Genesis of trondhjemite by low-pressure low-melt fraction anatexis of hornblende-gabbro at Alvand Plutonic Complex (Hamedan, NW Iran): insights from geochemical modelling

Amphibole-dominated dehydration melting of gabbro is the primary process responsible for the genesis of adakites, low-K tonalites, modern trondhjemites, and plagiogranites as well as Archean tonalite-trondhjemite-granodiorite suites that represent the earliest examples of continental crust. Previous literature has mostly focused on the role of Al-rich amphibole during anatexis of a mafic source and many of these studies have investigated this process through experimental melting runs. However, due to experimental boundary conditions, little is known about partial melting of amphibole-bearing mafic rock at temperatures < 800°C for upper crustal conditions (pressure < 500 MPa). Classic and forward thermobarometric modelling suggests that in situ trondhjemite leucosomes, hosted by Cheshmeh-Ghasaban mafic metatexites (Alvand Plutonic Complex, Hamedan, NW Iran), represent a rare natural case study of a low-temperature incipient amphibole-dominated anatectic event of a mafic source with a primary assemblage (Pl+Hbl+Cpx+Bt+Opx) typical of a hornblende-bearing gabbroic rock.

With the goal of contributing to the understanding of the genesis of trondhjemite leucosomes through partial melting of hornblende-bearing mafic rocks, this paper is focused on the role of the dominant protolith-forming minerals during incipient crustal anatectic events. In particular, this work is intended as a companion paper of Saki et al. (2021) and uses part of its geochemical dataset from the Cheshmeh-Ghasaban (CG) mafic migmatite suite (Hamedan, NW Iran) where the connection between a gabbro protolith and in situ trondhjemite leucosomes has been demonstrated (Saki et al. 2020(Saki et al. , 2021. Results are discussed in the context of the existing literature. This study, exploring the CG mafic metatexites, provides new evidence on how the very early stage of partial melting of a hornblende-bearing mafic rock is developed in upper crust environment.
The intrusive Alvand plutonic complex generated a welldeveloped thermo-metamorphic aureole made up of cordierite-andalusite-sillimanite-bearing hornfels and cordierite-bearing migmatites (e.g., Sepahi et al. 2019;Saki et al. 2020) in the local low-grade regional metamorphic basement (known in literature as "Hamedan Phyllite," e.g., Mohajjel et al. 2003). Peak conditions for the thermal aureole were estimated at~750°C and 4 kbar (Sepahi 2008, Sepahi et al. 2013Sepahi et al. 2009Sepahi et al. , 2013Sepahi et al. , 2020Saki et al. 2012Saki et al. , 2020Baharifar et al. 2004;Shahbazi et al. 2014;Sheikhi Gheshlaghi et al. 2020). The metapelitic migmatites show a U-Pb zircon age of~170 Ma (Sepahi et al. 2019), and are mostly found in the eastern (Simin-Khaku locality) and southern (Tuyserkan locality) sectors of the inner aureole (e.g., Saki et al. 2021). These migmatites are characterized by the diffuse occurrence of S-type leucosomes and pegmatites (e.g., Sepahi et al. 2019;Sheikhi Gheshlaghi et al. 2020;Saki et al. 2012Saki et al. , 2020Saki et al. , 2021. The presence of mafic metatexite migmatites, characterized by the presence of both in situ and in source trondhjemite leucosomes within the CG Hbl-gabbro protolith, was reported and investigated by Saki et al. (2020Saki et al. ( , 2021. Saki et al. (2020) studied these mafic migmatites by integrating (i) field observations, (ii) microfabric and textures, and (iii) mineral and bulk rock chemistry and investigated the migmatization event through qualitative analysis of partial melting reactions and classic and forward thermobarometry. Saki et al. (2021) followed this with a quantitative investigation of the gabbrotrondhjemite connection utilizing (i) major-element mass balance modelling, (ii) trace and REE elements equilibrium batch melting (EBM) modelling, (iii) pseudosection analysis applied to the Hbl-gabbro protolith, and (iv) a preliminary comparison between trondhjemite leucosomes and the chemistry of experimental melts from literature. They concluded that an origin for in situ trondhjemite leucosomes are compatible with Fig. 1 Geological framework. a Schematic geological map of Iran (modified after Ghasemi and Talbot 2006;Saki et al. 2021). The Sanandaj-Sirjan zone is indicated in yellow. The blue square is the study area presented in b. b Simplified geological map of the Alvand plutonic complex (after Saki et al. 2021). The white star indicates the Cheshmeh-Ghasaban metatexite migmatites and the sampling locality. c Field observation: an example of the outcropping mafic metatexite migmatite characterized by net-structured texture and in situ leucosomes. d Petrography: the Hbl-gabbro protolith hosting an in situ leucosome micropatch. The Hbl-gabbro shows a holocrystalline texture with a primary assemblage made up of plagioclase (Pl P ), hornblende (Hbl), clinopyroxene (Cpx), orthopyroxene (Opx), biotite (Bt), and ilmenite (Ilm), whereas the leucosome is characterized mainly by a plagioclase (Pl L ) and quartz (Qz L ) association 1-2% partial melting of the Hbl-gabbro through an amphibole-dehydration melting process near the solidus at mid-to-upper crustal conditions of ≈700-750°C and 300-450 MPa.

