[math-fun] oldest stars?
[math-fun] oldest stars?
You can read the methodology here http://arxiv.org/abs/astro-ph/0703414 but it looks like they rely on earlier work for relative abundance. See, for example, http://iopscience.iop.org/0004-637X/591/2/936/fulltext/
--the age estimates depend on knowing "initial" isotope ratios. These are then compared with "now." The initial ones seem to me to be a complete guess -- they say vaguely there are "theoretical models" of what they ought to be. Well, that seems to me to be dubious, especially if we are talking about 1 specific star's initial values, as opposed to say, the whole universe average at some time. So: I have trouble believing they can date single stars that old that accurately. However, on the bright side, they have about 5 different kinds of isotope "clocks" they were able to examine on this star, each checking on the others. That makes things sound better. On 2/12/14, math-fun-request@mailman.xmission.com <math-fun-request@mailman.xmission.com> wrote:
Send math-fun mailing list submissions to math-fun@mailman.xmission.com
To subscribe or unsubscribe via the World Wide Web, visit http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun or, via email, send a message with subject or body 'help' to math-fun-request@mailman.xmission.com
You can reach the person managing the list at math-fun-owner@mailman.xmission.com
When replying, please edit your Subject line so it is more specific than "Re: Contents of math-fun digest..."
Today's Topics:
1. Re: Connected components in random Cartesian mazes (Dan Asimov) 2. oldest stars? (Warren D Smith) 3. Simple model of Earth magnetic field, which sounded promising for a little while (Warren D Smith) 4. Resistor network puzzle (Tom Karzes) 5. Re: oldest stars? (Charles Greathouse)
----------------------------------------------------------------------
Message: 1 Date: Wed, 12 Feb 2014 11:28:05 -0800 From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Connected components in random Cartesian mazes Message-ID: <2A761C13-86D5-462A-A60B-027D55622367@earthlink.net> Content-Type: text/plain; charset=us-ascii
< http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords...
.
On Feb 12, 2014, at 6:55 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Perhaps it would be difficult to reproduce this experiment today.
Is it even possible to purchase carbon paper anymore?
I heard a program on NPR (Planet Money, perhaps?) where they said that the last bastion of carbon paper was India, where the govt still records lots of official stuff typed on paper with carbon duplicates/triplicates/...
At 02:25 PM 2/11/2014, Richard E. Howard wrote:
The most fun paper in this field (in my opinion) is by Last and Thouless in 1971.
In this era of Higgs Boson-sized experimental budget, it is a study in elegance. They punched carefully randomized holes in carbon paper (2D conducting sheet) and measured the resistivity as a function of hole density.
The experiment trumped the theory at the time and the apparatus (for once) actually cost less than the pencil/paper theory...
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
------------------------------
Message: 2 Date: Tue, 11 Feb 2014 19:48:50 -0500 From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] oldest stars? Message-ID: <CAAJP7Y3aK0UAr0A06PTEdmW+MNyo+5yqTHoBDRUrq-BU0zRJfA@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
New York Times science section today discusses very old stars, in our galaxy, found by searches for ones with very small iron content. They then claim the oldest confirmed age of a star is 13.2 Gyr, confirmed by use of uranium and thorium half-lives. http://phys.org/news98033554.html
QUESTION: Huh? How can you date a star by measuring its U and Th isotope content? It seems to me you'd have to know its isotope ratios when it started, and you don't.
Obviously, these stars are not the oldest, since they contain iron that came from still-older stars -- but they come close to being first generation.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
------------------------------
Message: 3 Date: Wed, 12 Feb 2014 15:25:07 -0500 From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Simple model of Earth magnetic field, which sounded promising for a little while Message-ID: <CAAJP7Y06tu1dXAf8XM-ZWOKhc-soz9YRcXDGweP1g6p4atTmEQ@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
The Cambridge Encyclopedia of Earth Science claims what generates the Earth's magnetic field is not understood. Here I suggest a simple model.
