Night 2:The Microquasar Wakes Up
Signal or statistical fluctuation?
Signal or statistical fluctuation?
Remember that hunters live surrounded by noise.
And there’s no possible shortcut. The only thing we can do is learn to deal with it effectively.
Daniel taught you to perform an OFF observation OFF subtract it. But let me tell you something: that’s not going to be enough.
Sometimes the noise actually takes the form of a signal. And then we think we’re seeing something, when actually what we have in front of us is a ghost called statistical fluctuation.
How can we be sure that we’re looking at is even hint that Cyg-X1 has woken up? How can we know that it’s not a bad statistical joke?
The only way to do this is to have a signal that is very (emphasis on very) difficult to be produced by a statistical fluctuation from no signal. This is what we call “significance” and it’s measured in units of “sigmas”.
In physics you can say you have a discovery when you have 5 sigmas. If you only have 3 sigmas, then you have some hint that needs more data to know if there is something or not. With less significance it almost comes down to guess work as to whether something is there or not.
When you have 5 sigmas you can be sure that statistical fluctuations could only give you a result like the one you have seen 0.00006% of the time. If you have 3 sigmas it will be 0.27% of the time.
The sigmas are a measurement of how much we can trust our results. Having 5 sigmas means that there is only a 1/35 million chance that what we’re seeing is nothing but noise disguised as a signal.
Sometimes I think that besides being gamma-ray hunters we’re sigma hunters :_(
In the notebook, I’ll show you the significance and sigmas using the example of Cyg-X1 (for which we have already calculated the sigmas) and random numbers (which is what the noisegive us).
The curse of the 3 sigmas
Let’s see if we can see the meaning of the 2.7 sigmas we have managed to get.
As usual, let’s start by loading the necessary libraries
import numpy as np
from SimularBackground import *
%matplotlib inline
I’ve created a function that simulates 10000 observations for which there is no signal. The expected number of events for ON and OFF observations are the same. That doesn’t mean that we always have the same number of events for ON and OFF. It’s like when you throw two dice, the expected average value of the sum of the two dice is 7, but that does not mean that sometimes they do not add up to 2 or 12.
For each of these simulated observations (which would take an entire lifetime to do them and only them!), I calculate the Significance that is given in units of sigmas.
grafica("Significancias")
The negative part of the distribution is for the cases in which there are more events in the OFF observations than in the ON ones, which doesn’t make much sense in terms of physics. It’s simply due to what we call statistical fluctuations. The positive part of the distribution in this case is also statistical fluctuations by construction. But in real observations like the one we’re analysing from Cyg-X1, we can’t distinguish between a statistical fluctuation or a true signal.
That’s to say, the more sigmas our significance has, the less likely it is to be a statistical fluctuation. You can see from the graph that the number of times I have a certain value of sigmas decreases when the sigma grows.
In fact, we’re going to calculate the probability of having a statistical fluctuation that gives me a greater significance than the one we have with the Cyg-X1 data.
# First, I recover from the graph the number of "Times" that I have each "Significance"
# I do this with a couple of functions that I've already created
Veces=valores("Numero de Veces")
Significancias=valores("Significancias")
# Now I use a library function that I have loaded NumPy, which adds up for each bin
# the values of all previous bins. For example, I go from (3,6,0,4,1) to (3,9,9,13,14)
VecesAcumuladas = np.cumsum(Veces)
# And with this it's easy to calculate the fraction of times that I have a greater significance
# than any value. First I calculate the probability for each of the values
# of sigma in the graph
Probabilidad = 1.0-VecesAcumuladas/(VecesAcumuladas.max())
# And finally, I use a loop (for x in range (0.100)) for which x varies from
# 0 to 100, and look for those instances when the value of the significance is greater than 2.68
# and that's where I will have my probability:
for x in range(0,100):
if Significancias[x] > 2.68 :
print ("The probability that the noise does not generate a significance of 2.68 or greater is:", Probabilidad[x]*100, "%")
break
The probability that the noise won’t generate a significance of 2.68 or higher is 0.22%
I think we can all agreee that a 0.22% probability is quite small. But not small enough. Scientists want to make sure that what we’re seeing is what is actually happening. To be sure that statistical fluctuations are not leading to fake discoveries the scientific field normally requires that the Significance be 5 sigmas. That is a probability of 0.000025%
Note: Defining functions helps us to go step-by-step, but if you’re interested in knowing what is defined in the functions, don’t hesitate to ask us in the forum.
Dictionary of the gamma ray hunter
Active Galactic Nuclei
There's party going on inside!
This type of galaxy (known as AGN) has a compact central core that generates much more radiation than usual. It is believed that this emission is due to the accretion of matter in a supermassive black hole located in the centre. They are the most luminous persistent sources known in the Universe.
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Black Hole
We love everything unknown. And a black hole keeps many secrets.
A black hole is a supermassive astronomical object that shows huge gravitational effects so that nothing (neither particles nor electromagnetic radiation) can overcome its event horizon. That is, nothing can escape from within.
Blazar
No, it's not a 'blazer', we aren't going shopping
A blazar is a particular type of active galactic nucleus, characterised by the fact that its jet points directly towards the Earth. In other words, it’s a very compact energy source associated with a black hole in the centre of a galaxy that’s pointing at us.
