Yi Zeng

Pai Peng

Qiu-Jiao Du
email: qiujiaodu@cug.edu.cn

Yue-Sheng Wang
email: yswang@tju.edu.cn

Badreddine Assouar
email: badreddine.assouar@univ-lorraine.fr

Subwavelength seismic metamaterial with an ultra-low frequency band gap

Keywords: seismic metamaterials, ultra-low frequency band gap, surface waves, Rayleigh waves, three-component structures

A subwavelength seismic metamaterial (SMs) consisting of a three-component SM plate (SMP) and a half space is proposed to attenuate ultra-low frequency seismic surface waves. The design concept and models are verified firstly by lab-scale experiments on the SM consisting of a two-component SMP and a half space. Then we calculate the band structures of the one-dimensional and two-dimensional subwavelength SMs, and evaluate their ability to attenuate Rayleigh waves. A wide ultra-low frequency band gap can be found. And the Rayleigh waves are deflected by the subwavelength SM and converted into bulk waves in the frequency range of this band gap. When the number of the unit cells of the subwavelength SM is sufficient, the transmission distance and deflection angle of the Rayleigh waves are constant at the same frequency. This discovery is expected to open up the possibility of pragmatic 2 seismic protection for large nuclear power plants, ancient buildings and metropolitan areas.

Introduction

Millions of earthquakes occur every year on the planet we live in. [START_REF] Reitherman | Earthquakes and engineers: an international history[END_REF] According to the statistics of China Earthquake Networks Center, there have been 836 major earthquakes of magnitude 6 and above in the past 100 years (1919-2018), i.e. an average of more than eight times a year. The major casualties caused by Earthquakes are due to the collapse of buildings. The destruction of some important buildings and facilities will bring devastating disasters and irreparable damage, such as nuclear power plants and ancient buildings. The seismic metamaterials (SMs) [START_REF] Finocchio | [END_REF][3][4][5] proposed in recent years can prevent these things in a clever way.

SMs with periodically arranged structures have band gaps (BGs). [6][7][8][9] In the frequency ranges of the BGs, the seismic waves cannot pass through the SMs. In 2014, an experiment with cylindrical holes arranged periodically verified that this SM can attenuate seismic waves in the BG. 3 When the shape of the holes is changed or some special material is filled in the holes, the BG characteristics and the attenuation effect of the SMs on the seismic waves can still be found. [10][11][12] In addition, the research on SMs based on half-space conditions has also received much attention. It has been found that the forest can attenuate the seismic surface waves, because these trees in the forest, which can be modeled as pillars over a half space, can open the BG of the surface waves. 13 Therefore, various pillars placed on the ground have been extensively studied and experimentally verified. [14][15][16][17] It is worth mentioning that the use of Matryoshka-like structures, 18 fractal structures 19,20 and "rainbow trapping effect" 4 can realize the attenuation of seismic surface waves over a wider range of frequency. Among them, Miniaci et al. 20

demonstrated the possibility of lowering

BGs in elastic systems by introducing self-similar structures at multiple scales experimentally. In addition, some multi-component SMs have been proposed to attenuate the seismic bulk waves and surface waves. [START_REF] Finocchio | [END_REF][21][22][23][24][25][26][27] However, the SMs, which are often made of a very soft coating and a very heavy core, 10 can attenuate seismic waves below 5 Hz which contains the resonant frequencies of many large buildings and metropolises. There are also some works 28,29 that consider the effectiveness of SMs in layered soils. It is consistent with the fact that the substrate in practice is composed of multiple layers of soil. 30 These works will facilitate the practical applications of SMs. Although SMs clamped by bedrock have a zero-frequency BG, they are only suitable for areas where the embedded depth of bedrock is shallow. 29,31 In this paper, a subwavelength SM consisting of three-component seismic metamaterial plate (SMP) on a half-space is proposed to attenuate ultra-low frequency seismic surface waves in a variety of geological situations. We first review the surface wave transmission experiments of the two-component SM composed of two-component SMP on a half-space. 32 This is the experimental basis of the three-component SMs in this paper. Then we calculate the band structures of the one-dimensional (1D) and two-dimensional (2D) SMs, check their attenuation ability to Rayleigh waves, and specifically discuss the propagation of Rayleigh waves in the SM in the range of the ultra-low frequency BG (UFBG). The subwavelength SM does not need bedrock or fixed boundary condition to clamp the bottom of the pillars metamaterials. This explains that the UFBG and the wide BG can be more universally implemented theoretically than the previous works. 29,31 And the subwavelength SM uses traditional building materials, making it a very practical design.

Methods

Numerical simulations

In this paper, we use Solid Mechanics Module of COMSOL Multiphysics to calculate the band structures and the propagation of Rayleigh waves in the SM. The meshes are free triangular mesh with quadratic serendipity element for 2D models, free tetrahedral mesh with quadratic Lagrange element for 3D models. The minimum wavelength involved in this work is approximately 5.6 m (3.7a) when the frequency is 22 Hz. In simulation, the maximum sizes of the mashes is set to a/5, which is about 1/18 of the minimum wavelength. Therefore, the meshes are small enough to get the converge results. 33,34 For the one-dimensional periodic SM, the reduced wave vector from 0 to π/a (a is the period of the SM) is used to obtain the eigenvalues 35 . For the two-dimensional periodic SM, which is highly symmetrical, the wave vector along Γ -X direction 36 is used to calculate the band structures. We mainly target Rayleigh waves which are often concerned in the study of SMs as they can travel far away and are extremely harmful to buildings in the mid-and far-fields. So the excitation condition in the frequency domain calculation is mainly used to obtain Rayleigh waves, which has sagittal displacement with a maximum value of 0.01m both in the x and z directions on the surface. 4,17 When we calculate the attenuation ability of SMs, the transmission spectrum is defined as TS = 20×log10 (A1/A0) where A1 is the acceleration of a point behind the SM, and A0 is the acceleration of the same point when there is no SM. Therefore, the amplitude of the excitation does not change the value of TS in the simulation calculation and the attenuation of seismic waves by SM is under linear elastic conditions. (c) and 1(d) respectively.

Lab-scale experimental setup

In the experiment, the sample comprising foam-steel composite is zoomed in the upper right corner of Fig. 1(e). The size of the steel core is 140 mm x 40 mm x 40 mm, and the thickness of the flexible foam plate is 5 mm. The size of the glass box is 1.2 m x 0.5 m x 0.5 m, and the material of the substrate is sand. In order to reduce the reflection of the elastic wave by the glass wall, pebbles are placed around the wall. 24 The details of the experimental instruments used in the present work are consistent with this reference 32 . A thick layer of high-damping plastic foam is placed under the glass box to achieve a similar effect to the vibration isolation platform.

The accelerations are carried out by using two accelerometers placed on two symmetrical points (labels D and E in Fig. 1(e)). One (label D) is placed in the free zone where there is no interaction between the SM and the seismic wave, and the other ((label E)) is located behind the SM. Suppose that the acceleration values of points D and E are AD and AE, respectively. Then the attenuation spectrum of SM on the surface wave is 20 x log10(AE/ AD) shown in Fig. 1(f 1. All parameters used in the simulation are consistent with those in the lab-scale experiment.

Comparing the two band structures, we can find that when the SMP is placed on the half space, the original band is basically unchanged, but the sound cone (dark gray area in Fig. 1(d)) is added due to the existence of the half space. So, we can not only keep the BG of the SMP itself in Fig. 1(d). It is found that the addition of the substrate does not affect the original band structure of SMP. That is to say, the band structure of the SM composed of the two-component SMP and a half space is almost equal to band structure of the two-component SMP plus the sound cone. The sound cone, the boundary of which is formed by the slowest bulk wave propagating in the substrate, can be used to immediately identify real propagating surface waves, bulk modes as well as leaky surface modes and spurious PML modes. 37,38 Therefore, the wide BG of the SMP itself is preserved. At 110 Hz -300 Hz, we can verify that the SM can attenuate the surface waves well by lab-scale experiments and simulated calculations of the supercell, which corresponds to the BG in Fig. 1(d). The geometric model, material parameters, and position of the supercell and substrate used in the simulation calculations are consistent with the lab-scale experiments. In addition, the boundary formed by the glass wall is replaced by a low reflection boundary to reduce reflected waves.

This lab-scale experiment demonstrates that the two-component SM can attenuate the surface waves in the frequency range of the BG well, but this SM is powerless for the lower frequency surface waves. However, our previous work 32 shows that this SM composed of SMP and substrate can strongly attenuate surface waves in numerical simulation and lab-scale experiments. In addition, this kind of SM only needs to be laid on the base layer, which reduces costs and simplifies construction. The functional shortcomings of the two-component SM prompt us to further improve the SM to possess the above-mentioned advantages and also attenuate surface waves at ultra-low frequencies. In the following, the effect of SM composed of the three-component SMP and substrate is systematically investigated on the attenuation of surface waves in the ultra-low frequency range.

Discussions of the SM

From the above simulations and lab-scale experiment of the SM consisting of the two-component SMP and half space, it can be seen that the band structure of the SM is almost equal to the band structure of the SMP plus the sound cone. This SM can effectively attenuate the seismic surface waves to protect the buildings. Next, we will use FEM calculations to discuss the band structure and attenuation effect of the subwavelength SM consisting of the three-component SMP and a half space on the seismic surface waves. The UFBG of the subwavelength SM is discussed under the one-dimensional (1D) and two-dimensional (2D) periodic models. = 0.5a, H = 20a. The material parameters are illustrated in Table 1. 11 Figure 2(c) shows a schematic diagram of the system used to calculate the transmission spectrum. Since the UFBG of the subwavelength SM is mainly studied and discussed in this paper, and the wavelength of the seismic surface wave is large in the range of the UFBG, the values of the geometric parameters involved here are all large, especially the depth (500a) of the substrate, the distance (340a) from the source (point A in Fig. 2(c)) to the ULSM and the number (1600) of the unit cells of the subwavelength SM. Point B (Fig. 2(c)) is the signal collection point. Suppose that the acceleration at point B located after the SMP is A1, and the acceleration at point B without the SMP is A0. Then the transmission function is defined as 20 x log10(A1/ A0).

