Unusual time and date sundial in northern Italy
Above Fig 1: A view under the large colonnade towards the medieval cathedral and a renaissance church in Bergamo, Italy. On the stone floor under the columns is a fine meridian line in white marble inlaid into the flag-stone floor with an analemna marked for solar noon on every day of the year. The sun shines through a small hole in the black disc at the top of the arch. The sun did mark the day of 20th April. my birthday (Fig 2, 3) The correct time of local midday was 13.20 35sec pm European Summer Time.
The Bergamo Analemna
By Ivor Clarke
In April my wife and I had a short holiday at Lake Garda in northern Italy. It was the first time we had visited one of Italy's many lakes and we enjoyed the mountain and lake scenery, as well as the food and drink, plus all the old towns and cities we visited in the short time we were there. One of the interesting old towns visited was Bergamo, a town of 120,000 nestling at the foot of the Alps not far, only 40km, from Milan. It is a town in three "sections" with a new modern town at the bottom on the Lombardy plane, an old city, Città Alta (high city) inclosed by walls built in the 17th century set high on steep hills and at the very top is an old town/village (we didn't try to go up to this as we were told there was not a lot to see and we would not have had time.)
To reach the old town our coach dropped us all off at a funicular railway station, the Citta Alta Funicolare built in 1887, this saves a long climb up of over 85m, and which ends right on one of the piazza and from which one of the main streets lead into the towns centre. This without doubt is the best way to the old town. Bergamo is a delightful place full of uneven cobbled streets, old and new shops, coffee shops and restaurants, churches and old buildings dating back from the last 500 years. Following the twisting main street for a few minutes leads into the centre Piazza Vecchia with its central fountain. In this main square at one side is the medieval Duomo (cathedral) and a renaissance church, also a tall stone tower overlooking the piazza, on the other side is the town library. All round the piazza are restaurants and bars. To reach the cathedral you pass under a large colonnade where the city council used to hold their hearings, on the stone floor under the columns is a fine meridian line in white marble inlaid into the flag-stone floor with an analemna marked for solar noon on every day of the year. (Fig 1) The underlying sundial was built in 1798 by Albrici sac. Giovanni to indicate the passage of the sun on the meridian that is true at noon local time.
At first glance it looks like a north south marker line, but on closer inspection its true nature shows at midday local time if the sun is shining. On the day of our visit the sun was shining from a flawless blue sky, but we were over a hour and a half early. Two lines on each side of the north/south line show 15 minutes before and after midday. The inscription reads, 'Latitude 45° 42' 11" Nord, Longitude 9° 39' 46" Est' and on the other side, 'Altitvdine M 360.85 sul Livello Dell Adriatico'. (Fig 5) At the far end is a compass rose with a date of 1857. This date was when the analemna figure of 8 was added. So how does this line under a portico show the date and time? In Fig 1 looking down the length of the line towards the cathedral, just under the top of the arch in the colonnade can be seen a circular metal plate with a hole in the centre. This is what makes the analemna work, through a small gap between the side of the cathedral and the other buildings is just enough sky to let in a couple of hours of sunlight to illuminate the midday line under the arches! And through this small gap between buildings, lets the sunlight shine under the portico for over 100 feet on the shortest days of midwinter to the end of the analemna! By this time of year the sun would be just skimming the top of part of the cathedral roof.
On the day of our visit it was my birthday, so after we had walked round, we returned later to see if the sun would really mark the day of 20th April (Fig 2, 3 and 11, this is looking towards the library). It did! The correct time of local midday was 13.20pm CET. It does go out by 1 day due to leap years, but looked fine to me. It was nice to see that the time keeping and date all came together. The time when the sun reached the centre line was 13.20 35sec European summer time on the clock of my camera (which was correct to about 10 sec). This of cause is local time for Bergamo, not European Time which is a modern invention. The sun moves across the sky at slightly different speeds depending on the position of the Earth in its orbit. To correct this, Mean Solar Time, i.e.. the time on your watch is standardised across the world. True Solar Time is therefore different to Mean Time (Fig 4, 6 & 9) by 14+ minutes behind in mid February, 6 minutes mid August but ahead by 3 minutes in mid May and a whopping 16 minutes early at the start of November. The difference between solar time and mean time is called equation of time and is represented as a figure of 8 called a lemniscate (this is the sideways 8 symbol commonly used for infinity). All this is caused by eccentricity in the Earth's elliptical orbit being closest to the sun on January 3rd (perihelion at 147,105,761km) and furthest on July 4th (aphelion, 152,102,197km). This causes the Earth to move faster; a greater distance along its orbit when nearer the sun in January and slower when 5 million km further out in July. Because the Earth moves quicker in January the sun will appear to take longer to reach local mid-day because the Earth has to rotate more than 360° to point to the mid-day sun. In July the effect is reversed with the Earth rotating quick enough to bring the sun to local mid-day early. During all year the Earth spins at exactly the same rate of 23h 56m 4s, this is the sidereal period in relation to fixed stars and it takes an extra 4 minutes to rotate to make a day of 24 hours in relation to the sun, Fig 9.
