Granite Cooling

"For the conductivities chosen here, no 800 °C intrusion, no matter how large, can maintain against conduction an anomaly greater than 200 °C within 5 km of the surface for more than 4 m.y." — Lawrence Cathles, Economic Geology 75th Anniversary Volume, 1981¹

"Simple thermal considerations preclude the possibility that a magma chamber the size of the Half Dome pluton could have existed as a liquid at shallow crustal depths for that long." — Drew Coleman, Walt Gray and Allen Glazner, Geology, 2004²

Summary

A batholith like the Sierra Nevada is a stack of granite bodies tens of kilometres thick, and its magma arrived at 700 to 900 °C.  This article asks how long that rock took to cool.  A global Flood gives it about a year.  The young-earth literature gives it either 3,000 years or 6 to 10 days, depending on which paper is open.

Nine conclusions, stated first.

1. The creationists are right that granite magma moves fast. Nick Petford and colleagues wrote in Nature in 2000 that after partial melting, "the follow-on stages of segregation, ascent and emplacement can be geologically extremely rapid—perhaps even catastrophic."³ A pluton less than a kilometre across can fill in under 40 days. Kevin Henke, their sharpest critic on this topic, concedes it.⁴
2. They are right that there was never one giant magma chamber. Coleman, Gray and Glazner showed in 2004 that the Tuolumne Intrusive Suite in Yosemite was built from many small injections, "perhaps as sheets or dikes."² What the creationists leave out is the other half of the same paper: the injections span at least 10 million years, and the zircon ages fall in map order from the outer contact to the core.
3. They are right that water cools rock faster than rock does. Snelling and Woodmorappe's headline number, 3,000 years for a batholith 16.5 km thick, is Cathles' own chart read correctly at 5.5 times his worked example. The arithmetic is not the problem.
4. But 3,000 years is 3,000 Flood years, and it is not "cooled." Cathles' chart measures the time to shed 75 per cent of the initial temperature contrast. An 800 °C body in 200 °C rock is still at 350 °C when that clock stops. Snelling and Woodmorappe say so, and they decline to claim cooling within the Flood: "This discussion does not imply that all of the large batholiths had cooled by the time they were uplifted after the Flood."⁵
5. The 6 to 10 days in Snelling's later papers is not a thermal result. It comes from polonium half-lives in radiohalos. The same 2008 paper that concludes 6 to 10 days quotes 30,000 years for conduction and 3,500 to 5,000 years for the fastest hydrothermal model it knows, and never reconciles them. Snelling 2005 also cites the 1998 paper as having shown cooling "within the time limits of the Flood year,"⁶ which the 1998 paper says it does not show.
6. Conduction alone takes 100,000 to 10 million years for a body kilometres thick. J. C. Jaeger's 1957 solution, with latent heat included, gives complete solidification of a granite sheet in 0.016 D² years with D in metres:⁷ 400,000 years for 5 km, 6.4 million for 20 km. Turcotte and Schubert's textbook gets 10.9 days for a 2 metre dike by the same physics.⁸ Cathles' ceiling for any intrusion near the surface is 4 million years, so the honest mainstream number is millions of years, not hundreds of millions.
7. Water cannot buy the missing factor of a thousand. By Cathles' own scaling law, a batholith that reaches his 75 per cent mark in one year needs 28 to 70 darcies of permeability through its whole thickness. Measured granite tops out at 100 millidarcies. Lister's theoretical maximum for freshly cracked rock is about 10 darcies, and his cracking front advances at about 30 metres a year, so the centre of a 16.5 km body is not even permeable for 275 years. The creationists concede that the permeability of a cooling granite is unknown.
8. The rock keeps its own clocks, and they run in temperature order. Zircon ages across the Tuolumne suite span 95 to 85 million years, and its six precise ages fall in map order with error bars of 0.1 to 0.8 million years. Sierra Nevada granite crystallised at 125 to 80 million years by uranium-lead and passed through 45 to 75 °C at 40 to 85 million years by helium in apatite. A body cooled in a week would give every thermometer the same date. Russell Humphreys' own helium model, in the same RATE volume as Snelling's chapter, caps Flood-year granite at about 90 °C above today.⁹
9. Granite's own heat is the small heat problem. The California arc holds about 0.7 million cubic kilometres of granite.¹⁰ Cooling it in a year releases about 1.7 × 10²⁴ joules, about 105 watts per square metre of the whole Earth. One arc is survivable on paper; ten are not. Either way it is orders of magnitude below the heat of catastrophic plate tectonics and accelerated decay. The granite problem is not radiating the heat. It is conducting it out of kilometres of rock.

Verdict.  Rapid emplacement is real and mainstream.  Rapid cooling is not.  Conduction, convection and thermochronology all put a batholith's cooling at 10⁴ to 10⁷ years.  A Flood year misses by three to seven orders of magnitude.

Part 1: What the young-earth case gets right

The creationist granite literature is Andrew Snelling and John Woodmorappe's 1998 paper for the International Conference on Creationism, Snelling's 2005 RATE chapter on radiohalos, his 2008 paper in Answers Research Journal, and Tas Walker's two Journal of Creation pieces of 2003 and 2007.^56111213  Four of its claims are sound.

