The Dark Tower; density? (APOD 08 May 2008)

[neufer]

http://apod.nasa.gov/apod/ap080508.html

http://en.wikipedia.org/wiki/The_Dark_T ... 7_novel%29

<<The Dark Tower is a novel written by C. S. Lewis that appears to be the beginning of an abandoned science fiction novel intended as a sequel to Out of the Silent Planet. The story deals with an early rendition of interdimensional travel. A fictional Lewis himself narrates but Elwin Ransom appears as a supporting character. The story begins with a discussion of time travel among several academics at a university (subsequently identified as Cambridge) during summer vacation. They conclude that it is impossible to violate the laws of space-time in such a way. However, after the discussion, one of the men (Orfieu) unveils an invention he believes allows people to see through time. The group uses this "chronoscope" to observe an alien world they call "Othertime" (he does not know if it is future or past), where a group of human automatons work to construct a tower at the bidding of the story's villain, the Unicorn, a devilish character with a single horn growing out of his forehead. The Unicorn stings people, apparently volunteers, causing them to become automatons (the "Jerkies").>>

[BMAONE23]

Interesting Neufer,
I'll have to look that one up. I was thinking along Stephen Kings 7 book series The Dark Tower. Very similar in some respects.

[Sputnick]

Hey you whoever wrote the blurb for this 'dark tower' photo you have some weird imagination, get outside more often, along the riverside or somewhere .. it looks to me more like a skeletal fish. I also wish whoever writes the blurbs would stop writing as if apod viewers were 8 year olds.

Thanks for the story line, Neufer. It seems the Chronoscope was looking at today's society, and the unicorn is the advertising industry injecting us with desire for more, more, more, more of every material thing, which is easy to do as most of us are automatons having no life or soul, surrounding ourselves with shiny toys that present an image of life and respectability.

[trackcoach]

My students want to get an idea of the density of the Dark Tower and other features like reflection and emmision nebulae.

[neufer]

My students want to get an idea of the density of the Dark Tower and other features like reflection and emission nebulae.

Knowing the density of the sun and it's diameter in light seconds;
how dense would a 25 solar mass Bok globule be
contained in a sphere the diameter of a light year?

Using that estimate how dense should The Dark Tower be?
--------------------------------------------
Bok globule (From Wikipedia)
http://en.wikipedia.org/wiki/Bok_globule

<<A Bok globule is a dark cloud of dense dust and gas in which star formation takes place. Bok globules are found within H II regions, and typically have a mass of about 10–50 solar masses contained within a region about a light year or so across. They contain molecular hydrogen (H2), carbon oxides and helium, and around 1% (by mass) of silicate dust. Bok globules most commonly result in the formation of double or multiple star systems.

Bok globules are still a subject of intense research. Known to be some of the coldest objects in the natural universe (as cold as 3 kelvins) their structure and density remains somewhat a mystery. Methods applied so far have relied on column density derived from near infrared extinction and even star counting in a bid to probe these objects further.>>
--------------------------------------------

[bystander]

Hey you whoever wrote the blurb for this 'dark tower' photo you have some weird imagination, get outside more often, along the riverside or somewhere .. it looks to me more like a skeletal fish. I also wish whoever writes the blurbs would stop writing as if apod viewers were 8 year olds.

It seems you lack imagination, after all. Rotate the picture 100 degrees clockwise. There's your tower. As for 8 yo, is that too high a level for you?

[Sputnick]

Too high a level eh Bystander! Ha Ha Ha. I'll bet you couldn't even see the skeletal fish As far as turning the picture, I consider it far too dangerous to tip my monitor sideways Let's just be cool, eh 8) Drink some Kool Aid Drop the tirade Let the past fade rap the present and hit the get-sent (that's 'sub-mit' for the nit- wits)

[iamlucky13]

I'll bite on neufer's suggestion.

The sun has a mass of 2.0 x 10^30 kilograms.
A light-year is 9.5 x 10^9 km.

So the volume of a 1 light-year sphere is 4.5 x 10^29 cubic kilometers.

Our hypothetical 25 solar mass Bok globule then has a density of about 110 kilogram per cubic kilometer. Easier to visualize, perhaps, would be per cubic meter. Divide by 1000^3 and convert to grams:

0.00011 grams per cubic meter.

