2020년 11월 20일 금요일

BICEP2 관측과 인플레이션의 중력파(1부)

BICEP2 관측과 인플레이션의 중력파(1부)

BICEP2 and Gravitational Wave from Inflation (Part1)

https://youtu.be/qcp6nSCw9mU

[주의] 이래 글은 위의 동영상을 보고 나름대로 요약 및 해석을 덧 붙인 글입니다. 이 블로그에 글을 쓰는 저는 취미 독학자 입니다. 오류가 있을 수 있으니 제시된 링크들을 참조 하십시요. 이 동영상은 2014년에 발표한 BlCEP2의 논문을 기초로 제작된 것입니다. BICEP2의 관측과 그에대한 주장들은 현재까지도 논란 중 입니다.

[00:00] 초기 우주 급팽창(인플레이션 이론, Inflation theory)의 증거라고 여겨지는 빛의 B-형(B-mode)편광을 관측하기 위한 BICEP2 관측실험의 결과를 소개하고 관측 자료를 분석해본다. 이 동영상은 빛의 편광은 E-형 이어야 하는데 회오리 치듯이 나선형의 B-형으로 변한 것은 급팽창 과정에서 발생한 중력파로 인한 것이며 결국 이는 빅뱅의 직접적인 증거라는 주장을 설명한다.

* 이 주장은 현재 논란중이다. [BICEP] B-형 편광은 우주 먼지에 의한 것이라는 주장도 있으며 중력파 이외에 중력 렌즈 현상 때문에 편광 방향이 휘어 보인다는 이론도 있다.[B-모드 편광]

우주 전반에 균일한 열복사 온도를 보여주는 우주 마이크로파 배경 복사(CMB, Cosmic Microwave Background)는 우주 대폭발의 증거로 받아들여지고 있다. 대폭발(Big Bang)직후(10^-36~10^-34초) 급팽창이 일어난 증거로서 마이크로파의 B-형 편광을 예상 했고 이를 관측하기 위한 실험이 BICEP2다. BICEP2 관측을 통해 무엇을 관측했는지 이 관측자료가 어떤 의미인지 분석해 보자. 우주에 대한 이해를 높일 수 있을 것이다.

[02:05] 먼저 빛의 편광에 대해 알아보자. [전파라고 부르는 전자기 파의 총칭으로서] 빛은 전기장과 자기장이 직각으로 파도치며 두 장이 이루는 면에 직각으로 진행한다. 세가지 상대적인 직각직각이라는 조건을 제하고 두 장이 짝을 이뤄 어떤 각도로 기울어 질지, 혹은 어느 방향을 취할지는 [무작위로] 제각각이다. 말하자면 전기장이 위아래로 진동할지 좌우로 진동할지 혹은 그 사이 어느 각도로든 진동할 수 있다.


[02:35] 빛의 편광(polarization)은 전기장이 진동하는 방향으로 정의된다. 위의 그림에서 보듯이 두 빛은 같은 파장과 주파수 그리고 진폭을 가졌더라고 전기장이 진동하는 방향이 다르므로 편광이 다른 빛으로 정의된다. 우리가 일상적으로 접하는 빛, 예를 들어 전구에서 방출되는 빛은 모든 방향으로 편광된 빛이 섞여 있다. 따라서 이 빛은 편광되지 않은(unpolarized) 빛이라고 한다. 이 빛이 거울에 반사되면 반사면과 평행인 빛으로 편광된다. 편광된 빛만 통과 하므로서 빛의 투과량을 감쇄 시킬 수 있는데 선그래스의 원리다. 수평편광은 산란시키고 수직편광만 통과시켜 빛의 양을 줄인다. 선그래스가 유난히 번들번들 빛나는 이유는 편광필터에 산란되어 상당량의 빛이 반사되었기 때문이다. 그리고 이 빛들은 편광 되어 있다. 입자(particles)에 의해 빛이 편광될 수 있다는 점에 주목하자.

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[3:46] 전자기파의 편광은 나중에 다시 다루기로 하고, 우주배경복사(CMBR)와 대폭발(Big Bang) 이론의 관계를 살펴보자. 138억년 전에 매우 뜨겁고 밀집되어 있던 우주가 갑자기 시공간 (space-time)으로 팽창했다. 공간이 늘어나 냉각되었다. 먼지와 가스들이 서로의 중력에 뭉쳐져 (중력붕괴, collapse under gravity) 별이 되고 은하를 형성했다. 그중에 행성도 만들어지고 인간도 생겨났다. [먼지와 가스들의 재료가 될 수소 원자는 대폭발 후 38만년 후에 형성됐다.]

[04:20] 대폭발과 중성 수소 원자가 처음 생겨난 아주 짧은 기간 동안 우주는 아주 뜨겁고 밀집되어 있었다. 엄청난 에너지를 품은 뜨거운 공간은 자유전자와 양성자가 분리된 플라즈마(plasma) 상태였다. 너무나 밀집되어 있어서 빛이 통과할 수 없다. 빛이 방출되었지만 자유전자에 부딧혀 산란된 빛은 멀리 나갈 수 없다.