Magma rises fast

The old picture had granite magma rising as a slow blob over millions of years.  Petford, Cruden, McCaffrey and Vigneresse retired that picture in Nature in 2000.³  Their abstract:  "far from being geologically sluggish—granite magmatism is a rapid, dynamic process operating at timescales of ≤100,000 years, irrespective of tectonic setting."³  Their Table 1 puts ascent by dike flow at 10⁻¹ to 10² years, and their filling arithmetic gives "lower and upper bounds on pluton filling times of less than 40 days to more than 1 Myr for plutons less than 1 km to more than 100 km across."³

Snelling 2008 quotes this accurately.¹¹  Henke's 1999 reply to Snelling and Woodmorappe⁴ grants it:  "Geologists should accept the possibility of fast emplacement by dikes because it's based on good data.  Modern uniformitarianism (actualism) must accept any scientifically valid evidence, whether it supports rapid events and natural catastrophes or slow processes and old events."⁴

Plutons are built in pieces

Glazner, Bartley, Coleman, Gray and Taylor wrote in GSA Today in 2004.¹⁴  Their abstract:  "Field and geochronologic evidence indicate that large and broadly homogeneous plutons can accumulate incrementally over millions of years.  This contradicts the common assumption that plutons form from large, mobile bodies of magma."¹⁴  Coleman, Gray and Glazner's companion paper in Geology² concludes that the Tuolumne data "are consistent with emplacement as a series of small intrusions, perhaps as sheets or dikes."²

The popular creationist article of 1998¹⁵ said much the same:  "many plutons are only a few kilometres thick, and some are made up of thin (100–1,000 m) sheets stacked on top of one another."¹⁵  A thin sheet cools far faster than a blob of the same volume.  What the incremental model costs the creationists is in Part 5.

Water cools rock faster than rock does

Rock is a poor conductor.  Water moving through cracks carries heat away much faster.  Norton and Knight's 1977 paper in the American Journal of Science¹⁶ ran eight two-dimensional models of a pluton emplaced at 920 °C and found that convection takes over from conduction once host-rock permeability passes 10⁻¹⁴ cm², about a thousandth of a millidarcy.¹⁶  Cathles' 1977 paper in Economic Geology¹⁷ added boiling and found that "Cooling is dramatically accelerated as permeability is increased."¹⁷  Both papers are cited correctly for the mechanism throughout the creationist literature.

The creationists also get the heat capacity right.  Their popular summary says that "A large granite body will heat to boiling point only about its equivalent mass in water."¹⁵  A kilogram of granite cooling from 800 to 100 °C releases about 7 × 10⁵ joules of sensible heat plus about 3 × 10⁵ of latent heat, so about 10⁶ joules.  Heating a kilogram of water from 20 to 100 °C takes 3.3 × 10⁵ joules, and boiling it another 2.3 × 10⁶.  So a kilogram of granite brings three kilograms of water to the boil, or turns 0.4 kilograms to steam.  There is enough water on Earth.  The question is whether it can get through the rock, and that is Part 4.

Crystal size is not a clock

Textbooks used to teach that coarse grain means slow cooling.  Walker's 2003 paper collects good field evidence against that rule.¹²  Granitic dikes far thinner than the plutons they cut are still visibly crystalline.  Pegmatites carry crystals of centimetres to metres in bodies far smaller than the plutons they intrude, which is larger crystals in the faster-cooling body.  Snelling 2008 adds measured growth rates:  a 5 mm plagioclase crystal "could have grown in as short a time as one hour, but probably no more than 25 years."¹¹  This article grants all of it.  Big crystals do not prove long times.  The timescale comes from heat transport, not texture.

Part 2: The young-earth claim, number by number

The creationist literature makes two different claims about cooling time, and they differ by five orders of magnitude.

1998: three thousand years

Snelling and Woodmorappe's 1998 paper is the only young-earth thermal model of a batholith.  Its case is hydrothermal convection, with permeability setting the rate.  The headline result, from their Figure 3:  "An infinitely-long batholith that is 11 km wide, 16.5 km thick, and is buried 20 km below the surface of the ground, when at zero rock permeability (that is, conductive cooling only) needs a few million years to cool.  But with the intensity of convective cooling that is allowed by a permeability K of 10 millidarcies (easily exceeded—see below), the time to cool this batholith falls to a mere 3,000 years."⁵

Figure 3 is redrawn from Figure 6 of Cathles' 1981 chapter in the Economic Geology 75th Anniversary Volume, and the number can be checked against it.¹  Cathles' worked example is an intrusion 2 km wide and 3 km high with its top 3.66 km down:  "about 100,000 years" by conduction alone, "about 20,000 years" at 0.25 millidarcies, and "about 5,000 years" at 1 millidarcy.¹  Every dimension of Snelling and Woodmorappe's batholith is exactly 5.5 times Cathles'.  Cathles states his two scaling laws in words:  for conduction, "an intrusive body twice the size of, but of similar geometry to, another will take four times as long to cool";¹  for convection, "the time to cool should be directly proportional to scale (i.e., the height of the intrusion, H) and inversely proportional to permeability, k'."¹

So conduction gives 100,000 × 5.5² = 3.0 million years, their "a few million years."  Convection at 10 millidarcies gives 5,000 × 5.5 × (1 / 10) = 2,750 years, their "a mere 3,000 years."  Cathles' appendix formula, run from his own anchor of 15,400 years at 2.25 km height and 0.25 millidarcies,¹ gives 2,823 years.  The creationist number is not a misreading.  It is Cathles' number, correctly rescaled.

