B Minov
email: bminov@sckcen.be

L Dupré

M J Konstantinović

Magnetic after-effect study of dislocation relaxation in Fe-based alloys

Keywords: numbers: 75.60Lr, 62.40.+i, 61.72Lk, 61.72.J-, 61.72.Yx

Dislocation-related relaxation processes are studied by measuring the magnetic after-effect spectra as a function of temperature in a variety of non-deformed and cold-worked iron alloys. In the α-Fe and Fe-1%Cu alloys the peak centered at about 320 K appears as a consequence of plastic deformation. On the basis of the behavior of its parameters, such as the temperature position of the peak, the full width at half maximum, and the integrated intensities, this feature is assigned to the relaxation process of thermally-activated dislocation motion.

Introduction

Experimental techniques based on mechanical [1, 2, 3] and magnetic [4,5,6,7] relaxation phenomena are typically used to study processes related to thermal activation of a variety of lattice defects, in particular those that can be described as point defects. In body-centered-cubic (bcc) α-iron, both the Internal Friction (IF) and Magnetic After-Effect (MAE) measurements show the existence of relaxation processes that are assigned to the thermal motion of interstitially-dissolved atoms such as carbon and nitrogen, for example. These so-called Snoek-relaxation peaks appear in the temperature dependent IF and MAE spectra as a consequence of thermally-activated redistribution of interstitials in the lattice [8]. The analysis of the peak parameters, i.e. peak maximum, full width at half maximum (FWHM), and intensity, allows accurate determination of the kinetic parameters, such as the activation energy, distribution of relaxation times and concentration of interstitial atoms, respectively. All parameters extracted from IF and MAE experiments, in the case of both carbon and nitrogen relaxation processes, show excellent agreement with each other [9].

However, clear correspondence between dislocation-relaxation processes in the IF and MAE experiments is not yet established, in spite the fact that in both experiments dislocation-relaxation processes have been observed and reported [START_REF] Bordoni | [END_REF]10,11,12,13,14,15,16]. Such thermally-activated relaxation processes occur as a consequence of dislocation moving in a periodic lattice potential i.e. by dislocation overcoming the Peierls potential with the help of coherent atomic thermal fluctuations [START_REF] Bordoni | [END_REF]11]. In the MAE experiment the dislocation-relaxation processes may occur as the consequence of interaction between dislocations and Bloch walls [14,17], so there is no reason to discard possibility to observe the complementarity between IF and MAE techniques in that respect too.

In α-Fe at least three different dislocation-relaxation processes are observed in the temperature dependent IF spectra, and are denoted as α (around 30 K), β (around 240 K), and γ (around 330 K)-peaks (measured at about 1 Hz) [10]. In addition, the cold-worked samples with increased carbon content exhibit the peak at about 520 K which occurs as a consequence of carbon-dislocation interaction e.g. Snoek-Köster-relaxation. Interestingly, magnetic relaxation peaks which were associated to the thermal activation of dislocations are observed at 18 K, 430 K, 513 K and 625 K [14,15,17,18]. The properties of high temperature peaks strongly depend on carbon content, so they are assigned as the magnetic analogue of Snoek-Köster relaxation process. The low temperature peak (18 K) could be correlated to the α-relaxation according to its temperature position, but strong doubts exist in the literature [18]. Most intriguing temperature region is around 200 K -300 K since, due to the presence of carbon and nitrogen Snoek relaxation processes (290 K and 320 K measured at about 1 Hz [8]) it has been argued that the γ-relaxation is almost fully suppressed [19]. Still, most of the cold-worked iron alloys and steels show the existence of complex dislocationrelated relaxation processes in the temperature region around 200 K -300 K [20], which are not fully understood [21].

This work gives additional information about defect dynamics in iron-copper alloys, which can be used for better understanding of mechanical behavior of these alloys [22]. In this study we performed the MAE and IF measurements of non-deformed and coldworked low-carbon α-Fe, and MAE measurements of thermally aged Fe-1%Cu alloy focusing on the temperature region between 200 K and 500 K. In both materials we observed distinct relaxation processes at about 320 K which occur as a consequence of the plastic deformation. The numerical analysis of its activation energy indicates that this structure can be assigned to the dislocation-relaxation process equivalent to the IF dislocation-relaxation process, with the activation energy of about 1.00 to 1. 16 eV. Moreover, we analyze the behavior of the MAE relaxation processes in Fe-1%Cu alloy as a function of aging times. We found that all peaks, including dislocation peak, show the same behavior as analogous processes observed by the IF technique.

Experiment

The α-Fe alloy is fabricated by the zone refining method. The Fe-1%Cu alloy is prepared by argon-arc melting a low carbon steel in air, and adding the corresponding weight percent of pure copper. The details of the sample preparation are published elsewhere [23,24,25]. The chemical composition of the material used in this study is given in table 1. The various stages of copper precipitation are achieved by a thermal aging process of Fe-1%Cu samples, consisting of time-dependent heat treatments at 773 K (500 o C) in argon atmosphere, and subsequent fast quenching into water. The duration of heat treatments varied from 0.1 h to 480 h. This aging temperature is chosen in order to achieve the peak hardening in a reasonable time (15 h) [26], while different aging times are chosen in order to create different hardening stages.

