Astronomy Rewind: Keeping Our Data Alive

When I was growing up, there was a small outbuilding between my house and the stand of woods behind our property. The previous owner had built it as a little house in its own right, everything on a miniature scale, so that while it looked like an actual house — with front door, nice windows, even a porch and small deck on the back — it was comprised of only one room inside. This man’s kids had used it as a playhouse, but when I got my hands on it, I turned it into what a young boy thought of as his ‘lab,’ with microscope, chemistry set and telescope.

On the walls I put photographs I had bought at Chicago’s Adler Planetarium, and I can still see those blurry images of Saturn, Jupiter and the Milky Way, all taken at the Palomar Observatory, and almost as breathtaking for what they didn’t reveal as what they did. I gradually augmented these photos with sky charts and other imagery, and would use these to plan my observing sessions with the 3-inch reflector I would take out into the yard.

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Image: A classic photo (though not one of my Palomar images). This is M31, then known as the Great Andromeda Nebula, its nature as a separate galaxy not being known when the photograph was taken in 1888 by Sir Isaac Roberts. Reproduced in A Selection of Photographs of Stars, Star-clusters and Nebulae, Volume II (The Universal Press, London, 1899), this is the image whose long exposure time first.revealed M31’s spiral structure. Photos like these may look quaint compared to the brilliant detail and color of today’s work, but studying the sky over long periods of time may tease out new information, making even our older datasets useful tools for exploration. Credit: Isaac Roberts.

You would think old astronomical photographs would have a place only in memories like these, but I’m reminded of the vigorous debate that broke out not long ago over the anomalous star KIC 8462852, and Bradley Schaefer’s contention that, on the basis of archival imagery, it could be shown to have undergone a long-term dimming (see KIC 8462852: A Century Long Fade? for more on this — there are likewise numerous articles in the archive).

Schaefer was using a collection of some 500,000 sky photographs in the archives of Harvard College Observatory, covering the period from 1890 to 1989. A program called Digital Access to a Sky Century@Harvard (DASCH) has been digitizing the observatory’s archives, offering a way for astronomers to re-examine historical imagery. DASCH has only digitized a fraction of the archives but it’s a work in progress. What else can we do to reinvigorate such material?

One answer is a project called Astronomy Rewind, whose aim is to restore tens of thousands of astronomical images — photographs, radio maps and other sky-related material — from a wide variety of sources, placing them into context in digital sky atlases and catalogs. The project is part of the Zooniverse platform that gave us Galaxy Zoo a decade ago and now includes ‘citizen science’ projects in a variety of disciplines. Here the idea is to turn our attention to the contents of scientific journals and collate their imagery over time.

American Astronomical Society journals go back to the 19th Century and became accessible electronically in the 1990s. The volunteers will catalog the types of images, separating photographs with and without sky coordinates, maps of planets with or without latitude and longitude grids, graphs and diagrams, focusing on labeled images or those with sufficient detail to make a clear determination of orientation and sky position. Other images will be sent to Astrometry.net, which identifies areas of sky by comparing photos to star catalogs.

The project depends upon human judgement and pattern recognition at a large scale:

“You simply couldn’t do a project like this in any reasonable amount of time without ‘crowdsourcing,'” says Julie Steffen, AAS Director of Publishing. “Astronomy Rewind will breathe new life into old journal articles and put long-lost images of the night sky back into circulation, and that’s exciting. But what’s more exciting is what happens when a volunteer on Zooniverse looks at one of our journal pages and goes, ‘Hmm, that’s odd!’ That’ll be the first step toward learning something new about the universe.”

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Image: An early view of Orion. This is a digital print of a photographic plate from the Ritchey 60-inch telescope at Mount Wilson Observatory, made in 1908. Credit: Mt. Wilson Observatory.

The journals involved at present are The Astronomical Journal, Astrophysical Journal, Astrophysical Journal Letters and the ApJ Supplement Series. Images are to be annotated and extracted into digital files that will end up in data repositories as well as becoming part of the Astronomy Image Explorer and becoming viewable in the data visualization tool and sky atlas WorldWide Telescope.

Once up to speed, Astronomy Rewind hopes to process 1,000 journal pages daily, with each page examined by at least five different people to produce consensus. This number is based upon other projects at Zooniverse, where 1.6 million volunteers have classified 4 billion images over the last ten years. Peer-reviewed publications, over 100 of them, have flowed from the Zooniverse work, and as the KIC 8462852 story shows, the potential for discovery is here.