[04:50] 공간이 팽창하여 냉각되자 (운동에너지를 잃은) 전자와 양성자가 결합해 중성 수소가 형성되기 시작했다. 자유전자의 수가 줄어들자 빛은 멀리 퍼져 나갈 수 있게 되었다. 비로서 우주가 투명해졌다. 빅뱅이 일어난 후 38만년이 지났을 때이다.

[05:05][자유전자의 밀도가 낮아져] 투명해진 우주공간에 퍼져 나간 빛 (전자기파)이 오늘 날 우리가 보는 하늘의 모습이다. 우주 전체에 걸쳐 고르게 빛이 분포하는데 마이크로 웨이브 밴드(~160Ghz)에서 본 현재 모습이다. 어떤 물리적 에너지 교환도 빛의 속도를 넘지 못함에도 우주 전반에 걸친 온도 분포의 등방성을 보여주는데 이는 빅뱅 후 우주가 급속히 팽창하여 오늘에 이르렀기 때문이다. 따라서 CMBR의 등방성은 빅뱅이 남긴 흔적이라고 받아들여지고 있다.

[05:45] 전 우주의 온도 분포가 완전히 균일한 것은 아니며 다소 불균일 함을 보이는데 그 크기는 1만분의 1가량으로 매우 작다[ΔT/T = 1.23x10^-3K]. 이런 온도 분포의 불균일함과 함께 복사에 미묘한 편광(polarization)도 관측 되었다. 이런 편광은 어디에서 기인하는 것일까? 우주가 투명해지기 전, 플라즈마의 자유전자와 빛줄기가 상호 작용을 일으키던 상황을 짚어보자.

* 관측 위성(COBE/Plank/WMAP)으로 우주 배경복사 마이크로파의 세기가 가장큰 파장은 λ=1.9mm(ν_max=~160.2Ghz)으로 관측 되었다. 이는 우주 전체를 흑체(black body)로 봤을때 2.725K 의 온도에 해당하는 흑체복사 스펙트럼과 일치한다. [우주 마이크로파 배경]. 흑체복사 에너지 분포 [플랑크 법칙][빈 변위 법칙]

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우주에서 방출되는 빛(전자기파)는 모든 방향으로 편광된 빛들의 혼합이다. 편광은 어떻게 생겨난 것일까?

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[06:41] 편광되지 않은[전기장이 수직인 빛과 수평인 빛 이외 모든 각도로 기울어져 섞여있는] 빛의 다발(un-polarized lights)이 우측에서 자유 전자 쪽으로 입사 했을때 자유전자에 의해 산란되어  화살표(화면에서 튀어나오는) 방향으로 산란되는[=경로가 굽어져 나오는] 빛을 구해보자.

[뜨거운 프라즈마 가스에서] 방출된 빛은 실제로는 모든 각도로 편광이 이뤄진 빛이 섞여 있다. 즉, 편광되지 않은 빛이 자유전자의 왼쪽에서 입사한다고 하자. 입사하는 빛줄기를 수평 및 수직 편광된 빛으로 단순화 시켜서 전자의 진동에 따라 두가지 편광을 고려할 수 있다. 입사한 빛이 자유전자와 충돌[빛의 전기장과 자유전자의 상호작용]하여 수평 혹은 수직으로 진동 시킬 수 있다.

입사한 빛다발이 자유전자를 수평으로 진동시킨 경우 수평진동하는 전자는 수평편광 필터가 되어 이후 입사하는 빛은 수직 편광된 빛만 통과시키고 수평편광 빛은 산란된다. 관찰 방향에서 이 빛은 관측되지 않는다.

수직편광된 빛이 먼저 자유전자를 상하로 진동시킨 경우 수평편광된 빛은 통과하고 수직편 광된 빛은 산란된다. 관찰 방향에서 산란된 수직편파된 빛의 일부가 관측된다.

빛은 자유 전자로 전방향에서 입사한다. 이번에는 위에서 아래로 빛이 입사하는 경우 산란되어 관측되는 빛을 보자.

관측방향에서 산란된 빛을 보자. 산란은 모든 방향에서 일어날 수 있다는 점을 감안하면 산란되어 관측된 빛 역시 편광성을 특정할 수 없다.

만일 자유전자로 입사되는 방향에 따라 빛이 방출된 지점의 온도가 다르다고 하자. [방출된 빛은 흑체복사다.] 온도에 따라 최대 파장의 차이도 있고 빛의 세기도 차이가 있다. 뜨거운 영역에서 방출된 빛으로 관측지점에서 편광성을 결정 할 수 있다. 이 편광성을 가지고 널리 퍼져 나가 오늘날에 이르렀다.