Two things about it are easy to miss.  First, what the chart measures.  Cathles' caption says the diagram gives "the time required for an intrusive body to cool by either conduction or ground-water convection to 25% of its initial temperature contrast relative to ambient."¹  Snelling and Woodmorappe say so too:  "the cooling in Figure 3 starts with solidus temperatures and ends at 25% of the difference between ambient temperatures and solidus temperature.  The remainder of the cooling to ambient crustal temperatures is not covered by Figure 3 …"⁵  So the 3,000 years excludes the superheat and latent heat above the solidus, and excludes the last quarter of the drop.  An 800 °C body in 200 °C rock is at 350 °C when that clock stops.

Second, what the paper claims.  It does not claim cooling inside the Flood:  "This discussion does not imply that all of the large batholiths had cooled by the time they were uplifted after the Flood."⁵  The popular version in Creation magazine commits to the same figure:  "Less than 3,000 years would be needed to cool most plutons," offered as consistent with "a 6,000–7,000 year-old earth."¹⁵  That is an honest position.  It is also 3,000 times a Flood year.

2005 and 2008: six to ten days

Snelling's chapter in RATE Volume II, and his 2008 paper built on it, say something else.  The 2008 abstract:  "the co-formation in the same biotite flakes of adjacent uranium and polonium radiohalos, the latter from short-lived parent polonium isotopes, requires that crystallization and cooling of the granitic plutons only took about 6–10 days."¹¹

The derivation is not thermal.  Polonium-218 has a half-life of about three minutes.  Radiohalos anneal above 150 °C, so a polonium halo must have formed below that temperature, yet the polonium had to arrive in hydrothermal fluid from the still-hot magma.  The 2005 chapter concludes that "all the processes involved in the model together place a limit of 6–10 days for the cooling of the host granitic plutons."⁶  Snelling is explicit that "this timescale is constrained by the half-lives of these isotopes, and not by the assumption that these granites formed during the Flood year."⁶  Whether the radiohalos support that reading is for the forthcoming polonium radiohalos article.  The point here is narrower:  the 6 to 10 days is imported from radiohalo geochemistry and asserted to be the cooling time.  No heat-transport calculation in either paper produces it.

The 2008 paper quotes the thermal literature and does not square it with its conclusion.  Page 18 reports that "Clemens (2005) determined that a 3 km thick sheet of granitic magma would take around 30,000 years to completely solidify from the initially liquid magma."¹¹  The same page reports the fastest convective model it knows, Hayba and Ingebritsen's, in which "a small pluton (1km × 2 km, at 2 km depth) is estimated to have taken 3,500–5,000 years to cool depending on the system permeability."¹¹  That is 150,000 times longer than 6 to 10 days, for a body one-sixteenth the thickness of the 1998 batholith.  The paper's reply is that the models ignore the "relatively thin, tabular structure of plutons," with no number for what the tabular structure would buy.  Snelling knows the heat is a problem.  The 2005 chapter's section "The Heat Problem" says that "an additional, as yet unknown mechanism would have been needed to remove the heat generated by the accelerated radioisotope decay."⁶

The two halves cite each other

The 2005 chapter says that "some of the evidence that shows how the formation and cooling of granitic plutons could be achieved within the time limits of the Flood year has already been documented by Snelling and Woodmorappe [1998]".⁶  The 1998 paper's answer is 3,000 years, and it says it does not imply the batholiths had cooled by the end of the Flood.  Walker 2003 makes the same attribution, crediting Snelling and Woodmorappe with having "soundly answered" how plutons could be "emplaced, cooled, and unroofed in a couple of months."¹²  The reader is told the thermal problem was solved in 1998 and the radiohalos only tighten a solved result.  No young-earth paper has published a thermal model that reaches a Flood year, and the one thermal model they have says it does not.

Walker's 30,000 years

Walker 2007 writes that "Based on conduction alone (i.e. ignoring the cooling effect of fluids) it would take only 30,000 years to completely solidify from the initially liquid magma."¹³  His footnote gives Clemens 2005, page 14, not his own calculation.  Jaeger's coefficient in Part 3 gives 144,000 years for a 3 km sheet.  Even Larsen's 1945 figure, which ignores latent heat and which Jaeger called a gross underestimate, gives 63,000.  Henke traces the same 30,000-year number to Clemens 1998, where it is the solidification time of a 1,000 km³ pluton, a volume rather than a sheet.⁴

Walker also quotes his critic P. Blake asking in 1999 how he fits "7,000 years worth of granitoid cooling into 60 days".¹³  His reply is that granite forms faster than once thought.  He does not answer the arithmetic.  Of Clemens' 1,200-year estimate for filling a batholith through a dike he writes:  "A period of 1,200 years is probably the longest he could comfortably stretch the time.  A slightly modified combination of parameters (such as dyke dimensions, magma viscosity and fluid content) would make the biblical timeframe even more plausible."¹³  That chooses the parameters to reach the answer.