We have to remember as we look into old astronomical materials that we continue to accumulate data at a faster and faster rate. We’re learning how to sift through older material as we build the database from which details that may have escaped our attention decades ago can come to light, perhaps to be reinterpreted in the context of subsequent findings. An earlier effort, the ADS All-Sky Survey, was originally set up to analyze imagery from old astronomy papers, but using computers for the job wasn’t always effective. Now we turn volunteer eyes on the cosmos as we bring digital technologies and older printed journals together.

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Ceres: Axial Tilt and Surface Ice

Earth’s axial tilt (its obliquity) is 23.5 degrees, a significant fact for those of us who enjoy seasonal change. The ’tilt’ is the angle between our planet’s rotational axis and its orbital axis. If we look at Earth’s obliquity over time, we find a 41,000 year cycle that oscillates between 22.1 and 24.5 degrees. Here the Moon becomes useful, with recent studies showing that without it, Earth’s obliquity could vary by 25° (some earlier analyses took this number much higher).

Now we have new data from the Dawn spacecraft at Ceres relating the dwarf planet’s axial tilt to the locations where frozen water can be found on its surface. This is interesting stuff, because it depends upon the spacecraft’s ability to measure the world it orbits.

“We cannot directly observe the changes in Ceres’ orientation over time, so we used the Dawn spacecraft’s measurements of shape and gravity to precisely reconstruct what turned out to be a dynamic history,” says Erwan Mazarico, a co-author of a paper on this work based at NASA’s Goddard Space Flight Center in Greenbelt, Maryland.

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Image: This animation shows how the illumination of Ceres’ northern hemisphere varies with the dwarf planet’s axial tilt, or obliquity. Shadowed regions are highlighted for tilts of 2 degrees, 12 degrees and 20 degrees. Credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA.

What we learn from the paper just published in Geophysical Research Letters is that in the last three million years, Ceres’ axial tilt has ranged from 2° to 20°. The last time of maximum obliquity of 19° was about 14,000 years ago, while its current tilt is just 4°, meaning seasonal effects over the course of a current Cerean year (4.6 Earth years) will be slight.

Charting Ceres’ obliquity allows researchers to examine which areas remain most deeply shadowed even during times of maximum tilt, and the current work, led by JPL’s Anton Ermakov, reports that craters that are shadowed during times of maximum obliquity show bright deposits that are most likely water ice. Ceres’ surface temperatures range from 130 to 200 Kelvin (-143° C to -73° C), but regions that rarely see sunlight are more likely to have ice deposits than sunlit areas where ice can sublimate directly into vapor.

Deeply shadowed areas at the poles never receive direct sunlight when Ceres’ axial tilt is as low as it is today — this is an area of about 2,000 square kilometers — but increasing obliquity reduces the shadow region to as little as 1 to 10 square kilometers. The researchers call craters with areas that stay in shadow over long periods of time ‘cold traps’ because volatiles that readily vaporize cannot escape once deposited there. We’ve already learned from Dawn that 10 such craters contain bright material, and one is already known to contain ice.

The northern and southern hemispheres have two persistently shadowed regions each at 20° tilt, and so far we have found bright deposits in three of the four. All of this should call up thoughts of the polar regions of the Moon, a body that has little variability in its tilt because of the influence of the Earth. Mercury, too, stabilized by its proximity to the Sun, shows little axial tilt, and on both objects, we are finding evidence of water ice in shadowed craters at the poles. As with Mercury, the Moon’s ice surely comes from the impact of asteroids and comets, whereas what we find on Ceres may, at least in part, come from the dwarf planet itself.

Remember that the European Space Agency’s Herschel Space Observatory found a tenuous atmosphere on Ceres several years ago, a possible source of water molecules that can accumulate in the cold traps. Meanwhile, note that Ceres’ axial tilt varies on a cycle of about 24,500 years, a figure researchers consider to be a surprisingly short time given the size of the variation. Ceres’ surface ice, then, gives us insight into its geological history as we continue to probe the question of whether the small body continues to give off water vapor.

The paper is Ermakov et al., “Ceres’s obliquity history and its implications for the permanently shadowed regions,” published online by Geophysical Research Letters 22 March 2017 (abstract).

