Red Giant Brightness Variations Still Mysterious

As the get older, Sun-like stars become red giants. 30-50 percent of these red giants exhibit a strange variability in their brightness that has so far eluded explanation. Image Credit: ESO/S. Steinhofel

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Like everything else in the Universe, stars get old. As they become older, stars like our own Sun “puff up”, becoming red giants for a period before finally settling down into white dwarfs. During this late period of their stellar lives, about 30% of low-mass red giants exhibit a curious variability in their brightness that remains unexplained to this day. A new survey of these types of red giants rules out most of the current explanations put forth, making it necessary to find a new theory for their behavior.

Red giants are a stage in the later part of a Sun-like star’s life when most of the fuel powering nuclear fusion in the core of the star is exhausted. The resulting lack of light pressure pushing out against the force of gravity causes the star to collapse in on itself. When this collapse occurs, though, it heats up a shell of hydrogen around the core enough to reignite fusion, resulting in an increase in nuclear fusion that causes the star to become bigger due to the increased light pressure. This can result in the star becoming 1,000 to 10,000 times more luminous.

Variability in the light output of red giants is natural -they swell up and shrink down in a consistent pattern, resulting in brighter and dimmer light outputs. There is, however, a difference in the brightness of roughly a third to one half of these stars that happens over longer time periods, to the tune of up to five years.

Called the Long Secondary Period (LSP), the changing brightness of the star happens over longer timescales than the shorter period pulsation. It is this long-term variation in brightness that remains unexplained.

A new detailed study of 58 variable red giants in the Large Magellanic cloud by Peter Wood and Christine Nicholls, both of the Research School of Astronomy and Astrophysics at the Australian National University, shows that the proposed explanations of this mysterious variability fall short of the measured properties of the stars. Nicholls and Wood used the FLAMES/GIRAFFE spectrograph on ESO’s Very Large Telescope, and combined the information with data from other telescopes like the Spitzer Space Telescope.

There are two leading explanations of the phenomenon: the presence of a companion object to the red giants that orbit in such a way to change their brightness, or the presence of a circumstellar dust cloud that somehow blocks the light coming from the star in our direction on a periodic scale.

A binary companion to the stars would change their orbit in such a way that they would approach and recede from the vantage point of the Earth, and if the companion passed in front of the star it would also dim the light streaming from the red giant. In the case of a binary companion, the spectra of the brightness change among all of these stars is relatively similar, meaning that for this explanation to work, all of the red giants exhibiting the LSP variation would have to have a companion of a similar size, approximately 0.09 times the mass of the Sun. This scenario would be extremely unlikely, given the large number of stars that show this brightness variation.

The effect of a circumstellar dust cloud could be a possible explanation. A cloud of circumstellar dust that obscures the light from the star once per orbit would dim its light enough to explain the phenomenon. The presence of such a dust cloud would be revealed by an excess of light coming from the star in the mid-infrared spectrum. The dust would absorb light from the star, and re-emit it in the form of light in the mid-infrared region of the spectrum.

Observations of LSP stars show the mid-infrared signature that’s a telltale sign of dust, but the correlation between the two doesn’t mean that the dust is causing the brightness variation. It could be that the dust is a byproduct of ejected mass from the star itself, the underlying cause of which could be associated with the change in brightness.

Whatever the cause of the oscillation of brightness in these red giants may be, it does make them eject mass in large clumps or in the form of an expanding disc. Obviously, further observations will be necessary to track down the reason for this phenomenon.

The results of the observations made by Nicholls and Wood have been published in The Astrophysical Journal. Two articles describing their findings are available on Arxiv, here and here.

Source: ESO, Arxiv papers

Cool – Literally – Extrasolar Planet Imaged

Yet another planet outside of our Solar System has been directly imaged, bumping the list up past ten. Given that the first visible light image of an extrasolar planet was taken a little more than a year ago, the list is growing pretty fast. The newest one, planet GJ 758 B is also the coolest directly imaged planet, measuring 600 degrees Kelvin, and it orbits a star that is much like our own Sun. GJ 758 B has a mass of between 10-40 times that of Jupiter, making it either a really big planet or a small brown dwarf.

Unlike many of the other directly imaged planets, GJ 758 B resides in a system remarkably like our own Solar System – the star at the center is Sun-like, and the orbit of the planet is at least the same distance from its star as Neptune is from our own. Current observations put the distance at 29 astronomical units.