Model of 1D SM

To prevent unwanted reflections, we add a perfectly matched layer (PML) with a thickness of 50a which is about the same as the incoming wavelength at low frequencies, as shown in Fig. 2(c). Among them, the PML scaling factor and the PML scaling curvature parameter are 1. Some works 12,39 also use low reflection boundaries to achieve similar results.

Band structure and transmission spectrum of 1D SM

For a 1D three-component SMP based on local resonance, a BG can easily occur.

As shown in Fig. 3(a), a narrow BG appears in the range of 10.0 -14.0 Hz. Even if the unit cells in Fig. 2(a) are periodically arranged in two dimensions, the BG is very narrow. 22 It is conceivable that such a narrow BG cannot meet our needs. However, when we place this SMP on a half space (i.e. the SM), we are surprised to find two wide BGs (0 -9.0 Hz and 9.4 -22.0 Hz) for surface waves. And one of them is a UFBG. By comparing the band structures in Figs. 3(a

3(b)

. It is worth noting that there are still bulk modes in the frequency range of the UFBG without any surface mode. This result proves that this work is completely different from the previous ones 29,31 which do not have modes in the UFBG. In Fig. 3(d), the effective density, shear modulus and bulk modulus of the SMP are obtained by using numerical methods. 40 We can see that the BG of SMP is due to the appearance of its negative effective mass density.

Through the transmission spectrum of the subwavelength SM, we can also see the existence of these two wide BGs. In the range of the UFBG, we see that the seismic surface waves are well attenuated in the range of 0.5 -9.0 Hz. However, for the seismic surface waves close to zero frequency, the attenuation effect needs to be improved. Because the number of unit cells in the proposed subwavelength SM is infinite because of the periodic boundary condition when calculating the band structure, while the number of the unit cells in the subwavelength SM is finite (1600 unit cells) when calculating the transmission spectrum. Therefore, we hypothesize that the number of the unit cells of the ULSM and the lower limit of the attenuation zone in the transmission spectrum are closely related.

Discussion on the UFBG of 1D SM

To discover the relationship between the number of the unit cells of the subwavelength SM and the lower limit of the attenuation zone in the transmission spectrum, we simulate and plot the displacements of surface waves of the system varying with the frequency by calculating the transmission spectrum. As shown in Fig. 4(a), we use the subwavelength SM of 1600 unit cells placed from 0 m to 2400 m for calculation. The transmission distance of the Rayleigh waves increases in the subwavelength SM exponentially with the decrease of frequencies from 5.0 Hz to around 0.5 Hz. It is found that in a higher frequency range between 3 Hz to 5 Hz, we can also attenuate seismic surface waves with very few seismic metamaterial units.

When the frequency is less than 0.5 Hz, Rayleigh waves pass through the 1600 unit cells of subwavelength SM. We can speculate that if the number of unit cells in the subwavelength SM increases, the propagation of the lower-frequency Rayleigh waves can be attenuated. Physically speaking, this subwavelength SM is a novel SM with the UFBG. For practical applications, it is also very convenient to select the number of unit cells according to the frequency range that we consider. We have studied the transmission of Rayleigh waves in the subwavelength SM at 2.2 Hz to demonstrate the mechanism of the subwavelength SM. As shown in Fig. 4(c), when the Rayleigh waves enter the subwavelength SM, they are deflected at a certain angle and converted into bulk waves. As shown in Figs 4(c) and 4(d), the waves at the left end of the SM are Rayleigh waves. The energy of Rayleigh waves is mainly concentrated in the depth of two wavelengths below the surface. The Rayleigh waves are converted into bulk waves in the SM, because there is no surface wave mode in the SM at the frequency of the UFBG, but the bulk wave modes exist.

To explain this phenomenon, we draw a dotted line with the frequency of 2.2 Hz on the band structure of the subwavelength SM shown in Fig. 4(b). At 2.2 Hz, there is no surface wave mode in the subwavelength SM. However, there are a large number of bulk wave modes outside the sound cone. That is to say, at 2.2 Hz, only the bulk wave modes exist in the subwavelength SM. Therefore, Rayleigh waves will be deflected and converted into bulk waves as shown in Fig. 4(c). This principle is also used to achieve low-consumption energy transmission and other functions in topological metamaterials and has been validated in experiments. 41,42 We also use the subwavelength SM of 100 unit cells placed from 0 m to 150 m with for the calculation of the transmission spectrum in Fig. 4(d). We find that the deflection of Rayleigh waves is almost the same as the subwavelength SM with 1600 unit cells. When the Rayleigh waves propagate to the position of X = 60 m (presumably at the position of the 40th unit cell), most of the energy has turned from the surface to the bulk below the surface. This also shows that when the number of the unit cells of the subwavelength SM is sufficient, the transmission distance and deflection angle of the Rayleigh waves in the subwavelength SM are constant at the same frequency. In practical applications, the method of arranging the number of the unit cells of the subwavelength SM according to the specified frequency range is effective.

In order to investigate the influence of the material parameters of the substrate on the UFBG, we consider the effect of the Young's modulus and mass density of the substrate on the upper frequency bounds of the UFBG for the 1D subwavelength SM.

The material parameters of the substrate are selected within the actual soil parameters 19 . However, when the Young's modulus of the substrate increases from 10 MPa to 100 MPa, and the mass density of the substrate is between 1600 kg/m 3 and 2200 kg/m 3 , the upper boundary (9.0 Hz) of the UFBG does not change. In this range of the Young's modulus and the mass density, the upper boundary of the UFBG is determined by the band of the local resonance of the SMP, which is invariable. From the effect of the Young's modulus and mass density of the substrate on the upper frequency bounds of the UFBG for the 1D SM, we can find that the subwavelength SM is suitable for different soils in different regions. This also shows that the subwavelength SM is universal.

The values for material parameters of the substrate are swept and are intended for qualitative comparison only 40 . Through the simulation calculation and discussion, we find this important universal equation: the band structure of the SM composed of the SMP and a half space is almost identical to band structure of the SMP plus the sound cone. It is noteworthy that this conclusion is incorrect when the heavy core of the unit cell of the SMP connects the substrate. 10,11 The above 1D SWSM can be modelled as a two-layered medium as shown in Fig. 5(a). The green part is the effective medium of the SMP. Its upper boundary is the free boundary, and the thickness is a = 1.5 m. In the low frequency region (0 -5 Hz) away from local resonance, as shown in Fig. 3(d), the effective mass density of the SMP is about 2000 kg/m 3 . And the effective Young's modulus Ee = 27.12 GPa, Poisson's ratio υe = 0.3. The substrate shown in Fig. 5(a) is a half-space of soil.

For the layered medium shown in Fig. 5(a), the dispersion curve of the Rayleigh wave can be calculated by the fast scalar method. 43 As shown in Fig. 5(b), the dispersion curve of the layered medium only supports a single waveguide mode and exhibits a typical inverse dispersion. [START_REF] Yang | Forward Modeling of Zigzag Dispersion and Pavement Systems Dispersion Curves[END_REF] The wave velocity of Rayleigh waves increases with the frequency increasing in the two-layered medium in the range of 0 -0.0125 Hz. And there is a cut-off frequency (0.0125 Hz). It means that, when the frequency is greater than the 0.0125 Hz, Rayleigh waves will not exist in the effective two-layered medium. This also verifies the correctness of the UFBG because 0.0125 Hz is close to zero.

In practice, the substrates are composed of multiple layers of soil. [28][29][30] For illustration, we divide the substrate into three layers of soil. 29 Each layer has a thickness of 10 m as shown in Fig. 6(a). Each layer of soil has an identical Poisson's ratio of 0.3 and a density of 1800 kg/m 3 . The Young's modulus from the top layer to the bottom layer is 5, 100 and 2000 MPa. The values for material parameters of the substrate are intended also for qualitative comparison only. 40 The UFBG still exists and the width is unchanged as shown in Fig. 6(b). This shows that even if the substrate is composed of multiple layers of soil, this SM can still attenuate ultra-low frequency seismic surface waves.

Model of 2D SM

In order to verify that the above the subwavelength SM still has a UFBG in the three-dimensional space, we have studied the 2D SM as shown in Fig. 7(b). Similarly, we also calculate the band structure of the unit cell of the 2D three-component SMP shown in Fig. 7(a). The unit cell of the 2D SM consists of a unit cell of the 2D three-component SMP and a half space. The geometric parameters (a, a1, a2 and H) and the material parameters of the four materials (concrete, rubber, steel and soil) are consistent with those of the 1D SM. We set the Bloch period boundary conditions on the four vertical boundaries of the 2D SMP; and the upper and lower boundaries are free. The Bloch period boundary condition is set on the four vertical boundaries of the 2D SM; the lower boundary is set as the fixed boundary condition, and the upper boundary is set as the free boundary condition. The system used for transmission spectrum calculation is similar to Fig. 2(c), so it is not illustrated here. 17 Although they can obtain BGs at low frequencies, the width of the BGs needs to be expanded. 38,[START_REF] Liu | [END_REF]46 As shown in Fig. 8(a), the BG of the 2D three-component SMP is very narrow and only exists around 10.0 -12.0 Hz. Even if the unit cells of such three-component SMP are three-dimensionally periodically arranged, the width of the BG is also narrow. 23 However, the 2D SM has two wide BG for surface waves, and one of them is an ultra-low BG. By comparing the band structures in Figs. 8(a) and (b), we can easily find that the band structure of the subwavelength SM consisting of the 2D three-component SMP and a half space is almost equal to the band structure of the 2D three-component SMP plus the sound cone. This is also the reason for the wide ultra-low BG.

We calculate the transmission spectrums of Rayleigh waves in the 1D and 2D SMs (along ΓX direction) with 100 unit cells at 0.5 -5.0 Hz which is within the UFBG.

