# The 2015 instrument model

## Overview

The RIMOreduced IMO, or Reduced Instrument Model is a FITSFlexible Image Transfer Specification file or a set of FITSFlexible Image Transfer Specification files containing selected instrument characteristics that are needed by users who work with the released data products. It is described in detail in The HFI(Planck) High Frequency Instrument and LFI(Planck) Low Frequency Instrument RIMO ICDInterface Control Document (ref). See also Planck-2015-A02[1] and Planck-2015-A07[2]. There will be two RIMOs, one for each instrument (the HFI(Planck) High Frequency Instrument RIMO will consists of several parts), which will follow the same overall structure, but will differ in the details. The type of data in the RIMO can be:

Parameter
namely scalars to give properties such as a noise level or a representative beam FWHMFull-Width-at-Half-Maximum
Vector or Table
to give, e.g., filter transmission profiles or noise power spectra, beam window functions. When possible, namely when they are of equal length, such as the noise power spectra, an effort is made to put them together into a table, otherwise they are given as separate vectors.
Image
namely 2-D "flat" array, to give, e.g., the beam correlation matrices

The FITSFlexible Image Transfer Specification file begins with primary header that contains some keywords that mainly for internal use and no data. The different types of data are written into different BINTABLE (for parameters and tables) or IMAGE (for 2-D arrays) extensions, as described below.

The HFI(Planck) High Frequency Instrument-RIMO separates the beam window functions and associated data from the main set of parameters, and this because the beam window functions are delivered for two cases covering 100% and 75% of the sky, as described in detail below.

### File Names

HFI(Planck) High Frequency Instrument 2015 RIMOreduced IMO
HFI_RIMO_R2.00.fits
LFI(Planck) Low Frequency Instrument 2015 RIMOreduced IMO
LFI_RIMO_R2.50.fits

## Detector-level parameter data

The detector parameter data are given in the form of a table giving the parameter values for each detector. The table columns (whose names are in BOLD ITALICS) are:

Bolometer name - DETECTOR
These are the detector names. For HFI(Planck) High Frequency Instrument these will be of the form 217-3 for SWBs or 100-3b for PSBs, and for LFI(Planck) Low Frequency Instrument they will have the form 27M or 18S. There are 52 HFI(Planck) High Frequency Instrument detectors and 22 LFI(Planck) Low Frequency Instrument detectors.
Focal plane geometry parameters - PHI_UV, THETA_UV, and PSI_UV
These parameters give the geometry of the focal plane, or the positions of the detectors in the focal plane in the Dxx reference frame. The angles that give the rotation of the beam pattern from a fiducial orientation (forward beam direction (z-axis) pointing along the telescope line of sight, with y-axis aligned with the nominal scan direction) to their positions in the focal plane. The fiducial position is that given by the Star Tracker. All angles are in radians. These parameters are derived from observations of bright planets; see Detector pointing for details.
Polarization parameters - PSI_POL, EPSILON
These are the direction of maximum polarization, defined with the beam in the fiducial orientation described above, that is, before rotation onto the detector position, and the cross-polarization contamination (or leakage). These values are determined from ground-based measurements.
Beam parameters - FWHMFull-Width-at-Half-Maximum, ELLIPTICITY, POSANG
These are the mean FWHMFull-Width-at-Half-Maximum of the scanning beam (in arcmin, the beam ellipticity (no units), and the position angle of the beam major axis. The scanning beam is that recovered from the observation of bright planets; details in Beams section.
Noise parameters - NETNoise Equivalent Temperature (LFI(Planck) Low Frequency Instrument), NETNoise Equivalent Temperature_TOT (HFI(Planck) High Frequency Instrument), NETNoise Equivalent Temperature_WHT (HFI(Planck) High Frequency Instrument), NETNoise Equivalent Temperature_OOF (HFI(Planck) High Frequency Instrument), F_KNEE, ALPHA, F_MIN (LFI(Planck) Low Frequency Instrument), F_MAX (LFI(Planck) Low Frequency Instrument
Three NETs are given: one determined from the total noise (rms of the noise timeline, excluding glitched data and other non-valid data), one determined from the white noise level of the noise amplitude spectrum, and one determined from fitting a 1/f noise spectrum, described by the function to the noise Power spectrum. In the latter, the F_KNEE and ALPHA parameters are the frequency where the 1/f component meets the white noise level, and the slope of the former. so that the slope is is about twice the slope of the amplitude spectrum. The NETs are in units of Kcmb * sqrt(s) for 30 - 353 GHz, and MJy/sr * sqrt(s) for 545 and 857 GHz.
Detector sampling frequency - F_SAMP, which is self-explanatory.

