# Predicting Structures in the Zone of Avoidance

Jenny G. Sorce, Matthew Colless, Renée C. Kraan-Korteweg, Stefan Gottlöber

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Jenny G. Sorce, Matthew Colless, Renée C. Kraan-Korteweg, Stefan Gottlöber. Predicting Structures in the Zone of Avoidance. Monthly Notices of the Royal Astronomical Society, 2017, 471 (3), pp.3087-3097. 10.1093/mnras/stx1800. hal-01582411

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# Predicting structures in the Zone of Avoidance

Jenny G. Sorce,<fnref n="1" />,<fnref n="2" />* Matthew Colless,<fnref n="3" /> Renée C. Kraan-Korteweg<fnref n="4" /> and Stefan Gottlöber<fnref n="2" />

Accepted 2017 July 12. Received 2017 July 12; in original form 2017 March 10

## ABSTRACT

The Zone of Avoidance (ZOA), whose emptiness is an artefact of our Galaxy dust, has been challenging observers as well as theorists for many years. Multiple attempts have been made on the observational side to map this region in order to better understand the local flows. On the theoretical side, however, this region is often simply statistically populated with structures but no real attempt has been made to confront theoretical and observed matter distributions. This paper takes a step forward using constrained realizations (CRs) of the local Universe shown to be perfect substitutes of local Universe-like simulations for smoothed high-density peak studies. Far from generating completely ‘random’ structures in the ZOA, the reconstruction technique arranges matter according to the surrounding environment of this region. More precisely, the mean distributions of structures in a series of constrained and random realizations (RRs) differ: while densities annihilate each other when averaging over 200 RRs, structures persist when summing 200 CRs. The probability distribution function of ZOA grid cells to be highly overdense is a Gaussian with a 15 per cent mean in the random case, while that of the constrained case exhibits large tails. This implies that areas with the largest probabilities host most likely a structure. Comparisons between these predictions and observations, like those of the Puppis 3 cluster, show a remarkable agreement and allow us to assert the presence of the, recently highlighted by observations, Vela supercluster at about $180 h^{-1}$ Mpc, right behind the thickest dust layers of our Galaxy.

**Key words:** methods: numerical – methods: statistical – techniques: radial velocities – large-scale structure of Universe.

## 1 INTRODUCTION

Galactic dust obscures a large fraction of the sky, called the Zone of Avoidance (ZOA; Shapley 1961). This region, apparently devoid of galaxies, used to be avoided by observers because of the inherent difficulties, resulting from the strong dust extinction, in analysing the galaxies there. However, to understand local flows and the cosmic microwave background (CMB; Penzias & Wilson 1965) dipole (e.g. Henry 1971; Corey & Wilkinson 1976; Smoot, Gorenstein & Muller 1977; Planck Collaboration 2014), coverage of the whole sky is essential. Numerous studies in the past have indeed shown the relation between surrounding structures and the CMB dipole (Lahav 1991; Kocevski & Ebeling 2006; Erdoğdu et al. 2006a; Bilicki et al. 2011; Gibelyou & Huterer 2012). The lack of data in the ZOA (which covers about 10–15 per cent of the sky depending

on the wavelength of observations) means that astronomers must rise to this challenge.

Many local large-scale structures are indeed bisected by the Galactic plane. Two of them, Perseus-Pisces and the Great Attractor, actually lie across the ZOA on exactly opposite sides of the Local Group (e.g. Pantoja et al. 1994; Seeberger, Huchtmeier & Weinberger 1994a; Pantoja et al. 1997). Because they are partially obscured, determining the winner in this tug of war on the Local Group constitutes a daunting task (see e.g. Seeberger, Saurer & Weinberger 1992; Seeberger et al. 1994b). Similarly, identifying the connections between structures lying across the ZOA, if they exist, is essential to measure the longest structures and verify their compatibility in terms of both size and abundance with predictions from the standard cosmological model or from the observations of fluctuations in the CMB (Kraan-Korteweg & Lahav 2000; Sheth & Diaferio 2011). At present, most CMB dipole estimates assume a homogeneously filled ZOA or an extrapolation of structures on either side of the ZOA, which prevents them from achieving

<footnote n="1">¹Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France</footnote>

<footnote n="2">²Leibniz-Institut für Astrophysik, D-14482 Potsdam, Germany</footnote>

<footnote n="3">³Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia</footnote>

<footnote n="4">⁴Department of Astronomy, University of Cape Town, 7700 Rondebosch, South Africa</footnote>

<footnote>* E-mail: jsorce@aip.de</footnote>
high-precision measurements. Thus, there exists a real need to map
the structures across the ZOA (see Kraan-Korteweg & Lahav 2000,
for a complete review on the subject).

A great deal of effort has already been deployed to observe
galaxies within the ZOA (e.g. Kraan-Korteweg et al. 1994; Kraan-
Korteweg & Lahav 2000; Kraan-Korteweg 2005; Donley et al. 2006;
Williams, Kraan-Korteweg & Woudt 2014; Ramatsoku et al. 2016;
Said et al. 2016; Staveley-Smith et al. 2016, for a non-extensive
list with the last two references as complete reviews) or at least
to reduce its extent by using observations at less-affected wave-
lengths (e.g. Sorce, Courtois & Tully 2012; Neill et al. 2014; Sorce
et al. 2014b). A complementary approach is to use observations
surrounding the ZOA to reconstruct the missing information in it
(Hoffman 1994; Erdoğdu et al. 2006b). In this paper, we propose a
method for quantifying the probability of the presence of structures
in different areas of the ZOA.

The study is conducted within the framework of constrained sim-
ulations of the local Universe (e.g. Bertschinger 2001; Gottlöber,
Hoffman & Yepes 2010). Unlike ordinary cosmological simula-
tions, these simulations stem from initial conditions constrained
by observational data to resemble the local Universe. These ob-
servational data can be either radial peculiar velocities of galax-
ies (Kravtsov, Klypin & Hoffman 2002; Klypin et al. 2003; Sorce
et al. 2014a) or redshift catalogues (Lavaux 2010; Heß, Kitaura &
Gottlöber 2013). The initial conditions are retrieved either back-
wards (Bertschinger 1987; Hoffman & Ribak 1991, 1992; Ganon
& Hoffman 1993; van de Weygaert & Bertschinger 1996; Pistolas
& Hoffman 1998; Lavaux et al. 2008) or forwards (Heß et al. 2013;
Jasche & Wandelt 2013; Kitaura 2013; Wang et al. 2013). In the
latter case, the initial density field is sampled from a probability dis-
tribution function consisting of a Gaussian prior and a likelihood. A
complete overview of the different methods is given in Wang et al.
(2014) and an extension of the backwards method to non-Gaussian
fields is proposed in Sheth (1995).

