---
bibliography:
- 'Planck\_bib.bib'
- 'Zodi.bib'
- 'SSO4ken/SSO\_extra.bib'
title: ' 2013 results. XIV. Zodiacal emission'
---

,[–]{}

Introduction {#sec:introduction}
============

This paper, one of a set associated with the 2013 release of data from the [^1] mission [@planck2011-1.1], describes the measurement of Zodiacal emission using  data.

Zodiacal light, or the reflection of sunlight from small dust particles in our Solar System, can be seen by eye at dawn or dusk in dark locations, and contributes significantly to the diffuse sky brightness at optical and near-infrared wavelengths. The study of Zodiacal emission, or the thermal re-emission of absorbed energy from these interplanetary dust (IPD) particles has been enabled by the advent of infrared astronomical techniques, and it is now known to dominate the diffuse sky brightness over most of the sky between 10 and 50$\micron$ [see, for example, @Leinert1997].

Full-sky, infrared satellite surveys, in particular, have allowed us to begin to determine the structure of the density of the IPD [@Hauser84; @kelsall1998; @fixsendwek2002; @Pyo2010]. One of the full-sky models of Zodiacal emission most easily adapted for  and most commonly used at longer wavelengths is based on work from the Cosmic Background Explorer Diffuse Infrared Brightness Experiment (*COBE*/DIRBE) team [@kelsall1998 hereafter K98]. Others are presented in [@Good1986], [@Rowan-Robinson1990; @Rowan-Robinson1991], [@Jones1993], [@Vrtilek1995], [@Wright1998], and [@Rowan-Robinson2012]. The K98 model comprises the well-known diffuse cloud, three sets of dust bands first discovered by *IRAS* [@Low1984], and a circumsolar ring and Earth-trailing feature, hinted at in *IRAS* and confirmed in DIRBE [called a ‘blob’ in K98. See @Reach1995 and references therein].

@fixsendwek2002 have used data from the Far Infrared Absolute Spectrophotometer (FIRAS) to extend measurements of the diffuse cloud to longer wavelengths, but given its modest angular resolution and large uncertainties in the submillimetre region, could not say more about the smaller angular-scale Zodiacal features. ’s sensitivity allows it to detect and measure the emissivity of the diffuse Zodiacal cloud at long wavelengths, and its angular resolution also allows it to characterize the smaller-scale components of the Zodiacal.

This paper continues as follows: in Sect. \[sec:planck:mission\] we describe the relevant aspects of the  mission for this analysis, along with it’s observation strategy and data processing; in Sect. \[sec:detection\] we describe how  detects Zodiacal emission; and in Sect. \[sec:model\] we briefly describe the *COBE* Zodiacal emission model. The fit to the /HFI data is described in Sect. \[sec:fit\], and the results of the fit are discussed in Sect. \[sec:discussion\]. We conclude in Sect. \[sec:conclusion\].

The  Mission {#sec:planck:mission}
============

, comprised of the High Frequency Instrument, or HFI, and the Low Frequency Instrument, or LFI, was launched in May of 2009. The mission as a whole is described in [@planck2013-p01]. This work uses only data at frequencies of 100GHz and higher. At these frequencies,  observed the entire sky in six broad frequency bands from 100 to 857GHz, with corresponding angular resolutions from roughly 97 to 46 [@planck2013-p03c].

Orbit, Scanning Strategy and Dates of Observation
-------------------------------------------------

While ’s orbit and scanning strategy are described in depth in [@planck2011-1.1] and [@planck2013-p01], we give a synopsis of the elements relevant to our analysis here.

 orbits around the second Sun-Earth Lagrange point, and is thus always close to the Ecliptic plane and about 1.01 AU from the Sun and 0.01 AU from the Earth. Its focal plane scans the sky once per minute, with each detector always observing on a circle approximately $85^\circ$ from its spin axis. A simplified video showing this scanning strategy can be found at the ESA website[^2]. In addition, and not visible in the video noted above, the spin axis traces the Sun-Earth vector, but with an additional “cycloid” component, so that in the Sun-Earth frame the spin axis is always $7.5^\circ$ degrees from the Sun-Earth vector and circles around it twice per year. This cycloid component results in differing total amounts of IPD in ’s line of sight for different observations of the same point on the distant celestial sphere. This is shown schematically in Fig. \[fig:Scan\].

![ Schematic representation of the geometry of ’s measurements, which shows that it can view different amounts of Zodiacal emission while looking at the same point on the distant sky. The plane of the ecliptic is in the plane of the diagram. The Sun is in the center of the circles. The solid black line represents the orbit of the Earth and . The dashed line at the outer edge of the shaded ring represents the orbit of Jupiter, beyond which we assume there is no contribution to the Zodiacal emission from IPD. Panel (a) shows a case where the phase of the scan cycloid and the location of the observed point on the sky yield two measurements for which the lines of sight through the IPD is roughly equal, and the same Zodiacal signal is seen. Panel (b) shows a case where the phase of the scan cycloid and the location of the observed point on the sky yield different total columns of IPD along the lines of sight, and thus a different Zodiacal signal is seen in each of the two measurements. *Note that this figure is highly stylized and not to scale.* []{data-label="fig:Scan"}](Scan.pdf){width="88mm"}

As nearly the entire sky is seen twice each year, the Planck team divides the observations into “surveys” of approximately six-month duration. The exact definition of the beginning and end of each survey was agreed upon within the  team. The basic characteristics are that each survey lasts about six months and covers a maximum of sky, with a minimum of overlap between the beginnings and ends of the survey. During any single one of these surveys, some pixels near the ecliptic poles are observed multiple times, as are the pixels near the ecliptic plane which are seen both at the beginning and at the end of the survey. The bulk of the sky, however, is observed only during well-defined periods, usually less than a single week. In Fig. \[fig:jd\] we show the Julian dates of observations of those pixels on the sky for which the observation times during survey 1 spanned one week or less. The analogous plot for survey 2 is similar in nature, and the corresponding maps for surveys 3 and 4 are quite similar to those of surveys 1 and 2, as the scanning strategy for surveys 3 and 4 were almost identical to those of surveys 1 and 2, respectively.

![The Julian date of observation of pixels on the sky during survey 1, for a single detector, in Galactic coordinates. There are only very small differences between maps for different detectors. The grid lines show ecliptic coordinates, with the darker lines representing the ecliptic plane and the line of zero ecliptic longitude. Undefined pixels, which were either not observed at all, or which were observed multiple times over a period that spanned more than one week and are thus not used in this analysis, are shown as the uniform gray band.[]{data-label="fig:jd"}](jd_h857-1_s1_d07_v53.jpg){width="88mm"}

Data Processing
---------------

The overall HFI data processing is described in [@planck2011-1.7] and [@planck2013-p03]. Given the time-dependent nature of the Zodiacal signal seen with the  scanning strategy, this analysis is done using the individual survey 1-4 maps. This allows us to exclude from the analysis regions of the sky and periods of time where the column of IPD viewed by  is not constant.

