) + M (4f) ij (Θ) cos(4ρ -4ψ + ϕ (4f ) ij ).
An apodized Galactic mask has been applied, considering 50 % of the sky. We have assumed two cases: (i) the optical axis of the HWP is centered in the LFT focal plane; and (ii) the HWP rotation axis is shifted by 5 •. There is less cancellation in the second ORIGINAL UNEDITED MANUSCRIPT case. The induced bias ∆r on the tensor-to-scalar ratio r using the likelihood described in Sect. 5. 3. 2 is indicated in Table  17. Table  17 : Contribution of the IP to the ∆r parameter. The most pessimistic case of a shifted HWP is used for evaluation of the effect after correction with two different schemes: for model 1, when the ϵ i coefficients are estimated independently for each detector; and for model 2 when we use the scaling relation ϵ(Θ, ϕ) accounting for the exact relative phase dependance of this parameter with respect to the azimuthal angle of the detector locations ϕ around the HWP rotation axis (two detectors at different locations in the FP see the same 4f IP effect with a known delay, as described further in the text).
ORIGINAL UNEDITED MANUSCRIPT template and exploits from the large intensity signal to recover the ϵ parameters. Because the monopole is not recovered within the map-making process, it is jointly fitted with the ϵ parameters, and so is marginalized over, in order to remove its leakage in the polarization maps. The procedure is described in Ref. [305]. The residual B-mode spectra of the IP after correction are shown in Fig. 40  and the values of ∆r are indicated in Table  17. Three years of observation is assumed here. We observe that the bias is greatly reduced after mitigation. We argue that the phase of the residual effect in the map is random after mitigation because the errors on ϵ are limited by noise, so if more frequency channels are included in the analysis the net effect after component separation should be reduced.
ORIGINAL UNEDITED MANUSCRIPT ζ. Instead, in the map-making procedure, we make use of the unperturbed, nominal HWP profile, i. e. , M IX s ≡ M IX (h 1,2 , ζ 1,2 , β). In order not to be dependent on a specific realization of the systematic perturbations, we simulate 10 realizations for each σ ∆x , by always keeping CMB and foreground fixed. For each band, we compute a template map m templ with M IX TOD (ν) = M IX s (ν) (so, no error on the HWP parameters) from the same foreground and CMB maps as above. These templates are used to obtain residual maps; this yields maps of residuals m res that are minimally affected by the foreground color effect and mostly due to the mismatch between M IX TOD (ν) and M IX s (ν). For each map of residuals, masked with a 70 % Galactic mask, the corresponding B-mode spectrum is computed and added to the fiducial CMB B-mode spectrum.
We model the gain for each detector, i, as a time-varying gain function, G i (t), which is injected in a signal timestream as d i (t) = G i (t) [I(t) + Q(t) cos(4ρ -2ψ) + U (t) sin(4ρ -2ψ)] , (53) 100/156 ORIGINAL UNEDITED MANUSCRIPT where ρ is the HWP rotation angle and ψ is the detector polarization orientation. We model the gain function G i (t) as a product of a term g 0 i that is constant in time and varying from detector to detector, and another term g i (T bath (t)) that depends on the thermal bath temperature T bath (t), varying in time, i. e. , G i (t) = g 0 i g i (T bath (t)). In a simulation we generate some time variation of T bath (t) using a model of the power spectrum P bath in the frequency domain: P bath = A 2 bath 1 Hz f , (54) where A bath is the amplitude of P bath at a frequency f of 1 Hz.
The other subdominant potential sources of gain variation in time include fluctuations of the magnetic field, loading power, bias current, and gains of the cold and warm readout electronics. Given the power spectrum models for those fluctuations, we are in principle able to estimate the systematic effects in a similar manner, but this remains future work. The absolute gain is a conversion factor from the recorded values, usually in volts, to the physical value in units of thermodynamic temperature K CMB. The absolute gain can be calibrated using the solar dipole signal during scans of the sky. 26 We estimate the expected ORIGINAL UNEDITED MANUSCRIPT accuracy of the absolute gain measurement assuming the existence of 1/f noise with a knee frequency of 20 mHz for the channels having the lowest white noise for 1 year.
