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(Spectral) Timing with Stingray

(Spectral) Timing with Stingray

This talk describes the motivation for the Python package Stingray, designed for spectral timing analysis of astronomical time series observed with X-ray telescopes.

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Daniela Huppenkothen

August 20, 2020
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  1. (Spectral) Timing with Stingray Daniela Huppenkothen DIRAC, University of Washington

    eScience Institute, University of Washington ! Tiana_Athriel " dhuppenkothen # dhuppenk@uw.edu
  2. These slides: https://speakerdeck.com/ dhuppenkothen/spectral-timing-with- stingray Documentation: https://stingray.readthedocs.io/en/ latest/index.html Tutorials: https://github.com/stingraysoftware/

    notebooks Iconic 60s Theme Song: https://youtu.be/sgkk-MMif-4?t=50
  3. Some Scientific Examples

  4. How do black holes accrete matter?

  5. General Relativity plasma physics + magnetic fields jet physics +

    particle acceleration stellar winds
  6. Time [s] Frequenc Time Malzac 2008 Photon Energy [keV] Photon

    Energy * Flux [detector units] “soft state” “hard state” high-frequency/low-frequency X-ray brightness total brightness Spectral States Credit: Sera Markoff
  7. Yamaoka et al (2010); Huppenkothen et al. (2019) Variability: GX

    339-4
  8. Yamaoka et al (2010); Huppenkothen et al. (2019) Variability: GX

    339-4 Fast Fourier Transform
  9. Yamaoka et al (2010); Huppenkothen et al. (2019) Variability: GX

    339-4 Fast Fourier Transform
  10. Yamaoka et al (2010); Huppenkothen et al. (2019) Variability: GX

    339-4 Fast Fourier Transform stochastic variability (red noise)
  11. Yamaoka et al (2010); Huppenkothen et al. (2019) Variability: GX

    339-4 Fast Fourier Transform stochastic variability (red noise) white noise
  12. Yamaoka et al (2010); Huppenkothen et al. (2019) Variability: GX

    339-4 Fast Fourier Transform stochastic variability (red noise) quasi-periodic oscillation (QPO) white noise
  13. Credit: Sera Markoff Heil et al 2014 c) Figure 2.

    a: Graphic illustrating where various states appear within the power-colour diagram. The area of overlap between the hardest and softest states is also indicated. b: Power colour-colour plot for all observations of the transient objects within the sample with labels indicating 20-degree azimuthal or ‘hue’ regions from which the power spectra given in c were found. The plot is colour-coded for each 20◦ bin with the same colours used in c. c: Example power spectra for each of the 20 degree ranges of hue around the power colour-colour diagram. Colours and indices refer to the 20◦ angular bins used in b. Further high-frequency/low-frequency X-ray brightness total brightness
  14. X-ray reverberation around accreting black holes 5 Fig. 3 Time

    lag (8–13 keV relative to 2–4 keV) versus frequency for a hard state obser- vation of Cyg X-1 obtained by RXTE in December 1996. The trend can be very roughly approximated with a power-law of slope −0.7, but note the clear step-like features, which correspond roughly to different Lorentzian features in the power spectrum (Nowak 2000). Cygnus X-1: Nowak, 2000 1 10 0.5 2 5 0.5 Energy (keV) Fig. 9 The ratio spectrum of 1H0707-495 to a continuum model (Fabian et al. 2009). T broad iron K and iron L band are clearly evident in the data. The origin of the soft exce below 1 keV in this source had been debatable, but in this work was found to be dominat by relativistically broadened emission lines. 10−5 10−4 10−3 0.01 −50 0 50 100 150 200 Lag (s) Temporal Frequency (Hz) Fig. 10 The frequency-dependent lags in 1H0707-495 between the continuum dominat hard band at 1–4 keV and the reflection dominated soft band at 0.3–1 keV. and found significant high-frequency soft lags in 15 sources. Plotting the am 1H0707-495: Uttley et al, 2014 Time Lags
  15. X-ray reverberation around accreting black holes 5 Fig. 3 Time

