Add hardness-intensity diagram, power colors, and bad interval filling to spectral timing tutorial

[matteobachetti]

The spectral timing tutorial now includes a section where small gaps in data are filled with simulated data, and another with the calculation of power colors (with a discussion on how to use them to determine the spectral state)

Resolve #77

[mgullik]

Hi @matteobachetti,

here there are some comments on the very useful spectral-timing tutorial that you updated recently.
I've been extremely pedantic, but I think a tutorial should be like that, the user can always skip information if they want.

• In the histogram plt.hist(bti_lengths, bins=np.geomspace(1e-10, 10000, 20)) it would benefit to have x-axis label, something like bad-time-interval length (s) and on the y-axis Numbers of intervals, just to be super pedantic.
• when you write the line of code ev_filled = events.fill_bad_time_intervals(max_length=2, buffer_size=200) I would add a comment saying that max_length is in seconds.
• in the text above this line the tutorial writes that the BTI <1 s can be filled, but then you use max_length = 2. This might be confusing. Why don't we say BTI =< 2 sec ?
• lc_filled = ev_filled.to_lc(1), I would write lc_filled = ev_filled.to_lc(dt=1). I know that you've already used to_lc in the tutorial, but if someone skip the first bit is useful to have the explicit expression (again, very pedantic but...)
• you write "# Using the same intervals as the Wang+ paper. Segment_size is not specified, so we are using single GTIs" but then you use segment_size=256, it's not that clear to me what you mean with single GTIs, it seems you use segment_size = 256. If segment_size is another information (e.g. for the power-spectrum), I think you need to specify it.
• I would add a comment on why in the HID where you compare Jingyi Wang's data and this particular observation there is only one red star and several blue dots. Is it because you separated every bit GTIs and probably took the full OsbID?

On Power colours:

• "Power colors (Heil et al. 2015) are an alternative to spectral colors to understand the spectral state of an accreting source." -> Power colors (Heil et al. 2015) are an alternative to spectral colors but in the timing regime. The power colors are the ratio of the variability at different timescale, basically they inform us on the slope of the power spectrum in different Fourier frequency regime. The can be use to understand the spectral state of an accreting source (see Heil et al. 2015).
• "PC1: the ratio of the variances in the intervals 0.25-2 and 0.00390625-0.03125" I think they are in units of Hz, correct?
• I know pedantic, but here dynps = DynamicalPowerspectrum(events, segment_size=256, sample_time=1 / 256, norm="leahy") I would specify what is sample_time = 1/256. It is not connected to segment_size right? And also, why don't you show the dynamical power spectrum? It could be useful as well (at least referring to another tutorial if it's there e).

[matteobachetti]

@mgullik thanks for the review, I think I addressed all your comments.