The air around us, on the other hand, has a density of about 1200 grams per cubic meter, or over 10 million times as much.

Yet, even this is perhaps 1000 to a million times as dense as the space around it.

Here's more info. I believe the Dark Tower would be classified as a molecular cloud.

http://en.wikipedia.org/wiki/Interstellar_medium

[iamlucky13]

I see the dragon from Neverending Story.

[Sputnick]

Einstein - Bah Humbug - 10 years to correct his errors - my errors will NEVER be corrected. (That's why I gotta rely on grace, eh)

[JohnD]

I think that CS Lewis, a most scholarly academic, was referring in his title to the poem, "Childe Roland to the Dark Tower came" by Browning, who in turn took it from King Lear and the words,
"Child Rowland to the dark tower came,
His word was still 'Fie, foh, and fum
I smell the blood of a British man."

Bet you didn't know that nursery rhyme was from Shakespeare!
Though William may be been quoting a child's rhyme, as his character was feigning madness.

The motif has been used by lesser (Stephen King) and not so lesser (Tolkein) authors since.
Actually, there may be a PhD thesis in that!
Start with Lewis and Tolkein, both Oxford dons and members of the Inklings, a literary club atthe Universty in the '30s, who both write works that use "The Dark Tower" as motif! See Wiki: http://en.wikipedia.org/wiki/Inklings

End of aside.

I really posted to ask - the astronomical Dark Tower is said to be part of a 'stellar association'.
See Wiki also: http://en.wikipedia.org/wiki/Stellar_association
There, this is described as, "10 to 100 or more stars ..... [sharing] a common origin, but have become gravitationally unbound and are still moving together through space."

How is this different from a globular cluster? Not in origin, but a cluster includes stars that orbit a common gravitational centre - they are close enough to be gravitationally bound. How can a group of stars that are as close or closer than those in a cluster be "gravitationally unbound"?

John

[bystander]

I really posted to ask - the astronomical Dark Tower is said to be part of a 'stellar association'.
See Wiki also: http://en.wikipedia.org/wiki/Stellar_association
There, this is described as, "10 to 100 or more stars ..... [sharing] a common origin, but have become gravitationally unbound and are still moving together through space."

How is this different from a globular cluster? Not in origin, but a cluster includes stars that orbit a common gravitational centre - they are close enough to be gravitationally bound. How can a group of stars that are as close or closer than those in a cluster be "gravitationally unbound"?

I think the difference is in quantity. 'Stellar associations' contain 10's or 100's of stars, 'open clusters' contain 1,000's or 10,000's of stars, and 'globular clusters' contain 10,000's or 100,000's of stars. The fewer the stars, the lesser the association (less stellar mass, less gravitational attraction).

[BMAONE23]

It likely may have something to do with the fact that the Bound stars orbit eash other En-mass while the unbound stare have no discernable central orbit.

[Pete]

A light-year is 9.5 x 10^9 km.

So the volume of a 1 light-year sphere is 4.5 x 10^29 cubic kilometers.

Caution! A light-year is 9.46 trillion kilometers: 1 ly = 9.46 x 10^12 km, and a sphere of radius 1 ly encloses a volume of 3.5 x 10^39 km^3. A 25-solar mass sphere would have a mean density of 1.4 x 10^-17 kg / m^3, one hundred million billion (10^17, but you have to say it like Dr. Evil from Austin Powers!) times less dense than air at sea level, which has a density of ~1.2 kg / m^3.

Taking the Milky Way's mean interstellar medium density to be something like 10^6 gas (hydrogen) atoms per cubic meter, or roughly 7 x 10^-21 kg / m^3, a hypothetical 25 solar mass, 1-ly Bok globule would be roughly 2,000 times denser than typical ISM. That's still far less dense than the best possible lab vacuum, making it difficult to get an intuitive sense of the densities of objects like the Dark Tower.