Recently, Sorce et al. (2016) released simulations constrained
with the second radial peculiar velocity catalogue (Tully et al. 2013)
of the Cosmic Flows project (e.g. Courtois & Tully 2012; Tully &
Courtois 2012) using a backwards method. Although estimating
peculiar velocities constitutes an observational challenge, there is
a double advantage in using them: first they are highly linear and
correlated on larger scales than the density field. Consequently,
the ZOA can still be recovered when it becomes larger than the
correlation length of the density field with a sufficiently sampled
velocity field; second, peculiar velocities are excellent tracers of the
underlying gravitational field as they account for both the baryonic
and the dark matter. The backwards method permits producing
a large number of realizations in a short amount of (computing)
time which is paramount for such statistical studies. Running the
simulations from the large set of initial conditions produced from
the method is the most demanding of computer time.

Actually, as shown in Section 2, running such constrained sim-
ulations is not an absolute necessity when the goal is to study the
smoothed high-density peaks of the large-scale structure at red-
shift zero. There is thus no reason either to use forward methods
with high computational demands to get the reconstruction of the
local Universe with the non-linearities. Basically, studying the lin-
ear reconstruction of the local Universe obtained with a backwards
method (e.g. Zaroubi et al. 1995; Zaroubi, Hoffman & Dekel 1999),
or more precisely the constrained realizations (CRs) of the latter
(Bertschinger 1987; Hoffman & Ribak 1992; van de Weygaert &
Bertschinger 1996), to actually have access to structures in the ZOA
up to large distances as well as to their probability, is sufficient.

Indeed, the reconstruction technique by definition goes to the null
field (the overdensity $\delta$ equals 0) in the absence of data or in the pres-
ence of very noisy data while, by extension, the CR technique sta-
tistically restores the missing structures. Namely, while the Wiener
filter reconstruction presents smoother and smoother structures up
to reaching the null field with increasing distances from the centre
of the data set, the CR compensate this smoothing by combining
the constraints with a random field, thus allowing us to fully access
structures even beyond the volume sampled by the data set. De-
tailed equations are given in Appendix A. The goal of this paper is
to show that this restoration is not statistically random and depends
on the surrounding structures up to large distances. Hence, it is
possible to predict where the structures are more likely to be in the
ZOA, as shown in Section 3. In Section 4, theoretical predictions
are compared with observations, and the conclusions of this work
are presented in Section 5.

## 2 METHODOLOGY

### 2.1 Preparing constrained realizations

The scheme used by the CLUES project to build constrained initial
conditions and run the simulations is described in detail in Sorce
et al. (2016). Since only some parts of the process are of interest
here, the steps to produce realizations constrained by observational
radial peculiar velocity catalogues and a brief description of their
purpose are the only aspects recapitulated here:

(i) grouping of galaxies in the radial peculiar velocity catalogue
to remove non-linear virial motions (e.g. Tully 2015a,b) that would
cause problems when using the linear reconstruction method;

(ii) minimization of the biases (Sorce 2015) in the grouped radial
peculiar velocity catalogue and

(iii) production of linear density and velocity fields constrained
by the grouped and bias-minimized observational peculiar veloc-
ity catalogue combined with a random realization (RR) to sta-
tistically restore the missing structures using the CR technique
(Bertschinger 1987; Hoffman & Ribak 1991, 1992).

The Planck cosmology framework ($\Omega_m = 0.307$, $\Omega_A = 0.693$, $H_0 = 67.77$, $\sigma_8 = 0.829$; Planck Collaboration et al. 2014) is used
as a prior.

### 2.2 Constrained realizations versus constrained simulations

Running constrained simulations is useful to study the formation
and evolution of the large-scale structures as well as the small
non-linear scales. However, when interested only in the large-scale
structure present today, there is no need to simulate the full for-
mation history of these structures – the linear reconstruction is
sufficient. This reconstruction can be obtained with the Wiener fil-
ter technique (linear minimum variance estimator, abbreviated as
WF; Zaroubi et al. 1995, 1999). Where data are available, the WF-
reconstructed field reproduces the observed large-scale structure
(e.g. Zaroubi et al. 1999; Courtois et al. 2012). The WF method
is also able to reconstruct across the ZOA provided that the lat-
ter does not cover too large a volume (i.e. nearby, at low redshift;
Hoffman 1994; Zaroubi 2000). The further from the observer, the
worse the extrapolation is, and in fact structures are not recon-
structed in the ZOA at large distances – the WF simply goes to
the null field. By contrast, the CR technique restores statistically
structures in that zone by adding a random field.
The goal of this paper is to determine if there are some regions in the ZOA that have a higher probability of hosting a structure than others. To pursue this work, statistical analyses are required. This constitutes another argument in favour of studying the structures directly in the fields obtained with the CR technique, since running lots of constrained and random (for statistical comparison) simulations consumes a lot of computer time. One might argue that CR fields are not suitable substitutes for full simulated fields at the level of interest for this paper, and of course CR fields present only the linear structures and obviously are in no way exact substitutes for the fully simulated fields. However, as long as CR fields and simulated fields present a very similar large-scale structure for high-density peaks in the ZOA, one can be used for the other in statistical tests.

To demonstrate that CR fields can be taken as substitutes for simulated fields for our purpose, 15 simulations from Sorce et al. (2016) and the 15 corresponding CR fields (so that simulations and CRs share the same random part) are compared. We apply a cloud-in-cell scheme on a 256³ grid to the particle distributions of the 15 simulations at z = 0 with a subsequent Gaussian smoothing on a scale of $5h^{-1}$ Mpc. The resulting smoothed density field of any constrained simulation is then converted to the overdensity field. The CR technique indeed only produces the overdensity field. Each simulated overdensity field is then compared to that of another constrained simulation, to that of a constrained realization, and to that of the CR sharing the same random field. For each pair of each category (simulation/simulation; simulation/CR; simulation/CR sharing the same random field), we build an overdensity-overdensity plot (i.e. cells of overdensity field #1 versus cells of overdensity field #2). If the two fields were identical, all points would lie on the 1:1 relation (cell value in field #1 is equal to cell value in field #2). The difference between two fields is determined as the one-sigma, hereafter $1\sigma$, scatter (or standard deviation) around this 1:1 relation. We repeat this procedure for all the pairs of each category and then the mean and the variance of the $1\sigma$ scatters are derived.