“The discovery of GJ 758 B, an extrasolar planet or brown dwarf orbiting a star that is similar to our own sun, gives us an insight into the diversity of substellar objects that may form around Solar-type stars,” said Dr. Joseph Carson, from the Max Planck Institute for Astronomy. “This in turn helps show how our own Solar system, and the environments that are conducive to life, are just one of many scenarios that may be the outcome of planet or brown dwarf formation around Sun-like stars.”

Another object, labeled “C?” in the image above, could potentially be another companion to the star. Further observations will be required to determine whether the object in fact orbits the star or is merely another star in the background of the image which is not part of the system.

The mass of the star still has yet to be exactly determined, thus the 10-40 Jupiter mass range. It is 600 degrees Kelvin, which corresponds to 326 Celsius and 620 Fahrenheit, about the hottest temperature that a conventional oven can reach. Though this may seem hot, it’s actually pretty cool for an extrasolar planet. Even though it is so far away from its Sun that, like Neptune, it receives very little warmth from the star it orbits, GJ 758 B is in a stage of formation where the contraction of the planet due to gravity is converted into heat.

A size comparison of the GJ 758 system and corresponding members of our own Solar System, with the Earth for reference. Image Credit: Credit: MPIA/C. Thalmann
A size comparison of the GJ 758 system and corresponding members of our own Solar System, with the Earth for reference. Image Credit: Credit: MPIA/C. Thalmann

Dr. Markus Janson from the University of Toronto, a co-author of the paper announcing the imaging, said, “This is also why the mass of the companion is not well known: The measured infrared brightness could come from a 700 million year old planet of 10 Jupiter masses just as well as from a 8700 million year old companion of 40 Jupiter masses.” The paper detailing the results will be published in Astrophysical Journal Letters, but is available here on Arxiv.

The planet was imaged using the Subaru Telescope’s new High Contrast Instrument for the Subaru next generation Adaptive Optics (HiCIAO) instrument, which utilizes the technology of adaptive optics to eliminate the interference of our atmosphere that blurs images in ground-based telescopes. The imaging of GJ 758 B is part of the commissioning run of the HiCIAO instrument, which plans to take a larger survey to detect extrasolar planets and circumstellar disks in the next five years.

Source: Max-Planck Institute for Astronomy

House Subcommittee Holds Hearing on Spaceflight Safety

Witnesses give statements to the House Committee on Science and Technology’s Subcommittee on Space and Aeronautics hearing on spaceflight safety yesterday. Image Credit: Subcommittee on Space and Aeronautics

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The U.S. House of Representatives Subcommittee on Space & Aeronautics held a hearing yesterday on the issue of how to ensure the future safety of human flight into space for both commercial and governmental agencies. The hearing was attended by a number of witnesses that represented NASA, one from the Commercial Spaceflight Federation, the CEO of a risk-analysis firm, and a former astronaut. The subcommittee was chaired by Rep. Gabrielle Giffords.

This hearing comes on the tails of the Augustine Commission final report, which examined the future of spaceflight in the U.S. and laid out a “flexible path” plan that includes utilizing private, commercial firms for human transport into Low Earth Orbit (LEO) and the International Space Station.

Yesterday’s hearing was meant to help inform members of Congress about the safety concerns presented to manned flights, and what future regulations will be needed if commercial companies start to have a larger role in human spaceflight. The hearing’s charter states as its purpose:

On December 2, 2009 the Subcommittee on Space and Aeronautics will hold a hearing focused on issues related to ensuring the safety of future human space flight in government and non-government space transportation systems.  The hearing will examine (1) the steps needed to establish confidence in a space transportation system’s ability to transport U.S. and partner astronauts to low Earth orbit and return them to Earth in a safe manner, (2) the issues associated with implementing safety standards and establishing processes for certifying that a space transportation vehicle is safe for human transport, and (3) the roles that training and experience play in enhancing the safety of human space missions.

Witnesses at the hearing included Chief of Safety and Mission Assurance for NASA Bryan O’Connor, Constellation Program Manager Jeff Hanley, Aerospace Safety Advisory Panel Council Member John C. Marshall, President of the Commercial Spaceflight Federation Bretton Alexander, Vice President of Valador, Inc. Dr. Joseph R. Fragola, and former astronaut Lt. Gen. Thomas P. Stafford, USAF, who flew in some of the Apollo and Gemini missions.