The MAE measurements are performed in the temperature range 200 K < T < 500 K, by using an open magnetic circuit, working at 275 Hz and measuring the time dependence of the reciprocal value of initial susceptibility χ, i.e. the initial reluctivity, r(t,T)= 1 χ(t,T ) [27]. The typical sample size is 1.3 mm × 1.3 mm × 30 mm. The data acquisition of the different susceptibility isotherms started at 1 s (t 1 ) after a well defined field metric demagnetization of the sample and ended at t 2 ∼ 180 s.

The IF spectra are measured in an inverted torsional pendulum, working at the frequency of about 1.8 Hz, in a temperature range from 100 K to 600 K. From the free decay signal, the resonance frequency, ω, and the internal friction coefficient, Q -1 , are determined. The Q -1 is proportional to the ratio of the energy dissipated during one cycle to the maximum elastic energy stored in the sample. The measurements have been performed at a strain amplitude of about 10 -4 , in a He atmosphere with a heating rate of about 1.5 K/min, and no magnetic field is applied. Since there is no change of the magnetic interaction in the materials in the temperature region considered in this work, the change of the IF background due to application of the magnetic field is a constant value and does not depend on the temperature. Because of that, the measurements with or without the magnetic field will lead to the same conclusions.

A second set of samples is, prior to the measurements, subjected to a torsional cyclic plastic deformation in a consistent way at room temperature. The degree of deformation is estimated as βd/L, where β, d and L are twisting angle, diameter and sample length, respectively.

Results and discussion

The temperature dependent MAE and IF spectra of non-deformed and cold-worked α-Fe samples are shown in figure 1. In the case of non-deformed alloys, by increasing the temperature, the MAE spectra exhibit a peak at about 260 K, denoted as E 1 . On the basis of its overall shape, the temperature position and the full width at half maximum (FWHM ∼ 30 K), the peak is assigned to the Snoek-relaxation of carbon interstitials [8]. As a consequence of plastic deformation, the MAE spectra exhibit the appearance of an additional structure, denoted as E 2 and centered around 320 K, see figure 1a. The FWHM of the E 2 peak is about 80 K -100 K which indicates that this relaxation is governed by a distribution of relaxation times which is typical for spatially extended defects such as dislocations. The temperature dependent IF spectra of the cold-worked sample in the heating (dashed line) and cooling (dotted line) regimes are presented in figure 1b. The internal friction spectra in the cooling regime are shifted lower values in order improve the graph clarity. The temperature dependence of the frequency is shown only for the heating the heating regime spectrum are analyzed by a standard Debye-relaxation expression [1]:

Q -1 ∼ ∆ ωτ 1 + (ωτ ) 2 (1)
where ∆ is the relaxation strength, and τ is the relaxation time which follows an Arrhenius equation τ = τ 0 exp( H kT ) with the activation enthalpy H. The results of the fit, including separate contributions of each relaxation process and an exponential background, are shown by full lines. By increasing the temperature the heating-regime spectrum exhibits three peaks centered around 310 K, 320 K, and 500 K, which on the basis of previous investigations are recognized as the Snoek-, cold-work-dislocation (CWD) -peak, and the Snoek-Köster relaxation processes [8,28,29], respectively. In a cooling regime, the E 2 peak is fully annealed, while the carbon related peaks, e.g. the Snoek-and Snoek-Köster peaks are still clearly visible.

The activation energies of the E 1 and E 2 relaxation processes observed in MAE and IF spectra are analyzed on the basis of two methods.

(a) The Arrhenius plots. The relaxation times involved in both MAE and IF measurements follow an Arrhenius equation with identical values of activation energy, H, and pre-exponential factor, τ 0 [30]. The τ (MAE) = (t 2 -t 1 )/ln(t 2 /t 1 ) and τ (IF) = (2πω) -1 , where t 1 and t 2 are the two measuring time points characterizing two isochronal MAE curves. In figure 2, τ is plotted as a function of 10 -3 /T for the corresponding peaks in several isochronal MAE curves as well as for the IF peaks. In such plots the straight lines connecting the MAE and IF results are expected if the results belong to the same relaxation process [30]. Indeed, this is confirmed for both E 1 and E 2 relaxation peaks, see figure 2. The estimated parameters of the E 1 and E 2 relaxation processes are collected in table 2.

(b) Numerical technique. Figure 3 shows isochronal relaxation curves, i.e. the temperature dependent relative change of the reluctivity, r:

∆r r 1 = ∆r(t 1 , t 2 , T ) r(t 1 , T ) = r(t 2 , T ) -r(t 1 , T ) r(t 1 , T ) . (2)
t 1 = 1 s, and the curves are shown for various t 2 in the range from 8 s to 180 s. The calculated curves (full lines) are approximated by the sum of separate contributions including two relaxation processes and an exponential background. The numerical fit of two relaxation processes is performed on the basis of the point defect model [31]:

∆r(t 1 , t 2 , T ) = A(T ){[E i (-t 1 /τ 1 )-E i (-t 2 /τ 1 )]-[E i (-t 1 /τ 2 )-E i (-t 2 /τ 2 )]}. (3)
The A(t) and E i (-t i /τ k ) represent the temperature-dependent relaxation amplitude, and exponential integral with the measuring times t 1 and t 2 , respectively. τ 1 and τ 2 are the relaxation times as obtained from the Arrhenius equation for the minimum (τ 1 = τ 0 exp( H 1 kT )) and maximum (τ 2 = τ 0 exp( H 2 kT )) energy across the range ∆H (i.e. H 1 = H -∆H/2; H 2 = H + ∆H/2). In other words, τ 1 and τ 2 are the lower and upper bounds of relaxation times at temperature T. For each relaxation peak several isochronal curves are simultaneously fitted until the best agreement between measured and calculated spectra are obtained. This allows the estimation of the relaxation processes parameters H, ∆H and τ 0 which are collected in table 2.