In the top panel of Fig. 1, the result is three points (blue, black and red symbols for each of the categories simulation/simulation, simulation/CR, simulation/CR sharing the same random field), with error bars, computed only for cells with positive overdensities. The procedure is repeated in smaller sub-boxes of size $320 h^{-1}$ Mpc, where most of the observational constraints are, and in the ZOA (i.e. cells are compared only in this area: the ZOA is taken to be a 20° cone with the apex at the centre of the box and oriented in the same direction in the realizations as in the observations). The resulting points are shown in the middle and bottom panels of Fig. 1. We repeat the process, changing the threshold to select higher and higher overdensity regions.

Fig. 1 shows that the $1\sigma$ scatters increase with the threshold in accord with the expectation that, although the large-scale structure is reproduced, high-density peaks might be shifted by a few megaparsecs from one realization to another and from the simulation to the CR. In addition, because simulations also probe the non-linear regime, and hence allow larger fluctuations, the $1\sigma$ scatters are higher when comparing two simulations than when comparing a simulation and a CR. That is, the chance of getting a large contrast between cells coming from two different simulations is higher than for cells coming from a simulation and a CR; and indeed in the latter, linear-regime, case the fluctuations are reduced.

The main result from Fig. 1 is that the differences between two simulations, or between a CR and a simulation built with different random fields, are larger on average than the difference between

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Mean (points) and scatter (error bars) of the standard deviations ($\sigma$) obtained from cell-to-cell comparisons carried out on pairs of overdensity fields smoothed on a $5h^{-1}$ Mpc scale at $z=0$ for the whole $500h^{-1}$ Mpc box (top), for the $320h^{-1}$ Mpc sub-box (middle), and for the ZOA (bottom). The mean standard deviations are given as a function of the overdensity threshold. Pairs consist of two constrained simulations (filled blue square), one constrained simulation and one constrained realization, (filled black circle) and one constrained simulation and one CR sharing the same random part (filled red triangle).</figcaption></figure>

the simulation and the CR sharing the same seed (at least for the high-density peaks of interest in this paper). Admittedly, the differences are more pronounced when considering the full boxes rather than the smaller boxes or the ZOA. In the first case, it is expected because of the decrease in cosmic variance when working with constrained simulations compared to working with random simulations (e.g. Sorce et al. 2016). The inner parts of the boxes are more constrained (have more constraints) and thus they resemble more to the local Universe as well as to each other in the different simulations (hence the smaller $1\sigma$ scatters than for the full boxes). This is also expected in the second case because the ZOA is not as well constrained as the other parts of the box given the scarcity of the data, especially at increasingly higher distances. The difficulty of reconstructing across the ZOA increases linearly with the distance from the observer. In addition, the error bars of the $1\sigma$ scatter increase with the reduction of the number of cells compared between two realizations (i.e. with the reduction of the compared zones).

In that context, the scatters between the simulation and the CR sharing the same random field are even lower than between two simulations, or between a CR and a simulation with different random fields. This suggests that for our purpose (a statistical study of high-overdensity peaks in the ZOA), one can be taken as a substitute for the other. Taking CR fields as substitutes for the simulated fields to derive statistics on the large-scale structure in the ZOA, we produce 200 CR fields on 256³ grids as well as 200 random fields (sharing the same random part as the corresponding CR field) on the same grid size at a small computational cost.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Histograms of the number of cells with an overdensity above the threshold given in the top right corner of each panel (1.0, 1.5 or 2.0) as a function of the number of realizations. The dotted black line and solid black line represent, respectively, the probability distribution functions of cells in, respectively, random and constrained realisations having an overdensity value above the threshold. The bottom panels are zooms of the positive tails of the distributions. The red dashed line shows the distribution of the residual between the constrained and the random probabilities for a given cell. The blue dot-dashed lines are the distributions if cells are only counted if they exhibit an overdensity value above the threshold *only* in the CR and *not* in the RR sharing the same random seed. In this case, a cell is counted only when the overdensity is entirely due to the constraints: the random part alone would not have induced an overdensity above the given threshold. See the text for a more detailed explanation.</figcaption></figure>

# 3 PROBABILITY OF STRUCTURES

## 3.1 Random Versus Constrained Probabilities

The first goal is to quantify the constraining power of the CR technique in the ZOA. That is, at a given location in the ZOA, do the CR fields present a structure with a greater probability than the random fields, or are the structures simply randomly distributed in a manner consistent with the cosmological model? With 200 CRs and 200 RRs, it is straightforward to study the probability that a cell is overdense (i.e. hosting a structure) in both the random and constrained cases.

To determine these probabilities in the ZOA, cells belonging to the ZOA need first to be identified. Since we smooth the realizations over $5h^{-1}$ Mpc, cells of $5h^{-1}$ Mpc filling up the entire ZOA constitute the optimal choice. We split the ZOA into cells of $5h^{-1}$ Mpc and compute their overdensity value. We count the number of times a cell belonging to the ZOA has a value above a given threshold over 200 CRs. For clarity and simplicity, the paraphrase 'threshold-pass cell' is used to mean hereafter 'a cell with a value above a given overdensity threshold'. Finally, looping over all the ZOA cells, the number of cells that are threshold-pass in a certain number of CRs is obtained and the probability distribution function of a cell to be

threshold-pass is calculated. The same procedure is repeated with the RRs to obtain the random probability distribution function of a cell to be threshold-pass.