Fig 7. Dennis di Cicco original 1978/79 multi exposure of the sun at exactly 8.30am, 44 times during a year on a fixed film camera. At one of the equinoxes and winter and summer solstice exposed the sun rising from dawn until just before 8.30am.
The analemna has been photographed several times in the past by taking a shot of the sun at exactly the same time of day, every week of the year on the same piece of film. Then a final 'normal' shot is made to show the local area and landscape. The first was recorded by Dennis di Cicco (Fig 7) during 1978/79 in New England, USA. He used a solar filter on a fixed camera to record the sun at exactly 8.30am roughly once a week (44 times in this case) and then at one of the equinoxes and winter and summer solstice exposed the sun rising from dawn until just before 8.30am. Of cause a lot of luck is involved in this and I reckon it would take a couple of years at least to do this from cloudy UK. When completed the trace of the sun shows as an extended figure of 8 in the picture. Early morning views will show the figure of 8 lying to the east, midday and the analemna will be upright and afternoon lying westward, in other words acting like a clock hand sweeping across the sky with the small part of the 8 at the top in the northern hemisphere. Other planets will have their own pattern of the analemna, Mars is shown in Fig 10. Mercury's would be nearly a straight line east and west, Venus would take a few years to complete an ellipse owing to its slow rotation, Jupiter's is an ellipse too and the rest figure of 8's.
Fig 8 & Fig 9
Fig 10 & Fig 11
The inscription on the line said Longitude of 9° 39' 46" Est which is about 38 minutes before mid-day sun at Greenwich (1° east or west adds or subtracts 4 minutes or 1 hour for 15°). As the sun passed the line of the analemna this was about 2min 30sec earlier which is correct for this time of year, see Fig 2/3. So after 150 years the Earth still rotates in the same way and goes round the sun following its orbit correctly which is comforting. I am amazed that after 3,500 years the sun still rises over Stonehenge on midsummers day in the right place and shows very little sign of any wobble in the Earth's axis which would cause the sun to rise to the left or right of the Heel Stone.
Parallax, Aberration and Nutation
By Mike Frost
In popular histories of science, you often read something to the effect that, when Copernicus suggested that the Earth went round the Sun rather than vice-versa, the only opposition was from stick-in-the-mud medievalists who refused to see the blindingly obvious.
Quite the opposite was true. Copernicus’s opponents included some very capable minds, people who were quite rational in their opposition to his ideas. This was because there was actually strong observational evidence that Copernicus was wrong.
The major problem was the lack of parallax. If the Earth rotated around the Sun, Copernicus’s opponents argued, why didn’t observers see the nearer, brighter stars move against the fainter, more distant stars?
Parallax is familiar on Earth. Look at the Moon, with your left eye closed, and cover it with your outstretched thumb. Close your left eye and open your right eye – the thumb will no longer cover the Moon. In the same way, if two stars, one nearby and bright and the other distant and faint, appeared to be close on one side of the Earth’s orbit, then surely when Earth move to the other side of the Sun, six months later, their relative positions ought to change?
There are, of course, complications. Is it true that stars appear brighter because they are closer, or are some stars intrinsically brighter? From our twenty-first century perspective, we know that both cases can happen. Some stars – Sirius, Alpha Centauri – are bright because they are our stellar neighbours; but other stars – Deneb, Canopus – are bright because they are among the biggest and brightest of all stars. This wasn’t known at all in Copernicus’s day. Indeed, for all they knew then, all stars could have been at exactly the same distance from Earth, on the outermost sphere of the universe.