Both methods for both relaxation processes give very similar results. In the case of the Snoek-peak, our results agree well with the literature [9]. For the E 2 peak, it is found that the activation energy is very close to the value of the γ-peak observed in the IF spectra (1.06 eV) [11]. Besides, the FWHM of the E 2 peak (∆H = 0.15 eV) which is proportional to the distribution of relaxation times, is also in good agreement with IF data. Because of that, we assign the E 2 peak to dislocation-relaxation process. The agreement between measured and calculated spectra is found to be not so good for the tails of relaxation distribution function. This is the consequence of non-adequacy of the model, which is strictly specking valid only for the point defect relaxations [18]. However, this disagreement do not endanger the determination of the activation energy. Due to non-adequacy of the model, one can be concerned about the precise determination of FWHM only, but this result also indicates that the relaxation process can not be associated to the point defect relaxations. Further, we analyze the MAE spectra of thermally aged Fe-1%Cu alloys. The temperature dependent non-deformed and cold-worked MAE spectra of Fe-1%Cu alloy thermally aged at 773 K for 20 h are shown in figure 4. In cold-worked samples, the peak at about 320 K is observed in addition to the Snoek-peak. This peak clearly appears as the consequence of plastic deformation, with the intensity which increases by increasing the degree of plastic deformation, see figure 4. Moreover, the peak position at about 320 K corresponds well to the E 2 peak position observed in α-Fe.

Figures 5 and6 show the temperature dependent MAE spectra of non-deformed and cold-worked thermally aged Fe-1%Cu samples, respectively. The intensity of Snoek peak of the non-deformed samples, denoted as E 1 ND , decreases by increasing the aging time, until about 180 h where it diminishes. For the sample aged for 0.1 h, the carbon Snoekpeak is found to be about 2.5 times more intense in comparison with the Snoek-peak in α-Fe alloy, see figure 1. This observation nicely correlates with reported carbon contents in these alloys, see table 1. The temperature position of the peaks maximum as well as the FWHM do not change as a function of aging time. In the spectra of cold-worked samples the Snoek-peak and cold-work-dislocation peak are marked as E 1

CW and E 2 , respectively. The spectra are clearly more complex in comparison with non-deformed samples because of the partial overlap of the peaks.

The main change of the MAE spectra, caused by different thermal aging times, is observed in the behavior of peak intensities. The analysis of the peak intensities is performed by fitting the spectra with Gaussian peak shapes, since it produces a much better fit in comparison with the point defect model, see [START_REF] Bordoni | [END_REF]. The integrated intensities of the E 1 peak, observed in the MAE spectra of both non-deformed (ND) and coldworked (CW) samples, as well as the intensities of the E 2 peak are presented in figures 7a, b as a function of the aging time. Their behavior is compared with results from already measured IF spectra [32] here reproduced at figures 7c, d.

As already discussed in our previous work [32], the intensity decrease of the Snoek peak (E 1 ND ) in non-deformed samples indicates a strong influence of the copper precipitates to the carbon kinetics, see figure 7a. Indeed, the process of carbon redistribution is most probably a result of the lattice strain field, created by the growth of copper precipitates. This could cause an enhanced carbon migration in the lattice, leading to carbon segregation at the precipitate interfaces or at the grain boundaries. This effect is also confirmed in the cold-worked samples, on the basis of the E CW 1 peak intensity behavior. The only difference is that the intensity values of the E CW 1 peak are situated below the E 1 ND peak intensities, due to a partial segregation of carbon atoms to dislocations during plastic deformation. The MAE and IF peak intensity behaviours disagree with each other at very short aging times (up to 1 h), see figure 7c. This is an early and intense precipitation regime which could cause large variation of the Snoek-peak intensities (large error-bars).

The E 2 peak, in both cases, exhibits a gradual increase reaching a local maximum at about 15 h, and the second increase at high aging times, see figures 7b, d. The intensity increase up to 15 h is a consequence of dislocation-precipitate interaction and can be correlated to the peak hardening [32]. Namely, the growth of copper precipitates at early precipitation stages obstructs the dislocation motion, and increases the dislocation density in the material, which is manifested as the E 2 peak intensity increase. Second E 2 intensity increase, observed after 180 h, is a consequence of carbon redistribution. Due to carbon removal from the lattice the E 2 dislocation-relaxation peak gains intensity at the expense of Snoek-Köster relaxation peak (not observed in MAE, but clearly observed in the IF experiment [32]).

Finally, the most important observation is the existence of the similarities between intensity behavior of MAE and IF cold-worked relaxation-peaks. This indicates that the same features are observed in both MAE and IF spectra. This concerns both Snoek and cold-worked peaks. This fact provides an additional proof of MAE-IF complementarity already observed in α-Fe concerning dislocation-related relaxation process.

