Observations of gamma-ray burst reveal surprising ingredients of early galaxies

ScienceDaily (Nov. 2, 2011) — An international team of astronomers led by the Max Planck Institute for Extraterrestrial Physics has used the brief but brilliant light of a distant gamma-ray burst as a probe to study the make-up of very distant galaxies. Surprisingly the new observations revealed two galaxies in the young Universe that are richer in the heavier chemical elements than the Sun. The two galaxies may be in the process of merging. Such events in the early Universe will drive the formation of many new stars and may be the trigger for gamma-ray bursts.

Gamma-ray bursts are the brightest explosions in the Universe. They are first spotted by orbiting observatories that detect the initial short burst of gamma rays. After their positions have been pinned down, they are then immediately studied using large ground-based telescopes that can detect the visible-light and infrared afterglows that the bursts emit over the succeeding hours and days. One such burst, called GRB 090323, was first spotted by the NASA Fermi Gamma-ray Space Telescope. Very soon afterwards it was picked up by the X-ray detector on NASA's Swift satellite and with the GROND system at the MPG/ESO 2.2-metre telescope in Chile. From the GROND observations, the astronomers estimated the minimum rate of star formation, which has to be several times higher than the one in our Galaxy. They could, however, only determine a minimum value because the detected emission could be heavily affected (i.e. absorbed) by the presence of dust in the galaxies. The real rate of star formation, once the (unknown) dust absorption has been taken into account, could easily be 50 times higher than in the Milky Way.

The burst was also studied in great detail using ESO's Very Large Telescope (VLT) just one day after it exploded. These observations show that the brilliant light from the gamma-ray burst had passed through its own host galaxy and another galaxy nearby. These galaxies are being seen as they were about 12 billion years ago. Such distant galaxies are very rarely caught in the glare of a gamma-ray burst.

"When we studied the light from this gamma-ray burst we didn't know what we might find. It was a surprise that the cool gas in these two galaxies in the early Universe proved to have such an unexpected chemical make-up," explains Sandra Savaglio (Max-Planck Institute for Extraterrestrial Physics, Garching, Germany), lead author of the paper describing the new results. "These galaxies have more heavy elements than have ever been seen in a galaxy so early in the evolution of the Universe. We didn't expect the Universe to be so mature, so chemically evolved, so early on."

As light from the gamma-ray burst passed through the galaxies, the gas there acted like a filter, and absorbed some of the light from the gamma-ray burst at certain wavelengths. Without the gamma-ray burst these faint galaxies would be invisible. By carefully analysing the tell-tale fingerprints from different chemical elements the team was able to work out the composition of the cool gas in these very distant galaxies, and in particular how rich they were in heavy elements.

It is expected that galaxies in the young Universe will be found to contain smaller amounts of heavier elements than galaxies at the present day, such as the Milky Way. The heavier elements are produced during the lives and deaths of generations of stars, gradually enriching the gas in the galaxies. Astronomers can use the chemical enrichment in galaxies to indicate how far they are through their lives. But the new observations, surprisingly, revealed that some galaxies were already very rich in heavy elements less than two billion years after the Big Bang. Something unthinkable until recently.

The newly discovered pair of young galaxies must be forming new stars at a tremendous rate, to enrich the cool gas so strongly and quickly. As the two galaxies are close to each other they may be in the process of merging, which would also provoke star formation when the gas clouds collide. The new results also support the idea that gamma-ray bursts may be associated with vigorous massive star formation.

Energetic star formation in galaxies like these might have ceased early on in the history of the Universe. Twelve billion years later, at the present time, the remains of such galaxies would contain a large number of stellar remnants such as black holes and cool dwarf stars, forming a hard to detect population of "dead galaxies," just faint shadows of how they were in their brilliant youths. Finding such corpses in the present day would be a challenge.

"We were very lucky to observe GRB 090323 when it was still sufficiently bright, so that it was possible to obtain spectacularly detailed observations with the VLT. Gamma-ray bursts only stay bright for a very short time and getting good quality data is very hard. We hope to observe these galaxies again in the future when we have much more sensitive instruments, they would make perfect targets for the E-ELT," concludes Savaglio.

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The above story is reprinted from materials provided by Max-Planck-Institut für extraterrestrische Physik (MPE).

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Journal Reference:

S. Savaglio et al. Super-solar Metal Abundances in Two Galaxies at z~3.57 revealed by the GRB090323 Afterglow Spectrum. Monthly Notices of the Royal Astronomical Society, 2011

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Mathematically detecting stock market bubbles before they burst

ScienceDaily (Oct. 31, 2011) — From the dotcom bust in the late nineties to the housing crash in the run-up to the 2008 crisis, financial bubbles have been a topic of major concern. Identifying bubbles is important in order to prevent collapses that can severely impact nations and economies.