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Rosetta: Chronicling Cometary Change

Learning about the changes that occur on a cometary surface over time was a primary goal of the European Space Agency’s Rosetta mission, which orbited comet 67P/Churyumov-Gerasimenko between August 2014 and September 2016. This was a period when the comet was swinging through the inner Solar System as it closed to perihelion. Now we have vivid evidence of the changes the comet experienced as recorded by Rosetta.

Consider a report in Nature Astronomy, which chronicles outburst activity on the comet associated with the spectacular collapse of a cliff face. Located in the Seth region of the comet on a prominent cliff edge was a 70-meter long fracture about 1 meter wide. During the period of observation, as Rosetta drew ever nearer perihelion, buried ices turned to vapor at an increasing rate, pulling dust out into space, with occasional outburst activity. Rosetta observed an outburst on July 10, 2015 that was associated with this region.

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Image: Comet cliff collapse before and after. Credit: ESA.

A scant five days later, the place where the fracture had been now showed a bright, sharp edge, with a host of meter-sized boulders at the foot of the 134-meter high cliff that had not been there before. The assumption is that the cliff collapse and outburst were linked. Water ice buried deep inside the comet was thus exposed, to gradually turn to vapor in the following months. The exposed face was found to be six times brighter than the average surface brightness of the cometary nucleus in the period immediately after the event.

Activity like this has a profound effect on the cometary surface. As this ESA news release explains, the material that fell from the cliff and accumulated at its foot weighs in at about 10,000 tonnes, with about 100 tonnes being lost into space. “We see a similar trend at the foot of other cliffs that we have not been so fortunate to have before and after images, so this is an important validation of cliff collapse as a producer of these debris fields,” says Maurizio Pajola (NASA Ames/University of Padova, Italy), who led the new study.

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Image: Fallen cliff debris. Credit: ESA.

Researchers believe that daily and seasonal temperature variations may have driven fractures deeper into the subsurface of the comet than was previously thought, making it more vulnerable to the temperature changes of its journey into the inner system. What we have here is a priceless look before and after a major event, confirming the importance of cliff collapses in molding the surface of a comet and perhaps provoking outburst activity. Adds Pajola:

“If the fractures permeated volatile-rich layers, heat could have been transferred to these deeper layers, causing a loss of deeper ice. The gas released by the vapourising material could further widen the fractures, leading to a cumulative effect that eventually led to the cliff collapse. Thanks to this particular event at Aswan, we think that the cumulative effect led by strong thermal gradients could be one of the most important weakening factors of the cliff structure.”

We also have a new study in Science examining the broad range of terrain change on Comet 67P during Rosetta’s two years of close observation. Here numerous processes appear to be at work, each with the potential for working serious change. In situ weathering involves the weakening of materials through the heating and cooling cycle, both daily and seasonal, that can result in gas outflows and cliff collapses like the one we just examined. But we also have forces created by the comet’s spin rate as it moved toward perihelion, thought to have created a new fracture observed by Rosetta.

A previously known fracture some 500 meters long runs through the comet’s neck in the region called Anuket. Although observed in August of 2014, the fracture was found to have become extended by another 30 meters by December of that year. And by June of 2016, the new fracture, 150 to 300 meters long, had opened parallel to the original fracture.

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Image: Comet changes: new fracture and boulder movement in Anuket. Credit: ESA.

We also see movement in boulders on the surface of Comet 67P, perhaps linked to the fracture activity, perhaps not. In one case, a boulder 30 meters wide and weighing 12,800 tonnes was observed to have moved 140 meters in the comet’s Khonsu region. This movement is thought to have occurred during the perihelion period, when several outbursts were observed close to the boulder’s position. Erosion of the nearby surface could be the culprit here, allowing the boulder to roll downslope. Equally possible: A strong outburst could have lifted it to its new location.

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Image: Comet changes: A moving boulder in Khonsu. Credit: ESA.

Sublimation is a major cause of erosion, as is falling dust returning to the surface after an outburst, both of which can sculpt the cometary landscape. In some areas, scarps in several smooth plains have been seen to retreat by tens of meters — as much as a few meters a day during perihelion. Meanwhile, in regions of smooth plains like Comet 67P’s Imhotep, new circular features are found that were once obscured by surface material. The likely cause here is sublimation of underlying ice, which has removed up to 3 meters of material in one area.