The HFI instrument has a number of horns at each measurement frequency [@planck2013-p03c Fig. 9]. Working with individual horn maps, rather than the co-added frequency maps, allows us to adjust the response of each detector so that they are uniform for a source with a Zodiacal spectrum, rather than that used for a CMB spectrum, as is done in the standard processing [@planck2013-p03d]. At 100, 143, 217, and 353GHz, some of these horns contain two polarization sensitive bolometers [PSBs; @Jones2003]. As we are not addressing polarisation here, for those horns that have PSBs, we combine the maps from each of the two detectors within the given horn with a simple average.

As the evaluation of the model to be presented in Sect. \[sec:model\] involves calculating emission from a number of points along each line of sight and summing them, the computations are time consuming. To mitigate this to some extent, we use $13\parcm7\times13\parcm7$ pixels, rather than the original $1\parcm7\times1\parcm7$ HFI pixels, reducing the number of map pixels from 50 million to a bit less than 800 thousand [that is, we use HEALPix pixels with $N_\mathrm{side}$ of 256 rather than 2048; @gorski2005]. While this does reduce our sensitivity to finer scale structures, it is not a serious hindrance, since we will be making comparisons with DIRBE, which had a still larger beam. Smaller pixels will be used in future work as more detail is teased out of the data.

Pre-launch estimates of ’s ability to detect Zodiacal emission and an estimate of the possible level of contamination at the highest  frequencies were presented in [@maris2006]. More recent predictions have addressed the possibility of Zodiacal contamination at lower frequencies [@diego2010] and speculated that emission from dust in the outer Solar System might contribute to large-scale anomalies which have been reported in data from the Wilkinson Microwave Anisotropy Probe (*WMAP*) at large angular scales [@maris2011; @Hansen2012].

Detection {#sec:detection}
=========

The existence of the Zodiacal emission in the  maps is straightforward to demonstrate by exploiting the fact, noted above, that different  surveys often sample different columns of IPD while observing the same location on the distant celestial sphere. Fig. \[fig:surveymaps\] shows the first (top) and second (middle) survey maps for the 857-1 detector, along with the difference of these two maps (bottom). Similar differences for all HFI frequencies, using data from all horns at each frequency, are shown in the left-hand panel of Fig. \[fig:beforeAndAfterJackknives\]. There are at least three features that stand out in the map difference: (1) The scale has been reduced immensely, but the Galactic plane is still visible in this difference map; (2) the “arcs” at the top and the bottom of the difference map are the images of the Galactic centre as seen through the instrument’s far sidelobes (FSLs); and (3) the Zodiacal emission can be seen as the variations following the ecliptic plane. We begin with the Zodiacal emission.

![Single-survey maps in Galactic coordinates for the 857-1 detector. *Top:* Survey 1 map. *Middle:* Survey 2 map. *Bottom:* Survey 2 minus survey 1 difference map. This bottom image shows the Zodiacal emission and the residual Galactic emission effects discussed in the text. The units are MJy/sr, assuming a spectrum inversely proportional to frequency. Undefined pixels are shown in gray. These occur in pixels which either have not been observed during the survey, were observed during the passage of a planet, or a small number of other events. In the top two plots, pixels which were observed over periods longer than a week were not masked, and thus the masked regions are smaller in the top two images than that in the difference (bottom) panel.[]{data-label="fig:surveymaps"}](857-1_W_TauDeconv_survey1_I.jpg "fig:")\
![Single-survey maps in Galactic coordinates for the 857-1 detector. *Top:* Survey 1 map. *Middle:* Survey 2 map. *Bottom:* Survey 2 minus survey 1 difference map. This bottom image shows the Zodiacal emission and the residual Galactic emission effects discussed in the text. The units are MJy/sr, assuming a spectrum inversely proportional to frequency. Undefined pixels are shown in gray. These occur in pixels which either have not been observed during the survey, were observed during the passage of a planet, or a small number of other events. In the top two plots, pixels which were observed over periods longer than a week were not masked, and thus the masked regions are smaller in the top two images than that in the difference (bottom) panel.[]{data-label="fig:surveymaps"}](857-1_W_TauDeconv_survey2_I.jpg "fig:")\
![Single-survey maps in Galactic coordinates for the 857-1 detector. *Top:* Survey 1 map. *Middle:* Survey 2 map. *Bottom:* Survey 2 minus survey 1 difference map. This bottom image shows the Zodiacal emission and the residual Galactic emission effects discussed in the text. The units are MJy/sr, assuming a spectrum inversely proportional to frequency. Undefined pixels are shown in gray. These occur in pixels which either have not been observed during the survey, were observed during the passage of a planet, or a small number of other events. In the top two plots, pixels which were observed over periods longer than a week were not masked, and thus the masked regions are smaller in the top two images than that in the difference (bottom) panel.[]{data-label="fig:surveymaps"}](survey_jack_857-1_year1.jpg "fig:")

Since these are difference maps, the Zodiacal emission is seen in the ecliptic plane as both positive and as negative, depending upon the relative geometry of the IPD and the  satellite when a given location was observed in the two surveys. While the amplitude of the Zodiacal emission signal is reduced in this differential process [this will be described in Sect. \[sec:model\], and in particular Fig. \[fig:zodiMaps\]; see also @maris2006], it has the advantage that the bulk of the Galactic and extra-galactic signal, the main contaminants in the analysis at high frequencies, is efficiently removed with little effort. What remains of the Galactic signal arises from effects such as beam asymmetries and imperfections in the transfer function removal [@planck2013-p03c]. To mitigate these residual Galactic effects, we generally do not use data within 10 degrees of the Galactic plane in this analysis. We have confirmed that changing this cut to 5 or to 20 degrees does not change the conclusions of this analysis, and emphasize that contrary to other analyses, the fact that we are analysing difference maps makes this work less sensitive to Galactic contamination.

It should be noted that the Zodiacal emission is much dimmer than many other background components in the  data. Whereas the Zodiacal emission dominates the sky in some *IRAS* and *COBE* bands, this is never the case for , with the cosmic infrared background and Galactic dust dominating at high frequencies, and the CMB itself dominating at lower frequencies. This makes our differencing scheme appealing, but also restricts the analysis in some ways. It is, for example, difficult to look at individual scans, or slices of the sky, as has been done successfully with *IRAS*. We are obligated to use almost the entire sky, and use a model of the Zodiacal emission to interpret variations, rather than being able to directly interpret the total Zodiacal emission on the sky.

