54 - SOHO Solar images 2000, Sunsets on Mercury, X-ray Astronomy 2, Tying the Knot - Coventry and Warwickshire Astronomical Society

MIRA 54

Autumn 2000

SOHO Images of the sun taken around the summer solstice

A visible light image taken on the 17th June, showing sunspots

X-ray image showing bright areas where sunspot activity is high taken on the 22nd June

Part of the MPEG movie made by the LASCO instrument for 20th June showing the coronal mass ejections along with the bright planets Jupiter and Venus at the left

All of these images are from the SOHO web site.

The Editors Bit

To me the summer time is a time for doing other things apart from looking at the stars and planets. For one thing you can‘t see any, even if its not cloudy or hazy, it never gets dark (well it never ever gets dark in Bedworth unless there‘s a massive power cut!). So do I hang my head in shame at not being a dedicated observer? Should I get up in the early hours to see the latest comet. I did try to see Comet LINEAR in July through the clouds, but failed. This year the summer, if you can call it that, has been poor all over northern Europe with the south getting cooked. Even away on holiday in early June in Rhodes, I hardly saw any stars through the light pollution and the slight prevailing heat haze. Even dedicated solar observers have had a tough time trying to see the Sun this year. I have had a few glances at it and I‘ve not yet seen a naked eye sunspot but I have seen lots of smaller spots through projected binocular images. So you see I can‘t be a dedicated observer or I would be tearing my hair out with the lousy weather we‘ve had and I‘m not. But I do keep up-to-date with what‘s going on above with the astronomy magazines and quick looks on the internet at the SOHO images of the Sun as on this issues cover. So I feel I‘m not missing out on the sky and all the amazing things being reported from probes at Mars, satellites looking at our star, from the new telescopes coming on stream, from all the new techniques and theories on both TV and radio, in the news papers and magazines. A flood of discoveries from the fact that more scientists are alive at this moment than have ever lived before. All of this information is to much for anyone to take in, so that‘s why people specialize in a subject. You can get to know quite a lot about a small part of the whole cosmos, but it‘s very difficult to know a bit about all of it. Even when you think you have a pretty good grasp of your favourite subject, some bright spark will find out a new fact which will upset the standard theory and off you go again! Is there water on Mars? Why is the universe expanding faster? Are there Earth sized worlds orbiting other stars? Is anyone looking at us wondering the same thing?

Ivor Clarke
Editor

Sunsets on Mercury

by Mike Frost

(If you haven‘t already read the preceding story in the last issue of MIRA, 'Prisoner Cell Block Hg' please do so before reading this article. I wouldn't want to spoil the plot twist for you)

Writing an article to explain the science in a story seems to me like an admission of defeat; it rather implies that I couldn‘t put the science across clearly in the first place. However, the orbital dynamics of the planet Mercury are rather interesting and I think a more detailed explanation is worthwhile.
The motion of the Sun across the sky of a planet is a combination of two separate components, the rotation of the planet itself and the motion of the planet around the Sun. Living on Earth, we tend to forget the second component, but on Mercury it produces some remarkable complications.
Let‘s start with a few numbers. Mercury is the innermost planet in the system, it‘s average distance from the Sun is only 36 million miles, compared with Earth‘s 92 million miles. Because it is so close to the Sun, the orbital period of Mercury around the sun, Mercury‘s year, is only 88 Earth days.
On Earth, we are accustomed to the day, the rotational period, being much less than the year. But that isn‘t true elsewhere in the Solar system, and it certainly isn‘t true on Mercury. Mercury spins around on its axis once every fifty-five days; in fact, one rotation of Mercury lasts precisely two thirds of a Mercurial year. Again, on Earth we don‘t see any connection at all between the length of the day and the length of a year. A year is about 365·24 days long and those extra 0·24 days cause all sorts of complications with leap years and so on. Inhabitants of Mercury are spared leap years, the orbital period and the rotational period are connected by an exact 2:3 ratio. Why? Is it co-incidence? Or design? In fact, it‘s tidal friction. Mercury is one of several bodies in the Solar system where tidal friction has slowed down the rotational period to a 'resonance', or exact ratio, with the orbital period.
How does the resonance work? Take a look at Diagram 1, which illustrates how an observer on a planet in a 2:3 resonance will see the sun move. The planet in Diagram 1, however, is NOT Mercury, as it rotates around its Sun in a perfectly circular orbit; we shall see shortly what happens for Mercury‘s elliptical orbit.

Diagram 1. This illustrates how an observer standing on a planet in a 2:3 resonance will see the sun move across his sky from sunrise, the line shows one revolution of the planet, but it takes another ½ revolution before he reaches sunset!