In the HFI(Planck) High Frequency Instrument RIMOreduced IMO, this table includes entries for the RTSrandom telegraphic signal bolometers (143-8 and 545-3), which are approximate or 0.00 when not evaluated.

## Map-level parameter data

The map-level data table contains the effective beam solid angle (total and out to different multiples of the beamFWHM) and noise information. It is written into a BINTABLE extension named MAP_PARAMS whose structure is different for HFI(Planck) High Frequency Instrument and LFI(Planck) Low Frequency Instrument and is as follows. The noise description below is very simplified; a more accurate rendition can be obtained from the half-ring maps. Regarding the characterization of systematics, the user should use the survey differences.

### HFI(Planck) High Frequency Instrument

FREQUENCY (String)
a 3-digit string giving the reference frequency in GHz, i.e., of the form 217
OMEGA_F, OMEGA_F_ERR (Real*4)
the full beam solid angle and its uncertainty, in armin2
OMEGA_1, OMEGA_1_DISP (Real*4)
the beam solid angle out to 1FWHM, and its dispersion, in arcmin2
OMEGA_2, OMEGA_2_DISP (Real*4)
the beam solid angle out to 2FWHM, and its dispersion, in arcmin2
FWHMFull-Width-at-Half-Maximum (Real*4)
FWHMFull-Width-at-Half-Maximum of a Gaussian beam having the same (total) solid angle, in armin2. This is the best value for source flux determination
FWHMGAUS (Real*4)
FWHMFull-Width-at-Half-Maximum derived from best Gaussian fit to beam maps, in armin2. This is the best value for source identification
NOISE (Real*4)
This is the typical noise/valid observation sample as derived from the high-l spectra of the half-ring maps, in the units of the corresponding map

For the Omega columns, the 'DISP' (for dispersion) column gives an estimate of the spatial variation as a function of position on the sky. This is the variation induced by combining the scanning beam determined from the planet observations with the scanning strategy, as described in Beams.

### LFI(Planck) Low Frequency Instrument

FREQUENCY (String)
a 3-digit string giving the reference frequency in GHz, i.e., of the form 030, 044, 070
FWHMFull-Width-at-Half-Maximum (Real*8)
FWHMFull-Width-at-Half-Maximum of a Gaussian beam having the same (total) solid angle, in arcmin
NOISE (Real*8)
This is the average noise in Ts1/2
CENTRALFREQ (Real*4)
This is the average central frequency in GHz
FWHMFull-Width-at-Half-Maximum_EFF, FWHMFull-Width-at-Half-Maximum_EFF_SIGMA (Real*4)
This is the average FWHMFull-Width-at-Half-Maximum of the effective beam, in arcmin, and its dispersion
ELLIPTICITY_EFF, ELLIPTICITY_EFF_SIGMA (Real*4)
This is the average ellipticity and its dispersion
SOLID_ANGLE_EFF, SOLID_ANGLE_EFF_SIGMA (Real*4)
This is the average full beam solid angle, in arcmin2, and its dispersion

## Effective band transmission profiles

The effective filter bandpasses are given in different BINTABLE extensions. The extension is named BANDPASS_{name}, where name specifies the detector or the maps. For the latter, the bandpasses are a weighted average of the bandpasses of the detectors that are used to build the map, using the same weights that are used in the mapmaking. These merged bandpasses are given for the full channel maps (all detectors of the frequency channel) and for the PSBs only in each frequency channel for HFI(Planck) High Frequency Instrument. For details on the measurements and compilation of the bandpasses see Planck-2013-IX[3]. For details on the measurements and compilation of the LFI(Planck) Low Frequency Instrument bandpasses see Planck-2015-A05[4].