Model {#sec:model}
=====

The goal of this section is to describe the Zodiacal and far sidelobe templates we will create to fit to the map at the bottom of Fig. \[fig:surveymaps\].

Zodiacal Components
-------------------

The *COBE*/DIRBE Zodiacal emission model is described in depth in K98, but we review the salient parts here.

### Diffuse cloud {#sec:cloudmath}

The density of the diffuse IPD cloud, having both radial and vertical dependence, is taken to be of the form $$n_c\left(\mathbf{R}\right)
   =
   n_0
   R_c^{-\alpha}
   \left\{
    \begin{array}{cl}
     e^{-\beta\left(\zeta^2/2\mu\right)^\gamma} 
      & \mathrm{if}\ \zeta <  \mu \\
     e^{-\beta\left(\zeta -\mu/2\right)^\gamma} 
      & \mathrm{if}\ \zeta\geq\mu \\
    \end{array}
   \right.,$$ where $$R_c 
    = 
    \sqrt{\left(x-x_0\right)^2 + 
          \left(y-y_0\right)^2 +
          \left(z-z_0\right)^2},$$ $$\zeta = \left|Z_c\right|/R_c,$$ $$\begin{aligned}
    Z_c
    & = & 
    \left(x-x_0\right)
    \cdot\sin\left(\Omega_R\right)
    \cdot\sin\left(i_R\right) 
    \nonumber
    \\
    & - &
    \left(y-y_0\right)
    \cdot\cos\left(\Omega_R\right)
    \cdot\sin\left(i_R\right) 
    + \left(z-z_0\right)\cdot\cos(i_R),
  \end{aligned}$$ and $\alpha$, $\beta$, $\gamma$, $\mu$, $x_0$, $y_0$, $z_0$, $\Omega_R$, and $i_R$ are parameters describing the location and shape of the cloud. This form (and others used elsewhere which are similar) is based on an approximation of a model of particles orbiting the Sun, accounting for drag from the Poynting-Robertson effect, and with a modified fan distribution used to describe the changes in density above and below the plane of the ecliptic. See K98 for more details and references.

The numerical values for the parameters can be found in K98, or from the LAMBDA website[^3]. This is shown, for both survey 1 and survey 2, as well as their difference, assuming an emissivity of one, in the bottom row of Fig. \[fig:zodiMaps\].

$\begin{array}{cc|c}
     \includegraphics[width=60mm]{Z857JackSim_survey1_band3.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_band3.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_band3.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_band2.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_band2.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_band2.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_band1.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_band1.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_band1.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_cring.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_cring.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_cring.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_tblob.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_tblob.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_tblob.jpg}
   \\
   \hline
     \includegraphics[width=60mm]{Z857JackSim_survey1_cloud.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_cloud.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_cloud.jpg}
  \end{array}$

### Dust bands {#sec:bandmath}

The Zodiacal dust bands were first seen by *IRAS* [@Low1984], and appear as pairs of bright, parallel bands equally spaced above and below the ecliptic plane. They were quickly associated with asteroid families, and then understood to be the relics of asteroid collisions or collapses [@Dermott1984; @sykes86]. [@Reach1997] study them in detail.

The K98 model contains three bands[^4] called, reasonably enough, bands 1, 2 and 3. They appear at ecliptic latitudes around $\pm 1\pdeg4$, $\pm 10\deg$, and $\pm 15\deg$. *IRAS*, having higher angular resolution than DIRBE, was able find more bands, dubbed $\alpha$, $\beta$, $\gamma$, E/F, G/H, J/K, and M/N [@Sykes1990], though some are more firmly detected than others.

The K98 band 1, or *IRAS* band $\gamma$, was originally associated with the Eos family of asteroids [@Dermott1984], but [@Grogan2001] called this into question and @Nesvorny2003 [hereafter N03] found better correspondence with the Veritas family of asteroids.

K98 note that their band 2 is a blend of *IRAS* bands $\alpha$ and $\beta$ [@Sykes1990]. [@sykes86] tentatively associated the $\alpha$ band with the Themis family of asteroids, and @Nesvorny2008 [hereafter N08] has narrowed this association to a cluster within this family associated with the Beagle asteroid. The $\beta$ band was associated by [@sykes86] with the Koronis family of asteroids, and N03 narrowed this to the Karin cluster within the Koronis family. Anticipating the discussion in Sect. \[subsec:Bands\], we note also that the $\beta$ band appears brighter than the $\alpha$ band [@Sykes1988; @Reach1997; @Nesvorny2008].

K98 states that their band 3, that furthest from the ecliptic plane, has been associated with both the Io and Maria families of asteroids [@Sykes1988; @Reach1997], corresponding to *IRAS* bands J/K and M/N. N03 have more recently noted, however, that 4652 Iannini and/or 845 Naema may be better asteroid associations for the J/K band-pair and that 1521 Seinajoki may work better for the M/N pair. We summarize these associations in table \[tab:bandInfo\].

   K98   $\delta_\zeta$    *IRAS*    $i_p$         $i_p$          Type      Age            a        
  ----- ---------------- ---------- ------- ------ ----------- ------- ------------- -------------- -------
    1         8.78        $\gamma$   9.35      490 Veritas        9.26  C / Ch/...        8.3        3.169
                          $\alpha$   1.34      656 Beagle         1.34  .../.../ C    $\lesssim$10   3.157
                          $\beta$    2.11      832 Karin          2.11  .../.../ S        5.8        2.866
                                               845 Naema         11.96  .../ C /...   $\gtrsim$20     ...
                                              4562 Iannini       12.17  .../.../ S    $\lesssim$5    2.644
                            M/N      15.0     1521 Seinajoki     15.02  .../.../...       ...        2.852

For each of the three dust bands in the *COBE* model, the density is given by $$n_{B}\left(\mathbf{R}\right)
    =
    \frac{3N_0}{R}
    e^{-\left(\zeta/\delta_\zeta\right)^6}
    \left(1 + \frac{(\zeta/\delta_\zeta)^{p}}{v_B}\right)
    (1-e^{-(R/\delta_R)^{20}}),
    \label{eq:bandDensity}$$ where we have used a simplified notation based on that of K98, where one can also find the numerical values for the parameters. Note that Eqn. \[eq:bandDensity\] matches the code used for the Zodiacal model (which can be found on the LAMBDA website), but that there is a factor of $1/v_B$ difference between Eqn. \[eq:bandDensity\] and Eqn. 8 of K98 ($v_B$ is a shape parameter, not a frequency). Also, K98 assumed that the emissivities of the three sets of bands were all equal. We relax this assumption below and allow the emissivities of each of the sets of bands to be different. The bands are shown, assuming unit emissivity, as the first, second, and third rows in Fig. \[fig:zodiMaps\].