    lag (8–13 keV relative to 2–4 keV) versus frequency for a hard state obser- vation of Cyg X-1 obtained by RXTE in December 1996. The trend can be very roughly approximated with a power-law of slope −0.7, but note the clear step-like features, which correspond roughly to different Lorentzian features in the power spectrum (Nowak 2000). Cygnus X-1: Nowak, 2000 1 10 0.5 2 5 0.5 Energy (keV) Fig. 9 The ratio spectrum of 1H0707-495 to a continuum model (Fabian et al. 2009). T broad iron K and iron L band are clearly evident in the data. The origin of the soft exce below 1 keV in this source had been debatable, but in this work was found to be dominat by relativistically broadened emission lines. 10−5 10−4 10−3 0.01 −50 0 50 100 150 200 Lag (s) Temporal Frequency (Hz) Fig. 10 The frequency-dependent lags in 1H0707-495 between the continuum dominat hard band at 1–4 keV and the reflection dominated soft band at 0.3–1 keV. and found significant high-frequency soft lags in 15 sources. Plotting the am 1H0707-495: Uttley et al, 2014 Time Lags Temporal variations and energy spectra are intricately linked
  16. V404 Cygni 1939 first nova detection 1989 first X-ray detection

    with GINGA 2015 June/July continued monitoring at all wavelengths from ground + space 2015 early August outburst ends 2015 June 15 Swift/BAT detection
  17. V404 Cygni Huppenkothen et al, 2017

  18. short-lived QPO* with a frequency ~10 times lower than expected

    *quasi-periodic oscillation V404 Cygni Huppenkothen et al, 2017
  19. short-lived QPO* with a frequency ~10 times lower than expected

    *quasi-periodic oscillation 18 mHz V404 Cygni Huppenkothen et al, 2017
  20. short-lived QPO* with a frequency ~10 times lower than expected

    *quasi-periodic oscillation 18 mHz 18 mHz V404 Cygni Huppenkothen et al, 2017
  21. possibly signature of jet precession or a warped outer accretion

    disk 18 mHz 18 mHz V404 Cygni *quasi-periodic oscillation Huppenkothen et al, 2017
  22. *quasi-periodic oscillation Huppenkothen et al, 2017 V404 Cygni Typical QPO*,

    but very strong and transient
  23. *quasi-periodic oscillation Huppenkothen et al, 2017 ~100 mHz V404 Cygni

    Typical QPO*, but very strong and transient
  24. *quasi-periodic oscillation Huppenkothen et al, 2017 ~100 mHz V404 Cygni

    Typical QPO*, but very strong and transient see also: stingray.modeling sub-module
  25. How are magnetar bursts produced?

  26. Magnetars • neutron stars • radius ~10km • mass ~1.4

    Msun • period ~1-10 seconds • magnetic field B~1014 G
  27. Magnetars

  28. star quakes or reconnection? Magnetars

  29. “Find star quakes in neutron stars.” https://danielahuppenkothen.wordpress.com/2019/07/25/translating-science-between-disciplines/

  30. “Find star quakes in neutron stars.” “Calculate the probability of

    a quasi-periodic signal in a time series that also contains a stochastic, non-stationary process.” https://danielahuppenkothen.wordpress.com/2019/07/25/translating-science-between-disciplines/
  31. None
  32. Doesn’t work! ☹

  33. Gregory & Loredo (1992)

  34. Gregory & Loredo (1992) Also doesn’t work! ☹

  35. Why is this so difficult to do?

  36. credit: Richard Freeman, flickr.com/photos/freebird710/, CC licensed

  37. credit: Richard Freeman, flickr.com/photos/freebird710/, CC licensed constant background

  38. credit: Richard Freeman, flickr.com/photos/freebird710/, CC licensed constant background Wijnands +

    van der Klis 1998
  39. Willem van de Velde the Younger, “The Gust”

  40. Willem van de Velde the Younger, “The Gust” variable background!

  41. Willem van de Velde the Younger, “The Gust” variable background!

    Lachowicz+Done, 2010
  42. Willem van de Velde the Younger, “The Gust” variable background!