If the constraints were not affecting the ZOA at all, i.e. if constraining the realizations was not giving some insight into the ZOA structures, then the constrained and random probability distribution functions should be statistically identical. This would imply that the structures in the ZOA are completely randomly distributed and abide only by the prior cosmological model in both the random and the constrained cases. Fig. 2 shows that this is not the case: the histograms of probabilities or the distributions of threshold-pass cells (one threshold per panel in the top row) as a function of the number of realizations in which they are found differ between the constrained (solid black line) and random (dotted black line) realizations. For instance, the top left panel of Fig. 2 shows that the random probability for a cell to be threshold-pass at the 1.0 overdensity level follows a Gaussian distribution with a mean at 15 per cent (30 out of 200 realizations, dotted black line). Thus, there is on average about a $15 \pm 3$ per cent chance of finding an overdensity greater than 1.0 in a cell. The constrained probability however does not follow a Gaussian distribution, the solid black line distribution is skewed (skewness 1.5) and flatter (kurtosis 11),
confirming that constraining the realization also affects the ZOA. The middle and right-hand panels of the top row on Fig. 2 confirm that such observations are valid also for higher overdensity thresholds.

From these different probability distribution functions, it becomes clear that cells with probabilities in the high tail of the distribution for CRs, most likely, host a structure that is produced by the constraints surrounding the ZOA. The bottom row of Fig. 2 zooms in on the high tail of the probability distribution functions calculated at a given threshold to highlight the existence of such cells.

To reinforce our claims, we pursue our quest for statistical differences between CRs and RR s in the ZOA by deriving two more probability distributions that are hereafter called the global probability and the individual probability:

(i) The global probability for a given cell is defined as the difference between its constrained and random probabilities. At a fixed overdensity threshold, the number of RR s in which a given cell is threshold-pass is subtracted from the number of CRs in which this cell is also threshold-pass. The procedure is repeated over all the different cells in the ZOA to derive the global probability distribution function.

(ii) The individual probability for a given cell is a bit more complex. Considering one CR, a given cell is counted as threshold-pass only in the case that in the RR sharing the same random seed as the CR, this same cell is *not* threshold-pass – i.e. the cell is threshold-pass in the CR only. In other words, we require that the constraints force the cell to become threshold-pass and the random component used in the CR technique to restore the missing structures would not have induced an overdensity greater than the threshold in that cell. The process is then repeated over the 200 realizations and then over all the cells filling the ZOA to derive the individual probability distribution function.

The global and individual probability distribution functions are plotted in Fig. 2 as the red dashed and blue dot-dashed lines, respectively. These curves confirm the statistical difference between CRs and RR s in the ZOA. Whatever the threshold level is, the global probability distribution function is a Gaussian centred on zero with (for instance) a standard deviation of 8 per cent for a 1.0 overdensity threshold. This distribution implies that some constrained cells have on average a greater (or lower) probability to be threshold-pass than their random counterparts. This indicates that structures (both overdensities and underdensities) are more likely to exist in the ZOA because of the constraints than solely because of the prior cosmological model and its associated statistical fluctuations. It confirms that the random and constrained probability distribution functions differ and that the probability of each cell to be threshold-pass is different in the random and constrained cases. The individual probability distribution function goes further since the random seed is also fixed. With a mean at 13 per cent and a standard deviation of 8 per cent for a 1.0 overdensity threshold, this distribution is even more remarkable: some cells are clearly threshold-pass solely because of the constraints. The RR s have a very low probability of generating overdensities in the cells that are in the high tail of the individual probability distribution function on a one-to-one random seed basis.

Since there is a clearly demonstrated difference between threshold-pass cells in CRs and RR s, we can proceed to pursue the analysis of structures in the constrained field to locate the most probable structures in the ZOA.

## 3.2 Locations of constrained structures

In the rest of this section, we focus on cells that have a threshold-pass probability with a $3\sigma$ level of significance. For instance, for the 1.0-overdensity threshold, the probability that the cell is threshold-pass must be at least 24 per cent (=$15$ per cent + $3 \times 3$ per cent, i.e. the mean of the random probability distribution function plus three times its standard deviation) for the cell to be considered. The probability distribution being quasi-Gaussian, a positive $3\sigma$ level is an appropriate choice for selecting the statistically significant cells in the positive tail of the distribution and removing the others. To locate these cells (or potential structures) in space, the top left panel of Fig. 3 shows as black contours the average overdensity field of the 200 CRs in three $2h^{-1}$ Mpc thick supergalactic slices centred on the observer. Keeping the same contour values, the same plot is shown for the average overdensity field of the 200 RR s on the right side. The red lines identify the ZOA in the different supergalactic slices. While the average of the 200 RR s presents a quasi-null field (green contours) everywhere, there are, as expected from our statistical study of simulations, clearly distinct structures in the average of the CRs, including in the ZOA that is of interest here. Such an observation means that similar structures are repeatedly at the same location in the CRs while the locations of similar structures differ substantially from one RR to another. Consequently, while they annihilate each other when averaging in the random case, they reinforce each other in the constrained case. This claim is further supported by the standard deviation of the 200 CRs shown in the bottom left panel of Fig. 3: the CR technique decreases the cosmic variance between the different constrained overdensity fields with an increasing effect from the outer to the inner part (where most of the constraints are). However, these plots of the slice structures do not show either the entire ZOA nor the likelihood of a structure in the ZOA of the local Universe. Although the standard deviation indeed highlights the part of the box that is the most constrained, it does not exhibit particular information on each one of the structures especially those in the ZOA. To get additional information, the $>3\sigma$ cells are plotted in the bottom panel of Fig. 3 with a size proportional to the probability that they are threshold-pass and a colour indicating their distance in the supergalactic direction perpendicular to the plotted slice.

Structures with the highest probabilities (bigger dots) of containing structures are located at nearer distances along the line of sight, simply because the technique is better able to reconstruct structures when the ZOA is less extended (i.e. nearby). However, there are some more distant structures that also exhibit probabilities with $3\sigma$ significance. Such structures, further from the regions where constraints are (since the ZOA covers a greater physical extent), need to be considered more fully and compared with observational expectations and predictions. Such comparisons are conducted in the next section.