A paper published this month in the SIAM Journal on Financial Mathematics addresses just this issue. Opening fittingly with a quote from New York Federal Reserve President William Dudley emphasizing the importance of developing tools to identify and address bubbles in real time, authors Robert Jarrow, Younes Kchia, and Philip Protter propose a mathematical model to detect financial bubbles.

A financial bubble occurs when prices for assets, such as stocks, rise far above their actual value. Such an economic cycle is usually characterized by rapid expansion followed by a contraction, or sharp decline in prices.

"It has been hard not to notice that financial bubbles play an important role in our economy, and speculation as to whether a given risky asset is undergoing bubble pricing has approached the level of an armchair sport. But bubbles can have real and often negative consequences," explains Protter, who has spent many years studying and analyzing financial markets.

"The ability to tell when an asset is or is not in a bubble could have important ramifications in the regulation of the capital reserves of banks as well as for individual investors and retirement funds holding assets for the long term. For banks, if their capital reserve holdings include large investments with unrealistic values due to bubbles, a shock to the bank could occur when the bubbles burst, potentially causing a run on the bank, as infamously happened with Lehman Brothers, and is currently happening with Dexia, a major European bank," he goes on to explain, citing the significance of such inflated prices.

Using sophisticated mathematical methods, Protter and his co-authors answer the question of whether the price increase of a particular asset represents a bubble in real time. "[In this paper] we show that by using tick data and some statistical techniques, one is able to tell with a large degree of certainty, whether or not a given financial asset (or group of assets) is undergoing bubble pricing," says Protter.

This question is answered by estimating an asset's price volatility, which is stochastic or randomly determined. The authors define an asset's price process in terms of a standard stochastic differential equation, which is driven by Brownian motion. Brownian motion, based on a natural process involving the erratic, random movement of small particles suspended in gas or liquid, has been widely used in mathematical finance. The concept is specifically used to model instances where previous change in the value of a variable is unrelated to past changes.

The key characteristic in determining a bubble is the volatility of an asset's price, which, in the case of bubbles is very high. The authors estimate the volatility by applying state of the art estimators to real-time tick price data for a given stock. They then obtain the best possible extension of this data for large values using a technique called Reproducing Kernel Hilbert Spaces (RKHS), which is a widely used method for statistical learning.

"First, one uses tick price data to estimate the volatility of the asset in question for various levels of the asset's price," Protter explains. "Then, a special technique (RKHS with an optimization addition) is employed to extrapolate this estimated volatility function to large values for the asset's price, where this information is not (and cannot be) available from tick data. Using this extrapolation, one can check the rate of increase of the volatility function as the asset price gets arbitrarily large. Whether or not there is a bubble depends on how fast this increase occurs (its asymptotic rate of increase)."

If it does not increase fast enough, there is no bubble within the model's framework.

The authors test their methodology by applying the model to several stocks from the dot-com bubble of the nineties. They find fairly successful rates in their predictions, with higher accuracies in cases where market volatilities can be modeled more efficiently. This helps establish the strengths and weaknesses of the method.

The authors have also used the model to test more recent price increases to detect bubbles. "We have found, for example, that the IPO [initial public offering] of LinkedIn underwent bubble pricing at its debut, and that the recent rise in gold prices was not a bubble, according to our models," Protter says.

It is encouraging to see that mathematical analysis can play a role in the diagnosis and detection of bubbles, which have significantly impacted economic upheavals in the past few decades.

Robert Jarrow is a professor at the Johnson Graduate School of Management at Cornell University in Ithaca, NY, and managing director of the Kamakura Corporation. Younes Kchia is a graduate student at Ecole Polytechnique in Paris, and Philip Protter is a professor in the Statistics Department at Columbia University in New York.

Professor Protter's work was supported in part by NSF grant DMS-0906995.

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Journal Reference:

Robert Jarrow, Younes Kchia, and Philip Protter. How to Detect an Asset Bubble. SIAM J. Finan. Math., 2011; 2, pp. 839-865 [link]

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here

Mathematically detecting stock market bubbles before they burst

ScienceDaily (Oct. 31, 2011) — From the dotcom bust in the late nineties to the housing crash in the run-up to the 2008 crisis, financial bubbles have been a topic of major concern. Identifying bubbles is important in order to prevent collapses that can severely impact nations and economies.

A paper published this month in the SIAM Journal on Financial Mathematics addresses just this issue. Opening fittingly with a quote from New York Federal Reserve President William Dudley emphasizing the importance of developing tools to identify and address bubbles in real time, authors Robert Jarrow, Younes Kchia, and Philip Protter propose a mathematical model to detect financial bubbles.

