Temperature differences between lavas erupted at ocean islands and mid-ocean ridges are crucial to documenting the existence of mantle plumes. Olivines are useful for T estimation because they provide a less homogenized account of the melting process compared to glass and whole rock samples. Olivine-liquid equilibria, and olivine phenocrysts from Hawaii, Iceland, and several mid-ocean ridge localities, indicate higher melting temperatures compared to mid-ocean ridges (MORs) by at least ∼250 ± 52°C and 165 ± 62°C, respectively. When translated to differences in mantle potential temperature, ΔTp, Hawaii and Iceland potential temperatures are hotter than ambient MORs by 213–235 and 162–184°C, respectively, similar to estimates required by geodynamic models for mantle thermal upwellings. Absolute mantle potential temperatures are more uncertain as they depend on estimates of melt fraction and depth of equilibration, but olivine-liquid equilibria support the following estimates: TpHawaii = 1688°C; TpIceland = 1637°C; TpMORs = 1453–1475°C. All of these estimates include the effects of H2O, Na2O + K2O, and SiO2 on olivine-melt equilibria and are robust against other variations in source or liquid composition, such as FeO and CO2. These estimates show that at least at Iceland and Hawaii, volcanism is driven by large temperature anomalies whose magnitudes are consistent with the existence of thermally driven mantle plumes.
 Plume advocates have called for ΔT to be between 160–280°C [e.g., Sleep, 1990; Schilling, 1991], while opponents of the thermal plume hypothesis have attempted to argue that ΔT is small [Anderson, 1998], and some would like to replace mantle thermal anomalies with source heterogeneity [e.g., Bonatti, 1990; Green and Falloon, 2005; Presnall and Gudfinnsson, 2005]. The implications for mantle circulation could not be more clear: Since Morgan  first proposed that hot spot volcanism is caused by thermally driven upwelling currents, dynamic modelers have suggested that plumes are a principal mode of mantle convection [e.g., Davies, 1999], and geochemists have argued that OI basalts reflect deep-seated, thermally driven cycling of elements and isotopes [e.g., Hofmann and White, 1982; Zindler and Hart, 1986; Hofmann, 1997]. If ΔT is small, our understanding of mantle circulation is clouded, and the existence of thermal plumes is cast in doubt.
 The concept of a mantle potential temperature, Tp, is very useful when discussing ΔT. Tp represents the hypothetical temperature the mantle would have, were it to reach Earth's surface decompressed and unmelted [McKenzie and Bickle, 1988]. At MORs, Tp estimates range from 1260–1280°C [Presnall et al., 2002; McKenzie and Bickle, 1988] to 1410–1475°C [Asimow et al., 2001; Kinzler and Grove, 1992b]. At Iceland, MacLennan et al. [2001a] estimate that Tp = 1480–1520°C, and at Hawaii, Watson and McKenzie  estimate that Tp = 1558°C. Petrologic estimates of ΔTp, between OI and MOR localities, also vary, from >250°C [Klein and Langmuir, 1987; Watson and McKenzie, 1991], to 100–150°C [Shen and Forsyth, 1995; Presnall et al., 2002], to as low as near 0°C [Green et al., 1999]. With the exception of Green et al. , these estimates are derived from basalt compositions, or incidentally from calculations of crustal thickness. However, basalts represent a homogenized account of the mantle melting process, and are unlikely to yield the maximum temperatures experienced during melting. And estimates from ocean crust thickness rely on knowledge of melt productivity and the depth intervals of melting, both of which are imprecisely known. This paper presents an alternative method for estimating T, using the forsterite (Fo) contents of olivine phenocrysts and olivine-liquid equilibria. These techniques are used to test the mantle plume hypothesis by determining the thermal anomalies that drive volcanism at Hawaii and Iceland.