## 4 OBSERVED AND PREDICTED STRUCTURES

Observers working on the ZOA prefer working in Galactic coordinates (longitude and latitude). To compare the theoretical results with observations, we convert the grids in supergalactic coordinates to Galactic coordinates, and split the ZOA into small cells of Galactic longitude, Galactic latitude and distance ($l, b, d$). We compute the overdensities in these cells and gather the cells into partial spherical shells of depth $10h^{-1}$ Mpc. We then determine the overdensity contours on the projected distribution of cells. Several of these contour
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Top panels: averaged overdensity fields (black solid contours) of 200 constrained (left) and 200 random (right) realization fields in the $2h^{-1}$ Mpc thick X–Y, Y–Z and X–Z supergalactic slices centred on the observer. The green contours show the transition between overdensities and underdensities ($\delta = 0$), the dashed contours stand for the underdensity and the red lines delimit the ZOA in the different slices, corresponding to $(l, b) = (-10^{\circ}, +10^{\circ})$ in Galactic coordinates. The name of a few local structures is given in blue on top of the averaged constrained field (GW stands for ‘Great Wall’ and PP for ‘Perseus-Pisces’). Bottom panels: left: standard deviation of the 200 constrained overdensity fields (black solid contours). Labels give the value of the standard deviation. ; right: dots stand for 1.0-overdensity threshold-pass regions with a $3\sigma$ signal; see the text for a more detailed explanation. Dot sizes are proportional to the probability of cells to be threshold-pass. Their location in the third dimension (Z, X and Y directions from left to right, top to bottom, respectively) is indicated by the colour scale.</figcaption></figure>

maps of overdensity in partial spherical shells, centred on distances between 75 and $215h^{-1}$ Mpc, are shown in Figs 4, 5 and 6.

Galaxies and clusters observed in the ZOA from various surveys are plotted on top of the contours. colours and symbols are as follows: (1) small red filled circles are part of our Nançay observations of the Puppis 3 cluster; (2) small green filled circles are from the HIZOA-S survey (Staveley-Smith et al. 2016); (3) small blue filled circles are from Radburn-Smith et al. (2006); (4) small light

blue filled circles are from the 2MASS redshift survey (Huchra et al. 2012) and (5) the big red filled circle is a cluster from the Clusters In the Zone of Avoidance (CIZA) project (Ebeling, Mullis & Tully 2002). Note that small shifts in the Galactic longitude of galaxy points were applied in two panels (second panel of Fig. 5 and second panel of Fig. 6). These shifts were less than $5^{\circ}$. The accuracy of the WF is about $2-3h^{-1}$ Mpc. A small $5^{\circ}$ shift at distances greater than $50h^{-1}$ Mpc is thus completely justified and even
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 4.** Galactic coordinate representation of the average overdensity field of 200 CRs (black contours). The partial spherical shells shown are 10 $h^{-1}$ Mpc thick and are centred on structures in the ZOA at distances of 75 $h^{-1}$ Mpc and 95 $h^{-1}$ Mpc. Red, green and light blue filled circles are galaxies observed in three different ZOA surveys. There is a remarkable agreement between the computed overdensity field and the observations of Puppis 3 in the top panel. The two bottom panels probe distances of 95 $h^{-1}$ Mpc, where two galaxy groups have previously been identified (middle panel). The bottom panel suggests the presence of a mass concentration in the Cygnus constellation. Galaxies observed on both sides of this concentration reinforce its existence. The observations and the average reconstruction are in very good agreement.</figcaption></figure>

expected. In the rest of this section, the probability quoted for each detected structure is the percentage of CRs in which the structure is detected at the 1.0 overdensity threshold.

## 4.1 The Puppis 3 cluster, other galaxy groups and a Cygnus concentration

The top panel of Fig. 4 shows a remarkable agreement between the observed galaxies (red filled circles) in the Puppis 3 cluster at about 70 $h^{-1}$ Mpc, first hinted at by Chamaraux & Masnou (2004) and confirmed by Staveley-Smith et al. (2016), and the average reconstructed field (black solid contours); the Puppis 3 cluster has a

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 5.** Galactic coordinate representation of the average overdensity field of 200 CRs (black contours). The partial spherical shells shown are 10 $h^{-1}$ Mpc thick and are centred on structures in the ZOA around (l, b) = (130°, 0°) at a distance of 165 $h^{-1}$ Mpc (top panel) and around (l, b) = (80°, 0°) at a distance of 170 $h^{-1}$ Mpc (bottom panel). The red filled circle in the bottom panel shows the location of the Cygnus A cluster observed in the CIZA project at a distance about 170 $h^{-1}$ Mpc. There is a remarkable agreement between the computed overdensity field and the location of Cygnus A. The top panel shows two reconstructed structures that need to be observationally confirmed.</figcaption></figure>

21.5 per cent probability in the reconstruction, namely it is significant at the 2σ level. Interestingly enough, we note that Erdoğan et al. (2006b) also theoretically predicted that cluster (C11 in their paper). The agreement is remarkable in the sense that they base their reconstruction on the 2MASS redshift survey while we base ours on the second radial peculiar velocity catalogue of Cosmicflows, namely the two data sets are of different natures and do not share the same spatial distribution of data points.

The middle panel of the figure is remarkable in two ways: (1) two distinct clumps of galaxies at 95 $h^{-1}$ Mpc are not only clearly observed but also reconstructed with about 25 per cent probabilities (more than a 3σ significance level) and (2) they correspond to galaxy groups with lower density than clusters and so would not necessarily be expected to appear in the reconstruction. These groups were identified by Crook et al. (2007) in the Two Micron All Sky Survey Extended Source Catalogue (Skrutskie et al. 2006) using a percolation algorithm. Finally, the bottom panel of the figure suggests the presence of a mass concentration in the Cygnus constellation close to Deneb and the North America Nebula (NGC7000). Galaxies from the 2MASS redshift survey (light blue filled circles) observed on both sides of this concentration strengthen its most probable existence. The structure is significant at more than the 2σ level (23 per cent probability). Actually, Erdoğan et al. (2006b) predicted a structure at about 100 $h^{-1}$ Mpc, (l,b) = (100°, -7°) that they call C13, i.e. not far from the aforementioned mass concentration.
from the 200 realizations. The probability distribution functions are
defined as follows:

(i) Constrained probability distribution: the procedure described above is looped over the 200 CRs and then reiterated over all the cells. The result is the probability distribution of cells in the ZOA being threshold-pass.

(ii) Random probability distribution: same as before but for the 200 RRs.

(iii) Global probability distribution: for a given cell and threshold, once the procedure is looped over the 200 CRs on the one hand and over the 200 RRs on the other hand, the two resulting counts are subtracted. The procedure is repeated for all the cells. It gives the probability distribution of a cell in the ZOA being threshold-pass once the random probability has been subtracted.

