# Light curve

The light curve is a graph of intensity of an object (a variable star in most cases), as a function of time. The light curve of the observered object is usually presented in a form of a graph that has time on the independent axis and the intensity in magnitudes on the other axis. Each point in the graph represents single measurement, which in simple cases corresponds to a single input CCD frame.

To make a light curve of an observed object, we need a set of photometry files with cross-reference information (matched photometry files). An user have to the program which stars are variable stars and comparison stars. In case of aperture photometry, he also have to choose an aperture.

The Muniwin program allows an user to apply further corrections and include additional information to a light curve, all of which will be discussed later in the text.

This chapter explains how to make a light curve of stationary objects, such as variable stars and exoplanets. For a guide on making a light curve of moving objects (minor Solar System bodies) follow this link.

## Before you start

Before you start the reduction of your own CCD frames, you may need to perform several pre-processing steps. Though it isn’t necessary, combining the several correction frames into so-called “master” ones is advisory, because it reduces the noise and makes the result more precise. The method of making master correction frames is described in separate chapters.

See also

Master-dark frame and Master-flat frame

## Creating a new project

First of all, we will create a new project. To begin with processing of a variable star observation, we create a new project. To do so, open the Project menu and activate the New item. A new dialog appears.

The dialog for making a new project.

Fill in a name that will be assigned to the project. Because the name of the file that keeps track of the data related to the project, the project file, is derived from the name, some characters cannot appear in the project name, do not use: / ? % * : | “ < and >.

The field Location shows a path to the directory where a new project will be created. Edit the path to change the location, you can also click the Browse button to select a directory in a separate dialog.

The dialog also displays a list of available profiles. A profiles provides an intial set of configuration parameters into a new project. When you confirm the dialog, you should be in the main window again now. The table of input files shown there is empty.

The main application window with the table of input files, now empty.

See also

New project (dialog) and Main window.

## Input files

Now, we are going to tell the program which files we are going to work on. These files are called the input files. Their list is displayed in the table in the main application window. When the application is closed, the list of files are saved to the disk and it is restored back when the program is launched again.

Supposing that the table now consists of files from your previous task, let’s get rid of them. Please, use Files ‣ Clear files to start a new task instead of just removing the files from the table. Besides the clearing the table of input files, this function resets all internal variables, too.

Now, we need to populate the table with the CCD frames we’re going to reduce. There are two methods how to achieve that - adding a individual files or adding all files from a folder. Which way is the best for you depends on organization of your observations on the disk. I’d suggest you to make a folder for each year, a folder for each night in it, the a subfolder for a name of object or another view field identification and finally a subfolder named upon the color filter (if you use more of them). In this case, the “Add frames from a folder” method is more convenient.

Click on Files ‣ Add frames from folder in the main menu. A new dialog appears. In the dialog, find a folder where the inputs files are stored in. Click on an entry in the Places pane to go to one of a preselected folders, double click in the middle pane enters the folder. The buttons in the upper part of the dialog shows your current position in the directory tree, you can use them to go to one of the parent folders. Enter the folder with the input files - you should see them in the middle pane. Then, click on the Add button to add files to the table of input files. The program shows the number of added files in the separate dialog. The Add frames from folder dialog is not closed automatically and allows a user to continue. Click on the OK button to close the dialog and return to the main window.

The “Add folder” dialog with the place selection box (left), the file selection box (middle) and the preview panel (right).

If you want to reduce only a subset of files from a folder, click on Files ‣ Add individual frames in the main menu. A new dialog appears, similar to the previous one. In the dialog, find a folder where the inputs files are stored in. Click on an entry in the Places pane to go to one of a preselected folders, double click in the middle pane enters the folder. The buttons in the upper part of the dialog shows your current position in the directory tree, you can use them to go to one of the parent folders. In the middle pane, select the files using the `Ctrl` modifier to include and exclude a single file and the `Shift` modifier to include a range of files. Then, click on the Add button to add selected files to the table of input files. The program shows the number of added files in the separate dialog. The Add individual frames dialog is not closed automatically and allows a user to continue. Click on the OK button to close the dialog and return to the main window.

The “Add files” dialog with the place selection box (left), the file selection box (middle) and the preview panel (right).