In the century after Copernicus died, huge strides were made in astronomy. Galileo turned the telescope to the heavens and discovered innumerable stars, like dust, sprinkled along the Milky Way. Kepler discovered the laws of planetary motion, and Newton explained them with a universal theory of gravity. Painstaking measurements of star positions were taken; by Brahe in the pre-telescopic era and by Flamsteed and others with optical aid. Yet observing parallax remained elusive.
The first person to make a dedicated attempt to observe parallax was another of the great names of the seventeenth century, Robert Hooke. Hooke aimed to observe stellar parallax, but he proposed a novel technique. He wanted to observe the annual parallax of stars, not against their stellar neighbours, rather against the rotational axis of the Earth. The advantage of Hooke’s method is that the observer doesn’t have to worry about the effects of refraction (or bending) of light in the Earth’s atmosphere – there is no refraction for light which arrives vertically.
Conceptually, imagine observing from a planet whose rotational axis lines up with the axis of rotation around the Sun, so there is no axial tilt and no seasons. An observer at the North Pole of that planet, looking vertically upwards (towards the zenith), would see the planet’s Pole Star vertically overhead, because the planet’s rotational axis points at that Pole Star. But, if the observer looked very closely, he would expect to see the Pole Star a small distance away from the zenith, slowly rotating around the zenith during the course of a year, because of parallax.
Fig 1 – All stars move across the sky (possibly during the daytime), reaching the highest point in the sky, culmination, as they cross the meridian. At the latitude of London, Gamma Draconis culminates very close to the zenith, directly overhead.
In our real world, things are more complicated. Earth’s axis of rotation is tilted at 23° degrees to the ecliptic. What this means is that no single star lies directly overhead; instead, from Greenwich’s location at 52° degrees North, the zenith is occupied by a succession of stars which are 38° degrees from the Pole Star. The brightest of these is Gamma Draconis, in the constellation of Draco, the dragon. Gamma Draconis is overhead once each day, sometimes during the daytime. To be strictly accurate, Hooke was measuring the culmination of the star, the highest point reached in the sky, and looking for very slight variations in culmination over the course of a year.
Hooke built his zenith telescope in his rooms at Gresham College in London. He soon discovered that zenith observations were technically difficult to make; the telescope flexed with the weather, and had to be re-calibrated before each use. With this telescope he managed only four observations of gamma Draconis before giving up. Yet he managed to convince himself that he had successfully observed a stellar parallax. He was wrong. All he had succeeded in doing was measuring experimental error; the actual parallax of gamma Draconis is a thousandth of what he claimed to have seen.
Robert Hooke was nothing if not ambitious. After the Great Fire of London, he was assistant to Christopher Wren in the rebuilding of the city of London. He designed the Monument to that disaster, which stands to this day at the north end of London Bridge. The Monument is hollow, with stairs running into a basement. Robert Hooke hoped that it would house a huge transit telescope, 202 feet high. Unfortunately no such telescope was ever built.
Hooke was a gifted experimenter; arguably the most widely talented ever. But perhaps his talents spread too wide for the difficult challenge of measuring parallax. What was needed was a dedicated astronomical observatory with full-time observers. Fortunately, for reasons which had more to do with nautical navigation than astronomical investigation, the world’s first government-sponsored observatory was established, during Hooke’s lifetime, at Greenwich.
John Flamsteed was the first astronomer at the Greenwich observatory. He was also interested in the measurement of parallax, and built himself an extraordinary observatory in the grounds of the Greenwich Observatory. He found a well, and deepened and widened it so that an observer could lie at the bottom, observing vertically upwards. It was not a pleasant place to observe from! No usable observations could be made and the observatory was abandoned “because of the dampness of the place”.
Flamsteed was succeeded by Edmond Halley, who was one of the great observational astronomers, but he declined to try to measure parallax. Instead it was Halley’s contemporaries who made the next move. There was a second, private London Observatory, at Kew, owned by Samuel Molyneux, a wealthy member of parliament and a keen amateur astronomer. Molyneux had determined to have another crack at observing parallax. He built a telescope, similar to Hooke’s, but much more resilient and accurate. Molyneux’s telescope, built by George Graham, could measure star positions to an accuracy of one arc second.
Molyneux began making observations with this transit telescope in autumn 1725. He decided that he needed an observing partner, a full-time astronomer, to help him make observations, and interpret what they found. He asked Revd. James Bradley, the Savilian Professor of Astronomy at Oxford. Bradley was also a very capable observer, who had learnt his skills with his uncle, Revd. James Pound of Wanstead; both Pound and Bradley had assisted Edmond Halley at Greenwich.