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Image: Comet changes: Ripples and scarps in Hapi. Credit: ESA.

The movement on the surface of the comet is strikingly swift. In the comet’s neck region, a smooth area once likened to sand dunes on Earth when first observed, ripple formations began showing expanding circular features that reached diameters of 100 meters over a period of three months. These then faded and gave rise to new sets of ripples. In addition, honeycomb-like features have been observed in the Ma’at region on the comet’s northern hemisphere, showing a marked increase in roughness as perihelion approached.

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Image: Comet changes: surface textures in Ma’at. Credit: ESA.

Rosetta shows us that this comet’s surface is geologically active on short and long time-frames, although its overall appearance has not significantly changed, based on ground-based studies conducted over the last few years. Ramy El-Maarry (University of Colorado, Boulder), who led the study, speculates that earlier perihelion passages were far more active, when the comet would have held a higher amount of volatiles and the major landforms on the surface would have attained their current configuration. Whatever the case, Rosetta’s study of Comet 67P’s changing surface vividly shows a surface of growing fractures, evolving cliffs and boulders in motion, a scene we had expected but are now able to analyze in detail for the first time.

The paper on the cliff collapse is Pajola et al., “The pristine interior of comet 67P revealed by the combined Aswan outburst and cliff collapse,” published online by Nature Astronomy 21 March 2017 (full text). The El-Maarry et al. paper is “Surface changes on comet 67P/Churyumov-Gerasimenko suggest a more active past,” published online by Science 21 March 2017 (abstract). This ESA news release is also helpful.

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Runaway Stars in Orion

Unexpected things can happen when you’re looking for exoplanets. Ask Kevin Luhman (Penn State), whose search for free-floating planets in the Orion Nebula is now telling us something interesting about star formation in general. In a small region dominated by young stars called the Kleinmann-Low Nebula, some 1300 light years from Earth near the center of the Orion Nebula complex, Luhman and team have come across evidence of a multiple star system whose members have flown rapidly apart due to gravitational interactions with their peers.

Luhman’s team was using the Hubble instrument’s Wide Field Camera 3 to run the planet-hunting survey, working with Massimo Robberto (Space Telescope Science Institute) and a group of international colleagues. A star referenced only as ‘source x’ turned up in a comparison between 2015 imagery in the infrared and infrared observations made in 1998 with the Hubble telescope’s Near Infrared Camera and Multi-Object Spectrometer. The surprise: ‘Source x’ had changed its position substantially in those 17 years.

Working out the star’s velocity, the team concluded that it was moving at about 210,000 kilometers per hour. Moving backwards in time, the researchers could chart the star’s travels, and found that in the 15th Century AD, ‘source x’ had been in the same location in the Kleinmann-Low Nebula as two other runaway stars, known as Becklin-Neugebauer (BN) and “source I,” that are now traveling in opposite directions from each other. Discovered in the infrared in 1967, BN has been found to be moving at 95,000 kilometers per hour, while ‘source I’ is clocked at 35,000 kilometers per hour, deeply shrouded in dust and previously observed only through radio telescope studies.

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Image: This dramatic view of the center of the Orion Nebula reveals the home of three speedy, wayward stars that were members of a now-defunct multiple-star system. The stellar grouping broke apart 500 years ago, flinging the three stars out of their birthplace. The box just above the Trapezium Cluster outlines the location of the three stars. A Hubble close-up view of the stars is shown at top right. The birthplace of the multi-star system is marked “initial position.” Two of the stars — labeled BN, for Becklin-Neugebauer, and “I,” for source I — were discovered decades ago. Source I is embedded in thick dust and cannot be seen. The third star, “x,” for source x, was recently discovered to have moved noticeably between 1998 and 2015, as shown in the inset image at bottom right. Source x is traveling at an unusually high speed of 210,000 kilometers per hour, which is 30 times faster than the velocity of most stars in the nebula. Credit: NASA, ESA, K. Luhman (Penn State University), and M. Robberto (STScI).

“The new Hubble observations provide very strong evidence that the three stars were ejected from a multiple-star system,” says Luhman. “Astronomers had previously found a few other examples of fast-moving stars that trace back to multiple-star systems, and therefore were likely ejected. But these three stars are the youngest examples of such ejected stars. They’re probably only a few hundred thousand years old. In fact, based on infrared images, the stars are still young enough to have disks of material leftover from their formation.”

