Astronomers: 'Dark' galaxy discovered
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Harvest Dancer - 24 Feb 2005 20:34 GMT I found this fascinating.
http://www.cnn.com/2005/TECH/space/02/24/dark.galaxy/index.html
Astronomers: 'Dark' galaxy discovered
(SPACE.com) -- Astronomers have discovered an invisible galaxy that could be the first of many that will help unravel one of the universe's greatest mysteries.
The object appears to be made mostly of "dark matter," material of an unknown nature that can't be seen.
Theorists have long said most of the universe is made of dark matter. Its presence is required to explain the extra gravitational force that is observed to hold regular galaxies together and that also binds large clusters of galaxies.
Theorists also believe knots of dark matter were integral to the formation of the first stars and galaxies. In the early universe, dark matter condensed like water droplets on a spider web, the thinking goes. Regular matter -- mostly hydrogen gas -- was gravitationally attracted to a dark matter knot, and when the density became great enough, a star would form, marking the birth of a galaxy.
The theory suggests that pockets of pure dark matter ought to remain sprinkled across the cosmos. In 2001, a team led by Neil Trentham of the University of Cambridge predicted the presence of entire dark galaxies.
The newfound dark galaxy was detected with radio telescopes. Similar objects could be very common or very rare, said Robert Minchin of Cardiff University in the UK.
"If they are the missing dark matter halos predicted by galaxy formation simulations but not found in optical surveys, then there could be more dark galaxies than ordinary ones," Minchin told SPACE.com.
In a cluster of galaxies known as Virgo, some 50 million light-years away, Minchin and colleagues looked for radio-wavelength radiation coming from hydrogen gas. They found a well of it that contains a hundred million times the mass of the Sun. It is now named VIRGOHI21.
The well of material rotates too quickly to be explained by the observed amount of gas. Something else must serve as gravitational glue.
"From the speed it is spinning, we realized that VIRGOHI21 was a thousand times more massive than could be accounted for by the observed hydrogen atoms alone," Minchin said. "If it were an ordinary galaxy, then it should be quite bright and would be visible with a good amateur telescope."
The ratio of dark matter to regular matter is at least 500-to-1, which is higher than I would expect in an ordinary galaxy," Minchin said. "However, it is very hard to know what to expect with such a unique object -- it may be that high ratios like this are necessary to keep the gas from collapsing to form stars."
Long road to discovery Other potential dark galaxies have been found previously, but closer observations revealed stars in the mix. Intense visible-light observations reveal no stars in VIRGOHI21.
The invisible galaxy is thought to lack stars because its density is not high enough to trigger star birth, the astronomers said.
The discovery was made in 2000 with the University of Manchester's Lovell Telescope, and the astronomers have worked since then to verify the work. It was announced today.
"The universe has all sorts of secrets still to reveal to us, but this shows that we are beginning to understand how to look at it in the right way," said astronomer Jon Davies of Cardiff University in the UK. It's a really exciting discovery." Additional radio observations were made with the Arecibo Observatory in Puerto Rico. Follow-up optical work was done with the Isaac Newton Telescope in La Palma. Astronomers from the UK, France, Italy and Australia contributed to the research. The project is now searching for other possible dark galaxies.
Dark matter makes up about 23 percent of the universe's mass-energy budget. Normal matter, the stuff of stars, planets and people, contributes just 4 percent. The rest of the universe is driven by an even more mysterious thing called dark energy.
shane - 24 Feb 2005 23:08 GMT <snip>
> The object appears to be made mostly of "dark matter," material of an > unknown nature that can't be seen. Again, in the nicest possible way,-- Hoe can something appaear that can't be seen? :) <snip>
 Signature shane And the truth shall set you free.
Mitch Perkins - 24 Feb 2005 22:34 GMT > <snip> > > The object appears to be made mostly of "dark matter," material of an > > unknown nature that can't be seen. > > > Again, in the nicest possible way,-- > How can something appear that can't be seen? :) The question appears to be bothering you. Wish I could answer it.
Mitch
shane - 24 Feb 2005 23:52 GMT >><snip> >> [quoted text clipped - 10 lines] > > Mitch Its not bothering me at all, I just found the phrase amusing as an oxymoron, (the phrase not me, although my somewhat quirky sense of humour gets me into trouble occasionally).