### Circumsolar ring and Earth-trailing feature {#sec:ringmath}

The functional form for the density of the circumsolar ring is taken to be $$n_{B}\left(\mathbf{R}\right)
   =
   n_{SR}\cdot e^{-\left(R-R_{SR}\right)^2/\sigma_{rSR}^2-\left|Z_R\right|/\sigma_{zSR}}.$$ Similar to the treatment of the bands, K98 assumed that the emissivity of the circumsolar ring was the same as that of the Earth-trailing feature, below. We also relax this assumption, and allow them to be different. The shape of the expected signal from the circumsolar ring is shown in the fourth row of Fig. \[fig:zodiMaps\].

The density of the Earth-trailing feature is given by $$n_{B}\left(\mathbf{R}\right)
    = 
   n_{TB}\cdot 
   e^{-\left(R-R_{TB}\right)^2/\sigma_{rTB}^2-\left|Z_R\right|/\sigma_{zTB}
                  -\left(\theta-\theta_{TB}\right)^2/\sigma_{\theta TB}^2}.$$ We note that for both the circumsolar ring and the Earth-trailing feature, there is a typo in the text of K98 – a factor of 2 in the denominator of the first and third terms in the exponential has been added in the text, compared to what is in the code. We follow the code. The expected signal from the Earth-trailing feature is shown in the fifth row of Fig. \[fig:zodiMaps\].

### Integrated Emission

The total Zodiacal emission is calculated as $$I_x\left(\nu\right) 
   = 
   \epsilon_x\int d\mathbf{R}
    \cdot 
   n_x\left(\mathbf{R}\right)
    \cdot 
   B\left(\nu, T\left(\mathbf{R}\right)\right),$$ where $x$ is the Zodiacal component, $\nu$ is the frequency, $\mathbf{R}$ is a location in the Solar System, and $B\left(\nu, T\left(\mathbf{R}\right)\right)$ is the Planck function for the given frequency and temperature at the given location, given by $T_0/R^\delta$, with $T_0$ and $\delta$ being parameters. $\epsilon$ is the emissivity for the given component, which we will be finding with our fit. $n_x$ is the density for the given component, described above. The integral is done along the line of sight, from the location of the satellite to 5.2AU.

Galactic Emission Seen Through Sidelobes {#subsec:galFSL}
----------------------------------------

Like all real telescopes,  has some small sensitivity to radiation arriving at the telescope from off-axis, often called spillover or ‘far sidelobes’. Note that here we are referring to light coming from more than five degrees from the instrument’s nominal pointing direction, which should not be confused with ‘near sidelobes’, discussed in the HFI transfer function and beams papers [@planck2013-p03c see also [@tauber2010b]]. Figure \[fig:sidelobeDiagram\] shows the main stray light routes.

![Origin of far sidelobes. The ‘SR Spillover’ (for ‘Secondary Reflector Spillover’; the lowest set of rays on the left of the figure) arrives at the focal plane from outside the secondary mirror, directly from the sky. The ‘PR Spillover’ (for ‘Primary Reflector Spillover’), arrives at the focal plane from above the primary mirror and reflects off of the secondary to arrive at the focal plane. The set of rays between these two contributions represents the main beam. The ‘baffle’ contribution, light reaching the focal plane after reflecting from the inner sides of the baffles, is not shown here. It is often included as part of the SR Spillover. Adopted from [@tauber2010b]. []{data-label="fig:sidelobeDiagram"}](Rays-sketch-2.pdf){width="88mm"}

The secondary reflector (SR) spillover arises from radiation that reaches the focal plane without reflecting off of the primary reflector. As such, a major component is radiation from the general direction of the telescope boresight, though well outside the main beam. The ‘baffle’ contribution to the SR spillover results from radiation which reflects off of the baffles to arrive at the focal plane. The primary reflector (PR) spillover arises from radiation that comes to the satellite from just above the primary mirror, reflects off the secondary mirror and arrives at the detectors.

At the highest  frequencies, the Galactic centre is bright enough to be seen through these far sidelobes, even if faintly. Since the orientations of these sidelobes change as the instrument scans, the survey differences done to detect the Zodiacal emission are also sensitive tests of the FSLs. Though the Galactic emission mechanism and amplitude is different, analogous effects are discussed for the LFI in [@planck2013-p02d].

To this point, resource constraints have limited this study to a single far sidelobe calculation for all detectors. We use a GRASP calculation of the far sidelobes for the 353-1 horn [see Fig. 9 of @planck2013-p03c] and do not attempt to correct for differences in frequency or location for other horns. While this is not optimal, and will be improved in later releases, we note that the primary, large-scale features of the far sidelobes are defined by the telescope, rather that the horns or their placement, so first-order effects should be captured. Some of the limitations imposed by this are discussed in Sect. \[sec:farSidelobeResults\].

To make templates of what we might see from the Galactic centre through the far sidelobes, we use the  simulation software described in [@reinecke2006], but use GRASP calculations of the the various far sidelobe components instead of main beams. As inputs to the simulations, we use the actual  maps at the appropriate frequency. This allows us to account for differences in the brightness of the Galaxy as a function of frequency with minimal effort – the Galactic templates should already be calibrated in the correct units at the given frequency. The far sidelobe templates are made at the timeline level and run through the relevant parts of the pipeline software. In particular, the offset removal, or ‘destriping’ must be done on the templates before fitting in order to get reasonable fit results. The resulting templates made using these FSL calculations with a  857GHz sky as input are shown in the bottom three rows of Fig. \[fig:FSLs\].

$\begin{array}{cc|c}
     \includegraphics[width=60mm]{Z857JackSim_survey1_Dipolar_direct.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_Dipolar_direct.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_Dipolar_direct.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_Dipolar_secondary.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_Dipolar_secondary.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_Dipolar_secondary.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_Dipolar_baffle.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_Dipolar_baffle.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_Dipolar_baffle.jpg}
   \\
   \hline
     \includegraphics[width=60mm]{Z857JackSim_survey1_Galactic_direct.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_Galactic_direct.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_Galactic_direct.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_Galactic_secondary.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_Galactic_secondary.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_Galactic_secondary.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_Galactic_baffle.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_Galactic_baffle.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_Galactic_baffle.jpg}
  \end{array}$

One factor for which we do not account with these templates is the difference in spillover between the different frequencies [@Lamarre2010; @tauber2010b]. Since we illuminate more of the telescope at lower frequencies than at higher frequencies, if our templates simply scale with the spillover, we will expect different fit values for our templates at different frequencies.

