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content/en/case-studies/gw-discov.md

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 {{< figure src="/images/content_images/cs/gw_sxs_image.png" class="fig-center" caption="**Gravitational Waves**" alt="binary coalesce black hole generating gravitational waves" attr="(**Image Credits: The Simulating eXtreme Spacetimes (SXS) Project at LIGO** )" attrlink="https://youtu.be/Zt8Z_uzG71o" >}}
 
-<blockquote cite="https://www.youtube.com/watch?v=BIvezCVcsYs">
-    <p>The scientific Python ecosystem is critical infrastructure for the research done at LIGO.</p>
-    <footer align="right">David Shoemaker, <cite>LIGO Scientific Collaboration</cite></footer>
-</blockquote>
-
-## About [Gravitational Waves](https://www.nationalgeographic.com/news/2017/10/what-are-gravitational-waves-ligo-astronomy-science/) and [LIGO](https://www.ligo.caltech.edu)
-
-Gravitational waves are ripples in the fabric of space and time, generated by
-cataclysmic events in the universe such as collision and merging of two black
-holes or coalescing binary stars or supernovae. Observing GW can not only help
-in studying gravity but also in understanding some of the obscure phenomena in
-the distant universe and its impact.
-
-The [Laser Interferometer Gravitational-Wave Observatory (LIGO)](https://www.ligo.caltech.edu)
-was designed to open the field of gravitational-wave astrophysics through the
-direct detection of gravitational waves predicted by Einstein’s General Theory
-of Relativity. It comprises two widely-separated interferometers within the
-United States—one in Hanford, Washington and the other in Livingston,
-Louisiana—operated in unison to detect gravitational waves. Each of them has
-multi-kilometer-scale gravitational wave detectors that use laser
-interferometry.  The LIGO Scientific Collaboration (LSC), is a group of more
-than 1000 scientists from universities around the United States and in 14
-other countries supported by more than 90 universities and research institutes;
-approximately 250 students actively contributing to the collaboration. The new
-LIGO discovery is the first observation of gravitational waves themselves,
-made by measuring the tiny disturbances the waves make to space and time as
-they pass through the earth.  It has opened up new astrophysical frontiers
-that explore the warped side of the universe—objects and phenomena that are
-made from warped spacetime.
+<blockquote cite="https://www.youtube.com/watch?v=BIvezCVcsYs"> <p>The scientific Python ecosystem is critical infrastructure for the research done at LIGO.</p> <footer align="right">David Shoemaker, <cite>LIGO Scientific Collaboration</cite></footer> </blockquote>
 
+## About Gravitational Waves and [LIGO](https://www.ligo.caltech.edu)
+
+[Gravitational waves](https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves) are ripples in the fabric of spacetime, generated by cataclysmic events in the universe such as collision and merging of two black holes, coalescing binary stars, supernovae or [compact binaries](https://wwwmpa.mpa-garching.mpg.de/~hsr/researchcb-en.html). Observing GW can not only help in studying gravity but also in understanding some of the obscure phenomena in the distant universe and its impact. Two of the most recent events in the context of gravitaional waves are the focus of this case study:
+
+* [GW observations from LIGO/Virgo GW150914](https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves): The original discovery of gravitational waves from a binary black hole merger 
+* [GW observations from LiGO/Virgo * GW170817](https://en.wikipedia.org/wiki/GW170817): The first direct detection of neutron start mergers 
+
+The [Laser Interferometer Gravitational-Wave Observatory
+(LIGO)](https://www.ligo.caltech.edu) was designed to open the field of
+gravitational-wave astrophysics through the direct detection of gravitational
+waves predicted by Einstein’s General Theory of Relativity. It comprises two
+widely-separated interferometers within the United States—one in Hanford,
+Washington and the other in Livingston, Louisiana—operated in unison to detect
+gravitational waves. Each of them has multi-kilometer-scale gravitational wave
+detectors that use laser interferometry.  The LIGO Scientific Collaboration
+(LSC), is a group of more than 1000 scientists from universities around the
+United States and in 14 other countries supported by more than 90 universities
+and research institutes; approximately 250 students actively contributing to the
+collaboration. LIGO discovery GW150914 is the first observation that is
+significant in being the first observation both confirming the existence of
+gravitational waves as well as proves the ability to directly measure them. 
+
+Gravitational waves allow scientists to observe and study the universe in a
+brand new way, ushering in the era of gravitational wave astronomy.
 