See also

Add frames from folder (dialog) and Add individual frames (dialog).

## Frame reduction

Reduction of CCD frames is a process that takes source CCD frames, performs their conversion and calibration, detects stars on each frame and mearures their intensity and finally finds correlation (match) between objects that were found in the data set. The process of reduction prepares the data that are necessary for making a light curve or a variable star.

The reduction consists of several steps - conversion, calibration, photometry and matching. They can be invoked step-by-step manually. The preferred way is to use the Express reduction dialog that allows to perform these steps in a batch. Using the menu, activate the Reduce ‣ Express reduction item. A new dialog appears. The dialog has several options aligned to the left, Each of them relates to an optional step in the reduction process.

The dialog for setting parameters of the reduction process

Fetch/convert files

Check the Fetch/convert files. In this step, the program makes copy of the source CCD frames. This is necessary, because the following calibration steps will modify them and we don’t want the program to change our precious source data.

Dark-frame correction

A raw CCD frame consists of several components. By the calibration process, we get rid of those which affect the result of the photometry. In some literature, the calibration is depicted as the peeling of an onion. There are three major components which a raw frame consists of - the current made by incident light, current made thermal drift of electrons (so-called dark current) and constant bias level. In standard calibration scheme, which we will demonstrate here, the dark-frame correction subtracts the dark current and the also the bias. Because of the nature of the dark current, it is necessary to use a correction frame of the same exposure duration as source files and it must be carried out on the same CCD temperature, too. Thus, the properly working temperature regulation on your CCD camera is vital.

Flat-frame correction

Then, we have to compensate the spatial non-uniformity of a detector and whole optical system. These non-uniformities are due to the fabrication process of a CCD chip and they are also natural properties of all real optical components, lenses in particular. The flat-frame correction uses a flat-frame to smooth them away. The flat-frame is a frame carried out while the telescope is pointed to uniformly luminous area. In practice, this condition is very difficult to achieve, the clear sky before dusk is usually used instead.

Photometry

The photometry is a process that detects stars on a CCD frame and measures their brightness. Unlike the previous steps, the result is saved to a special file, so-called the photometry file. There are a lot of parameters which affect the star detection and also the brightness computation. In this example, the default values work fine, but I would suggest you to become familiar with at least two of them - FWHM and Threshold - before you start a real work. Check the Photometry option.

FWHM

  The FWHM parameter specify the expected width of stars on a frame. The value is the Full Width at Half Maximum in pixels. The parameter controls the behavior of the low-pass digital filter, which is used in the star detection algorithm.

Threshold

  The Threshold parameter specify the lowest brightness of detected stars. Fainter objects are considered to be background artifacts and thus sorted out. The value is dimensionless coefficient.

Once you tune up the parameter for your environment, usually it is not necessary to adjust them for every task, unless the quality of your images varies considerably. In the first iteration, you can use the default values (FWHM = 3.0 and Threshold = 4.0) and do the photometry. Click on the Reduce ‣ Photometry item in the main menu and confirm the new dialog by the OK. Then, by double click on a frame in the main window open the preview window and check the results. If there are stars which have been detected as a close binary although it is not true, you should increase the FWHM value. If the stars you are interested in are not detected, try decrease the Threshold value. If it doesn’t help, decrease the FWHM. If there is a lot of background artifacts detected as a real stars, increase the Threshold. By several iterations, adjust the parameters, so all the stars you are interested in are detected and there are no false binaries.

Matching

The previous command treated all source files independently. As a result of this, a star #1 in one file is not necessarily the same as a star #1 in another file. The matching is a process which finds corresponding stars on source frames and assigns an unique identifier. Check the Matching option.

It is necessary to select one frame from the set of source frames that all other frames are matched to, this frame is called a reference frame. In my experience, the frame with the greatest number of stars works the best. Back to our example, let’s pick up the first one.

Invoking the reduction process

In previous steps, we have configured parameters of the reduction process and we are ready to start it. Click the OK button. During the execution a new window appears displaying the state of the process; all the information is also presented there. This window will be automatically closed after finishing the process. Wait for the process to finish.

The dialog displayed during time demanding operations.