Bradley and Molyneux began serious observations from Kew in November 1725. Within a few days they knew that they had detected that Gamma Draconis moved relative to the zenith as it culminated overhead. But there was a big surprise. The motion from night to night was in the wrong direction!
Fig 2 (top) – The variation Bradley expected to see in the culmination of Gamma Draconis due to parallax.
Fig 3 – The variation Bradley and Molyneux actually saw, due to aberration.
For parallax, the greatest variation in night-to-night culmination of Gamma Draconis ought to occur at the equinoxes. But as Molyneux and Bradley accumulated more and more observations, it became clear that the observed variation was three months out of phase, and the two observers had seen the greatest variation almost at the beginning of their observing run. After a year’s observation, it was clear that whatever they were observing happened with a period of exactly one year – so it had to be connected somehow to the Earth’s motion around the Sun. Yet it was in the wrong direction to be parallax. Moreover, their observations of fainter stars at the same latitude as Gamma Draconis indicated that these, too, displayed exactly the same motions. Whatever was going on, it was not the parallax motion of a bright nearby star against distant faint stars.
For two years Bradley pondered the mystery. Molyneux died in April 1728, unexpectedly, aged 39, without ever knowing the explanation for the perplexing observations. Then suddenly, one day in autumn 1728, Bradley had a Eureka moment. Thomas Thomson tells the story in his 1812 “History of the Royal Society”:
“At last, when [Bradley] despaired of being able to account for the phenomena which he had observed, a satisfactory explanation of it occurred to him all at once, when he was not in search of it. He accompanied a pleasure party in a sail upon the River Thames. The boat in which they were was provided with a mast, which had a vane on top of it. It blew a moderate wind, and the party sailed up and down the river for a considerable time. Dr. Bradley remarked, that every time the boat put about [turned], the vane at the top of the boat’s mast shifted a little, as if there had been a slight change in the direction of the wind. He observed this three or four times without speaking; at last he mentioned it to the sailors, and expressed his surprise that the wind should shift so regularly every time they put about. The sailors told him that the wind had not shifted, but that the apparent change was owing to the change in the direction of the boat, and assured him that the same thing invariably happened in all cases. This accidental observation led him to conclude, that the phenomenon which had puzzled him so much was owing to the combined motion of light and Earth”.
You can see the same thing is when you drive a car in a rainstorm. Notice how at speed the front windscreen collects more rain than the back window. The rain is coming down vertically, but you are driving into it – the result of these two motions is that the rain appears to traveling almost horizontally. The Earth is doing the same thing, though the effect isn’t anything like as dramatic because the speed of the Earth around the Sun is only a tiny fraction of the speed of light. But the effect is essentially the same – when the Earth is one side of the Sun, the vector sum of light’s speed and the Earth’s speed is slightly different from what you get on the other side of the solar system.
Bradley had discovered something completely unexpected – he had demonstrated, for the very first time, the Earth’s motion around the Sun! The effect was called aberration. Bradley was even able to use the magnitude of the effect to estimate the speed of light, improving on previous estimates by Ole Rohmer and others (from the magnitude of aberration, Bradley could calculate the ratio of the speed of light to the speed of the Earth around the Sun; however this latter speed was not yet known accurately because the astronomical unit was yet to be measured accurately.
Once aberration had been explained, its effects could be calculated and then subtracted away from measurements, leaving a residual error which, hopefully, was due to parallax. Bradley continued to observe the zenith. He built a second, even more accurate transit telescope at his late uncle’s home in Wanstead; this telescope is now on display at the Greenwich Observatory.
Extraordinarily, once again he found something different and completely unexpected. After subtraction of the aberration effect, the culmination point for Gamma Draconis and other stars varied through the year, but once more the motion could not be explained by parallax. Not only was the observed error not in the right direction, now the variation didn’t even repeat itself year-on-year!
Once again Bradley had to figure out what was going on. This time he had a clearer idea, one which he had considered but rejected when trying to puzzle out aberration. His idea was that the movement of Gamma Draconis was due to a wobble in the Earth’s axis. Over thousands of years, the axis precesses like a spinning top. But perhaps there was also a, smaller, previously unknown component, which varies on a timescale of years rather than millennia.
