6.1 Introduction

Overview

The module aspylib.cdr has been written to process the measured lightcurves and extract some useful information from them. The following operations can be done in AsPyLib v1.2.1:

Time corrections

• shift of date to mid-exposure,
• correction of time delay due to light propagation (asteroid),
• conversion to heliocentric Julian dates (variable stars)

For periodic lightcurves

• searching the period that gives the smallest fit residual,
• fit with Fourier series and calculation of period, amplitude, date of maximum, phase ephemerid, etc.

In the future the module may be extended to contain more functionalities (fit of exoplanet transits, search for multiple non-harmonic periods, etc). It has been named “cdr” to remind the website CdR-CdL (“courbe de rotation, courbe de luminosite” in French) from Raoul Behrend.

Terminology

To avoid any confusion we give here the definitions of a few terms which are commonly used in the documentation of AsPyLib.

“Instrumental magnitude” refers to the magnitude that is obtained directly with the equations of aperture photometry. For a given star it is equal to -2.5*log(flux) with “flux” being the sum of all star pixels, after subtraction of the level of the sky background in each pixel. The instrumental magnitude of a star is the first measured quantity, and does not represent anything useful. It may vary considerably during the night, depending on the variations of air mass and sky transparency.

“Differential magnitude” is obtained by taking the difference between the star instrumental magnitude, and the average instrumental magnitude of a small set of “reference stars”. This subtraction removes all effects linked to the observation conditions (air mass, transparency...). At first order, for a given star (assuming it is not variable) the differential magnitude should be approximately constant. In practice it is common to observe a slow drift, due to color differences between the measured and reference stars. The differential magnitude depends on the choice of reference stars, and still cannot be compared to values from a catalog.

Required file format for lightcurve data

The lightcurve information should be provided to AsPyLib in text files following a strict format. This format is compatible with the CourbRot software: this means that you can also send your files to Raoul Behrend and your measurements will be probably included in the CdR-CdL database !

Here’s an example:

The file must be in plain text (= non-formatted). It has two parts: a header part, followed by a data part.

Header part

• the following header keywords are mandatory: “FMT”, “NOM”, “MES” and “POS”. They must be used with the same ordering (“FMT” comes first, then “NOM”, etc)
• other keywords compatible with CourbRot are allowed (see description of CourbRot format)
• all other headers lines shall start with a semicolon (;)

Mandatory keywords

• “FMT” describes how the data are organised. For AsPyLib the following must be used: “FMT DVR” with as many “R” as there are reference stars. The “D” stands for “date” (column 1 in the data part), the “V” stands for “value” (column 2) and each “R” corresponds to one reference star and its column.
• “NOM” gives the name of the observed target.
• “MES” gives the names of all observers (complete first name and last name), separated with a comma. At the end of the line, the IAU observatory code (if any) can be added after the sign “@”.
• “POS” gives the exposure of the images, in seconds. “POS 0 xx” can be used for images posed xx seconds, with datation at mid-exposure. “POS -1 xx” must be used for datation at start of exposure. AsPyLib will use this keyword to shift the dates to mid-exposure, if required.

Data part

• each line in the data part starts with a numeric character (0-9)
• the data consists of n columns separated by tabulations
• first column contains the Julian dates, either at the start of the exposures or at mid-exposures
• second column contains the instrumental magnitudes for the target
• all other columns (at least one) correspond to the instrumental magnitudes for the reference stars.