After finishing, the icon in the file table changes; the information about the time of observation, the length of the exposition and the used filter is filled in. In case some of the frames could not be processed successfully, the entry is be marked with a special icon and in the Status column the error message is indicated.

The main application window after the recution.

See also

Express reduction (dialog).

## Making a light curve

Reduce the source CCD frames (see the chapter “Reduction of CCD frames”). Then click on the Plot ‣ Light curve item in the main menu. A new dialog appears. The dialog allows an user to set up the options for the light curve. If you want only a subset of frames from the project to be included in the curve, check the selected files only option in the box. The program can also include several corrections and coefficients to the output file, these features are discussed later in the text.

Confirm the dialog by the OK button.

The dialog for making a light curve.

See also

Plot light curve (dialog)

## Selecting the stars

The next dialog shows the reference frame and allows an user to select variable, comparison and check stars. The detected stars are highlighted. Click on the variable star using left mouse button. A context menu opens. Select the Variable. The star is now drawn in red color now and the label “var” is placed near to it. Using the same procedure, select one comparison star and one or more check stars. I would recommend you to use two check stars. Confirm the selection by the OK button.

The dialog for selection of a variable star (red), a comparison star (green) and check stars (blue).

See also

Choose stars (dialog)

## Choosing an aperture

Now, we have to choose the aperture. You can image the aperture as a virtual circular pinhole, placed on each star on a frame to measure its brightness. All pixels that are inside the pinhole are included in computation leaving out the background pixels. The best aperture should be big enough to include most of the star’s light, on the other hand, the bigger aperture is used the more background is included and the more noisy the result is. Because of this, the photometry process computes the brightness of each star in a set of predefined apertures of radius in the range of 2 and 30 pixels.

To select the best aperture, we can take advantage of a comparison and check stars - providing that they are constant, we can compute the differential magnitudes between each couple of them on each other and then compute the variance or standard deviation from the mean level. For the best aperture, the deviations are minimal.

In the next dialog, the graph shows the standard deviation for each aperture. Find the aperture with the minimal deviation and click on it using the left mouse button. A context menu appears. Select the Select aperture item. The point is drawn in red color now and the label is placed near to it. Confirm the selection by the OK button.

The dialog for selection of an aperture.

See also

Choose aperture (dialog)

## Plotting a light curve

Now, the program has got enough information to make a light curve. It is presented in a new window which appears automatically.

The dialog with a light curve graph.

See also

Light curve (dialog)

## Saving a light curve to a file

In the window with a light curve, click on the File –> Save` item in the local menu. A new dialog appears. Locate the folder where you want to save the results and fill in the name of the output file. Confirm the dialog by the Save.

The light curve is saved to a text-based file. On its first line, the names of the columns are stored. The second line shows the aperture and color filter used. The data are stored on the following lines. Each line corresponds to a single source frame. In the first column, there is a time of observation (center of exposure) expressed as a Julian date. The second column consists of differential instrumental brightness of the variable stars with respect to the comparison star in magnitudes (V-C). The error estimation is stored in the next column. Following columns consist of differential magnitudes of comparison star and check stars and their error estimations.

It is also possible to save a light curve in other formats.

See also

Export light curve in AAVSO format

## Heliocentric correction

While the Earth orbits the Sun, the distance between the observed object and the observer changes during a year. Although the amplitude of these changes is negligible with respect to the mean distance, it becomes significant when you are interested in a time interval between two events, like times of minimum of a eclipsing variable star. In this case, the finite speed of light is not unimportant. The value of the heliocentric correction is the time that the light needs to travel from the Earth’s actual position to the center of the Earth’s orbit. The value may be either positive, when the Earth is nearer to the object than the Sun, or negative in the opposite case.

It is possible to make a light curve that includes the value of the heliocentric correction for each measurement in a separate column. Optionally, it is also possible to save the output table which has heliocentric Julian date in its first column.

To compute the heliocentric corrections for an existing light curve, click on the Edit ‣ Properties in the local menu in the light curve window. A new dialog opens. Check the option Compute heliocentric correction. When you are making a new light curve, it is also possible to turn this feature on (see above). Confirm the dialog by the OK button.

When the heliocentric correction is turned on, you have to fill the object’s celestial coordinates to the appropriate edit boxes in the dialog, the fields may be filled automatically if the input CCD frames or a catalogue file unsed in the matching step contain such information.