The 2:3 resonance, I hope you can see, produces a surprising journey. Consider one planetary orbit starting at the lefthand side of the diagram, with both the planet‘s rotation and its orbit around the sun progressing counter-clockwise. I‘ve marked the path of an observer who sees dawn at the left of the diagram. Note how, throughout the orbit, the observer remains in daylight. By the time the planet returns to its starting point, after one orbit of the Sun, the observer is just about to cross the terminator at sunset. The observer then spends the next orbit completely in darkness, before seeing dawn again, right at the start of orbit three. So the actual day, sunrise to sunrise, on this planet, is the equivalent of two years; three times as long as the rotational period.
You may be surprised that the apparent and the actual rotational period differ by a factor of three. Why? It‘s because the rotational period is so slow and the orbital period relatively fast. Does the same thing happen on Earth? Well, yes, but to nothing like the same extent. Earth does not rotate once every twenty-four hours. The actual rotational period is just over twenty-three hours and fifty-six minutes. The extra four minutes (to be more precise, 1/365th of a year) is because of the orbital motion of the sun through the sky. We call twenty-three hours and fifty-six minutes Earth‘s sidereal day (literally, relative to the stars) and twenty-four hours the synodic day (literally, relative to the Sun). Mercury‘s sidereal day is fifty-five Earth days long, and its synodic day one hundred and seventy-six Earth days.
Got that? Look at it another way. In twenty four hours, Earth spins through just over 361 degrees, slightly over a full circle, but the Earth‘s orbital motion round the Sun means we have to subtract one and bit degrees, giving an apparent rotation of exactly 360 degrees. On Mercury the balance between the two is much more even. In twenty-four hours on Mercury, the planet has spun through just over six degrees (360 divided by 55), but the Sun has moved, on average, by four degrees (360 divided by 88) because of Mercury‘s orbit. So the net effect is that the Sun crawls through only two degrees of the sky, giving an apparent year of around 180 (360 divided by 2) Earth days.
However, there is a crucial complication, which makes things really interesting. Mercury‘s orbit is not circular. At perihelion, Mercury is only 29 million miles from the Sun; at aphelion it is 43 million miles away. Earth‘s orbit isn‘t circular either; like Mercury and indeed everything else in the Solar system it orbits the Sun in an ellipse, but one that is much closer to being a circle. We call the 'circularity' of an ellipse its eccentricity. Eccentricity has a precise definition but all you need to know is that perfect circles have eccentricity of zero, whereas, as eccentricity approaches one, the orbit becomes flatter and more 'cigar-shaped'. Earth has eccentricity of 0.017 and Mercury 0.206.
How does a planet‘s rotational period vary as it proceeds round its orbit? Not at all. Mercury spins around at the same rate regardless of how close it is to the Sun (as does the Earth, of course). The rate at which the Sun moves, however, is a different matter.
The laws of orbital motion were first discovered by Johannes Kepler, and explained a century later by Isaac Newton. I have already described Kepler‘s first law, planets move around the sun in ellipses, with the sun at one focus. Kepler‘s second law describes how planets speed up and slow down at various points in the orbit. Here is the second law — the line joining planet and sun sweeps out equal areas in equal times. What does that mean? Simply that the planet speeds up as it approaches the Sun, and that the Sun‘s apparent motion through the sky becomes faster.
How much faster? Well, on Mercury the effect is quite extreme, and in Diagram 2, I‘ve tried to redraw Diagram 1 to illustrate it. I hope you can see that, while the Sun scurries through the sky in the further reaches of Mercury‘s orbit, at perihelion the Sun stays in virtually the same position in the sky. If the Sun is overhead as you are approaching perihelion, it will stay virtually overhead for several days either side of perihelion.
Note that I have cheated a bit on the diagram. Mercury is a very small planet, only 3000 miles in diameter, so the size depicted for Mercury is not at all to scale compared with the size of the orbit. To work out exactly what happens to the Sun‘s apparent motion needs some careful calculations, which I have made for you.
My calculations make a couple of further assumptions. First of all, I assume that Mercury has no axial tilt. This is a pretty good assumption, as Mercury‘s axis is only 0·1° degrees from vertical to its plane of orbit, compared with Earth‘s 23·0° degrees. My second assumption, not so good, is that the Sun is a point source of light. From Earth this is good for most practical purposes; the Sun is only half a degree across, but of course Mercury is much closer to the Sun and the angular size increases as Mercury approaches perihelion. Nonetheless I think my conclusions hold.

Diagram 2. You can see that, while the Sun scurries through the sky in the further reaches of Mercury's orbit, at perihelion the Sun stays in virtually the same position in the sky. If the Sun is overhead as you are approaching perihelion, it will stay virtually overhead for several days either side of perihelion.

Here are the numbers for selected periods in Mercury‘s 88-day orbit. At the start of day 1 it lies at aphelion, furthest from the Sun. In days 1-44 it is approaching closer and closer to the Sun, until on day 44 it reaches perihelion. Days 45-88 are similar to 1-44, in the opposite order; I‘ve included days 45 and 46 to show this.

How do we interpret the numbers? Well, note that the numbers in the second column are constant; that indicates that the planet spins around at a constant speed. But the numbers in the third column increase as Mercury approaches perihelion, because Mercury is speeding up. The fourth column is the difference of the second and third. You‘ll see that, at the start of the orbit, the contribution from Mercury‘s spin is dominant, and the Sun moves relatively rapidly through the sky. However, as Mercury approaches the Sun, the motion of the Sun speeds up, and the two terms become closer in size. By day 38, the two terms virtually cancel out; the Sun only appears to move 0·23° degrees through the sky in 24 hours. By day 40 the Sun is essentially motionless in the sky.
But for the remaining 4 days to perihelion, and the four days after it, the orbital term wins out. The Sun is moving through the sky in the wrong direction. How will this appear in the sky? Well, to be honest, from most of Mercury it will be difficult to notice, as the speed across the sky is so slow. But suppose for a moment, that it‘s the end of day 37, you have just landed on Mercury at a point where the Sun has just set. The Sun continues to drop slightly further below the horizon. By the end of day 40, the Sun is a third of a degree below the horizon. But then it changes direction, starts rising again, and some time on day 42, unsets itself. Not until day 48 does the Sun begin to drop back towards the horizon; then on day 50 the Sun sets for the second and final time during the mercurial 'day'.
You‘ll see that the Sun doesn‘t drop below the horizon very far, only a fraction of a degree. But don‘t forget that Mercury doesn‘t possess an atmosphere; so sunsets and sunrises will be abrupt events. In fact, the view could be staggeringly beautiful. By locating yourself at the right point on Mercury‘s surface, you can position the Sun, at standstill, just below the horizon for days and days, creating yourself a long-lasting solar eclipse. Moreover, with the Sun four times as close as it is on Earth, all the really amazing sights we glimpse for just seconds at eclipse time, the corona, chromosphere, solar flares and so on, will be four times bigger, sixteen times brighter and visible for days on end! Far from being the location of a prison, I predict the double-sunset zone of Mercury will become home to a solar observatory and quite possibly one of the hottest tourist destinations for the next millennium.
Note that most of Mercury doesn‘t get to see a double sunset, because of the resonance of day and year. You will only see a double sunset, if the first sunset occurs between days 36 and 40 after aphelion, or between 124 and 128 days after aphelion. If you are lucky enough to see a double sunset, then stay exactly where you are on Mercury, and 88 Earth days later you will see the opposite effect, a double sunrise, and 88 days later you‘ll be back where you started with a double sunset. So only two small bands of longitude (about 1·5° degrees longitude across), on opposite sides of Mercury, will ever see a double sunset. At other longitudes, the Sun‘s switchback behaviour occurs at different times during the day. For example, Mercury‘s ?prime meridian‘ or zero-longitude meridian has been allocated, by the International Astronomical Union, to the sub-solar point at perihelion. This is potentially a very confusing location, as it has up to three middays in quick succession, followed 88 days later by three midnights!
Aside from seeing multiple middays, the longitude bands at which the Sun is overhead at perihelion (two bands of course, on opposite sides of Mercury) are the location of Mercury‘s tidal bulge. Mercury is a solid body, of course, so there is no opportunity for liquid tides like we have on Earth. However, the tidal forces, easily at their strongest when Mercury is at perihelion, may have forced Mercury into an ellipsoidal, or Rugby-ball, shape, with the pointy bit facing the Sun at perihelion. We see that the 2:3 resonance naturally presents one end of the Rugby ball, then the other, each time Mercury approaches closest to the Sun. This is why the configuration is stable; any further slowing down of Mercury would generate a torque on the tidal bulge, which would speed the planet up again.
It‘s natural to ask whether or not any other planets in the Solar system feature a double sunset. Remember the two requirements, a long rotational period, comparable with the length of the year, and an eccentric orbit, so that the angular speed of the Sun can vary. Venus, next planet out from the Sun, meets the first requirement. The sidereal day is of 243 days is actually longer than the Venusian year of 225 days. However, Venus has the least eccentric orbit in the Solar system, even more circular than Earth‘s. Also, Venus rotates in a retrograde direction, so that the Sun‘s apparent motion due to Venus‘s rotation is in the same direction as the motion due to Venus‘s orbit. The angular velocity of the Sun across the sky of Venus varies only between 3·0° and 3·1° degrees per Earth day, giving 117 Earth days to one synodic Venusian day. So there are no double sunsets on Venus; but there is an unusual feature, the Sun rises in the west and sets in the east. Except that you would have to wait 58 days between sunrise and sunset and you wouldn‘t see anything anyway, as the sky on Venus is permanently covered by clouds of sulphuric acid. Venus is not a likely tourist destination.
Earth and Mars rotate much more quickly (about 24 hours in each case) and the gas giants quicker still. Pluto is far too far away to worry about double sunsets. The only other candidates for double sunsets in the solar system would appear to be sun-grazing asteroids such as Icarus. However, the few asteroids which have had accurate periods measured have all turned out to be rotating in hours rather than in days. So Mercury may well be the only object in the Solar system that sees the Sun change direction in its sky.
Finally, it is worth asking if any satellites in the Solar system see their parent planets change direction in the sky. There is one obvious candidate; our own Moon, which meets the two criteria admirably. The Moon‘s rotational and orbital periods are in a 1:1 tidal resonance, which in plain language means that the Moon always shows the same face to us, daytime 'relative to Earth' on the Moon lasts for ever. However, the Moon is also in an eccentric orbit, and the Earth‘s angular velocity through the lunar sky varies between plus and minus 1.5° degrees per day. The net effect of this is that parts of the Moon, on the edge of the hemisphere facing us, see the Earth set and then unset itself during a 28 day orbit round the Earth. From our point of view, on the Earth‘s surface, the Moon‘s face appears to wobble to-and-fro during a 28 day lunar cycle. We call this wobble libration and it enables us to observe more than 50% of the Moon’s surface.
So, I don‘t suppose that Clarissa would be too impressed, but she and Clive were witness to one of the solar system‘s more impressive (and lesser known) phenomena; the standstill of the Sun on the horizon of Mercury, followed by its unsetting and then a second sunset.
Clever Clive!