Field observation and petrography
In this companion paper, we present the field occurrences, petrography, and mineralogy characterizing the studied Hblgabbro protolith and the in situ trondhjemite leucosomes.
The CG gabbros, with an area of >20 Km 2 (Fig. 1b), represent the most significant outcrop of mafic rocks in the Alvand complex. Here both Ol-gabbro and Hbl-gabbro are exposed and locally a primary contact is recognized (Saki et al. 2021 and references therein). Close to this contact, the Hbl-gabbro shows evidence for migmatization ( Fig. 1c) characterized by the presence of in-source and in situ leucosomes (sensu Sawyer 2008) in millimetric-to metric-scale veins, dikes, patches, net structure, veinlets, and lenses. Locally, schollen migmatite fabric is observed. The low volume of leucosome (<10 vol%) is typical of a metatexite migmatite (e.g., Sawyer 2008). To note, Sepahi et al. (2009) had already reported the thermally metamorphosed gabbros and Eshraghi and Mahmoudi Gharai (2003) previously documented "agmatites in gabbros" in the "Tuyserkan" quadrangle geological map, whereas no leucosome outcrop was found or documented in the Ol-gabbros (Saki et al. 2021).

Methodology
Five samples from the CG Hbl-gabbro protolith and five samples from in situ trondhjemite leucosomes were selected for whole-rock analyses. Samples were analysed for major, trace, and REE elements at Activation Laboratories (Canada) by ICP-OES and ICP-MS (code 4Lithoresearch). For major elements, the uncertainty (1s) is estimated less than 2% for concentrations higher than 5 wt%, and less than 5% for concentrations between 0.1 and 5 wt%. For trace elements, the precision is 5% and 10% for the values in the ranges 1-100 ppm and 0.1-1ppm, respectively. Whole-rock chemistry is presented in Table 1. The dataset is integrated with analyses of nine leucosome from Saki et al. (2020Saki et al. ( , 2021 and one Hbl-gabbro from Saki et al. (2021) collected from the same studied outcrops. These data are also reported in Table 1 for comparison. The total alkali vs. silica (TAS) diagram (after Middlemost 1994) is here chosen as proxy diagram for the purpose of a homogeneous dataset presentation. In the following, we adopted the mineral abbreviation recommended by Whitney and Evans (2010).
For the purpose of partial melting modelling using major elements, trace elements (Sr, Y), and REE (Dy, Yb), we calculated the compositions for average Hbl-gabbro protolith (Av-Gb; green star in diagrams of Figs. 2 and 3) and trondhjemite leucosome (Av-Lc; yellow star in diagrams of Figs. 2, 3, and 7). They are presented in Table 2.

Workflow
Starting from the same mineral assemblage (Pl+Hbl+Cpx) used in Saki et al. (2021) and using the current calculated protolith and leucosome average compositions, we test the equilibrium batch melting (EBM) model by integrating biotite and orthopyroxene (analyses of Saki et al. 2021) to (i) refine the K D coefficients characterizing this partial melting event, (ii) to constrain the role of all the main protolith-forming All the major elements data have been recalculated to 100 wt% on anhydrous basis with FeO* as total FeO. b Chondrite-normalized rare earth elements (REEs) diagram (Sun and McDonough 1989). c CaO-Na 2 O-K 2 O diagram for Cheshmeh-Ghasaban leucosomes. The fields of experimental melts produced at low pressure (P< 500 MPa) through amphibole (green field), biotite (blue field), and amphibole+biotite (dark red) dehydration melting are also indicated. d Normative An-Ab-Or diagram for the studied leucosomes. Literature data for "Hbl-Gabbro" and "Trondhjemite" are from Saki et al. (2021). Field of trondhjemites from Trondheim Region (Norway; cyan field, Nilsen et al. 2003) is also reported mineral phases, and (iii) to better constrain through a forward modelling the P-T conditions of the Hbl-gabbro anatexis.