To illustrate the relative contributions of these various templates, in Fig. \[fig:evolution\] we show a series of maps. Maps in each row are similar to those in the previous row, except that one more template or group of templates has been added to form the new row. For all rows, the first column corresponds to data from the first   survey, the second column corresponds to data from the second  survey, and the third column is the difference of the second column minus the first. The first row shows the sum of all the far sidelobes; the second row shows the result when we add dust band 1 to the far sidelobes – note that the scales change from the first to the second row; the third row shows the sum of the far sidelobes and the first two bands; the fourth row shows the sum of the far sidelobes and all the dust bands; the fifth row shows what’s in the fourth row, plus the circumsolar ring and Earth-trailing feature; finally, the bottom row shows the sum of the far sidelobes and all Zodiacal templates (and the scales have again changed). As this is simply illustrative, we have assumed unit emissivities for the Zodiacal components, and multiplied the far sidelobe components by a factor of 15 (which we will see in Sect. \[sec:fit\] is representative of the most extreme, multi-moded case). With these caveats in mind, the survey difference of the sums of all the components, the lower right image, can be compared to the bottom image in Fig. \[fig:surveymaps\].

$\begin{array}{cc|c}
     \includegraphics[width=60mm]{Z857JackSim_survey1_5.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_5.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_5.jpg}
   \\
   \hline
     \includegraphics[width=60mm]{Z857JackSim_survey1_6.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_6.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_6.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_7.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_7.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_7.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_8.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_8.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_8.jpg}
   \\
     \includegraphics[width=60mm]{Z857JackSim_survey1_10.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_10.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_10.jpg}
   \\
   \hline
     \includegraphics[width=60mm]{Z857JackSim_survey1_11.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_survey2_11.jpg}
   & \includegraphics[width=60mm]{Z857JackSim_surveyD_11.jpg}
  \end{array}$

Spectrum {#sec:fit}
========

We fit the data shown in the bottom panel of Fig. \[fig:surveymaps\], as well as the analogous data at other frequencies and for the second year of observations, to a constant plus combinations of the templates shown in Sect. \[sec:model\], Figs. \[fig:zodiMaps\] and \[fig:FSLs\].

For each fit, we assume that the survey difference map at sky pixel $p$, called $D_{p}$, can be modelled as $$D_{p} 
  = 
  \sum_t 
  \left(
   \epsilon_{2,t}\cdot T_{2,t,p}-\epsilon_{1,t}\cdot T_{1,t,p}
  \right)
  + \mathrm{constant},$$ where $\epsilon_{\left[1|2\right],t}$ is the emissivity fit for template $t$ during survey 1 or 2 at the given frequency and $T_{\left[1|2\right],t,p}$ is the value of the $t^\mathrm{th}$ template at pixel $p$ for survey 1 or 2, calculated as described in Sect. \[sec:model\]. For example, for our ‘basic’ fit, we will have 19 templates – one each for the diffuse cloud, circumsolar ring, Earth-trailing feature and each of the three dust bands, as well as one each for the Galactic far sidelobes. All of these are repeated twice; once for each survey in a yearly difference map. Finally we also fit to an overall constant, to which  is not sensitive. We then minimize $$\chi^2 = \sum_p \left(\Delta_{p} - D_{p}\right)^2.$$

Separating the templates into surveys has the disadvantage of increasing the number of parameters in our fits. While we do not expect either the emissivity of the Zodiacal emission or the far sidelobe calculations to change from survey-to-survey, we separate them in this way for two reasons. The first is simply as a basic reality check – if we see significant differences between fits to two different surveys, we should be sceptical. Beam asymmetries or transfer function effects, for example, might cause differences from survey-to-survey, as might imperfections in the model itself.

The second reason is to calculate the error bars. As just noted, we are often as concerned by systemic effects as much as by “random” noise. By separating the data by survey, we may calculate error bars using the standard error of the successive measurements as a proxy for the uncertainties, rather than propagating white noise estimates. This should allow us a more conservative estimate of our uncertainties, which accounts for model deficiencies or low levels of systematics which change by survey (the aforementioned beam asymmetries and transfer functions, for example).

A note about weighting: the bulk of the Zodiacal emission is, of course, in the ecliptic plane. , on the other hand, has more statistical weight, on a pixel-by-pixel basis, at the ecliptic poles. We therefore use uniform weights over pixels, rather than statistical weights, since this would down-weight specifically the regions with our signal.

As mentioned above, we fit each of the two years’ survey difference maps to a cloud, circumsolar ring, Earth-trailing feature, three bands and three far sidelobe templates, plus a constant. The results for the four 857 GHz horns are shown in Fig. \[fig:fit857\]. Averaging over horns and surveys at all six HFI frequencies yields Fig. \[fig:noDipoleSidelobesFit\]. Numerical values are given in tables \[tab:fullFit\], \[tab:fullFitBands\] and \[tab:galacticSidelobeFit\].

![image](1111101111000__857__10.0){width="180mm"}

![image](Emis_1111101111000_bcut10.0_T0286.0_delta0.4669_alpha1.337_beta4.142_gamma0.942_mu0.189)

   $\nu$ (GHz)                                            
  ------------- -------------------- -------------------- --------------------
       857         0.301 $\pm$ 0.008    0.578 $\pm$ 0.359    0.423 $\pm$ 0.114
       545         0.223 $\pm$ 0.007    0.591 $\pm$ 0.203   -0.182 $\pm$ 0.061
       353         0.168 $\pm$ 0.005   -0.211 $\pm$ 0.085    0.676 $\pm$ 0.149
       217         0.031 $\pm$ 0.004   -0.185 $\pm$ 0.143    0.243 $\pm$ 0.139
       143        -0.014 $\pm$ 0.010   -0.252 $\pm$ 0.314   -0.002 $\pm$ 0.180
       100         0.003 $\pm$ 0.022    0.163 $\pm$ 0.784    0.252 $\pm$ 0.455

  : Emissivities of the diffuse cloud, circumsolar ring, and Earth-trailing feature from fit result averages.[]{data-label="tab:fullFit"}

   $\nu$ (GHz)        Band 1              Band 2              Band 3
  ------------- ------------------- ------------------- -------------------
       857       1.777 $\pm$ 0.066   0.716 $\pm$ 0.049   2.870 $\pm$ 0.137
       545       2.235 $\pm$ 0.059   0.718 $\pm$ 0.041   3.193 $\pm$ 0.097
       353       2.035 $\pm$ 0.053   0.436 $\pm$ 0.041   2.400 $\pm$ 0.100
       217       2.024 $\pm$ 0.072   0.338 $\pm$ 0.047   2.507 $\pm$ 0.109
       143       1.463 $\pm$ 0.103   0.530 $\pm$ 0.073   1.794 $\pm$ 0.184
       100       1.129 $\pm$ 0.154   0.674 $\pm$ 0.197   1.106 $\pm$ 0.413