현재 관측되는 우주 배경의 편광은 138억년 전의 흔적이다. 초기 우주의 밀집된 플라즈마에서도 온도 불균일이 있었고 그로 인해 생긴 편광을 측정 했다는 것인데 우주배경의 온도분포의 차가 만분의 1임을 감안하면 이는 엄청난 정밀 측정이다! BICEP2 이 관측 해려 했던 것이 바로 이 편광이다.

[10:06] 남극에 설치된 BlCEP2의 관측장비(전파 망원경)의 모습이다. 건조하고 높은 고도에 위치하여 CMB 관측의 최적지다. 은하 중심 방향에서도 떨어져 있어서 우리 은하내 뿐만 아니라 외부 은하의 별 전파원의 영향도 작다. 말그대로 아무것도 없는 배경을 향하고 있다.

위 사진의 오른쪽은 BICEP2 망원경의 수광부(focal plane) 모습이다. 초전도 전이단 센서(Transistion-Edge Sensor: TES)라고 하는데 파장이 1.9mm에 불과한 150Ghz 대역의 전파를 수신하는 안테나를 (유리)박막 위에 초전도 물질을 증착시켜 만든 것이다. 초전도체는 열잡음을 줄이기 위해 0.25K에서 작동한다. 수신된 마이크로파의 손실을 최소화하기 위해 안테나는 물론 필터와 증폭기 회로들을 모두 박막위에 집적시켰다. 총 512개의 배열 안테나로 구성되었다[BICEP2 2014 Release lmage Gallery].

[11:00] 관측으로 얻어진 영상은 광범 위한 하늘에 펼쳐진 빛의 편광 지도다[경도(R.A) 범위가 50도에서 -50도, 위도(Dec.) 범위는 -50도에서-65도]. 청색과 적색은 온도차로 무려 백만분의 1도(μK)다. E-형과 B-형의 두 가지 편광 패턴을 보였다.

[12:30] 초기우주 플라즈마의 온도차에 의한 편광은 E-형만 발생한다[전기장에 의해 자유전자를 흔들어 일어난 편광이다.]. 따라서 우주 마이크로파 배경 복사에도 E-형만 검출되어야 했다. 하지만 BICEP2 팀의 정밀관측(온도 편차가 0.3μK 범위)해 보니 B형 편광이 관측되었다. 이 B-형 편광은 어떻게 생겨난 것인가? 첫번째 가능성은 우주배경복사로 퍼져 나가면서 다른 은하나 무거운 천체의 영향을 받아서 틀어질 수도 있고, 두번째로 BICEP2 팀의 주장인데 인플레이션 급팽창으로 인해 발생한 중력파로 인해 시공간이 휘어 발생한 것이라고 한다. 이 B-형 편광은 단지 온도차(플라즈마 밀도차)에 의해 생겨날 수는 없으며 시공간의 수축과 팽창의 결과라는 것이다. 이런 강력한 시공간의 변화를 일으킬 수 있는 요인은 빅뱅 밖에 없다. BICEP2 팀이 주장하는 인플레이션의 증거에 대해 다음편에 살펴보기로 한다.

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B-형, E-형 편광 참조[Some Light Quantum Mechanics by 3Blue1Brown]

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[2부

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[참고]

1. The B-Mode Story You Haven’t Heard, NOVA

2. Cosmic Inflation Pt.1, Pt.2, Harvard Astronomy Video

2020년 9월 3일 목요일

10.08 - 평가문제(Module 10: Riding the Gravity Wave)

10.08 - 평가문제(Module 10: Riding the Gravity Wave)

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10.07 - Summary: The Final Countdown

10.07 - Summary: The Final Countdown [커세라 강의 페이지]



Black holes on the media are portrayed as matter-thirsty objects with infinite hunger. They tear astronauts apart, cause incalculable damage, and facilitate impossible feats of time travel. These often misunderstood objects have been discovered and studied only over the last half century.

지난 50여년간 수많은 미디어에 노출되며 악명을 쌓아온 블랙홀. 이로인해 몰이해에로 이어졌다.

Black holes reveal to us the depth and breadth of the known universe, and the tremendous success of general relativity, but they do hide their dark sides.

As the brightest objects in the universe quasars and blazars are powered by supermassive black holes accreting material onto accretion disks. Recent black hole mergers observed by LIGO reveal just how many black holes are out there. And observations from the Event Horizon Telescope give us our first glimpse at Sagittarius A*, our galaxy's very own supermassive black hole. But physicists are well aware that we have much more to learn about black holes, and to pass that knowledge on to artists and filmmakers who have a passion for science.

최근들어 블랙홀 관측이 이뤄지면서 블랙홀을 더 이해하게 되었고 더많은 예술가들과 영화 제작자들이 과학적 열정을 가지게 됐다.

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In this course, we learned that a black hole forms, if we can find a way to squash the mass of an object down into a small volume with a radius less than or equal to the Schwarzschild radius.


It's difficult to make a black hole since this matter is squeezed into smaller volumes, other forces will tend to oppose this motion and push outwards.

For instance, in a star, nuclear reactions in the core of the star heat up the star and provide an outward gas pressure that balances gravity. As a result, we have stars that can live long stable lives for billions of years, potentially providing heat to life on orbiting planets.