The major-element mass balance model of Bryan et al. (1969) was used in Saki et al. (2021) to test the hypothesis of EBM (White et al. 2009;Lucci et al. 2016) for the genesis of trondhjemite leucosomes from the partial melting of the Hbl-gabbro. In EBM modelling, it is assumed that Residual Assemblage (Minerals) = Protolith Source − Leucosome. If the composition of the protolith is assigned to matrix b, and all elemental equations are solved for b, then b= Leucosome+ Minerals. When the chemistry of leucosome and minerals are known and expressed in matrix A, it is possible to determine their proportion (in matrix c) by least square approximation method. The similarity between the residual matrix b' (with b' = c X A) and the matrix b (the protolith) is quantified through the sum of the square of the residuals (Σr 2 ) as the following: Models are considered acceptable when Σr 2 < 1.0. The proportion of the leucosome is expressed with the variable F in matrix c.
Considering (i) the in situ character of the leucosomes and their equilibrium with the residuum until the end of the anatexis, (ii) the paucity/absence of gabbro remnants within the leucosomes, and (iii) the results obtained by Saki et al. (2021), it is then assumed the studied partial melting event is compatible with an equilibrium batch melting process (Shaw 1970;Zou 1998;Ersoy 2013), where the proportions of the involved mineral phases were those of the magmatic assemblage of the protolith. Following Saki et al. (2021), we use the Shaw (1970) equation chosen for equilibrium batch melting: where C 0 is the elemental concentration in the protolith, D 0 is the bulk mineral/melt partition coefficient, F is the fraction of produced melt, and C L is the corresponding calculated elemental concentration in the batch melt. The

Major element mass balance model
The results of major-element mass balance model applied to the average protolith and leucosome compositions are presented in Table 3, where mathematically reliable solutions for the genesis of leucosomes (Σr 2 0.02-0.49; models A to D) are reported.
The model A (Σr 2 0.49) shows that the high-SiO 2 (≈78 wt%) leucosome may be generated by ≈1% of partial melting of the gabbroic source with a residuum made up of Pl 38 Hbl 49 Cpx 11 . When Bt is included (model B, Σr 2 0.43), the major-element mass balance modelling shows a residuum of Pl 37 Hbl 46 Cpx 12 Bt 2 and highlights in the matrix c the negligible role of the trioctahedral phyllosilicate with respect to the Ca-Al minerals. When the Opx is added to the matrix A (models C and D), the mass balance modelling produces unrealistic results with invariably negative values in matrix c (highlighted in red) for the Opx. These negative values are here interpreted as an excess or a non-involvement of this phase in the Mineral = Protolith − Leucosome equation.
These results confirm the very low degree of partial melting calculated by Saki et al. (2021) and highlight an anatexis event dominated by Tschermak-bearing (Hbl+Cpx) and anorthite-  bearing (Pl) phases. Furthermore, the higher number of rock samples considered in the model permits to refine the amount of each phase involved in the batch melting event, confirming a scenario (Fig. 2c) of amphibole-dominated dehydration melting (e.g., Beard and Lofgren 1991) to generate the studied in situ trondhjemites.

Trace and REE element EBM models
Based on the previously presented major-element mass balance modelling, and consistency with the work of Saki et al.  3(a, b)) of the average Hbl-gabbro protolith (Av-Gb with Sr ≈486, Y ≈15, Dy ≈2.8, and Yb ≈1.4). However, the studied trondhjemite samples show a wide distribution with respect to the average composition in plots of Y vs. Sr/Y (Fig. 3(a)) and Yb vs. Dy/Yb (Fig. 3(b)). We therefore decided to explore the role of each mineral phase involved through the effect of their mineral/melt partition coefficients. From calculated partition coefficients in Table 4, it is possible to observe how Sr is mainly controlled by the plagioclase. An increase of the anorthite-plagioclase effect ( Pl D Sr up to 1.21) is capable to describe leucosomes with low Sr/Y ratio (Fig. 2c), whereas higher involvement of Tschermak-bearing inosilicates ( Hbl+ Cpx D Y up to 1.068, with Hbl D Y : Cpx D Y =3:1) controlling Y is capable to better approximate melts with higher Sr/Y ratio ( Fig. 2d) with respect to the average composition. However, only when the two effects are coupled is it possible to fully describe the leucosomes in the Sr-Y system.