    Lachowicz+Done, 2010
  43. Huppenkothen et al. 0501+4516; left: light curve with a time

    resolution of 0.001 s. Structure in the burst profile and ws flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low he Astrophysical Journal, 768:87 (25pp), 2013 May 1 Huppenkothen et al. igure 1. Fermi GBM observation of burst 0808234789 from SGR J0501+4516; left: light curve with a time resolution of 0.001 s. Structure in the burst profile and ail is clearly visible. Right: periodogram of the burst light curve shows flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low requencies, owing to the complex shape of the light curve. A color version of this figure is available in the online journal.) 2.1. Monte Carlo Simulations of Light Curves: Advantages and Shortcomings Monte Carlo simulations of light curves are a standard tool n timing analysis (see, for example, Fox et al. 2001). The nderlying idea is simple: one fits an empirically derived (or hysically motivated) function to the burst profile. One then enerates a large number of realizations of that burst profile, ncluding appropriate sources of (usually white) noise, such as Poisson photon counting noise. The periodograms computed rom these fake light curves form a basis against which to ompare the periodogram of the real data. For each frequency in, a distribution of powers is produced, with a mean that epends both on the Fourier-transformed burst envelope shape nd the noise processes introduced into the light curve, while Note that the probability derived from the Monte Carlo simulations must be subjected to a correction for the number of frequencies and bursts searched (the number of trials, also called Bonferroni correction or “look-elsewhere effect”), since for a large number of frequencies and light curves searched, we would expect a number of outliers that would otherwise be counted as (spurious) detections. The Monte Carlo method outlined above is versatile and powerful, but it has limitations. The most important limitation comes from our lack of knowledge of the underpinning physical processes producing the observed light curve. Only if the null hypothesis accurately reflects the data—apart from the (quasi-) periodic signal for which we would like to test—is the test meaningful. If important effects that distort either shape or distribution of the powers are missed, then the predictions Huppenkothen et al (2013, 2014)
  44. Huppenkothen et al. 0501+4516; left: light curve with a time

    resolution of 0.001 s. Structure in the burst profile and ws flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low he Astrophysical Journal, 768:87 (25pp), 2013 May 1 Huppenkothen et al. igure 1. Fermi GBM observation of burst 0808234789 from SGR J0501+4516; left: light curve with a time resolution of 0.001 s. Structure in the burst profile and ail is clearly visible. Right: periodogram of the burst light curve shows flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low requencies, owing to the complex shape of the light curve. A color version of this figure is available in the online journal.) 2.1. Monte Carlo Simulations of Light Curves: Advantages and Shortcomings Monte Carlo simulations of light curves are a standard tool n timing analysis (see, for example, Fox et al. 2001). The nderlying idea is simple: one fits an empirically derived (or hysically motivated) function to the burst profile. One then enerates a large number of realizations of that burst profile, ncluding appropriate sources of (usually white) noise, such as Poisson photon counting noise. The periodograms computed rom these fake light curves form a basis against which to ompare the periodogram of the real data. For each frequency in, a distribution of powers is produced, with a mean that epends both on the Fourier-transformed burst envelope shape nd the noise processes introduced into the light curve, while Note that the probability derived from the Monte Carlo simulations must be subjected to a correction for the number of frequencies and bursts searched (the number of trials, also called Bonferroni correction or “look-elsewhere effect”), since for a large number of frequencies and light curves searched, we would expect a number of outliers that would otherwise be counted as (spurious) detections. The Monte Carlo method outlined above is versatile and powerful, but it has limitations. The most important limitation comes from our lack of knowledge of the underpinning physical processes producing the observed light curve. Only if the null hypothesis accurately reflects the data—apart from the (quasi-) periodic signal for which we would like to test—is the test meaningful. If important effects that distort either shape or distribution of the powers are missed, then the predictions Huppenkothen et al (2013, 2014) Lots of Bayesian statistics later …
  45. Huppenkothen et al. 0501+4516; left: light curve with a time