FACTS: 1. The field is roughly a dipole pointed approximately North, and at previous times in Earth history has pointed approximately South instead. North and South (with respect to rotation axis) appear to be stable states, but pointing in other directions (or nonexistent field) appears to be an unstable state which quickly vanishes and is replaced by one of the two stable states. This historical record is revealed by magnetism trapped in volcanic rocks at time of formation, versus that time. You can see a graphic in http://en.wikipedia.org/wiki/Geomagnetic_reversal which shows 9 N-pointing and 9 S-pointing periods occurred during the last 5 Million years, each with apparently-random durations.
There may also have been additional switchovers with short durations. The short ones are hard to detect. The best known such short-duration event was the "Laschamp event" in about the year 39000 BC, a reversal lasting only about 440 years with the actual change of polarity lasting around 250 years. The reversed field was 75% weaker and the strength dropped to only 5% of the current strength during the transition. This resulted in greater radiation reaching the Earth, causing greater production of beryllium 10 and higher levels of carbon 14. Perhaps these short events are best regarded as failed attempts to reverse -- we drop to a low field state, and then that state is attracted to the two N- or S-pointing stable states. If attracted back to the original one then we get a "failed reversal" instead of a genuine reversal.
The switchover-times are each <=50,000 years. There was at least one 40 million year span containing no reversal, but overall average has been about 2.2 reversals per million years.
2. The Moon has only tiny magnetic field, mostly a few nanoTesla. (Versus: Earth's is 25-65 microTesla.) Comparably-tiny fields: Mars, Venus. Intermediate strength: Mercury. Jupiter's field is 10X Earth's. Saturn also has a strong field. Uranus and Neptune have large magnetic fields, but they are not well axis aligned.
MY MODEL: The field is generated by a "dynamo" from convection currents of hot electrically conductive fluid inside the planet. Moon and Mars have no field since they have no such internal convection currents, they are geo-tectonically dead in the sense they have no volcanos (although Mars at an earlier time did have volcanos) and no plate tectonics, indicating internal convection currents are much weaker and less-well defined (i.e. tend to cancel out over time averaging). Venus still has active volcanos, but its lack of magnetic field will be explained below. Mercury's, Saturn's, and Jupiter's fields are presumed to be generated by same mechanism as Earth's. The more gravity and more internal heat a (non-dead) planet has, the more powerful its convection and hence more powerful its fields -- also axis alignment more-perpendicular to planet-sun direction helps generate more field for reason explained below -- all explaining why Mercury<Earth<Saturn<Jupiter.
Now my claim is that the convection currents flow outward from core toward equator. The fluid then cools, and drops back to the core from the poles. This requires that (and is predicted by) the poles tend to exert more cooling effect than the equator.
If so, then a N- or S-pointing magnetic field, will induce (via Lorentz force) an equator-circling electrical current, This in turn will reinforce the field. Result is a stable "dynamo" powered ultimately by internal heat (radioactively generated and/or left over from planet formation). For Earth, situation is complicated by the presence of oceans over thin crust, and continents over thick crust. Presumably there is more cooling in the ocean regions and/or volcanic regions. Also there are "hot spots" such as Hawaii. Also the Earth's rotation axis precesses and is not exactly perpendicular to the Earth-sun line. All this complexity, plus fluid "turbulence," presumably has something to do with why we get occasional reversals. I would presume the field continually fluctuates and whenever (rarely) a fluctuation is comparable to the field itself, then we are ready for either a reversal or failed-reversal.
In the case of Venus, there are no plate tectonics (although there is volcanism) and there is a huge atmosphere which redistributes heat efficiently, meaning the equator may not have a much greater cooling effect than the poles.
For Uranus and Neptune the sun is so far away that its thermal effects are pretty negligible, explaining why their fields are not axis aligned (and Uranus has a huge axial tilt too, so even if the sun's heat non-negligible, that'd still mostly cancel out its effects).
SO???
That seemed pretty easy. Why wasn't this thought of ages ago?