Petford, cited accurately and used for the wrong quantity

Snelling 2008 quotes Petford's "extremely rapid—perhaps even catastrophic" twice, and the "less than 40 days."  Both are real Petford text.  Three things are dropped.  Petford's headline timescale is 100,000 years or less, dominated by melting and segregation.  The 40 days is the fast end for a pluton under 1 km across;  the same equation gives over a million years for a 100 km body, and Snelling drops the size condition.  And Petford's paper is about filling a pluton, not cooling one.  Glazner and colleagues read the same model as predicting "intrusion over 1000 to 10,000,000 years for a pluton the size of the Tuolumne, but the authors prefer timescales of less than 100,000 years for large plutons."¹⁴

Part 3: The conductive arithmetic

The D² law

Heat conduction has one rule of thumb, and Turcotte and Schubert's Geodynamics⁸ states it in a sentence:  "An order of magnitude estimate of the time it takes to solidify a magma body of a minimum dimension a is the thermal time constant a²/κ."⁸  κ is the thermal diffusivity, about 10⁻⁶ square metres per second for rock.  Multiply the thickness by a thousand and the time goes up a million times.

The textbook works an example with latent heat included.  For a basaltic dike 2 metres wide, with a latent heat of 320 kJ per kilogram, a 1000 K temperature drop and a diffusivity of 0.5 mm² per second, "the time required to solidify this intrusion is 10.9 days."⁸

J. C. Jaeger solved the same problem for granite in 1957, in the American Journal of Science, with the latent heat of crystallisation that earlier workers had left out.⁷  For a granite sheet of thickness D metres, "Solidification is complete after 0.016D² years instead of the 0.007D² years found from Larsen's less accurate calculation."⁷  He also found the bottleneck:  "It appears that the time of cooling is determined by conduction in the country rock rather than in the sill."⁷

Jaeger's coefficient gives 23 days for a 2 metre sheet, close to Turcotte and Schubert's 10.9 days for basalt.  Two standard treatments, 45 years apart, agree within a factor of two.  For a sheet 100 metres thick it gives 160 years.  For 1 km, 16,000 years.  For 5 km, 400,000 years.  For 20 km, 6.4 million years.

A slab calculation, with every input named

The young-earth literature never publishes a slab calculation for a body of batholithic thickness.  Here is one.  It is this article's own arithmetic, not a citation, with every input printed so a reader can redo it.

Inputs.  Thermal diffusivity κ = 1.0 × 10⁻⁶ m² s⁻¹, which is 31.6 m² per year;  Turcotte and Schubert use this value throughout, and Cathles uses 1.11 × 10⁻⁶ with a granite range of 0.97 to 2.03 × 10⁻⁶.¹  Density 2,700 kg m⁻³.  Specific heat 1,000 J kg⁻¹ K⁻¹.  Latent heat of crystallisation 3 × 10⁵ J kg⁻¹.  Magma at 800 °C into country rock at 200 °C, cooled to 300 °C, so the temperature contrast falls from 600 K to 100 K.

Fast bound.  A slab with both faces held at the country-rock temperature, latent heat ignored.  The centre of the slab follows the fundamental mode, and reaching one sixth of the initial contrast takes t = 0.206 D² / κ.

Slow bound.  A sheet inside an infinite medium of the same rock, with no free surface and latent heat ignored, so the country rock warms up as the pluton cools.  The centre temperature is an error function of D / (4 √(κt)), and the same target takes t = 2.83 D² / κ.

Jaeger's published coefficient sits between the two bounds, about 2.5 times the fast one, which is about what including latent heat should cost.  The slow bound assumes no free surface, so it runs past the 4 million years Cathles allows within 5 km of the ground.  Against a Flood year the ratio is 10⁵ to 10⁷.  Against Snelling's 6 to 10 days it is 10⁷ to 10⁹.

Cathles' ceiling and Glazner's half million years

Two mainstream sources give the same order of magnitude by different routes, and both are lower than the "hundreds of millions of years" a creationist reader may expect.

Cathles put an upper bound on all conductive cooling near the surface:  "no 800 °C intrusion, no matter how large, can maintain against conduction an anomaly greater than 200 °C within 5 km of the surface for more than 4 m.y."¹  Four million years is the ceiling, and the young-earth side needs to beat 10⁴ to 10⁶ years, not 10⁸.

Glazner and colleagues ran a finite-difference model of a silicic body 5 km thick and 20 km wide at 900 °C, top at 15 km depth, in a 20 °C per kilometre geotherm, with latent heat included.  Their caption:  "The entire body is below 750 °C in ca. 500,000 years.  The >3 m.y. lifetime of the Half Dome Granodiorite contradicts this single-pulse result."¹⁴  That is only the time to leave the magmatic state, and Glazner notes that his two-dimensional model "cools significantly more slowly than a fully three-dimensional model" and that fluid convection in the wall rocks "will speed cooling greatly."¹⁴  So it is an upper bound on his own single-pulse model.  It is still 500,000 Flood years.

A calculator, forthcoming

A small tool will ship beside this article so that every number above can be reproduced with any input changed.  It is a one-dimensional explicit finite-difference conduction model in Deno TypeScript, on about 400 nodes spanning the slab and five slab-thicknesses of country rock each side, with latent heat handled as an apparent heat capacity across the crystallisation interval.  Inputs, with defaults:  thickness 5,000 m;  initial temperature 900 °C;  liquidus 900 °C and solidus 650 °C;  ambient from depth at 20 °C per kilometre;  density 2,700 kg m⁻³, specific heat 1,000 J kg⁻¹ K⁻¹, conductivity 2.7 W m⁻¹ K⁻¹, latent heat 3.0 × 10⁵ J kg⁻¹ with a switch to turn it off;  faces pinned at ambient or an infinite medium;  an optional hydrothermal enhancement applying Cathles' scaling, time proportional to height and inverse to permeability, normalised to his 15,400 years at 2.25 km and 0.25 millidarcies;  and a list of target temperatures.  It will not be published until it reproduces Turcotte and Schubert's 10.9 days, Jaeger's 0.016 D², and Glazner's 500,000 years to below 750 °C.  It plots the slab centre, the contact and a point in the country rock against time, with three markers on the axis:  one year, 6 to 10 days, and 3,000 years.

