Getting a Feel for Cosmic Events

By: William Bryk

Monday morning, October 30, 1961, began quietly on an abandoned patch of tundra in an archipelago located in the extreme north of Russia. A grain tumbled in the mild wind, floating here and there until finally smacking the ground, sending several bacteria to their unfortunate end. Moments later, quite unexpectedly, a 50 megaton nuclear blast ripped through the region, completely obliterating everything within a 20-mile radius (1).

What was just demonstrated is a difference in power of 24 orders of magnitude. The grain hitting the ground might have had a peak power output on the order of one watt (depending on its mass and impact velocity), while the peak power output of mankind’s most powerful bomb in history, nicknamed “Tsar Bomba,” was around 5 yottawatts, or 5. 102⁴ watts (1 watt of power equals 1 joule of energy per second) (2).

The above comparison combines into one picture energies at two extremes of the brain’s conceptual limits. Now imagine, instead, that the grain-ground collision actually represented the power output of the Tsar Bomba itself. By zooming out to this new power scale, we have left the realm of the everyday and have ventured into a way of thinking that our brains cannot genuinely comprehend. On this scale, the power output of a 100-kilometer-wide asteroid impact at tens of kilometers per second would be represented by a firecracker, and the power output of all the explosives used in World War II detonating simultaneously would not even be detectable to a human (3). So what power output would a Tsar Bomba explosion on this scale represent? Multiplying the old bomb’s yottawatts by 24 orders of magnitude again, we get approximately 10⁴⁹ watts. 10⁴⁹ watts is the power of a Tsar Bomba explosion on an imagined scale in which a tiny ripple in the dirt represents the power of an actual Tsar Bomba. It seems no event could possibly cause such an outrageous explosion. Yet, on September 14, 2015, scientists at the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected one, thankfully in a galaxy far far away.

Too Many Zeroes

Yes, in a foreign region of the cosmos 1.3 billion light years away, two black holes dozens of times the mass of our sun collided into one in less than a second, generating a peak power output of 3.6 . 10⁴⁹ watts (4, 5). The black hole collision caused ripples in spacetime so disruptive that they were detected on Earth even after having spread out for 1.3 billion years, making headlines around the globe as the first direct evidence of gravitational waves. But how many people can say they really grasp the sheer magnitude of the quantities involved? Among the many impressive characteristics, one stands out: 3.6 . 10⁴⁹ watts. How can we possibly make sense of such a colossal quantity, equivalent to 360,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000 hundred-watt light bulbs?

In such helpless situations, it seems natural to turn to someone who spends their whole career dealing with these figures – an astrophysicist! Enter Harvard’s very own Professor Irwin Shapiro. Professor Shapiro studies gravitational phenomena, and has made historic discoveries including Shapiro Time Delay, which is one of the four classic solar system tests of general relativity. If anyone can help, Professor Shapiro is the one. When asked how, as an astrophysicist, he makes sense of the physical scales involved in the events that he studies, he responded, “They are so immense that I don’t really try, but usually just stick to the relevant mathematical expressions, ten to some high power – whatever the units!” Clearly, then, our cognitive goal is not necessarily achievable.

But why even take on the challenge of grasping such large quantities? Well, one might argue that there is a difference between knowing that Earth is one of eight planets revolving around a star and knowing that we are standing on one of eight massive spheres, half of us upside down, drifting at tens of kilometers per second around a gigantic ball of superheated gas, all drenched in absolute darkness, a cosmic scene comparable to dust particles spiraling around a light bulb in an otherwise pitch-dark gymnasium. We can continue describing the astronomical speeds, energies, masses, and time-scales involved until what was previously a simple fact about our planet becomes a revelation about our place in this cosmic dance of rock and gas. So, with that sort of mission in mind, we set out to understand 3.6 . 10⁴⁹ watts.