  : Emissivities of the three dust bands from fit result averages.[]{data-label="tab:fullFitBands"}

  ------- ----------------- ----- ----------------- ---------------- -------
   $\nu$                                                             
   (GHz)                               Direct            Baffle      
    100    -25.8 $\pm$ 5.7    7    26.3 $\pm$ 15.7   56.7 $\pm$ 5.7    10
    143    -9.1 $\pm$ 4.1     6    13.0 $\pm$ 4.8    23.8 $\pm$ 5.4    10
    217     0.6 $\pm$ 1.1     5     6.3 $\pm$ 2.1    6.5 $\pm$ 1.3      6
    353    -1.2 $\pm$ 0.5     1    -4.3 $\pm$ 2.1    3.6 $\pm$ 0.7      1
    545     7.7 $\pm$ 1.7    15     8.8 $\pm$ 3.1    7.9 $\pm$ 1.0      1
    857    17.1 $\pm$ 3.4    1.5   23.9 $\pm$ 4.2    16.7 $\pm$ 3.1   0.005
  ------- ----------------- ----- ----------------- ---------------- -------

  : Fit coefficients for the Galaxy seen through the far sidelobes.[]{data-label="tab:galacticSidelobeFit"}

$\begin{array}{cc|c}
   \includegraphics[width=60mm]{Z857SurveyJackknifeWiZodi.jpg} &
   \includegraphics[width=60mm]{Z857SurveyJackknifeNoZodi.jpg} &  
   \includegraphics[width=60mm]{Z857Correction.jpg} \\
   \includegraphics[width=60mm]{Z545SurveyJackknifeWiZodi.jpg} &
   \includegraphics[width=60mm]{Z545SurveyJackknifeNoZodi.jpg} &  
   \includegraphics[width=60mm]{Z545Correction.jpg} \\
   \hline
   \includegraphics[width=60mm]{Z353SurveyJackknifeWiZodi.jpg} &
   \includegraphics[width=60mm]{Z353SurveyJackknifeNoZodi.jpg} &  
   \includegraphics[width=60mm]{Z353Correction.jpg} \\
   \includegraphics[width=60mm]{Z217SurveyJackknifeWiZodi.jpg} &
   \includegraphics[width=60mm]{Z217SurveyJackknifeNoZodi.jpg} &  
   \includegraphics[width=60mm]{Z217Correction.jpg} \\
   \includegraphics[width=60mm]{Z143SurveyJackknifeWiZodi.jpg} &
   \includegraphics[width=60mm]{Z143SurveyJackknifeNoZodi.jpg} &  
   \includegraphics[width=60mm]{Z143Correction.jpg} \\
   \includegraphics[width=60mm]{Z100SurveyJackknifeWiZodi.jpg} &
   \includegraphics[width=60mm]{Z100SurveyJackknifeNoZodi.jpg} &  
   \includegraphics[width=60mm]{Z100Correction.jpg} 
   \end{array}$

Discussion {#sec:discussion}
==========

As discussed in the HFI processing paper [@planck2013-p03] and in the  explanatory supplement [@planck2013-p28], these fits are used to create the implied Zodiacal and sidelobe emission in each HFI observation, which can then be removed and the maps are recreated. The survey 2 minus survey 1 difference maps for the 857-1 horn both before and after Zodiacal and far sidelobe removal, are shown in Fig. \[fig:beforeAndAfterJackknives\]. In this section we discuss the fit implications further.

Far Sidelobes {#sec:farSidelobeResults}
-------------

In addition to fit values obtained for the Galaxy seen in each component of the far sidelobes, the Cols. labelled ‘Pred.’ in table \[tab:galacticSidelobeFit\] show the expected values of the spillover, normalized to that of the 353GHz channel, from [@tauber2010b]. These are the ratios of the expected spillover in each frequency, compared to that at 353GHz, the frequency for which the sidelobe calculations were done. Since the fit values account for the changes in Galactic emission with frequency, if our predictions and data were perfect, the fit values would match those of the predictions.

The FSL signature is clearly visible at 857GHz in the bottom panel of Fig. \[fig:surveymaps\], and this is reinforced in table \[tab:galacticSidelobeFit\]. As the 857 and 545GHz channels are multi-moded, the differences are not that surprising; it is difficult to do the calculations necessary for the prediction. In addition, the specifications for the horn fabrication were quite demanding, and small variations, though still within the mechanical tolerances, could give large variations in the amount of spillover.

For the lower frequency, single-moded channels, however, the situation is different. There is no clear detection of PR spillover. While the significant negative values may indicate some low-level, large-scale systematic, there seems to be nothing with the distinctive signature of primary spillover at frequencies between 100 and 353GHz.

For the direct contribution of the secondary SR spillover, the situation is similar at 353GHz, but at 217 and 143GHz we are finding a 3$\sigma$ detection at about the level expected, while at 100GHz the value is about 2.5 times higher than expected, though the signal-to-noise on the detection is less than 2$\sigma$. The baffle contribution to the SR spillover seems to be in accord with expectations at 353 and 217GHz, and higher than what is predicted at 100GHz.

The values for the PR spillover, which is the most distinctive of the far sidelobe patterns, and presumably the easiest to disentangle from other effects, would indicate that the PR spillover values in table 2 of [@tauber2010b] may be slightly overestimated. The values for the direct contribution of the SR spillover roughly confirm the far sidelobe calculations. The baffle contribution to the SR spillover seems a bit high. We take the ensemble of these numbers as rough confirmation that our beam calculations are not drastically incorrect, but do not use the specific numbers in either [@planck2013-p03c] or [@planck2013-p03b]. Similar conclusions are drawn for the LFI in [@planck2013-p02d].

We have also included a template of the Dipole as seen through the far sidelobes in the fits in some fits to check to see if they are detected. As expected, they are not. The results quoted above are from fits which do not include these Dipole templates.

Diffuse cloud {#diffuse-cloud}
-------------

Figure \[fig:noDipoleSidelobesFit\] shows the emissivity of the diffuse cloud falling off with increasing wavelength, as would be expected for particles with characteristic sizes of order 30. The dashed line in this figure shows a flat emissivity to 150, with values proportional to the frequency-squared at longer wavelengths, for comparison with Fig. 2 of [@fixsendwek2002], who used FIRAS data to investigate the far-infrared/sub-millimetre behaviour of the Zodiacal cloud. These results are consistent with their conclusions[^5].

As the diffuse cloud is so much brighter in the mid-infrared than in the CMB, its relatively low level at  wavelengths has been exploited in [@planck2013-p03d] to set in-flight limits on any possible out-of-band leaks in the instrument’s spectral transmission.

