# BOSS Tiling and Geometry

## Overview

The fibers on the fiber-optic BOSS spectrograph are attached to holes drilled into metal plates. The image projected onto each plate subtends an angle of 7° on the sky. Tiling is the process by which plates are positioned in a pattern that maximizes the fraction of targets that can be assigned fibers (which we define as “tiling efficiency” or “tiling completeness”), while minimizing the number of plates that are required to observe the full survey—or, equivalently, maximizing the fraction of fibers that are used for unique science targets (which we define as “fiber efficiency”).

Large-scale structure, as well as galactic structure, causes inhomogeneities in the angular density of targets on the sky. Thus, a uniform distribution of tile centers will not achieve both goals of high tiling and fiber efficiency. The BOSS tile distribution achieves a tiling efficiency of >93% for all BOSS targets, with a fiber efficiency of >90%. The primary reason that a target does not get assigned a fiber is fiber collisions, which we will define below. The tiling completeness of targets not involved in a fiber collision is >99%.

Much of the content of this page can be found in the SDSS tiling paper; Blanton et al. 2003, AJ 125, 2276.

A comprehensive tutorial of the tiling process, fiber collisions, and fiber assignment, can be found at the legacy tiling page.

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## Changes to tiling within BOSS

The pedagogical discussion of the tiling process linked above contains some information specific to the tiles used in the SDSS-I/II survey. The main BOSS changes for tiling are:

• The number of fibers per plate is 1000. 895 of these are allocated for unique science targets (although they are not always used as such), 100 are allocated to standard stars and sky, and 5 are required to be placed on repeat observations of targets from other plates.
• Fiber collisions occur when two objects are close enough together such that two holes cannot be drilled and plugged on the plate. In SDSS-I/II, the collision radius was 55″. In BOSS, the collision radius is 62″.

## Survey Footprint

Before describing the detailed geometry of the spectroscopic mask created by all the tiles and chunks, a simple place to start is the overall survey footprint. The figure below shows the survey footprint, which subtends 10,269 square degrees of sky. The spectroscopic observations are restricted to be within this footprint, although the spectroscopic plate coverage is not 100%. This is a subset of the DR8 imaging footprint, which covers 14,555 square degrees.

The boss_survey.fits file in DR9.

 Figure 1: Footprint of the Spectroscopic Survey

## Tiling Chunks

Although the concept of a “tiling chunk” is discussed on the legacy page, the concept of a chunk is important for discussing the geometry of the survey, as well as the evolution of the target selection algorithms for both galaxies and QSOs.

A chunk is a set of tiles—usually, but not always, a spatially contiguous set—that are designed all at the same time. Thus, the targets within a given chunk all come from a common target selection algorithm. The tiling solution, i.e., the distribution of tile centers, is determined for each chunk individually. As of DR9, there are 31 chunks. Early chunks were small, 50-100 plates. These chunks were kept small as target selection was evolving with time. Later chunks were much larger.

Figure 2 below shows the geometry of the chunk boss2. This chunk contains 47 plates and covers 144 square degrees. A sector is defined as a region covered by a unique set of tiles. Each sector in Figure 2 is color coded by the fraction of LRGs that were assigned fibers. The regions where the plates overlap have a significantly higher tiling completeness.

 Figure 2: Geometry for chunk boss2

Figure 3 below shows the entire footprint of the survey, now color-coded such that each chunk is a distinct color. In this figure, boss2 is the dark blue chunk in the upper left-hand side of the plate. Note that, although these chunks cover the entire survey, the number of chunks will increase as the survey progresses: subsets of older chunks will be retiled as target selection is refined and new ancillary targets are added to the survey.

 Figure 3: All BOSS chunks (as of 4/2012)

Here is a chart showing the target selection algorithms (TSA) for galaxies, QSOs and standard stars for each chunk. Each entry links to the boss target selection page, which details the various algorithms used to select targets from the imaging over the course of the survey.