A financial bubble occurs when prices for assets, such as stocks, rise far above their actual value. Such an economic cycle is usually characterized by rapid expansion followed by a contraction, or sharp decline in prices.

"It has been hard not to notice that financial bubbles play an important role in our economy, and speculation as to whether a given risky asset is undergoing bubble pricing has approached the level of an armchair sport. But bubbles can have real and often negative consequences," explains Protter, who has spent many years studying and analyzing financial markets.

"The ability to tell when an asset is or is not in a bubble could have important ramifications in the regulation of the capital reserves of banks as well as for individual investors and retirement funds holding assets for the long term. For banks, if their capital reserve holdings include large investments with unrealistic values due to bubbles, a shock to the bank could occur when the bubbles burst, potentially causing a run on the bank, as infamously happened with Lehman Brothers, and is currently happening with Dexia, a major European bank," he goes on to explain, citing the significance of such inflated prices.

Using sophisticated mathematical methods, Protter and his co-authors answer the question of whether the price increase of a particular asset represents a bubble in real time. "[In this paper] we show that by using tick data and some statistical techniques, one is able to tell with a large degree of certainty, whether or not a given financial asset (or group of assets) is undergoing bubble pricing," says Protter.

This question is answered by estimating an asset's price volatility, which is stochastic or randomly determined. The authors define an asset's price process in terms of a standard stochastic differential equation, which is driven by Brownian motion. Brownian motion, based on a natural process involving the erratic, random movement of small particles suspended in gas or liquid, has been widely used in mathematical finance. The concept is specifically used to model instances where previous change in the value of a variable is unrelated to past changes.

The key characteristic in determining a bubble is the volatility of an asset's price, which, in the case of bubbles is very high. The authors estimate the volatility by applying state of the art estimators to real-time tick price data for a given stock. They then obtain the best possible extension of this data for large values using a technique called Reproducing Kernel Hilbert Spaces (RKHS), which is a widely used method for statistical learning.

"First, one uses tick price data to estimate the volatility of the asset in question for various levels of the asset's price," Protter explains. "Then, a special technique (RKHS with an optimization addition) is employed to extrapolate this estimated volatility function to large values for the asset's price, where this information is not (and cannot be) available from tick data. Using this extrapolation, one can check the rate of increase of the volatility function as the asset price gets arbitrarily large. Whether or not there is a bubble depends on how fast this increase occurs (its asymptotic rate of increase)."

If it does not increase fast enough, there is no bubble within the model's framework.

The authors test their methodology by applying the model to several stocks from the dot-com bubble of the nineties. They find fairly successful rates in their predictions, with higher accuracies in cases where market volatilities can be modeled more efficiently. This helps establish the strengths and weaknesses of the method.

The authors have also used the model to test more recent price increases to detect bubbles. "We have found, for example, that the IPO [initial public offering] of LinkedIn underwent bubble pricing at its debut, and that the recent rise in gold prices was not a bubble, according to our models," Protter says.

It is encouraging to see that mathematical analysis can play a role in the diagnosis and detection of bubbles, which have significantly impacted economic upheavals in the past few decades.

Robert Jarrow is a professor at the Johnson Graduate School of Management at Cornell University in Ithaca, NY, and managing director of the Kamakura Corporation. Younes Kchia is a graduate student at Ecole Polytechnique in Paris, and Philip Protter is a professor in the Statistics Department at Columbia University in New York.

Professor Protter's work was supported in part by NSF grant DMS-0906995.

Recommend this story on Facebook, Twitter,
and Google +1:

Other bookmarking and sharing tools:

Story Source:

The above story is reprinted from materials provided by Society for Industrial and Applied Mathematics.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Journal Reference:

Robert Jarrow, Younes Kchia, and Philip Protter. How to Detect an Asset Bubble. SIAM J. Finan. Math., 2011; 2, pp. 839-865 [link]

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here

Crab Nebula Emits Largest Gamma Ray Burst Ever Seen, Puzzles Astronomers

Crab Nebula Emits Largest Gamma Ray Burst Ever Seen, Puzzles Astronomers | Popular Science@import "/files/css/d6aad7f7d1d1484a4d015f8ad6128167.css";@import "/files/css/33f6b7ecb4513ed2fe6c670880a27187.css"; home Login/Register Newsletter Subscribe RSS GadgetsComputersCamerasSmartphonesSmart TVsVideo GamesMore From Our Partner: CEAGCarsConceptsHybridsElectric CarsAuto DIYMore From Our Partner: DriversideScienceFuture of the EnvironmentEnergyHealthPopSci Eco TourTechnologyMilitaryAviationSpaceRobotsDIYProjectsHacksToolsAuto DIYMore From Our Partner: Toolmonger GalleriesVideosColumnsThe GrouseSex FilesGreen Dream How It WorksAuto DIYFeatures Facebook Digg Stumbleupon Reddit Print Email Crab Nebula Emits Largest Gamma Ray Burst Ever Seen, Puzzles Astronomers By Clay Dillow Posted 05.12.2011 at 2:43 pm 5 Comments
The Crab Nebula (And Its Enigmatic Eruption) The nebula set against a full-sky gamma ray map, showing the Crab Nebula's location in the crosshairs. NASA