 Mineral compositions are useful for temperature estimation because they are resistant to compositional reequilibration. Thus minerals that are formed at different temperatures, though thrown together during a magma-mixing event, provide a compositional archive of premixed liquid compositions and temperatures. Green et al.  examined olivine compositions and, interestingly, observed that maximum Fo contents for olivines from several MORs match or exceed maximum Fo at Hawaii. Using model liquid compositions, they concluded that ΔTp ≈ 0°C. Proponents of the thermal plume hypothesis appear to be left with the uncomfortable position of having to claim that high Fo olivines at MORs are xenocrysts, while similar such olivines at Hawaii are not. However, a reconsideration of olivine saturation temperatures, following Roeder and Emslie  and Langmuir and Hanson , suggests that high Fo olivines need not imply high mantle temperatures.
 Olivine-liquid equilibria are particularly useful for T estimation because (1) the ratio [XFe/XMg]ol/[XFe/XMg]liq (or KD(Fe-Mg)ol-liq) is nearly constant over a wide range of temperatures, bulk compositions and fO2 conditions [Roeder and Emslie, 1970] (except for a slight increase at high P and T [Herzberg and O'Hara, 1998]) and (2) the ratio XMgol/XMgliq (Kd(Mg)) is highly sensitive to temperature (XFe and XMg are cation fractions of Fe and Mg, respectively; see section 2.2.3). Roeder and Emslie  and Langmuir and Hanson , among others, have shown how these relationships can be used to predict the T at which a given liquid is saturated with olivine. Expressions for Kd(Mg) and XFeol/XFeliq (Kd(Fe)) as a function of T are recalibrated, using high-pressure partial melting experiments (Figures 1 and 2; section 2.2).
2.1. Model Input
 If high Fo olivines from a given rock sample are to be used to estimate mantle melting temperatures, then at some point in their history, they must have approached equilibrium with a liquid. It matters little whether the crystals in question precipitated from a liquid somewhere in the magmatic plumbing system, or melted free from a mantle residue, provided they gained their compositions through exchange with a liquid phase. Indeed, in the later case, such crystals might not show evidence of crystallization (e.g., melt inclusions, etc. [Natland, 2003]), but may yield more direct evidence of mantle melting conditions. At Hawaii, high Fo olivine phenocrysts are well recognized to represent entrained liquid precipitates [Murata and Richter, 1966; Helz, 1987; Baker et al., 1996; Norman and Garcia, 1999]. At MORs, high Fo olivines are less well studied, but must their high Fo crystals be regarded as xenocrysts in order to maintain that melting temperatures at MORs are lower than those at Hawaii? Certainly, arguments to the effect that low Fo olivine grains are phenocrysts, while similar such crystals with arbitrarily high Fo olivines are xenocrysts, are far from compelling, regardless of the locality in question. The burden of proof would appear to rest with those who propose that olivine phenocrysts have no association to a melting or crystallization event. Once an olivine composition has been identified, T can be estimated graphically using the models of Roeder and Emslie  and Langmuir and Hanson , if either XFeliq or XMgliq are known (see section 2.2.3.). Because the Kd(Fe)ol-liq is close to 1, XFeliq of primitive liquids can be estimated more precisely than XMgliq, provided that whole rock or glass compositions can be traced to an olivine control line [e.g., Langmuir et al., 1992; Herzberg, 2004]. As will be shown, XFeliq (and FeOliq, in wt.%) can thus sometimes provide a useful check on estimates of T.
 It is very important to know KD(Fe-Mg)ol-liq, because since it is nearly constant, it is possible to predict the Mg# (XMg/[XMg + XFe]) of the liquid from which a given olivine has equilibrated. Analysis of 750 experimental observations of olivine-liquid equilibrium show that KD(Fe-Mg)ol-liq is insensitive to composition with multivariate models capturing little more than 20% of the variation of KD(Fe-Mg)ol-liq. The only predominant trend is in regard to P, as illustrated in Figure 1. Because residual correlations of KD(Fe-Mg)ol-liq with T or compositional parameters are poor, it is likely that the much of the residual variation reflects experimental error. When pressures of equilibration are imprecisely known, it is probably best to apply aggregate mean values (Figure 1) [see also Herzberg and O'Hara, 1998].