 Signature shane And the truth shall set you free.
Luigi Caselli - 24 Feb 2005 22:46 GMT > <snip> > > The object appears to be made mostly of "dark matter," material of an [quoted text clipped - 3 lines] > Hoe can something appaear that can't be seen? :) > <snip> Maybe from some indirect observation? So it can't appear but only have influence on some other visible objects near to the strange "dark" galaxy... Measuring these effects we can suppose the existence of dark matter..,
Luigi Caselli
shane - 25 Feb 2005 10:22 GMT >><snip> >> [quoted text clipped - 10 lines] > > Luigi Caselli I agree, my point was that we usually use the word appear with things that are visible.
 Signature shane And the truth shall set you free.
syvanen@ucdavis.edu - 25 Feb 2005 20:02 GMT > >><snip> > >> [quoted text clipped - 12 lines] > > > I agree, my point was that we usually use the word appear with things
> that are visible. No oxymoron. Not visible is literally no visible light, ie no photons that activate our vision receptors. What is so difficult about this?
Mike Syvanen
Axel Harvey - 25 Feb 2005 21:48 GMT > I agree, my point was that we usually use the word appear with things
> that are visible. > -- > shane > And the truth shall set you free. Hmmm... It appears that I have missed lunch because of reading silly Usenet again.
Harvest Dancer - 24 Feb 2005 23:03 GMT > <snip> > > The object appears to be made mostly of "dark matter," material of an [quoted text clipped - 6 lines] > shane > And the truth shall set you free. I think you just Watt yourself. There are ways to detect that which cannot be seen.
If you don't believe me, go into any room of your house, close your eyes, and walk until you detect a wall.
Jason Harvestdancer
Glenn - 24 Feb 2005 23:33 GMT > > <snip> > > > The object appears to be made mostly of "dark matter," material of [quoted text clipped - 13 lines] > If you don't believe me, go into any room of your house, close your > eyes, and walk until you detect a wall. I see your point.
shane - 25 Feb 2005 10:23 GMT >><snip> >> [quoted text clipped - 18 lines] > > Jason Harvestdancer But if i keep my eyes closed would the wall appear. I am not against the idea of beig able to detect something by inference, just the invisible 'apperaing'
 Signature shane And the truth shall set you free.
Harvest Dancer - 25 Feb 2005 18:44 GMT > >><snip> > >> [quoted text clipped - 20 lines] > idea of beig able to detect something by inference, just the invisible > 'apperaing' A little known but public fact is that the Stealth Bomber is detectable. You cannot, however, detect it directly by radar.
Due to the prevelance of cell phones and other radio technology, the sky above us is filled with radio communication waves. A stealth bomber will appear as a hole in that canopy. It is useless to try to fire a missile at a hole, but you can detect the stealth bomber's presence by virtue of the hole's presence.
Be against an idea all you want, it doesn't make the idea less true.
Jason Harvestdancer
unrestrained_hand@hotmail.com - 24 Feb 2005 23:32 GMT > <snip> > > The object appears to be made mostly of "dark matter," material of an [quoted text clipped - 6 lines] > shane > And the truth shall set you free. <sigh>
>From the article: "The newfound dark galaxy was detected with radio telescopes." And then: "The well of material rotates too quickly to be explained by the observed amount of gas. Something else must serve as gravitational glue. "
There are many ways to infer the presence of something without seeing it with your eyes. Some ways are more reliable than others.
Or do you believe the furniture in your house disappears when you close your eyes?
Kermit
shane - 25 Feb 2005 10:37 GMT >><snip> >> [quoted text clipped - 27 lines] > > Kermit No, and i am in agreeance that the invisible can be detected by other means, just not generally by it 'appearing' which in normal usage is to do with the visible part of the spectrum. For example, we talk of invisible ink which is visible under UV light, which means that it appears in the visible spectrum under certain circumstances. But the appearance and the visible spectrum are combined. My Chez Watt nomination, which appears to have exceited more interest than it was worth, was aimed at the oxymoron of the invisible being detected by its appearance, not at the science of detecting objects by other than visible means.
