Astronomy

Could the duration of some gamma ray bursts be information from outside our universe?

Could the duration of some gamma ray bursts be information from outside our universe?


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Could we be in a system where a large mass explodes dispersing matter in all directions until gravity pulls it together with matter from other explosions until the maximum mass limit is reached, causing another BIG BANG and the perpetual cycle starts again? Could the gamma rays of unknown sources detected by the Compton gamma ray observatory be information from space outside our universe (outsidespace). Could a gamma ray of short duration describe a small universe and a long duration a large universe?


Gamma Ray Bursts

A gamma-ray burst (GRB) is a brief flash of gamma rays coming from an astrophysical source at great distances from us, often from hundreds of millions of light years away. Gamma rays are a kind of light (like visible light, microwaves, or X-rays) that is very energetic, and whatever produces gamma rays must therefore contain (and unleash) a large amount of energy in a very short amount of time. Thus the study of gamma ray bursts is a study of some of the most violent events in the universe.

GRBs were discovered in the late 1960s and early 1970s by Earth-orbiting satellites designed to keep watch against covert nuclear weapons testing, but it was quickly realized they originate well outside our solar system. Their origins remained mysterious for several decades because they came and went so quickly -- often within a few seconds -- and because their position couldn't be pinpointed to better than a few degrees on the sky. For comparison, the full Moon is about 0.5 degrees across, and a telescope at moderate magnification has a field of view less than half that -- a few degrees is a huge area to search, especially when you've only got a few seconds to do it!

In 1997, an Italian-Dutch satellite known as Beppo-SAX used its combination of gamma-ray and x-ray detectors to pin down the precise position of a gamma-ray burst, and it was soon discovered that the source of the burst was at cosmological distance -- hundreds of millions of light years away. In the decade since this discovery, hundreds of GRBs have been localized, some having both X-ray and optical counterparts, and all of them have been associated with explosive events in galaxies at very large distances from us.


Gamma Ray Bursts ( GRB s) are the most violent explosions in the Universe, with some releasing more energy in 10 seconds than what the Sun will emit in its entire 10 billion year lifetime! First discovered in the late 1960s by military satellites, little progress was made in understanding these energetic events until 25 years later when the Compton Gamma Ray Observatory with the Burst and Transient Source Experiment ( BATSE ) was launched. Roughly one GRB per day was detected by this space observatory, and initial results showed that these objects were distributed homogeneously on the sky. They also seemed to come in two different types the more common long bursts lasting more than 2 seconds, and short bursts with durations of less than 2 seconds. That the burst of gamma rays can last such a short period of time indicates that whatever the origin, it must be contained within a very small region, as objects cannot vary faster than the time it takes for electromagnetic radiation to travel across them.

GRB research has progressed enormously since the late 1990s due mostly to the establishment of a rapid response network of satellites and ground-based observatories which observe each burst soon after detection. Such observations have revealed that GRB s are located in the distant Universe, are accompanied by afterglows at less energetic wavelengths, and that at least some are associated with very energetic supernova explosions called hypernovae. Observations have also verified that GRB s should be classified according to their burst duration, and suggested that long and short bursts may arise from two different progenitors. In current models, long bursts are produced through the core-collapse of a massive star to a black hole, and short bursts are thought to occur when two neutron stars merge to form a black hole.

Whatever the progenitor system, if we assume the energy is emitted equally in all directions, vast amounts of energy (substantially more than what is produced in a supernova explosion) must be generated in a very short time. Theorists were hard pressed to come up with such a mechanism and have instead suggested that the energy of the explosion is beamed into a narrow cone of emission. This reduces the energy production requirements to more physically achievable levels (roughly the level of an energetic supernova), but also means that there are many more GRB s than what we observe – we only see the ones that are aimed in our direction. The estimated number of GRB s per day therefore depends heavily on how narrow the beam of emission is thought to be. Astronomers estimate that the opening angle of the beam is only a few degrees, meaning that although we observe about 1 GRB per day, the actual number of GRB s is more like 500 per day!

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National Aeronautics and Space Administration

Perhaps the greatest mystery for astronomers who look at the sky at very short wavelengths has been the incredibly brief and intense bursts of gamma-rays from seemingly random locations in the sky. A few times a day, the sky lights up with a spectacular flash, or burst, of gamma-rays. Often, this burst outshines all of the other sources of cosmic gamma-rays added together. The source of the burst then disappears completely. No one can predict when the next burst will occur or from what direction in the sky it will come. For thirty years, astronomers have been trying to understand the nature and origin of these gamma-ray bursts (GRBs).