Tying the Knot

by Mike Frost

As usual, I base my story somewhere in the vicinity of known science. Elsewhere, the Gordian Knot was tied around the yoke of a wagon in the palace of King Gordius of Phyrigia, where it was said that whoever could undo it would be a great leader. The knot was very tangled and convoluted, but Alexander the Great sliced through it with a single sweep of his sword. Ever since, Cutting the Gordian Knot has meant solving a difficult problem by some unexpected means.

”Dearly beloved, we are gathered here together . . ."

It was a beautiful day for a wedding. This one was special; it was the marriage of my old friend, Clive, of the Interplanetary Dangerous Sports Club, and his attractive but rather domineering fiancee, Clarissa. And I was the best man. I stood at Clive‘s side by the altar, fingering the box containing the ring. The groom looked very nervous. Although he‘d spent weeks being measured for his morning suit, it didn‘t quite seem to fit. Clarissa‘s mother eyed her future son-in-law suspiciously. Clarissa‘s father, doubtless relieved to be offloading his demanding daughter, still held her arm. Clarissa gave him a quick smile. ”Not long now daddy." She looked stunning, a vision in silk.

The bridesmaids looked rather tasty too.

I was so busy admiring them that I didn‘t really pay attention to what the vicar was saying. Until it got to the bit where he said; "If any man has any just impediment to this marriage, let him speak now, or forever hold his peace.”

There was silence in the nave of the church, although you could hear birds singing in the churchyard. Sunlight streamed through the stained glass windows, illuminating the rather wild, unkempt, bearded chap who had just marched in through the church doors.

”I object!!!!” He shouted, in a strangled east-European accent.

There was a sharp intake of breath from the congregation. All the party at the altar turned round to see who was talking. Clarissa gave a low moan. Her mother shot the man a look I‘d last seen in Walking with Dinosaurs.

”I object!!!!” The man cried again. ”Clive is already married! To my daughter!”

All hell broke loose. Clarissa screamed and threw herself into her father‘s arms. Her mother gave a small sigh and collapsed to the floor.

Clive himself looked puzzled. Then a flash of recognition crossed his face.

”Oh, you must be Olga‘s father. Pleased to meet you!”

* * * *

The vicar had managed to hustle six of us into the vestry, and barricaded the doors shut behind us. Clarissa‘s father had been deputed to make sure no one else got in. Clarissa and her mother were comforting each other, although it already looked as though Clarissa‘s mother had recovered sufficiently enough to be able to napalm a small village, if that would help. The vicar made sure he was positioned between the two women and the bearded man, who was puffing himself up ready for an argument. Clive was trying to look invisible in a corner.

I felt that my place was with the bridesmaids, who obviously needed consoling at this stressful time. But the vicar wouldn‘t let me leave.

”Look out for the groom.” He whispered; then motioned for everyone to be quiet.

”Let‘s hear what this gentleman has to say.” He said, and indicated that the bearded man should have the floor.

”Thank you sir,” said the bearded man, ”Forgive my colloquial; English not my first language. I am from Russian family of good repute.”

He sighed. ”Alas, my daughter Olga. Wild child. I look for ivory tower of learning. She seeks western university of degenerate social mores and Dangerous Sports Club. Clive‘s university top of list.”

Clive and I exchanged a quick glance of triumph for our alma mater. ”Yeah!” Olga‘s father looked at us coldly.

”Olga free to lead own life; wastes it participating in dangerous sports. Seeks ever wilder thrills. Until bungee trip to black hole.”

I shot another glance at Clive. He had been on the bungee jumping trip to the event horizon of the black hole in M87. What hadn‘t he told me? But Clarissa‘s mother wasn‘t going to let anyone else run events for very long.

”This is all very interesting, I‘m sure, and I think we all sympathise with you over your uncontrollable daughter — I know I do. But what does this have to do with this wedding?”

”Will explain," said Olga‘s father. ”Russian federation still eyed with suspicion by authorities in Virgo cluster; refused to grant Olga visa. Almighty tantrum by daughter. But wobbly no good; immigration still stony-faced.” He paused, shaking his head sadly.

”So what happened??!!” cried Clarissa‘s mother, losing patience.

”I married her,” said Clive, very quietly.