The attenuation effect of the two kinds of subwavelength SM is almost the same, and the 2D ULSM is slightly better than the 1D SM at low frequencies (0.5 -4.0 Hz). This shows that the 2D SM can also attenuate ultra-low frequency surface waves in the three-dimensional space.

Discussion on the UFBG of 2D SM

As shown in Fig. 9, by comparing the propagations of Rayleigh waves in the 1D and 2D SMs (xz section diagram) with 100 unit cells at 4.0 Hz, the Rayleigh waves in the 2D SM also convert from surface waves to bulk waves, and the deflection angle of the Rayleigh wave is almost the same as that of the 1D SM. This shows that the 2D SM can attenuate surface waves in the frequency range of its UFBG to protect the target building. Its mechanism is consistent with that of the 1D SM.

Conclusion

In summary, through the lab-scale experiments and numerical simulation of the SM consisting of the two-component SMP and a half space, we demonstrate this new design methodology to create SMs to attenuate seismic surface waves. In addition, lab-scale experiments are also the important basis for the application of three-component subwavelength SM. Then we propose a three-component subwavelength SM consisting of the three-component SMP and a half space. By investigating the influence of the material parameters of the substrate on the 1D SM, we find that the band structure of the SM composed of the SMP and a half space is almost equal to the band structure of the SMP plus the sound cone. By analyzing the propagation of Rayleigh waves in the 1D and 2D SMs in the frequency range of the UFBG, we find that Rayleigh waves are deflected at a certain angle and converted into bulk waves. When the number of the unit cells of the subwavelength SM is sufficient, the transmission distance and deflection angle of the Rayleigh waves in the subwavelength SM are constant at the same frequency. In summary, the SM consisting of only one layer of the SMP buried underground and substrate has an ultra-low frequency BG and can convert Rayleigh waves into bulk waves in the frequency range of the BG. Meanwhile, the simple design of this SM is conducive to its manufacturing and practical application and the efficiency of the SM to attenuate Rayleigh waves is also very significant. All the phenomena demonstrate that the subwavelength SM can attenuate surface waves in the frequency range of its UFBG to protect the target building. This subwavelength SM is expected to protect large nuclear power plants, ancient buildings and metropolises from damage by seismic waves. This paper not only demonstrates the application prospects of subwavelength SM, but also provides design guidance for surface wave researchers.

Figure captions

Figure 1 (

 1 Figure 1(a) shows that the unit cell of the two-component SMP consists of a steel core

). 3 of models 3 . 1

 331 Discussion Experimental verification of numerical model of two-component SM In order to verify if the new design of SMs can attenuate seismic surface waves, we have performed lab-scale experiment for a supercell of eight unit cells (four rows) of two-component SM to measure the transmission spectrum. The geometric parameters are: a = 5 cm, b = 1 cm, c = 4 cm, h = 15 cm and H = 20a. The material parameters 32 are illustrated in Table

Figure 2 (

 2 Figure 2(a) shows a unit cell of 1D three-component SMP, which is set to a

  ) and 3(b), we can easily find that the band structure of the 1D SM consisting of the 1D three-component SMP and a half space is almost equal to the band structure of the 1D three-component SMP plus the sound cone. Therefore, the UFBG and the wide BG are generated shown in Fig.

3. 2 . 5

 25 Band structure and transmission spectrum of 2D SMMetamaterials based on the local resonance is a subject of debate and discussion.

Figure 1 (

 1 Figure 1 (a) The unit cell of two-component SMP. (b) The unit cell of two-component SM

Figure 2 (

 2 Figure 2 (a) The unit cell of the 1D three-component SMP. (b) The unit cell of 1D SM. (c) A

Figure 3 (

 3 Figure 3 (a) Band structure of the 1D three-component SMP. (b) Band structure of the 1D SM.

Figure 4 (

 4 Figure 4 (a) The displacements of surface waves of the system varying with the frequency by

22

 22

Figure 5 (

 5 Figure 5 (a) Effective two-layered medium of 1D SM, (b) Rayleigh waves dispersion curve of

Figure 6 (

 6 Figure 6 (a) Schematics of the unit cell and (b) band structure of the proposed SMP on three

Figure 7 (

 7 Figure 7 (a) The unit cell of the 2D three-component SMP. (b) The unit cell of 2D SM. Note

Figure 8 (

 8 Figure 8 (a) Band structure of the 2D three-component SMP. (b) Band structure of the 2D SM.

Figure 9

 9 Figure 9 The propagations of Rayleigh waves in (a) 1D SM and (b) 2D SM (xz section

FiguresFigure1Figure2 25

 25 Figures

Figure3 26

 26 Figure3

Figure4 27

 27 Figure4

Figure5 28

 28 Figure5

Figure6 29

 29 Figure6

Figure7 30

 30 Figure7

Figure8 31

 31 Figure8

Figure9 32

 32 Figure9

Table 1 .

 1 Material parameters of the unit cell and the half space

	Material	Density (kg/m 3 )	Young's modulus (Pa)	Poisson's ratio
	Rubber	1300	1.2 x 10 5	0.47
	Concrete	2500	4 x 10 10	0.3
	Steel	7784	2.07 x 10 11	0.3
	foamed plate	1053	1.6 x 10 5	0.39
	Soil	1800	2 x 10 7	0.3

Acknowledgments

We thank the National Natural Science Foundation of China (NNSFC) under Grant Nos. 41974059 and 11702017, the Key Program of the National Natural Science Foundation of China (NNSFC) under Grant No. 41830537, and the National Programme on Global Change and Air-Sea Interaction (GASI-GEOGE-02).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.


Nathalie Ysard
email: nathalie.ysard@ias.u-psud.fr

Farid Salama

Helen Jane Fraser

eds. Harold Linnartz

Dust evolution: going beyond the empirical

Keywords: (ISM:) dust, extinction, ISM: evolution

A key element when modeling dust in any astrophysical environment is a self-consistent treatment of the evolution of the dust material properties (size distribution, chemical composition and structure) as they react to and adjust to the local radiation field intensity and hardness and to the gas density and dynamics. The best way to achieve this goal is to anchore as many model parameters as possible to laboratory data. In this paper, I present two examples to illustrate how outstanding questions in dust modeling have been/are being moved forward by recent advances in laboratory astrophysics and what laboratory data are still needed to further advance dust evolution models.

Introduction

Interstellar grains are a major actor in the chemical, physical, and dynamical evolution of matter in the cosmos. Their emission dominates the observations of galaxies over the mid-IR to submillimetre electromagnetic spectrum (Galliano et al. 2018) and should therefore be one of the most powerful diagnostic tools to trace processes at the heart of issues central to contemporary astrophysics and in particular those leading to the formation of stars and planets. However, this power is compromised by gaps in our knowledge of the exact properties of dust. Above all, it is now well established that dust is not the same everywhere (e.g. Planck Ccollaboration XI 2014, Rémy et al. 2018): it is the evolution of grains in all its complexity that must be understood and modelled to allow an optimal use of the astronomical data. It is only very recently that interest in such a refined study of grains has gone beyond the theoretical stage. Indeed, with the advent of telescopes such as ALMA, VLTI-MATISSE, JWST, and SKA, we now (will) have access to data with unprecedented spatial and spectral resolutions. With these telescopes, the small transition zones between the phases of the interstellar medium (ISM), where most of the grain evolution takes place, are (will) be spatially resolved. In addition, technological progress now makes it possible to calculate the optical properties of very complex grains in a reasonable time. However, such a degree of refinement in dust models can only be achieved if as many parameters as possible are anchored to the data obtained by laboratory astrophysicists: pure and mixed material optical properties; impact of UV photons, cosmic rays, and grain-grain collisions on dust composition, size and structure again in relation with their optical properties; etc. If not, the number of degrees of freedom of these models will always be too large for the interpretation of astronomical observations to lead to definitive conclusions on grain properties.

This paper is organized as follows. Section 2 gives a short overview of the latest dust observational constraints in the Milky Way from diffuse to dense ISM and where they contradict with current dust model predictions. Section 3 then presents two examples of recent laboratory experiments that are likely to resolve some of these contradictions in the near future. Finally, Sect. 4 gives concluding remarks.

2 Observational constraints vs. modeling Diffuse interstellar medium. Startling observations have recently sparked a renewed interest in the diffuse ISM from the community. This low brightness optically thin medium was thought to be rather homogeneous in terms of grain properties and more or less well explained by current dust models. That was before the advent of the Planck-HFI data, which shattered this image of a relatively simple medium.

Confronting the Planck all-sky data with independent optical extinction estimates, the Planck Collaboration showed that the emission-to-extinction ratio predicted by standard grain models (Draine & Li 2007, Compiègne et al. 2011) is wrong by a factor up to 2 (Fanciullo et al. 2015, Planck Collaboration XXIX 2016). This factor directly reflects upon dust mass estimates. Then, investigating diffuse linesof-sight with N H < 3 × 10 20 H/cm 2 , they further showed that the dust luminosity is independent of its temperature, whereas its opacity decreases with increasing temperature (Planck Collaboration XI 2014). This was totally counter-intuitive regarding what we thought we knew about diffuse ISM dust. Indeed, for a given set of dust properties, the luminosity should increase with temperature whereas the opacity should remain constant, this means that dust already evolves in the diffuse ISM (see also Siebenmorgen et al. 2018). This evolution was confirmed by further studies, showing for instance an increase in the dust opacity by around 40% when N H > 5 × 10 20 H/cm 2 , in parallel with very little variations in E(B -V )/N H (NGuyen et al. 2018). Variations in the submillimetre dust opacity along with variations in the gas-to-dust mass ratio were observed in individual diffuse regions and from cloud-to-cloud (Reach et al. 2017), with one plausible explanation being that "... grain properties may change within the clouds: they become more emissive when they are colder, while not utilizing heavy elements that already have their cosmic abundance fully locked into grains". This means that the diffuse-ISM dust evolution would not be driven by silicate forming elements but rather by cycling of carbon in and out of dust. While significant changes in dust opacities were unexpected, significant variations in the gas-to-dust mass ratio were no less so. Until very recently, this ratio, referred to as the Bohlin's ratio (Bohlin et al. 1978), was believed to be canonical. However, the latest observations showed that it is rather higher than previously thought by 20 to 60% and subject to local variations (Liszt 2014, Lenz et al. 2017, Murray et al. 2018, NGuyen et al. 2018). All these models vs. observations inconsistencies raise fundamental questions about the optical properties of grains that should be answered thanks to laboratory measurements.