 Signature shane And the truth shall set you free.
unrestrained_hand@hotmail.com - 25 Feb 2005 18:54 GMT > >><snip> > >> [quoted text clipped - 29 lines] > > No, and i am in agreeance that the invisible can be detected by other
> means, just not generally by it 'appearing' which in normal usage is to > do with the visible part of the spectrum. For example, we talk of [quoted text clipped - 8 lines] > shane > And the truth shall set you free. Ah, in which case I apologize for talking to you as though you were an idiot. My bad. It appears that you are not...
Kermit
John Wilkins - 25 Feb 2005 22:38 GMT > >><snip> > >> [quoted text clipped - 38 lines] > appearance, not at the science of detecting objects by other than > visible means. It's rather like the curious case of the dog that barked in the night...
 Signature John S. Wilkins john@wilkins.id.au AA#2207 web: www.wilkins.id.au blog: evolvethought.blogspot.com Fiat lunch!
unrestrained_hand@hotmail.com - 26 Feb 2005 03:45 GMT > > >><snip> > > >> [quoted text clipped - 44 lines] > web: www.wilkins.id.au blog: evolvethought.blogspot.com > Fiat lunch! But the dog *didn't bark in... oh.
Yes, yes... I see what you're saying. It does appear that way. The resemblance is striking, or perhaps the non-resemblence. Well, heck, you know what I mean.
Kermit "A man's reach should exceed his grasp, or what's a metaphor?"
TomS - 26 Feb 2005 12:10 GMT "On Sat, 26 Feb 2005 09:38:10 +1100, in article <1gskacm.wxutnr9vxcstN%johnSPAM@wilkins.id.au>, John Wilkins stated..." [...snip...]
>It's rather like the curious case of the dog that barked in the night... "... the curious incident of the dog in the night-time." (From "Silver Blaze")
 Signature ---Tom S. <http://talkreason.org/articles/chickegg.cfm> "... a new kind of phobia which is now widely prevalent among the American public ... pithecophobia, or the dread of apes - especially the dread of apes as relatives or ancestors. ... this phobia has become almost pandemic ..." William K. Gregory, Two Views of the Origin of Man, Science: June 24, 1927
Troels Forchhammer - 28 Feb 2005 09:55 GMT <snip>
> No, and i am in agreeance that the invisible can be detected by other > means, just not generally by it 'appearing' which in normal usage is > to do with the visible part of the spectrum. It is not the object ('the newfound dark galaxy') itself that appears -- it 'appears to be' which has a different meaning that simply 'appears'.
In this case the 'appearance' relates to inferences that appear from the collected data, presumably to the naked eye (though probably a solid amount of interpretation is involved as well <G>).
 Signature Troels Forchhammer Valid e-mail is t.forch(a)email.dk
Your theory is crazy, but it's not crazy enough to be true. - Niels Bohr, to a young physicist
Ernest Major - 24 Feb 2005 23:36 GMT ><snip> >> The object appears to be made mostly of "dark matter," material of an [quoted text clipped - 3 lines] >Hoe can something appaear that can't be seen? :) ><snip> Not having seen the original papers, rather than press reports, I can be certain what is being talked about, but it may be the case that they've detected (seen) the cloud of hydrogen by its radiation (probably at radio wavelengths) and have deduced that a much larger mass of other material is required to be present for it to be gravitationally bound.
 Signature alias Ernest Major
josephus - 25 Feb 2005 01:32 GMT >><snip> >> [quoted text clipped - 10 lines] > radio wavelengths) and have deduced that a much larger mass of other > material is required to be present for it to be gravitationally bound. The article said it was detected by Wales and Pueto Rico. both of these are radio telescopes. They detected 500 million suns worth of hydrogen. that is baryonic matter. Dark matter may be present, but regular matter is there also.
This gas cloud may be a proto galaxy. josephus
josephus
shane - 25 Feb 2005 10:41 GMT >><snip> >> [quoted text clipped - 10 lines] > radio wavelengths) and have deduced that a much larger mass of other > material is required to be present for it to be gravitationally bound. I believe you are correct, but my nomination was not to do with detecting the invisible but with detecting the invisible by its appearing, which normally means being visible. I was nominating the oxymoron not the science behind it.