Each witness gave statements to the panel, all of which is available in .pdf format on the committee’s site. After hearing the testimony of these witnesses, Rep. Giffords said:

“At the end of the day, I am left with the firm conviction that the U.S. government needs to ensure that it always has a safe way to get its astronauts to space and back. As I have said in the past, I welcome the growth of new commercial space capabilities in America and do not see them as competitors with, but rather complementary to the Constellation systems under development. Based on what we’ve heard today, I see no justification for a change in direction on safety-related grounds. Instead, I am very impressed with the steps that have been taken to infuse safety into the Constellation program, and want to encourage their continued efforts to make Ares and Orion as safe as possible.”

Part of the reason for the hearing was to compare the safety of commercial vehicles to the Constellation program for getting astronauts to the International Space Station after the Shuttle program is shut down. Constellation won’t be ready to go until 2015 at the earliest, so the gap of five years could potentially be filled by private contractors.

Of course, you might notice that only one of the members of the witness panel of six represents commercial interests, which has caused some critics – like the Orlando Sentinel – to call the safety hearing a “Pro-Constellation rally.” The Space Politics blog also pointed this lack of representation out.

Though commercial aerospace companies like SpaceX, Masten Space Systems and XCOR weren’t represented directly on the witness panel, they are members of the Commercial Spaceflight Federation. Bretton Alexander stressed the importance of safety in his statement, and also pointed out that private space companies could take over the majority LEO launches here at home to allow NASA and its partners the resources to go to the Moon (and beyond).

Source: House Committee on Science and Technology’s Subcommittee on Space and Aeronautics press release

Vatican Astronomer on the Colbert Report

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The curator of meteorites at the Vatican, Guy Consolmagno, SJ was on the Colbert Report Tuesday to talk about the existence of extraterrestrials with Colbert. Consolmagno is author of a book about astronomy and its relation to the Catholic faith. Of course, Colbert handled the discussion in his own tongue-in-cheek joking manner, but Consolmagno was a good sport. This is just another in a series of public media events illustrating the Vatican’s position on the possibility of alien existence.

The Pope’s chief astronomer, Rev. Jose Gabriel Funes, announced last May that belief in the existence of extraterrestrial life is not in conflict with faith in God. Last month, the Vatican held a 6-day international conference to examine the likelihood of finding extraterrestrials, and discussing the impact such a finding would have on faith in God. During the conference, many scientists presented on the scientific evidence available on the possibility that aliens exist.

Stellar Escapees Await Detection

Stars wandering outside the galactic plane of the Milky Way could number in the billions. Image Credit: APOD

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The structure of the Universe and the formation of stars from concentrated dust leads them to be clumped into galaxies of all sorts. But adrift between the galaxies may be billions of undiscovered lonely stars. These escaped stars, thrown out of their homes by gravitational interactions, may number in the billions for the Milky Way galaxy alone, and would provide details of historic galactic formations and mergers.

The theory that escaped and wandering stars exist isn’t new, and ejected stars from other galaxies have already been observed (see Hyperfast Star Ejected from the Large Magellanic Cloud). Our Milky Way formed as the result of many mergers with smaller dwarf galaxies, and as a result of these gravitational train wrecks, billions of stars could have been thrown out of the system, breaking free of their gravitational bonds to wander between the galaxies forever.

Wandering stars – those that have loosely bound orbits around a galaxy  – and escaped stars that have left the galaxy altogether could be discovered in the near future by the Large Synoptic Survey Telescope, planned for development in Chile, and Pan-STARRS. In the December 10 issue of Astrophysical Journal Letters, a team of astronomers led by Michael Shara of the American Museum of Natural History explores the provenance of these drifters, and estimates the lower limit of their numbers to be 0.05% of the Milky Way galaxy’s stellar population. That places their numbers well in the billions.

Red giant stars and classical novae have been detected outside the Milky Way, but only in clusters. Finding the individual escaped stars would be a challenge because of how dim they would appear. Because of the mechanism that ejects them  from the Milky Way, many would be older and redder, having formed when the galaxy was much younger. But the phenomenon of novae and supernovae would allow upcoming large scale sky surveys to pick up the few that exploded.