In presence of a magnetic field, non-spherical grains tend to align with their main axis parallel to the field lines. Dichroic extinction of the radiation field by dust grains then results in polarization, parallel to the magnetic field in extinction and perpendicular to it in emission. The Planck telescope provided the first all-sky map of dust polarized emission in the submillimetre. Once again, the diffuse ISM observations do not match the predictions of the standard grain models (Planck Collaboration XXI 2015). Indeed the spectral shape of the polarization fraction in the submillimetre is flatter than expected and as for unpolarized data, the polarized extinction-to-emission ratio is higher by a factor of ∼ 2.5 than model predictions (e.g. Draine & Fraisse 2009). This shows that existing dust models do not correctly describe either the dust optical properties or the mechanism of their alignment with the magnetic field.

Extinction observations have also recently brought their share of surprises. In particular, extinction in the mid-IR appeared to be flatter than predicted by current models (Wang et al. 2013). This has been explained by invoking the presence of micron-sized graphitic grains (Wang et al. 2015), far from the usual size distribution centered around 100 nm used to explain the dust thermal emission, polarized or not. However, such big grains would produce an additional thermal emission component conflicting with the Planck observations at ∼ 3 mm. An alternative explanation is that the optical constants used to describe ISM grains need to be reassessed in the light of the newest laboratory measurements on analogues of ISM silicates (Demyk et al. 2017, Mutschke et al. 2019).

Dense interstellar medium. Talking about "the" dense ISM is a bit tricky since this term covers a wide variety of regions with very different physical conditions. They do, however, have one factor in common: their grains are no longer isolated but have coagulated to form large aggregates. The growth of grains is most probably initiated by the accretion of gas phase elements and the coagulation of the grains with one another, in parallel or followed by ice mantle formation. In molecular clouds and denser cold cores, this growth was first evidenced by the decrease in the mid-IR to far-IR emission ratio (e.g. Stepnik et al. 2003), showing the disappearance of the smallest grains. Growth is also evidenced by a decrease in the dust temperature from about 20 K in the diffuse ISM to less than 15 K in denser regions (e.g. Juvela et al. 2011) along with an increase in the dust far-IR/submillimetre opacity and spectral index (e.g. Roy et al. 2003, Rémy et al. 2018). In the meantime, the total-to-selective extinction ratio R V significantly increases when A V > 3 (e.g. Whittet et al. 2001, Campeggio et al. 2007). Dust growth is also evidenced by an increased scattering efficiency from the near-to mid-IR when the local density increases (e.g. Foster et al. 2006, Pagani et al. 2010). All these observations are in agreement with grain growth by coagulation to form aggregates. However, the models disagree as to the answer to the simplest a priori question: up to what size do the grains grow? Indeed, depending on how grains are modeled the answer can vary by up to one order of magnitude from ∼ 0.5 to 5 µm (e.g. Steinacker et al. 2015, Lefèvre et al. 2016, Ysard et al. 2016) , which has a strong impact on the predictions of chemistry and dynamics simulations aimed at understanding the formation of prestellar cores from molecular clouds. The differences between the models come from the level of complexity integrated into the grain description in terms of its geometric structure and chemical composition.

Polarization observations, both in emission and extinction, also point towards variations in the grain properties when the ISM density increases (Fanciullo et al. 2017). Moreover, these variations cannot just be changes in the grain size distribution but must encompass changes in grain shape, porosity, and chemical composition (Juvela et al. 2018) in parallel with a loss in the efficiency of the grain alignement with the local magnetic field. Is this loss due to a decreased efficiency in the processes at the origin of grain alignement or to changes in the grain structure? Answering this question is of prime importance as it determines the level of aggregate coupling to the magnetic field as well as their surface-to-mass ratio, impacting thus both the gas dynamics and chemistry.

Beyond the significant increase in R V when A V > 3 and variations in the mid-IR extinction curve, extinction data provide constraining information on the structure, composition and size of aggregates through the observation of ice and silicate bands (e.g. Dartois et al. 1998, Boogert et al. 2015). Indeed, the exact band positions and shapes vary with the ice layer thickness, the grain size distribution and composition, and the aggregate structure. However, there are still many open questions. For instance, which happens first: grain-grain coagulation or ice layering? This determines what kind of materials are in contact in the aggregates and will most probably affect the band profiles. Similarly, we know that the shape of the individual grains composing the aggregates affects the silicate band profiles: is there an effect on the ice bands? The advent of the JWST should allow great advances in our understanding of ice properties at the scale of individual clouds and protoplanetary discs, however this will be possible only if prior laboratory experiments do give constraints on all these questions.

Laboratory astrophysics inputs

Comparison of observational constraints with existing dust models clearly shows that much information from the laboratory is needed to advance our understanding of cosmic dust. Here, we concentrate on two examples that are probably soon going to change the way dust is modelled: (i) optical properties of amorphous silicates (e.g. Demyk et al. 2017) ; (ii) dust size distribution (e.g. Lorek et al. 2018).

Optical properties: the example of amorphous silicates. Almost all dust models make use of silicate optical properties somehow derived from the semi-empirical astro-silicates defined by Draine & Lee (1984) (see for instance Désert et al. 1990, Zubko et al. 2004, Compiègne et al. 2011, Jones et al. 2013, Siebenmorgen et al. 2014, Guillet et al. 2018). Starting from olivine optical properties, the experimental dielectric function was modified to fit astronomical observations of the silicate vibration bands at ∼ 10 and 18 µm from hot dust in the Trapezium region and from circumstellar dust. For wavelengths longer than 20 µm, the silicate emissivity was assumed to decrease in λ -2 . This semi-empirical model has been extremely useful as for years no laboratory data were available on a sufficiently large wavelength range. However, as described in the previous section, it was recently shown that, in the far-IR to submillimetre, the astro-silicates are not emissive enough and their spectral index is too steep, and that in the mid-IR their spectral features are too sharp. Recently, laboratory measurements on interstellar silicate analogues were performed from the mid-IR to the submillimetre by Demyk et al. (2017). The analogues were amorphous magnesium-rich glassy silicates with the stoichiometry of olivine and pyroxene (X35 and X50A/B samples, respectively, in Demyk et al. 2017). These measures of mass absorption coefficients (MACs) are of the utmost importance. Indeed, the measured bands at ∼ 10 and 18 µm are much wider than those of astro-silicates (see Figs. 1 and 4 in Demyk et al. 2017), which is in line with recent astronomical observations (Wang et al. 2013). Moreover, far from decreasing monotonically in λ -2 , the spectral index of the far-IR MACs varies as a function of wavelength, temperature, and analogue stoichiometry from ∼ λ -1 to λ -3 (see Fig. 3 in Demyk et al. 2017).

In order to compare these new laboratory measurements to the widely used astro-silicate model, a simplistic estimate of the complex refractive index m = n + ik corresponding to the olivine X35 sample is presented in Fig. 1 (left figure). The X35 sample was chosen because it is a priori the least promising of the samples presented by Demyk et al. (2017) with a very steep MAC in the far-IR, a MAC which is also much lower than that of the other samples (see Fig. 4 in Demyk et al. 2017). The calculations were performed assuming that the sample consists in an assembly of isolated 0.1 µm spheres and following the Kramers-Kronig relations (private communication from K. Demyk, A.P. Jones, V. Gromow, and C. Mény, paper currently in preparation). Starting from this new refractive index and using the Mie theory, the corresponding absorption and scattering efficiencies, Q abs and Q sca respectively, were estimated (right figure in Fig. 1). To easily compare these results to the THEMIS model (The Heterogeneous dust Evolution Model for Interstellar Solids, Jones et al. 2013, Koehler et al. 2014), metallic nano-inclusions of Fe and FeS (10% in volume) are included in the X35 grains. Three points are worth noting. First, as expected the X35 mid-IR spectral features are less sharp than those of the THEMIS version of astrosilicates. Second, the laboratory X35 silicate are twice as emissive for 80 < λ < 200 µm and 25% more emissive for λ > 300 µm. The emissivity should be even higher for the three other samples X40, X50A, and X50B presented in Demyk et al. (2017). Third, the X35 spectral index is flatter for λ < 300 µm. Looking at the MAC spectral shapes in Fig. 4 of Demyk et al. (2017), it is expected that this will be valid up to longer wavelengths for the other samples. These very preliminary results therefore show that switching from semi-empirical optical properties such as astro-silicates to optical properties anchored to laboratory measurements should a priori resolve the main contradictions between current dust models and astronomical observations of the diffuse ISM in extinction, total emission, and polarization.