정역학 평형으로 오랜동안 항성으로 지내다가,


Black holes can form when very high mass stars can provide enough heat from nuclear reactions, to provide the gas pressure and keep up hydrostatic equilibrium. The laws of nuclear fuel leads to the implosion of the star that can in some cases create a black hole. Another way to create a black hole is to smash two neutron stars together. If the resulting mass of material has a high enough mass it can collapse into a black hole.

핵반응이 넘쳐 초신성으로 폴발한 후 블랙홀로 변하기도 한다. 작은 블랙홀이 충돌하여 더 큰 블랙홀이 되기도 한다.


I don't know about you, but I'm feeling overwhelmed by all the information I learned from the course. I really want to go back now to the scenes in Star Trek that we discussed at the beginning of the course, to compare what we saw then to what we know now. As you probably recall, in 2009 Star Trek movie reboot, red matter is employed as a quick method of creating a black hole.

While there is still no scientific basis for red matter or even the creation of a black hole through current human technologies, the destruction of the planet Vulcan due to a black hole is still a frightening thought.


We now know that even if it were possible to create a black hole say in a particle accelerator like the Large Hadron Collider, the black hole would be tiny. It will be so small that its temperature would be millions of times hotter than the sun. And quantum effects would quickly work on evaporating the black hole through Hawking radiation.

If the mass of the red matter black hole were similar to the mass of a proton, then the Hawking radiation would make black hole unstable, and it would disappear in a tiny fraction of a second after it was formed.

This might create a small burst of energy, but not nearly enough to destroy a planet. That's not where the scientific inaccuracy stop either.

Let's say that red matter did create a miniature black hole that caused the collapse of the planet surface, the planet wouldn't vanish as it did in the movie instead, the infalling matter would accrete around the black hole, heating up to thousands and millions of degrees. Instead of watching the collapse, you would see instead blinding x-ray radiation, literally blinding if you happen to be close.

Although scientists have never observed such low mass black hole, it's likely that all models applied to accretion disks, larger black holes would scale appropriately.

I don't bring up these issues because the scientific inaccuracies make Star Trek a poor movie, quite the opposite in fact. Without shortcuts around some of the difficult scientific principles, Star Trek would just be another documentary about black holes. But when scientific principles are applied correctly like they were in Interstellar, the whole story gains a renewed significance. Where Star Trek lives in the realm of science fiction, we can envision ourselves in a scientifically accurate future like Interstellar portrays.

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We can often find shortcuts taken by filmmakers and artists while portraying the astonishing environments around black holes, but the reality of black holes is much stranger than anything that has yet been captured on film.

Science fact, as it were, still beats science fiction for the strangeness of black holes. Einstein's insights into the structure of space-time, insights that required a powerful imagination along with an app for mathematics, were a giant leap from the Newtonian framework of gravitation.

As a result, we know that in our universe there's a trade-off between how quickly you can travel and how quickly the clocks in your reference frame tick. Even thinking about that is giving me a bit of a brain cramp.

Imagining space-time is nothing compared to speculating about the interior of black holes. In both Disney's The Black Hole and Christopher Nolan's Interstellar, characters are portrayed as crossing the event horizon.

As astounding as the effects may be, the events portrayed in these movies taking place within the event horizon of a black hole is pure speculation.

Physicists make use of Penrose diagrams to try and explain the interior of black holes. Modern theories predict that anything that enters into a black hole will have to collide with the singularity, which is likely fatal. We talked about the escape from a black hole as an impossibility, but we also know that the process of Hawking radiation allows the escape of particles from a black hole when pairs of particles and anti-particles are created near the event horizon.

So, which is it? Can particles escape from black holes, but not something big like me? As quantum physicists are keen on saying, information cannot be destroyed. So, what happens when I drop a memory device into the black hole? Can I read that information out of the Hawking radiation at a later time? Does the black hole somehow encode everything falling into it as the universe's most compact hard-drive?

In time, we can observe black holes in greater detail, we may not be able to learn the answers to these questions. These are the questions that I spend a lot of time pondering and I hope that I've gotten you thinking about them as well. It has been an honor teaching you.

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The idea of a black hole has been around for a long time and more recently a key component of many science fiction tales. Optical observations of black hole binaries have allowed us to look at the companions to black holes, watching them move in orbit around the binaries common center of mass.

Using this information, we have been able to find out more about the types of stars that hang out with black holes. We have been able to learn about how they can transfer material to the black hole, and how black holes can get their food.

X-ray and radio observations of black hole binaries have given us the opportunity to learn more about what's going on close to the black hole by giving us an insight into accretion processes. These views allow us to test theories about the physics of matter in the presence of extreme gravity.

While we are currently unable to visit the black hole ourselves, observations of them have taught us much more about the universe.

The closest known black hole to us is V616 Monocerotis. It lives about 3,500 light years away from us. V616 Mon is a black hole that lives in a binary system with an orange companion star. The black hole weighs in at about seven solar masses.