The bandpasses are given as 4-column tables containing:

### HFI(Planck) High Frequency Instrument

WAVENUMBER (Real*4)
the wavenumber in cm-1, conversion to GHz is accomplished by multiplying by [mks].
TRANSMISSION (Real*4)
the transmission (normalized to 1 at the max for HFI(Planck) High Frequency Instrument)
ERROR (Real*4)
the statistical uncertainty for the transmission profile.
FLAG (Integer)
a flag indicating if the data point is an independent frequency data point (nominally the case), or an FTS instrument line shape (ILSInstrument Line Shape)-interpolated data point. The frequency data has been over-sampled by a factor of ~10 to assist in CO component separation efforts Planck-2013-IX[3]Planck-2013-XIII[5].

The number of rows will differ among the different extensions, but are the same, by construction, within each extension. Tables with the unit conversion coefficients and color correction factors for the HFI(Planck) High Frequency Instrument detectors (and LFI(Planck) Low Frequency Instrument in some instances), including uncertainty estimates based on the uncertainty of the HFI(Planck) High Frequency Instrument detector spectral response are given in this appendix.

### LFI(Planck) Low Frequency Instrument

WAVENUMBER (Real*8)
the wavenumber in GHz.
TRANSMISSION (Real*8)
the transmission (normalized to have an integral of 1 for LFI(Planck) Low Frequency Instrument)
UNCERTAINITY (Real*4)
the statistical uncertainty for the transmission profile (not provided for LFI(Planck) Low Frequency Instrument)
FLAG (Character)
a flag, not used by now by the LFI(Planck) Low Frequency Instrument

The number of rows will differ among the different extensions, but are the same, by construction, within each extension.

## Detector noise spectra (Only HFI(Planck) High Frequency Instrument)

HFI(Planck) High Frequency Instrument
these are the ring noise amplitude spectra averaged over about 5000 rings in order to give a representative spectrum. The spectra of all 50 valid bolometers are given in a single table. The spectra have a maximum frequency (Nyquist) of 90.18685Hz, also given the the F_NYQ keyword, and are built over 32768 points, giving a lower frequency of 2.75 mHz.

The keyword F_NYQ gives the Nyquist frequency, and can be used together with the number of points in the spectrum to reconstruct the frequency scale. The BINTABLE has Ndetector columns by Npoints rows.

## Beam Window Functions

Beam window functions and associated error descriptions are written into a BINTABLE for each detection unit, where detection unit consists of an auto or a cross product (for HFI(Planck) High Frequency Instrument only) of one (or two) frequency maps or detset maps used in the likelihood. Here they are:

For the HFI(Planck) High Frequency Instrument
• the 6 HFI(Planck) High Frequency Instrument frequency channels + 3 psb-only subsets, producing 45 extensions
• 100, 143, 217, 353, 545, 857, 143p, 217p, 353p
• 26 detsets, producing 351 extensions; the detsets used are, by frequency channel:
• 100-DS1, 100-DS2,
• 143-DS1, 143-DS2, 143-5, 143-6, 143-7,
• 217-DS1, 217-DS2, 217-1, 217-2, 217-3, 217-4,
• 353-DS1, 353-DS2, 353-1, 353-2, 353-7, 353-8,
• 545-1, 545-2, 545-4,
• 857-1, 857-2, 857-3, 857-4

Note for HFI(Planck) High Frequency Instrument these (and also the associated covariance matrices) are given in separate files named HFI(Planck) High Frequency Instrument_RIMOreduced IMO-Beams-nnnpc_Rm.nn.fits, where nnn is 100 or 075 and indicates the percentage (pc) of the sky included (see Masks and Beams sections).

