F Kiefer

A Vidal-Madjar

A Lecavelier Des Etangs

V Bourrier

D Ehrenreich

R Ferlet

G Hébrard

P A Wilson

Fe I in the Beta Pictoris circumstellar gas disk II. The time variations in the iron circumstellar gas

Keywords: Individual: Beta Pictoris, Circumstellar disk, Exocomets

β Pictoris is a young planetary system surrounded by a debris disk of dust and gas. The gas source of this disk could be exocomets (or "falling and evaporating bodies", FEBs), which produce refractory elements (Mg, Ca, Fe) through sublimation of dust grains at several tens of stellar radii. Nearly 1700 high resolution spectra of β Pictoris have been obtained from 2003 to 2017 using the HARPS spectrograph. In paper I, we showed that a very high S/N ratio allows the detection of many weak Fe I lines in more than ten excited levels, and we derived the physical characteristics of the iron gas in the disk. The measured temperature of the gas (∼1300 K) suggested that it is produced by evaporation of grains at about 0.3 au (38 R⋆) from the star. Here we describe the yearly variations of the column densities of all Fe I components (from both ground and excited levels). The drop in the Fe I ground level column density after 2011 coincides with a drop in Fe I excited levels column density, as well as in the Ca II doublet and a ground level Ca I line at the same epoch. All drops are compatible together with photoionisation-recombination equilibrium and β Pic like relative abundances, in a medium at 1300 K and at 0.3 au from β Pictoris. Interestingly, this warm medium does not correlate with the numerous exocomets in the circumstellar environnement of this young star.

Introduction

The β Pictoris system is particularly famous for harboring one the most massive debris disk in the close neiborhood of the Sun (Smith & Terrile 1984). Despite being 20 Myr old (Mamajek & Cameron 2014), this star has gone through the phase of dissipating dust and gas in its protoplanetary disk, which remnant should be a gas-poor dust-poor debris disk. Observations however show that the disk is one of the most dusty gas-poor disk among known debris disk [START_REF] Artymowicz | [END_REF], Vidal-Madjar et al. 1998). With the age of β Pictoris being much larger than typical timescales of destruction of dust particles (<1 Myr), this led to the conjecture that a replenishment from either collisions or evaporation of hidden planetesimals was necessary to explain the overabundance of dust in this system [START_REF] Backman | Protostars and Planets III[END_REF], Lecavelier et al. 1996).

Moreover, absorption spectroscopy of β Pic revealed the presence of a stable gas component at the star's radial velocity and variable absorptions attributed to transiting stargrazing exocomets (Ferlet et al. 1987[START_REF] Beust | [END_REF]) ; see also the review of Vidal-Madjar et al. (1998). The origin of the stable gas disk is still unknown, although highly suspected to be connected to the star-grazing exocomets that strongly evaporate dust and ionized species. Exocomets might be the common vector of gas and dust replenishment Send offprint requests to: F. Kiefer (e-mail: flavien.kiefer@iap.fr) in the disk of β Pictoris (Weissman 1984, Lecavelier et al. 1996, Li et al. 1998).

β Pictoris was observed with the HARPS instrument (see e.g. Pepe et al. 2011) for several years, from 2003 to 2017 thanks to large programs of follow-up (Lagrange et al. 2012, Kiefer et al. 2014, Lagrange et al. 2018). Thousands of spectra were gathered and several hundreds of exocometary events detected (Kiefer et al. 2014). In Paper 1 (Vidal-Madjar et al. 2017, VM17 hereafter), stacking the 1686 HARPS spectra collected between 2003 and 2015, we presented the measurements of the physical properties of the iron gas from the detection of a large number of FeI absorption lines, from the ground level up to the 12969 cm -1 excited level. We concluded that the measured temperature of the gas (∼1300 K) coincides with the sublimation temperature of iron from solid compounds, and therefore that this gas is likely produced by the evaporation of grains at about 38 R ⋆ or 0.32 au from the star. Moreover, the ground level absorption lines of Fe I presented evidences of two components at different radial velocities. The component centred on the same radial velocity as the one found for the excited levels at 20.41±0.05 km s -1 for which we derived the temperature of 1300 K, and a blueshifted component at 20.07±0.02 km s -1 .

Independently, [START_REF] Welsh | [END_REF] found that the ground level Fe I absorption lines in the same β Pic HARPS spectra were experiencing a strong drop of equivalent width between 2011 and 2013. They proposed that the source of the Fe I experiencing the drop is the "D-family" of exocomets identified in Kiefer et al. (2014). These exocomets are composed of strongly evaporating bodies lying about a common orbit, with heliocentric radial velocities in the range +20 to +50 km s -1 .