Polarization Efficiency. The uncertainty of the polarization efficiency is modeled as an uncertainty of the couplings of the Stokes parameters of Q or U , described in the Mueller 103/156 ORIGINAL UNEDITED MANUSCRIPT matrix as M QQ and M U U. The polarization efficiency uncertainties are sourced by the HWP and detectors. When the polarization efficiency error of the detectors are uncorrelated, the effect may be scaled proportional to the inverse of the square root of the number of detectors, yielding effects of negligible amplitude. On the other hand, an uncertainty in the HWP gives a significant impact, since it is common to all the focal-plane detectors. The polarization efficiency is related to the absolute normalization of the E-and B-mode power spectra. The net effect of including the efficiency from the HWP with the frequency band-average is calibrated using the E-mode power spectrum for higher multipoles, while its frequency dependence in the band will be calibrated using the ground facility.
ORIGINAL UNEDITED MANUSCRIPT offset measurements are uncorrelated. This assumption is not appropriate when the correlation coefficient is larger than 1/N , however. We describe the bandpass uncertainty using a single parameter γ c defined in Eq. (  22 ), where subscript c is either the dust or synchrotron component. We employ the discussions in Ref. [246]  to give the systematic bias ∆r for the bandpass uncertainty with the usage of the PMU. The systematic effects are evaluated as a function of the uncertainties of γ c for LiteBIRD's 15 frequency channels individually with the application of the foreground subtraction procedure  [246]. With a requirement of ∆r to be less than 5. 7 × 10 -6 , the requirements on the measurement accuracy of γ c is in the range of 10 -4 to 2. 5 × 10 -3 , depending on the frequency channels for the detector arrays.
We multiply the likelihood L(r) in Eq. (  36 ) by a function 106/156 ORIGINAL UNEDITED MANUSCRIPT   (36). The dark blue line is obtained after de-bising using marginalization. The net effect of this procedure is to subtract the systematic bias and to inflate the width of the likelihood function by an increase of the covariance of the power spectrum. The larger σ α is, the smaller is the systematic bias, since the larger σ α gives almost no constraint in the α value a priori, and is equivalent to fitting α. We employ the template spectrum M ℓ as the dust spectrum, which is evaluated by the component-separation process. We justify this by the fact that the main systematic effects are caused by polarization leakage from the higher frequency channels where the dust foreground dominates, and the shape of resultant systematic power spectra for those effects is similar to that of the dust component.
ORIGINAL UNEDITED MANUSCRIPT including systematic effects, is δr ≃ 0. 9 × 10 -3 , which enables us to distinguish no primordial gravitational waves from the Starobinsky model  [14]  with a significance greater than 5 σ. LiteBIRD can also help reduce the Galactic dust contamination of the CIB on large angular scales, which may further improve the constraint on r. Further reduction of the lensing Bmode power spectrum can be achieved with future lensing measurements from ground-based CMB surveys, such as the CMB-S4 experiment  [52]  and its precursors, but only in the sky region that overlaps with LiteBIRD. 43% delensing r < 0. 9 × 10 3 (68%) Fig. 45 : Marginalized posterior distributions of the tensor-to-scalar ratio parameter r with (blue) and without (black) a delensing factor, which could be obtained by a multi-tracer template obtained by Planck CIB and lensing maps reconstructed with the help of WISE  [315].
ORIGINAL UNEDITED MANUSCRIPT This occurs at recombination as well as during the EoR. Re-scattering of the CMB photons at reionization generates an additional polarization anisotropy at large angular scales, because the horizon size at this epoch subtends a much larger angular size  [36]. The CMB is affected by the total column density of free electrons along each line of sight, parameterized by its Thomson-scattering optical depth, τ. The wavenumber of the fluctuations contributing to quadrupole temperature anisotropy, as seen by an electron at a redshift z, is given by k ≃ 3/[r Lr(z)] where r L = 14 Gpc is the comoving distance from Earth to our last-scattering surface, and r(z) is the comoving distance to redshift z. For example, a redshift of z = 7. 7 gives r(7. 7) = 9. 1 Gpc. We observe this wavenumber at a multipole of ℓ ≲ k r(7.