2.2.1. T and Compositional Effects
 The ratio XMgol/XMgliq has been the focus of several olivine-liquid thermometers [e.g., Roeder and Emslie, 1970; Ford et al., 1983; Beattie, 1993; Sugawara, 2000]; however, to apply these models XMgliq must be known. In contrast, the olivine saturation surface of Roeder and Emslie [1970, Figure 7] and Langmuir and Hanson [1981, Figure 7] provide a graphical means of T estimation that allows one to substitute XFeliq, or a XFeliq − XMgliq trend line, for XMgliq input. To apply the olivine saturation surface to potentially very high P-T conditions, expressions for Kd(Mg) = f(T) and Kd(Fe) = f(T) are calibrated from the experiments noted in Figure 1. These observations of olivine + liquid equilibrium cover the pressure range 0.0001–15.5 GPa (Figure 2; Table 1), and were obtained on a range of anhydrous, hydrous, enriched and depleted peridotite and basaltic bulk compositions. The equations are derived from linear least squares regression analysis using T only (Models A and B; Table 1) and T, SiO2liq, Na2Oliq + K2Oliq and H2Oliq (wt.%) as independent variables (Models C and D; Table 1). Residuals from the more comprehensive models, C and D, are uncorrelated with T, P or other Xi (except for CO2, see section 2.2.2.). FeOliq, when not reported for 1-atm experiments, was calculated using Kress and Carmichael  and reported values of fO2. For high-pressure experiments it was assumed that FeOtotal = FeOliq; application of the models of Holloway et al.  indicates that over the fO2 range 10−7–10−20 the results are little affected.
KD(Mg) and KD(Fe) are the cation fraction ratios, XMgol/XMgliq and XFeol/XFeliq, respectively (see text for further explanation); T is temperature, in °C; quantities such as [SiO2]liq, [Na2O + K2O]liq, and [H2O]liq are empirical corrections represented as weight% values for an equilibrium liquid; standard deviations for coefficients are indicated in parentheses.
Presnall et al.  have argued that the presence of small amounts of CO2 in the mantle could dramatically reduce mantle temperatures. Experiments from Dalton and Presnall [1998a, 1998b] (not used for calibration of the models in Table 1) are thus used to check for a CO2 effect on Kd(Mg). Interestingly, although predicted values for Kd(Mg) for the CO2-bearing experiments are too high (Figure 2a), as also observed for H2O-bearing experiments (Figure 2a), the displacement is very small considering the very large amounts of CO2 (14.5-45.3 wt.%). The hydrous experiments, in contrast, exhibit similar or larger displacements, but range to only 7.9 wt.% H2O (Figure 2a). But the Dalton and Presnall [1998a, 1998b] liquids are also very low in SiO2, which causes a similar displacement, to high predicted values of Kd(Mg). When model C is applied (which corrects for SiO2liq), Kd(Mg) values for the “lower” CO2 experiments (14.5–30.8 wt.% CO2) are accurately predicted, while the “higher” CO2 experiments (>40 wt.% CO2) have predicted values of Kd(Mg) that are too low. The latter result might seem counterintuitive, but if valid, the “high” CO2 experiments merely indicate that while carbonate liquid forms at the expense of silicate phases when CO2 is added, that olivine is dissolved at a rate less rapid than that at which silicate liquid is consumed. If nothing else, though, these experiments indicate that (1) CO2 contents as high as 30% in the liquid do not appreciably affect Kd(Mg) or the T calculations of the present work and (2) if a correction for CO2 is required, it would provide a small positive correction to Kd(Mg), which would lead to highercalculated temperatures for a given olivine-liquid composition pair in CO2-bearing systems (in Figure 3, addition of CO2 shifts isotherms downward; addition of H2O shifts isotherms upward). For the comparatively very low values of CO2 expected at OIs and MORs [Dixon et al., 1997], the data of Dalton and Presnall [1998a, 1998b] show that a CO2 effect for olivine-liquid-derived temperatures can be neglected.