Part 4: What water can and cannot do

The creationist case is that water changes everything.  It changes a lot, and the mainstream papers that say so also say how much.

The pluton itself must be permeable

Norton and Knight's abstract states the condition:  "cooling rates for the pluton are not significantly shortened unless the pluton permeability is also > 10⁻¹⁴ cm²."¹⁶  Water circulating around a sealed pluton barely changes how fast it cools.  The pluton has to crack.  Their conclusions repeat it:  "only in those systems that contain permeable plutons is the cooling rate increased."¹⁶

Their Table 3 gives the fraction of the initial thermal anomaly still present after 200,000 years:  40 per cent by conduction, 20 per cent for a pluton fractured twice early on, and 80 per cent for a batholith, which still keeps 45 per cent after 1.2 million years.  In the fast case, "the upper 0.9 km of the pluton cools at 0.12 °C/yr for 5000 yrs, and the next lower 1 km cools at 0.02 °C/yrs for 17500 yrs".¹⁶  That is the closest thing to a fast granite in the mainstream literature, and it is 180,000 times slower than 6 to 10 days.

Snelling and Woodmorappe cite Norton and Knight for the mechanism and never quote Table 3.  They do concede the condition.  Measured granites reach 1 to 100 millidarcies,⁵ but those are cold granites.  "By contrast, the permeability of a granite in the actual process of cooling remains unknown."  The models they cite "assume that an initially-impermeable granite does not become appreciably permeable until it cools below about 360 °C, at which time its ductile behavior gives way to brittle behavior, and thus jointing becomes possible."⁵  Their fix is that Flood tectonism keeps cracking the ductile rind open, listed as work to be done:  "These rates of repeated creation of joints (under catastrophic tectonism) and the opposing rates of 'healing' in still-ductile rock need to be quantified."⁵  Twenty-eight years later, no one on that side has quantified them.

The original convective model: 100,000 years for a body a quarter the size

Cathles' 1977 paper is the model everything else scales from:  a pluton 2.25 km high and 1.5 km wide, top 2.75 km down, intruded at 700 °C into water-saturated fractured rock, with boiling included.  He chose permeabilities of 0.05 to 0.5 millidarcies "to be representative of the low range of permeabilities in fractured igneous rock and the range over which convective heat transport becomes important and then dominates conductive heat transport."¹⁷  Crystalline rock at the Los Alamos hot-dry-rock site measured about 0.002 millidarcies.

With no water, "The maximum surface heat flow occurs 65,000 years after intrusion".¹⁷  With water, "the thermal anomaly is pretty well erased in 100,000 years at which time the integrated mass flux is at most only 250 kg per sq cm".¹⁷  A quarter the thickness of Snelling and Woodmorappe's batholith, at 25 times the Los Alamos permeability, and it takes 100,000 years.

The water budget matters more than the time.  "In a formation with permeability of 0.05 md, 90 kg of water circulate through each sq cm of the top central portion of the intrusive in the 100,000 year cooling time computed.  For a permeability of 0.25 md this figure is 250 kg per sq cm, and for a formation permeability of 0.5 md, the figure is 300 kg, per sq cm."¹⁷  Ten times the permeability moves only three times the water, because the heat that drives the convection is fixed.

The fastest modern number

Hayba and Ingebritsen's 1997 paper in the Journal of Geophysical Research¹⁸ is the most modern model the creationists cite.  It runs a pluton 2 km wide and 1 km thick at 2 km depth through the HYDROTHERM code, across the whole range where conduction gives way to advection.  Its own summary:  "depending upon permeability, the effective life span of a system driven by a single 2 x 1 km pluton can range from about 30,000 years to less than 10,000 years."¹⁸  At the top of the range studied:  "Systems with permeabilities of 10⁻¹⁴ m² last for only about 5000 years, and boiling conditions develop only near the surface.  Slightly more permeable (10⁻¹³·⁵ m²) systems last for less than 3500 years and do not appear to boil."¹⁸

Snelling and Woodmorappe report the fast end exactly:  "Based on a small pluton (2 × 1 km, at 2 km depth), the model indicates that the cooling time is 5,000 years (at a system permeability of 10 md).  Increasing the permeability to 33 md shortens the time to only 3,500 years."⁵  Their unit conversion is right;  10⁻¹⁴ m² is 10 millidarcies.  Three things are wrong with the use.  The quantity is renamed:  Hayba and Ingebritsen say the hydrothermal system lasts that long, not that the pluton has cooled, and their conduction-dominated cases keep the rock near the pluton hot "for more than 50,000 years."¹⁸  The two cases quoted are the top of the range studied, presented as representative.  And the body is 2 by 1 km.  Snelling and Woodmorappe concede this in the next sentence:  "the program HYDROTHERM has not been applied to plutons of batholitic dimensions."⁵  It still has not.