[neufer]

I think that CS Lewis, a most scholarly academic, was referring in his title to the poem, "Childe Roland to the Dark Tower came" by Browning, who in turn took it from King Lear and the words,
.
"Child Rowland to the dark tower came,
His word was still 'Fie, foh, and fum
I smell the blood of a British man."
.
Bet you didn't know that nursery rhyme was from Shakespeare!
Though William may be been quoting a child's rhyme, as his character was feigning madness.

<<Child Rowland (or Roland) is a hero of an old Scottish ballad. From such references as are preserved, it would seem that the ballad tells of a young lad, guided by Merlin, seeking in Elf-land his kidnapped sister and gaining her through great peril. The actual ballad is lost and "Poor Tom" may here be reciting the first line. From the heroic old ballad, "Poor Tom" passes to the stock exclamation attributed to villainous giants on the track of a hiding hero.>> - Asimov's _Guide to Shakespeare_

[neufer]

A light-year is 9.5 x 10^9 km.

So the volume of a 1 light-year sphere is 4.5 x 10^29 cubic kilometers.

Caution! A light-year is 9.46 trillion kilometers: 1 ly = 9.46 x 10^12 km, and a sphere of radius 1 ly encloses a volume of 3.5 x 10^39 km^3. A 25-solar mass sphere would have a mean density of 1.4 x 10^-17 kg / m^3, one hundred million billion (10^17, but you have to say it like Dr. Evil from Austin Powers!) times less dense than air at sea level, which has a density of ~1.2 kg / m^3.

Taking the Milky Way's mean interstellar medium density to be something like 10^6 gas (hydrogen) atoms per cubic meter, or roughly 7 x 10^-21 kg / m^3, a hypothetical 25 solar mass, 1-ly Bok globule would be roughly 2,000 times denser than typical ISM. That's still far less dense than the best possible lab vacuum, making it difficult to get an intuitive sense of the densities of objects like the Dark Tower.

This is about right although the problem as posed:

Knowing the density of the sun and it's diameter in light seconds;
how dense would a 25 solar mass Bok globule be
contained in a sphere the diameter of a light year?

Using that estimate how dense should The Dark Tower be?

Discusses a Bok globule with DIAMETER (not radius) of a light year.

I was hoping that some would know that
there are about 30,000,000 seconds in a year
and that the sun is about
a million miles (~ 5 light seconds) in diameter .

So 1 sun (with an average density of water)
would be expanded 6,000,000 times linearly
or 216 x 10^18 in volume.

A 25 solar mass Bok globule:
25 suns/ (216 x 10^18) ~ 10^-19 water density.

1000 cc's of water & 1 cubic meter of air STP both weigh
about 1 kg so we are dealing with ~10^-16 air density.

Loschmidt's number (the number of molecules in one cubic centimeter
of an ideal gas at standard temperature and pressure) = 2.7 × 10^19

so one is talking about 2700 N2 sized molecules per cc
vs. ~0.1 hydrogen atom per cubic centimeter in interstellar space.

The more massive Dark Tower is
about 40 times bigger (linearly)
than our Bok globule but equally opaque
so maybe just 2700/40 ~ 65 N2 sized molecules per cc here
vs. ~0.1 hydrogen atom per cubic centimeter in interstellar space.

[astrolabe]

Okaaay......who are you really and what have you done with Art Neuendorffer?

[iamlucky13]

A light-year is 9.5 x 10^9 km.

So the volume of a 1 light-year sphere is 4.5 x 10^29 cubic kilometers.

Caution! A light-year is 9.46 trillion kilometers: 1 ly = 9.46 x 10^12 km, and a sphere of radius 1 ly encloses a volume of 3.5 x 10^39 km^3. A 25-solar mass sphere would have a mean density of 1.4 x 10^-17 kg / m^3, one hundred million billion (10^17, but you have to say it like Dr. Evil from Austin Powers!) times less dense than air at sea level, which has a density of ~1.2 kg / m^3.

Taking the Milky Way's mean interstellar medium density to be something like 10^6 gas (hydrogen) atoms per cubic meter, or roughly 7 x 10^-21 kg / m^3, a hypothetical 25 solar mass, 1-ly Bok globule would be roughly 2,000 times denser than typical ISM. That's still far less dense than the best possible lab vacuum, making it difficult to get an intuitive sense of the densities of objects like the Dark Tower.

D'OH!

Thanks