(iv) Individual probability distribution function: for a given cell, threshold and random seed, the cell is counted as being threshold-pass if it meets the requirement of having an overdensity value above the threshold only in the CR and not in the RR sharing the same random seed. The procedure is reiterated over the 200 CR/RR pairs and then over all the cells in the ZOA. It results in the probability distribution of a cell in the ZOA being threshold-pass solely because of the constraints; the random part alone would not have induced an overdensity sufficiently high for the cell to be threshold-pass.

If the constraints did not affect the reconstruction of the ZOA, the constrained and random probability distributions would be identical; this is not the case. While the random probability distribution is a Gaussian, the constrained one is skewed and flatter, revealing that cells in the high tail of the constrained distribution most likely host a structure – their probability is increased due to the constraints.

That the random and constrained probability distributions differ is confirmed by the shape of the global probability distribution function. This function is a Gaussian; this implies that some cells have a probability to host a structure that is greater over 200 CRs than these same cells in 200 RR s associated with the same prior cosmological model. The individual probability distribution is even more remarkable: it confirms that some cells host structures by the sole action of the constraints; the random part alone would not cause the cells to be threshold-pass.

The probability derived for each cell allows us to locate the re-
constructed structures in the ZOA that have the highest probability
(i.e. in which we can have the greatest confidence). These structures
are confronted with observations. As expected, since the reconstruc-
tion technique works well nearby, where the physical extent of the
ZOA is least, there is good overall agreement between reconstructed
and observed structures close by. For instance, the Puppis 3 cluster
at about 70 h⁻¹ Mpc is successfully reconstructed. More notably,
this agreement extends farther away: the Cygnus A cluster at about
170 h⁻¹ Mpc is equally well reconstructed. The agreement for these
two known structures confirm the effectiveness of the techniques
and encourages us to study even larger distances and deeper into
the ZOA. Looking at 180 h⁻¹ Mpc, we find a structure reconstructed
with 27.5 per cent probability (i.e. at the 1.0 overdensity threshold
there is a structure in 27.5 per cent of the CRs) that is almost cen-
tred on the location of the recently discovered Vela supercluster
(Kraan-Korteweg et al. 2017). The signal for this structure is sig-
nificant at the 4σ level. This prediction is remarkable in the sense
that it is inferred with observational data, 98 per cent of which are
within 160 h⁻¹ Mpc and 50 per cent of which are within 61 h⁻¹ Mpc.
Furthermore, probing slightly larger distances still, we also see the
second wall at about 220 h⁻¹ Mpc behind the centre of the Vela
supercluster also brought to light by (Kraan-Korteweg et al. 2017);

this second wall is reconstructed despite being outside the region
covered by the data used as constraints.

This study lends support to the existence of two merging wall-like
structures forming the Vela supercluster, with a central core exactly
behind the deepest part of the ZOA. This supercluster might resolve
the misalignment of clustering dipoles and account for the residual
bulk flows.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the Gauss Centre for Super-
computing e.V. (www.gauss-centre.eu) for providing computing
time on the GCS Supercomputer SuperMUC at LRZ Munich. The
authors thank the referee for constructive comments that helped to
improve the manuscript. This research has made use of the SIMBAD
data base and the VizieR catalogue access tool, operated at CDS,
Strasbourg, France as well as of the TOPCAT interactive graphical
tool developed by Mark Taylor. JS acknowledges support from the
Astronomy ESFRI and Research Infrastructure Cluster ASTERICS
project, funded by the European Commission under the Horizon
2020 Programme (GA 653477). RKK thanks the South African
National Research Foundation for their support.

REFERENCES

Bertschinger E., 1987, ApJ, 323, L103

Bertschinger E., 2001, ApJS, 137, 1

Bilicki M., Chodorowski M., Jarrett T., Mamon G. A., 2011, ApJ, 741, 31

Bistolas V., Hoffman Y., 1998, ApJ, 492, 439

Chamaraux P., Masnou J.-L., 2004, MNRAS, 347, 541

Corey B. E., Wilkinson D. T., 1976, in BAAS, Vol. 8, Bull. Am. Astron. Soc., p. 351

Courtois H. M., Tully R. B., 2012, ApJ, 749, 174

Courtois H. M., Hoffman Y., Tully R. B., Gottlöber S., 2012, ApJ, 744, 43

Crook A. C., Huchra J. P., Martinbeau N., Masters K. L., Jarrett T., Macri L. M., 2007, ApJ, 655, 790

Donley J. L., Koribalski B. S., Staveley-Smith L., Kraan-Korteweg R. C., Schröder A., Henning P. A., 2006, MNRAS, 369, 1741

Ebeling H., Mullis C. R., Tully R. B., 2002, ApJ, 580, 774

Erdoğdu P. et al., 2006a, MNRAS, 368, 1515

Erdoğdu P. et al., 2006b, MNRAS, 373, 45

Ganon G., Hoffman Y., 1993, ApJ, 415, L5

Gibelyou C., Huterer D., 2012, MNRAS, 427, 1994

Gottlöber S., Hoffman Y., Yepes G., 2010, preprint (arXiv e-prints: 1005.2687)

Henry P. S., 1971, Nature, 231, 516

Heß S., Kitaura F.-S., Gottlöber S., 2013, MNRAS, 435, 2065

Hoffman Y., 1994, in Balkowski C., Kraan-Korteweg R. C., eds, ASP Conf. Ser. Vol. 67, Unveiling Large-Scale Structures Behind the Milky Way, Astron. Soc. Pac., San Francisco, p. 185

Hoffman Y., Ribak E., 1991, ApJ, 380, L5

Hoffman Y., Ribak E., 1992, ApJ, 384, 448

Huchra J. P. et al., 2012, ApJS, 199, 26

Jasche J., Wandelt B. D., 2013, MNRAS, 432, 894

Kitaura F.-S., 2013, MNRAS, 429, L84

Klypin A., Hoffman Y., Kravtsov A. V., Gottlöber S., 2003, ApJ, 596, 19

Kocevski D. D., Ebeling H., 2006, ApJ, 645, 1043

Kraan-Korteweg R. C., 2005, in Röser S., ed., Rev. Mod. Astron., 18, 48

Kraan-Korteweg R. C., Lahav O., 2000, A&A Rev., 10, 211

Kraan-Korteweg R. C., Fayette V., Balkowski C., Fairall A. P., Henning P. A., 1994, in Balkowski C., Kraan-Korteweg R. C., eds, ASP Conf. Ser., Vol. 67, Unveiling Large-Scale Structures Behind the Milky Way, Astron. Soc. Pac., San Francisco, p. 99