A less significant role for plagioclase is instead observed when approaching the Dy-Yb system (Table 4), where the selected HREE elements are mostly controlled by the Ca-Al inosilicates. In particular, Dy is nearly to be totally controlled by Hbl, whereas a Hbl D Yb : Cpx D Yb =3:1 relationship exists for Yb, comparable to that previously observed for Y. While calculated variations of the bulk D Dy are not capable to describe the leucosome chemistry (Fig. 2f), opposite a minimum variability of the Hbl+Cpx D Yb (0.908-0.998) is effective in describing near all the leucosomes (Fig. 2g). Again, only when the minor effect of D Dy is coupled with D Yb is the whole dataset of trondhjemites described. Clinopyroxene and hornblende show similar effects in controlling the selected trace and REE elements during the partial melting event; however, the relation Cpx D << Hbl D is observed, suggesting that only Pl+ Hbl played a main role during this incipient anatexis.

Classic and forward modelling thermobarometry: the path to anatexis
To assess the pressure-temperature (P-T) conditions of genesis of CG trondhjemite leucosomes, we integrate here (i) classic thermobarometry as derived from the Zircon-saturation thermometry (T Zr , Watson and Harrison 1983) and the Monazitesolubility model (T REE , Montel 1993) and (ii) forward modelling thermobarometry through the pseudosections method. Results are then discussed also considering the previous results obtained by Saki et al. (2020Saki et al. ( , 2021. The zircon-saturation model provides information on saturation condition of zircon within an hydrous felsic Alsaturated magma (Watson and Harrison 1983) and therefore provides a minimum estimate for magma temperature prior to the extensive crystallization and cooling (e.g., Miller et al. 2003;Lucci et al. 2018). The trondhjemite leucosomes show values of Zr in the range 34-124 ppm, corresponding to T Zr = 684-694 ± 25°C (Table 1) and to a weighted mean value of 723 ± 13°C (±1s standard deviation of the weighted mean, MSWD = 0.98, n=14). The monazite-solubility model (Montel 1993) is based on the effect of LREE content in Capoor felsic melt and operated assuming the whole-rock composition as representative of a frozen liquid. The solubility LREE temperatures were calculated for variable water content (0.1-6.0 wt% H 2 O); results are reported in Table 1. These two models show convergence (T REE = T Zr ± 20°C) at (i) 733 ± 19°C (MSWD 0.58, n=7) for anhydrous conditions (H 2 O 0.1 wt%) in samples GH-L2, GH-L4, GH-L5, GH-Mig4, GH-Mig5, GH-Mig8, and CG-Lu1 and (ii) 710 ± 19°C (MSWD 0.22, n=7) for hydrous conditions (1-6 wt% H 2 O) in samples GH-L1, GH-L3, GH-Mig6, CG-Lu2, CG-Lu3, CG-Lu4, and CG-Lu5. When these two clusters are merged, the obtained weighted mean T REE (722 ± 13°C, MSWD = 0.60, n=14) overlaps that from zircon-saturation model. In agreement with the existing literature on SiO 2 -rich felsic melts (e.g., Miller et al. 2003;Rossetti et al. 2013;Lucci et al. 2018), the convergence of these two models could represent the temperature at the onset of crystallization, also resembling the temperature of the anatectic source (e.g., Rossetti et al. 2013).