Bradley was right. This time he had discovered nutation, a slight wobble in the Earth’s axis caused by the interaction of the gravitational pulls of the Moon and the Sun. The Moon’s orbit around the Earth is almost elliptical, but the ellipse doesn’t quite join up, so the Moon’s perigee or closest approach to Earth moves around the Earth, completing one circuit every 18.6 years. The largest component of nutation has this periodicity.
Bradley had not found what he was looking for, but his failure led to fame amongst the scientific community. He had discovered not one but two new phenomena. He had proved the Earth’s motion around the Sun, he had found an undiscovered motion of the Earth’s polar axis, and as a bonus he had estimated the speed of light.
When Edmond Halley died in 1742, Revd. James Bradley became the third Astronomer Royal. He is much less known than Halley or Flamsteed, but I think he deserves to be famous for his two momentous discoveries. He was Astronomer Royal for twenty years, during which time he supervised the replacement of the observatory telescopes with state-of-the art instruments.
But James Bradley never did find conclusive evidence of parallax. This was because the effect turns out to be far smaller than he, or anyone else, had expected. Aberration shifts the culmination position of a star (any star) by forty arc seconds over the course of a half-year. Nutation is a few arc seconds. The largest known stellar parallax is less than an arc second. The actual parallax of Gamma Draconis is only a fiftieth of a degree, two thousand times smaller than the aberration seen by Bradley.
Bradley discovered aberration, serendipitously, in 1728, and nutation, serendipitously, two years later. It was to be nearly a century and a half before observing techniques improved enough to detect stellar parallax. But that, as they say, is a story for another day…
Sources / Further Reading
“Parallax – The Race to Measure the Cosmos”, Alan W. Hirshfeld (Henry Holt, 2002)
The Significance of Aberration
By Mike Frost
As the Editor will bear witness, the preceding article took me a long time to produce – I spent months telling him that I had nearly finished it. Even when I had finished it and handed it in, I was still not happy. I did feel that I had told the story of Robert Hooke, Samuel Molyneux and Reverend James Bradley accurately and (hopefully) coherently. But I felt that, even if I had got the history right, I had still not succeeded in my original aim, which was to explain why the discovery of aberration was so important.
Let’s have another go.
What I wanted to put across was the concept that aberration was the first direct proof of the motion of the Earth around the Sun. Other evidence – the removal of epicycles from the motion of planets, the phases of Venus, the discovery of satellites orbiting Jupiter – were really only circumstantial proof that Earth was not the centre of the solar system.
So how is aberration different? Let me try to explain by detailing some arguments advanced against aberration. They are pretty silly arguments, but I sometimes find that the refutation silly arguments leads one to a clearer understanding of the underlying problem.
First argument - Aberration doesn’t exist
Not an argument with convincing evidence behind it, although I have seen it advanced (I’ve visited some pretty weird websites researching this subject). But – playing devil’s advocate - do you know anyone who has ever measured aberration? It’s technically difficult to measure; and not very aesthetically interesting once you’ve measured it, so no-one bothers. Nonetheless, it was within the observing capacity of Bradley, and well within today’s observing capacity.
For example, a position measuring space-probe such as the Kepler probe, which repeatedly observes large number of stars, searching for transiting planets, has to take aberration into account, otherwise it wouldn’t be pointed in the right direction. I emailed David Koch of the Kepler team, who confirmed that, not only is aberration taken into account when calculating where to find a target star in the field of view, but this correction changes across the field of view and at different times in the year.
So let’s not worry about the first argument any further.
Second argument - Aberration does exist, and is observable, but it is due to the motion of distant stars, not of the Earth
Again, this is not a very convincing explanation. We’re back in an extreme version of a geocentric universe. But it’s instructive to follow through the consequences of the hypothesis. Could it possibly be that the distant stars are all moving around the sky in just such a way as to mimic the effect of aberration? The distant stars would have to move in bigger ellipses than the nearer ones, and of course all the motions would have a periodicity of exactly one year. Not a very convincing cosmology – but perhaps there’s a deity out there testing our faith.
But there’s an effect we should consider. If aberration is due to the motion of the Earth around the Sun, then as we move around the solar system, we should expect to see a differently-sized aberration effect. If we measure aberration on Mars, which moves around the Sun more slowly, we’d expect to see smaller aberration.