Conclusion

Magnetic after-effect measurements were performed in order to study dislocation dynamics and dislocation related relaxation processes in Fe-based alloys. By analyzing the temperature-dependent isochronal relaxation spectra of non-deformed and coldworked α-Fe and thermally aged Fe-1%Cu, we observed the structure at about 320 K which uniquely occurs as a consequence of plastic deformation and can be clearly distinguished from the relaxation of carbon interstitials at about 260 K. This peak is, on the basis of relaxation-process parameters such as the activation energy, half-width

Figure 1 .

 1 Figure 1. Magnetic after-effect (a) and internal friction (b) spectra as a function of temperature of non-deformed (ND) and cold-worked (CW), as-provided α-Fe samples.

Figure 2 .

 2 Figure 2. Arrhenius plot for both E 1 and E 2 peaks observed in the spectra of plastically deformed α-Fe alloy. The MAE data are obtained from isochronal curves of t 2 = 8 s, 32 s, 60 s, 120 s and 180 s.

Figure 3 .

 3 Figure 3.Isochronal magnetic relaxation spectra fitted by numerical technique. t 1 = 1 s, t 2 = 8 s (1), 32 s (2), 60 s (3), 120 s (4), 180 s(5). Symbols correspond to measured points and lines to their numerical approximations.

Figure 4 .

 4 Figure 4. Magnetic after-effect spectra as a function of temperature of thermally aged for 20 h, Fe-1%Cu samples, with different degree of plastic deformation. The degrees of plastic deformations are mentioned in the figures. The circles are the experimental data and full lines are results of the fit.

Figure 5 .

 5 Figure 5. Magnetic after-effect spectra as a function of temperature of non-deformed (ND), thermally aged Fe-1%Cu samples. The circles are the experimental data and full lines are results of the fit. Aging times are mentioned in the figure.

Figure 6 .

 6 Figure 6. Magnetic after-effect spectra as a function of temperature of cold-worked (CW), thermally aged Fe-1%Cu samples. The circles are the experimental data and full lines are results of the fit. Aging times are mentioned in the figure.

Figure 7 .

 7 Figure 7. The integrated intensities as a function of the aging time of the E 1 and E 2 -peaks obtained by MAE (a and b) measurements, respectively. The integrated intensities as a function of the aging time of the Snoek (E 1 )-and cold-work-dislocation (CWD -E 2 )-peaks obtained by IF (c and d) measurements, respectively. Non-deformed -ND and cold-worked -CW samples.

Table 1 .

 1 The nominal composition of investigated alloys.

	Material Nominal composition (wt. %)
	α-Fe	(∼ 30-40 ppm C)
	Fe-1%Cu 1% Cu (∼ 70-100 ppm C)

Table 2 .

 2 Summary of results obtained from analyses of magnetic relaxation processes due to different techniques.

	Arrhenius		Numerical
	H (eV)	τ 0 (s)	H	∆H(eV)	τ 0 (s)
	E 1 0.90 ± 0.04 10 -16±0.5 0.86 ± 0.04	0.04	10 -16±0.5
	E 2 1.16 ± 0.1	10 -16±2 1.00 ± 0.02	0.15	10 -16±2


Benoît Sittler

Adrian Aebischer

Olivier Gilg
email: olivier.gilg@gmail.com

Post-breeding migration of four Long-tailed Skuas (Stercorarius longicaudus) from North and East Greenland to West Africa

Keywords: Satellite tracking, post-breeding migration, staging area, upwelling, rates of travel, Long-tailed Skua, Stercorarius longicaudus, Greenland Falkenraubmöwen ernähren sich während der Brutzeit hauptsächlich von Lemmingen und stellen wenig bekannt. Mit Hilfe von 9.5 g schweren, solarbetriebenen Satellitensendern konnten

The Long-tailed Skua is a specialist predator of lemmings during summer and hence an important component of the Tundra ecosystems, but most of its life cycle takes place offshore and remains largely unknown outside of the breeding season. Using 9.5g solar-powered satellite transmitters, we could document for the first time the post-breeding movements of the Long-tailed Skua, from its high-Arctic breeding-grounds in North and Eastern Greenland, to the tropical waters of West Africa. The birds travelled the ca. 10.000 km of this migration in only 3-5 weeks, covering 800-900 km/day during active migration, which also occurred during night time. Leaving their breeding areas in August (except for one failed breeder), the Long-tailed Skuas first moved south along the coast of East Greenland towards a staging area off the Canadian Great Banks where they stayed for 1-3 weeks.

From there, they crossed the Atlantic Ocean eastwards in just one week and entered the African waters near the Madeira Archipelago in September. Although we only monitored four birds for 1.5 to 3 months, migration routes were relatively similar between birds breeding in different locations and in different years.