Grain size distribution. An important point that comes out in many observational astrophysics studies 10 -8 10 -4 10 0 grain mass, m (g) p = -3.5 p = -3 p = -2.5 p = -2 10 -16 10 -12 10 -8 10 -4 10 0 grain mass, m (g) amax = 0.1 µm amax = 10 µm amax = 1 mm amax = 10 cm 10 -1 10 0 10 1 10 2 10 3 a0 (µm) 10 0 10 1 κ1300µm (cm 2 /g) -3.5 -3.0 -2.5 Power-law exponent 10 -1 10 0 10 1 10 2 10 3 10 4 amax (µm)

Figure 2: Top: Mass distribution function m 2 f (m) per logarithmic mass bin, where f (m) is the number of grains in the [m, m + dm] mass interval, with a constant gas-to-dust mass ratio set at 100. The left figure shows log-normal size distributions for variable centroid sizes a 0 with a min = 0.01 µm and a max = 10 cm. The middle figure shows power-law size distributions for variable power-law exponents p with a min = 0.01 µm and a max = 10 cm. The right figure also shows power-law size distributions but with a fix power-law exponent p = -3.5 and a min = 0.01 µm, and variable a max . Bottom: Corresponding mass absorption coefficients at 1.3 mm κ 1.3 mm for log-normal size distributions as a function of a 0 (left), power-law size distributions as a function of p (middle) and a max (right).

is the question of the mass of the observed objects. A relatively common way to estimate it is to use grain continuum emission from the far-IR to the (sub)millimetre range and to assume that the dust mass absorption coefficient, κ, at a given wavelength is known: κ = 3/4ρ dn/da Q abs /a da for a given grain size distribution dn/da and a grain volume density ρ. This was done, for example, for dense cloud cores by Planck Collaboration XXII (2011) and for protostellar discs by Busquet et al. (2019). However, many parameters are hidden behind the choice of an opacity as it depends on the grain size distribution, chemical composition, geometrical structure, and temperature distribution along the line-of-sight (itself dependent on the object geometry and illumination conditions). Let us focus on the influence of the size distribution on the opacity. The classical choice are power-law size distributions dn/da ∝ a p , where p is most often set at -3.5 and sometimes varied, alone or in combination with the maximum grain size a max (see top middle and right figures in Fig. 2), to account for grain growth in dense regions (e.g. Weidenschilling 1977, Natta & Testi 2004, Draine 2006). This type of size distribution is what is typically expected if grains are the result of collisional fragmentation cascades as in debris discs (e.g. Davis et al. 1990, Tanaka et al. 1996). However, recent studies have shown that the grain size distribution during the collapse of dense prestellar cores and in protoplanetary discs can differ drastically from a power-law (e.g. Birnstiel et al. 2018). For instance, Lorek et al. (2018) modelled grain growth in protoplanetary discs from a local perspective, focussing on grains "... that would be concentrated in pebble-clouds by streaming instability and that would provide the building blocks of comets formed by the gravitational collapse of these clouds". What makes this particular study interesting for us is that it is based on the latest laboratory results from Güttler et al. (2010) and Windmark et al. (2012) to predict the outcomes of grain-grain collisions (sticking, bouncing, fragmentation, erosion, mass transfer), from Güttler et al. (2010), Blum (2008), Gundlach et al. (2011), andGundlach et al. (2015) for the sticking properties of water ice and silicate monomers, and from Güttler et al. (2009) and Weidling et al. (2009) to assume that not only compact grains but also aggregates can bounce. Considering various monomer sizes, radial positions in the disc, levels of turbulence, gas surface densities, etc., Lorek et al. (2018) always find size distributions differing quite notably from power-laws and that can be effectively modelled by log-normal type laws (see their Figs. 2 and 3 for instance and our top left figure in Fig. 2):

dn/da ∝ exp -1/2 (ln(a/a 0 )/σ)
2 , where a 0 is the centroid of the size distribution and σ its width.

Figure 2 presents the mass absorption coefficents κ for power-law (varying p or a max ) and log-normal size distributions (varying a 0 ) at 1.3 mm. They are calculated for porous spherical grains (porosity of 50%) of which 2/3 of the volume is occupied by amorphous silicates containing metallic nano-inclusions of Fe and FeS and 1/3 by amorphous carbon. The optical properties are those of the THEMIS model. Huge differences between the two types of size distributions are found. The two power-law κ show no variation when -4 < p < 2.5 and 1 µm < a max < 10 cm. Only when p > -2.5 or a max < 1 µm increases of 1.7 and 1.3, respectively, are found. Variations with a 0 in the case of log-normal distributions are stronger. For 0.1 < a 0 < 10 µm, κ is almost constant, it then increases by a factor of ∼ 7 when a 0 increases to ∼ 170 µm, and decreases by a factor of ∼ 48 when a 0 further increases to 1 cm (a factor of ∼ 7 when compared to a 0 = 1 µm). This comes from the fact that, contrary to the power-law case, log-normal size distributions have a characteristic size a 0 which dominates the κ estimate. According to the Mie theory, when a λ, the increase in Q abs is proportional to a leading to a constant κ ∝ Q abs /a. For larger sizes, but still smaller than the wavelength, the increase in Q abs is stronger, resulting in an increasing κ. For sizes comparable to or larger than the wavelength, Q abs ∼ 1 and is no longer dependent on the grain size, thus a decreasing κ ∝ 1/a with increasing a 0 . The exact sizes at which the variations are observed as well as the level of increase or decrease in κ depend on the chemical composition of the grains but the general trends with increasing a 0 remain the same (constant → increase → decrease). This illustrates how much the choice of a size distribution is crucial when modeling κ to infer masses of ISM clouds or protoplanetary discs. Indeed, the variations in κ presented here directly reflect on mass estimates. Laboratory experiments on grain growth are thus of the utmost importance if one wants to avoid the large uncertainties introduced by the choice of a size distribution in dust mass estimates.

Conclusion

The quality of recent and future observations (e.g. Spitzer, Herschel, Planck, ALMA, SKA, JWST, Millimetron, SPICA...), in terms of spatial and spectral resolutions and sensitivity, means that grain models can no longer suffer from any approximation. Indeed, all existing dust models fail to explain all observations simultaneously. The best way to solve this problem is to anchor as many model parameters as possible to laboratory data even if this is far from being an easy task. The two examples presented earlier show how experiments to measure silicate optical properties and grain growth appear very promising to advance dust modelling. These are obviously not the only experiments the impact of which could be decisive for grain modelling. For instance, replicating the Demyk et al. (2017)'s experiments with amorphous carbon grains would probably be very instructive. In addition, laboratory experiments on the influence of grain shape on their phase function will be essential to understand self-scattering in protoplanetary discs. Experimental results on processing of grains by cosmic rays and UV photons should also be better incorporated into dust models (in terms of variations in size distribution and optical properties), for example to understand the future JWST observations of photo-dominated regions and protoplanetary discs. In this context, the latest laboratory measurements of PAHs and nano-carbon dust optical properties will be of prime importance. For larger grains, having the laboratory measured optical constants for various ice mantle compositions (e.g. amorphous water ice, mixtures of H 2 0, CO and CO 2 ices) on a wide wavelength range would be a significant upgrading for dust models.

Figure 1 :

 1 Figure1: Left: imaginary part k (dashed lines) and real part n (solid lines) of the complex refractive index. Gray lines show the THEMIS silicates with metallic nano-inclusions of Fe and FeS (see text for details andKoehler et al. 2014). Black lines show the X35 sample considering the same metallic nanoinclusions as in THEMIS. Right: corresponding scattering efficiency Q sca (dashed lines) and absorption efficiency Q abs (solid lines) for a 0.1 µm sphere.


Carsten Bundt
email: bundt.carsten@gmail.com

Lara Bardi

Frederick Verbruggen

C Nico Boehler

Marcel Brass

Wim Notebaert

Reward anticipation changes corticospinal excitability during task preparation depending on response requirements and time pressure

Keywords: reward, response preparation, primary motor cortex, corticospinal excitability, transcranial magnetic stimulation

The preparation of an action is accompanied by transient corticospinal (CS) excitability changes. Motivation can modulate these changes. Specifically, when a cue indicates that a reward can be obtained, CS excitability initially increases, followed by a pronounced decrease. This dynamic could reflect processes related to reward expectancy, processes related to action preparation, or a combination of both. Here we set up two experiments to dissociate these accounts. A rewarded choice reaction time task was used in which individuals were cued at the beginning of each trial whether or not a response would be required at target onset and whether or not a reward could be obtained. We used single-pulse transcranial magnetic stimulation (spTMS) over the left primary motor cortex (M1) early (shortly after cue onset) or late (shortly before target onset) preceding target onset to examine CS excitability during motivated action preparation. Electromyography (EMG) was obtained from the right first dorsal interosseous (FDI) muscle. In the first experiment, we used a lenient response deadline, whereas a strict response time-out procedure was employed in the second experiment. Reward modulated CS excitability differentially only in the second experiment:

CS excitability was highest during reward anticipation for the early stimulation epoch and was reduced for the late stimulation epoch when individuals were required to prepare a response, while CS excitability remained unchanged during non-reward anticipation. Our findings suggest that the reward effect on CS excitability is dependent on the actual implementation of effort to attain reward (i.e., the preparation of an actual action), as well as on temporal requirements (i.e., time pressure) invoked by the task.

Introduction

Our ability to prepare for specific tasks and actions allows us to respond rapidly to changing environmental demands [START_REF] Bode | Decoding sequential stages of task preparation in the human brain[END_REF][START_REF] Brass | The role of the frontal cortex in task preparation[END_REF][START_REF] Brass | Decomposing components of task preparation with functional magnetic resonance imaging[END_REF].