There was dead silence for several seconds. Then Clarissa burst back into tears and threw herself howling into her mother‘s bosom. Clarissa‘s mother gave Clive a look that suggested his remaining life would be neither long nor pleasant.

”I mean,” said Clive, ”it was only to allow Olga to apply for a visa. I didn‘t love her or anything.” Then he looked at Olga‘s father, ”Oh sorry, didn't mean to...”

”Apology accepted,” he said, ”understand Olga‘s persuasiveness. Do anything to avoid further tantrums. But marriage certificate still valid. And marrying second time against law.”

”But,” Clive said, ”she‘s no longer.” Then he too burst into tears.

The vicar, who was clearly used to dealing with scenes like these on a regular basis, had to take charge again and restore order. Eventually, Clarissa sat by the registry book, clearing her smeared mascara, and Clive, in the other corner of the vestry, took to blowing his nose loudly.

”Ready to begin again?” Said the vicar. Clive nodded.

”We drew lots to see who‘d make the bungee jump, and who‘d pilot the two tether space ships. Olga and I won the lots and got to make the bungee jumps. We dropped out of orbit and prepared to make the pass close to the black hole event horizon. In our separate spaceships, we each carried out checks of our own equipment. But, you know, Olga hadn‘t done this kind of thing very often, and she wasn‘t thorough enough with her preparations.”

”You see,” said Clive, sniffing loudly, ”Olga‘s jump went wrong. Maybe she hadn‘t calculated the stresses, maybe she just hadn‘t taken enough care. But when she jumped, when she fell towards the black hole, when the bungee rope tightened, and caught round her ankles, to pull her up to safety, the knot came undone on Olga‘s bungee rope. And she fell into the black hole.”

There was a shocked silence, for a second or two, as we contemplated Olga‘s terrible fate. Then Clarissa’s mother looked purposefully and directly at Clive.

”So she‘s DEAD. And so you are a WIDOWER, are you not?” She gave Olga‘s father the most dismissive of glances. ”You have my deepest sympathises. But let‘s get on with the marriage of my daughter to this . . this idiot.” She gestured angrily at Clive.

I had tried very hard to keep out of the arguments; my only thoughts were to take care of the ring until it was safely onto Clarissa‘s finger, and then to take care of the bridesmaids at the reception. But my conscience kicked in now. I coughed for attention.

”Excuse me. I‘m afraid things aren‘t quite that simple.”

Clarissa‘s mother fixed me with her raptor-like stare. ”What do you mean, ‘things aren‘t quite that simple?‘ This man‘s daughter married my prospective son-in-law. The bride fell into a black hole. So now she‘s dead, and he‘s free to marry my daughter. And frankly, he had better take more care of her.”

”Sorry to be a nuisance,” I said, feeling myself sinking deeper into quicksand, ”but there really is a problem. You see, in our frame of reference, Olga isn‘t dead yet.”

Clarissa‘s mother looked ready to tear my throat out, but fortunately the vicar was in the way. ”As a man of the cloth,” he said, ”I know a lot about running weddings, but I‘m not completely au fait with the workings of black holes. What exactly do you mean by a ‘frame of reference‘?"

”Never mind that!” screamed Clarissa, ”IS THE MINX DEAD OR ISN‘T SHE!?”

I waited for the vicar to restore order. ”As far as we are concerned,” I said, ”time slows down in the vicinity of the event horizon of a black hole. Clive found this out when he returned from bungee jumping onto the event horizon. While only minutes had passed for him, months had passed in the outside universe. But Clive only approached close to the event horizon. Poor Olga, after her knot came undone, crossed that horizon. And as she crossed the event horizon, from our perspective, time stopped completely for her. In our frame of reference, she is still crossing the horizon, still alive, and still married to Clive.”

Clarissa burst into tears again. ”Oh mummy, you were right. Clive‘s just as worthless as you said. I shouldn‘t have let you spend all that money on the wedding.”

Clarissa‘s mother comforted her. ”Hush, sweetest, we‘re not finished yet. We might still get that ring on your finger. We might still get to enjoy the reception daddy paid so much for.” She turned to the vicar.

”I have no idea if this know-all of a best man has any idea what he is talking about. Let us assume that he does. It seems to me that Clive and this Olga woman have been separated by several million light years for several years. If that doesn‘t constitute grounds for divorce, what does?” I could see that the vicar sympathised with her reasoning, but my conscience was still tickling me.

”It isn‘t that simple.” I said, my heart sinking. ”Clive has been separated from Olga for several years, but, from Olga‘s point of view, she‘s only been married to Clive for a few days. Remember, she‘s only just reached the event horizon.”

”Well why don‘t we ask her?” Clarissa‘s mother snarled. I shook my head.

”In theory, we could communicate with her on the event horizon. In practice, time has slowed down so much that individual photons now arrive hours apart. Practically, she has already fallen into the black hole.”

”So she has died in the black hole.” Interjected Clarissa‘s father, who had been encouraged by the prospect of seeing some return on his money.

”Not yet.” I said. ”In Olga‘s frame of reference, her end came mercifully quickly.” I gave Olga‘s father a respectful nod. ”About two hours after she crossed the event horizon, in her time, she reached the singularity of the black hole. Some time before that, the gravity of the black hole spaghettified her — I‘m sure it must have been quite a journey. But, from our perspective, she hasn‘t even entered the black hole yet.”

The vicar was still trying to keep on top of events. ”You tell us that time flows differently for different people, but it leaves me concerned for the spiritual well-being of poor Olga. How can God judge her soul, if she isn‘t even dead in our frame of reference? Surely there must be a day of reckoning?”

I thought about that one. ”Yes, there is. Eventually the black hole will evaporate.”

Clarissa‘s father interjected. ”And then we‘ll know she‘s dead for certain."

”Absolutely. You won‘t be able to tell her from all the other quarks in the explosion."

”Great!!" said Clarissa‘s mother. ”So when can we serve the divorce papers??!"

”The evaporation? That won‘t happen for another hundred or so billion years."

I thought that Clarissa‘s mother was going to strangle me, but the vicar rushed to my defence. ”Just a few more questions. Astrophysically, do we agree, Olga is still trapped on the event horizon?"

I nodded, and so did the others, grudgingly. The vicar continued. ”Practically, however, she is dead to us." We nodded again.

”But legally??"

That stumped us. The vicar nodded sagely. ”I see this kind of thing all the time. There are some disputes that must be settled before the courts, and this is one of them. None of us have any real idea what the law has to say on this matter, or if indeed our legislators have even considered the circumstances. But I am afraid, ladies and gentlemen, that I cannot allow Clive and Clarissa to be married today."

Well, I thought he had summed up the situation quite nicely. Clarissa‘s father began to remove the barricades, so that the decision could be announced to the congregation. I was about to make my way through the door when Clarissa‘s mother grabbed my arm in a vice-like grip.