Circumsolar ring and Earth-trailing feature {#circumsolar-ring-and-earth-trailing-feature}
-------------------------------------------

We draw no conclusions about the circumsolar ring or the Earth-trailing feature. The fit values obtained for their emissivities are inconsistent from frequency-to-frequency, their values often being negative. This remains true for  data when the fits are done requiring that the two components have the same emissivities, as was done in K98.

Inspection of the panels labelled ‘Ring’ and ’Feat.’ (i.e., the middle- and lower-left panels) of Fig. \[fig:fit857\] show systematic differences between results from even- and odd-numbered surveys (that is, the circles and squares seem to be systematically different, regardless of whether they are blue or red). ’s observing pattern was different for odd and even numbered surveys, but very similar for either even numbered surveys alone, or for odd numbered surveys alone. Random noise is not an issue, since the measurements with similar observations are repeatable, so this is either an indication that the circumsolar ring and Earth-trailing model templates themselves need improvement at  wavelengths, or that systematic errors are affecting these specific components.

We note that the conclusions presented elsewhere in this work remain essentially the same whether or not we include the circumsolar ring and Earth-trailing feature.

Bands {#subsec:Bands}
-----

An interesting feature of Fig. \[fig:noDipoleSidelobesFit\], and the primary result of this work, is the difference in the emissivities of the bands compared to that of the diffuse cloud, pointing towards differences in the particles in these different components. While there may be hints of this in the longest wavelength DIRBE data, the effect becomes clear at  wavelengths. This is not necessarily unexpected. The composition of the diffuse cloud is still disputed, but is often claimed to be both asteroidal and cometary [see, for example, @Kortenkamp1998; @Nesvorny2010; @Tsumura2010]. Since the bands, on the other hand, are understood to be asteroidal debris only [@sykes86], the difference may simply be a reflection of these different origins.

The fact that the fitted emissivities of bands 1 and 3 rise above unity is perplexing. At first glance, one might imagine some new, cold component in the cloud which would cause an excess that might be interpreted as an excess in emissivity in some other component. However, to peak around 545GHz, this component would have to have a temperature of the order of 10K, and therefore be much more distant than most of the dust usually associated with the Zodiacal cloud. While enticing, it is difficult to understand how such a component could survive the differencing process used in this analysis, which reduces signals from distant sources more than those nearby, or how such a component could mimic an excess in two dust bands above from the ecliptic plane, but not do the same in the other Zodiacal cloud components.

One might worry that covariance between between the various components might be causing problems in the fitting procedure. To check this, we have repeated the fit including and omitting various combinations of the the circumsolar ring and Earth-trailing feature, or both, and assuming their emissivities were independent or equal. In no case did the difference between the diffuse cloud and the dust bands disappear.

The excess may ultimately be explained by degeneracies in the model for the density of the bands. As presented in Sect. \[sec:bandmath\], the normalisation of the density of particles is completely degenerate with the emissivity for each band. In addition, the emission is also roughly proportional to the temperature normalisation, because we are observing in the Rayleigh-Jeans tail of the Zodiacal emission. While any overall change in the temperature of the IPD particles would scale all components of the Zodiacal emission, because temperature is nearly inversely proportional to distance from the Sun, the location of the bands are important. While the excess over 1 is too large to be explained by errors in distance and thus temperatures alone, one might appeal to a change in a combination of distance, particle density normalisation and emissivity of these bands in particular to arrive at mutually consistent results for both  and DIRBE. As this will involve simultaneous work with both  and DIRBE data, it is beyond the scope of this paper.

Bands 1 and 3 also seem to show different behaviour than band 2. Since bands 1 and 3 are both at high ecliptic latitude, while band 2 is not, one might again worry that one of the other templates to which we are fitting might have significant overlap with a subset of the bands, which in turn causes an apparent difference in emissivities. To check this, we have repeated the fits with and without various combinations of the cloud, circumsolar ring and Earth-trailing feature, as well as the far sidelobes. In all cases, bands 1 and 3 are always significantly different than dust band 2. When the diffuse cloud itself is omitted from the fit, the emissivity of dust band 2 goes up, but is still distinctively different from that of dust bands 1 and 3.

As dust band 2 is a combination of the *IRAS* $\alpha$ and $\beta$ bands, one may also worry that one of these two is more important for the shorter *IRAS* and *COBE* wavelengths, but that the other might be more important for the longer  wavelengths. We note that its emission is dominated by contributions from the Karin/Koronis family [see @Nesvorny2008 Fig. 1], but have therefore confirmed specifically that varying the $\delta_\zeta$ parameter of the second band between values appropriate for either $\alpha$ or $\beta$ does not remove this difference (see table \[tab:bandInfo\]).

If the age of band 2 were significantly different from those of bands 1 and 3, we might argue that Poynting-Robertson drag had depleted some of the bands of more smaller particles than the others [@Wyatt2011]. N03 and N08, however, have estimated the ages of most of the asteroid families which might be associated with the bands (reproduced in table \[tab:bandInfo\]), and the age of any of the associations with band 2 is between those of any of the possible associations with bands 1 or 3. These same figures tend to rule out modifications of the material properties due to photo-processing or solar wind exposure for differing periods. Band 2 also seems to be roughly the same distance from the Sun as the other two bands, so it is difficult to appeal to differences in environment as the cause.

We speculate on the following to explain any differences: Veritas, the asteroid family proposed to be associated with dust band 1, is classified as carbonaceous [@Bus2002]. As noted above, the *IRAS* $\beta$ band, associated with the Karin family of asteroids, seems to dominate the emission from dust band 2. Karin and its larger sibling, Koronis, are classified as siliceous, or stony, objects [@Bus2002; @Carvano2010]. While the dust band 3 has a number of asteroid families which may be contributing to it (see table \[tab:bandInfo\]), we propose that the emission is dominated by carbonaceous-based asteroid families (three quarters of the asteroids in the Solar System are carbonaceous), and that the difference in emissivities between dust band 2 and dust bands 1 and 3 arises from this difference in composition. The differing emissivities may be either due to this intrinsic composition difference, or the size-frequency distribution of particles that results from different kinds of asteroids colliding [@Grogan2001 for example]. This explanation would not be valid if it were to turn out that dust band 3 was dominated by dust associated with the Iannini asteroid, for example, as it is siliceous.

Implications for the CMB
------------------------

The right-hand column of Fig. \[fig:beforeAndAfterJackknives\] shows the Zodiacal emission implied by the fits, created by subtracting the maps made applying the Zodiacal emission correction from those that were made without it applied. One can see here the difference in the relative amplitudes of the bands versus the diffuse cloud, the bands being relatively more important at low frequencies than at high. Figure \[fig:Cls\] shows the power spectra of the Zodiacal correction maps, all in units of $\left(\mu\mathrm{K}_\mathrm{CMB}\right)^2$. Here, the cloud is seen at multipoles of less than about 10, while the bands and other structures are see in higher multipoles.