Chunk Name Galaxy TSA QSO TSA Standard TSA
boss1 comm comm comm
boss2 comm2 comm2 comm2
boss3 main002 main002 main004
boss4 main002 main002 main004
boss5 main005 main005 main005
boss6 main005 main005 main005
boss7 main007 main006 main005
boss8 main007 main006 main005
boss9 main007 main006 main005
boss10 main007 main006 main005
boss11 main007 vcat-2010-07-02 main005
boss12 main008 main008 main005
boss13 main008 main008 main008
boss14 main008 main008 main008
boss15 main009 main008 main008
boss16 main009 main010 main008
boss17 main009 main011 main008
boss18 main009 main012 main008
boss19 main009 main013 main008
boss20 main009 main013 main008
boss21 main009 main013 main008
boss22 main009 main013 main008
boss23 main009 main013 main008
boss24 main009 main014 main008
boss25 main009 main014 main008
boss26 main009 main014 main008
boss27 main009 main014 main008
boss28 main009 main015 main008
boss29 main009 main016 main008
boss30 main009 main016 main008

## Manipulating Geometry with Mangle

All geometry files, or masks, are created using the software package mangle. To mangle, a mask is an arbitrary union of arbitrarily weighted angular regions bounded by arbitrary numbers of edges. The restrictions on the mask are only (1) that each edge must be part of some circle on the sphere (but not necessarily a great circle), and (2) that the weight within each subregion of the mask must be constant. For more information, check out mangle web page.

Here are a couple of examples of using the geometry files for the purpose of calculating a correlation function. In both examples, “polygonfile” can be the tiling geometry file discussed below. Note that the tiling geometry does NOT have weight set currently. Different users may define different sets of targets, thus this field is set to 1 everywhere as a default.

• polyid [polygonfile] [list of targets (ra/dec)] polyid.out
This command takes a list of targets and tells you what polygon each target is in. This allows you to sum up the number of targets in each polygon to compute completeness values. This command can also be used with the veto mask (described at the end of this page) to remove targets and randoms from the sample as well.
• ransack -r100000 [polygonfile] ransack.out
This command creates 10,000 random points using the angular selection function defined in the polygonfile, outputted in ra and dec in the ransack.out file.

## Tiling Geometry

Although DR9 consists of only one third of the survey, the full distribution of tile centers has been set. Thus, the tiling geometry of the full spectroscopic survey is fully known.

The full tiling geometry can be found here with a description of the fields given here.

## Veto Masks

Some regions of the sky are not observable for myriad reasons. To create a consistent set of targets and a proper distribution of random points within they tiling geometry, the excluded areas within the survey are given in the veto masks. These veto masks are also created and manipulated with the mangle software. All of these masks are exclusion masks: if a random is within the mask, it should be vetoed. The veto masks include:

• Bright Star Mask
• Centerpost Mask
• Bad Field Mask
• Collision Priority Mask

### Bright Star Mask

The bright star mask blocks out regions around bright stars in the Tycho-2 catalog. The radius of each masked region is a function of the apparent brightness of the star. For both galaxy and QSO targets, the bright star mask is used to remove targets from the list. No BOSS targets should be within the bright star mask; it should be used to remove randoms.

The bright star mask can be found here.

### Centerpost Mask

The inner 92″ of every plate has a hole for the centerpost. No target within 92″ of a plate center can be assigned a fiber. The centerpost mask can be found here.

### Bad Field Mask

Some imaging fields have bad photometry. Targets can still be located within bad fields, thus both targets and randoms within bad fields should be rejected. The bad field mask can be found here.

### Collision Priority Mask

The collision priority mask places 62 arcsecond circles around all targets that have higher priority than the BOSS galaxy targets. Priority in this context refers to allocation of fibers in the event of a fiber collision. This mask is for all higher priority targets, regardless of whether they knocked out a galaxy target or not. It is in mangle polygon format. The mask is available as a .ply file on the DR9 Science Archive Server.