Why should we bother looking for Gravitational Waves?

26/4/2019 mid sem Holiday is almost up. I Better get started on that ASTR 800 (Advanced Topics in Astrophysics) paper.

Break is over, better get started on that term paper.

So I want to talk about Gravitational Waves, more so the importance of finding gravitational waves.

Why do we need to find these elusive ripples of propagating space time called Gravitational Waves?

For a long time Gravitational Waves seemed to be secluded within the realm of theoretical physics. The idea was born out of the mind of Einstein while the experimentalists in the room which included Richard Feynman and Joe Weber could only dream of detecting them. Some of those early  experimentalists although daring in the quest for gravitational waves are no longer with us, were not able to make it to witness the progress we have made today.

But the first Ligo Gravitational Wave observation happened in 2016 and we can now pinpoint their origins to Supermassive Black Hole Binaries (SMBHB) and Neutron Star Binaries (NSB). Wherever there are really dense astronomical objects orbiting each other in an inspriling cosmic death dance. That is where the origin of gravitational waves can be pinpointed to.

In-fact these events are responsible for the formation of heavier elements in the Universe like Gold and Platinum. So you are essentially buying for your spouse a briproduct of the most violent collisions in the Universe.... just like my relationships.

But why do Astronomers have a vested interest in detecting these gravitational waves?

Well that is an interesting question actually. I mean are not observations in the EM domain enough to learn us all we can about the Universe that we live in and the Cosmos from which we spring?

Well, I can tell you that the answer to that is No. Because of something called Multi Messenger Astronomy.

We live in the age of Mutli-Messenger Astronomy (MMA) which is this idea that we can acquire much more information about the universe by looking at signals that reach us in different ways. Here are the 4 ways that information about the Universe can reach us.

• EM - Light. The classic Medium of Discovery. From Planets to Pulsars this is how its been done since back in the day.
• Gravitational Waves - Ripples of Propagating space time. These can tell us about the merging of really dense objects in the Universe. Black Holes and Netutron Stars
• Neutrinos - Elusive Tiny Particles travelling at the speed of light.
• Cosmic Rays - High Energy Particles. Can tell us about  Gamma Ray bursts

Some of things out there may be detectable by the many different media, others in singularly different ones. but there is a wealth of information that can be conveyed by analyzing the same cosmological phenomena in the different messenger media.

One example is how the Gravitational Waves detected by LIGO are quickly followed up by observations by Radio Telescopes. etc.

But what really convinced me about MMA  surrounds some discoveries that happened around the time of my birth (1992). That is the discovery of PSR B 1257 + 12 and the planets that surround it. Draugr, Poltergeist and Phobetor.

I wonder if it will have an atmosphere. Not that we really need one if we ever get to explore it. I figure we'll carry our own atmosphere with us.

These 3 planets orbit the husk of a star that went supernova a long time ago. That star is survived today as a pulsar that periodically emits beams of electromagnetic radiation  The planets were discovered by measuring the variation in Doppler shift of pulsation Period.

This planet marks the discovery of an extrasolar planet via means of Pulsar Timing.  One of the worlds was discovered to be twice the size of the moon at 0.02 Earth Mass, the smallest planet ever to be discovered. In all the planets discovered by the Kepler mission in the modern age. Pulsar Timing in 1992 (the year that I was born) revealed to us a world in a category of its own. A tiny little speck orbiting a Pulsar.

That remarkable discovery was made via an indirect observation by studying subtle changes in the propagation of light. we didn't see the planet optically but implied its existence by looking at the effect it had on the pulsar signal, thus confirming its existence.

Now extend that to Gravitational Waves and the information they carry, and the things we might come to learn of when we detect Grav Waves. What new wonders undreamt of in our own time would will we discover by studying gravitational waves? 

Lets find out...

AGNs and Cross Matching Algorithms

17/4/2019 Cross Matching in a nutshell.

We begin our story with Active Galactic Nuclei colloquially known as AGN. In a nutshell they are Supermassive Black Holes surrounded by accretion disks of matter that shoot out jets of radiation in the form of radio lobes that are pretty exotic things to see in the radio spectrum.

Here is an artists rendition:

This is what they look like in the Radio

They are primordial objects found in the early universe. To borrow a quote from Armand Delsemme "When the Quazars shone their dazzling brilliance"... that "dazzling brilliance" refers to the fact that AGNs can shine at much higher than normal luminosity in all over the EM spectrum.