The model system NCKFMASHT (Na 2 O-CaO-K 2 O-FeO*-MgO-Al 2 O 3 -SiO 2 -H 2 O-TiO 2 ) was chosen assuming the total iron as FeO due to the presence of ilmenite in the preserved primary mineral assemblage and lack of any secondary Fe 3+ -bearing phases. Three forward models were developed: the main one and two testbeds to verify its reliability on identifying the melt-in conditions. Concerning the main model (hereafter "model A"), the solid-solution models selected are "Augite(G)" for clinopyroxene (Green et al. 2016), "Opx(W)" for orthopyroxene (White et al. 2014), "Amph (DPW)" for Ca-hornblende (Dale et al. 2005) , "Bio (TCC)" for biotite (Tajcmanova et al. 2009), "feldspar" for feldspar (Fuhrman and Lindsley 1988), and "melt(G)" for melt (Green et al. 2016). The analyzed loss on ignition (LOI) was assumed as H 2 O content, coherently with the existing literature on partial melting modelling (e.g., Rossetti et al. 2020;Saki et al. 2021). The ilmenite (Ilm) end-member is also used in the calculation. The first testbed (hereafter "model T1") was developed using the same solid-solution models of model A but considering water-present conditions (H 2 O in excess). The second testbed (hereafter "model T2") was developed using LOI as H 2 O content but a different set of solidsolution models: "melt(G)" for melt (Green et al. 2016), "Augite(G)" for clinopyroxene (Green et al. 2016), cAmph(G) for Ca-hornblende (Green et al. 2016), Pl(I1,HP) and Fsp(C1) for ternary feldspar (Holland and Powell 2003), Bi(W) for biotite (White et al. 2014), Opx (W) for orthopyroxene (White et al. 2014), and Ilm (WPH) for . c Temperaturepressure-melt (wt%) representation of the progressive amount of melt generated through the partial melting of the average Av-Gb Hbl-gabbro protolith ilmenite (White et al. 2014). Further details are in the solution. dat file enclosed in the Perple_X package, whereas the reference database is the hp62ver.dat file, an update version of the Holland and Powell (2011) thermodynamic dataset. The single-phase volume isopleths (melt, Pl, Hbl, Cpx, Opx, Bt) and the mineral composition isopleths (i.e., an in plagioclase) were drawn by PyWerami (version 2.0.1, downloaded from the website http://petrol.natur.cuni.cz/~ondro/pywerami: home). The melt and mineral phases involved were expressed in weight % (wt%) and were in accordance with the results from the EBM models. Starting from the work of Saki et al. (2021), the pseudosections were constructed from 700 to 800°C and between 250 and 450 MPa. The results of forward modelling thermobarometry are shown in Figs. 4, 5, 6, and 7. The representative and simplified model A pseudosection calculated for the bulk chemistry of the Av-Gb average protolith is presented in Fig. 4 a, where the melt appearance (red dashed curve) is constrained at ≈725-730°C.
The melt and mineral phase isopleths (wt%) as derived from the pseudosections calculation are used to investigate the evolution of the partial melting evolution and are presented in Figs. 4 a and b and 5. In particular, the melt isopleths (wt%) are here used as a proxy of the anatexis. A three-dimensional temperature-pressure-melt abundances (T-P-melt) diagram ( Fig. 4c) is also proposed to better visualize the melt appearance (melt-in curve) in the system and its progressive production at higher temperatures. Replicate testbeds models T1 and T2 for water-saturated conditions (Fig. 5a, b) and different solid-solution models (Fig. 5c, d), respectively, show melt generation at ≈720-730°C comparable to the main model A (Fig. 4). However, with respect to main model A, the two testbed models fail in accurately reproducing the CG metatexite. The model T1 with H 2 O in excess (Fig. 5a) is characterized by a very high melt-production rate (Fig. 5b) in contrast with the observed low volume of in situ leucosomes. Opposite, the model T2 based on a different set of solution models (Fig. 5b) shows a reasonable low meltproduction rate (Fig. 5d) but fails in correctly reproducing the primary assemblage of the Hbl-gabbro as shown by the lack of primary orthopyroxene in the pre-melting protolith.
Consequently, the main model A represents the best forward modelling thermobarometry approximation of the anatexis of the CG Hbl-gabbro to generate the in situ trondhjemite leucosomes.
How did the protolith-forming Pl+Hbl+Cpx+Bt+Opx primary assemblage participate to the partial melting event? The possible solution to this point is explored hereafter using mineral volume and mineral composition isopleths as calculated for the main model A (Fig. 5).
