The Scientific Performance of Planck

The performance of Planck is largely driven by that of its instruments. The Table below (as well as the printable version) is an overview of the main instrumental characteristics and goal performance:

Estimated Planck Instrument Performance Goals
Telescope	1.5 m. (proj. apert.) aplanatic; shared focal plane; 1%
	Viewing direction offset 85o from spin axis; Field of View ~8o
Instrument	LFI^			HFI
Center Frequency (GHz)	30	44	70	100	143	217	353	545	857
Detector Technology	HEMT radio receiver arrays			Bolometer arrays
Detector Temperature	20 K			0.1 K
Cooling Requirements	H2 sorption cooler			H2 sorption + 4K J-T stage + Dilution
Number of Unpolarised Detectors	0	0	0	0	4	4	4	4	4
Number of Linearly Polarised Detectors	4	6	12	8	8	8	8	0	0
Angular Resolution (arcmin)	33	24	14	9.5	7.1	5.0	5.0	5.0	5.0
Bandwidth (GHz)	6	8.8	14	33	47	72	116	180	283
Average per pixel	2.0	2.7	4.7	2.5	2.2	4.8	14.7	147	6700
Average * per pixel	2.8	3.9	6.7	4.0	4.2	9.8	29.8
^ Due to financial reasons, the 100 GHz channel of LFI has been deleted from the baseline payload in January 2003.
Sensitivity (1) to intensity (Stokes I) fluctuations observed on the sky, in thermodynamic (x10-6) temperature units, relative to the average temperature of the CMB (2.73 K), achievable after two sky surveys (14 months).
A pixel is a square whose side is the FWHM extent of the beam. Note that these figures are calculated for the average integration time per pixel. In fact the integration time will be very inhomogeneously distributed on the sky and will be much higher in certain regions of it.
*Sensitivity (1) to polarised intensity (Stokes U and Q) fluctuations observed on the sky, in thermodynamic (x10-6) temperature units, relative to the average temperature of the CMB (2.73 K), achievable after two sky surveys (14 months).

It is important to emphasize that the above performance levels are goals rather than requirements. This means that the instruments have been designed to reach or exceed the goal performances. The required performances are less stringent than the goals (by a factor of about 2 in the case of sensitivities), and represent the minimum performance that must be achieved in order to fulfill the objectives of the mission. All Planck channels have already demonstrated their ability to meet the required performances, and a good fraction of them have also demonstrated the goal performances.

In addition, the above table represents only the raw instrumental performance. The final, scientifically relevant performance of the mission will depend not only on the raw instrumental performance, but also on the detailed nature of various astrophysical foregrounds (such as galactic and extragalactic emissions), the behavior of many systematic effects which produce spurious signals (such as straylight), and the ability to remove these signals from the measured data by means of data processing algorithms. The current estimates of the scientific performance of Planck are based on simulations of the measurement process, which include such effects to the best of available knowledge.

One of the principal objectives of Planck is to produce maps of the whole sky in nine frequency channels. These maps will include not only the CMB itself, but also all other astrophysical foregrounds. A typical simulated map (in this case at 100 GHz) is shown below. The angular resolution and intrinsic noise characteristics of the detectors limits the fidelity of these maps; systematic effects and calibration uncertainties add to the uncertainty.

Figure 1: A simulation of the 100 GHz map of the sky as seen by Planck, in ecliptic coordinates (sinusoidal projection). The CMB dipole component is not included in this map. The scale is in degrees Kelvin. The main feature seen is the disk of the Milky Way.

All nine Planck sky maps will be combined to produce a single map of the Cosmic Microwave Background anisotropies. The key that allows to reach this objective is the wide spectral coverage achieved by Planck. Each astrophysical foreground has a distinct (albeit at present poorly known) spectral characteristic. Specialized data processing algorithms will use this information to iteratively extract the signal due to each foreground component, until only the CMB signal remains. Instrumental systematic effects, as well as local uncertainties in the parameters characterizing the foregrounds will degrade the intrinsic detector noise level. The angular resolution achieved in the map will be between 5 and 10 arcminutes, depending on the details of the data processing and the foregrounds. Clearly, near the galactic plane the CMB will be swamped by the (strongly fluctuating) galactic emission. An impression of what the final CMB anisotropy map may look like is provided by the simulation below. The basic scientific goal of the Planck mission is to measure the CMB anisotropies at all angular scales larger than 10 arcminutes, with an accuracy set by astrophysical limits, i.e. small scale fluctuations of foreground emission.

Figure 2: A simulation of the CMB anisotropies at an angular resolution and sensitivity level typical of what can be achieved by Planck, based on a ₀="1" CDM model.

All of the information present in the CMB component will be used to derive its angular power spectrum, an example of which is shown here below. The angular power spectrum is a statistical description of the distribution of CMB temperatures on the sky.

Figure 3: This is a simulation (taken from W. Hu's web page) of the angular power spectrum of the CMB as recovered from Planck data. The simulation assumes a given spectrum for the sky (this is shown by the continuous line), then simulates the observation process (in this case using 3 LFI channels, 4 HFI channels and 3 HFI polarization channels). The vertical boxes show the uncertainty range in the recovery of each multipole (the corresponding angular scale is shown on the top horizontal scale). Recovery of the polarized CMB component is also shown. At large angular scales the uncertainties are limited by cosmic variance, while at small angular scales they are limited by the angular resolution and sensitivity of the instruments. This particular simulation did not take into account systematic effects and foreground removal, which would increase the size of the boxes.

The shape of the angular power spectrum is very sensitively dependent on fundamental cosmological parameters, such as the rate of expansion, the density of the Universe, its curvature, and many others. Therefore the Planck data can be used to constrain them to high accuracy. The Table below shows estimates of the accuracy with which some of these parameters can be recovered, using either of the two on-board instruments. Clearly the combination of both will increase the accuracies finally achieved.

Table 1: 1 errors in estimates of cosmological parameters (spatially flat universe), from Efstathiou and Bond 1999. We use the notation _i = _i h² to denote physical densities ( _b, _c and are the baryon, CDM and cosmological constant densities, respectively). Q denotes the quadrupole amplitude, n_s (n_t) stands for the scalar (tensor) spectral index, while h is the Hubble constant. The first column denotes the errors in the recovery of parameters when no constraints on them are made. The second assumes a specific relationship between tensor (gravitational wave) and scalar modes. The third column assumes no tensor modes are present.

Parameter	No constraints	r=-7 nt	r=0
b/ b	0.0064	0.0056	0.0056
c/ c	0.0042	0.0042	0.0039
	0.012	0.012	0.011
Q	0.0013	0.0010	0.0011
r	0.33	0.023	------
ns	0.0049	0.0032	0.0042
nt	0.4	0.0032	------
h/h	0.0045	0.0045	0.041

Planck will not only yield CMB anisotropies, but also near-all-sky maps of all the major sources of microwave emission, opening a broad expanse of astrophysical topics to scrutiny. Some highlights chosen among these topics are summarized in Table 2.