    resolution of 0.001 s. Structure in the burst profile and ws flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low he Astrophysical Journal, 768:87 (25pp), 2013 May 1 Huppenkothen et al. igure 1. Fermi GBM observation of burst 0808234789 from SGR J0501+4516; left: light curve with a time resolution of 0.001 s. Structure in the burst profile and ail is clearly visible. Right: periodogram of the burst light curve shows flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low requencies, owing to the complex shape of the light curve. A color version of this figure is available in the online journal.) 2.1. Monte Carlo Simulations of Light Curves: Advantages and Shortcomings Monte Carlo simulations of light curves are a standard tool n timing analysis (see, for example, Fox et al. 2001). The nderlying idea is simple: one fits an empirically derived (or hysically motivated) function to the burst profile. One then enerates a large number of realizations of that burst profile, ncluding appropriate sources of (usually white) noise, such as Poisson photon counting noise. The periodograms computed rom these fake light curves form a basis against which to ompare the periodogram of the real data. For each frequency in, a distribution of powers is produced, with a mean that epends both on the Fourier-transformed burst envelope shape nd the noise processes introduced into the light curve, while Note that the probability derived from the Monte Carlo simulations must be subjected to a correction for the number of frequencies and bursts searched (the number of trials, also called Bonferroni correction or “look-elsewhere effect”), since for a large number of frequencies and light curves searched, we would expect a number of outliers that would otherwise be counted as (spurious) detections. The Monte Carlo method outlined above is versatile and powerful, but it has limitations. The most important limitation comes from our lack of knowledge of the underpinning physical processes producing the observed light curve. Only if the null hypothesis accurately reflects the data—apart from the (quasi-) periodic signal for which we would like to test—is the test meaningful. If important effects that distort either shape or distribution of the powers are missed, then the predictions Huppenkothen et al (2013, 2014) Lots of Bayesian statistics later …
  46. Huppenkothen et al. 0501+4516; left: light curve with a time

    resolution of 0.001 s. Structure in the burst profile and ws flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low he Astrophysical Journal, 768:87 (25pp), 2013 May 1 Huppenkothen et al. igure 1. Fermi GBM observation of burst 0808234789 from SGR J0501+4516; left: light curve with a time resolution of 0.001 s. Structure in the burst profile and ail is clearly visible. Right: periodogram of the burst light curve shows flat Poisson noise at high frequencies, and an excess of power over the Poisson level at low requencies, owing to the complex shape of the light curve. A color version of this figure is available in the online journal.) 2.1. Monte Carlo Simulations of Light Curves: Advantages and Shortcomings Monte Carlo simulations of light curves are a standard tool n timing analysis (see, for example, Fox et al. 2001). The nderlying idea is simple: one fits an empirically derived (or hysically motivated) function to the burst profile. One then enerates a large number of realizations of that burst profile, ncluding appropriate sources of (usually white) noise, such as Poisson photon counting noise. The periodograms computed rom these fake light curves form a basis against which to ompare the periodogram of the real data. For each frequency in, a distribution of powers is produced, with a mean that epends both on the Fourier-transformed burst envelope shape nd the noise processes introduced into the light curve, while Note that the probability derived from the Monte Carlo simulations must be subjected to a correction for the number of frequencies and bursts searched (the number of trials, also called Bonferroni correction or “look-elsewhere effect”), since for a large number of frequencies and light curves searched, we would expect a number of outliers that would otherwise be counted as (spurious) detections. The Monte Carlo method outlined above is versatile and powerful, but it has limitations. The most important limitation comes from our lack of knowledge of the underpinning physical processes producing the observed light curve. Only if the null hypothesis accurately reflects the data—apart from the (quasi-) periodic signal for which we would like to test—is the test meaningful. If important effects that distort either shape or distribution of the powers are missed, then the predictions Huppenkothen et al (2013, 2014) Lots of Bayesian statistics later … implemented in stingray!
  47. Why Stingray?