Gamma-ray bursts were first discovered by Ray Klebesadel at Los Alamos National Laboratory. He was working on a project responsible for monitoring the Soviet compliance with the Nuclear Test Ban Treaty. A series of satellites called Vela were put into orbit to perform this task. After the first 4 satellites were up, Klebesadel and his colleagues started to look through the data they sent back to Earth. Primarily, they were looking to make sure everything was working as expected and that nature was not generating any sort of signal that could trick the satellites into thinking a nuclear explosion has occurred. This was a painstaking task of looking through stacks of computer printouts by hand. In fact, instead of graphs that would quickly show what happened, Klebesabel's people had to examine columns of numbers and look for significant changes in their values. In mid-1969, Klebesadel was examining data taken on July 2, 1967. He noticed a spike in the data, a dip, a second spike, and a long, gradual tail off. "One thing that was immediately apparent was that this was not a response to a clandestine nuclear test," Klebesabel said at a conference held about GRBs in Huntsville, AL in 1998. His team checked for possible solar flares and supernovae, and found none.

After this first event was noticed, other similar events were quickly discovered in the data printouts. With the timing between Vela 5 and 6 synchronized to within 1/64th of a second, the Vela team was able to triangulate the locations of the bursts by comparing differences in arrival times at widely separated satellites. They confirmed their suspicion that the bursts came from outside the solar system. Already, by their random scatter across the sky, the data hinted that the sources were out in the Universe rather than being confined in our Galaxy. By 1973, when Klebesadel and his team were ready to publish the results in Nature and present them at the American Astronomical Society meeting, there were at least 16 confirmed bursts.

Using a hard X-ray detector on board the IMP-6 satellite (which was intended to study solar flares), Tom Cline and Upendra Desai of NASA/GSFC were the first to confirm Klebesadel’s findings and provide some spectral information which showed that the burst spectra peaked at gamma-ray energies. Thus the events were not simply the high-energy tail of an X-ray phenomenon. A collimated gamma-ray telescope on board OSO-7 was also able to confirm a direction to one of the events, supporting the original conclusion of cosmic origin. These confirming results, published close on the heels of the original discovery, gave the whole scenario an aura of enhanced mystery. The excitement created in the astronomical community was evidenced by a burst of publications of instrumental and theoretical papers on the newly discovered "cosmic gamma-ray bursts".

Over the next 20 or so years, a catalog of GRBs was constructed and many theories were discussed as to their origin. Great debates were even held within the astronomical community as to whether the bursts were occurring in our Galaxy or in other galaxies. The addition of each newly observed burst tended to reveal not much more than that they never repeated from the same source. The launch of the Compton Gamma-Ray Observatory in 1991 ushered in a new era of GRB observations. The Burst and Transient Source Experiment (BATSE) was capable of monitoring the sky with unprecedented sensitivity. As time passed and the catalog of bursts observed by BATSE grew, one thing became clear: the bursts were in no way correlated with sources in our Galaxy. It began to be accepted that GRBs must originate in galaxies far, far away. In 1997, the Italian-Dutch BeppoSAX satellite made a breakthrough in our understanding of GRBs. Using a particularly effective combination of gamma-ray and X-ray telescopes, BeppoSAX was able to detect afterglows from a few GRBs and precisely locate the sources so that other telescopes could study the same locations in the sky. This work showed that GRBs are indeed produced in very distant galaxies, requiring the explosions producing them to be extremely powerful.

The next big breakthrough in understanding GRBs occurred when an enormously powerful event was detected on January 23, 1999 (designated GRB990123). It was observed with an unprecedented range of wavelengths and timing sensitivities. A small automated optical telescope responded to alerts from orbiting gamma-ray and X-ray telescopes to begin observing the GRB within 22 seconds of the burst’s onset. while the GRB was still on-going. Subsequent observations took place over the next few weeks in the gamma-ray, UV, optical, IR, millimeter, and radio. The object was determined to have a redshift of 1.6, putting it at a cosmological distance and implying a staggering energy release. In fact, if the energy were emitted equally in all directions, twice the rest mass energy of a neutron star would be required. If the energy is being beamed out in a preferred direction that happens in this case to point directly toward Earth, however, the required energies are more reasonable and easier to explain. Multiwavelength, prompt observations of many bursts will be required in order to determine the central engine (or engines. there may be more than one mechanism!) of GRBs.