The furthest known black hole, ULAS J1342+0928 was discovered in 2017. This supermassive black hole has a mass of 800 million solar masses. Its light has taken 13.1 billion years to get to us and was emitted only 619 million years after the Big Bang.

The discovery of distant black holes allows us to learn more about the early universe, the formation of the first supermassive black holes, and the formation of galaxies.

The smallest known black hole, XTE J1650-500, with a mass that is approximately five times the mass of our sun. This means the event horizon radius is only 15 kilometers. The largest known black hole is S5 0014+81, an optically violent variable quasar. This black holes mass is 40 billion solar masses.

And it's also one of the most luminous black holes, emitting radiation equivalent to 10 to the power 14 suns. The faintest black hole is something harder to determine. One contender is that is Swift J1357.2-0933, a stellar mass black hole in a binary system, located only 4,900 light years away. And it emits light that is only 100 times brighter than the sun in the X-ray band.

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I want to thank you for joining us on this learning expedition. While black holes appear to be mysterious, we have learned that the basic ideas and observations can be described using known scientific principles.

Astrophysicists are well aware that a theory of quantum gravity is required to explain quantum phenomena associated with black holes on tiny scales. However there are plenty more unknown unknowns, that we can only just begin pondering about, like the nature of gravitational waves.

The observations of gravitational radiation from merging black holes and neutron stars has opened up a new way to learn about black holes. We can't know what will be discovered, but we can guess some possibilities. I'm hoping we will observe gravitational waves from merging supermassive black holes at the centers of galaxies.

Maybe we'll get to see the first evidence for a binary system composed of a neutron star and a black hole, giving off gravitational waves as they merge. It may also be possible to see gravitational waves when stars are tidally disrupted by black holes.

I hope that you have gained the tools to understand new discoveries about black holes, and to communicate those ideas clearly. Maybe one day I will read about your new discovery.

Thank you.

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[인터뷰] [커세라 페이지]
How does a neutron star's vibrations affect binary inspiral?
Interview with Dr. Jocelyn Read, Professor at California State Fullerton

When we talk about a binary of black holes or a binary of neutron stars orbiting each other, the main signature of the gravitational waves comes at twice the frequency of the orbit basically. Each time one of the objects passes, say, in front of you, that's stirs up another cycle of the gravitational wave signal which eventually reaches the observer.

But just like you have, say, a wineglass has a particular resonant frequency and you see, say, an opera singer sings the right note and the wineglass can shatter. So one of the research projects that I worked on, was understanding how the energy of the orbiting system, when the orbital frequency, the frequency of the orbits matches up with the natural frequency of an individual star that can transfer energy into the stars vibration.

So this can do some pretty dramatic things like similar to how a wineglass can shatter if you hit the right note, the solid crust of the neutron star might shatter if it sweeps through the right frequency in the orbit. So some collaborators and I worked through, that that might cause some high-energy flares that you could see in association with a gravitational wave signal or independently even.

So these oscillations taking away energy from the orbits, if they're strong enough and it has to be a huge amount of energy to affect the gravitational wave, but they can also drive the stars to merge earlier, so instead of spending the energy in orbiting, the energy goes into the vibration of the stars instead and that actually leads them to crash together. So they're losing energy to gravitational waves and then they lose extra energy to this vibration.

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10.06 – 펄사 타이밍 어레이(Pulsar Timing Arrays)

10.06 – 펄사 타이밍 어레이(Pulsar Timing Arrays) [커세라 강의 페이지]



Since existing gravitational observatories can only detect the strongest waves created in collisions of massive black holes and neutron stars, future detectors are being made with ever increasing sensitivities to find more subtle changes in the fabric of spacetime.

현존하는 중력관측소는 아직 블랙홀이나 중성자별 처럼 강력한 중력파만을 감지할 수 있지만 미래에 감도가 더욱 향상되면 미세한 시공간의 변화도 탐지해 낼 수 있게 될 것이다.

One concept being developed is called a Pulsar Timing Array, which would allow scientists to probe Einstein's general theory of relativity and the effects of gravitational waves over thousands of light years.

수천광년 떨어진 곳에서 날아오는 아인슈타인의 상대론의 중력파를 감지할 수 있는 중력파 관측 기술로 펄사 타이밍 어레이(Pulsar Timing Array)가 개발중이다. 

Since a pulsar is a rotating neutron star which emits a jet of radiation, if the beam of the jet points towards Earth, we detect a short radio burst. Those radio bursts arrive at regular intervals, sweeping across the earth for every rotation of the pulsar.

펄사는 강력한 전파원이다. 펄사는 중성자별이 자전하면서 주기적으로 전파를 방출하기 때문에 지구에서 보면 펄스(주기적으로 간헐적인 전파신호)로 관측된다. 