2.2.3. Computational Methods
Figures 3a and 3b show an olivine saturation surface with thermal contours updated using equations (A) and (B) (Table 1). The contours are nearly flat because Kd(Mg) is much more sensitive to T than Kd(Fe). The strategy for use of this diagram follows that of Langmuir and Hanson : olivine stoichiometry requires that XMgol + XFeol = 0.667, where XMgol and XFeol are calculated as cation fractions (e.g., the weight% of oxides such as Al2O3, K2O and Na2O are divided by the molecular weights of AlO3/2, KO1/2, and NaO1/2, etc.). By definition, Kd(Mg) = (XMg)ol/(XMg)liq, and Kd(Fe) = (XFe)ol/(XFe)liq, which on rearrangement yield XMgol = [XMgliq][Kd(Mg)], and XFeol = [XFeliq][Kd(Fe)]. Thermal information is gained from the fact that Kd(Mg) = f(T) and Kd(Fe) = f(T). By substitution of these expressions we obtain, [XMgliq][Kd(Mg)] + [XFeliq][Kd(Fe)] = 0.667, and with further substitution of the expressions of Table 1 (models A and B), we have the T-sensitive and composition-independent olivine saturation surface:
For a given liquid composition, the T (°C) that satisfies equation (1) is the T at which a given liquid will be saturated with olivine. Equation (1) is used to calculate the isotherms in Figures 3 and 5; Figures 6 and 7b utilize the T- and composition-dependent equations (C) and (D) in place of (A) and (B) in equation (1) (Table 1). Lines radiating from the origin of these figures are lines of constant Fo (Mg# of olivine) (and constant Mg#liq), as proscribed by the value of KD(Fe-Mg)ol-liq. As an example of the use of Figure 3a, consider a liquid with XFeliq = 0.10 and XMgliq = 0.13. This liquid will reach olivine saturation at 1300°C, and the equilibrium olivine will have the composition Fo80. If an olivine composition is known, T can also be estimated from the isotherms based on the intersection of a line of constant Fo (the observed olivine composition) with a known value of XFeliq or XMgliq or an XFeliq-XMgliq trend line that is determined by the addition or subtraction of olivine. When error on the models of Kd(Mg) and Kd(Fe) are propagated through the saturation surface, the approximate model error on T is ±45°C.
 At Hawaii it is well understood that liquid and whole rock compositions are controlled by olivine fractionation and accumulation, that is, an “olivine control line” [e.g., Wright and Fiske, 1971; Rhodes and Vollinger, 2004a]. Rocks with high MgO thus do not necessarily represent liquids, but rather are aggregates of evolved liquids and more primitive olivine phenocrysts. These phenocrysts represent early precipitates that are remobilized, especially during high-volume eruptions [Murata and Richter, 1966; Helz, 1987; Clague et al., 1991; Baker et al., 1996; Norman and Garcia, 1999]. It is therefore difficult to estimate MgOliq (wt.%) for primitive magmas because it is unclear where along an olivine control line the primitive liquid composition is located. However, because Kd(Fe) is usually very close to unity, FeOliq (wt.%) is often little affected by olivine crystallization and hence is nearly constant along an olivine control line. Figure 4 compares MgO and FeO for rocks from Phase 2 of the Hawaii Scientific Drilling Project [Rhodes and Vollinger, 2004a], and Hawaiian picrites from various Hawaiian volcanoes [Norman and Garcia, 1999]. A regression line through these data has a slope of 0.004 (Figure 4); it is essentially flat. Primitive FeOliq contents at Hawaii are thus 11.4 ± 0.03 wt.%. At MORs, few localities yield rocks with sufficiently high MgO to reach olivine control. An exception is the Siqueiros transform along the East Pacific Rise, which yields picritic basalts with up to 21.1 wt.% MgO, and maximum olivine compositions of Fo 91.5 [Perfit et al., 1996]. A fit through Siqueiros rocks with MgO > 9 wt.% yields a slope of 0.005 with a mean of 7.9 wt.% (Figure 4). Notably, one sample with 7 wt.% FeO appears to overshoot the flat FeO trend (Figure 4). As it is conceivable that only the lowest FeO contents represent primitive FeOliq values [Natland, 2003], mean and minimum values of FeOliq (and XFeliq) values are considered for error calculations. Ferric/ferrous ratios are calculated from total Fe (analyzed as Fe2O3) using the model of Kress and Carmichael , assuming fO2 is buffered at wustite-magnetite at Hawaii [Rhodes and Vollinger, 2004b] and at 1 log unit below Ni-NiO at MORs and at Iceland [Heister et al., 2004] (Figure 6); within this range of fO2, uncertainty in fO2 is encompassed by the already-noted uncertainty in FeOliq.