For the LFI(Planck) Low Frequency Instrument
• the 3 LFI(Planck) Low Frequency Instrument frequency channels (auto- products only), producing 3 extensions
• 30, 44, 70
• the 3 LFI(Planck) Low Frequency Instrument 70GHz detector pairs (auto- products only), producing 3 extensions
• 18-23, 19-22, 20-21

The extension names are of the form BEAMWF_U1XU2 where U1 and U2 are one (possibly the same) detection unit from one of the main groups above (i.e. there are no cross products between detsets and frequency channels, or between HFI(Planck) High Frequency Instrument and LFI(Planck) Low Frequency Instrument). Each extension contains the columns:

NOMINAL (HFI(Planck) High Frequency Instrument, Real*4)
the beam window function proper,
BL (LFI(Planck) Low Frequency Instrument, Real*4)
the beam window function proper,
EIGEN_n (Real*4, n=1-5 for the HFI(Planck) High Frequency Instrument, n=1-4 for the LFI(Planck) Low Frequency Instrument)
the five/four corresponding error modes.

and the following keywords give further information, only for the HFI(Planck) High Frequency Instrument:

NMODES (Integer)
the number of EIGEN_* modes,
LMIN and LMAX (Integer)
the starting and ending (both included) multipoles of the vectors NOMINAL and EIGEN_*
LMIN_EM and LMAX_EM (Integer)
that give the range of the valid samples of the EIGEN_* vectors. Here LMAX_EM is always less than or equal to LMAX. On the range LMAX_EM+1 to LMAX the values of EIGEN_* are set to NaN, while the values of NOMINAL only are a Gaussian extrapolation of the lower multipole window function, only provided for convenience.
CORRMAT (string)
the name of the extension containing the corresponding beam correlation matrix

## Beam Correlation Matrix

Two beam correlation matrices are given for the HFI(Planck) High Frequency Instrument, in two IMAGE extensions:

CORRBEAM_FREQ (Real*8)
for the frequency channels (21 units), 105x015 pixel matrix,
CORRBEAM_DSET (Real*8)
for the detsets (351 units), 1755x1755 pixel matrix

Each is a symmetric matrix with 1-valued diagonal, made of NBEAMS*NBEAMS blocks, each block being NMODES*NMODES in size. The n$^{th}$ row- (and column-) block entry relates to the B(l) model whose name is indicated in ROWn = BEAMWF_U1XU2 keywords, and the corresponding eigenmodes are stored in a HDU of the same name.

Each extension contains also the following keywords:

NDETS (Integer)
the number of detector units
NBEAMS (Integer)
the number of beams = NSETS * (NSETS+1) / 2
NMODES (Integer)
here 5
L_PLUS (Integer)
Eigenmode > 0 to break degeneracies
BLOCKn (string)
for n=1-NBEAMS, gives the name of the extension containing the beam WF and error eigenmodes for the nth block

and some other ones for internal data checking and traceability

No beam correlation matrices are produced by the LFI(Planck) Low Frequency Instrument by now. And for HFI(Planck) High Frequency Instrument these, together with the beam window functions, are given in a file separate from the main RIMO (see subsection above).

## References

1. Planck 2015 results. II. LFI processing, Planck Collaboration, 2016, A&A, 594, A2.
2. Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beam processing, Planck Collaboration, 2016, A&A, 594, A7.
3. Planck 2013 results. IX. HFI spectral response, Planck Collaboration, 2014, A&A, 571, A9
4. Planck 2015 results. IV. LFI beams and window functions, Planck Collaboration, 2016, A&A, 594, A4.
5. Planck 2013 results. XIII. Galactic CO emission, Planck Collaboration, 2014, A&A, 571, A13