Kraan-Korteweg R. C., Cluver M. E., Bilicki M., Jarrett T. H., Colless M., Elagali A., Böhringer H., Chon G., 2017, MNRAS, 466, L29
Kravtsov A. V., Klypin A., Hoffman Y., 2002, ApJ, 571, 563

Lahav O., 1991, in Holt S. S., Bennett C. L., Trimble V., eds, AIP Conf. Ser., Vol. 222, After the first three minutes. Am. Inst. Phys., New York, p. 421

Lavaux G., 2010, MNRAS, 406, 1007

Lavaux G., Mohayaae R., Colombi S., Tully R. B., Bernardeau F., Silk J., 2008, MNRAS, 383, 1292

Neill J. D., Seibert M., Tully R. B., Courtois H., Sorce J. G., Jarrett T. H., Scowcroft V., Masci F. J., 2014, ApJ, 792, 129

Pantoja C. A., Giovanardi C., Altschuler D. R., Giovanelli R., 1994, AJ, 108, 921

Pantoja C. A., Altschuler D. R., Giovanardi C., Giovanelli R., 1997, AJ, 113, 905

Penzias A. A., Wilson R. W., 1965, ApJ, 142, 419

Planck Collaboration, 2014, A&A, 571, A27

Planck Collaboration et al., 2014, A&A, 571, A16

Radburn-Smith D. J., Lucey J. R., Woudt P. A., Kraan-Korteweg R. C., Watson F. G., 2006, MNRAS, 369, 1131

Ramatsoku M. et al., 2016, MNRAS, 460, 923

Said K., Kraan-Korteweg R. C., Staveley-Smith L., Williams W. L., Jarrett T. H., Springob C. M., 2016, MNRAS, 457, 2366

Seeberger R., Saurer W., Weinberger R., 1992, in Klare G., ed., Astronomische Gesellschaft Abstract Series, Vol. 7, p. 177

Seeberger R., Huchtmeier W. K., Weinberger R., 1994a, A&A, 286, 17

Seeberger R., Saurer W., Weinberger R., Lercher C., 1994b, in Balkowski C., Kraan-Korteweg R. C., eds, ASP Conf. Ser., Vol. 67, Unveiling Large-Scale Structures Behind the Milky Way, Astron. Soc. Pac., San Francisco, p. 81

Shapley H., 1961, Galaxies. Harvard Univ. Press, Cambridge

Sheth R. K., 1995, MNRAS, 277, 933

Sheth R. K., Diaferio A., 2011, MNRAS, 417, 2938

Skrutskie M. F. et al., 2006, AJ, 131, 1163

Smoot G. F., Gorenstein M. V., Muller R. A., 1977, Phys. Rev. Lett., 39, 898

Sorce J. G., 2015, MNRAS, 450, 2644

Sorce J. G., Courtois H. M., Tully R. B., 2012, AJ, 144, 133

Sorce J. G., Courtois H. M., Gottlöber S., Hoffman Y., Tully R. B., 2014a, MNRAS, 437, 3586

Sorce J. G., Tully R. B., Courtois H. M., Jarrett T. H., Neill J. D., Shaya E. J., 2014b, MNRAS, 444, 527

Sorce J. G. et al., 2016, MNRAS, 455, 2078

Staveley-Smith L., Kraan-Korteweg R. C., Schröder A. C., Henning P. A., Koribalski B. S., Stewart I. M., Heald G., 2016, AJ, 151, 52

Tully R. B., 2015a, AJ, 149, 54

Tully R. B., 2015b, AJ, 149, 171

Tully R. B., Courtois H. M., 2012, ApJ, 749, 78

Tully R. B. et al., 2013, AJ, 146, 86

van de Weygaert R., Bertschinger E., 1996, MNRAS, 281, 84

Wang H., Mo H. J., Yang X., van den Bosch F. C., 2013, ApJ, 772, 63

Wang H., Mo H. J., Yang X., Jing Y. P., Lin W. P., 2014, ApJ, 794, 94

Williams W. L., Kraan-Korteweg R. C., Woudt P. A., 2014, MNRAS, 443, 41

Zaroubi S., 2000, in Kraan-Korteweg R. C., Henning P. A., Andernach H., eds, ASP Conf. Ser. Vol. 218, Mapping the Hidden Universe: The Universe behind the Milky Way – The Universe in HI, Astron. Soc. Pac., San Francisco, p. 173

Zaroubi S., Hoffman Y., Fisher K. B., Lahav O., 1995, ApJ, 449, 446

Zaroubi S., Hoffman Y., Dekel A., 1999, ApJ, 520, 413

## APPENDIX A: THE WIENER FILTER AND CONSTRAINED REALIZATION TECHNIQUES

The Wiener filter technique is the optimal minimal variance estimator given a data set and an assumed prior power spectrum. Data

dominate the reconstruction in regions where they are dense and accurate. On the opposite, when they are noisy and sparse, the reconstruction is a prediction based on the assumed prior model. It schematically multiplies data by $\frac{\text{Power spectrum}}{\text{Power spectrum}+\text{error}^2}$. Consequently, when data are too noisy or absent, the null field is reached. The CR technique adds the fluctuations of an independent RR to re-establish statistical structures. In other words, the CR adds an RR of the residual between the observed field and the minimal variance estimator of this field (the Wiener filter reconstruction). Briefly, the overdensity $\delta^{\text{CR}}$ and velocity $v^{\text{CR}}$ fields of CRs are expressed in terms of the RR fields $\delta^{\text{RR}}$, $v^{\text{RR}}$ and the correlation matrices. For a list of M constraints $c_i$:

$$ \delta^{\text{CR}}(\mathbf{r}) = \delta^{\text{RR}}(\mathbf{r}) + \sum_{i=1}^{M} \langle \delta(\mathbf{r})c_i \rangle \eta_i \quad (A1) $$

$$ v_{\alpha}^{\text{CR}} = v_{\alpha}^{\text{RR}}(\mathbf{r}) + \sum_{i=1}^{M} \langle v_{\alpha}(\mathbf{r})c_i \rangle \eta_i \quad \text{with } \alpha = x, y, z, \quad (A2) $$

where $\eta_i = \sum_{j=1}^{M} \langle C_i C_j \rangle^{-1} (C_j - \bar{C}_j)$ are the components of the correlation vector $\eta$. $\bar{C}_i$ are random constraints with the noise and $C_i = c_i + \epsilon_i$ are mock or observational constraints plus their uncertainties. Hence, $\langle C_i C_j \rangle$ is equal to $\langle c_i c_j \rangle + \epsilon_i^2 \delta_{ij}$ assuming errors constitute a purely statistical noise with a Gaussian distribution. The constraints can be either densities or velocities. $\langle AB \rangle$ notations stand for the correlation functions involving the assumed prior power spectrum.