The fastest spinning pulsar, PSR J1748-2446AD, which lives within the globular cluster of Terzan 5, 18,000 light years from earth, rotates 716 times per second, which would sound like an F5 tone if the radio pulses were converted to sound. A spinning pulsar is of great interest, because some pulsar's rotation rates are incredibly stable. So much so, that they can arrival the precision of atomic clocks. So, PSR J1748, the fastest spinning pulsar has been measured to rotate exactly once every 0.01395952482 seconds, with an error of less than 600 femtoseconds.

1만 8천광년 떨어져 있는 빠르게 자전하는 펄사 PSR J1748-2446AD는 초당 716회 돈다. 지구에서 관측하면 716 헤르츠 신호의 펄스로 가청 주파수로 변환하면 '파'에 해당하는 음이다[Musical Pitches]. 펄사의 자전은 매우 안정되어 있어서 펄스의 주기가 원자시계 만큼이나 정확하다. 실제로 PSR J1748 펄사의 자전 주기는 0.01395952482 초로 오차는 600 펨토초(1백조 분의 1초, 10^-15초) 밖에 않된다.

This incredibly precise timing, is one of the most accurately measured observables in all of astrophysics. By the way, this pulsar was discovered by Dr. Jason Hessels, who graduated with a Bachelor of Science in Honors Physics from the University of Alberta.

The precision of a pulsars rotation rate is very much like a clock ticking at regular intervals. Just like the effects of gravitational Doppler shift that redshift photons as they escape from a gravity well, gravitational waves alter the timing of pulses from pulsars.

정밀한 펄사의 자전주기는 시계의 똑딱임과 유사하다. 광자가 중력 장벽을 빠져 나올때 적색 편이를 일으키듯이 중력파가 펄사의 똑딱임을 변화 시킨다.



In order to actually do anything useful though, you need several pulsars in an array. Now, you know why they're called pulsar timing arrays.

[원문 설명에 애매함이 있음]
이를 실제로 활용하기 위해선 배열형으로 펄사를 탐지해야한다. 이를 가리켜 펄사 타이밍 어레이라 한다. [여러개의 탐지 시설/혹은 안테나를 묶어 하나의 커다란 고성능 안테나로 사용하는 방법. 위상배열(Phased-Array)이 있다.]

It may be easier to imagine pulsar timing arrays as similar to the technology that underpins the Global Positioning System, or GPS. The GPS sensors in smartphones and navigation devices work by listening carefully for radio signals from GPS satellites high in orbit above Earth. By comparing the arrival time of the pulses from each GPS satellite, your device can triangulate your position on the surface of the earth.

펄사 타이밍 어레이는 GPS 기술에 비유할 수 있다. 다수의 GPS 위성에서 전파 신호를 수신하여 도착된 시각차를 삼각 측량법으로 계산하면 지표면상의 위치를 정확히 알 수 있다. [다수의 위성 사이에 정확하게 동기를 맞춰 발사한 펄스 신호가 지상에 도달하면 거리에 따라 시간차를 갖는다. 이 시간차를 측정은 위상차에 의해 계산된다. 이는 위상배열 안테나와 같은 원리다.]

NASA's NICER/SEXTANT X-ray telescope, which is on the International Space Station, is observing a collection of X-ray pulsars to test out the feasibility of using pulsar arrays as future navigational aids. By listening to the regular pulses from several nearby pulsars, you could triangulate your position anywhere in interstellar space around those pulsars.

우주정거장에 설치된 NASA의 NICER/SEXTANT X선 방원경으로 펄스 신호를 수집하여 미래의 우주선 항행 시스템을 실험하고 있다. 몇개의 펄사로부터 펄스 신호를 수집하여 삼각측량법으로 우주선의 위치를 파악하려는 것이다. [ISS Utilization: NICER/SEXTANT]




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This map, created by the Jet Propulsion Laboratory, was affixed to the Pioneer 10 spacecraft, which after completing a survey of Jupiter became the first satellite with sufficient escape velocity to leave the solar system. The image shows the relative positions of pulsars near Earth with their particular timings encoded on the line that joins them. If this map were discovered, the position of Earth could be deduced.

펄사를 활용한 위치지정은 이미 1972년과 1973년에 각각 발사된 파이어니어 10호와 11호에 장착된 '파이어니어 금속판(Pioneer Plaque)'에 지구의 위치를 새겨 넣었다. 지도에 위도와 경도로 위치를 특정 하듯이 지구에서 가까운 14개의 펄사의 거리와 방향 그리고 주기를 새겨 놓았다




14개 펄사의 방향이 모인 곳이 지구의 위치다. 펄사에서 지구의 거리와 방향을 선을 그어 표시 했고 각 펄사의 식별부호로 주기를 2진수로 기록했다. 펄사의 주기는 1973년에 관측한 것이므로 보이저호가 발사된 연도를 표시하시도 한다. 우주에서 가장 흔한 중성 수소의 천이시 방출되는 전자기파 1420Mhz의 주기(0.000000007=7x10^10초)를 시간의 기본단위로 사용했다.