Something strange is afoot in the Crab Nebula. Famous for beaming a steady dose of radiation at Earth at regular intervals thanks to the spinning neutron star at its center, the nebula has long been of interest to astronomers. So one can imagine their interest when an enormous gamma-ray flare five times more powerful than any previously detected burst from the region, making these "the highest-energy electrons known to be associated with any cosmic source," according to NASA.

The Crab Nebula is basically the remnants of a supernova located about 6,500 light years away (in Taurus, for those of you keeping tabs on the heavens at home). What was once the star’s core is now an expanding gas cloud anchored by a superdense neutron star that rotates 30 times per second, each time swinging a beam of intense radiation toward the Earth.

Related ArticlesAstronomers Find Massive, Previously Undetected Gamma Radiation Bubbles Adorning the Milky WayShedding Some Light on Gamma Ray BurstsStrongest X-Ray Burst Ever Seen Bombards NASA's Swift Observatory, Temporarily Blinding ItTagsTechnology, Clay Dillow, crab nebula, Fermi space telescope, gamma-ray bursts, gamma-rays, SpaceThat’s been going on, from our perspective here, for thousands of years. And it’s been doing so with regularity, 30 times per second, ceaselessly. A handful of short-lived gamma-ray flares have been detected over the years, but nothing that fell outside the range of what’s considered normal cosmic violence.

Then, on April 12, the Fermi Gamma-ray Space Telescope--and later Italy’s AGILE satellite--picked up this monster of a flare 30 times more intense than the nebula’s normal energy output and five times more powerful than any previous uptick in energy. Four days later an even brighter flare erupted. Then, two days after that, the strange activity ceased without explanation.

Astronomers theorize that the flares must be coming from somewhere within a one-third of-a-light-year radius of that central neutron star, and that the area doing the emitting must be close to the size of our own solar system. And to offer some perspective on the energy unleashed, the electrons in these emissions must have energies some 100 times greater than the highest achievable energies in the LHC.

But what caused them is still unknown. The prevailing theory seems to be that the magnetic field around the neutron star suddenly rearranged itself, accelerating particles quickly to nearly the speed of light. As high speed electrons interact with the shifting magnetic field, gamma-rays are produced. Observations are ongoing. In the meantime, it gives us an excuse to post brilliantly pretty images of the Crab Nebula, like the one above.

[NASA]

Previous Article: Video: New ZeroTouch Interface is a Touchscreen Without the ScreenNext Article: Financial Trading Algorithms Aren't Just Making Deals, They're Making War 5 Comments Link to this comment diogogmiranda 05/12/11 at 7:25 pm

Wait, let me understand something here. If the Crab Nebula is 6,500 light years away from here, it means that the light traveling from there takes 6,500 years to get here.
So that happened 6,500 years ago, tight?
If so, how come they're talking in the present? And how long does it take for the radiation to travel compared to the light?

Thanks

Link to this comment yeahilikescience 05/13/11 at 12:28 am

Radiation and light travel at the same speed because visible light is just a form of radiation, the only part of the electromagnetic spectrum that our eyes can detect due to our photoreceptors.

Could it possibly be that something with considerable mass collided with the neutron star, causing a great release of energy because of the star's immense gravity? After all, something approximate to a marshmallow colliding with a neutron star releases about the equivalent energy to an atomic bomb.

Link to this comment yeahilikescience 05/13/11 at 12:30 am

And they're talking in the present because technically speaking, due to space time relativity, all time is now. And because although it happened 6500 years ago 6500 light years away, it is occurring for us to observe now.

Link to this comment OtakuElite 05/14/11 at 1:48 am

What I'm confused about is that the increase in energy means that the rotation of the gas cloud temporarily increased, and "... the magnetic field around the neutron star suddenly rearranged itself, accelerating particles quickly to nearly the speed of light."

So my question is, wouldn't those bursts of increased energy be moving faster than the other pulses, moving out of sequence with the other 30 times per second bursts we can witness here? The statement about nearly the speed of light just leads me to believe it is moving faster then the previous pulses.

Link to this comment JediMindset 05/14/11 at 11:59 am

wow. maybe this has something to do with 2012. its all falling into place. and real science is proving it.

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