Conceptual Building Blocks

We begin with the universe’s basic commodity – stars. Stars, much like living organisms, can be said to go through life cycles of their own. For much of its life, a star exists because a large enough agglomerate of gas in outer space is compressed so heavily under its own gravitational attraction that nuclear fusion is enabled. Nuclear fusion, the same atomic merging process that humans managed to create down here on Earth in the form of fusion bombs, is responsible for the immense energy output of stars. Take our sun, for example. With a diameter about a hundred times that of Earth, the sun is basically a gigantic hydrogen fusing factory. Each second, it converts one hundred Great Pyramids of Giza worth of hydrogen into helium, releasing the energy equivalent of 2 billion Tsar Bombas (6). So if you continue to fill all the streets of Manhattan with Tsar Bombas (each 8 meters long, 2 meters diameter) to a height of two empire state buildings and press a big red button each second, you would get the sun. We only survive these cataclysmic eruptions, because Earth is located 150 million kilometers away. As Professor Shapiro pointed out, if the sun were the size of a basketball, the Earth would be a tiny peppercorn located 25 yards away! This makes it ever more surprising that the sun is what provides the base energy for almost all physical and organic processes on Earth’s surface – storms, precipitation, life. The sun will be our reference point, so it’s important to pause and internalize the power of just one ordinary star.

The Beast Within

At some point during their multi-million or multi-billion year factory lifestyle, stars will run out of fuel to fuse. But some of these cosmic monsters don’t leave without a bang. If a star is massive enough, it could end its life in a high-energy explosion known as a supernova, and sometimes, for even larger stars, a hypernova. Before attempting to fathom the energy of a hypernova, it helps to understand why they happen in the first place. There are several models that explain hypernovas. A simplified explanation of one model – the collapsar model – is that when a large star stops fusing, it loses its constant outward pressure, and collapses under its own weight. Meaning, the gravitational pressure compressing the atoms into one another is so strong that it overcomes the sensible force that prevents particles from occupying the same position, creating a claustrophobic situation of cosmic proportions. What could emerge from this exotic physical collapse is an unbelievable amount of emitted energy, and a black hole.

Astronomers have been detecting hints of such hypernovas ever since the Cold War. These blasts of energy, initially believed to be Soviet nuclear tests in space, remained a mystery for several decades until it gradually became clear that the universe has its own nuclear arsenal on scales previously unimaginable (7). In 2015, scientists detected a hypernova unlike any that had ever been observed. This killer hypernova, appropriately named ASASSN-15lh, erupted with as much power as 600 billion suns (8). To get a sense of how much power that really is, let’s refer back to the scale in which the sun is a basketball and Earth is a small peppercorn. Place our basketball-sun on the 1-yard line of Gillette Stadium, MA (with Earth at the 25-yard line). Now, how far away would be the next closest star, Proxima Centauri, which is four light years away? The answer is that Proxima Centauri would be another basketball, located in Beijing! What would happen if this star were to explode in a hypernova like ASASSN-15lh? This basketball in Beijing going berserk in hypernoval fashion would be brighter in peppercorn-Earth’s skies than our basketball-sun located in the same football stadium! If the sun’s power output were represented by a 100- watt light bulb, then ASASSN-15lh would be the equivalent of one Hiroshima bomb exploding each second.

Yet, for all this power, ASASSN-15lh only squeezed out a meager 2 . 103⁸ watts at peak output. An insane figure, for sure, but nothing close to the 3.6 . 10⁴⁹ that we seek. To get closer to fathoming that value, we need to delve into a new kind of cosmic creature.

Zooming Out

If stars are the cosmic citizens, then a galaxy is the planet on which these stars dwell. Instead of distributing themselves uniformly throughout the universe, stars have a gravitational tendency to group themselves into large, majestic, rotating agglomerates we call galaxies, the true giants of the cosmos. Our own galaxy, the Milky Way, contains roughly 100 billion of these glowing balls of fusion and spans 100,000 light years in diameter (9). How can we conceive of such a behemoth?

Imagine that the Milky Way were shrunk down to the size of the Continental United States (a factor of 250 trillion). Our sun is roughly 1.4 billion meters in diameter, so dividing by 250 trillion, you get that each sun-like star would be 6 micrometers wide on this scale, about the size of the nucleus in mammalian cells. Thus this U.S. version of the Milky Way would be a huge disk of complete darkness scattered here and there with microscopic pinpoints of light every 150 meters or so. It’s not the most exciting picture of a galaxy, but it does give a somewhat accessible scale to work with. Imagine all the cities, the towns, the neighborhoods, the vast fields, each swarmed with innumerable tiny points of light. If you were to take a census of the 100 billion stars in the Milky Way, counting one each second, it would take well over 3,000 years to complete. If each star were instead, for some reason, a grape tomato, the 100 billion tomatoes would fill Gillette Stadium to the brim.