Changes in corticospinal (CS) excitability have been observed during action preparation using transcranial magnetic stimulation (TMS) with concurrent electromyography (EMG) [START_REF] Duque | Role of corticospinal suppression during motor preparation[END_REF][START_REF] Greenhouse | Nonspecific inhibition of the motor system during response preparation[END_REF][START_REF] Lebon | Influence of delay period duration on inhibitory processes for response preparation[END_REF]. To assess action preparation, TMS over the primary motor cortex (M1) can be combined with a cue-target delay paradigm in which a cue specifies which action must be prepared before onset of a target [START_REF] Duque | Role of corticospinal suppression during motor preparation[END_REF]. After the presentation of such preparatory cue, CS excitability generally decreases within the cue-target delay period for effectors that are involved in task execution as well as for anatomically or functionally related effectors [START_REF] Duque | Role of corticospinal suppression during motor preparation[END_REF][START_REF] Greenhouse | Nonspecific inhibition of the motor system during response preparation[END_REF]. Such CS excitability changes during action preparation have been interpreted as reflecting a "tug-of-war" between distinct action representations that are modulated by decision-related factors [START_REF] Bestmann | Transcranial magnetic stimulation: Decomposing the processes underlying action preparation[END_REF]. Examples for such decision-related factors are the estimation of biomechanical costs [START_REF] Cos | Rapid prediction of biomechanical costs during action decisions[END_REF] and the subjective value [START_REF] Klein-Flügge | Time-dependent changes in human corticospinal excitability reveal value-based competition for action during decision processing[END_REF]) associated with a particular action alternative. For instance, if an action would require the individual to exert more effort than an alternative action, such difference would be reflected by motor system state changes. Specifically, [START_REF] Cos | Rapid prediction of biomechanical costs during action decisions[END_REF] reported that as early as 150 ms after target onset, CS excitability is increased for a biomechanically easier response compared with a biomechanically more difficult response. These findings show that decision-related factors strongly influence our actions in a continuous manner. One of the major factors that drives our actions, however, is the potential reward that is associated with a particular action. To that end, the current study investigates the effect of reward prospect on CS excitability and how such effect is dependent on action preparation and engagement in the task.

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Reward has been found to dynamically modulate CS excitability during action preparation [START_REF] Chiu | Opposing effects of appetitive and aversive cues on go/no-go behavior and motor excitability[END_REF][START_REF] Suzuki | Motor cortex-evoked activity in reciprocal muscles is modulated by reward probability[END_REF][START_REF] Vassena | Unsigned value prediction-error modulates the motor system in absence of choice[END_REF]. However, the dynamic of reward modulation remains unclear. Some studies found that increased motivation was accompanied by increased CS excitability prior to target onset. In other words, the preparation of a potentially rewarded response was associated with higher CS excitability compared with a response where no reward was available. In contrast, we recently found that CS excitability decreased throughout the delay period after a reward-promising cue, whereas CS excitability did not change significantly for no-reward cues [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF]. Compared to no-reward cues, reward cues initially increased CS excitability, followed by a decrease during the later preparation stages (Fig. 1). The reward-related decrease of CS excitability at late stages during the delay period is consistent with other studies [START_REF] Duque | Role of corticospinal suppression during motor preparation[END_REF][START_REF] Greenhouse | Inhibition during response preparation is sensitive to response complexity[END_REF][START_REF] Greenhouse | Nonspecific inhibition of the motor system during response preparation[END_REF][START_REF] Lebon | Influence of delay period duration on inhibitory processes for response preparation[END_REF], whereas the initial increase of CS excitability was unexpected.

Fig. 1 Schematic illustration of reward-related modulation of CS excitability during the preparatory delay period as reported in [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF]. For reward compared to no-

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reward cues CS excitability increased early in the delay period, which was followed by a decrease closer to target onset.

The current study aimed to investigate two alternative accounts for this reward-related modulation. One possible explanation is that reward activates the motor system in a fast and automatic fashion, similar to the idea of incentive salience or reward 'wanting' [START_REF] Berridge | Parsing reward[END_REF]. We will refer to this explanation as the 'wanting-account'. An alternative explanation of our findings is that the effect of reward on CS excitability is not fast and automatic, but is a reflection of the control (or effort) that is exerted at a specific moment. We will refer to this alternative explanation as the 'control-account'. Goal-directed behavior such as response preparation is dependent on various controlled processes that ensure successful task performance. Such control over task-related processes, however, is intrinsically costly due to limited capacity of the control system and individuals may be reluctant to employ all available cognitive resources at a time [START_REF] Shenhav | Toward a rational and mechanistic account of mental effort[END_REF]. Incentivizing behavior, however, has been found to improve performance. In contrast to the wanting-account, the control-account would predict that the effect of reward on CS excitability would be absent when no response is prepared and no control over task-relevant processes is required.

To dissociate both accounts, we designed a task in which two advance cues were presented in rapid succession (see Fig. 2). The first cue (the 'action cue') indicated whether the upcoming target would require a response or not. The second cue (the 'motivational cue') informed individuals whether they could accumulate an extra point for fast and accurate performance or not. After a delay, a small circle (i.e., the target) appeared left or right from fixation, and participants were required to either withhold or execute a response to the location (depending on the action cue presented at the beginning of the trial). Before target onset, single-pulse TMS (spTMS) was applied over the left M1 and EMG was obtained from At the neurophysiological level, both accounts make distinct predictions. The wantingaccount predicts that the mere perception of a reward cue leads to increased CS excitability for reward compared to no-reward cues during the early stimulation epoch (i.e., 400 ms after motivational cue onset) irrespective of whether a response must be prepared or not. In contrast, the control-account predicts that the reward-related modulation of CS excitability is response-dependent: we should observe modulation when individuals need to prepare a response, but no modulation when no response is required as control over task-relevant processes would be redundant. Behaviorally, we hypothesized that both accounts make similar predictions such that reward compared to no-reward cues would speed up responses on preparation trials.

Experiment 1

In the first experiment we examined the influence of reward on CS excitability during the preparation of an action (preparation condition) compared to when individuals did not need to prepare any action (no-preparation condition) under no pronounced time pressure. We hypothesized that if the effect of reward on CS excitability was dependent on the preparation of a response (i.e., control-account), reward would only affect CS excitability in the preparation condition. However, if reward had a non-specific effect on CS excitability (i.e., wanting-account), reward should equally modulate CS excitability on preparation and nopreparation trials.

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Methods

Participants

Twenty-five participants took part in the first experiment. One subject was excluded because of a technical error that resulted in no analyzable neurophysiological data. The statistical analyses reported below were based on the data of the remaining twenty-four individuals (17 female; mean age= 22.13 ± SD=2.23 years of age). Participants were screened for psychiatric and neurological disorders, as well as for factors that could interfere with a safe application of TMS [START_REF] Rossi | Safety, ethical considerations, and application guidelines for the use of transcranial magnetic stimulation in clinical practice and research[END_REF]. All participants gave written informed consent and were monetarily compensated (25€) for their participation in the study. Moreover, participants were informed that the best-performing individual would receive an extra bonus in the form of a 25€ voucher for a local multimedia store. The study was in agreement with the Declaration of Helsinki (World Medical Association, 2013) and was approved by the local ethical committee at Ghent University Hospital.

Stimuli and apparatus

Participants were seated in a comfortable chair in front of a computer screen with an eye-to-screen distance of approximately 50 cm. Responses were provided via a QWERTY keyboard that was turned 180° horizontally with the function keys facing the participant (c.f., [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF][START_REF] Klein | Influence of reward on corticospinal excitability during movement preparation[END_REF][START_REF] Klein | Top-down suppression of incompatible motor activations during response selection under conflict[END_REF].

Participants were required to place their left and right index finger tips on the keyboard between the F8 and F9, and F4 and F5 buttons, respectively. A response was executed by performing an index finger abduction movement towards the medial response key (i.e., either an abduction movement with the left index finger towards the F8 key, or an abduction movement with the right index finger towards the F5 key) and to eventually press the respective button.

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TMS stimulation and EMG recordings

TMS stimulation and EMG recording were identical to our previous study [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF]. Sintered 11 × 17 mm active Ag-AgCl electrodes were placed onto the right first dorsal interosseous (FDI) and the metacarpophalangeal joint, respectively and two ground electrodes were placed onto the right hand's dorsum. The EMG signal was recorded by an ActiveTwo system (www.biosemi.com), amplified via internal gain scaling, high-pass filtered at 3 Hz and digitized at 2048 Hz.

The left primary motor cortex was stimulated using a 70 mm figure-of-eight coil, which was connected to a biphasic stimulator (Rapid2; The Magstim Company Ltd.). The coil was positioned tangentially over the right hand's motor area in left M1 (posterior-anterior induced current flow) and held by a mechanical arm during the experiment. TMS coil positioning was defined as the scalp location at which the most reliable MEPs were evoked. This location was marked and enabled the experimenter to monitor accurate coil positioning throughout the experiment. The average resting motor threshold (rMT) of all individuals was M=60.75% ± SD=6.6% of the maximal stimulator output. The eventual TMS pulse intensity was set to 110% of the rMT.

Procedure

Each trial started with an asterisk presented in the center of the screen for 500 ms (see Fig. 2 for a schematic illustration of the trial procedure). On some trials, baseline CS excitability was assessed during this fixation period (see below). Subsequently, either a ")(" or "X" was presented for 300 ms above fixation (i.e., action cue). These action cues indicated if an action had to be prepared (i.e., preparation condition, indicated by ")(") or not (i.e., nopreparation condition, indicated by "X"). The preparation condition required individuals to provide a response at target onset, while in the no-preparation condition, individuals were

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required not to respond at target onset. The presentation of an action cue was followed by another 600 ms fixation period. After this, the motivational cue was shown for 300 ms above fixation. Specifically, "+1" and "+0" indicated that reward (R) or no-reward (N) could be obtained for fast and accurate performance on the current trial, respectively. Note that participants received reward on no-preparation trials as well, but only if they managed to withhold a manual response. To ensure that participants attended the reward information even after they were informed that they did not need to respond (i.e., during no-preparation trials), the motivational cue was occasionally presented in blue ink color (i.e., catch trial). On these trials, participants were asked to provide a verbal response (i.e., they were required to say "blue") as soon as they detected a blue-colored reward cue (c.f., [START_REF] Gupta | Urges for food and money spill over into motor system excitability before action is taken[END_REF]. Prior to the experiment, participants were told that if they failed to detect a sufficient amount of blue-colored motivational cues, their accumulated reward would be withheld [START_REF] Gupta | Urges for food and money spill over into motor system excitability before action is taken[END_REF]. After the presentation of the motivational cue, another fixation period of 600 ms (i.e., delay period) followed. On some trials, CS excitability was examined during this delay period (see below). If the motivational cue was presented in blue ink color and indicated a catch trial, the trial was terminated after this delay period and a new trial was initiated. If the motivational cue did not indicate a catch-trial, the action-cue reappeared above fixation and was accompanied by a circle presented left or right from it (i.e., target stimulus). On preparation trials, participants were required to provide a left or right index finger response when the target appeared left or right of fixation, respectively. The duration of the presentation of the target (and simultaneously the duration of the response deadline) was determined by the mean reaction time during a preceding practice phase (see below). After individuals provided a response or the deadline had passed, a fixation period followed (200 ms) and subsequent feedback was provided (1000 ms). If the response was correct and timely, the feedback indicated whether or not reward has been obtained on current trial (i.e., "+1" or

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9 "+0" appeared above fixation), and the total reward amount accumulated throughout the course of the experiment was presented below fixation. Note that the correct 'response' on nopreparation trials was no key press. If the response was incorrect or too late, "fout" (Dutch for "wrong") or "te laat" (Dutch for "too late") was presented above fixation. Each trial was separated by a jittered inter-trial-interval (ITI) fixation period (900-1100 ms).