”Where do you think you‘re going?” she demanded of me. I muttered something about seeing to the bridesmaids.

”Well, young man, you have obviously not paid attention to your book of wedding etiquette.” She was right there; I had completely ignored the copy she had thoughtfully provided me with.

”Vicar, come here!" she commanded. Suddenly her husband was steering the vicar firmly towards his wife and me. I felt things were about to get out of control.

”Young man,” Clarissa‘s mother said steely, ”on the bride‘s wedding day, if the groom cannot go through with the ceremony, then there is one further duty incumbent on the Best Man."

The grip on my arm was getting tighter.

”Now, where did you put that ring?”

* * * *

Reader, I nearly married her.

Fortunately, the vicar was able to convince Clarissa‘s parents that there was no legal contract forcing the best man to marry the jilted bride; they accepted his word only grudgingly after much further argument. During which time the congregation dispersed, and the bridesmaids disappeared with the photographer and his assistant. Not a good day.

The lawyers we consulted drooled at the anticipation of extensive litigation over the legal status of poor Olga. The case, they said, would make legal history, and would certainly progress to the highest court of appeal. Indeed, they added, it was not entirely certain as to whether or not the case would reach its completion before the evaporation of the black hole rendered the final judgment irrelevant. We decided not to proceed with the case.
Which would have been the end of the story, except for one curious event a few weeks later. I dropped into a pub in town, not my local, for a quick drink, and was amazed to see Clive at the bar, enjoying a drink with Olga‘s father. At least, I think it was Olga‘s father. By the time I reached the bar, Olga‘s dad was gone, and Clive was about to leave. He was startled to see me.

”Wasn‘t that Olga‘s father?" I said.

”Who?" said Clive, shiftily.

”WHO??!! You know, the Russian guy whose daughter you married . . . Remember?”

”Russian guy?” said the barman, absently, ”that was Jim Smith, from the Dangerous Sports Club. Never been to Russia in his life, far as I know, but he does a great Russian wild man impersonation. Why are you looking at me like that, Clive??”

I decided not to enquire any further, and bought a round of drinks instead. Clive looked at his pint and proposed a toast.

”To knots!” He cried, and raised his glass, ”May you take great care over tying them..."

”To knots," I countered, ”especially when you cut the Gordian variety."

”Yeah, whatever." said Clive.

But I think he understood what I meant.

X-ray Astronomy - Part 2

The Sources of Radiation

by Paritosh Maulik

In the last issue of MIRA, Number 53, we looked at the various detectors and methods used to detect X-rays in astronomical observations and how they differ from optical telescopes, in this article we look at the sources of the this still mysterious form of emissions.

Before the X-ray sources were confirmed by observations, physicists suggested that in a binary system of a normal star and a dense companion, like a black hole or a neutron star, material can exchange from one to the other and these could be the possible cosmic X-ray sources. There are basically three types of possible systems:

1) Roche — Lobe Overflow of the Primary
The Low Mass X-ray Binary system: One of the pair is a normal star is similar to or less than the Sun‘s mass. The point at which the gravitational pull from each other is equal and opposite is call the Roche-lobe. If the orbits of the stars is very close, the Roche-lobes occurs close to the normal star. A funnel like situation develops and mass can be dragged out from the normal star to the compact star. An accretion disk will develop around the compact star. All the material in the disk will not have same angular momentum, so as material in the disk spirals into the compact object under its strong gravitational pull, it can heat to a temperature which is high enough for the gas to emit X-rays.

2) High Mass X-ray Binary
In this case the X-ray binary consists of one massive star about 10 times the mass of the sun or greater and the companion is either a neutron star or a black hole. Radiation from the primary causes gases which are ionised, ie. in a charged or plasma state, to move out from the primary; this is called radiation pressure. When the companion star accretes this plasma, it converts some of the plasma into X-rays.

3) Capture of circumstellar material from a Be star primary
This X-ray binary consists of a Be star and a neutron star. Be stars are a special type of star which rotate very rapidly and eject a large amount of matter at random intervals from its equatorial plane. Strong spectral emission lines of hydrogen and helium are present. When this material comes under the influence of the secondary star, accretion takes place and X-rays are generated. But since the emission of matter occurs at random, the X-ray source is a transient one.

Pulsing and Flashing Binary Stars
A X-ray binary system in which one of the stars is a neutron star. X-ray emission has been seen to occur either as pulses or in short bursts. The neutron stars generally have very strong magnetic fields, amongst the highest in the universe. This magnetic field can cause matter from the companion binary to funnel into the magnetic pole of the neutron star. The presence of this strong magnetic field causes the X-rays generated by this process to be very directional and since the system is rotating, the net effect is like a beam from a lighthouse. Both of these stars also rotate on their own axes. When the material falls near to the magnetic poles of the neutron star, it gives off X-rays and since it is also rotating on its own axis, it appears as pulses of X-rays.
Although we have said that the magnetic field associated with the neutron stars is strong, the low mass X-ray binary systems sometimes show a weaker magnetic field; in these systems, the flow of material is somewhat irregular, and hence the X-ray emission. This is called Quasi-Periodic Oscillations. These oscillations originate from the interaction between the neutron star and the accretion disc or the irregular flow of material. Study of these systems can give clues of the interaction between the neutron stars and its surroundings.
In a X-ray binary system, if we can determine the orbital parameters of the primary star from the Doppler shift, we can calculate the mass of the secondary. If the mass of the secondary is around 1.4 times the solar mass, it is a neutron star; if the mass is far higher around 2 solar masses, the companion or the secondary star is a black hole.