But our civilization hasn't reached the point of navigating with pulsar timing arrays. Instead, we're patiently listening to them for evidence of large scale gravitational waves passing in between Earth and the pulsars.

아직 우리의 문명이 펄사 타이밍 어레이를 활용해 항성간 여행의 단계에 이르진 못했다. 하지만 펄사와 지구사이를 지나는 대규모 중력파를 꾸준히 탐지하는 중이다.

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When a gravitational wave passes in between the Earth and a pulsar, it causes a distortion of spacetime that affects how signals propagate. Generally speaking, the signals from pulsars will either appear delayed or accelerated due to the influence of a passing gravitational wave.

지구를 스치는 중력파가 시공간을 왜곡한 결과 신호전파[빛의 전달 경로]에 영향을 준다.

Just like a black hole creates a gravitational potential well and the associated effects of gravitational redshift and time dilation, so too can a gravitational wave create immeasurable effect as it passes by.

Imagine for example that you usually drive to work or school on a flat road. The time it takes you to get from point A to point B along your route takes about the same amount of time. What would happen if all of a sudden along the route, a hill appeared? Or what if a depression appeared in the road instead? In both cases, the time it takes you to go from A to B will change ever so slightly depending on the size of the hill. A gravitational wave in spacetime is just like this hill.

예를들어 A지점에서 B지점까지 이동하는 시간을 재보자. 평지라면 매번 이동할 때마다 시간은 동일하다. 갑자기 경로상에 언던이 나타나거나 웅덩이가 나타나면 이동시간은 느려지거나 빨라질 수도 있다.

Only since it's a wave, it will be a moving hill. If the timing of a gravitational wave is just right, it compresses the space time that the pulsar signals are travelling through offsetting the arrival time by a small difference, which is called the timing residual.

중력파는 움직이는 언덕과도 같다. 시공간을 줄일 수도 있고 늘릴 수도 있다. 이동 구간신호에 약간의 시간차를 잃으킨다. 이 시간차를 잔류시간(timing residual)이라 한다.

The timing residual is a measurement of the difference between the expected arrival time of the signal and the observed arrival time. Since gravitational waves can both stretch and squeeze spacetime whether the signal is delayed or accelerated will depend on the geometry of the pulsar timing array and the incident gravitational waves.

잔류시간은 예상 시간과 실제 소요사간의 차이를 측정한다. 시공간을 늘이거나 줄일 수 있는 중력파로 인해 신호전파는 펄사 타이밍 어레이와 입사되는 중력파에 의해 지연되거나 가속되기도 한다.

 
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So far, this method of monitoring pulsar timing arrays has not resulted in any observations of gravitational waves. However, techniques like these are a complement to the interferometer based gravitational observatories, and will eventually contribute to the detection of more massive binary collisions.

아직 펄사 타이밍 어레이 방식으로 이렇다할 관측 결과를 내고 있지는 않고있다. 하지만 이 방법은 간섭계 기반의 중력파 관측을 보완하여 이중성 관측에 효과를 보게될 것이다. 


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[인터뷰] [커세라 페이지]

What is a pulsar timing array?
Interview with Dr. Ingrid Stairs, Professor at the University of British Columbia

For the poolside timing array, they were looking at an array of pulsars over the sky, but basically all around the sky. So we really need an international collaboration to use telescopes all over the world to do this and the idea is to look for correlations.

So commonalities in the pulse arrival times of these pulses that are around the sky.

So since they're acting like lighthouses though, these are very very regular spinners, stable rotators.

So if they have pulses that come a little earlier, a little late there's some reason for it.

And with the pulsar timing of array, we're looking for pulses that are close together in the sky to be early together or late together.

Pulses that are sort of 90 degrees apart to be out of sync, one comes early, the other comes late. And then pulsars that are a 180 degrees apart on the sky, opposite sides of the sky to be more in sync again, not completely, but mostly.

And so if we can see that pattern in the timing from the pulses all over the sky, we will have some confidence that we've seen a gravitational wave passing near the Earth.

And probably we're going to see gravitational waves from a whole collection of these supermassive black hole binaries, which are slowly spiraling into each other.

We're catching them, we're aiming to catch them at orbital periods of a few years. So not right at the point where they're about to merge, but getting in there.

And we think these should be all over the sky, because galaxy mergers are happening all over the sky.

And if every galaxy has a supermassive black hole at its center which we think they do, then those two black holes should naturally sink in together toward the center of the new galaxy and and produce gravitational waves as they're doing it.

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10.05 – 중력파 망원경(Gravitational Telescopes)

10.05 – 중력파 망원경(Gravitational Telescopes)  [커세라 강의 페이지]



Gravitational waves are extremely weak. These waves wouldn't be felt by a human, for example, or any other living creature for that matter. So in order to detect gravitational waves, scientists must use the most sensitive instruments ever invented. What devices are suitable for measuring incredibly small changes? Well, lasers of course, and that means we'll also need our good friend, the Michelson-Morley interferometer.