 ### Key Objectives
 
 * Though its [mission](https://www.ligo.caltech.edu/page/what-is-ligo) is to
   detect gravitational waves from some of the most violent and energetic
-  processes in the Universe, the data LIGO collects may have far-reaching
-  effects on many areas of physics including gravitation, relativity,
-  astrophysics, cosmology, particle physics, and nuclear physics.
+processes in the Universe, the data LIGO collects may have far-reaching effects
+on many areas of physics including gravitation, relativity, astrophysics,
+cosmology, particle physics, and nuclear physics.
 * Crunch observed data via numerical relativity computations that involves
   complex maths in order to discern signal from noise, filter out relevant
-  signal and statistically estimate significance of observed data 
+signal and statistically estimate significance of observed data 
 * Data visualization so that the binary / numerical results can be
   comprehended.
 
@@ -55,81 +51,87 @@ made from warped spacetime.
 * **Computation**
 
     Gravitational Waves are hard to detect as they produce a very small effect
-    and have tiny interaction with matter.  Processing and analyzing all of
-    LIGO's data requires a vast computing infrastructure.After taking care of
-    noise, which is billions of times of the signal, there is still very
-    complex relativity equations and huge amounts of data which present a
-    computational challenge:
-    [O(10^7) CPU hrs needed for binary merger analyses](https://youtu.be/7mcHknWWzNI)
-    spread on 6 dedicated LIGO clusters 
+and have tiny interaction with matter.  Processing and analyzing all of LIGO's
+data requires a vast computing infrastructure.After taking care of noise, which
+is billions of times of the signal, there is still very complex relativity
+equations and huge amounts of data which present a computational challenge:
+[O(10^7) CPU hrs needed for binary merger
+analyses](https://youtu.be/7mcHknWWzNI) spread on 6 dedicated LIGO clusters 
 
 * **Data Deluge**
 
     As observational devices become more sensitive and reliable, the challenges
-    posed by data deluge and finding a needle in a haystack rise multi-fold.
-    LIGO generates terabytes of data every day! Making sense of this data
-    requires an enormous effort for each and every detection. For example, the
-    signals being collected by LIGO must be matched by supercomputers against
-    hundreds of thousands of templates of possible gravitational-wave signatures.
+posed by data deluge and finding a needle in a haystack rise multi-fold.  LIGO
+generates terabytes of data every day! Making sense of this data requires an
+enormous effort for each and every detection. For example, the signals being
+collected by LIGO must be matched by supercomputers against hundreds of
+thousands of templates of possible gravitational-wave signatures. 
 
 * **Visualization**
 
-    Once the obstacles related to understanding Einstein’s equations well
-    enough to solve them using supercomputers are taken care of, the next big
-    challenge was making data comprehensible to the human brain. Simulation
-    modeling as well as  signal detection requires effective visualization
-    techniques.  Visualization also plays a role in lending more credibility
-    to numerical relativity in the eyes of pure science aficionados, who did
-    not give enough importance to numerical relativity until imaging and
-    simulations made it easier to comprehend results for a larger audience.
-    Speed of complex computations and rendering, re-rendering images and
-    simulations using latest experimental inputs and insights can be a time
-    consuming activity that challenges researchers in this domain.
+    Once the obstacles related to understanding Einstein’s equations well enough
+to solve them using supercomputers are taken care of, the next big challenge was
+making data comprehensible to the human brain. Simulation modeling as well as
+signal detection requires effective visualization techniques.  Visualization
+also plays a role in lending more credibility to numerical relativity in the
+eyes of pure science aficionados, who did not give enough importance to
+numerical relativity until imaging and simulations made it easier to comprehend
+results for a larger audience.  Speed of complex computations and rendering,
+re-rendering images and simulations using latest experimental inputs and
+insights can be a time consuming activity that challenges researchers in this
+domain.
 
-{{< figure src="/images/content_images/cs/gw_strain_amplitude.png" class="fig-center" alt="gravitational waves strain amplitude" caption="**Estimated gravitational-wave strain amplitude from GW150914**" attr="(**Graph Credits:** Observation of Gravitational Waves from a Binary Black Hole Merger, ResearchGate Publication)" attrlink="https://www.researchgate.net/publication/293886905_Observation_of_Gravitational_Waves_from_a_Binary_Black_Hole_Merger" >}}
+{{< figure src="/images/content_images/cs/gw_measurement.png" class="fig-center" alt="gravitational waves measurement" caption="**LIGO measurement of gravitational waves at Hanford and Livingston comparing signals to those expected due to a black hole merger event**" attr="(**Graph Credits:** LIGO Scientific Collboration & Virgo Collaboration" attrlink="https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102" >}}
 