We tentatively believe GRBs are produced by material shooting towards us at nearly the speed of light, which was ejected during the collision of two neutron stars or black holes. Alternatively, the events could arise from a hypernova, the huge explosion hypothesized to occur when a supermassive star ends its life and collapses into a black hole. However, our sample size is small and our knowledge base shallow.


Astronomers discover clues that unveil the mystery of fast radio bursts

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) in Guizhou, China. Credit: Bojun Wang, Jinchen Jiang & Qisheng Cui

Fast radio bursts, or FRBs—powerful, millisecond-duration radio waves coming from deep space outside the Milky Way Galaxy—have been among the most mysterious astronomical phenomena ever observed. Since FRBs were first discovered in 2007, astronomers from around the world have used radio telescopes to trace the bursts and look for clues on where they come from and how they're produced.

UNLV astrophysicist Bing Zhang and international collaborators recently observed some of these mysterious sources, which led to a series of breakthrough discoveries reported in the journal Nature that may finally shed light into the physical mechanism of FRBs.

The first paper, for which Zhang is a corresponding author and leading theorist, was published in the Oct. 28 issue of Nature.

"There are two main questions regarding the origin of FRBs," said Zhang, whose team made the observation using the Five-hundred-meter Aperture Spherical Telescope (FAST) in Guizhou, China. "The first is what are the engines of FRBs and the second is what is the mechanism to produce FRBs. We found the answer to the second question in this paper."

Two competing theories have been proposed to interpret the mechanism of FRBs. One theory is that they're similar to gamma-ray bursts (GRBs), the most powerful explosions in the universe. The other theory likens them more to radio pulsars, which are spinning neutron stars that emit bright, coherent radio pulses. The GRB-like models predict a non-varying polarization angle within each burst whereas the pulsar-like models predict variations of the polarization angle.

The team used FAST to observe one repeating FRB source and discovered 11 bursts from it. Surprisingly, seven of the 11 bright bursts showed diverse polarization angle swings during each burst. The polarization angles not only varied in each burst, the variation patterns were also diverse among bursts.

"Our observations essentially rules out the GRB-like models and offers support to the pulsar-like models," said K.-J. Lee from the Kavli Institute for Astronomy and Astrophysics, Peking University, and corresponding author of the paper.

Four other papers on FRBs were published in Nature on Nov. 4. These include multiple research articles published by the FAST team led by Zhang and collaborators from the National Astronomical Observatories of China and Peking University. Researchers affiliated with the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the Survey for Transient Astronomical Radio Emission 2 (STARE2) group also partnered on the publications.

"Much like the first paper advanced our understanding of the mechanism behind FRBs, these papers solved the challenge of their mysterious origin," explained Zhang.

Magnetars are incredibly dense, city-sized neutron stars that possess the most powerful magnetic fields in the universe. Magnetars occasionally make short X-ray or soft gamma-ray bursts through dissipation of magnetic fields, so they have been long speculated as plausible sources to power FRBs during high-energy bursts.

The first conclusive evidence of this came on April 28, 2020, when an extremely bright radio burst was detected from a magnetar sitting right in our backyard—at a distance of about 30,000 light years from Earth in the Milky Way Galaxy. As expected, the FRB was associated with a bright X-ray burst.

"We now know that the most magnetized objects in the universe, the so-called magnetars, can produce at least some or possibly all FRBs in the universe," said Zhang.

The event was detected by CHIME and STARE2, two telescope arrays with many small radio telescopes that are suitable for detecting bright events from a large area of the sky.

Zhang's team has been using FAST to observe the magnetar source for some time. Unfortunately, when the FRB occurred, FAST was not looking at the source. Nonetheless, FAST made some intriguing "non-detection" discoveries and reported them in one of the Nov. 4 Nature articles. During the FAST observational campaign, there were another 29 X-ray bursts emitted from the magnetar. However, none of these bursts were accompanied by a radio burst.

"Our non-detections and the detections by the CHIME and STARE2 teams delineate a complete picture of FRB-magnetar associations," Zhang said.

To put it all into perspective, Zhang also worked with Nature to publish a single-author review of the various discoveries and their implications for the field of astronomy.

"Thanks to recent observational breakthroughs, the FRB theories can finally be reviewed critically," said Zhang. "The mechanisms of producing FRBs are greatly narrowed down. Yet, many open questions remain. This will be an exciting field in the years to come."


Far away from home

Even though astronomers had finally figured out what caused short gamma-ray bursts, one big mystery remained: their location. Unlike their longer-lasting cousins (long gamma-ray bursts), many of the short ones tended to come from regions of the universe relatively far away from galaxies. They're not a part of the normal stellar population.

