Glossary and guide to Celeste parameters

The Celeste model has a lot of parameters. Many are specific to Celeste; some are standard astronomical concepts which nonetheless may be unfamiliar to non-astronomers working on Celeste. Most have been documented in one or another publication about Celeste, but those go quickly out of date, and units are often unclear. This page is intended to provide a precise description of the many terms and parameters you will come across.

General terminology

• Light source or just source: refers to a star or galaxy, or generically an object in an image which we wish to make inference about.
• FITS file: a standard, widely-used file format in astronomy. A FITS file can contain one or more extensions, each of which contains an image (a 2-D array of values, interpreted as counts) and headers (a list of key-value pairs, possibly with comments). FITS files can contain non-image data but we don't do that.
  • Two useful cross-platform FITS viewers: ds9 (good for viewing images, unable to show tables), fv (able to show tables, better for browsing multi-extension files, also shows images but I prefer ds9 for imagery)
• nanomaggy (nMgy): a unit of flux; the physical unit of brightness throughout Celeste. (But see About SDSS and Stripe 82 for details on interpreting pixel values.)
• SDSS, Stripe 82, run/camcol/field: see About SDSS and Stripe 82
• Degrees, arcminutes, arcseconds: these are units of "position" in the sky, each 1/60th of the previous one. See Wikipedia.
• Catalog: a list of light sources (in a particular image or sky region), usually including parameters of the source, either estimated in some way or as "ground truth" (i.e., for synthetic imagery).
• Photo: the name of the legacy image analysis pipeline used to generate catalogs from imagery. This is the previous state-of-the-art which Celeste aims to improve upon.
• Photo-electrons, nelec, counts, data numbers (DNs), gain, calibration: see About SDSS and Stripe 82.

Image parameters

• Optical sensitivity "iota": the number of photo-electrons (the quantity that is Poisson distributed, and thus is modeled by Celeste) per nMgy of flux. See About SDSS and Stripe 82.
• Sky level (SkyIntensity): the background brightness of an image; this amount of brightness would be observed even in an area of sky with no light sources present. See About SDSS and Stripe 82.
• World coordinate system (WCS): see Coordinate systems
• Point spread function (PSF): in an ideal world, a point source of light out there in space would create a single bright pixel in our image. In reality, because of imperfect optics and the atmosphere, light gets scattered or blurred before hitting our image sensors. We represent this by a point spread function: a 2-D function f(i,j) indicating how much light is generated at pixel (i,j) by a point source of light at pixel coordinate (0, 0). The function is nonnegative and should sum (or integrate) to one. The PSF generally varies between images and even between locations within an image, though the latter is not currently supported by Celeste. Celeste represents the PSF in pixel coordinates. We can represent it by a continuous function (e.g., a mixture of Gaussians, the current approach) or by an image (a soon-forthcoming approach to replace the mixture of Gaussians); in either case, the PSF is effectively convolved with an imagined "true" image to produce the observed image. SDSS records information about the PSF in the FITS header.

Source parameters

Parameters for all sources (stars and galaxies):

• Position: the (x, y) center of the source, in world coordinates (degrees, in our case). Corresponds to (ids.u[1], ids.u[2]).
• Brightness: total flux of the source, in nMgy, in the "r" color band (see below). Corresponds to ids.r1[s] and ids.r2[s], which represent the mean and variance of a normal distribution for log brightness; s=1 for inferred brightness if the object is a star and s=2 if the object is a galaxy.
• Color: Celeste works with images taken in five different color bands, called the u, g, r, i, and z bands. (Imagine taking five pictures of the same scene with your camera, one with a red filter over the lens, one with a green filter, etc.) "Color" in Celeste is represented as the four ratios of brightness from one band to the next; in combination with the brightness in one band (r, the "reference band"), these values determine brightness in all bands. ids.c1[i, s] represents the mean of a normal distribution on the log-ratio of the (i+1)-th band divided by the i-th band; ids.c2[i, s] holds the variance. As with brightness, s determines whether the inferred parameters are for a star or galaxy.
• Star/galaxy mixture: ids.a[1] is the probability that a source is a star, ids.a[2] that it is a galaxy.

Parameters for galaxies only:

• Prototype mixture: Celeste represents galaxies as ideal brightness profiles. We start with a circularly symmetric profile, then squish it into an ellipse and rotate it into a particular orientation. Even for a perfectly circular galaxy, though, we have to decide how brightness falls off with radius. We mix between two different profiles for this, the exponential profile and the de Vaucouleurs profile. (Both are ultimately approximated by mixtures of Gaussians, when it comes down to it.) ids.e_dev represents the mixture between these two profiles; e_dev == 1 means 100% de Vaucouleurs (that's what "dev" is short for).
• Half-light radius: the radius which contains half of the source's total flux. We measure it in pixels. This is only really defined for a circular source, so for an elliptical source, we define the half-light radius by transforming the elliptical source into a circular one while preserving area (i.e., stretching along the minor axis and shrinking along the major axis so as to preserve area), then taking the half-light radius of the resulting circular source. (Of course, sources in real images are not perfectly elliptical; this transformation is based on our fitting of ideal profiles.) This corresponds to ids.e_scale, but you must multiply e_scale by the square-root of the axis ratio to get half-light radius (see #437).
• Axis ratio: the length of the minor axis divided by the length of the major axis; a measure of ellipticity. Corresponds to ids.e_axis.
• Angle: the angle between the major axis of the source and the x-axis, measured in radians north of east. Corresponds to ids.e_angle.

Common short variables names

Yes, you will encounter some one- and two-letter variable names throughout Celeste, but there are common conventions:

• ea: short for ElboArgs, which stores all of the information needed to evaluate the variational objective function (images, model parameters, number of light sources, etc.)
• vp: short for VariationalParams, the parameters of the model (enumerated above) which we optimize
• s: generally indexes a light source, in 1...ea.S