Building up a database of these intergalactic novae and supernovae would give astronomers better information on their orbital characteristics, which in turn would allow for improved modeling of how the Milky Way formed: knowing where the stars are now and what their velocity is gives information as to where they were in the past. Research into older, high-velocity stars that travel back into the Milky Way is ongoing, and would supplement the figure for how many of these galactic jailbreakers exist.

Source: Arxiv, nod to Scientific American

The LHC Will Discover the Higgs. Wanna Bet?

Want to bet on whether the Higgs will be discovered? You can. Image Credit: Alexander Unzicker/CERN

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If you’re of the opinion that the Large Hadron Collider – which just became the most powerful supercollider ever built by humans on Monday – will ultimately triumph in its quest to find the Higgs boson, you might be able to make a few bucks. If you’re wrong, well, you might lose a few, too. That’s right, along with betting on the elections, Academy Awards, and the snowfall in New York, the discovery of the Higgs boson is a tradeable commodity.

A physics and math lecturer in Munich, Dr. Alexander Unzicker, wants you to place a bet on whether or not the Higgs will be discovered at the LHC at the prediction market site Intrade. You can bet on whether it will be discovered by the end of December 2009, or by the end of each year until 2013, according to your own bravado. The contracts available are based on a $10 scale, so your winnings or losses may be in the single digits range.

According to his site, if you have inside information on the subject, it’s not illegal. So if you work at the LHC and are fairly confident in the positive identification of the Higgs, it might be worth your while.

Unzicker claims inspiration for the idea from Immanuel Kant, who wrote in his most famous work, The Critique of Pure Reason:

The usual test, whether that which any one maintains is merely his persuasion, or his subjective conviction at least, that is, his firm belief, is a bet. It frequently happens that a man delivers his opinions with so much boldness and assurance, that he appears to be under no apprehension as to the possibility of his being in error. The offer of a bet startles him, and makes him pause. Sometimes it turns out that his persuasion may be valued at a ducat, but not at ten. For he does not hesitate, perhaps, to venture a ducat, but if it is proposed to stake ten, he immediately becomes aware of the possibility of his being mistaken–a possibility which has hitherto escaped his observation. If we imagine to ourselves that we have to stake the happiness of our whole life on the truth of any proposition, our judgement drops its air of triumph, we take the alarm, and discover the actual strength of our belief. Thus pragmatical belief has degrees, varying in proportion to the interests at stake.

If you haven’t had the fortune (as have I) of four years studying philosophy, this passage from Kant can be neatly summed up with the old adage, “Put your money where your mouth is.” Stephen Hawking has been in on this game for a while, betting Gordon Kane $100 that the Higgs will not be found by the LHC.

Of course, this isn’t the only betting you can do on matters of scientific import. At Stranieri.com, you can bet on a number of long-term predictions, including whether we will receive communication from intelligent beings outside the solar system in the next 50 years. The bets you make there are long-term (some are for over 200 years into the future), and the money held is used for philanthropic purposes.

From reading his site, it’s evident Unzicker is not of the opinion that the Higgs will be found. Are you? Would you be willing to bet on it? Leave your opinions in the comments.

Source: Physicsworld.com, Unzicker’s site. Kant quote taken from Fullbooks.com

Superbright Supernova First Observed of Antimatter Variety

The supernova 2007bi, circled in the image above, might be the first confirmation of a pair-instability supernova. Image Credit: Nearby Supernova Factory

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The supernova 2007bi wasn’t your typical supernova: it was 10 times brighter than a Type Ia supernova, making it one of the most energetic supernova events ever recorded. Astronomers from the University of California Berkeley have analyzed the explosion, which was recorded by a robotic survey in 2007, and found that it is likely the first confirmed observation ever made of a pair-instability supernova, a type of extremely energetic supernova that has been theorized but never directly confirmed.