Introduction

The Long-tailed Skua (Stercorarius longicaudus) is an important component of the Arctic terrestrial vertebrate community. Across most of its breeding range, it depends on cyclic lemming densities to breed [START_REF] Andersson | Breeding behaviour of the Long-tailed Skua Stercorarius longicaudus (Vieillot)[END_REF][START_REF] Andersson | Population ecology of the Long-Tailed Skua (Stercorarius longicaudus Vieill.)[END_REF][START_REF] Andersson | Reproductive tactics of the long-tailed skua Stercorarius longicaudus[END_REF][START_REF] Larson | Site tenacity of the Long-tailed Skua Stercorarius longicaudus -a study of the population at Stekenjokk[END_REF][START_REF] Maher | Ecology of the Long-tailed Jaeger at Lake Hazen, Ellesmere Island[END_REF][START_REF] Meltofte | Reproductive response to fluctuating lemming density and climate of the Long-tailed Skua Stercorarius longicaudus at Zackenberg, Northeast Greenland, 1996-2006[END_REF] and both species strongly interact [START_REF] Gilg | Cyclic dynamics in a simple vertebrate predator-prey community[END_REF]. Along with a few other predators, the Long-tailed Skua regulates the Collared Lemming (Dicrostonyx groenlandicus) dynamics in Northeast Greenland [START_REF] Gilg | Functional and numerical responses of four lemming predators in high arctic Greenland[END_REF][START_REF] Schmidt | Vertebrate predator-prey interactions in a seasonal environment[END_REF], especially during the peak phase of the lemming cycle when, along with the Snowy Owl (Nyctea scandiaca) and the Arctic Fox (Alopex lagopus), it is responsible for the rapid summer decline in lemming numbers [START_REF] Gilg | The summer decline of the collared lemming (Dicrostonyx groenlandicus) in high arctic Greenland[END_REF].

Conditions experienced by seabirds during migration and on their wintering grounds are assumed to impact their subsequent reproductive performance [START_REF] Furness | Techniques to link individual migration patterns of seabirds with diet specialization, condition and breeding performance[END_REF]. De [START_REF] Jd | Ecology of the Long-tailed Skua, Stercorarius longicaudus Vieillot, 1819, at Scoresby Sund, East Greenland. Part three: clutch size, laying date and incubation in relation to energy reserves[END_REF] has shown that Long-tailed Skuas breeding in Northeast Greenland arrive with maximal fat reserves in spring. The pelagic habitats they use during the non-breeding period (9-10 months of the year) must hence provide them with sufficient food resources to initiate breeding but are also, in turn, indirectly impacting the lemming population dynamics. Little is known, however, about the flyways and wintering grounds used by the species, the most pelagic of all Skuas [START_REF] Furness | The Skuas[END_REF][START_REF] Olsen | Skuas and Jaegers[END_REF]. With the exception of some local concentrations reported from the Benguela upwelling [START_REF] Lambert | Ein Überwinterungsgebiet der Falkenraubmöwe, Stercorarius longicaudus Vieill. 1819, vor Südwest-und Südafrika entdeckt[END_REF][START_REF] Ryan | The distribution and abundance of Long-tailed Skuas off southern Africa[END_REF]), a cold nutrient rich current off the coasts of Namibia and South-Africa, there are nearly no ring recoveries for the species during the non-breeding period and flyways have been inferred from only a limited number of offshore observations. Recent developments in satellite telemetry, with transmitters weighing less than 10g, have opened new perspectives for the study of medium sized bird (between 300 and 500g). Because it breeds in remote Arctic areas and spends the rest of the year in similarly remote offshore waters, the Long-tailed Skua is a perfect candidate species for these new research techniques. The present study presents the timing, duration, and flyways of four Greenlandic Long-tailed Skuas during their postbreeding migration, as part of a comprehensive long-term research of terrestrial vertebrates in Northeast Greenland [START_REF] Gilg | Cyclic dynamics in a simple vertebrate predator-prey community[END_REF][START_REF] Sittler | Response of stoat (Mustela erminea) to a fluctuating lemming (Dicrostonyx groenlandicus) population in North East Greenland: preliminary results from a long term study[END_REF].

Material and methods

Four Long-tailed Skuas were captured and fitted with satellite transmitters (PTTs) in 2006 and 2007 in the -North and East Greenland National Park‖ (Table 1). All birds were breeding. In 2007 we captured the birds on the nest using a bow net, while in 2006 they were captured within a few meters of the nest, using a small mist net (ca. one square meter) fixed on two handhold poles and rapidly raised in front of attacking birds.

All birds were equipped with 9.5g solar-powered PTTs from Microwave Telemetry Inc (Columbia, USA). Transmitters were attached to the birds as a backpack using Teflon ribbon and four silver rings to build the harness. The PTT and harness (ca. 2g) weighted less than12g, which was on average 3.9% (±0.15 SD) of the body mass of the birds. The PTTs fitted on the two birds in 2006 were set to a constant duty cycle of 7/38h (on/off, respectively), the two PTTs attached in 2007 had a constant duty cycle of 7/25h on/off. PTTs were located using the Argos positioning system (CLS 2008) that provides positions in seven precision classes. The location errors of the classes called LC3, LC2, LC1 and LC0 follow a normal distribution with a standard deviation of <150, <300, <1000 and >1000 m respectively. There is no accuracy estimate associated with the remaining classes (i.e. LCA, LCB and LCZ) but LCA have been showen to have the same accuracy as LC1 [START_REF] Hays | The implications of location accuracy for the interpretation of satellite-tracking data[END_REF][START_REF] Vincent | Assessment of Argos location accuracy from satellite tags deployed on captive gray seals[END_REF]. We used orthodromic distances to estimate the -daily rates of travel‖ of the birds [START_REF] Imboden | Formel für Orthodrome und Loxodrome bei der Berechnung von Richtung und Distanz zwischen Beringungs-und Wiederfundort[END_REF][START_REF] James | Migratory and reproductive movements of male leatherback turtles (Dermochelys coriacea)[END_REF] for time scales of 45±7 hours (in 2006) and 32±7 hours (in 2007). For these calculations, we used successive -best daily location‖ (i.e. in order of preference: LC3, LC2, LC1, LCA, LC0) produced during the 7 hour transmitting period. We never used LCB and LCZ in the calculations. We also estimated -hourly rates of travel‖ using successive high accuracy fixes (LC3, LC2 and LC1) for time periods between 0.5-2 hours (for more details see [START_REF] Gilg | Post-breeding movements of the northeast Atlantic ivory gull Pagophila eburnea populations[END_REF].