The pseudosection method indicates that the protolith prior to melting ("pre-melting protolith" field in diagrams of Fig.  6a-f) is characterized by the following assemblage Pl 47 Hbl 26-32 Cpx 10-12 Bt 6 Opx 2-6 , very close to that determined by petrog r a p h i c o b s e r v a t i o n s ( P l 4 0 -5 0 H b l 3 0 -3 5 C p x 1 0 -20 Bt <10 Opx <5 Qz <5 ). Furthermore, the predicted anorthite component (X-An = 0.60) in plagioclase fully overlaps the observed one (X-An = 0.57-0.60). When the protolith starts to melt (T > 725°C), the following conditions are observed: (i) the amount of plagioclase progressively decreases (Fig. 6a), (ii) the plagioclase is characterized by a progressive increase of the anorthite compound (Fig. 6b), (iii) the amount of hornblende (Fig. 6c) and biotite (Fig. 6e) progressively decrease, and (iv) the amount of pyroxenes (Cpx+Opx) progressively increase together with melt production. These trends can be interpreted as a batch melting event (i) developed at the expenses of the Pl+Hbl+Bt assemblage and (ii) associated to the growth of newly formed Cpx+Opx. These two conditions are compatible with well-known reactions published in literature (e.g., Rushmer 1991;Pattison 1991;Thompson and Ellis 1994;Graphchikov et al. 1999;Weinberg and Hasalová 2015) and qualitatively discussed by Saki et al. (2020) for the studied mafic migmatites: The refined major-trace-REE EBM modelling and the study of partition coefficients proposed in this work indicate that in situ trondhjemite leucosome corresponds to a very low degree (≈1-2%) of partial melting of the Hbl-protolith mainly controlled by Ca-Al-bearing phases such as hornblende and plagioclase, whereas the improved thermometry estimates based on the zircon-saturation and monazite-solubility models indicated that the melting event was developed at ≈720-730°C . Saki et al. (2021), through classic barometry modelling applied to hornblende in the mesosome, propose a pressure estimates of 360 ± 60MPa for the partial melting. Integrating these results with those obtained from the forward modelling thermobarometry model A (Fig. 7), it is possible to derive the following conclusions: (i) the anatexis responsible for the trondhjemite leucosome production is an incipient partial melting event developed close to the solidus at a relatively low temperature (< 750°C), (ii) the appearance of new generation of pyroxenes (Cpx+Opx) is accompanying the melt production since the very early stage, and (iii) the trioctahedral mica is not involved in the melting reactions for a very low degree (<2%) of partial melting and therefore reaction of Eq. (5) can be discarded. Concerning the latter point, when trondhjemite leucosome chemistry are plotted in a Na 2 O-CaO-K 2 O diagram (Fig. 2c), they fall close to the Na 2 O-CaO axis, within the field of experimental melts derived from low pressure (P<500 MPa) amphibole-dominated dehydration processes in amphibole-bearing mafic rocks, whereas a biotite participation would have led to melts with higher K 2 O contents (e.g., Gao et al. 2016 and references therein). The noninvolvement of biotite in the dehydration melting process is also supported by its preserved texture when approaching the in situ leucosomes. This is also in line with the existing literature (e.g., Patiño Douce and Beard 1995;Singh and Johannes 1996) where it has been demonstrated for P<500 MPa that (i) biotite can persist to higher temperatures than hornblende and (ii) a biotite-plagioclase assemblage starts to melt at 750-770°C, a temperature slightly higher than that obtained for CG trondhjemite leucosomes.
In the work of Saki et al. (2021), it was proposed a comparison between the chemistry of the CG trondhjemite leucosomes and that of experimental melts produced at 850-1100°C for P 100-500 MPa conditions by partial melting of amphibole-bearing source rocks (e.g., Beard and Lofgren 1991;Sisson and Grove 1993;Patiño Douce and Beard 1995;Springer and Seck 1997;López and Castro 2001;Gao et al. 2016). Following their approach and using SiO 2 content as differentiation index, through the application of the "Color Fill Contour" tool in OriginPro 8.5.0 software, we derived the isolines (dashed black lines in Fig. 8) for the 900°C and the 1000°C experimental melting temperatures, for all the major elements. A decrease in melting temperature corresponds to experimental melts (grey circles in Fig. 8) characterized by a progressive SiO 2 (wt%) content increase associated with an opposite decrease of Al 2 O 3 , TiO 2 , MgO, FeO tot , MnO, CaO, and P 2 O 5 (wt%) contents. No clear relationship is highlighted for Na 2 O and K 2 O contents. As explained by Sisson et al. (2005), experimental runs close to the solidus and for T< 800°C are usually not