Linking a powerful, rare event like this to its surroundings is a useful astronomical trick. For example, before we fully understood what causes the various kinds of supernovae, astronomers noticed that the Type II class tend to come from elliptical and spiral galaxies, while Type I come from basically wherever. That helped us understand their identities: Type II come from the deaths of massive stars, which are manufactured in abundance within star-forming ellipticals and spirals, whereas Type I come from the destruction of white dwarfs, a much more common and long-lived object that can live anywhere.

And so astronomers have been puzzled by the location of many short gamma-ray bursts. They most definitely come from stars (the neutron stars behind the kilonova events are the remnant cores of large stars), but the short gamma-ray bursts weren't embedded inside a population of older stars…or any stars at all, for that matter.

This led astronomers to suspect that before neutron stars slam together in a kilonova flash, complicated dynamics "kick" them out of their home and away from their host galaxies. Then, wandering the lonely intergalactic depths, the neutron stars coalesce, leading to a short gamma-ray burst, that one blast of light the only sign of their existence.


Colossal flare could be first evidence energy can be extracted from black holes

The popular conception goes that nothing can escape from a black hole. Once something passes the event horizon – the so-called point of no return – it stays there, forever, bound by a gravitational field not even light can escape.

But a rotating black hole generates vast amounts of energy, which, theoretically, can be extracted from the ergosphere, a region that sits just on the outside of the event horizon. This has been shown both theoretically and experimentally – and now a team of astrophysicists has found what they believe is observational evidence for it.

The smoking gun is the most powerful gamma-ray burst we’ve ever detected, GRB 190114C, a colossal flare clocking in at around a trillion electron volts (1 TeV), from 4.5 billion light-years away.

“Gamma-ray bursts, the most powerful transient objects in the sky, release energies of up to a few 10 54 erg in just a few seconds,” said astrophysicist Remo Ruffini of the International Center for Relativistic Astrophysics Network (ICRANet) headquartered in Italy.

“Their luminosity in the gamma-rays, in the time interval of the event, is as large as the luminosity of all the stars of the observable Universe! Gamma-ray bursts have been thought to be powered, by an up-to-now unknown mechanism, by stellar-mass black holes.”

Last year, Ruffini and his colleagues came up with a solution for this mechanism – a process they have called a binary-driven hypernova.

It starts with a close binary system consisting of a carbon-oxygen star at the end of its life, and a neutron star. When the carbon-oxygen star goes supernova, the material ejected can be rapidly slurped up by the companion neutron star. Thus, that companion passes the critical mass point and collapses into a black hole, which launches a burst of gamma rays, as well as jets of material from its poles at nearly light-speed.

(The core of the carbon-oxygen star collapses into a second neutron star, resulting in a black hole-neutron star binary.)

Now, in a new paper, Ruffini and his colleagues led by ICRANet’s Rahim Moradi have described the mechanism that can launch such a high-energy gamma-ray burst: the acceleration of particles along magnetic field lines inherited from the black hole’s parent neutron star. That magnetic field extracts rotational energy from the black hole’s ergosphere.

“The novel engine presented in the new publication,” Ruffini explained, “makes the job through a purely general relativistic, gravito-electrodynamical process: a rotating black hole, interacting with a surrounding magnetic field, creates an electric field that accelerates ambient electrons to ultrahigh-energies leading to high-energy radiation and ultrahigh-energy cosmic rays.”

Relativistic, or near light-speed, jets are not uncommon in active galactic nuclei, the supermassive black hole monsters at the cores of galaxies. These jets are thought to form from the accretion process, which goes as follows.

A huge disk of material swirls around the active black hole, falling into it from the inner edge, but not all of this material falls onto the black hole. Some of it, astronomers believe, is funneled and accelerated along magnetic field lines around the outside of the black hole to the poles, where it is launched into space in the form of collimated jets.

We know black holes and neutron stars can have powerful magnetic fields, and the evidence suggests these can act as a synchrotron (a type of particle accelerator). Evidence also suggests that a magnetic field synchrotron plays a role in launching a gamma-ray burst during the formation of a black hole.

Studying GRB 190114C, Moradi and his team have found a similar mechanism – but, rather than a continuous emission process, it’s discrete, repeating over and over, releasing each time a quantum of black hole energy to produce the observed gamma-ray emission following the gamma-ray burst.

Based on observations of GRB 190114C, the team was able to reconstruct the sequence of events.