Results

Altogether, the four PTTs produced 1019 Argos positions and the birds could be monitored for 45 to 86 days (mean 66 days; Table 1). Only one third (i.e. 376) of these locations were LC3, LC2, LC1 or LCA, but more than 70% of the -best daily positions‖ (i.e. 93 out of 131) were high accuracy fixes (LC3, LC2 and LC1).

Since 2006 and 2007 were two years with very low lemming densities in Mestersvig and Karupelv Valley, no Long-tailed Skuas bred successfully in either of these study sites during these years [START_REF] Gilg | Climate change and cyclic predator-prey population dynamics in the high-Arctic[END_REF]Benoît Sittler, unpublished data). The three birds monitored from this region left their breeding grounds 36-43 (Papikk), 42-43 (Niilar) and 12 days after they had been released (Table 1). The bird from Bliss Bugt (Blissy), the only bird that had possibly raised young (considering a fledging period of 25 days: [START_REF] Cramp | Handbook of the birds of Europe, the Middle East and North Africa. Volume III Waders to Gulls[END_REF], left its territory 31 days after release.

Hence, the start of the fall migration (i.e. the date of departure from the breeding grounds) occurred between July 19 th and August 15 th , in line with previous studies [START_REF] Jd | Ecology of the Long-tailed Skua (Stercorarius longicaudus Vieillot, 1819) at Scoresby Sund, East Greenland. Part two: Arrival, Site tenacity and Departure[END_REF][START_REF] Wiley | Long-tailed Jaeger (Stercorarius longicaudus)[END_REF]Benoît Sittler and Olivier Gilg, unpublished data).

After departure, all birds moved southward following the outer coast (note that -Blissy‖ did not take the shortest route over the Greenland icecap), passing between southeast Greenland and Iceland, towards a large (ca. 500.000 km²) staging area located off the Great Banks of Newfoundland in Canada (Figure 1). The first bird (Lucy) arrived there by the end of July, the others by the end of August. With the exception of Blissy, which was lost 20 days after it had started its migration (i.e. shortly before reaching this area), it took the birds 1-2 weeks to travel the 3.000 km from their breeding grounds in Northeast Greenland to this staging area (Figure 1). The three birds then stayed in this area for 8-20 days.

Two of the remaining birds could be further followed while they crossed the Atlantic Ocean towards North-West Africa. It took them one week to travel the 2500-3000 km from the staging area to the African waters, north of the Madeira Archipelago, where they arrived on September 12 th (Papikk) and 23 rd (Niilar), i.e. 21 and 39 days respectively after they had left their breeding grounds. From there, the last bird we monitored (Papikk) continued to move south, flying a few 100's of km offshore, and was finally lost one week later and 2500 km further south, off the coast of Guinea (ca. 10° Lat. N).

After they had left their breeding grounds, the rate of travel of the birds was usually between 100-400 km/day, with maximum rates of 800-900 km/day (Figure 2: upper panel). When adding together the daily legs of this route, the length of the post-breeding flyway, from Greenland to Guinea (through the Canadian waters -off the Great Banks-and the Madeira Archipelago) is about 10.000 km (Figure 2: central panel), and is 1500 km longer for birds like -Blissy‖ breeding in North Greenland.

The remaining distance to the main known wintering grounds (see Discussion) off South Africa is about 5000 km on a direct route crossing the Gulf of Guinea (according to [START_REF] Lambert | Seabird sightings in the waters off Angola, 1966-1988[END_REF], some migrating Long-tailed Skuas follow the coast of Angola while other cross the Gulf of Guinea offshore).

The hourly rate of travel calculated during migration with 63 successive pairs of high accuracy fixes was 14 km/h on average (maximum values: 53, 56 and 61 km/h). In several instances, we also found evidence of active nocturnal migration, as already suspected by [START_REF] Lambert | Nächtlichte Zugaktivität von Seevögeln im Golf von Guinea[END_REF]. Two such cases presented in detail in Table 2 (using four and six LC0 fixes) indicate that distances travelled during such events (i.e. >200 km), are not anecdotal when compared with the mean daily rate of travel (Figure 2: upper panel).