ORIGINAL UNEDITED MANUSCRIPT bump and supresses the small-scale power. However, since the small-scale power has been measured precisely, the value of exp(-2τ )A s is fixed; thus, for a given measured value of the high-ℓ power spectrum, the amplitude of the reionization bump scales as τ 2 A s ∝ τ 2 exp(2τ ). We can use this to determine the value of τ , which in turn provides an integrated constraint on the reionization history of the Universe because τ = σ T N e , where the column density of electrons is given by N e = c dt n e integrated from today to the beginning of reionization. This number can be compared with the expected number of electrons from ionization by star-forming galaxies and quasars (including X-ray emission from accretion disks around black holes); see Fig. [75] ; Planck (2013)  [332] ; Planck (2015)  [289] ; Planck (2016)  [330] ; WMAP +LFI (2018)  [333] ; Planck (2018)  [279] ; Planck -HFI (2019)  [334] ; WMAP +LFI (2020)  [335] ; and Planck (2020)  [331].
ORIGINAL UNEDITED MANUSCRIPT LiteBIRD will provide a cosmic-variance-limited determination of τ , i. e. , the sampling variance in the limit of zero instrumental noise. This is the smallest possible error bar, limited only by the fraction of sky (f sky ) available for the cosmological analysis. While ground-based experiments will provide an independent measurement of τ from gravitational lensing, with an uncertainty similar to the current Planck estimates over the coming years, a new, improved large-scale measurement will come from LiteBIRD. Assuming a fiducial value of τ = 0. 054 and an available sky fraction of f sky = 0. 7, the expected 68 % C. L. uncertainty on τ is 0. 002  [338] , which is 3 times better than today's tightest bounds from Planck  [331, 334, 339]. Not only is this a significant improvement over current measurements, but it will also be the definitive and most accurate measurement of τ from the CMB.
ORIGINAL UNEDITED MANUSCRIPT The information on the amplitude of fluctuations in the low-redshift Universe might be provided by the CMB lensing data from observations of the small-scale anisotropies (e. g. , those of the future Simons Array  [357] , SO  [51, 358] , and CMB-S4  [359, 360]  experiments), and/or by data from large-scale structure surveys tracing the matter distribution (e. g. , galaxy surveys with the Dark Energy Spectroscopic Instrument (DESI)  [361]  and the Legacy Survey of Space and Time (LSST)  [362] ). Distance measurements, such as those coming from BAO data, will further improve the constraints by adding information about the cosmic expansion history  [355]. To give a specific example, combining a cosmic-variance-limited measurement of τ (σ(τ ) = 0. 002) with observations of the small-scale CMB anisotropies from CMB-S4 and either BAO data from the DESI galaxy survey  [361]  or galaxy lensing/clustering data from the LSST survey of the Vera Rubin Observatory  [362] , will in both cases yield σ( m ν ) = 12 meV  [350].
This will result in a detection of the neutrino mass at the 5 σ level, for the minimum value of 60 meV, or larger. Fig. 49  shows the constraining power of ORIGINAL UNEDITED MANUSCRIPT these data combinations in the (τ, m ν ) plane, highlighting that a cosmic-variance-limited measurement of τ from LiteBIRD will be necessary for reaching a statistically significant detection of the neutrino mass from cosmological data. To complete the picture on the neutrino sector, the expected uncertainty on the effective number of relativistic species, N eff , from LiteBIRD alone is σ(N eff ) ≃ 0. 15  [363] , which is of the same order of magnitude as that obtained by Planck  [279]. On top of that, it would give an independent measurement, and an important cross-check, since any systematic effects would be different from those relevant for the high-ℓ Planck measurements, e.