![Power spectra of the Zodiacal correction maps shown in the right-hand column of Fig. \[fig:beforeAndAfterJackknives\]. Black plus signs, grey crosses, cyan triangles, orange diamonds, blue circles, and red squares represent, respectively, 857, 545, 353, 217, 143, and 100GHz. For the CMB channels, even multipoles are shown with filled symbols, while odd multipoles are shown with empty symbols. This “even-odd” pattern is a reflection of the symmetry around the ecliptic plane – odd multipoles are almost absent, as they would indicate structure in the maps that were anti-symmetric about the ecliptic plane. A standard $\Lambda$CDM CMB temperature spectrum is shown as the grey line roughly half-way down the plot, orders of magnitude above the Zodiacal spectrum in the  CMB channels.[]{data-label="fig:Cls"}](ZCorrectionCls.pdf){width="88mm"}

At 143GHz, The signal reaches a few $\mu\mathrm{K}_\mathrm{CMB}$ in the map, while the power spectrum has values of the order of one$\left(\mu\mathrm{K}_\mathrm{CMB}\right)^2$. The absence of power in the odd multipoles is a reflection of the north-south symmetry of the signal. These can be compared with the CMB temperature spectrum, which is shown as the black line about halfway between the top and the bottom of the plot[^6]. The Zodiacal emission correction spectra are orders of magnitude smaller than the CMB spectrum. The Zodiacal emission does not compromise ’s cosmological results.

Conclusion {#sec:conclusion}
==========

Zodiacal emission has long been an important foreground for searches for the extra-galactic background at infrared wavelengths. With the ever-increasing sensitivity of CMB experiments, it will soon become important to account for in sub-millimetre and CMB analyses as well.

The K98 model does fairly well in modelling the diffuse Zodiacal cloud emission at  wavelengths, as long as appropriate emissivities are assumed. It does less well, however, in modelling the other features. Because they appear to be more emissive at these frequencies than the cloud, the bands contribute more to the Zodiacal emission relative to the diffuse cloud at CMB frequencies (i.e., near 143GHz, or 2.1mm). The 2013  release includes both maps which have had Zodiacal emission removed, and maps which have not had Zodiacal emission removed. We note that [@planck2013-p06] found better results using maps that had not had the Zodiacal emission removed to make estimations of the CMB and other astrophysical components in the HFI maps. The component separation methods used there naturally correct for a large amount of Zodiacal emission, as it is spectrally similar to Galactic dust emission in the  CMB channels. In addition, one can see in Fig. \[fig:noDipoleSidelobesFit\] and table \[tab:fullFit\] that the diffuse cloud is not actually detected at 143GHz, the frequency which carries the most weight in  CMB analyses. The Zodiacal emission removal, of course, depends delicately on how this non-detection is treated. This will be addressed in future  releases.

Improvements in modelling of the circumsolar ring, Earth-trailing feature, and the dust bands, as well as inclusion of fainter and partial bands [e.g., @Espy2009] should be done to make truly “clean” CMB maps. As these bands are believed to be the products of asteroid collisions, further study of these bands at these wavelengths may also inform us on the nature of the intermediate-sized particles created during the destruction of the associated asteroids. We may hope to learn not only more about the size distribution, but also the differences between, for example, the results of a collisions involving siliceous and carbonaceous asteroids.

Just as material from asteroid collisions contributes to Zodiacal emission, material shed from comets must also contribute. As part of the HFI data reduction process, we mask out solar system objects which would cause “noise” in the final sky maps. We searched for comets as part of this process, but found only one (Christensen). For completeness, appendix \[sec:Ast\] presents this information, as it is not possible to extract from the data in the 2013  map release. We have not yet detected extended tails of comets.

One of the primary goals of the next stage of analyses, once this “nearby” IPD has been completely removed, will be to search for dust associated with the Kuiper Belt, or set limits upon it.

The full-mission  data release will include polarisation information. While it is not expected, limits will be put on possible contamination of the polarisation of the CMB by polarised Zodiacal emission, as has been done here for temperature.

Work is now underway to address all these points for the next  data release. While the signal is quite small – at CMB wavelengths the signal we are discussing is orders of magnitude smaller than the primary CMB anisotropies, it is detectable and should be subtracted from the data. There will be improvements in dust modelling, improvements in satellite modelling, and additions to address polarisation. The ultimate goal will be simultaneous analyses with *IRAS*, *COBE*, and Akari and other to understand the large-scale Zodiacal emission from the near-infrared to the microwave.

This paper benefited from exchanges with Dale Fixsen, Tom Kelsall and Janet Weiland. We acknowledge the IN2P3 Computer Center (<http://cc.in2p3.fr>) for providing a significant amount of the computing resources and services needed for this work. We acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA). Support for LAMBDA is provided by the NASA Office of Space Science.

The development of  has been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN, JA and RES (Spain); Tekes, AoF and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE (EU). A description of the  Collaboration and a list of its members, including the technical or scientific activities in which they have been involved, can be found at <http://www.sciops.esa.int/index.php?project=planck&page=Planck_Collaboration>.

Basic Behaviour
---------------

Figure \[fig:Asts\] demonstrates some of the basics of the asteroid detections. For each measurement, we denote the measurement as $f$, the distance between  and the object as $d$, and the distance between the Sun and the object as $s$. These quantities for the first measurement of each asteroid will be denoted $f_0$, $d_0$, and $s_0$. In the top panel, we show asteroids that were detected in multiple surveys. Assuming the temperature of the object at any time is inversely proportional to $\sqrt{s}$, we would expect $$f\sqrt{s} \propto \frac{1}{d^2},$$ which is roughly seen in the data.

![image](Asts.pdf)

In the bottom panel, we show the 545-to-857GHz spectral indices, as well as the 545-to-353GHz spectral indices for Ceres and Vesta.

[^1]:  (http://www.esa.int/Planck) is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states (in particular the lead countries France and Italy), with contributions from NASA (USA) and telescope reflectors provided by a collaboration between ESA and a scientific consortium led and funded by Denmark.

[^2]: <http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=47345>.

[^3]: Legacy Archive for Microwave Background Data Analysis – NASA (<http://lambda.gsfc.nasa.gov/>).

[^4]: While three bands are described in the text of K98, there are actually four in the code. There is, however, no ambiguity, as the density of the fourth band is set to zero in the code at the LAMBDA site.

[^5]: Care must be taken with direct comparisons between the emissivities quoted in [@fixsendwek2002], who quote emissivities relative to a 245K cloud, and those in this work, which follow K98 and assume a cloud of temperature 286K at 1AU from the Sun.

[^6]: Made with CAMB – <http://camb.info>