As far as I know, nobody has got around to measuring aberration on the surface of Mars. But we do have spacecraft at the L-2 Lagrangian node, orbiting the Sun at the same rate as us, but a million kilometres further away; and therefore faster. A probe at this location has to use a slightly but measurably greater value of aberration than on Earth. So we can rule out the second argument.
Third argument - Aberration is due to motion of the stars rather than motion of the observer.
Again, this is an extreme geocentric position. According to this theory, there is a vector sum of the speed of light and the speed of an object, but it’s the speed of the star emitting the light rather than the speed of the Earth. Once again, this would imply periodicities of a year throughout the universe. But can we rule it out?
I think we can. In fact, the direction of motion of the emitting stars has no effect on aberration. To see this, consider a thought experiment where there are two emitting bodies, which momentarily coincide. One is at rest with respect to our Solar system, the other is moving. Yet the rays of light which reach us from the two objects will also coincide – in other words, the velocity of the moving object is irrelevant.
Now, physics has moved on since James Bradley first discovered aberration. I suspect some of the readers of this article might be a little bit troubled by the assertion that aberration has to be due to the motion of the observer rather than the motion of the emitting star. Doesn’t that conflict with relativity?
It’s a valid question to ask. And I think the mystique of relativity means that most people will assume it’s a valid point – certainly, when I started thinking about aberration, I thought it was valid. But it isn’t. As I explained above, aberration can’t be due to motion by the emitting star.
So is relativity disproved? No – because relativity applies to inertial, non-accelerating motion. You can’t invoke relativity and transfer speed willy-nilly between two bodies, if one of those bodies is accelerating. A good example of this is the famous “twin paradox” where one of two twins goes off at near light speed to explore the universe, whilst the other stays at home. On their return to Earth, the exploring twin has aged less than the non-exploring twin, because of the effects of time dilation. But doesn’t relativity mean that one could consider the stay-at-home twin to have done the traveling? No, because the exploring twin has had to accelerate and decelerate in the course of the travels. In relativistic jargon, he occupies a non-inertial frame of reference.
The same thing is true for aberration. The reason why we see aberration has nothing to do with the motion of the distant stars. The only explanation which fits the observed behaviour is that Earth’s frame of reference is non-inertial. Or, to put it in terms which James Bradley would understand, aberration can only happen because the Earth is accelerating.
Physics has become more sophisticated in the last 300 years, but the implications of Bradley and Molyneux’s observations remain unchanged. They prove that the Earth moves around the Sun.
X-ray Interferometer Telescope
By Paritosh Maulik
To increase the resolution of telescopes, we can operate two or more telescopes in an interfering mode. This is common with optical and radio telescopes. But now NASA is thinking about doing the same with a x-ray telescope. Interference of two x-ray beams has been successfully demonstrated in the laboratory. The next step is to translate the concept into a working space based x-ray interferometer telescope to image black holes. The challenges are many. Here is a brief outline.
We are now certain that black holes do exit and most these are likely to be found at the centre of galaxies. The mass of these back holes could be millions to billion (106 to 109) solar masses. Because of the enormous mass compared to the size of these objects, their gravity is very high. In order to escape from such high gravity fields, the escape velocity is very high, even the highest achievable velocity, the velocity of light is not high enough to overcome the gravitational pull. Hence these are called black holes.
Although we may not be able to get any information from the black holes, the closest we may come to a black hole is the event horizon. At the event horizon, the escape velocity is greater than the speed of light. As the material is sucked in (accreted) by the black hole, its gravitational energy is converted into heat energy. The temperature rises to tens of millions of degrees. At such a high temperature, there is emission of x=ray. From the emission of such x-rays, the presence of black holes was confirmed. A joint Japanese – US observation has noted red shifting of x-ray lines due to the high gravity field near black hole. The XMM Newton starlight has also detected broad x-ray spectral lines from a Seyfert galaxy. A high gravity field near the black hole at the centre of the galaxy is believed to be the reason for the broadening of the spectral lines. If the characteristics spectrum is spread over a wider wavelength, we call it broadening of spectrum.
If we can image close to a black hole, we can study the behaviour of material close to a very high gravity field, and can attempt to verify the theory of general relativity. Regions of such high gravitational fields are not easy to come by. We expect x-rays emitted near the event horizon, to be bent by the high gravitational field and this will cause both red and blue shifting of the x-ray lines. The image is likely to appear as light from the accretion disc, bending around the black hole – distortion of space and time.