attempted because of the very small volumes of melt produced precluding trustworthy bulk analyses. However, observing the Harker diagrams of Fig. 8, it would be expected that melt generated at such low temperatures would present still higher SiO 2 content and even lower Al 2 O 3 , TiO 2 , MgO, FeO tot , MnO, CaO, and P 2 O 5 contents. When CG trondhjemites are plotted in Harker diagram of Fig. 8, they completely match the expected compositional characteristics for low T and low P melts derived by amphibole-dominated dehydration melting from a mafic protolith. Furthermore, their integration in these Harker diagrams permit also to graphically trace the 800°C isoline (red dashed lines) contributing to our knowledge on low-pressure amphibole-dominated incipient anatectic events affecting amphibole-bearing sources, and furthermore to the genesis of high-SiO 2 (>70 wt%) low-Al 2 O 3 (<15 wt%) trondhjemites (sensu Barker and Arth 1976).  Fig. 4 a is integrated with its selected melt (wt%) isopleths and zircon-saturation thermometry (T Zr ) weighted mean value (cyan dashed line) and 1s range (cyan dotted field) calculated for trondhjemite samples. The blue star represents Ti-in-Hbl thermometry and Al-in-Hbl barometry estimates from Saki et al. (2021). The pressure-temperature (P-T) genetic domain of Cheshmeh-Ghasaban trondhjemites is indicated with the yellow shaded area. Mineral abbreviations follow Whitney and Evans (2010)

Conclusions
The hornblende-bearing gabbros outcropping at Cheshmeh-Ghasaban locality are a key area to investigate mafic migmatites and amphibole-controlled anatexis developed in the upper crust. Outcomes of this work are the following: (i) The CG Hbl-gabbro are the source protolith of a mafic metatexite hosting up to 10 vol% of in situ high-SiO 2 low-Al 2 O 3 trondhjemites. (ii) The EBM modelling indicates that the trondhjemite leucosomes are generated by a very low (< 2%) degree of batch melting of the hornblende-bearing gabbroic protolith. (iii) The partial melting event were mainly controlled by primary Pl+Hbl+Cpx gabbroic assemblage, whereas Bt shows a negligible role and Opx does not participated to the anatexis.
(iv) The Pl is the main phase controlling Sr (LILE) content, whereas Hbl is deputy to regulating Y (HFSE) and Yb (HREE) contents; Cpx shows similar behavior of Hbl; however, due to the lower distribution coefficients ( Cpx D << Hbl D), it plays a minor role with respect to the Pl+Hbl assemblage. (v) Classic and forward modelling thermobarometry along with existing literature indicates thermobaric estimates of T ≈720-730°C at P ≈360 MPa, close to the solidus, for the Hbl-gabbro partial melting and genesis of the trondhjemites. (vi) The pseudosection method confirms the main role of Pl+Hbl and highlights the growth of peritectic Cpx+ Opx associated with the melt, coherently with Hbldominated melting reactions. (vii) The natural CG high-SiO 2 low-Al 2 O 3 trondhjemites match the expected chemistry for melts generated by Literature data for trondhjemite (Tdj) leucosomes are from Saki et al. (2021). Experimental melt chemistry data (grey circles) are from Beard and Lofgren 1991;Sisson and Grove 1993;Patiño Douce and Beard 1995;Springer and Seck 1997;López and Castro 2001;Gao et al. 2016 amphibole-dominated partial melting of a mafic source at T < 800°C and P < 500 MPa.
These results fully describe how trondhjemites can be generated by a low-temperature incipient melting controlled by Ca-Al-bearing Pl+Hbl assemblage of a hornblende-bearing mafic source in upper crust conditions. PRIN2017 Project 20177BX42Z_001 (intraplate deformation, magmatism, and topographic evolution of a diffuse collisional belt: insights into the geodynamics of the Arabia-Eurasia collisional zones) funded by MIUR-Italy. A. S. and M. M. acknowledge the grant No. SCU.EG99.44295 funded by Shahid Chamran University of Ahvaz-Iran. The constructive reviews of two anonymous reviewers as well as the professional handling of the Editor Abdullah M. Al-Amri greatly contributed to improve the manuscript.
Funding Open access funding provided by Università degli Studi Roma Tre within the CRUI-CARE Agreement. This research is part of the corresponding author postdoc programme at the Roma Tre University. This research was supported by the PRIN2017 Project 20177BX42Z_001 (intraplate deformation, magmatism and topographic evolution of a diffuse collisional belt: Insights into the geodynamics of the Arabia-Eurasia collisional zones) funded by MIUR-Italy. The research was also supported by Shahid Chamran University of Ahvaz (grant nos. EG98.44295 and SCU.EG98.44295).

Declarations
Competing interests The authors declare that they have no competing interests.
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