Remember interferometers leverage the wave nature of light to measure the difference in lengths between different beam paths. When coherent light, light that has the same phase such as laser light, is split between two different paths and is later recombined, its brightness will depend on how different the two paths were.

For example, if a red laser with a wavelength of 650 nanometers is introduced into an interferometer, it will produce a bright spot at the end of the detector if there's no difference in the beam path. If one of the arms differ in length by half of the red wavelength or 325 nanometers, the interference between the two beams produces zero light.

So small changes in the length of one arm of the interferometer can be measured by the changing brightness of the resulting pattern of light at the detector.


The original Michelson-Morley interferometer was developed to determine if the flow of ether caused a delay in one of the device's two arms instead of the difference in the arms' lengths. Like a boat travelling against the current of a river, the theory of light back then predicted that moving ether would cause a delay in the upstream arm.

The opposite was discovered; that there was never any delay no matter what the orientation of the device with respect to the motion through the supposed ether. This proved that light waves don't require a medium like ether to travel in and as a consequence, the speed of light is a constant.

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In order to leverage the sensitivity of interferometers, astronomers built the Laser Interferometer Gravitational-wave Observatory, whose acronym is LIGO, pronounced "L-eye-go" or sometimes "L-ee-go".


These are two massively improved versions of the Michelson-Morely interferometer built on either side of the continental United States. One detector is in Hanford, Washington while the other is precisely 3,002 kilometers away in Livingston, Louisiana. They each have two arms but instead of short meter long arms, like the original Michelson-Morley interferometer, each of the arms of LIGO is four kilometers long.


In addition to the length, each arm bounces light from the laser source back and forth about 280 times making each arm of LIGO equivalent to the length of 1,120 kilometers. 

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Why are LIGO's arms so long? Well, it's hunting for some of the weakest signals that the universe has ever thrown at us. In fact, in order for LIGO to detect the strongest gravitational waves, it needs to be able to distinguish a change over the four kilometer length of its detector arms, a difference in length 1,000 times smaller than the radius of a proton.

But one LIGO isn't enough to catch a gravitational wave, we need at least two. There are several major gravitational wave observatories in operation around the world. The two LIGO observatories were the first, followed by Virgo, and a host of others in operation and under construction around the world.


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If one LIGO detector is sensitive enough to measure a change in its arm length down to the level below the width of an atom, why make more? Well, the first and most important reason is noise. Yes, sounds, footsteps, earthquakes, and cosmic gravity quakes, all register in LIGO as a change in the length of LIGO's arms.

In order to filter out footsteps from a colliding black hole, you need a second detector. LIGO second detector, built in Livingston, Louisiana, has a different set of sounds, footsteps, and earthquakes. But presumably, the two LIGO detectors would both see the same gravitational wave coming from an intergalactic source.

To determine whether a wiggle in one LIGO detector is the result of a gravitational wave, scientists compare the data from the second. If there's a wiggle at nearly the same time, remember the detectors are separated by 3,002 kilometers, with nearly the same shape, scientists can be confident that they really saw a gravitational wave and not some researcher sneezing in the control room.

But there's another important reason to have more than one gravitational observatory; direction. With only two LIGO detectors, an incoming gravitational wave will not have a well-defined direction. Just like having two ears gives a stereo hearing, two LIGOs let us determine approximately where the sources.


Although with only two, there's still uncertainty about which direction it came from. In order to pin down the source of gravitational waves, a third gravitational observatory is necessary. In the case of the Kilonova explosion resulting from the merger of two neutron stars in 2017, the gravitational wave signal was also detected by a third gravitational wave observatory, Virgo, in Italy.

With all three gravity wave observatories up and running, most major astrophysical merges will be detected. Over the next few decades, these types of observatories will get more and more sophisticated, detecting dozens of compact object collisions in the universe. But things will get really interesting once we send these massive observatories into space.

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In order to really make the most sensitive gravitational wave observatories, scientists work hard to remove sources of error. Just like telescopes, which are better if they're on mountain tops but best if they're in space, a space-based gravitational observatory wouldn't have to worry about earthquakes or someone tripping on a banana peel near the detector.

Know the next generation of gravitational observatories will be built in space. The Laser Interferometer Space Observatory, whose acronym is L-I-S-A, universally pronounced as "L-ee-sa" but I would argue it should be pronounced "L-eye-sa" in this case.


LISA consists of three spacecraft which will trail behind earth in its orbit around the Sun, flying in a triangular formation. Each of LISA's arms extend between the three spacecrafts. Instead of a puny 1,120 kilometer effective arm length, LISA will have three 2.5 million-kilometer-long arms.


LISA will still be sensitive to small changes in the length between the arms but we'll have an incredible sensitivity of 20 picometers over the 2.5 million-kilometer-long arms. As a result, LISA will be able to detect much smaller and quieter collisions than LIGO but also begin probing into the processes by which compact objects are captured by but not collided with black holes.


Beyond LISA, which won't even launch until the early 2030's, future gravitational wave observatories will measure the rotation of compact objects like pulsars.

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