Cherenkov Radiation
It may sound like the name of a ames Bond villain, but this phenomenon is actually our maximum object of study
Cherenkov radiation is the electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. When a very energetic gamma photon or cosmic ray interacts with the Earth’s atmosphere, a high-speed cascade of particles is produced. The Cherenkov radiation of these charged particles is used to determine the origin and intensity of cosmic or gamma rays.
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Cherenkov Telescopes
Our favourite toys!
Cherenkov telescopes are high-energy gamma photon detectors located on the Earth’s surface. They have a mirror to gather light and focus it towards the camera. They detect light produced by the Cherenkov effect from blue to ultraviolet on the electromagnetic spectrum. The images taken by the camera allow us to identify if the particular particle in the atmosphere is a gamma ray and at the same time determine its direction and energy. The MAGIC telescopes at Roque de Los Muchachos (La Palma) are an example.
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Cosmic Rays
You need to know how to distinguish between rays, particles and sparks!
Cosmic rays are examples of high-energy radiation composed mainly of highly energetic protons and atomic nuclei. They travel almost at the speed of light and when they hit the Earth’s atmosphere, they produce cascades of particles. These particles generate Cherenkov radiation and some can even reach the surface of the Earth. However, when cosmic rays reach the Earth, it is impossible to know their origin, because their trajectory has changed. This is due to the fact that they have travelled through magnetic fields which force them to change their initial direction.
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Dark Matter
What can it be?
How can we define something that is unknown? We know of its existence because we detect it indirectly thanks to the gravitational effects it causes in visible matter, but we can’t study it directly. This is because it doesn’t interact with the electromagnetic force so we don’t know what it is composed of. Here, we are talking about something that represents 25% of everything known! So, it’s better not to discount it, but rather try to shed light on what it is …
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Duality Particle Wave
But, what is it?
A duality particle wave is a quantum phenomenon in which particles take on the characteristics of a wave, and vice versa, on certain occasions. Things that we would expect to always act like a wave (for example, light) sometimes behave like a particle. This concept was introduced by Louis-Victor de Broglie and has been experimentally demonstrated.
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Event
These really are the events of the year
When we talk about events in this field, we refer to each of the detections we make via telescopes. For each of them, we have information such as the position in the sky, the intensity, and so on. This information allows us to classify them. We are interested in having many events so that we can carry out statistical analysis a posteriori and draw conclusions.
Gamma Ray
Yes, we can!
Gamma rays are extreme-frequency electromagnetic ionizing radiation (above 10 exahertz). They are the most energetic range on the electromagnetic spectrum. The direction from which they reach the Earth indicates where they originate from.
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Lorentz Covariance
The privileges of certain equations.
Certain physical equations have this property, by which they don’t change shape when certain coordinates changes are given. The special theory of relativity requires that the laws of physics take the same form in any inertial reference system. That is, if we have two observers whose coordinates can be related by a Lorentz transformation, any equation with covariant magnitudes will be written the same in both cases.
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Microquasar
Below you will learn what a quasar is...well a microquasar is the same, but smaller!
A microquasar is a binary star system that produces high-energy electromagnetic radiation. Its characteristics are similar to those of quasars, but on a smaller scale. Microquasars produce strong and variable radio emissions often in the form of jets and have an accretion disk surrounding a compact object (e.g. a black hole or neutron star) that’s very bright in the range of X-rays.
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Nebula
What shape do the clouds have?
Nebulae are regions of the interstellar medium composed basically of gases and some chemical elements in the form of cosmic dust. Many stars are born within them due to condensation and accumulation of matter. Sometimes, it’s just the remains of extinct stars.
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Particle Shower
The Niagara Falls of particles!
A particle shower results from the interaction between high-energy particles and a dense medium, for example, the Earth’s atmosphere. In turn, each of these secondary particles produced creates a cascade of its own, so that they end up producing a large number of low-energy particles.
Pulsar
Now you see me, now you don't
The word ‘pulsar’ comes from the shortening of pulsating star and it is precisely this, a star from which we get a discontinuous signal. More formally speaking, it’s a neutron star that emits electromagnetic radiation while it’s spinning. The emissions are due to the strong magnetic field they have and the pulse is related to the rotation period of the object and the orientation relative to the Earth. One of the best known and studied is the pulsar of the Crab Nebula, which, by the way, is very beautiful.
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Quantum Gravity
A union of 'grave' importance ...
This field of physics aims to unite the quantum field theory, which applies the principles of quantum mechanics to classical systems of continuous fields, and general relativity. We want to define a unified mathematical basis with which all the forces of nature can be described, the Unified Field Theory.
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Quasar
A 'quasi' star
Quasars are the furthest and most energetic members of a class of objects called active core galaxies. The name, quasar, comes from ‘quasi-stellar’ or ‘almost stars’. This is because, when they were discovered, using optical instruments, it was very difficult to distinguish them from the stars. However, their emission spectrum was clearly unique. They have usually been formed by the collision of galaxies whose central black holes have merged to form a supermassive black hole or a binary system of black holes.
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Supernova Remnant
A candy floss in the cosmos
When a star explodes (supernova) a nebula structure is created around it, formed by the material ejected from the explosion along with interstellar material.
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Theory of relativity
In this life, everything is relative...or not!
Albert Einstein was the genius who, with his theories of special and general realtivity, took Newtonian mechanics and made it compatible with electromagnetism. The first theory is applicable to the movement of bodies in the absence of gravitational forces and in the second theory, Newtonian gravity is replaced with more complex formulas. However, for weak fields and small velocities it coincides numerically with classical theory.
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