All three of these stars are making their way out of the Kleinmann-Low Nebula at high speed, and they may be representative of what happens in young stellar clusters, where the spacing between infant stars is tight. Luhman’s team believes the Orion Nebula could have spawned numerous such interactions, with young stars being ejected from it in great numbers. As to the process at work, it probably results from two members of a multiple star system forming a tight binary or even merging, releasing enough gravitational energy to push all the stars in the system outward and creating a powerful outflow of material. And this bit from the paper on this work is interesting:

Some aspects of the interaction that ejected BN and sources I and x remain unclear, such as how these stars were able to retain or reform their circumstellar disks (Goddi et al. 2011; Plambeck & Wright 2017) and the source of their current kinetic energy… [T]he latter has been previously attributed to the gravitational potential energy released by a pair of stars forming a tight binary or merging, likely in what is now source I. The energy produced by the merger of stars with a total mass of source I (e.g., 1 and 6 M?) is an order of magnitude greater than the kinetic energy of the three stars, so that remains a plausible explanation.

Note that comment about circumstellar disks — how could stars undergoing this kind of gravitational upheaval maintain their disks? The paper’s earlier reference to the problem seems understated, and references another star, ‘source n,’ explained below: “It is challenging to explain the presence of the circumstellar disks around BN and sources I and n if they experienced interactions that were sufficiently close to produce the rapid ejection of BN.”

Challenging indeed, and doubtless the subject of further study. Such disks do indeed mark the youth of the stars involved, but we have a lot to learn about how these interactions would affect material around the stars themselves. Reminding us of the complexity of such analysis, the ‘source n’ mentioned above is yet another star with high proper motion, but one which Luhman and colleagues believe did not participate in the events affecting the other three.

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Image: This three-frame illustration shows how a grouping of stars can break apart, flinging the members into space. The first panel shows four members of a multiple-star system orbiting each other. In the second panel, two of the stars move closer together in their orbits. In the third panel, the closely orbiting stars eventually either merge or form a tight binary. This event releases enough gravitational energy to propel all of the stars in the system outward, as shown in the third panel. Credit: NASA, ESA, and Z. Levy (STScI).

It’s not often that we run into stellar phenomena that we can relate to events within our own written history, but here we have a date — 1475 plus or minus 6 years — that takes us back to a time when the Wars of the Roses convulsed England. Somewhere not long before the death of Edward IV, with his brother Richard III waiting in the wings and all hell about to (again) break loose, this distant star system was itself convulsed, its component parts flung into the deep. Finding ‘source x’ and relating it to its fast-moving cousins BN and ‘Source I” answers the puzzle of their motion and reminds us how violent early stellar evolution can be.

The paper is Luhman et al., “New Evidence for the Dynamical Decay of a Multiple System in the Orion Kleinmann-Low Nebula,” Astrophysical Journal Letters Vol. 838, No. 1 (16 March 2017). Abstract / preprint.

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Star in Tight Orbit around Black Hole

Beyond their obvious value in advancing our knowledge, astronomical discoveries can be thought of as exercises for the imagination, making us think about what we would see if we were actually near the phenomenon being observed. The view from a planet deep in a globular cluster can only be spectacular, and has been the subject of my own musings for many years. But this morning’s topic, a white dwarf star in a fantastically tight orbit around a black hole, leaves my imagination reeling. Just what would a scenario like the one playing out in the globular cluster 47 Tucanae, some 14,800 light years from Earth, look like up close?

Here we find, thanks to the space-based Chandra X-Ray Observatory and NuSTAR (Nuclear Spectroscopic Telescope Array), as well as the Australia Telescope Compact Array, a binary that consists of an apparent white dwarf orbiting a black hole every 28 minutes. The presence of large amounts of oxygen in the system gives weight to the idea that the companion is indeed a white dwarf, as an abundance of oxygen is a characteristic feature of white dwarfs.

The orbit here is so tight that the star is separated from the apparent black hole by a distance about 2.5 times the separation between the Earth and the Moon.