  48. Why Stingray? (I needed some software to do timing)

  49. • Limited functionality • Last updated 2009 (?) • Designed

    for spectroscopy • has some timing capabilities • https://space.mit.edu/CXC/isis/ + closed-source packages maintained by individual groups
  50. None
  51. https://github.com/StingraySoftware • 3 lead developers/maintainers (Huppenkothen, Bachetti, Stevens) • ~10

    contributors • 5 completed Google Summer of Code Projects • astropy-affiliated project • provides functionality for HENDRICS and DAVE Huppenkothen et al (2019)
  52. Fourier Transforms

  53. Fourier Transforms Complex Fourier Amplitude Frequency step: Nyquist frequency: For

    a tutorial, see van der Klis (1989)
  54. Fourier Transforms Parseval’s Theorem For a tutorial, see van der

    Klis (1989)
  55. Fourier Transforms Leahy normalization: Fractional RMS normalization: Pj = 2T|aj

    |2 N2μ2 Absolute RMS normalization: Pj = 2|aj |2 T use for period searches use for characterizing quasi-periodic signals For a tutorial, see van der Klis (1989)
  56. Top-level functionality Events Lightcurve Powerspectrum / Crossspectrum AveragedPowerspectrum / AveragedCrossspectrum

    Crosscorrelation / Autocorrelation Bispectrum Lag-Energy Spectra supporting functionality: statistics, good time intervals, I/O Sub-modules pulse modeling simulator deadtime
  57. Where to get help https://stingray.readthedocs.io https://github.com/stingraysoftware join the slack!

  58. Demo: The Stingray API

  59. Interlude: In which I geek out about Co-Spectral Statistics

  60. V404 Cygni is very bright Huppenkothen et al, 2017

  61. NuSTAR Credit: NuSTAR Observatory Guide Chaplin et al (2012)

  62. NuSTAR Credit: NuSTAR Observatory Guide Chaplin et al (2012) dead

    time
  63. Dead Time Bachetti et al (2015)

  64. Dead Time Bachetti et al (2015) The Astrophysical Journal, 800:109

    (12pp), 2015 February 20 (a) (b) (c) (d) Figure 1. Left: the cospectrum and the PDS are compared in the case of pure Poisson noise, without (a) and with (b) dead time. The simulated incid 225 cts s−1. The cospectrum mean is always zero. In these plots, it has been increased by two for display purposes. The frequency 1/τd is indicate √
  65. Dead Time Bachetti et al (2015) The Astrophysical Journal, 800:109

    (12pp), 2015 February 20 (a) (b) (c) (d) Figure 1. Left: the cospectrum and the PDS are compared in the case of pure Poisson noise, without (a) and with (b) dead time. The simulated incid 225 cts s−1. The cospectrum mean is always zero. In these plots, it has been increased by two for display purposes. The frequency 1/τd is indicate √ power spectrum of a constant light curve, no dead time
  66. Dead Time Bachetti et al (2015) The Astrophysical Journal, 800:109

    (12pp), 2015 February 20 (a) (b) (c) (d) Figure 1. Left: the cospectrum and the PDS are compared in the case of pure Poisson noise, without (a) and with (b) dead time. The simulated incid 225 cts s−1. The cospectrum mean is always zero. In these plots, it has been increased by two for display purposes. The frequency 1/τd is indicate √ The Astrophysical Journal, 800:109 (12pp), 2015 February 20 (a) (b) (c) (d) Figure 1. Left: the cospectrum and the PDS are compared in the case of pure Poisson noise, without (a) and with (b) dead time. The simulated incid 225 cts s−1. The cospectrum mean is always zero. In these plots, it has been increased by two for display purposes. The frequency 1/τd is indicate √ power spectrum of a constant light curve, no dead time
  67. Dead Time Bachetti et al (2015) The Astrophysical Journal, 800:109

    (12pp), 2015 February 20 (a) (b) (c) (d) Figure 1. Left: the cospectrum and the PDS are compared in the case of pure Poisson noise, without (a) and with (b) dead time. The simulated incid 225 cts s−1. The cospectrum mean is always zero. In these plots, it has been increased by two for display purposes. The frequency 1/τd is indicate √ The Astrophysical Journal, 800:109 (12pp), 2015 February 20 (a) (b) (c) (d) Figure 1. Left: the cospectrum and the PDS are compared in the case of pure Poisson noise, without (a) and with (b) dead time. The simulated incid 225 cts s−1. The cospectrum mean is always zero. In these plots, it has been increased by two for display purposes. The frequency 1/τd is indicate √ power spectrum of a constant light curve, no dead time power specrum of a constant light curve, with dead time
  68. Dead Time Bachetti et al (2015)

  69. Dead Time Bachetti et al (2015) Caution! The power spectrum

    and the cospectrum do not have the same statistical distribution!
  70. … a month’s worth of maths later ….