The confirmed observation of a pair-instability supernova has been long-awaited – the theory that they exist has been around since the 1960’s – but it appears as if the wait is over. The supernova 2007bi, seen by the Nearby Supernova Factory in April of 2007, is the first observed supernova that fits the bill for the unfathomably huge proportions of pair-instability supernovae explosions. A team of astronomers led by Alex Filippenko of the University of California Berkeley published their analysis in in the December 3rd issue of Nature. The discovery was initially made by the Nearby Supernova Factory, and emission spectra of the event was taken with the Keck Telescope and Very Large Telescope in Chile 

These type of supernovae occur only in stars above 100 solar masses, and are incredibly bright. Energetic gamma rays are created by the intense heat in the core of the star. These gamma rays, in turn, create antimatter pairs of electrons and positrons. Because of this antimatter production, the outward pressure exerted by the nuclear reactions in the core of the star is lessened, and gravity takes over, quickly collapsing the massive core of the star and creating a supernova.

There are theorized to be two kinds: those that explode with just enough force to allow for the mass around the leftover core of the star to recombine, and those that explode completely with not a smidgen left to form a black hole or neutron star. The supernova 2006gy, which had a luminosity 10 times that of a Type Ia supernova, is thought to be of the first variety. Here’s our story on that one, Could Antimatter be Powering Super-Luminous Supernovae? and Eta Carinae may also fit the profile.hese types of pair-instability supernovae will eject the outer shells of the star’s matter, settle down into an equilibrium, and repeat that process until the mass is low enough for a normal supernova to occur.

But 2007bi was much too massive to settle back down and explode multiple times. With a mass of 200 suns, the runaway thermonuclear explosion that happened in its core was energetic enough to effectively vaporize the entire star. Pair-instability supernovae in stars above 130 solar masses leave nothing behind in the way of black holes or neutron stars, but because they are so energetic and luminous, the increasing light from the explosion peaks over a very long time – 70 days in the case of 2007bi.

Though the team detected the supernova almost a week after the peak, they were able to calculate the duration of the light curve. They then studied the remnants of the explosion over the next 555 days as it faded away.

Filippenko said, “The central part of the huge star had fused to oxygen near the end of its life, and was very hot. Then the most energetic photons of light turned into electron-positron pairs, robbing the core of pressure and causing it to collapse. This led to a nuclear runaway explosion that created a large amount of radioactive nickel, whose decay energized the ejected gas and kept the supernova visible for a long time.”

The star was unique in another way: it lies in a nearby dwarf galaxy, which contains little else but the elements hydrogen and helium. Because of this, 2007bi is much like the stars that existed near the beginning of the Universe, before the trillions of supernovae populated the Universe with heavier elements. Looking more closely at dwarf galaxies – the Universe has them in spades, but they are quite dim – may be the key to observing more supernovae of this kind. Being able to study its explosion and aftereffects will give scientists a look into what the earliest massive stars acted like.

Source: Berkeley Lab press release

Countdown to Christmas: Hubble Advent Calendar

This is way cooler than those chocolate filled advent calendars that you can buy at the grocery store (although arguably less yummy): The Big Picture over at The Boston Globe is doing an advent calendar to count down the days until Christmas, only instead of opening a little door to nuggets of chocolate each day, you get huge chunks of Hubble eye candy!

Each day until Christmas you can feast your eyes on a new image from the Hubble Space Telescope like today’s shown above. Hubble has produced enough images over its lifetime to fill a few thousand advent calendars. If you happened to be worried about your waistline this holiday season, forget buying a calorie-bloated advent calendar and head on over to The Big Picture for the next 24 images, which are sure to be stunning.

Little cycling cap tip to The Bad Astronomer

Mars Odyssey Goes into Safe Mode

An artist's impression of the Odyssey orbiter around Mars. . Image Credit: NASA

The Mars Odyssey orbiter went into safe mode on Saturday, November 28th because of a glitch in the “memory error external bus” of the satellite. Odyssey will remain in safe mode at least until the end of the week, effectively slowing down communication with the two rovers, Spirit and Opportunity.

Odyssey is still operating at normal temperatures and communicating with the control team back on Earth. It stayed in safe mode over the weekend. After a full reboot today, the craft is on the mend and expected to be fully operational later this week.

“This event is a type we have seen before, so we have a known and tested path to resuming normal operations,” said Odyssey Project Manager Philip Varghese of NASA’s Jet Propulsion Laboratory in a press release.

Odyssey has been orbiting Mars since January 2002, mapping the surface and taking global measurements of the planet. Odyssey has also been the link to the Earth for the two rovers since 2004, acting as a communications relay that speeds up the transference of signals between the robots and the control team. Though Spirit and Oppy have their own antennae for communication, Odyssey can communicate with the Earth at 10 times the speed and with a fraction of the energy usage.