The carbon-oxygen star goes supernova, while the core collapses into a neutron star some of that ejected material falls back onto the newly formed neutron star, producing an X-ray glow – as observed by the Swift telescope.

Some of the material also falls onto the neutron star companion, pushing it over the mass limit to form a black hole – this process would have been smooth, taking just 1.99 seconds. Then material continues to fall onto the newly formed black hole, producing a gamma-ray burst from 1.99 to 3.99 seconds.

Finally, more material falling onto the black hole results in the formation of jets, and gamma radiation in the gigaelectronvolt range, from the extraction of rotational energy.

Other scientists may disagree with the findings a team last year found that the gamma-ray burst was the result of a collapsing magnetic field, for instance. It may not even apply to all gamma-ray bursts. Nevertheless, all the parts seem to fit the observations of GRB 190114C very neatly.

“The proof that we can use the extractable rotational energy of a black hole to explain the high-energy jetted emissions of gamma-ray bursts and active galactic nuclei stands alone,” Ruffini said.

“A long march of successive theoretical progress and new physics discovered using observations of GRBs has brought to this result which has been [awaited] for about 50 years of relativistic astrophysics.”


14.15: Gamma-Ray Bursts (GRBs)

A number of satellites have been built to observe GRBs. The Compton Gamma Ray Observatory determined that GRBs were from outside our Galaxy. (There is a class of gamma-ray objects within our galaxy, but not with the extreme power of GRBs). Some have speculated that GRBs are possibly at the edge of the early Universe and the death throes of extremely massive stars, which only lasted about 1 million years. These stars appear to eject Gamma Rays after a hypernova event , an extreme supernova which produces gamma radiation. GRBs also appear to come from within stellar nurseries.


Not just for finding planets: Exoplanet-hunter TESS telescope spots bright gamma-ray burst

DALLAS ( SMU ) &ndash NASA has a long tradition of unexpected discoveries, and the space program&rsquos TESS mission is no different. SMU astrophysicist and her team have discovered a particularly bright gamma-ray burst using a NASA telescope designed to find exoplanets &ndash those occurring outside our solar system &ndash particularly those that might be able to support life.

It&rsquos the first time a gamma-ray burst has been found this way.

Gamma-ray bursts are the brightest explosions in the universe, typically associated with the collapse of a massive star and the birth of a black hole. They can produce as much radioactive energy as the sun will release during its entire 10-billion-year existence.

Krista Lynne Smith , an assistant professor of physics at Southern Methodist University, and her team confirmed the blast &ndash called GRB 191016A &ndash happened on Oct. 16 and also determined its location and duration. A study on the discovery has been published in The Astrophysical Journal.

&ldquoOur findings prove this TESS telescope is useful not just for finding new planets, but also for high-energy astrophysics,&rdquo said Smith, who specializes in using satellites like TESS (Transiting Exoplanet Survey Satellite) to study supermassive black holes and gas that surrounds them. Such studies shed light on the behavior of matter in the deeply warped spacetime around black holes and the processes by which black holes emit powerful jets into their host galaxies.

Smith calculated that GRB 191016A had a peak magnitude of 15.1, which means it was 10,000 times fainter than the faintest stars we can see with the naked eyes.

That may sound quite dim, but the faintness has to do with how far away the burst occurred. It is estimated that light from GRB 191016A&rsquos galaxy had been travelling 11.7 billion years before becoming visible in the TESS telescope.

Most gamma ray bursts are dimmer &ndash closer to 160,000 times fainter than the faintest stars.

The burst reached its peak brightness sometime between 1,000 and 2,600 seconds, then faded gradually until it fell below the ability of TESS to detect it some 7000 seconds after it first went off.

How SMU and a team of exoplanet specialists confirmed the burst

This gamma-ray burst was first detected by a NASA&rsquos satellite called Swift-BAT , which was built to find these bursts. But because GRB 191016A occurred too close to the moon, the Swift-BAT couldn&rsquot do the necessary follow-up it normally would have to learn more about it until hours later.

NASA&rsquos TESS happened to be looking at that same part of the sky. That was sheer luck, as TESS turns its attention to a new strip of the sky every month.

While exoplanet researchers at a ground-base for TESS could tell right away that a gamma-ray burst had happened, it would be months before they got any data from the TESS satellite on it. But since their focus was on new planets, these researchers asked if any other scientists at a TESS conference in Sydney, Australia was interested in doing more digging on the blast.

Smith was one of the few high-energy astrophysics specialists there at that time and quickly volunteered.