On a proportion of trials (352 trials; 57.5% of all trials), TMS was applied over the left M1 during three different stimulation epochs. TMS pulses were applied during the ITI fixation period 200 ms prior to the presentation of the action cue to examine CS baseline excitability (TMS baseline ; 32 trials). To test both, the wanting-and the control-account, CS excitability was examined at early and late time epochs in the delay period following the presentation of the motivational cue (i.e., during the motivational cue-target delay period).

More specifically, TMS pulses were applied either 100 ms (TMS early ; 160 trials) or 500 ms after the motivational cue offset (TMS late ; 160 trials).

In total, the experiment consisted of 612 trials divided into five blocks. The first block (68 trials; thereof four catch-trials) served as practice phase where individuals were able to familiarize themselves with the experimental task. The mean reaction time of participants on correct preparation trials during this practice phase (M=426 ms ± SD=53.47 ms) was eventually used as the (individualized) target response deadline during the subsequent experimental blocks. No TMS was applied during the practice phase and trials were balanced across action cues (preparation/no-preparation), motivational cues (N/R), and responses (right/left). The practice phase was followed by four experimental blocks (136 trials each; experimental phase), which did include TMS application. In total, the test phase comprised 32 TMS baseline trials, 160 TMS early trials, 160 TMS late trials, 160 trials not including any TMS, as well as 32 catch-trials (i.e., blue cue trials). Each block consisted of randomized trials that

Data analysis: behavior

To exclude the possibility that the magnetic stimulation of M1 could interfere with behavioral measures [START_REF] Hasbroucq | Preparatory inhibition of cortico-spinal excitability: A transcranial magnetic stimulation study in man[END_REF], the behavioral analysis was based on trials that did not include any TMS pulse. In the RT, we included only correct responses that were not defined as premature (RT < 100 ms) or as too late (i.e., RT < individual mean RT in practice block). Furthermore, we excluded trials if the previous trial met one of the following criteria: the response was wrong, the response was too late, or the previous trial was a catch-trial.

For the preparation condition, the dependent variables RT and the percentage of late responses were then submitted to a paired-samples t-test (N vs. R), respectively. For the preparation and no-preparation condition, percentage correct responses were submitted to a paired-samples t-test (N vs. R), respectively. For paired-samples t-tests Cohen's d z was

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11 estimated by dividing the mean difference between samples by the standard deviation of the difference scores [START_REF] Lakens | Calculating and reporting effect sizes to facilitate cumulative science: a practival primer for t-test and ANOVAs[END_REF].

Data analysis: CS excitability

CS excitability changes were analyzed offline using custom software in MATLAB (MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States). One-second EMG epochs surrounding the TMS pulse (interval from 500 ms before the TMS pulse to 500 ms after the TMS pulse) were extracted. An automated search-algorithm identified the peak-to-peak motor-evoked-potential (MEP) amplitude during a window of 20-40 ms succeeding the TMS pulse. Prior to data collection had started, we decided to discard MEPs that were affected by pre-contraction (root mean square of background activity exceeding 0.1 mV during the 500 ms interval prior to the TMS pulse) or that were identified as outliers (i.e. values above or below three standard deviations from the mean calculated for baseline and delay-period TMS separately). Table 1 shows the average MEP size and the absolute number of trials that were included in the CS excitability analysis per experimentally manipulated level. MEP amplitudes were normalized relative to baseline and expressed as a percentage change score: (Condition/Baseline-1) × 100 [START_REF] Lebon | Influence of delay period duration on inhibitory processes for response preparation[END_REF]. Accordingly, positive values indicate activation, whereas negative values indicate suppression of CS activity. MEPs of valid trials were submitted to a repeated-measures ANOVA (rmANOVA) with action cue (preparation, no-preparation) × motivational cue (N, R) × stimulation epoch (early, late) as within-subjects factors. The alpha level for the rmANOVA was set at .05. Two-tailed one-sample t tests were used to examine whether CS excitability during the delay period was significantly suppressed relative to baseline [START_REF] Duque | Role of corticospinal suppression during motor preparation[END_REF][START_REF] Greenhouse | Nonspecific inhibition of the motor system during response preparation[END_REF][START_REF] Lebon | Influence of delay period duration on inhibitory processes for response preparation[END_REF] in which the alpha level was 2)). For one-sample t-tests Cohen's d z was calculated to estimate effect sizes [START_REF] Lakens | Calculating and reporting effect sizes to facilitate cumulative science: a practival primer for t-test and ANOVAs[END_REF].

Results

Behavior

In the preparation condition, RTs were significantly shorter during reward compared to no-reward trials (Fig. 3

CS excitability

Mean raw baseline MEP amplitudes were 1.55 mV (± 0.77 SD). The rmANOVA revealed that there was no main effect of action cue (no-preparation=-4.08% vs. preparation=-5.27%; F<1), nor a main effect of motivational cue (no-reward=-5.57% vs. reward=-3.79%;

F

Discussion

The first experiment examined the influence of reward on CS excitability. We observed a reduction of CS excitability from early to late stimulation epochs during preparation trials, which suggests that action preparation is associated with time-dependent CS excitability changes [START_REF] Bestmann | Transcranial magnetic stimulation: Decomposing the processes underlying action preparation[END_REF][START_REF] Duque | Physiological markers of motor inhibition during human behavior[END_REF]. No such changes in excitability were observed on no-preparation trials. Importantly, this overall pattern of CS excitability was not modulated by the motivational cue.

These results do not replicate our previous findings (c.f., [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF], and are in contrast with our initial hypothesis that reward compared to no-reward information differentially affects CS excitability. One possible reason for these findings may be the fact that there was only little time pressure on the participants. Specifically, a short initial practice phase determined the time participants had to respond to the target (i.e., response deadline) throughout the rest of the experiment. Given the low amount of late responses (around 1%), the chosen response deadline turned out to be very lenient. Such a lenient response deadline may result in low task demands where goal-directed behavior is achieved without (much) effort or engagement of the individual. In this context, incentivizing behavior may not

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improve performance above non-incentivized behavior as goal-directed behavior is preserved in both situations. To put it differently, if there is enough time (and resources) available to prepare for both reward and no-reward trials equally well, one may not prioritize reward over no-reward information to attain goal-directed behavior (c.f., [START_REF] Verbruggen | Limits of executive control: Sequential effects in predictable environments[END_REF]. However, in situations of high task demand (e.g., under time pressure) prioritization of task-relevant over task-irrelevant information becomes critical for successful goal-directed behavior and the differentiation between incentives and no-incentives may become more pronounced.

Experiment 2

In order to examine whether increased task demands would result in differential processing of reward and no-reward information at the motor level, we employed a stricter response deadline in Exp. 2, which encouraged faster responding and therefore tighter control over task preparatory processes and prepotency of responding [START_REF] Elchlepp | How to withold or replace a prepotent response: An analysis of the underlying control processes and their temporal dynamics[END_REF][START_REF] Leiva | Reorienting the mind: The impact of novel sounds on Go/NoGo performance[END_REF].

Methods

Twenty-three individuals participated (13 female; mean age=21.4 ± SD=1.8 years of age). Stimuli and trial procedure, TMS and EMG parameters, as well as data analyses were identical to Exp. 1 except for the following changes. First, the duration of the target presentation (and therefore the target response deadline) was determined by an adaptive tracking procedure (3-down/1-up) that allowed for the continuous adjustment of the response deadline. Specifically (and irrespective of the reward condition), on preparation trials, the adaptive tracking procedure subtracted 25 ms from the response deadline when the participant was able to provide three correct responses within the allowed time in a row, and added 25 ms

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to the response deadline when the participant made an erroneous or late response (c.f., [START_REF] Elchlepp | How to withold or replace a prepotent response: An analysis of the underlying control processes and their temporal dynamics[END_REF][START_REF] Leiva | Reorienting the mind: The impact of novel sounds on Go/NoGo performance[END_REF]. Table 2 shows the average MEP size and the absolute number of trials that were included in the CS excitability analysis for each experimental condition for Exp. 2.

Furthermore, the number of trials of some conditions was adjusted to reduce the duration of the experiment. In total, the initial practice block consisted of 68 trials (i.e. the same number as in Exp. 1). The four experimental blocks (112 trials each, experimental phase) were comprised of 32 TMS baseline trials and catch-trials, respectively. Moreover, 128 TMS early trials, TMS late trials, and non-stimulation trials were included, respectively.

Equivalent to Exp. 1, each block consisted of randomized trials that were balanced across action cues (preparation/no-preparation), motivational cues (N/R), TMS epoch (early/late) and responses (right/left). Each experimental condition (i.e., action cues, motivational cues, TMS epoch) consisted of 32 trials.

The average rMT was M=60.3% ± SD=7.3% of the maximal stimulator output (note that the rMT data was not archived for one subject, such that the rMT mean and SD reported here are based on all other individuals).