“This white dwarf is so close to the black hole that material is being pulled away from the star and dumped onto a disk of matter around the black hole before falling in,” says lead author Arash Bahramian (University of Alberta and Michigan State University). “Luckily for this star, we don’t think it will follow this path into oblivion, but instead will stay in orbit.”

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Image: An artist’s impression of a white dwarf star (left) in orbit around a black hole and so close that much of its material is being pulled away. There is a hotspot where the gas from the white dwarf hits the disc of matter swirling around the black hole. The black hole itself is surrounded by a cloud of ionised gas, which contains large amounts of oxygen. Credit: X-ray: NASA/CXC/University of Alberta/A.Bahramian et al.; Illustration: NASA/CXC/M.Weiss.

The orbital determination is made from the changes of brightness observed on a regular 28 minute cycle by Chandra. And the likely outcome of this tight pairing for the white dwarf is that it will eventually become something even more unusual. Says James Miller-Jones (Curtin University, Western Australia and the International Centre for Radio Astronomy Research):

“We think the star may have been losing gas to the black hole for tens of millions of years and by now has now lost the majority of its mass. Over time, we think that the star’s orbit will get wider and wider as even more mass is lost, eventually turning into an exotic object similar to the famous diamond planet discovered a few years ago.”

Small digression: More commonly known as a ‘carbon planet,’ an exotic world like the one Miller-Jones mentions draws on work from Marc Kuchner (NASA GSFC) and Sara Seager (MIT), who investigated the possibility that carbon-rich, oxygen-poor protoplanetary disks might form such planets. Here the visualization exercise gets another workout: Layers of diamond could exist within the mantle, possibly erupting to the surface during volcanic episodes. In addition to mountains of diamond, the surface could contain liquid or frozen tar and methane.

Although 55 Cancri e is frequently cited as a possible carbon planet, pulsar planets have also been suggested as candidates, and in connection with today’s story, it’s worth pointing out that carbon planets are also speculated to be found in globular clusters, where stars have a higher carbon-to-oxygen ratio than the Sun — hence Miller-Jones’ allusion to diamond planets in the quotation above. As to the binary in the globular cluster 47 Tucanae, called X9, the origin scenarios being discussed are intriguing. From the paper:

Low mass X-ray binaries (LMXBs) are systems in which a compact object [neutron star (NS) or black hole (BH)] accretes matter from a low mass companion (typically a main sequence star) through Roche-lobe overflow or wind-fed accretion (from a red giant). It has been long noticed that the population of LMXBs per unit mass in globular clusters (GCs) is orders of magnitude higher than that of the Galactic field… This overabundance has been associated with the high stellar density in GCs. While most LMXBs in the Galactic field are formed through binary evolution of primordial binaries, it has been shown that in GCs, the dominant channel to form LMXBs is through encounters. These scenarios include tidal capture by an NS or BH, exchange of a compact object into a primordial binary, or collision of a compact object with a red giant…

Here too the visualization game stretches the imagination. A black hole encounters a red giant star, with gas from the star being ejected and the remnants of the red giant’s atmosphere becoming a companion to the black hole in the form of a white dwarf. Whether or not we are looking at the result of such an encounter in X9, or whether this is actually a white dwarf paired with a neutron star that is stripping material from its companion, is not entirely clear, though X9 lacks many features of this kind of transitional millisecond pulsar.

“We’re going to watch this binary closely in the future, since we know little about how such an extreme system should behave,” says co-author Vlad Tudor (Curtin University/ICRAR). “We’re also going to keep studying globular clusters in our galaxy to see if more evidence for very tight black hole binaries can be found.”

Before now, the closest star around a likely black hole was the system called MAXI J1659-152, where the orbital period is 2.4 hours, much longer than the 28 minutes we see in X9. There is also evidence for a similar system in the galaxy M49 (about 56 million light years away in the Virgo Cluster). That one is believed to have an orbit even tighter than X9’s, but Miller-Jones points out that there is no direct measurement of its period, making this work on X9 the first time that an orbital period this short in a system containing a likely black hole has ever been measured. An interesting exercise for the imagination indeed.

Although the gravitational waves from this system are too weak to detect with present ground-based observatories, future space-based platforms may be able to detect them.

The paper is Bahramian et al., “The ultracompact nature of the black hole candidate X-ray binary 47 Tuc X9,” Monthly Notices of the Royal Astronomical Society 14 March 2017 (abstract / preprint).

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