Too shed light on that, let's do some crude numerical calculations. Assume convection speed of v = 1 cm/year -- same order as continent drift speeds. Total voltage induced circling equator (25000 mile circumf.) then is of order v * (50 microTesla) * (25000 miles) = 6.4 * 10^(-7) volts. Assuming 40 ohm*meter electrical resistivity for lava (this was a Hawaii measurement) the earth going round the equator is about a 10^(-5) ohm resistor. [However it actually is found that high pressures and high temperatures both act to decrease resistivity for molten rock apparently like Arhennius law exp(const/T), plus there are stairsteps caused by temperature surpassing ionization-energy thresholds.]
So this voltage would induce a current circling equator of order 0.06 Amps. That in turn would cause a magnetic dipole moment of about 8*10^12 * meter^2 * ampere which is 10^10 times smaller than the actual Earth dipole moment 8*10^22 * meter^2 * Ampere.
Oops. It seems still within the reasonable realm that the resistivity might be only 1 ohm*meter and the flow speed might be 10 cm/year. This would increase our predicted dipole moment by a factor of 40*10=400. The flow speeds necessarily will be larger still nearer the center of the Earth due to volumes being smaller there, and the magnetic fields there might be much larger due to larger currents at smaller distances. So assuming both 10X greater flow speed and magnetic field down there, we could get another factor of a few hundred. But this is still well short of the required 10^10 factor.
CONCLUSION: The model sounded great for a little while, but it is predicting too small fields compared to observation. What went wrong??
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
------------------------------
Message: 4 Date: Wed, 12 Feb 2014 12:43:15 -0800 From: Tom Karzes <karzes@sonic.net> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Resistor network puzzle Message-ID: <21243.56547.61304.994729@gargle.gargle.HOWL> Content-Type: text/plain; charset=us-ascii
This reminds me of an old puzzle:
You have an infinite square grid of 1 ohm resistors. What is the resistance between two adjacent nodes in the grid?
More precisely, you have an infinte square grid of nodes. Each horizontally adjacent pair of nodes is joined by a 1 ohm resistor, and each vertically adjacent pair of nodes is joined by a 1 ohm resistor. What is the resistance between two adjacent nodes (either horizontal or vertical)?
Tom
Richard E. Howard writes:
The most fun paper in this field (in my opinion) is by Last and Thouless in 1971.
In this era of Higgs Boson-sized experimental budget, it is a study in elegance. They punched carefully randomized holes in carbon paper (2D conducting sheet) and measured the resistivity as a function of hole density.
The experiment trumped the theory at the time and the apparatus (for once) actually cost less than the pencil/paper theory...
--R
------------------------------
Message: 5 Date: Wed, 12 Feb 2014 16:07:47 -0500 From: Charles Greathouse <charles.greathouse@case.edu> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] oldest stars? Message-ID: <CAAkfSGJx0aDsGx9vHyrriG8X7FRF0XendAUKsZP5e1EotocfSA@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
You can read the methodology here http://arxiv.org/abs/astro-ph/0703414 but it looks like they rely on earlier work for relative abundance. See, for example, http://iopscience.iop.org/0004-637X/591/2/936/fulltext/
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Tue, Feb 11, 2014 at 7:48 PM, Warren D Smith <warren.wds@gmail.com>wrote:
New York Times science section today discusses very old stars, in our galaxy, found by searches for ones with very small iron content. They then claim the oldest confirmed age of a star is 13.2 Gyr, confirmed by use of uranium and thorium half-lives. http://phys.org/news98033554.html
QUESTION: Huh? How can you date a star by measuring its U and Th isotope content? It seems to me you'd have to know its isotope ratios when it started, and you don't.
Obviously, these stars are not the oldest, since they contain iron that came from still-older stars -- but they come close to being first generation.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
------------------------------
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
End of math-fun Digest, Vol 132, Issue 29 *****************************************
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
participants (1)
-
Warren D Smith