Results

Behavior

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In the preparation condition, responses were significantly faster for reward compared to no-reward trials (366 ms vs. 381 ms; t(22)=3.279, p=.003, d z =.684) (Fig. 5). The percentage of correct responses in the preparation condition was not significantly different between reward and no-reward trials (99.46 vs. 98.91%; t(23)=-1.279, p=.214, d z =-.267).

Neither were percentage correct responses (i.e., correctly withholding a response) in the nopreparation condition different between reward and no-reward trials (99.56% vs. 99.56%; t<1). In the preparation condition, the percentage of late responses (i.e., responses that were not provided within the response deadline; Fig. 6) was significantly lower for reward compared to no-reward trials (15.2% vs. 25.4%; t( 22

CS excitability

Mean raw baseline MEP amplitudes were 1.55 mV (± 0.92 SD). Fig. 7

Discussion

In Exp. 2 faster responding was encouraged by the employment of a stricter response deadline using a trial-by-trial adjustment algorithm [START_REF] Elchlepp | How to withold or replace a prepotent response: An analysis of the underlying control processes and their temporal dynamics[END_REF][START_REF] Leiva | Reorienting the mind: The impact of novel sounds on Go/NoGo performance[END_REF]. Behaviorally, reward again sped up reaction times. Most interestingly, reward was associated with increased CS excitability in the preparation condition during the early stimulation epoch and was then followed by a CS excitability decrease.

General discussion

In two experiments, the effect of reward on CS excitability during response preparation was examined. It was hypothesized that if reward activates the motor system in a fast and automatic fashion, such activation would be present irrespective of whether an actual response must be prepared or not (i.e., wanting-account). In contrast, the effect of reward on the motor system may reflect the amount of exerted control that is increased when incentivized (i.e., control-account). In this case, reward should only affect CS excitability during actual response preparation but not when no response is being prepared as there is no

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(or significantly less) need to exert control to attain goal-directed behavior. It was expected that CS excitability is higher for reward compared to no-reward trials in early stages in the preparatory interval, while this pattern may reverse in late stages [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF]. When employing a lenient response threshold in Exp. 1, CS excitability was not modulated by motivational cues. In fact, no-reward and reward were both associated with higher CS excitability early in the delay period and relatively lower CS excitability late in the delay period. Employing a strict response threshold in Exp. 2 resulted in no CS excitability changes in the no-preparation condition during the delay period. However, in the preparation condition, reward was associated with higher CS excitability early, and lower CS excitability late in the delay period, whereas such decrease of CS excitability was not observed for noreward. Most importantly, CS excitability was higher in the preparation condition for reward compared to no-reward early in the delay period.

The main implications of the present study are twofold: First, our findings do not support the wanting-account. In both experiments, reward did not have any effect on CS excitability when response preparation was not required (no-preparation condition). To support the wanting-account, however, such reward effect would have been necessary to emerge even in conditions where no response was prepared. Such a pattern has been described earlier. Chiu and colleagues (2014) observed increased CS excitability after appetitive compared to aversive cues, irrespective of a response being required. Specifically, at the time CS excitability was measured, participants did not know whether a response was required or not and they probably prepared in both conditions.

The findings of the present study are in line with the control-account as reward did affect CS excitability only when response preparation was crucial for goal-directed behavior (preparation condition). Importantly, however, this effect appeared under increased task demands only (Exp. 2) and was absent under low task demands (Exp. 1). The finding that response was prepared could be explained by the concept of cognitive effort [START_REF] Shenhav | Toward a rational and mechanistic account of mental effort[END_REF]. More specifically, goal-directed behavior necessitates control over task-relevant processes to ensure successful task performance. These controlled processes, however, are inherently costly and individuals who need to exert cognitive effort to attain goal-directed behavior are reluctant to utilize all available resources at a time. The absence of any rewardrelated modulation of CS excitability in Experiment 1 may reflect cognitive resource preservation. Such preservation is only worthwhile, however, if goal-directed behavior can be retained and if task demands allow for it. Under increased task demands (Exp. 2), goaldirected behavior becomes more difficult and control over task-related processes increases. At the same time, the individual may become more susceptible to reward-promising cues in the environment that can 'pay' for increased cognitive effort.

One may wonder why, in Experiment 2, we did not observe lower CS excitability for reward compared to no-reward at late stages in the delay period when preparing a response.

These findings are in contrast to our previous findings [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF]. However, we did observe that CS excitability decreased from the early to the late stimulation epoch for reward trials, while such a decrease was not observed for no-reward trials. This relative pattern is similar to the findings of our previous study [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF]. For the present purposes, the most important finding is that reward-based modulation is only observed when preparing for a response, in line with a control account. Future studies aiming at this late decrease more specifically should also consider the effect of the baseline. To control for task-related differences when assessing baseline CS excitability, future studies could incorporate preblock baseline measures to avoid the experimental task biasing baseline CS excitability [START_REF] Labruna | Comparison of different baseline conditions in evaluating factors that influence motor cortex excitability[END_REF]. In conclusion, the present results show that during action preparation CS excitability is modulated by motivation (reward versus no-reward) only if the task demand -invoked by increased time pressure -is high. This modulatory influence of motivation on CS excitability may be a reflection of exerted control over task-relevant processes that is increased when incentivized. In contrast, when no action is prepared, motivation does not modulate CS excitability, which suggests that reward does not have an automatic effect on CS excitability in the present task.

  dorsal interosseous (FDI). We assessed CS excitability during three stimulation epochs: a) within the inter-trial-interval (ITI; 200 ms before the onset of the action cue) to examine baseline CS excitability; b) 400 ms after the motivational cue onset to examine CS excitability during early stages of action preparation; and c) 800 ms after the motivational cue onset to examine CS excitability during late stages of action preparation.

  action cues (preparation/no-preparation), motivational cues (N/R), TMS epoch (early/late) and responses (right/left). Each experimental condition (i.e., action cues, motivational cues, TMS epoch) consisted of 40 trials.

Fig. 2

 2 Fig. 2 Schematic trial procedure. Please refer to the main text for a detailed description of the

  set at .00625 to Bonferroni correct for the number of tests against baseline (action cue (2) ×

Fig. 3

 3 Fig. 3 Mean reaction time (A) and percentage correct responses (B) for no-reward (N) and

Fig. 4

 4 Fig. 4 CS excitability changes for Exp. 1. The figure shows the averaged CS excitability

  )=-3.934, p=.001, d z =-.820). The overall shorter RT and higher percentage of missed responses in Exp. 2 compared to Exp. 1 indicates that our tracking procedure encouraged faster responding and suggests that task demands are increased.

Fig. 5 Fig. 6

 56 Fig. 5 Mean reaction time (A) and percentage correct responses (B) for no-reward (N) and

Fig. 7

 7 Fig. 7 CS excitability changes for Exp. 2. The figure shows the averaged CS excitability

  CS excitability only under increased task demands and only when a

Table 1 .

 1 Average MEP size in millivolt (mV±SD) and the absolute number (n±SD) of trials included in the CS excitability analysis for each experimental condition in Exp 1.

	No-Reward

Table 2 .

 2 Average MEP size in millivolt (mV ±SD) and the absolute number (n±SD) of trials included in the CS excitability analysis for each experimental condition in Exp 2.

	No-Reward

  depicts CS excitability changes for Exp. 2. There was no significant main effect of action cue (no-

	preparation=-6.7% vs. preparation=5.8%; F(1,22)=1.650, p=.212, η p	2 =.70) or motivational
	cue (no-reward=-2.0% vs. reward=1.1%; F<1). However, CS excitability was significantly
	higher during early compared to late stages within the delay period (3.7% vs. -4.7%;
	F(1,22)=7.130, p=.014, η p	2 =.245). Moreover, a significant interaction between action cue and
	stimulation epoch was obtained (F(1,22)=5.254, p=.032, η p	2 =.193). Most interestingly, results
	indicated a significant three-way interaction between action cue, motivational cue and
	stimulation epoch (F(1,22)=7.417, p=.012, η p	2 =.252). Further analysis of this three-way
	interaction revealed that while there were no significant main or interaction effects in the no-
	preparation condition (Fs <1), in the preparation condition, CS excitability across both
	stimulation epochs was significantly altered by the motivational cue (F(1,22)=6.594, p=.018,
	η p 2 =.231). This was due to significantly higher CS excitability during the early compared to
	the late stimulation epoch for reward trials (23.36% vs. -5.62%; F(1,22)=11.161, p=.003,
	η p 2 =.337), but not for no-reward trials (4.62% vs. 0.75%; F<1). Furthermore, we observed
	significantly higher CS excitability for reward compared to no-reward trials during the early
	stimulation epoch (23.36% vs. 4.62%;F(1,22)=4.805, p=.039, η p	2 =.179), but not the late
	epoch, (-5.61% vs. 0.75%; F(1,22)=1.469, p=.238, η p 2 =.063.
	CS excitability did not significantly differ from baseline for any condition (ps>.098).

Acknowledgements

This work was supported by the Ghent University BOF initiative (BOF13/24j/080).

MB is supported by Belgian Science Policy Office (Interuniversity Poles of Attraction

Program; grant number P7/33). FV is currently supported by an ERC Consolidator grant (European Union's 362 Horizon 2020 research and innovation programme, grant agreement No 769595).

Data statement

The present study is based on [START_REF] Bundt | Reward anticipation modulates primary motor cortex excitability during task preparation[END_REF] and aimed for a similar sample size for comparison purposes. To that effect, we did not calculate sample sizes using power analyses a-priori for the present study. However, a post-hoc sensitivity analysis (two-tailed, alpha error probability: .05, power: .8) revealed effect sizes of .51 and .52 for Exp. 1 and Exp.

2, respectively. We confirm that all data exclusions, all inclusion/exclusion criteria, all manipulations, and all measures in the study are reported in the manuscript.

Inclusion/exclusion criteria, all manipulations, and all measures were established prior to data analysis. No part of the study procedures or analyses was preregistered prior to the research being undertaken. Study data, digital study materials, and the analysis code can be found at https://osf.io/atx26/.

Declaration of interest