ACT (DR6.02) Harmonic Beam Profiles

Harmonic beam profiles for the DR6.02 nighttime maps and selected nighttime null test maps.

The files are formatted as follows:

{split_type}_{array}_{freq}_night_beam_tform_{beam_type}.txt
"split_type" is either "coadd" or "set{0..3}". The sets refer to the four independent noise splits of the dr6.02 maps. The "coadd" split_type is a weighted average of the per-split beams. The "coadd" beam is used for the power spectrum likelihood. The "coadd" beam should be sufficient for most analyses, the per-split beams deviate by less than 1% from the coaddded beam for multipoles < 10_000.

"beam_type" refers to either "instant", "jitter_cmb" or "jitter_mono". The "jitter_cmb" type is the beam estimate after the CMB color-correction and the jitter correction have been applied. This beam is most appropriate for the CMB signal in the DR6.02 maps. The "instant" beam is the instantenous beam, i.e. the beam estimate before the CMB color-correction and jitter correction. The "jitter_mono" beam is an estimate of the mono-chromatic beam evaluated at a reference frequency (specified in the header of the file). The "jitter_mono" beams are used to construct the color-corrected beams that are used in the power spectrum likelihood.

The columns of the files are:

   Column 1: Multipoles
   Column 2: B_ell
   Column 3, 4, ..: dB1_ell, dB2_ell, ...

The beam transform B_ell is calibrated such that 2*pi*B_ell(ell = 0) = Omega_B (the beam solid angle). Note that the beam transform does not contain the pixel window function of the maps. See https://github.com/ACTCollaboration/DR6_Notebooks/blob/main/ACT_DR6_maps_demo.ipynb for an example of how to deconvolve the pixel window function from the maps.

Each dB#_ell is an independent mode of the uncertainty in B_ell. To average a result over the ensemble of beam realizations, generate trial beams
   B'_ell = B_ell + a1 * dB1_ell + a2 * dB2_ell + ...
where (a1, a2, ...) are drawn from the normal distribution with mean 0 and variance 1.
Note that the "jitter_mono" beam files do not contain the dB#_ell beam error modes.
The main beams are divided up into several types:

** Nominal **

Harmonic beam profiles for the DR6.02 maps.

** inout_split **

Harmonic beam profiles for the DR6.02 inner (s1) and outer (s2) null test maps.

** pwv_split **

Harmonic beam profiles for the DR6.02 low-PWV (pwv1) and high-PWV (pwv2) null test maps.

** elevation_split **

Harmonic beam profiles for the DR6.02 low-elevation (el1), mid-elevation (el2) and high-elevation (el3) null test maps.

** time_split **

Harmonic beam profiles for the DR6.02 s17-s18 (t1) and s19, s20, s21, s22 (t2) null test maps.

** Note on beam covariances **

To convert the error modes included in the "tform" beam files to a ell-by-ell covariance matrix, and then back to a set of error modes, you can use the following method:

   >> import numpy as np
   >> from scipy.sparse import linalg as la
   >> error_modes = np.loadtxt('example_night_beam_tform_jitter_cmb.txt', usecols=np.arange(2, 12)) # Shape is (17401, 10).
   >> cov_matrix = error_modes.dot(error_modes.T) # Shape is (17401, 17401).
   >> eigenvals, eigenvecs = la.eigsh(cov_matrix, 10)
   >> eigenvals = eigenvals[::-1]
   >> eigenvecs = eigenvecs[:,::-1]
   >> error_modes = np.sqrt(np.abs(eigenvals)) * eigenvecs

** Note on per-split beam covariance **

Since each split beam is created from the same per-season beams, the per-split beams are strongly correlated between splits. See Duivenvoorden et al. 2025 for a description of how to construct the covariance between the split beams.

*** Leakage beams ***

Harmonic leakage profiles for the DR6.02 nighttime maps and selected nighttime null test maps.
The leakage beams are described in detail in Duivenvoorden et al. 2025. In summary, leakage beams are provided as "gamma^{E,B}_ell" functions, which are defined as:
gamma^{E,B}_ell = b^{E, B}_ell / b^T_ell.
Here b^{E, B}_ell describe the leakage from T to E or B and b^T_ell is the "coadd_{arra}_{freq}_night_beam_tform_jitter_cmb.txt" file from the main beam product.
The leakage beams are divided up into two types:

** Nominal **

Harmonic leakage profiles for the DR6.02 maps.
The files are formatted as follows:
{array}_{freq}_gamma_t2{e,b}.txt
The columns of the files are:
   Column 1: Multipoles    Column 2: gamma^{E, B}_ell    Column 3, 4, ..: dB1_ell, dB2_ell, ...
Here, dB#_ell are beam error modes. See the description for the main beam for more details.

** inout_split **

Harmonic leakage profiles for the DR6.02 inner (s1) and outer (s2) null test maps.
There are two types of files, the:
gamma_ml_uranus_{array}_{freq}.txt
files contain the following columns:
   Column 1: Multipoles
   Column 2: gamma^E_ell
   Column 3: gamma^B_ell
   Column 4: standard deviation of gamma^E_ell per multipole
   Column 5: standard deviation of gamma^B_ell per multipole
Note that the standard deviation is a rather poor description of the uncertainty on gamma^{E, B}. Instead, one should use the second type of file to describe the uncertainty:
gamma_error_modes_ml_uranus_{array}_{freq}.txt,
which contain:
   Column 1: Multipoles    Column 2-4: dB1_ell, dB2_ell, dB3_ell error modes for gamma^E_ell
   Column 5-7: dB1_ell, dB2_ell, dB3_ell error modes for gamma^B_ell
Here, dB#_ell are beam error modes. See the description for the main beam for more details.

*** Daytime beams ***

These files represent beams for the daytime DR6.02 maps.
Note that the beams are only applicable to Stokes I because they include the low-multipole mapmaking transfer function that is present in the Stokes I maps but not in the polarization maps. The beams should work decently for polarization at multipoles above ell ~ 1000, but users should be careful and check that results are stable with choice of lmin.

The files are formatted as follows:

beam_full_{array}_{freq}_{region}_beam.txt
and contain the following columns:
   Column 1: Multipoles
   Column 2: The daytime beam, in units such that alm_daymap/daybeam should be compatible with alm_planck/planckbeam. The beam is not normalized to 1. It includes the transfer function and all gain normalization factors, such that it can be used directly on our dr6.02 maps.
   Column 3: A rough estimate of the uncertainty on the daytime beam. Unreliable.
   Column 4: The night beam produced from the same fit. Not meant to replace the nighttime beams, but provides a measurement of the night-time transfer function. Not 100% consistent with the nighttime beam at high ell, but Adri should be more reliable.
   Column 5: Uncertainty on the nighttime beam.
The exact calibration factors of the calibration to Planck assumed for the daytime beam are stored in the header of the file as "psgain". These calibration factors differ very slighlty from the actual calibration factors used (see Table 8 in Naess et al. 2025). If needed, the beam can be scaled by the ratio of calibration values.

To describe the uncertainty on the daytime beams, the following files:

beam_full_{array}_{freq}_{region}_modes.txt
Provide a set of beam noise modes that can be marginalized over to make day results independent of the night and planck maps:
   Column 1: Multipoles
   Column 2-8: Error modes for day / night.
   Column 9-15: Error modes for night / planck.

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