Spera's 50,000 years

Snelling and Woodmorappe build the "water makes it fast" half of their case on Frank Spera's 1980 paper in Science,¹⁹ which models plutons with hydrothermal convection switched on.  Spera's water result:  "A pluton with 0.5 percent water (R = 5 km) cools to the solidus temperature in 330,000 years, whereas one with 4 percent water cools in only 50,000 years, other factors remaining constant."¹⁹  Fifty thousand years is Spera's fastest case, the wettest melt he models, cooling only from liquidus to solidus.  Bigger bodies get worse:  "in convective cooling the solidification time varies approximately according to R^1.4."[spera-1980:scaling]

Snelling and Woodmorappe report Spera's ratios and never his times.  Their text says the cooling time "decreases almost ten-fold as the water content increases from 0.5 wt% to 4 wt%" and by "eighteen-fold" when the contact temperature drops from 700 to 500 °C.⁵  The figures behind those ratios are 330,000 to 50,000 years and 3.6 million to 200,000 years, and neither appears in their prose.  Henke called this a cover-up.⁴  That is too strong, because their Figure 2 is redrawn from Spera with a time axis running to 500,000 years.  The fair statement is that the ratios are in the text and the timescale is only on an axis.

What a Flood-year batholith would need

Here is the calculation the creationist literature has left open since 1998.  It uses only Cathles 1981, which they cite, and it is this article's own arithmetic.

Route A, Cathles' scaling law.  Convective cooling time is proportional to height and inverse to permeability.  Snelling and Woodmorappe's batholith reaches the 75 per cent mark in about 2,800 years at 10 millidarcies.  To reach it in one year needs 10 × 2,800 = 28,000 millidarcies, or 28 darcies, through the whole 16.5 km of pluton and its host.

Route B, water throughput.  Cathles gives the fluid flux at 0.25 millidarcies as 16 grams per square centimetre per year, proportional to permeability.¹  A column of granite 16.5 km tall masses 4.5 × 10⁷ kg per square metre.  Snelling's own water-to-rock ratio of about one, "enough energy due to inertial heat to drive roughly its mass in meteoric fluid circulation,"¹¹ means 4.5 × 10⁷ kg of water per square metre in a year.  That is 280,000 times the 0.25 millidarcy flux, so about 70 darcies.  Cathles 1977 showed the flux is sublinear in permeability, so the true requirement is higher still.

Compare with what has been measured or proposed, all from Cathles' own compilation unless noted.¹

The one number that could rescue a fast granite is Lister's, and Cathles reports it with its own brake:  "Lister has estimated that intrusion permeabilities of about 10 darcies may occur after thermal cracking by interaction with ground water but before substantial sealing by mineral deposition, static fatigue, or collapse.  After static fatigue and collapse, the permeability may be reduced to a few millidarcies.  The rate of advance of the cracking front is rapid, about 30 m/year."¹  From both faces of a 16.5 km body, the cracking front takes 8,250 / 30 = 275 years to reach the middle.  That is 275 Flood years before the centre can see any water, from the creationists' own source, independent of every other objection.  Snelling and Woodmorappe's answer is that Flood tectonism would crack the rock faster.  No one has published a rate.

They also concede the limit on "superconvection," the runaway convection near water's critical point that Ingebritsen and Hayba described in 1994:  it needs "a permeability of about 100 md (which is an order of magnitude larger than we have adopted for the cooling batholith:  Figure 3)" and "may occur during cooling of small plutons, but probably not of batholiths."⁵  One hundred millidarcies is still 300 times short of a Flood year.

So the Flood-year model needs three to seven times the highest permeability anyone has proposed even in theory, and 300 to 20,000 times anything measured, through a body 16.5 km thick, for a year, while the rock is still ductile.  A solution would have to show a mechanism that does that and disposes of the steam.

Part 5: The clocks in the rock

None of the arithmetic above is needed to settle the question, because the rock keeps its own record.

Tuolumne: zircon ages in map order

Coleman, Gray and Glazner dated eleven samples across the Tuolumne Intrusive Suite by uranium-lead in zircon, six of them to high precision.  Zircon closes to lead above 900 °C, so each age is the date that sample crystallised.  Their abstract:  "New U-Pb geochronologic data indicate that the Tuolumne Intrusive Suite, California, was assembled over a period of at least 10 m.y. between 95 and 85 Ma, and that the Half Dome Granodiorite intruded over a period approaching 4 m.y."²  The ages fall in map order from the outside in:  Glen Aulin 93.1 ± 0.1 million years and Kuna Crest 93.5 ± 0.7 at the margin;  Half Dome 92.8 ± 0.1 at its outer contact, 91.7 ± 0.2 in Yosemite Valley, 91.1 ± 0.1 at the top of Half Dome itself, and 88.8 ± 0.8 where it meets the Cathedral Peak Granodiorite.²  The error bars are one to two orders of magnitude finer than the spread.  A Tuolumne built in a Flood year would put every sample at the same age.

The same paper gives the creationists their filling rate:  "large plutons could be filled on time scales of 10¹–10⁴ yr".²  The increments are quick.  The gaps between them are what the ages measure, and a sheet injected in ten years still has to cool by Part 3.  Snelling 2008 cites neither Coleman nor Glazner, four years after the result that contradicts his single-batch tabular sheet was in print.