Discussion

Although our results are inferred from only four individuals, the consistency in the routes followed by these birds, and the fact that they originated in three different locations over two different years, supports the idea that the Long-tailed Skuas breeding in East and North Greenland use a specific postbreeding flyway and make use of a staging area off the Canadian Great Banks between ca. 48-51° Lat. N (Figure 1 and Figure 2: see plateau on lower panel). This pelagic region is well known for its high productivity (see e.g. http://oceancolor.gsfc.nasa.gov/SeaWiFS) and has also recently been suggested as a -hot-spot‖ for other seabird species [START_REF] Egevang | Tracking of Arctic terns Sterna paradisaea reveals longest animal migration[END_REF]; see also historical data in Wyne-Edwards 1935). Staging in this area probably allows the Long-tailed Skuas to restore fat reserves after the demanding breeding season before heading to the southern hemisphere through the low productive tropical waters off West Africa.

From this staging area, Long-tailed Skuas head eastward, crossing the Atlantic Ocean north of the Azores Islands and reaching Northwest Africa between mid August and late September. Only few autumn observations have been made from the coasts of West Africa, probably because the migrating birds pass far offshore (see Papikk and Niilar on Figure 1), but seawatching from the Cape Verde Peninsula in Senegal has provided an average of 18 birds per day in October between 1995 and 2008 (111 days of monitoring and 1988 birds counted; [START_REF] Dubois | La péninsule du Cap-Vert à Dakar, Sénégal, est-elle la "Mecque[END_REF], with a maximum of 123 birds on 27 October 2007 [START_REF] Nilsson | Senegal -Havsfågelskådning i världsklass[END_REF]). Numbers are probably even higher in late August and September (e.g. 69 Long-tailed Skuas counted in a single day the 31st of August 1990; [START_REF] Baillon | Seawatching from Cape Verde, Senegal[END_REF] see also Fig. 2 lower panel) but no regular monitoring has yet been undertaken during this period [START_REF] Dubois | La péninsule du Cap-Vert à Dakar, Sénégal, est-elle la "Mecque[END_REF].

At first glance, our results would suggest that the Greenland birds migrate to the South-African wintering zone, where large concentrations of this species have been reported in the past, rather than to South-America, as previously thought by some authors [START_REF] Harrison | Seabirds[END_REF][START_REF] Olsen | Skuas and Jaegers[END_REF]; but see below). [START_REF] Lambert | Ein Überwinterungsgebiet der Falkenraubmöwe, Stercorarius longicaudus Vieill. 1819, vor Südwest-und Südafrika entdeckt[END_REF] for example found great numbers of Long-tailed Skuas off the coast of Namibia (> 200 birds some days) and [START_REF] Ryan | The distribution and abundance of Long-tailed Skuas off southern Africa[END_REF], working off the South African coast, gave an estimate of 75.000 Long-tailed Skuas wintering between 34 and 44° Lat. S. (see also observations from [START_REF] Lambert | Seabird sightings in the waters off Angola, 1966-1988[END_REF] who counted up to 26 birds per day in October/November off the coast of Angola). Whether overestimated or not, these figures are at least suggesting that this region, a highly productive marine area due to the Benguela upwelling system [START_REF] Hutchings | Fish harvesting in a variable, productive environmentsearching for rules or searching for exceptions?[END_REF], is a key wintering area for the species. It probably hosts birds from many different origins, and possibly most if not all of the western Palaearctic populations.

However, we can't yet rule out the possibility that some at least of the Greenland birds continue their migration towards the other main wintering area reported in the Southern Atlantic Ocean: the Falkland current off Argentina. Up to 1500 birds were seen daily in this region in early November 1920 [START_REF] Cramp | Handbook of the birds of Europe, the Middle East and North Africa. Volume IV Terns to woodpeckers[END_REF][START_REF] Olsen | Skuas and Jaegers[END_REF], though later visits always provided much smaller numbers (Brown et al, 1975;[START_REF] Murphy | Ocean birds of South America[END_REF]Veit 1985;[START_REF] Wetmore | Observations on the birds of Argentina, Paraguay, Uruguay, and Chile[END_REF] or even failed to record the species at all (see e.g. [START_REF] Orgeira | Distributión especial de densidades de aves marinas en la platforma continental Argentina y Océano Atlantico sur[END_REF][START_REF] Tuck | A guide to seabirds on the ocean routes[END_REF]. Among all known wintering areas for this species, the remaining ones only host small numbers of wintering birds and are less likely to be used by Greenland Long-tailed Skuas. For example the east coast of Africa [START_REF] Lambert | The spatial and seasonal occurence of seabirds (Aves) off southern Mozambique[END_REF]) and the southwestern coast of South America [START_REF] Harrison | Seabirds[END_REF][START_REF] Howell | Noteworthy bird observations from Chile[END_REF][START_REF] Johnson | The birds of Chile and adjacent regions of Argentina[END_REF][START_REF] Tuck | Guide des oiseaux de mer. Delachaux et Niestlé, Neuchâtel Veit RR[END_REF], another region with productive upwelling zones, are thought to host birds originating from central Siberia [START_REF] Lambert | The spatial and seasonal occurence of seabirds (Aves) off southern Mozambique[END_REF] suggested that these birds use overland migration) and from eastern Siberia-Alaska, respectively. A few additional wintering areas may exist, e.g. off Australia and New Zealand, as suggested by irregular but repeated observations [START_REF] Harrison | Seabirds[END_REF][START_REF] Lewis | The status of long-tailed jaeger Stercorarius longicaudus in Australian waters[END_REF][START_REF] Marchant | Handbook of Australian[END_REF][START_REF] Melville | Long-tailed skuas Stercorarius longicaudus in New Zealand[END_REF][START_REF] Olsen | Skuas and Jaegers[END_REF][START_REF] Wood | Seasonal abundance, marine habitats and behaviour of skuas of central New South Wales[END_REF], and the species may even winter in the sub-Antarctic region where it has been seen from boats [START_REF] Kampp | Seabird observations from the South and Central Atlantic Ocean, Antarctica to 30°N[END_REF].