3.2. Estimates of ΔT = THawaii − TMOR
 As an initial test of the low-ΔT hypothesis, a side-by-side comparison of Hawaiian and Siqueiros samples is considered. In Figure 5, KD(Fe-Mg)ol-liq = 0.32 and the cation fractions of Hawaiian picrites [Norman and Garcia, 1999] and Siqueiros basalts [Perfit et al., 1996] are plotted. The near-vertical lines represent empirical fits through XMgliq-XFeliq trends, with intercepts fixed such that they trend through maximum and minimum XFeliq values for primitive (MgO > 9 wt.%) lavas. Though these lines approximate constant wt.% FeO, the lines are not perfectly vertical due to the recalculation of liquids as cation fractions. For a simple direct comparison, the wustite-magnetite fO2 buffer is applied to both suites.
Figure 5 shows that Siqueiros-type liquids will reach saturation with olivine at much lower temperatures compared to Hawaiian lavas, even though their olivines have similar or greater Fo contents (Figure 5). The important issue is not so much the Fo content of the olivine, nor Mg#liq. Rather, it is the value of Kd(Mg) at a given XFeliq. In other words, a high Fo olivine may precipitate from a high Mg# liquid, but if the high Mg#liq is accompanied by low XFeliq, then XMgliq must also be low. This means that Kd(Mg) will be high, which requires equilibration at low T. High Fo values and high Mg# values from Siqueiros occur at much lower XFeliq values compared to Hawaii and hence yield lower values for T. All else being equal, the mean temperature difference (ΔT = THawaii − TMOR) is ∼168 ± 56°C (Figure 5).
 But all else is not equal. At OIs, the source regions are likely more H2O-rich compared to MORs [e.g., Dixon et al., 2002]. In addition, with the imposition of a thick lithosphere (at least 75 km [Bock, 1991]), olivine equilibration pressures are almost certainly much greater at Hawaii compared to MORs [see Kinzler and Grove, 1992b; Herzberg and O'Hara, 1998]; probably in excess of 2.5 GPa [Herzberg and O'Hara, 1998; Putirka, 1999]. Hence a more appropriate value for KD(Fe-Mg)ol-liq at Hawaii is 0.35 (Figure 1). Figure 6 illustrates a more complete model for olivine saturation for both localities (see Figure 6 caption) using KD(Fe-Mg)ol-liq = 0.35 for Hawaii, water contents for MOR and OI sources from Dixon et al.  (assuming melt fraction, F, is 0.2 and the bulk distribution coefficient, DH2O, is 0), an XMgliq-XFeliq trend represented by the midpoint between mean and minimum XFeliq estimates (Figure 5), and the composition-dependent models of Kd(Mg) and Kd(Fe) of Table 1. The two highest Fo values reported by Green et al.  are used to illustrate error on T due to the estimation of maximum Fo content. These more complete models indicate a mean ΔT of ≈ 245 ± 52°C (Figure 6).