The Sierra Nevada's thermometers

House, Wernicke and Farley dated Sierra Nevada granite by helium in apatite.²⁰  That clock closes at low temperature:  "the transition between complete diffusive loss and quantitative retention of helium occurs over the temperature interval of 45° to 75 °C for crystals of ~125 micron prism diameter".²⁰  The rocks are "predominantly 125 to 80 Ma granite and granodiorite plutons of the Sierran magmatic arc", crystallised at 4 to 12 km depth.²⁰  Their helium ages run 40 to 85 million years and cluster near 60,²⁰ and apatite fission-track ages independently put the same basement at 3 to 4 km depth at about 70 million years.²⁰

So the same hand sample carries a hot clock and a cold clock, and the hot clock is always older.  The rock is recorded as sitting between 900 °C and 70 °C for tens of millions of years.  A pluton that cooled to ambient in 6 to 10 days would close every thermometer in the same week.  In the Coast Mountains of Alaska five clocks have been read in one rock, sample 8500-15 at Tracy Arm.²¹  In closure-temperature order:  zircon uranium-lead 60.4 million years, potassium-feldspar argon 54 to 50, zircon helium 49.3 ± 3.9, apatite fission track 32.6 ± 3.6, apatite helium 7.49.²¹  Reiners and colleagues call it "a remarkably smooth hyperbolic cooling history for this sample since crystallization at 60 Ma."²¹

The ceiling from inside RATE

The RATE volume that carries Snelling's 6 to 10 days also carries Russell Humphreys' helium-diffusion chapter.⁹  The two need different thermal histories for granite in the same year.  Humphreys' model assumes the Fenton Hill granodiorite has been at today's temperature throughout.⁹  He then asks how much heat it could have taken during the Flood without wrecking his 6,000-year result:  "for a Δt of 1 year, T_h would be about 90 °C above today's temperature.  For a Δt of 1 month, T_h would be about 140 °C hotter than today.  If the heat pulse had been much hotter or longer than those typical values, the diffusion age we calculate would have been significantly less than 4000 years".⁹  Snelling puts granitic plutons at 800 °C in the same year and needs them below 150 °C within days.  Humphreys allows 90 °C above ambient.  Three thermal histories for granite in twelve months, in adjacent chapters of one book.  The helium argument itself is covered in RATE and Helium in Zircons.

Part 6: The heat budget

Mihai Ducea's 2001 survey of the California arc¹⁰ gives the volume:  "Together, the segments of the California arc generated ~0.7 million km³ of granitic material."¹⁰  At 2,700 kg per cubic metre that is 1.9 × 10¹⁸ kg.  Cooling it from 900 to 300 °C at 1,000 J per kilogram per kelvin releases 6 × 10⁵ J per kilogram, plus about 3 × 10⁵ of latent heat, so 9 × 10⁵ J per kilogram and about 1.7 × 10²⁴ J for the arc.  Spread over the Earth's 5.1 × 10¹⁴ m² and released in one year, that is about 105 W per square metre, against 240 W per square metre of absorbed sunlight and 0.09 of present geothermal flux.  This is the article's own arithmetic, and it should not be inflated.  One arc's worth of granite, dumped in a year, roughly doubles the planet's radiative load and lifts the equilibrium temperature by tens of kelvin, which is survivable on paper.  Ten arcs' worth is 1,050 W per square metre and a radiative equilibrium near 390 K, which is not.  No defensible global Phanerozoic granite volume was found, so the multiplier is an assumption.

Either way, granite's own heat is the small term.  It is four to five orders of magnitude below the seafloor heat of catastrophic plate tectonics, and further still below the accelerated-decay heat in RATE and Helium in Zircons.  Humphreys concedes that water-cooling the granite only moves the problem:  "the heat carried by the water has to go somewhere else on earth, and that heat would be more than enough to melt the earth's crust globally."⁹  The granite problem is not radiating the heat.  It is conducting it out of kilometres of rock, and that is what Jaeger, Cathles and Spera all price at 10⁴ to 10⁶ years.

Objections and responses

Hydrothermal cooling is orders of magnitude faster than conduction, so conductive arithmetic is beside the point.  Granted, and its size is known.  Snelling and Woodmorappe's rescaling of Cathles drops from 3 million years to 3,000 at 10 millidarcies.  A factor of a thousand is real.  It leaves 3,000 years, to the 75 per cent mark, and the next factor of 3,000 needs tens of darcies through a body that is still ductile.  Cathles 1977 also showed that ten times the permeability moves only three times the water.

Cathles himself says intrusions cool rapidly, and puts a typical event near 10,000 years.  He does:  "A time typical of the cooling of a single intrusive event may indeed be close to the 10,000-year figure advocated recently by Elder (1977)."¹  That is for his 3 km example, to the 75 per cent mark, and it is 10,000 Flood years.

The heat was removed by the same miracle that removed the accelerated-decay heat.  This is the honest form of the young-earth position, and thermal arithmetic cannot refute a miracle.  Two things follow.  First, the granite heat is the small term, so a mechanism that disposes of 10²⁹ joules of plate-tectonic heat disposes of 10²⁴ without noticing.  Second, if the cooling was miraculous, the thermal literature stops being evidence.  Snelling 2008 cites Petford, Cathles and Hayba and Ingebritsen as though physics does the work, and the polonium radiohalos are offered as physical evidence of rapid natural cooling.  A miracle that cools a batholith in a week also has to leave Humphreys' Fenton Hill granodiorite within 90 °C of today, and has to deliver polonium from 400 °C fluid to biotite before it decays.  The young-earth side can have the miracle or the physical argument, not both.

