Mapping astronomical survey data on the sky, handsomely

# Skymapper

A collection of matplotlib instructions to map astronomical survey data from the celestial sphere onto 2D.

The purpose of this package is to facilitate interactive work as well as the the creation of publication-quality plots with a python-based workflow many astronomers are accustomed to. The primary motivation is a truthful representation of samples and fields from the curved sky in planar figures, which becomes relevant when sizable portions of the sky are observed.

What can it do? For instance, find the optimal projection for a given list of spherical coordinates and creating a density map from a catalog in a few lines:

import skymapper as skm

# 1) construct a projection, here Albers
# lon_0, lat_0: longitude/latitude that map onto 0/0
# lat_1, lat_2: reference latitudes for conic projection
lon_0, lat_0, lat_1, lat_2 = 27.35, -37.04, -57.06, -11.34
proj = skm.Albers(lon_0, lat_0, lat_1, lat_2)

# alternative: define the optimal projection for set of coordinates
# by minimizing the variation in distortion
crit = skm.stdDistortion
proj = skm.Albers.optimize(ra, dec, crit=crit)

# 2) construct map: will hold figure and projection
# the outline of the sphere can be styled with kwargs for matplotlib Polygon
map = skm.Map(proj)

# 3) add graticules, separated by 15 deg
# the lines can be styled with kwargs for matplotlib Line2D
# additional arguments for formatting the graticule labels
sep = 15
map.grid(sep=sep)

# 4) add data to the map, e.g.
# make density plot
nside = 32
mappable = map.density(ra, dec, nside=nside)
cb = map.colorbar(mappable, cb_label="$n_g$ [arcmin$^{-2}$]")

map.scatter(ra_scatter, dec_scatter, s=size_scatter, edgecolor='k', facecolor='None')

# focus on relevant region
map.focus(ra, dec)


The map instance has several members, most notably

• fig: the matplotlib.Figure that holds the map
• ax: the matplotlib.Axes that holds the map

The syntax mimics matplotlib as closely as possible. Currently supported are canonical plotting functions

• plot
• scatter
• hexbin for binning and interpolating samples
• colorbar with an optional argument cb_label to set the label
• text with an optional direction in ['parallel','meridian'] argument to align along either graticule

as well as special functions

• footprint to show the region covered by a survey
• vertex to plot a list of simple convex polygons
• healpix to plot a healpix map as a list of polygons
• density to create a density map in healpix cells
• extrapolate to generate a field from samples over the entire sky or a subregion

Exploratory and interactive workflows are specifically supported. For instance, you can zoom and pan, also scroll in/out (google-maps style), and the map will automatically update the location of the graticule labels, which are not regularly spaced.

The styling of graticules can be changed by calling map.grid() with different parameters. Finer-grained access is provided by

• map.labelParallelsAtFrame() creates/styles the vertical axis labels at the intersection of the grid parallels
• map.labelMeridiansAtFrame() creates/styles the horizontal axis labels at the intersection of the grid meridians
• map.labelParallelsAtMeridian() creates/styles parallels at a given meridian (useful for all-sky maps)
• map.labelMeridiansAtParallel() creates/styles meridians at a given parallel (useful for all-sky maps)

## Installation and Prerequisites

You can either clone the repo and install by python setup.py install or get the latest release with

pip install skymapper


Dependencies:

• numpy
• scipy
• matplotlib
• healpy

For survey footprints, you'll need pymangle.

## Background

The essential parts of the workflow are

1. Creating the Projection, e.g. Hammer, Albers, WagnerIV
2. Setting up a Map to hold the projection and matplotlib figure, ax, ...
3. Add data to the map

Several map projections are available, the full list is stored in the dictionary projection_register. If the projection you want isn't included, open an issue, or better: create it yourself (see below) and submit a pull request.

There are two conventions for longitudes in astronomy. The standard frame, used for instance for world maps or Galactic maps, has a longitudinal coordinates in the range [-180 .. 180] deg, which increase west to east (in other words, on the map east is right). The equatorial (RA/Dec) frame is left-handed (i.e. on the map east is left) and has coordinates in the range [0 .. 360] deg. To determine the convention, Projection has an argument lon_type, which can be either "lon" or "ra" for standard or equatorial, respectively. The default is lon_type="ra".

Map projections can preserve sky area, angles, or distances, but never all three. That means defining a suitable projection must be a compromise. For most applications, sizes should exactly be preserved, which means that angles and distances may not be. The optimal projection for a given list of ra, dec can be found by calling:

crit = skm.projection.stdDistortion
proj = skm.Albers.optimize(ra, dec, crit=crit)


This optimizes the Albers projection parameters to minimize the variance of the map distortion (i.e. the apparent ellipticity of a true circle on the sky). Alternative criteria are e.g. maxDistortion or stdScale (for projections that are not equal-area).

### Creating a custom projection

For constructing your own projection, derive from Projection. You'll see that every projection needs to implement at least these methods:

• transform to map from spherical to map coordinates x/y
• invert to map from x/y to spherical (if not implemented defaults to basic and slow BFGS inversion)

If the projection has several parameters, you will want to create a special @classmethod optimize because the default one only determines the best longitude reference. An example for that is given in e.g. ConicProjection.optimize.

### Creating/using a survey

Several surveys are predefined and listed in the survey_register dictionary. If the survey you want isn't included, don't despair. To create one can derive a class from Survey, which only needs to implement one method:

def contains(self, ra, dec) to determine whether RA, Dec are inside the footprint.

If this looks like the pymangle interface: it should. That means that you can avoid the overhead of having to define a survey and e.g. pass a pymangle.Mangle object directly to footprint().

### Limitation(s)

The combination of Map and Projection is not a matplotlib transformation. Among several reasons, it is very difficult (maybe impossible) to work with the matplotlib.Axes that are not rectangles or ellipses. So, we decided to split the problem: making use of matplotlib for lower-level graphics primitive and layering the map-making on top of it. This way, we can control e.g. the interpolation method on the sphere or the location of the tick labels in a way consistent with visual expectations from hundreds of years of cartography. While skymapper tries to follow matplotlib conventions very closely, some methods may not work as expected. Open an issue if you think you found such a case.

In particular, we'd appreciate help to make sure that the interactive features work well on all matplotlib backends.

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