3.3. Estimates of ΔT = TIceland − TMOR
 Iceland has perhaps garnered more controversy than Hawaii over whether it has a deep-seated thermal source, and so ΔT = TIceland − TMOR is perhaps of even greater interest. For these calculations, the strategies for Hawaii and MORs (sections 3.1 and 3.2) are employed. At Iceland, FeOliq does not appear to trend to a constant value as at Hawaii or Siqueiros (Figure 7a); T can still be estimated by the intersection of the constant Fo trend line and the trend of XMgliq-XFeliq, but T uncertainty is clearly increased. The depth extent of the melting column appears to be between 100-40 km [MacLennan et al., 2001a]; taking the midpoint of this range (P = 2.3 GPa), KD(Fe-Mg)ol-liq is set at 0.35. As at Hawaii and MORs (Figure 5), mean and minimum FeOliq contents, and the two highest Fo content olivines from MacLennan et al. [2001b] provide the brackets for estimates for TIceland (Figure 7). And as in Figure 6, a median trend is also used for T estimation (Figure 7b). The mean of these values yields TIceland = 1535°C, and TIceland − TMOR = 165 ± 62°C. If, as noted, FeOliq at MORs is closer to 7 wt.%, then TIceland − TMOR = 187°C.
3.4. Estimates of TpHawaii, TpIceland, TpMOR, and ΔTp
Figure 8 provides a summary of T estimates, and the effects of the propagation of model error (equations of Table 1) on T using a range of FeOliq and Fo values (Figures 6 and 7b). These values of T and ΔT (Figure 8) are temperatures of olivine-liquid equilibration, not mantle potential temperatures. To calculate ΔTp it is necessary to correct for the heat of fusion (an upward correction in T), and then decompression along a mantle adiabat to the surface (a downward correction in T) [Cawthorn, 1975]. The upward correction for T due to the heat of fusion can be approximated by the expression ΔTfus = F(Hfus/Cp) [Langmuir et al., 1992], where F is melt fraction, Hfus is the heat of fusion and Cp is heat capacity. The downward correction due to decompression can be calculated as ∂T/∂P = TαV/Cp, where V = molar volume and α is the coefficient of thermal expansion. The following calculations utilize Hfus = 128.3 kJ/mole; Cp = 192.4 J/mole·K; V = 4.57 J/bar;α = 3 × 10−5/K, which are derived from linearly weighted quantities for a mantle that is 60% forsterite, 20% diopside and 20% clinoenstatite, using calorimetric values and molar volumes from Richet , Richet and Bottinga , and Robie and Hemingway, 1995] (taken at 1700 K, where appropriate). Partial melting experiments of natural peridotite compositions indicate that F = 0.18 to obtain 15% MgOliq at low pressures (MORs: Baker and Stolper ) and F = 0.20 to obtain 20% MgOliq at high pressures (OIs: Walter ). (Because F is similar at MORs and Hawaii [see also Kinzler and Grove, 1992b; Feigenson et al., 2003]), the magnitude of ΔTp is not greatly affected). For cooling due to decompression, it is necessary to know the depth of equilibration. For these calculations, equilibration pressures are taken as 1.15 GPa for MORs [Kinzler and Grove, 1992b], 4.0 GPa at Hawaii [Herzberg and O'Hara, 1998], and 2.3 GPa at Iceland [MacLennan et al., 2001a]. With an adiabat of 12°C/GPa, the following values for Tp are obtained: TpHawaii = 1688°C; TpIceland = 1637°C; TpMOR = 1453–1475°C, which translate to the following differences in mantle potential temperature: ΔTpHawaii-MORs ≈ 213–235°C and ΔTpIceland-MORs ≈ 162–184°C. The lower value for TpMOR and consequent higher values for ΔTp, are based on FeOliq = 7 wt.% at MORs.