The associated correlation functions are given by:

$$ \begin{aligned} \langle \delta(\mathbf{r}')v_{\alpha}(\mathbf{r}'+\mathbf{r}) \rangle &= \frac{Haf}{(2\pi)^3} \int_0^{\infty} \frac{ik_{\alpha}}{k^2} W(kR)P(\mathbf{k})e^{-ik\cdot\mathbf{r}}d\mathbf{k} \\ &= -Haf r_{\alpha} \zeta(\mathbf{r}) \end{aligned} \quad (A3) $$

$$ \begin{aligned} \langle v_{\alpha}(\mathbf{r}')v_{\beta}(\mathbf{r}'+\mathbf{r}) \rangle &= \frac{(Haf)^2}{(2\pi)^3} \int_0^{\infty} \frac{k_{\alpha}k_{\beta}}{k^4} W(kR)P(\mathbf{k})e^{-ik\cdot\mathbf{r}}d\mathbf{k}, \\ &= (Haf)^2 \Psi_{\alpha\beta} \end{aligned} \quad (A4) $$

where P is the assumed prior power spectrum, W is a Gaussian smoothing kernel and R is the smoothing radius. Removing $\delta^{\text{RR}}$ and $v_{\alpha}^{\text{RR}}$ from equations A1 and A2 gives the density and velocity fields of the Wiener filter reconstruction.

## APPENDIX B: COMPARISONS WITH THE 2MASS REDSHIFT SURVEY-BASED RECONSTRUCTION OF THE ZOA

Reconstructing the local Universe using the 2MASS redshift survey, Erdoğdu et al. (2006b) predicted a certain number of structures up to $160 \ h^{-1} \ \text{Mpc}$. Table B1 lists the clusters they predicted in the ZOA that have either been observed or that need to be confirmed observationally. The table gives also the probability to have an overdensity at the location of these predicted or observed clusters according to this paper study. The agreement is remarkable. All the clusters but one (C19) are probable at least at the $1\sigma$ significance level. Most of them are significant at more than $3\sigma$ or even $4\sigma$. For obvious reasons, the probabilities are higher the more nearby the cluster is.
<table><caption>**Table B1.** Comparisons between clusters predicted by Erdoğdu et al. (2006b) and this paper: (1) and (6) name of the cluster as given by Erdoğdu et al. (2006b) or from observations, (2) and (7) distance of the cluster in h⁻¹ Mpc, (3),(4) and (8),(9) galactic coordinates in degrees and (5) and (10) probability of the cluster according to this paper study.</caption><thead><tr><th>(1)<br>Name</th><th>(2)<br>Distance (h<sup>-1</sup> Mpc)</th><th>(3)<br>l (°)</th><th>(4)<br>b (°)</th><th>(5)<br>Probability (%)</th><th>(6)<br>Name</th><th>(7)<br>Distance (h<sup>-1</sup> Mpc)</th><th>(8)<br>l (°)</th><th>(9)<br>b (°)</th><th>(10)<br>Probability (%)</th></tr></thead><tbody><tr><td>Puppis</td><td>20</td><td>240</td><td>-5</td><td>56</td><td>C20</td><td>120</td><td>160</td><td>-10</td><td>35.5</td></tr><tr><td>C1</td><td>20</td><td>200</td><td>5</td><td>59.5</td><td>C19</td><td>120</td><td>120</td><td>-10</td><td>27.5</td></tr><tr><td>C2</td><td>40</td><td>345</td><td>10</td><td>48</td><td>C18</td><td>120</td><td>100</td><td>3</td><td>28.5</td></tr><tr><td>C8</td><td>40</td><td>295</td><td>7</td><td>76.5</td><td>C17</td><td>120</td><td>15</td><td>-7</td><td>25</td></tr><tr><td>C5</td><td>40</td><td>195</td><td>0</td><td>24.5</td><td>C21</td><td>120</td><td>190</td><td>7</td><td>28.5</td></tr><tr><td>Peg</td><td>40</td><td>95</td><td>10</td><td>35</td><td>C19</td><td>140</td><td>115</td><td>-7</td><td>20.5</td></tr><tr><td>Cβ</td><td>40</td><td>120</td><td>7</td><td>34</td><td>C25</td><td>140</td><td>75</td><td>-7</td><td>27</td></tr><tr><td>Or</td><td>60</td><td>165</td><td>5</td><td>42.5</td><td>C29</td><td>140</td><td>330</td><td>-10</td><td>28.5</td></tr><tr><td>C9</td><td>60</td><td>240</td><td>8</td><td>23</td><td>C30</td><td>140</td><td>300</td><td>10</td><td>30.5</td></tr><tr><td>Hyd</td><td>60</td><td>285</td><td>5</td><td>48</td><td>C21</td><td>140</td><td>195</td><td>-3</td><td>26</td></tr><tr><td>C8</td><td>60</td><td>310</td><td>7</td><td>36</td><td>C31</td><td>160</td><td>160</td><td>-10</td><td>25</td></tr><tr><td>A3627</td><td>60</td><td>330</td><td>-5</td><td>30.5</td><td>C33</td><td>160</td><td>110</td><td>0</td><td>23</td></tr><tr><td>C12</td><td>80</td><td>330</td><td>-7</td><td>26</td><td>C32</td><td>160</td><td>45</td><td>0</td><td>28.5</td></tr><tr><td>C11 - Puppis 3</td><td>80</td><td>250</td><td>-4</td><td>21.5</td><td>C30</td><td>160</td><td>290</td><td>5</td><td>26</td></tr><tr><td>C13</td><td>100</td><td>100</td><td>-7</td><td>28</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

This paper has been typeset from a TEX/LATEX file prepared by the author.