 ## NumPy’s Role in the detection of Gravitational Waves
 
 Gravitational waves emitted from the merger cannot be computed using any
-technique except brute force numerical relativity using supercomputers.
-The amount of data LIGO collects is as incomprehensibly large as gravitational
-wave signals are small.
-
-NumPy, the standard numerical analysis package for Python,  was utilized by
-the software used for various tasks performed during the GW detection project
-at LIGO. NumPy helped in solving complex maths and data manipulation at high
-speed.  Here are some examples:
+technique except brute force numerical relativity using supercomputers.  The
+amount of data LIGO collects is as incomprehensibly large and requires careful
+processing like any other data science problem.  Although it is technologically
+more challenging to achieve the requisite sensitivity for capturing
+gravitaional waves and is way harder than dealing with large scale data, yet
+the latter is complex enough to require numerical processing skills of several
+Python tools including
+[NumPy](https://towardsdatascience.com/2020-how-a-i-could-help-astronomers-sorting-big-data-811571705707).
+
+NumPy, the standard numerical analysis package for Python,  was utilized by the
+software used for various tasks performed during the GW detection project at
+LIGO. NumPy helped in solving complex maths and data manipulation at high speed.
+Here are some examples:
 
 * [Signal Processing](https://www.uv.es/virgogroup/Denoising_ROF.html): Glitch
-  detection,  [Noise identification and Data Characterization](https://ep2016.europython.eu/media/conference/slides/pyhton-in-gravitational-waves-research-communities.pdf)
-  (NumPy, scikit-learn, scipy, matplotlib, pandas, pyCharm )
+  detection,  [Noise identification and Data
+Characterization](https://ep2016.europython.eu/media/conference/slides/pyhton-in-gravitational-waves-research-communities.pdf)
+(NumPy, scikit-learn, scipy, matplotlib, pandas, pyCharm )
+* GW data analysis
+  such as [GwPy](https://gwpy.github.io/docs/stable/overview.html) and
+[PyCBC](https://pycbc.org) uses NumPy and AstroPy under the hood for providing
+object based interfaces to utilities, tools and methods for studying data from
+gravitational-wave detectors. Both GwPy and pycbc libraries rely on NumPy for
+analysis of the "chirp" signal. For example, in pycbc, the time series data are
+stored in ndarrays and scipy.signal, which operates on NumPy arrays.
 * Data retrieval: Deciding which data can be analyzed, figuring out whether it
   contains a signal - needle in a haystack
 * Statistical analysis: estimate the statistical significance of observational
   data, estimating the signal parameters (e.g. masses of stars, spin velocity,
-  and distance) by comparison with a model.
+and distance) by comparison with a model.
 * Visualization of data
   - Time series
   - Spectrograms
-* Compute Correlations 
-* Key [Software](https://github.com/lscsoft) developed in GW data analysis
-  such as [GwPy](https://gwpy.github.io/docs/stable/overview.html) and
-  [PyCBC](https://pycbc.org) uses NumPy and AstroPy under the hood for
-  providing object based interfaces to utilities, tools and methods for
-  studying data from gravitational-wave detectors.
+* Compute Correlations Key [Software](https://github.com/lscsoft) developed in
 
 ## Summary
 
 GW detection has enabled researchers to discover entirely unexpected phenomena
 while providing new insight into many of the most profound astrophysical
-phenomena known. Number crunching and data visualization is a crucial step
-that helps scientists gain insights into data gathered from the scientific
-observations and understand the results. The computations are complex and
-cannot be comprehended by humans unless it is visualized using computer
-simulations that are fed with the real observed data and analysis.  NumPy
-along with other Python packages such as matplotlib, pandas and scikit-learn
-is [enabling researchers](https://www.gw-openscience.org/events/GW150914/) to
-answer complex questions and discover new horizons in our understanding of the
-universe.
+phenomena known. Number crunching and data visualization is a crucial step that
+helps scientists gain insights into data gathered from the scientific
+observations and understand the results. The computations are complex and cannot
+be comprehended by humans unless it is visualized using computer simulations
+that are fed with the real observed data and analysis.  NumPy along with other
+Python packages such as matplotlib, pandas and scikit-learn is [enabling
+researchers](https://www.gw-openscience.org/events/GW150914/) to answer complex
+questions and discover new horizons in our understanding of the universe.
 
 {{< figure src="/images/content_images/cs/numpy_gw_benefits.png" class="fig-center" alt="numpy benefits" caption="**Key NumPy Capabilities utilized**" >}}