 Signature shane And the truth shall set you free.
whopkins@csd.uwm.edu - 25 Feb 2005 19:17 GMT > <snip> [including snip of detailed explanation of how it was found]
> Hoe can something appaear that can't be seen? :) Undoubtedly the smiley conveys the awareness of the (intentional?) irony of replying to something with a question that the thing replied to is an answer of.
josephus - 25 Feb 2005 02:03 GMT > I found this fascinating. > [quoted text clipped - 81 lines] > contributes just 4 percent. The rest of the universe is driven by an > even more mysterious thing called dark energy. I note that you clearly separate the dark matter from the baryonic matter... the galaxy is dark but not like dark matter. It has hydrogen. josephus
Gian - 25 Feb 2005 20:13 GMT It must be a very old galaxy that run out of energy. When our sun runs out of energy, it will be dark. When all stars in the milky way run out of energy, out galaxy will be a dark galaxy.
> > I found this fascinating. > > [quoted text clipped - 85 lines] > matter... the galaxy is dark but not like dark matter. It has hydrogen. > josephus Grant Bazan - 28 Feb 2005 01:30 GMT I agree when ALL stars are through converting ALL material from predominantly H to Fe this may occur, but there is no model in existence that can forsee this happening for at least 10^40 years ! All you have to do is compose a simple differential equation describing how compositions change from generation to genetation to show that our meager existence of ~ 13 billion years can in no way give this result.
Grant Bazan
> It must be a very old galaxy that run out of energy. When our sun runs out of energy, it will be dark. When all stars in the milky way run out of energy, out galaxy will be a dark galaxy. > [quoted text clipped - 87 lines] >>matter... the galaxy is dark but not like dark matter. It has hydrogen. >> josephus glbrad01 - 25 Feb 2005 11:46 GMT It could be an ordinary galaxy, just not one within our observable universe's relative horizon or plane.
Brad
Jim Greenfield - 26 Feb 2005 02:18 GMT > It could be an ordinary galaxy, just not one within our observable > universe's relative horizon or plane. > > Brad Passing strange, how this exotic "dark matter" emitts good old standard EMR. So the dust/gas "body" is not emitting in the visible spectrum! All this says is that we need a better understanding of galaxy formation and dynamics, not that this is evidence for the "needed" (to prop GR/BB) "dark matter"
Jim G c'=c+v
glbrad01 - 26 Feb 2005 13:10 GMT >> It could be an ordinary galaxy, just not one within our observable >> universe's relative horizon or plane. [quoted text clipped - 11 lines] > Jim G > c'=c+v Remember back a couple of months ago (Space.com) when embryonic galaxies in formation were discovered where there (observed) should not be enough material matter and energy there in those particular supposed quite empty regions to light a candle much less spark and incubate in growth embryonic galaxy formation. Now we are detecting "see through" transparent--or shadow or ghost--whole galaxies via alternative means. To date I have read much concerning the probable existence of many universes, parallel universes and/or parallel planes of an overall Universe, but not a single thing concerning [more closely parallel] universes probably being interactive--and thus probably being detectable in some way--to some degree.
An oncoming titanic entity (such as a galaxy) into our observable universe might be preceded by a interacting shaped bow wave announcing its pending arrival in our universe. Or alternatively, a galaxy receding away from our observable universe into another, or on to another plane, might leave behind an interacting shaped wake or echo of itself in our universe, on our plane of Universe, for some time after its recession. All I'm really saying is that there has to be much more to the Universe at large, and at small, than we can ever even begin to observe or even to detect; or even to perceive or imagine from any one point, one world, one solar system, or one galaxy, in it.
Brad
George Dishman - 26 Feb 2005 13:24 GMT >> It could be an ordinary galaxy, just not one within our observable >> universe's relative horizon or plane. [quoted text clipped - 3 lines] > Passing strange, how this exotic "dark matter" emitts > good old standard EMR. It doesn't. What is detected is EMR from plain old neutral hydrogen. The Doppler shift also means they can assess the speed at which this disk of hydrogen is spinning. That and the measured size mean there must be 500 times as much of "something else" to hold the disk together. Without the gravity of that "something else", it would fly apart. The "something else" emits nothing detectable, hence it is called dark matter. This is the paper:
http://arxiv.org/abs/astro-ph/0502312
> So the dust/gas "body" is not emitting in the visible > spectrum! The dust/gas is emitting, but that is only 0.2% of the total material. The rest is not emitting and is completely transparent, yet it has as much mass as 100 billion solar systems.