3.5. Comparisons to Prior Estimates
 The above estimates for TpMOR are similar to or at the high end of estimates from Kinzler and Grove [1992b] and Green et al. , are lower than those from Putirka , and exceed but overlap within 1σ TpMOR estimates from Asimow et al. . High T estimates are not unexpected: maximum Fo contents should more closely approach the maximum temperatures experienced during melting compared to estimates from basalts. Moreover, values of TpMORs = 1454–1476°C are a much better match to mean temperature estimates from seafloor bathymetry (1450 ± 250°C at 95 km ≈ 1415 ± 250°C at Earth's surface [Stein and Stein, 1992]), compared to the very low values of 1260–1280°C of Presnall et al.  and McKenzie and Bickle . The present temperature estimates are furthermore robust against wt.% variations of various oxide components, including CO2 (see section 2.2.2). At hot spots, although respective estimates of ΔTp overlap within 1σ, the present estimates of Tp exceed estimates at Iceland by 117°C [MacLennan et al., 2001a] and at Hawaii by 130°C [Watson and McKenzie, 1991]. However, Watson and McKenzie , for example, calculate a ΔTp at Hawaii of 278°C, and obtain TpHawaii = 1558°C by reference to a background mantle potential temperature (TpMOR) of 1280°C [McKenzie and Bickle, 1988]. If referenced to TpMOR = 1450°C, their ΔTp yields TpHawaii = 1728°C, which exceeds the present value by 45°C. On the whole, then, there may be some convergence toward a background mantle Tp of 1450 ± 50°C, and a thermal anomaly at some hot spots in the range ≈160–250°C.
 So why do Green et al.  obtain such low values for ΔTp, even though they also examine maximum Fo contents? As noted, their estimates for TMOR are similar to the present values, but their THawaii is very low. This difference for THawaii appears to reflect a combination of Green et al.'s  use of too low a value of KD(Fe-Mg)ol-liq (0.30), and their apparent under-estimation of MgOliq for primitive Hawaiian magmas. As an example, if we apply Green et al.'s  values for MgOliq and Fool at Mauna Loa in their Table 1, and use KD(Fe-Mg)ol-liq = 0.30–0.35, Green et al.'s  FeOliq contents at Mauna Loa would be 8.6–10.0 wt.%, much lower than observed values (Figure 4). In contrast, Figure 6a (using observed FeOliq at Hawaii) implies primitive liquid compositions at Hawaii with 20 wt.% MgO, which also happens to be in accord with estimates from Feigenson et al. , based on their estimates of reconstructed liquid compositions. At the very least, the present estimates of Tp are more consistent with observed Hawaiian lava compositions.
 An updated olivine saturation surface model [Roeder and Emslie, 1970; Langmuir and Hanson, 1981] along with maximum Fo contents of olivines from Hawaii, Iceland and MORs, indicate that mantle potential temperatures are much greater at Hawaii and Iceland: TpHawaii − TpMOR = 213–235°C; TpIceland − TpMOR = 162–184°C. These estimates of ΔTp are above some estimates [Green et al., 1999; Ribe et al., 1995], but match well with estimates determined by geodynamic and other considerations (200°C: Sleep  and McKenzie ; 215 ± 35°C: Schilling ; 250–300°C: Ribe and Christensen ) [Klein and Langmuir, 1987; Watson and McKenzie, 1991]. Absolute estimates of Tp are less certain than estimates of ΔTp, as they depend on estimates of F and depth of equilibration, but olivine-liquid equilibria indicate that TpHawaii = 1688°C, TpIceland = 1637°C, and TpMORs = 1453–1475°C; the latter value is furthermore consistent with estimates based on seafloor bathymetry [Stein and Stein, 1992]. It should be emphasized that these temperatures account for measured differences in SiO2, H2O and alkali contents between Iceland, Hawaii and MOR liquids (Table 1) and do not depend on any other form of heterogeneity; the results are thus, for example, independent of potential Fe enrichment [e.g., Korenaga and Kelemen, 2000] or, as shown in section 2.2.2., enrichments in CO2 [Presnall et al., 2002]. Finally, these estimates of Tp and ΔTp clearly support the existence of thermally driven plumes. It thus appears unnecessary to rely solely on compositionally distinct mantle domains to explain sustained volcanism or elevated oceanic topography at hot spot volcanic centers.
 The topic of this paper was inspired from discussions with Cin-Ty Lee. The paper benefited greatly from those discussions and very thoughtful reviews and suggestions by J. Michael Rhodes and Marc Hirschmann. Thanks to Bill White for his editorial efforts. This work was supported by NSF grant EAR 03347345.