Black Holes
Although black holes have a feeling of inevitability about them, in reality these are the final phase of larger stars above 2 times the solar mass and shrinking into itself (collapsing). Once it has reached a critical radius called the Schwarzchld radius, the gravity is so high that even something travelling at the speed of light can not overcome the strong gravitational field.
Let us imagine a rocket is fired from the Earth, the energy on the rocket due to gravitation is given by E = GMm/r² where G is a constant, M is the mass of the Earth, m is the mass of the rocket and r is the distance between the rocket and the centre of the Earth. We can assume this to be approximately equal to the radius of the Earth. If the velocity of the rocket is v, its energy is: E = ½ mv².
The rocket can only escape if its energy is at least the same or greater than the gravitational energy. Now by solving these two equations we can work out the minimum velocity needed by the rocket to take off, i.e. escape. Thus v works out to be v = ( 2GM / r ) ½.
This equation tells us that the higher the gravity, the higher the escape velocity has to be for the rocket to break free from the gravity. Let us imagine we fire a spacecraft from the Earth and its velocity is around 12 km/sec. It would escape Earth‘s gravity, hence escape velocity. Now if we fire the same spacecraft from another launch pad somewhere with higher gravity, we would need still higher escape velocity.
The gravity in a black hole is so high that the escape velocity is higher than the velocity of light, in other words, something travelling at the speed of light cannot escape, i.e. even light can not escape. So if a star with a mass like the Sun shrinks to a radius of 3 km, it would be invisible, this size is called the Schwarzchld radius compared to about 700,000 km, the radius of the Sun now. Schwarzchld radius, R = 2 (G.M)/( c² ); G gravitational constant, M mass of the star, c velocity of light.
However, there can be massive black holes with masses of about 100m times the solar mass, and radius of millions of km. These can occur at the centre of galaxies. Most of the smaller black holes are of 2 to 15 times the solar mass and the radius is of the order of a few km.
As discussed, we can‘t see black holes, but if we can detect a binary system and work out the mass of one the stars, we can deduce if the companion star is a black hole. Such a system is expected to occur in Cygnus X-1. One of the possible candidates for black holes are binary X-ray sources. From the motion of the binary, the mass of the dwarf companion can be calculated. Once we know the mass, we can say if it‘s a neutron star or black hole. As we have seen earlier, if the mass is of the order of 2+ solar mass, it is likely to be black hole (Oppenheimer -Volkoff limit).
Being a black hole imposes a strong gravitational force on the companion star and material will fall into the black hole. As the gasses spin around the black hole, friction causes a sharp rise in temperatures, high enough to emit X-rays. This accretion of material does not occur at a steady rate, but at an uneven rate. This leads to variation of X-ray intensity; also in addition, if the companion star during its orbit eclipses the black hole, to the observer it appears as periodic emission.
Cygnus X-1, is a highly variable and irregular X-ray source and it is strong candidate to be a black hole. Its X-ray emission occurs in bursts of hundredths of a second. In an hundredth of a second light travels 3000 km. So an object can- not flash faster than the speed of light, we can expect it takes at least a hundredth of a second for the X-ray to travel through the dwarf. In other words the size is of the order of 3000 km; the diameter of the Earth is about 12700 km.
The companion to the blue supergiant star HDE226868, at 30 solar masses, works out to be about 6 — 15 solar masses. This system has a period of 5.6 days. A word of caution: the spectral data of HDE2268686 may also be interpreted as this star not being so heavy, which in turn bring the mass of the Cygnus X-1 to about 3 solar mass i.e. close to a neutron star.

Orbit and Mass of Binary Stars
By determining the orbital and Doppler shift parameters we can calculate the mass of the companion secondary star in a binary system. In a X-ray binary system, if the mass of the binary is of the order of about 1.4 solar mass, it is a neutron star; if the mass is greater than 2 solar mass, the companion star is a black hole and thus validating the theory.

Invisible Mass
It has been suggested that the total mass of the universe is 10 to 20 times the visible mass. The bulk of the visible mass was created during the big bang explosion and this invisible mass consists of fundamental subatomic particles. Collectively this is known as baryonic matter. The possible existence of the dark matter was estimated from the amount of light elements like hydrogen and helium formed during the big bang explosion. The properties of high temperature gas in clusters of galaxies and the high speed of movement of galaxies in this gas cloud, temperatures may be as high as 10⁸ K, hot enough to generate X-rays.
By determining the X-ray temperature, and gas characteristics, in clusters of galaxies, group of galaxies or a massive elliptical galaxy one can determine the mass. The analysis of the data show that the mass of the gas is around 3 — 5 times the mass of the stars and the baryoinic matter is the around 10 — 30% of the total mass in stars, in other words, the X-ray studies have shown that the dark baryonic matter can extend far beyond the visible limit of the galaxies.

Types of Supernovae
There are two types of supernovae
I) In a binary system of a red giant and a white dwarf, mass flows from the red giant to the white dwarf, the white dwarf can not support itself and collapses or implodes. These types of supernovae do not show hydrogen spectral line.
II) At the end of the life cycle of a massive star the nuclear synthesis comes to a near end, it can not support itself when the core transforms to iron. If the mass is large enough, it will collapse to become a supernovae. The massive stars are generally made of hydrogen in their atmosphere. So during the supernovae explosion hydrogen spectral lines can be seen. But if the star is too massive, the stellar wind may blow off all the hydrogen and a hydrogen line may not be present. White dwarfs are generally free from hydrogen and other elements. A word of caution: a type II supernovae was once termed as Ib, on the basis of hydrogen emission characteristics, before the physical processes involved were fully understood.
The core of an extremely large star is very small compared to its overall size. The nuclear synthesis going on in the star over millions of years gives rise to formation of elements heavier than hydrogen and helium. The supernovae explosion causes these elements to disperse into the interstellar space. The star becomes a supernovae remnant.
The nuclear energy of a stable star is enough to synthesise elements as heavy as iron. In order to make still heavier elements we need still higher energy. The supernovae explosion can provide this additional energy. This is how the different elements seen today are formed.
Supernovae explosion does not occur regularly, when they do, they are examined thoroughly. In earlier times these were reported as appearing and disappearance of new stars.

Cataclysmic Variables
The brightness of some stars goes through a periodic variation. This period is very regular, for example U Gem, the optical intensity reaches to a maximum of about 100 fold in around 120 days and then falls back to the original level in about 10 days. These are called Cataclysmic Variables or CV‘s. It is now known that these are binary systems, in which the primary is a white dwarf, the end phase of star; its nuclear reaction has ceased, its outer part has blown away; has a maximum mass of 1.44 solar mass, i.e the Chandrashekhar limit. Under such conditions the fundamental particles do not behave normally, the star stops collapsing, its surface temperature is greater than 10000°K. The star cools slowly becoming fainter and redder. The secondary is a sun like star. The gravitational force of the primary pulls matter on to the primary and the release of this gravitational energy is seen as a energy burst.
Cv‘s were first observed by the optical astronomers and they classified the CV‘s according to the nature of the outburst. Classical novae are those where the outburst occurs once and the intensity is very high. In white dwarf the fuel has run out and on receiving fresh fuel mainly hydrogen by the accretion process, reaction can start again.
Dwarf novae outbursts are smaller in amplitude but higher in frequency; these may appear to be similar to classical novae outbursts, but the main difference is there is a temporary increase in the rate of accretion onto the primary.
X-ray detectors on board the Uhru and Einstein missions suggested that many of the CV‘s are weak X-ray sources. The material leaving the secondary cannot fall straight into the primary. The material forms a disc ™ an accretion disc — around the primary. The friction within this layer heats up the material and it slowly spirals into the primary. Once the disc hits the surface of the primary the temperature can go up as high as 10⁶°K — high enough to generate X-rays. The surface of the primary is not a well defined and is now currently being studied.
It now appears that the majority of the CV‘s with strong X-ray emission have very powerful magnetic fields associated with a white dwarf. The magnetic field can be far more powerful than the Earth‘s magnetic field and can alter the shape of the accretion disc and produces stronger X-ray emissions.
CV‘s with nuclear fusion rather than just accretion is also possible. This is the case with classical nova outbursts. X-ray astronomy has revealed another group of objects, Super Soft Sources. The energy output from these sources is somewhat low about 0.5 keV. This suggests the surface temperature to be about 20000°K to 80000°K. The mass of the white dwarf is possible greater than that of the Sun. Theoretical calculations suggest that continuous nuclear reaction on the surface of a SSS may eventually lead to a supernovae explosion.

