We are going to detect the planets by observing drops in overall brightness. Before we are able to do this, we need to calculate the brightness. That is precisely the objective in this chapter.

We are going to create a CSV file with the first column the time of the measurement and the second column the brightness at that time.

For each row of data we would like to know how much Trappist-1 is radiating. What we are going to do is the following.

Take a row of data and sum all the values to get the overall brightness.

the first thing that we need to do is transform our data in to floating point numbers. When our csv module reads in a row of data, it is a piece of text. The map function helps in this regard.

brightness
    .map(function(values){ return parseFloat(values; )})

The summation of all the values can be written down very succinctly because the Array prototype has a trick up it's sleeve. The Array.prototype has a reduce method. We can use it to calculate the sum of all the brightness values. If we have our values in the variable brightness, we can determine the sum with

const sum = brightness
    .map(function(values){ return parseFloat(values; )})
    .reduce(function(partial_sum, value){
        return partial_sum + value;
    }, 0);

If we take a look at one of the images

we see that the background is not pitch black. This means that the background adds to the brightness, even though it does not contribute to the signal. So we start our journey with something we will come very familiar with, we will clean up our data.

What we are going to do is ignore the brightness value of anything below the average brightness. This transforms the image from above into the image below.

Still not perfect, but it is better than nothing.

In order to filter out the unwanted background we are going to need to know the average. We already know the sum, we just calculated it, so the average can be determined by

const average = sum / brightness.length;

Calculating the contribution of the values above the average can still be done succinctly. What we need to do is filter out the values that we want to sum. I.e. the values above the average.

const filtered_sum_= brightness
    .filter(function(value){ return value >= average; })
    .reduce(function(partial_sum, value){ return partial_sum + value; }, 0);

What we want to return in our transformer is the pair of the time, we is the first value of our row of data i.e. const time = data[0], and our filtered_sum.

return [time, filtered_sum];

Once you wrote your brightness results to a CSV file, they are ready for the following step. But if you are like me you probably want to see your results. This is where gnuplot comes in.

If you have saved your results as brightness.csv, the following gnuplot session will plot your data.

set datafile separator ','

plot [2905:2985] "brightness.csv" using 1:2

We will annotate the above example a little, so that you can use gnuplot on your own. The simple_csv library outputs CSV files with a comma as separator. This difference from the default assumption of gnuplot. Luckily this can be remedied with the first line.

The second line display the core of gnuplot; the plot command. The first argument, i.e. [2905:2985], defines the range on the x-axis. It is optional and will be inferred by gnuplot if it isn't present. If there would be a second argument of that form, i.e. [min:max], that would be the range on the y-axis. Here it is inferred.

The "brightness.csv" argument you probably recognize as the file you wrote your data to. The plot command will use data in this file to plot.

The last refers to columns in the data. using 1:2 tells the plot command to plot point with the first column as x-coordinate and the second column as y-coordinate.

For a more extensive explanation of gnuplot we refer you to the gnuplot homepage.

If you have gone to the trouble of outputting the brightness with and without the background, your plot could look like the one below.

Take a look at your data and write down what stands out to you. Discuss this with a neighbor.

Why is the average taken as a cut-off value? What are other options?

There is an obvious gap in our data. This is where the Kepler satellite stopped recording data due to a software reboot initiated by a cosmic ray event. Although the data was lost, the satellite still operates nominally.

Furthermore there is a trend in the overall brightness, more pronounced in the data with the background. This is also seen in our collage. We will have to smooth out that trend and that is precisely what we will in one of the next chapters.