> All this says is that we need a better > understanding of galaxy formation and dynamics, not > that this is evidence for the "needed" (to prop GR/BB) > "dark matter" Current ideas suggest that clumps of dark matter are important in starting the process of galaxy formation but predictions from computer simulations suggest there should be more clumps than there are visible galaxies. I think, putting it simply, when the dark matter clumped, there just wasn't enough hydrogen to go round. That means there should be clumps of dark matter with insufficient hydrogen for stars to form.
What has been found fits that description and if it is confirmed, then it is remarkable confirmation of both the existence of this invisible material and of the computer models that predicted these structures.
George
Friar Broccoli - 26 Feb 2005 16:11 GMT I am writing from talk.origins
>> Passing strange, how this exotic "dark matter" emitts >> good old standard EMR. > > It doesn't. What is detected is EMR from plain old > neutral hydrogen. Thanks for your explanation. Just to add a bit more clarification since there seems to be quite a bit of confusion. (not everyone may have understood)
All normal matter, including specifically hydrogen gas emits light/Electro Magnetic Radiation (EMR). Thus, for example, the walls of your house emit light/EMR in the middle of the night when it is otherwise completely dark. You feel that light/EMR as radiant heat. If you walk close to a window in winter it feels colder because the window is emitting less EMR.
The hydrogen gas from the "invisible" galaxy is emitting even less (lower frequency) EMR than a cold window. This low frequency light is detected as radio waves, but a radio telescope can easily see/detect this light/EMR.
I hope this makes things clearer instead of confusing things even more, I'm never sure.
> I think, putting it simply, when the dark matter clumped, > there just wasn't enough hydrogen to go round. Here I have a question: As you know galaxies and galaxy clusters are arranged in huge sheets. To me these sheets appear to have been formed when very early super-novas exploded and pushed the hydrogen/helium around them into bubble shaped sheets. In this case such an explosion could have pushed most of the gas out of this dark galaxy, before it had time to form stars of its own.
Now, I have not read ANY OF THIS anywhere, I just made it up as an inference from what I do know, but I frequently get things very very wrong. How close is the above to current understanding?
Cordially;
Friar Broccoli Robert Keith Elias, Quebec, Canada Email: kelias (from) clic * net Best programmer's & all purpose text editor: http://www.semware.com
--------- I consider ALL arguments in support of my views ---------
George Dishman - 26 Feb 2005 20:38 GMT >I am writing from talk.origins I'm reading in sci.astro but I'm not an astronomer, just an interested amateur, so my opinions may not be fully accurate. You have been warned ;-)
>>> Passing strange, how this exotic "dark matter" emitts >>> good old standard EMR. [quoted text clipped - 20 lines] > I hope this makes things clearer instead of confusing things even more, > I'm never sure. I think actually it may be confusing as it suggests thermal radiation though you do say "low frequency" so perhaps it's just a matter of presentation. What they are talking about is a very specific emission at a wavelength of 21cm. That is a frequency of 1.4204057 GHz, slightly lower than mobile phones.
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html
Being such a well-defined frequency, very slight changes can be meausured and the Doppler shift of the frequency allows the speed of the gas to be measured.
>> I think, putting it simply, when the dark matter clumped, >> there just wasn't enough hydrogen to go round. [quoted text clipped - 3 lines] > when very early super-novas exploded and pushed the hydrogen/helium > around them into bubble shaped sheets. Radiation pressure from stars blows the gas away:
http://antwrp.gsfc.nasa.gov/apod/ap011230.html
Quasars in the early universe could have created voids. The key thing is that a steadily burning star appies a force over millions of years whereas the blast from a nova lasts weeks to months.
However, the major cause is the effect of gravity as the universe expands. Gravity tends to hold clumps of matter together like the stretching of hot cheese when you pull a pizza apart. The topping doesn't get thinner evenly, the thinnest areas tend to stretch more until they snap. This is a computer simulation of how clouds of hydrogen might have looked, the resulting voids are smaller but it may illustrate the principle.
http://antwrp.gsfc.nasa.gov/apod/ap980224.html
The shock waves from novae tend to pass through the gas and the sudden change is more likely to trigger the formation of stars than to move the gas.
> In this case such an explosion > could have pushed most of the gas out of this dark galaxy, before it > had time to form stars of its own. It seems unlikely because the shock wave would usually cause more stars to form rather than blow the gas away. Even radiation pressure effects are felt over too small a range. The dark galaxy seems to be at least 16kpc across. That's about the same size as our galaxy.