Since there is strong x-ray emission near the event horizon of black holes, x-ray imaging is the best option to observe such high gravity fields associated with black holes. The x-ray spectrum has a very short wave length. So we need high angular resolution to observe an event horizon. Supermassive black holes of 106 or above stella mass occur at the centre of our galaxy or at the centre of active Galactic Nuclei. The event horizons associated with these supermassive black holes are about 106-107 times larger than those of typical stella black holes. Therefore the supermassive black holes are the ideal candidates to study. It has been suggested that supermassive black holes are bigger forms of staler black holes (about 10 times solar mass). Such staler black holes occur in our Galaxy. Models of supermassive black holes may also apply to the smaller back holes nearer to home.
The distortion of space, around the event horizon due the high gravity field, can also act as a gravitational lens. A black hole with 3*109 solar mass can be expected to have an event horizon 8 – 16µ as (arc second). This is a magnified image due to gravitational lensing. On the other hand the event horizon of a smaller nearby black hole, 10*106 to 100*106 (10 – 100 million) solar mass, will be around 0.1 to 1µ as. If we are looking for x-rays from near by stars or galaxies we may get away with x-ray telescope of about a milli-arcsecond (10-3 as) resolution; well known examples of such telescopes are the NASA Chandra and XMM Newton of ESO. Ideal candidates for such observations are the centres of M87, and the Milky Way. X-ray binaries in the Milky Way are also interesting objects to study.
But to study black holes and other compact objects in x-rays we need telescopes with higher resolution of the order of 0.1 micro arscsecond (0.1µ as) (0.1*10-6 as). These objects are not only small but far away as well.
How to increase the Resolution
We can increase the angular resolution of a telescope by increasing the diameter of the collecting mirror or the objective lens. We can further increase the resolution of telescope by combining the images from two telescopes working as interferometer. Optical and radio telescopes are now working in interference mode, but; such a system is yet to be tried out with x-ray optics. When we combine two or more telescopes, the effective collecting diameter of the mirror works out to be the separation distance, d, between the two telescopes (also called base line). The resolution is given by λ÷d, where λ is the wave length. Therefore in order to get a high resolution, we need λ÷d to be small. Since x=rays have shorter wavelengths, the separation distance, d, has to be small as well. Here is a short list of typical separation distance we need to achieve a resolution of 0.1µ as at different wave lengths.
Elements when exited, say by heating, emit characteristics optical or visible radiation. We see this as characteristics wavelengths in the optical spectrum. If the elements are exited to a still higher energy level, we get a characteristic x-ray spectrum of well defined x-ray wavelength(s). It is often easier to detect x-rays by semiconductor detectors. These detectors detect the energy of the x-ray beam and therefore it is often easier to define the characteristic x-ray from an element as characteristic energy in keV (kilo electron volt). Iron for example, shows a characteristic x-ray line around 6.4 keV. Such lines have been observed around suspected black holes. If we are to use this iron 6.4 keV x-ray line to study black holes, d in the above relationship has to be about 500m.
So it seems that if we are to have a close look around the black holes, we need a x-ray telescope in interferometer mode, with a high angular resolution and since x-rays have a short wavelength, the base line should be small as well. This may be an advantage. X=ray sources are bright; hence the mirror need not be very large. However there are some practical difficulties with x-ray optics. X-rays are absorbed by earth’s environment; the instrument has to be space based.
Working with X-ray Optics
Most of the materials, in the X-ray wave length, show refractive index of just under 1. On the other hand, the majority of transparent medium can bend light easily. These are the medium with high refractive index. This is why we can focus light with a lens. Most of the materials also tend to absorb x-rays. These problems make it difficult to work with x-ray beams. There have been a few methods to combine x-ray beams to form an interference pattern; here we shall discuss only one called Grazing Incidence Optics. In this method x-ray beams are allowed to reflect at a shallow grazing angle off a surface. The beam undergoes a total external reflection, as if reflected from a mirror. An advantage of this system is that, the reflecting surface does not need to have a very high surface finish.
With the sponsorship of NASA, a team from the University of Colorado has successfully built a x-ray interferometer in the laboratory; the goal was to find out, if a x-ray interferometer could be built using flat mirrors (flat reflecting surfaces) instead of curved mirrors used in other x-ray telescopes. It was also hoped that this experiment would help to establish the design principles for a working x-ray telescope using flat mirrors.