Gamma-ray Bursts
Approximately once a day there occurs sudden bursts of very powerful gamma rays which soon after the outburst, disappear. This phenomenon appears to occur at random and very little is known about this source.
It was once thought that the neutron stars within the Milky way was the sources of the gamma-ray bursts. But this idea is being questioned. Any successful model should be able to explain these very high energies and the emission mechanism based on our present knowledge. There appears to be two basic ideas
I) Sources are in the Milky Way: once it was thought that the neutron starts have a velocity of 200 km/s; now it appears that these can have velocity greater than 500 km/s. If this the case, then, these stars can move into a halo or corona around the galaxy at a distance of about 300 ly. Corona at such a distance may contain enough sources and from a distance such as Earth the distribution as appears to be uniform.
II) The sources are outside the Milky Way: The study of the other components of the electromagnetic spectrum associated with the GRB sources suggests that the majority of the these lie outside the Milky Way. The cosmological model implies homogeneity, any inhomogeneity is perhaps due to redshift effect. This model suggest that the energy release from this burst is around 10⁵³ to 10⁵⁴ erg. Similar level of energy release also takes place during supernovae explosions, but in a supernovae explosions, kinetic energy of the dust and gas cloud and visible light account for about 10⁵⁰erg of the energy release and only a small fraction is associated with the X-ray energy release. In the case of GRBs almost all of the energy release is in the X-ray / gamma-ray range.

Active Galaxies and Quasars
On the average, the total weight of a galaxy is about 11¹⁰ times solar mass stars; + 1¹⁰ times solar mass interstellar gas; + 10¹² times solar mass dark matter. But the calculations show that a large number of these, may be as high as 50% heavier. It now suggested that long long ago when the galaxies were younger, the stars in the core were closely packed. This led to collisions among stars; the stars merged and formed Massive Black Holes (MBH), with masses as heavy as 106 to 109 times solar mass. As discussed earlier, in a X-ray binary star system, an accretion disc forms and this produces a very large amount of radiation ranging from infrared to gamma-rays. This MBH and the accretion disc, is responsible for what is now termed as Active Galactic Nuclei (AGN).
Our own galaxy the Milky Way may have an AGN, but it appears to be somewhat quiet, and is not very prominent. Seyfert galaxies (see later) have moderately mass AGN while the accretion in the quasi-stellar objects with high-mass AGN , makes the quasi-stellar objects very luminous.
In about 10% of the AGN, the MBH and the accretion disc produce narrow beams of energetic particles and magnetic fields. These are ejected in opposite directions away from the disc. The radio jets travel almost at the speed of light and can spreads outwards. Radio galaxies, quasars and blazers (see later) are in fact AGN with strong jets. The way these AGN appear to us depends on their orientations.

Seyfert Galaxy
In the 1940‘s Carl Seyfert photographed the galaxy NGC4151 and observed that it has a very bright point like nucleus. Its spectrum is somewhat unusual, in addition to the continuous spectrum and absorption lines like stars, it also contain powerful emission lines. Some of these lines are common, like hydrogen lines, but some are unusual, such as twice ionised oxygen lines. It is suggested that the gas is at very high temperature. The broad spectral line is explained as Doppler shift in all directions, at a speed around 2000 km/s. The nucleus brightness can vary in a time period of months; this suggests the nucleus size to be less than 3 ly. The total luminosity can be equivalent to about 1010 times our Sun.
It is now believed that the Seyfert galaxies have a massive black hole in their centres. Around this MBH an accretion disc forms; the radiation raises the energy of the gas, its temperature rises and forms unusual spectral lines. Seyfert galaxies may be the lower -luminosity examples of the quasar activity. The majority of the Seyfert galaxies are either spiral or barred spiral galaxies.

Radio Galaxy
Radio observation have shown that some of the galaxies can emit powerful radio energy, as high as 10³⁸ W. The nucleus of these galaxies also emit strong radio energy and these nucleus appears to be at the centre of the observable galaxy. Jets stream out from the centre in two opposite directions into the interstellar medium. Additionally a pair of lobes can de detected. These lobes stretch outside the visible limit of the galaxy. At the centre of these galaxies are huge sources of electrons and protons with high energy. In the presence of a strong magnetic field, these particles can accelerate; this process of acceleration can cause a release of the energy of the particles by electromagnetic radiation at speed of light. This is termed as synchrotron radiation and is now the acceptable mechanism for the generation of the radio and X-ray emissions.