&ldquoThe TESS satellite has a lot of potential for high-energy applications, and this was too good an example to pass up,&rdquo she said. High-energy astrophysics studies the behavior of matter and energy in extreme environments, including the regions around black holes, powerful relativistic jets, and explosions like gamma ray bursts.

TESS is an optical telescope that collects light curves on everything in its field of view, every half hour. Light curves are a graph of light intensity of a celestial object or region as a function of time. Smith analyzed three of these light curves to be able to determine how bright the burst was.

She also used data from ground-based observatories and the Swift gamma ray satellite to determine the burst's distance and other qualities about it.

"Because the burst reached its peak brightness later and had a peak brightness that was higher than most bursts, it allowed the TESS telescope to make multiple observations before the burst faded below the telescope's detection limit," Smith said. &ldquoWe&rsquove provided the only space-based optical follow-up on this exceptional burst.&rdquo

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Figuring for Yourself

31: The ring around SN 1987A ([link]) initially became illuminated when energetic photons from the supernova interacted with the material in the ring. The radius of the ring is approximately 0.75 light-year from the supernova location. How long after the supernova did the ring become illuminated?

32: What is the acceleration of gravity (g) at the surface of the Sun? (See Appendix E for the Sun’s key characteristics.) How much greater is this than g at the surface of Earth? Calculate what you would weigh on the surface of the Sun. Your weight would be your Earth weight multiplied by the ratio of the acceleration of gravity on the Sun to the acceleration of gravity on Earth. (Okay, we know that the Sun does not have a solid surface to stand on and that you would be vaporized if you were at the Sun’s photosphere. Humor us for the sake of doing these calculations.)

33: What is the escape velocity from the Sun? How much greater is it than the escape velocity from Earth?

34: What is the average density of the Sun? How does it compare to the average density of Earth?

35: Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?

36: What is the escape velocity from the white dwarf in [link]? How much greater is it than the escape velocity from Earth?

37: What is the average density of the white dwarf in [link]? How does it compare to the average density of Earth?

38: Now take a neutron star that has twice the mass of the Sun but a radius of 10 km. What is the acceleration of gravity at the surface of the neutron star? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the neutron star (provided you could somehow not become a puddle of protoplasm)?

39: What is the escape velocity from the neutron star in [link]? How much greater is it than the escape velocity from Earth?

40: What is the average density of the neutron star in [link]? How does it compare to the average density of Earth?

41: One way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?

42: According to a model described in the text, a neutron star has a radius of about 10 km. Assume that the pulses occur once per rotation. According to Einstein’s theory of relatively, nothing can move faster than the speed of light. Check to make sure that this pulsar model does not violate relativity. Calculate the rotation speed of the Crab Nebula pulsar at its equator, given its period of 0.033 s. (Remember that distance equals velocity × time and that the circumference of a circle is given by 2πR).

43: Do the same calculations as in [link] but for a pulsar that rotates 1000 times per second.

44: If the Sun were replaced by a white dwarf with a surface temperature of 10,000 K and a radius equal to Earth’s, how would its luminosity compare to that of the Sun?

45: A supernova can eject material at a velocity of 10,000 km/s. How long would it take a supernova remnant to expand to a radius of 1 AU? How long would it take to expand to a radius of 1 light-years? Assume that the expansion velocity remains constant and use the relationship: $ ext=frac< ext>< ext>.$

46: A supernova remnant was observed in 2007 to be expanding at a velocity of 14,000 km/s and had a radius of 6.5 light-years. Assuming a constant expansion velocity, in what year did this supernova occur?

47: The ring around SN 1987A ([link]) started interacting with material propelled by the shockwave from the supernova beginning in 1997 (10 years after the explosion). The radius of the ring is approximately 0.75 light-year from the supernova location. How fast is the supernova material moving, assume a constant rate of motion in km/s?

48: Before the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?

49: What is the radius of the progenitor star that became SN 1987A? Its luminosity was 100,000 times that of the Sun, and it had a surface temperature of 16,000 K.

50: What is the acceleration of gravity at the surface of the star that became SN 1987A? How does this g compare to that at the surface of Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.

51: What was the escape velocity from the surface of the SN 1987A progenitor star? How much greater is it than the escape velocity from Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.

52: What was the average density of the star that became SN 1987A? How does it compare to the average density of Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.

53: If the pulsar shown in [link] is rotating 100 times per second, how many pulses would be detected in one minute? The two beams are located along the pulsar’s equator, which is aligned with Earth.