Light curve properties dialog (heliocentric correction)

Only one value of Julian date per each row can be exported to the file. You can choose between the geocentric and heliocentric J.D. in the “Save light curve” dialog - there is an appropriate option in the section “Export options”. However, in both cases, the file will contain the column HELCOR with values of the heliocentric correction for each observation.

There are other options how to obtain the object coordinates. For more options, click on the More button. A new dialog appears. In this dialog you can make your table of favorite objects. For known variable stars, the program provides a tools for searching the common variable star catalogs (GCVS, NSV and NSVS).

## Air mass coefficients

The air mass coefficient characterizes the attenuation of the star’s signal after it has traveled through the Earth’s atmosphere. While this effect is strongly dependent on the light’s wavelength (color), it must be taken account in computation of the color index (temperature) of an observer object. The attenuation also becomes significant when the color index of the variable and the comparison star are not close. The air mass coefficient is always positive value, it defined as 1.0 when the object is in the zenith and greater than one when the object is somewhere between the horizon and the zenith. The program also presents the value of altitude of the object above the horizon in degrees. Please note, that the value is positive to indicate altitude above the horizon while a negative value of altitude means that the object is below the horizon - it indicates that either times of observation, object coordinates or observer coordinates are wrong.

Although the C-Munipack program doesn’t perform any corrections to the measured intensity. It can compute the value for coefficient for each measurement and put those values into the output file to a separate column.

To compute the air mass coefficients for an existing light curve, click on the Edit ‣ Properties in the local menu in the light curve window. A new dialog opens. Check the option Compute air mass coefficients. When you are making a new light curve, it is also possible to turn this feature on (see above). Confirm the dialog by the OK button.

When the heliocentric correction is turned on, you have to fill the object’s celestial coordinates and observer’s geographic coordinates to the appropriate edit boxes in the dialog, the fields may be filled automatically if the input CCD frames or a catalogue file unsed in the matching step contain such information.

Light curve properties dialog (air mass coefficients)

When you save the light curve to a file, it will contain the column AIRMASS with values of the air mass coefficient and the column ALTITUDE with values of altitude of the object above the horizon in degrees.

There are other options how to obtain the object and observer coordinates. For more options, click on the More button. A new dialog appears. In this dialog you can make your table of favorite objects and locations. For known variable stars, the program provides a tools for searching the common variable star catalogs (GCVS, NSV and NSVS).

## Intensities (fluxes)

In some cases when further processing of the photometric data is involved, ensemble photometry for example, it is neccesary to get intensity (brightness) values of individual stars instead of the standard differential magnitudes. Some programs call such value the flux. The intensity is defined as integral of the light in an aperture minus contribution of a local background. The intensity can be transformed into magnitudes using Pogson’s law and a reference intensity. In the C-Munipack software, this value is called the raw instrumental magnitude.

The Muniwin software provides a special output mode called ‘Raw instrumental magnitudes’. If this mode is enabled, the light curve will contain a pair of values for each selected star and frame. The first value in pair is the intensity of a star expressed in magnitudes and the second value is its error estimation. The reference intensity was set to 10^10. Please look into the separate document ‘Theory of operation’ section ‘Aperture photometry’ on the conversion between the raw instrumental magnitude and the intensity.

To show the raw instrumental magnitudes for an existing light curve, click on the Edit ‣ Properties in the local menu in the light curve window. A new dialog opens. Check the option Show raw instrumental magnitudes. Confirm the dialog by the OK button. When you are making a new light curve, it is also possible to turn this feature on (see above) in the Make light curve dialog.

## Trimming outliers from the curve

Is is possible to manually trim outlying observations from the curve. You can select an individual point by a right click, you can also select more than one point by pressing a Shift key and left mouse button and drawing a rectangle in the graph. Then, click the right mouse button on a point in the selection to open the context menu. There are two options: When you select the option delete from data set, the selected measurements are removed from the current light curve, the data will be shown when you make another light curve or Rebuild the actual curve. The other option remove from project means that the frames corresponding to the selected measurements are removed permanently from the list of input files (see: Main application window) and such measurements won’t be included in any other output. It is not allowed to remove a reference frame.