Plutons were emplaced as many small sills, each of which cooled independently.  This is the mainstream model, and it is the creationists' best move.  It fails on timing.  A 100 metre sheet solidifies in 160 years by Jaeger's coefficient, and a 1 km sheet in 16,000.  Sheets cool independently only if each has cooled before the next arrives.  Inside a Flood year every sheet arrives within months, so a stack of hot sheets is thermally one slab, and the interior sheets cannot lose heat through hot sheets above and below them.  The Tuolumne ages show what independent cooling looks like:  increments separated by hundreds of thousands to millions of years.  Ducea's arc is 30 to 35 km of granitoid from top to bottom.

Zircon ages are unreliable, and accelerated decay compresses them anyway.  The argument in Part 5 does not need the absolute ages.  It needs their order and their spread.  Accelerated decay that scaled every age by the same factor would keep the Tuolumne ages in map order and keep the ratio of spread to error, and a suite emplaced in one year would come out at one age however fast the decay ran.  The thermochronometers are harder still, because their order tracks closure temperature, a diffusion property of each mineral and not a decay property.  The strongest young-earth reply is that if decay ran fast by different factors for uranium, potassium and the helium systems, the ratios between clocks need not be preserved.  No published accelerated-decay model predicts the observed ordering, and until one does this is an unanswered objection.

Crystal growth rates show that granite crystallises in hours to years.  Granted in Part 1.  Growing crystals and moving 10⁶ joules per kilogram out of a 16 km slab are different problems, and only the second sets the timescale.

Snelling and Woodmorappe misread Cathles' chart.  A skeptic's objection, and it is wrong.  Their 3,000 years is Cathles' chart read at 5.5 times his example, and his appendix formula gives 2,823.  What fails is the interpretation:  the quantity measured, the permeability assumed, and the gap to a Flood year.

Granite's own heat alone breaks a Flood year.  Also a skeptic's objection, and it overstates.  One arc's worth of granite released in a year is about 105 W per square metre, which the planet could radiate at a cost of tens of kelvin.  The heat becomes fatal at ten arcs, and it is dwarfed by the other Flood heat terms.

Precambrian granites look exactly like Phanerozoic ones.  Henke's point:  "Precambrian granites have much the same mineralogies, textures and structures as Cretaceous and other Phanerozoic granites, yet YEC dogma arbitrarily insists that Precambrian granites had a miraculous origin within a few days or less while Phanerozoic granites supposedly formed naturally over a maximum of a few thousand years."⁴  This article does not rely on the point;  it is recorded because a skeptic will raise it.

Issues and unanswered questions

• Clemens 2005, page 14, was not obtained. It is the cited source of the 30,000-year figure in Walker 2007 and Snelling 2008. No published cooling coefficient reproduces it for a 3 km sheet, and Henke traces the number to a 1,000 km³ volume in Clemens 1998. Until the page is read, the figure is reported as the creationists give it.
• No verified global Phanerozoic granite volume. The California arc is the documented unit, and the "ten arcs" multiplier in Part 6 is an assumption.
• Measured cooling durations of real batholiths are not printed here. Henke cites Paterson and Tobisch 1992 for the Quottoon and Separation Point batholiths taking 2 million years from 700 to 450 °C and the Sierra Nevada more than 10 million. The primary was not read, so the numbers are left with Henke.
• Lister 1974 and Ingebritsen and Hayba 1994 were not read. The 10 darcies, the 30 metres a year, and the 100 millidarcy superconvection threshold are cited through Cathles 1981 and Snelling and Woodmorappe.
• The calculator is not yet shipped. Until it is, the slab table in Part 3 rests on the two closed-form bounds and Jaeger's published coefficient.
• Snelling and Woodmorappe 1998 is cited by the page of ICR's re-typeset reprint, which prints 1 to 17 and does not carry the original page breaks of pages 527 to 545.
• Later replies on either side were not searched. Henke 1999 is the only mainstream reply checked here.

Verdict

The young-earth granite literature gets three things right, all about emplacement:  magma rises fast, plutons are built from sheets, and water carries heat far faster than rock does.  All three are mainstream.

It gets the cooling wrong, and its own sources say so.  The one young-earth thermal model gives 3,000 years, to the 75 per cent mark, on a permeability its authors call unknown, and it declines to claim a Flood year.  The 6 to 10 days that replaced it is a half-life argument with no thermal model behind it, published beside quotations of 30,000 and 3,500 years that it does not reconcile.  Conduction gives 10⁵ to 10⁷ years for a body kilometres thick, by a 1957 formula and a 2002 textbook that agree within a factor of two.  Convection at any permeability ever measured or proposed leaves 10⁴ to 10⁵ years, and a Flood year would need tens of darcies through ductile rock.  The rock's own clocks, zircon ages in map order across ten million years and helium ages tens of millions of years younger than the crystallisation ages in the same samples, record the cooling directly.  The heat is the small problem.  The rock is the large one.  A Flood year misses by three to seven orders of magnitude.

Sources