Top, Laboratory set up for the x-ray interferometer, using flat mirrors.
Bottom, Schematic light path of the x-ray interferometer to be used in the telescope.
The x-ray beam, after passing through the double slit, met the first set of reflecting surfaces at an angle of about 0.25°. These two surfaces were separated by 0.769mm at the front and 0.551mm at the back. These first two reflecting surfaces caused the beams to cross. The beams were in turn reflected by the secondary mirrors and were allowed to interfere on a surface at a distance of about 100 m where the interference pattern was picked up by a CCD.
From these trials they came up with a design for a practical x-ray interferometer for a space based telescope. They also worked out the positional stability and accuracy of location of the individual components needed for the working instrument.
These initial trials suggested that the stability of the optical system needs to be extremely high; for example, the positional stability is about 20nm and angular stability 5nm, baseline in the range of 1m to 1000m. Considering these difficulties it has been decided that there will be a pathfinder mission to confirm the design and this will be followed by the final mission MAXIM (Micro-Arcsecond X-ray Imaging Mission).
The target performances as follows
In the pathfinder telescope there will be two rings of flat mirrors and each ring will contain 32 mirrors. The interferometer baseline will be 1.4m. The size of the combined beam will be 3cm. Both of these rings will be housed in one spacecraft. The beam from the secondary flats (mirrors) will focus at a CCD of 30x30cm in size at a distance of 450km carried in a separate spacecraft. In addition to the interferometer there will be a Wolter telescope of 5as resolution. In Wolter telescope x-ray beam is brought to focus by reflecting (grazed) at shallow angle on curved surfaces. Chandra and XMM Newton employ such optics.
Primary Ring Diameter 140cm
Secondary Ring Diameter 30cm
Distance: Primary to Secondary 1000cm (10m)
Distance: Secondary to Detector 450km
Mirror Size 3 x 90cm
Graze Angle 2 degree
Number of Primary Mirrors 32
Number of Secondary Mirrors 32
There is a simplified light path of the interferometer in the telescope. The flats on top are primary flat collecting surfaces. The second set flats in the middle crosses the beam and forms an interference pattern on the detector at a distance of 450 km.
Two spacecrafts, separated by a distance of 450km, will be required to maintain their position to about 1mm! In order to avoid the effect of Earth on the stability of the x-ray interferometer system, the entire system will operate in a deep space orbit.
Originally the Pathfinder mission was scheduled for sometimes in the early 2010s, but the technical challenges are so high that, it will be unlikely to take place at least before the next decade.
If the pathfinder mission is technically challenging, the MAXIM mission sounds like something out of this world. Here is a brief outline of the system.
Collector unit: There will be 32 spacecrafts, each containing identical flat mirrors. The size of each mirror is 3m.
Converger unit: These 32 spacecrafts will maintain their position with respect to the Hub spacecraft. The interference takes place in the Converging spacecraft. The Hub and the converging spacecrafts maintain their position by optical interferometry.
This is briefly how it works.
Detection unit: Light from a star perpendicular to the optical axis of MAXIM system enters both the Hub and the Converging unit. The star light from the Hub is sent to the Converging craft there the Converger sends its light to a Delayline spacecraft. The reflection from the Delayline craft is sent back to the Convereger. Both beams combine to form an optical interferometer. The Delay line craft maintains its position with respect to the Converging craft via a laser beam. All this elaborate arrangement is intended to monitor and cancel any pointing error. The x-ray interference fringe formed at the converging unit will be picked up a CCD detector in another spacecraft at a distance of 5000km
In order to reduce thermal fluctuation, the instrument will point 90° to the Sun. Pointing to a selected object can take up to 6 hours of maneuvering. This will be done by Pulse Plasma Thrusters capable of moving in three dimensions. Planners of the project think that this is achievable. But the bottleneck appears to controlling the detector spacecraft 5000km away from the formation. There are two possible options
1) a second detector spacecraft; this will cover some beam if missed by the first detector
2) use one detector, but maintain its position by arcjet propulsion.
Although this project is a major technical challenge, and under the present economic climate may need over a decade or so get the go ahead, another x-ray telescope is under consideration, International X-ray Observatory (IXO). The present members are ESO, Japan Aerospace Exploration Agency and NASA. This mission will carry x-ray imagers, x-ray spectroscopy and x-ray polarimeter. It will be essentially an upgraded version of Chandra and XXM Newton.