More obviously because there would have to have been stars there in the first place for novae to occur. Only a small proportion of stars (those starting over a certain size) are able to go nova and the rest would still be shining. More likely it never had enough gas for clumps to form.
> Now, I have not read ANY OF THIS anywhere, I just made it up as an > inference from what I do know, but I frequently get things very very > wrong. How close is the above to current understanding? I hope I've added a little but don't take my comments as too well informed, I have lots more to learn :-)
George
Friar Broccoli - 26 Feb 2005 21:48 GMT > I'm reading in sci.astro but I'm not an astronomer, > just an interested amateur, so my opinions may not > be fully accurate. You have been warned ;-) No need to warn me. I'm confident that if you make even the tiniest error someone will step in to make a correction.
> Quasars in the early universe could have created voids. > The key thing is that a steadily burning star appies a > force over millions of years whereas the blast from a > nova lasts weeks to months. [...]
> The shock waves from novae tend to pass through the > gas and the sudden change is more likely to trigger > the formation of stars than to move the gas. I find this argument very convincing ... and I was SO pleased with my little theory :-(.
> However, the major cause is the effect of gravity > as the universe expands. Gravity tends to hold > clumps of matter together like the stretching of > hot cheese when you pull a pizza apart. I find this is a good replacement model.
> More obviously because there would have to have been > stars there in the first place for novae to occur. > Only a small proportion of stars (those starting over > a certain size) are able to go nova and the rest would > still be shining. More likely it never had enough gas > for clumps to form. This I don't buy at all. The Microwave Background Radiation (MBR) clearly suggests uniform initial conditions, at least for "ordinary" matter. Something had to push or pull that gas out of there. However, since you shot down my super-nova theory, I really don't have a good alternative.
> I hope I've added a little but don't take my comments > as too well informed, I have lots more to learn :-) Thanks, I found it a great help.
Cordially;
Friar Broccoli Robert Keith Elias, Quebec, Canada Email: kelias (from) clic * net Best programmer's & all purpose text editor: http://www.semware.com
--------- I consider ALL arguments in support of my views ---------
glbrad01 - 27 Feb 2005 10:20 GMT (snip)
>> More obviously because there would have to have been >> stars there in the first place for novae to occur. [quoted text clipped - 9 lines] > since you shot down my super-nova theory, I really don't have a good > alternative. (snip)
> Friar Broccoli Doesn't have to be "uniform initial conditions." Just 'uniform condition' will do (the average of all the varying local conditions lifted in dimension and placed in uniform opposing background to all locals). No initial condition. Not everything has to have, or has to have had, "initial conditions." The Universe is in the category of no initial conditions as one time event. It is uniformly primordial (relative to us) right now at (inside) the constant of the Planck event horizon.
Look at any illustration that takes you down from galaxies in compotent elements, down through all component element makeup to the atomic and subatomic levels, descending down and down to until reaching quantum chaos at the lowest order of magnitude relative to us. Then look at any illustration that takes you up and out into the large, taking you back in time, observationally, in taking you up and out, back and ever farther back until the illustration reaches the picture of...chaos (the identical squiggles always illustrated as the event horizon of chaos of the supposed Big Bang as is always illustrated for the event horizon of quantum chaos). A forever constant of primordial "initial conditions" existing (the primordial infinite in the primordial infinitesimal, as common throughout the Universe at small--thus throughout the Universe at large--as common can get). So no "initial conditions" ever having existed as a one time, and one time only, event.
Brad
Ulf Torkelsson - 28 Feb 2005 08:57 GMT > > [quoted text clipped - 14 lines] > > There are inhomogeneties in the universe at the time that the microwave background is formed, and we see them as the anisotropies of the microwave background. In particular the dark matter, which is not affected by the electromagnetic radiation can start to collapse and form clumps already before the decoupling of ordinary matter with the radiation. After the decoupling, matter will start to fall into the potential wells that are created by these clumps, and these are the regions where we will see the formation of galaxies. Incidentally it is natural in this model that the galaxies form in thin sheets, because it is likely that there will be one direction in which the collapse is faster than in the other directions, and then effectively the gas will compress first in this direction to two-dimensional sheets.
Ulf Torkelsson
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