  71. … a month’s worth of maths later ….

  72. Dead Time 4 Fig. 1.— Distribution of Leahy-normalized cospectral densities

    (left) and power spectral densities (right), respectively, for the simulated data. In dark grey, we show fine-grained histograms of the simulated powers. In red we plot the theoretical probability distribution the simulated powers should follow: A Laplace distribution with µ = 0 and = 2 for the cospectral densities and a 2-distribution with 2 degrees of freedom for the power spectral densities. The simulated powers adhere very closely to the theoretical predictions. defined in terms of the CDF as SF(x) = 1 CDF(x), en- codes the tail probability of seeing at least a value x X. This tail probability is often considered to be the p-value of rejecting the null hypothesis that a certain candidate Huppenkothen & Bachetti (2018) The co-spectral powers are well-described by a Laplace distribution
  73. Dead Time Huppenkothen & Bachetti (2018) ectral densities (left) and

    power spectral densities (right), respectively, for the simulated ms of the simulated powers. In red we plot the theoretical probability distribution the bution with µ = 0 and = 2 for the cospectral densities and a 2-distribution with 2 s. The simulated powers adhere very closely to the theoretical predictions. CDF(x), en- a value x X. be the p-value ain candidate oduced by the tribution with j < 0 j 0 (16) always smaller at for a given he null hypoth- variables. To ated two light Fig. 2.— Tail probabilities for the Laplace and 2 distributions,
  74. … but X-ray sources are variable?

  75. … but X-ray sources are variable? (here be dragons)

  76. 1936

  77. 1936 1978

  78. 1936 2018 1978

  79. 1936 2018 1978 Conclusion: it's still too hard (and maybe

    impossible)
  80. statistics is a thriving discipline, not a static set of

    recipes
  81. So what do I do about the cospectra?

  82. So what do I do about the cospectra? stay tuned

    for Approximate Bayesian Computation solution
  83. But: we can correct the periodogram (and the cospectrum) in

    some cases!
  84. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time
  85. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time
  86. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time
  87. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time white noise, dead time
  88. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time white noise, dead time
  89. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time white noise, dead time
  90. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018) red noise,

    no dead time white noise, dead time use to correct periodogram
  91. Fourier Amplitude Difference Correction Bachetti & Huppenkothen (2018)

  92. Caveat: this overestimates the rms amplitude when both flux and

    rms are very large
  93. Live Demo: Cospectra, Modelling, Simulations

  94. Extensions + Connections to other Packages command-line functionality built on

    Stingray GUI for exploratory data analysis https://hendrics.readthedocs.io https://github.com/StingraySoftware/dave https://docs.lightkurve.org easy conversion between Lightcurve objects
  95. Current + Future Work • fix bugs (there are always

    bugs) • improve API (aka: what were we thinking?!) • improve documentation (there is never enough documentation) • performance + memory optimization (current GSoC project) • better integration with current X-ray missions • rework the modeling interface (e.g. autodiff) • better integration with spectral modeling packages • better integration with astropy.timeseries and lightkurve • higher-order Fourier products
  96. Get Involved! Stingray is a project for the community, but

    there’s only so much we as maintainers can do …
  97. How to get involved (please do!) • find bugs (and

    report them as a GitHub Issue) • fix bugs (as a GitHub Pull Request) • make feature requests (also via GitHub Issue) • implement new features (also via GitHub Pull Request) • test documentation/tutorials (and report mistakes/fix bugs etc) • … Don’t know where to start? • “Good First Issue” tag on GitHub • join the slack + ask us! We’ll help :)
  98. https://github.com/StingraySoftware/stingray

  99. Please cite the ApJ paper if you use stingray! https://github.com/StingraySoftware/stingray

  100. Questions? Comments? Complaints?

  101. None