This glitch is really nothing new for the satellite – it’s much like having to reboot your laptop when it freezes up. The Mars Reconnaisance Orbiter would be the obvious backup for Odyssey, but the MRO has been in safe mode since August 26th. The MRO rebooted itself four times in 2009, and after the last reboot the spacecraft has stayed in safe mode to prevent any catastrophic damage to its memory.

NASA had planned to uplink files to the MRO to restore it sometime this week, but the uplink and recalibration of the satellite would take over a week, meaning that if Odyssey isn’t back up by the end of the week Spirit and Opportunity are on their own for a little while longer.

Odyssey is a key player in the efforts to free the Spirit rover, which has been stuck in a sand trap since May 1st of this year but is making progress. Because of a wheel stall problem that the control team thinks may be internal, an extrication attempt made on November 28th wasn’t successful. The Spirit control team hadn’t planned on making any more maneuvers to free the rover this week, as they are still analyzing the recent attempts to plan for future efforts at freeing its wheel.

Hopefully, by the end of next week we’ll be seeing two fully-functioning orbiters and a freewheelin’ Spirit.

Source: NASA press release

Quasar Caught Building Future Home Galaxy

An artist's impression of how quasars may be able to construct their own galaxies. Image Credit: ESO/L. Calcada

The birth of galaxies is quite a complicated affair, and little is known about whether the supermassive black holes at the center of most galaxies formed first, or if the matter in the galaxy accreted first, and formed the black hole later. Observations of the quasar HE0450-2958, which is situated outside of a galaxy, show the quasar aiding a nearby galaxy in the formation of stars. This provides evidence for the idea that supermassive black holes can ‘build’ their own galaxies.

The quasar HE0450-2958 is an odd entity: normally, supermassive black holes – also known as quasars – form at the center of galaxies. But HE0450-2958 doesn’t appear to have any host galaxy out of which it formed. This was a novel discovery in its own right when it was made back in 2005. Here’s our original story on the quasar, Rogue Supermassive Black Hole Has No Galaxy.

The formation of the quasar still remains a mystery, but current theories suggest that it formed out of cold interstellar gas filaments that accreted over time, or was somehow ejected from its host galaxy by a strong gravitational interaction with another galaxy.

The other oddity about the object is its proximity to a companion galaxy, which it may be aiding to form stars. The companion galaxy lies directly in the sights of one of the quasar’s jets, and is forming stars at a frantic rate. A team of astronomers from France, Germany and Belgium studied the quasar and companion galaxy using the Very Large Telescope at the European Southern Observatory. The astronomers were initially looking to find an elusive host galaxy for the quasar.

The phenomenon of ‘naked quasars’ has been reported before, but each time further observations are made, a host galaxy is found for the object. Energy streaming from the quasars can obscure a faint galaxy that is hidden behind dust, so the astronomers used the VLT spectrometer and imager for the mid-infrared (VISIR). Mid-infrared observations readily detect dust clouds. They combined these observations with new images obtained from the Hubble Space Telescope in the near-infrared.A color composite image of the quasar in HE0450-2958 obtained using the VISIR instrument on the Very Large Telescope and the Hubble Space Telescope. Image Credit: ESO

Observations of HE0450-2958, which lies 5 billion light years from Earth, confirmed that the quasar is indeed without a host galaxy, and that the energy and matter streaming out of the jets is pointed right at the companion galaxy. This scenario is ramping up star formation in that galaxy: 340 solar masses of stars a year are formed in the galaxy, one-hundred times more than for a typical galaxy in the Universe. The quasar and the galaxy are close enough that they will eventually merge, finally giving the quasar a home.

David Elbaz of the Service d’Astrophysique, who is the lead author of the paper which appeared in Astronomy & Astrophysics, said “The ‘chicken and egg’ question of whether a galaxy or its black hole comes first is one of the most debated subjects in astrophysics today. Our study suggests that supermassive black holes can trigger the formation of stars, thus ‘building’ their own host galaxies. This link could also explain why galaxies hosting larger black holes have more stars.”

‘Quasar feedback’ could be a potential explanation for how some galaxies form, and naturally the study of other systems is needed to confirm whether this scenario is unique, or a common feature in the Universe.

Source: ESO, Astronomy & Astrophysics