And in fact they do.

The radiation from the accretion disk is brightest in Optical and Ultraviolet

The Gas and Dust that surrounds the Black Hole is visible in the Infrared

Hot gas surrounding the black hole gets heated up and emits X Rays

The jets emitted by the black hole are visible for many lightyears in radio frequencies

So we point many different telescopes in the same direction in order to see them. There's a diverse ecosystem of telescopes and eyes on the sky that humanity has at its disposal. All of which can be used to study Active Galactic Nuclei

But there is a problem. y and X-ray telescopes are located in space and orbit the Earth with different periodicity. Optical Telescopes are placed on mountain tops all over the world, and radio telescopes are situated in barren deserts tucked far away from any radio frequency interference. 

How do we study the same brilliant dazzling objects with such different equipment?

Coordinating these instruments to look at the same object in the sky require a herculean task of cooperation and cross border collaboration that demonstrate capacity for humans to let go of their differences and unite in the effort of studying the Cosmos, ancient and vast from which we spring.

The solution to this problem is: Cross Matching Algorithms 

Here is a diagram of what cross matching implies:

Cross Matching Astronomical Objects from different Catalogs. VLA, SDDS, Hubble

This is what a naive cross matcher (pseudocode) would look like:

for l in range (0, len(cat A)):
    for m in range (0, len(cat B)):
        calculate offset = angulardistance (A, B)
        if offset < radius
            if offset = smallest value so far
            return best_match = (A, B, offset)

Where A, B are RA, Dec values for a catalog.

These have a connection to big data, and to the whole Billions and Billions thing in the Universe. I will talk about in following entries.

Matlab FFT on Sinusoidal Code

amp = 3;
freq = 5;
phi = pi/4;
fs = 50;
Ts = 1/fs;
l = 1; %second samples

sineWaveFunc(amp,freq,phi,Ts,l)

plot(t, s)
xlabel('time')
ylabel('Amplitude')
title('sineWave')

myPow = calcPower(fs, freq, s);

myFFT = findFFT(s);
%calculate power

N = length(s) + 1;  % to be even :)
S = fft(s,N);
SdB = 20*log10(S);  % or SdB = mag2db(S);
freqs = (0:N/2-1)*fs/N;

figure(2)
plot(freqs, SdB(1:N/2))
xlabel('frequency')
ylabel('amplitude')
title('spectrum')

function sinFFT = findFFT(s)
N = length(s) + 1;
sinFFT = fft(s, N);
%plot(sinFFT, N)
end

function pow = calcPower(fs, freq,s)
Nsamp = round(fs/freq);

pow = (1/Nsamp)*sum(abs(s(1:Nsamp)).^2);
end

function [s , t] = sineWaveFunc(amp,freq,phi,Ts,l)
t = 0:Ts:l;
s = amp*sin(2*pi*freq*t + phi);
end

DSP and Astronomy

10/3/2019 Astronomy = (DSP + Statistics + Data Science)

Look at this slide about windowing from DSP Guru Mitra

Sequence/Pulse Windowing is the act of turning a infinite length sequence into a finite length sequence by applying a window sequence

So that is what this massive phallic construct does:

Which can be broken down into geek speak like this:

Radio Telescopes are windows on the Universe

So if you have the infinities of a pulsar signal (That's artist embellishment right there) and apply all those DeDispersions, FFTs, phase binning. Then we can get a limited sequence called a power spectrum in terms of frequency and time.

Its just a windowed sequence of values

Or we can use it to blow each other up and all that other planetary chauvinism stuff.

Matlab Discrete Sinusoid

2/4/2019 Creating Discrete Sinusoidal

I'm going to go learn Cyclic Spectroscopy for Radio Astronomy Applications. Got distracted, plotted Sinusoids in Matlab instead.

I think it looks pretty

a = -80;
b = 80;
n = a:b; %sample length
fs = 0.0125;
phi = 0;
Amp = 6;

x = Amp*sin(2*pi*fs*n - phi);
x2 = (-Amp)*x

clf
stem(n, x, '-o')
axis([0 b -2 2]);
grid;
title('sinusoid')
xlabel('Time index n')
ylabel('Amplitude')
axis

%plotting an evil twin
hold on

stem(n, x2, '-*')