Both on migration routes and on wintering grounds, the Long-tailed Skua is often associated with the Sabine's Gull (Larus sabini; [START_REF] Olsen | Skuas and Jaegers[END_REF], which has a similar circumpolar breeding range. It is also interesting to note that the post-breeding flyway of the East Greenland Longtailed Skuas greatly overlaps with the one recently documented for 11 Arctic Terns (Sterna paradisaea) originating from the same region [START_REF] Egevang | Tracking of Arctic terns Sterna paradisaea reveals longest animal migration[END_REF]. While most of these birds (n= 7) moved along the African Coast heading to South Africa, four of these Terns crossed the Atlantic using an alternate flyway towards the coast of Brazil. Such a bi-directional migration pattern might also exist for the Long-tailed Skuas originating from the North Atlantic sector and would explain the records made off South America (see above). Indeed and as suggested above, after reaching the tropical waters off West Africa, some birds could make use of favourable easterly winds to continue westward (see [START_REF] Felicísimo | Ocean Surface Winds Drive Dynamics of Transoceanic Aerial Movements[END_REF]), hence following a -S-shape‖ flyway from breeding to wintering grounds.

Based on this review and considering our limited knowledge of the migration patterns and wintering areas of the Long-tailed Skua, it is obvious that if we want to document the different flyways and assess the exact borders and respective importance of the different wintering grounds, we should continue our efforts and initiate sister projects over the entire breeding range of the species. To date, Southwest Africa and Southeast South-America appear to be the two main wintering grounds for this species, but the relative importance of these areas is still unclear.

Unfortunately, and for reason that are still unknown, the PTTs we used were only working for a few weeks. Overcoming these difficulties, for example using geolocators [START_REF] Egevang | Tracking of Arctic terns Sterna paradisaea reveals longest animal migration[END_REF], would open new perspectives and may also shed new light on the spring migration which, according to [START_REF] Lambert | Ein Überwinterungsgebiet der Falkenraubmöwe, Stercorarius longicaudus Vieill. 1819, vor Südwest-und Südafrika entdeckt[END_REF] observations (he still noticed adult birds off Namibia in early May, i.e. one month only before they arrive on their breeding grounds), could be much faster than the autumn migration (i.e. ≥ 12.000 km in only one month). 1 the earliest and latest possible departure dates from breeding grounds are given when the exact data could not be documented 2 this bird left its breeding territory on the 9 th of July but remained within 50-100km of this area until July 18.

Fig. 1 :

 1 Fig. 1: Post-breeding flyway of four Long-tailed Skuas from North and East Greenland to West Africa (Papikk:square; Niilar: circle; Lucy: diamond and Blissy: triangle; details in Table1). The background map is a transverse mercator projection between 0-85° Lat. North and 0-60° Long. West (www.seaturtle.org/maptool;[START_REF] Coyne | Satellite Tracking and Analysis Tool (STAT): an integrated system for archiving, analyzing and mapping animal tracking data[END_REF]. Only the best daily locations (i.e. one position per day per bird) presented on the tracks (see Methods).

Fig. 2 :

 2 Fig. 2: Movements of four Long-tailed Skuas (Papikk: black circle; Niilar: open circle; Lucy: black diamond and

Table 1 :

 1 Summary data for the four studied Long-tailed Skuas and timing of their post-breeding migration

	Birds'	Trapping location
	names	(deg. Lat.N / Long. W)
	(mass)

Release date Duration of tracking Start date of fall migration in Greenland 1 Duration of staging off Canada Arrival off NW

							Africa
	Papikk	Karupelv Valley	30-6-2006	81 days	5-12 August	8 days	12-9-06
	(300g)	(72.50°/24°)
	Niilar	Karupelv Valley	3-7-2006	86 days	14-15 August	16 days	23-9-06
	(280g)	(72.50°/24°)
	Lucy	Mestersvig	2-7-2007	45 days	19 July 2	20 days	n.d.
	(278g)	(72.25°/24°)
	Blissy	Bliss Bugt	8-7-2007	52 days	8 August	n.d.	n.d.
	(295g)	(83.57° /30°)

Acknowledegments

We are grateful to the Groupe de Recherche en Ecologie Arctique and the Musée d'histoire naturelle de Fribourg for financial support, to Pascal Grand, Brigitte Sabard and Luc Hardy for their help in the field, to the Government of Greenland (Ministry of Domestic Affairs, Nature and Environment) for granting access and research permits in the -North and East Greenland National Park‖, and to Ross Bartley for his comments on an earlier draft of the manuscript.