PUTTING IT ALL TOGETHER

We now finally have the conceptual tools to take on our initial quest. What does 3.6 . 10⁴⁹ watts feel like? Well, we have seen that the ASASSN-15lh supernova had a peak power-output of approximately 2 . 103⁸ watts. We have also noted that there are around 1011 stars in our galaxy. Here we go. First, take one Milky Way galaxy full of stars. Next, compress this vast galaxy with billions of stars into the volume of a small moon.10 Then, take out a very large red button. Press the red button. At that moment, as if Hades himself had commenced a simultaneous uprising of all the dead within the underworld, each and every star goes hypernova on the level of ASASSN-15lh, collectively releasing an energy equivalent of 200 million million million million million Tsar Bombas per second. This is 3.6 . 10⁴⁹ watts. This is the power of the two black holes that collided 1.3 billion years ago.

After dealing with such astronomical figures in search of a conceptual understanding that may or may not have been satisfied, it is easy to come away feeling very small in relation to a universe that features cosmic bodies and events best expressed in scientific notation. But this logic doesn’t quite hold up, since it really is just a matter of perspective. There is a whole other side to the spectrum of physical quantities. For instance, if every atom in our bodies were replaced with a medium-sized grain of sand, a human would have the volume of a planet.11 So when you ask some random person on the street for directions, you are talking to a being with complexity matching that of Earth, hosting an intricate network of septillions upon septillions of molecules working together in harmony. From the perspective of an atom or bacterium, we humans are the cosmic bodies unimaginably large yielding unimaginable power. As the Professor Shapiro of the bacteria world might put it, humans operate at levels of “ten to some high power – whatever the units!”

If that is not enough to quench our thirst for significance, consider the role of fans at a football stadium. Aren’t they just as much part of the game? In a certain sense, we carry a significant role in the cosmic arena merely by being conscious spectators within it. And our increasingly advanced scientific instruments definitely make us qualified spectators. The detectors at LIGO, for example, discovered the black hole collision by detecting a gravitational wave disturbance of less than an atomic diameter in length! We might not make the most noise in this universe, but we surely are the best at listening.

William Bryk ‘19 is a freshman in Canaday Hall.

WORKS CITED

[1] CTBTO Preparatory Commission. https://www.ctbto.org/specials/testing-times/30-october-1961-the-tsar-bomba (accessed Mar. 9, 2016).

[2] Abbott, D. Proceedings of the IEEE. 2010, 98, 42-66.

[3] Kolecki, J. NASA GRC Mathematical Thinking in Physics. https://www.grc. nasa.gov/www/k-12/Numbers/Math/ Mathematical_Thinking/asteroid_hit. htm (accessed Mar. 21, 2016).

[4] Cofield, C. In Historic First, Einstein’s Gravitational Waves Detected Directly. Space.com [Online], Feb. 11, 2016. http://www.space.com/31900-gravitational-waves-discovery-ligo.html (accessed Mar. 9, 2016).

[5] Crockett, C. Black Hole Smashup Generated Yottawatts of Power. ScienceNews [Online], Mar. 10, 2016. https://www.sciencenews.org/article/ black-hole-smashup-generated-yottawatts-power (accessed Mar. 15, 2016).

[6] Christian, E. NASA Cosmicopia. http://helios.gsfc.nasa.gov/qa_sun. html (accessed Mar. 11, 2016).

[7] Woosley, S. The Death Star. BBC Science & Nature [Online], Oct. 18, 2001. http://www.bbc.co.uk/science/horizon/2001/deathstar.shtml (accessed Mar. 15, 2016).

[8] Billings, L. Found: The Most Powerful Supernova Ever Seen. Scientific American, Jan. 14, 2016. http:// http://www.scientificamerican.com/article/ found-the-most-powerful-supernova-ever-seen/ (accessed Mar. 15, 2016).

[9] Howell, E. How Big is the Milky Way? Universe Today [Online], Jan. 20, 2015. http://www.universetoday. com/75691/how-big-is-the-milky-way/ (accessed Mar. 17, 2016).

[10] Abbott, B. et al. Phys. Rev. Lett. 2016, 116, 1-16.

[11] Kross, B. Jefferson Lab. http://educa

Categories: Spring 2016

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