Quasars
These are radio sources and their output varies over very short periods, months or days. A galaxy or a radio galaxy does not vary its output over such a short period. The spectral pattern of these are somewhat different from stars and galaxies. The spectral lines are highly red shifted, which suggests that quasars are very far from us and formed very early.
Balzars are highly variable quasars and star like objects with AGN, the brightness varies over days, the emissions are polarised, high speed jets of plasma and radiation are also seen to be emitted from these objects. If one of its jets point towards the Earth, a relativistic effect occurs when the velocity of a particle approaches that of light; its rest mass increases and if the particle is charged, it emits electromagnetic radiation in a narrow beam. The higher the velocity of particles, the narrower is the beam.
Blazers emit a wide range of frequencies, ranging from gamma rays to radio. The radio signal is powerful, and occurs over a wide range of frequencies. The variability in the optical range, over days is a very important characteristic of balzars.
This group of objects can be classified into two subgroups, 1) Flat Spectrum Radio Quasars: strong broad emission lines, 2) BL Lac objects: near-featureless optical spectrum, may be associated with a compact radio source. About 200 BL Lac objects are now known.
Soft X-ray diffuse background (SXRB) is general low energy 0.1 - 2.5 keV (0.5 - 1.24 nm, wavelength). X-ray background radiation, not strictly associated with any given source. One of the common X-ray sources is hot plasma at 10⁶ K. This gives rise to X-rays in the lowest level 0.1 - 0.2 keV. This hot plasma consists of two parts; i) contained in the disc of the galaxy, surrounding the Sun, but it was not made by the Sun. This disc extends from about 150 to 600 ly and is not uniform in size. ii) general distribution in the halo of the galaxy.
X-ray from the extra-galactic sources such as AGN and quasars, also contribute to the back ground X-ray radiation. The exact sources may remain unresolved. The total energy level is higher, greater than 1 keV.
Instruments abroad rockets in the late 1960‘s first detected SXRB of the order of about 0.25 keV. Although the resolving power of these early instruments were limited, it became clear that the X-ray intensity was greater along the galactic latitude than plane of the galaxy. This observation was interpreted as the origin of the X-ray is extra galactic in nature, and the neutral interstellar medium (ISM) in the galactic plane absorbs the X-ray.
However there were some reports of high intensity X-ray distribution along the galactic plane and this distribution is non-uniform. But with further refinement of observations and theory, it was accepted that the X-rays detected along the galactic plane are also cosmic, i.e. extra-galactic in nature. Soon it became apparent that a model had to be developed to take into the account the non-uniform absorption of X-rays. For example, the X-ray energy distribution in the range of 0.75 keV is more or less uniform, while that in the range of 0.25 keV occurred in a band along the galactic plane. Several theories were put forward.
By studying other energy levels for the past 20 years the nature of the ISM became somewhat clearer. It was found that there is localised deficiency of the ISM in the galactic disc, as if there is a cavity around the Sun, where there is very little neutral hydrogen atoms; however this cavity was not related to the Sun. There are other localised zones ranging from 3 to 15 ly, where there is a drop in the hydrogen level. In addition, the low hydrogen areas surrounding the Sun also contained ionised hydrogen, the later appear to occur perhaps in one direction. It is now believed that the areas of low hydrogen (often termed a cavity) are the areas where there is hot plasma and this plasma gives rise to the SXBR in the galactic plane.

Present Status
Infrared spectroscopy as added further to the understanding of the hydrogen cavity. It turned out to be narrow (about 300 ly) and extends outward from the plane of the galaxy. As described earlier the hot plasma around 106 K within the hydrogen cavity gives rises to the SXBR in the range of 0.25 keV. This now called the displacement model. The origin of the hot plasma is not known for certain. The current thinking is that the cavity existed in the galactic disc, and around 105 years ago, there was supernova explosion, which caused the plasma to heat up.
There are other sources of SXRB, such as supernova remnants which spreads radiation over wider angular distribution. The presence of the hot plasma is now conclusively proven, but refined observations indicate that the 0.24 keV can exit outside the ISM in the galactic disc and if this is the case the question is how and why?
Supernova Remnants
A supernova remnant (SNR) is the leftover from a cosmic firework, a supernova explosion. Such explosions heat up the interstellar medium, distribute heavy elements throughout the galaxy, and accelerate cosmic rays.
Classification of SNR
i) Shell type remnant: The explosion shock wave expands like a ripples in a pond. It stirs up the interstellar material in space, heating the material as the shock wave progresses in the shape of a shell. Viewing from an edge, the shell appears like a ring and there is more hot gas in the line of sight compared to looking through the middle. This is called limb brightening.
ii) Crab-like remnants: These are also similar to the shell type of SNR, except, that there is a pulsar in the middle throwing out jets of fast moving materials. These look more like blobs rather than a ring. Sometimes these SNR are called plerions.
iii) Composite SNR: The appearance depends on the observer, to put it another way the selected wavelength of the viewing instrument; under certain wavelengths, the image may look shell like or crab like. There are two types of composite remnants, thermal and plerionic.
Thermal composites, when studied in the radio waveband, the SNRs appear as shell type. The radio wave is generated by synchrotron radiation. In the X-ray range, the same object looks crab like. The X-ray spectra have spectral lines; this suggests the presence of hot gas.
Plerionic composites, crab like in the radio and X-ray range and a shell is present. The X-ray spectra in the centre show spectral line, but near the shell a broad range, no distinctive peaks.

The Age of the SNR
Early historical data, both cave paintings and written documents record the arrival of ?guest stars‘, these may go back to several thousand years and we need to confirm this data by independent means. An early attempt was to determine the temperature of the hot gas from the X-ray spectroscopy. From this calculation the shock wave velocity can be calculated and thus the age. This method is simple, but there are other interactive processes taking place, which can heat up or cool down the gas and these are not dependent on the shock wave.
For the youngest SNR‘s the following method work well. The SNR expansion is measured as a function of time and since rate x time = distance, if we know the time and distance, we can find the rate of expansion. As an example, let us assume that, over 20 year period the supernova has expanded by 50%. 20 years ago the size was 100 and now the size is 150, an increase of 50%. In 1 year the size increases by 50/20 = 2.5%. 100% expansion occurs in 100/2.5 = 400 years. To be on the safe side we say that the explosion occurred less than 400 years ago and since then it has slowed down.

Why are Supernova Remnants Important to us: its Effect of SNR on the Milky Way
The universe is rich in hydrogen (about 73%) and about 25% helium with about 2% other heavier elements. Synthesis of the heavier elements occur in the stars and the through the Supernova remnants these elements eventually find their way into planets like Earth. A gas disc in the interstellar medium (ISM) may enrich to a high concentration in localised area, such as the spiral arm of the galaxies, for example, in the Milky Way. This through a process of gravitational collapse may set in motion star formation. It is the SNR who mix the newly formed elements into the ISM.
The shock waves also accelerate the electrons, protons and the ions close to the speed of light through the Fermi acceleration process. It is believed that a part of the ISM in our galaxy got entrapped into a supernova shock wave and the excess energy of these particles are responsible for the cosmic rays. Since these particles are entrapped, the cosmic rays keeps on occurring. These high energy particles shower the Earth, but once these strike air molecules, it produces a secondary cosmic ray shower, consisting of fundamental particles, photons and gamma-rays. The theory is not complete yet.
Essentially there are three stages of SNR life.
i) The shock wave interacts with the surrounding ISM; the temperature within the SNR is constant and the shell expands with a constant velocity.
ii) The SNR is now beginning to decelerate and cool. The products of the supernova explosion including the heavier elements slowly get mixed into the interstellar gas. The magnetic fluids inside the SNR shell becomes stronger.
iii) Snow-plough or Radiative Phase: The temperature is now is around 10⁶ K,; the SNR radiates energy. As it radiates it cools faster, it shrinks and becomes denser. As it shrinks it cools faster still, because the material mixes well and looses heat. Now it forms a thin shell and radiates most of its energy in the optical range. The velocity still slowing down, the outward expansions stops and the material inside starts to collapse under its own gravity. After millions of years the the core of the SNR will break out of the outer shell and will absorb into the interstellar medium.

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