Here we explore in more details the time variations of both ground and excited levels absorptions of Fe I in the "stable" circumstellar medium, and how they correlate with exocomet activity in the vicinity of the star.

The analysis is presented in Sect. 3. The discussions and conclusion are given in Sect. 4 and 5, including a study on the variations also observed in the Ca II doublet (at 3934 and 3968 Å) and the Ca I line (at 4227 Å).

Observations

β Pictoris has been observed with the HARPS spectrograph mounted on the 3.6m telescope of La Silla (ESO Chile) from 2003 to 2017 on a (mostly) regular basis (except between 2004 and 2007 and in 2012). Since β Pictoris is observable only during summer in southern hemisphere, the observations were done essentially from September to April of each season. The 1D-spectra were extracted via the standard, most recent, HARPS pipeline (DRS 3.5) including localization of the spectral orders on the 2D-images, optimal order extraction, cosmic-ray rejection, wavelength calibration, flat-field corrections, and 1D-reconnection of the spectral orders after correction for the blaze. More details can be found in VM17. We organized the spectra into different samples, each constituting one summer of observation, with the exception of the period 2004-2007. During this period, the average number of spectra observed per summer was 14, which is very small compared to the other periods average (234 spectra per summer). For that reason we created a special sample covering the 3 summers from 2004 to 2007. This repartition is summarized in Table 1 and Fig. 1.

Because of the high S/N ratio achieved, we were able to detect numerous Fe I absorption lines of the ground level, as well as, of several excited levels. All the detected Fe I lines are listed in Table 2. The energy of the initial electronic levels of the corresponding transitions are summarized in Table 3. In the paper we always refer to the individual levels by their energy expressed in cm -1 , as e.g. Fe I 416 for the first excited level at 416 cm -1 . We will collectively refer to the excited levels as Fe I Exc , as opposed to the ground level Fe I 0 . The profile of a few individual lines can be found in paper I, where we also describe the fitting procedure to derive the column densities, velocities and turbulent parameter. 3. Temporal variations of Fe I circumstellar gas

Fe I lines

A ki f ik E i E k (Å) (s -1 ) (cm -1 ) (cm

Variation of the Fe I ground level

The time variation of the "stable" Fe I ground level absorption lines is given in Table 4, and plotted on Fig. 2. We fitted one single component for each separated period of observation, using the Owens.f code (Hébrard et al. 2002, Lemoine et al. 2002). It fits a Gaussian line-spred-function of 3.6 pixels wide, further broadened by a turbulent parameter b, centered on a radial velocity v and with depth fixed by the column density N and the levels transition parameters as given in Table 2. The continuum is fitted simultaneously using a 4-degree polynomial. The two Fe I lines of the ground level are plotted on Fig. 2. The column density changes significantly, showing first a stable value of the order of 2.5 10 12 cm -2 lasting about 7 years, followed by a 3.5σ drop down to about 1.8 10 12 cm -2 , lasting at least 4 years. This drop of about 30 % in the Fe I total column density was already noted by [START_REF] Welsh | [END_REF] from the same HARPS observations. It seems that the column density is increasing again in 2017. Future observations should confirm this recent evolution.

The turbulent parameter b is stable up to a few hundreds of m s -1 indicating this gas ensemble is thermodynamicaly stable over nearly 12 years of observation. However, we observe a slow and monotonic reddening of the ground level absorption over years up until 2011, followed by a sudden blueshift simultaneous to the column density drop. Thus the column density variation must be stronger in the red wing than on the blue wing of the Fe I line.

In the light of the two components model of VM17, it strongly suggests that only the reddest component at 20.4 km s -1 is experiencing the drop. Moreover, we show in the next section that a column density drop is also observed in the absorption lines of the excited levels that are centered on 20.4 km s -1 . We will revisit the Fe I ground level absorption lines analysis with a 2 components model in Section 3.3.

Variation of the Fe I excited levels

To further study the time behaviour of the Fe I source, we examine the variations of the Fe I excited levels absorption lines. These evaluations are given in Table 5, as calculated by fitting simultaneously all Fe I excited levels absorption lines with Owens.f. We fixed that the radial velocity and turbulent parameters v Fe I Exc and b Fe I Exc are common to all excited levels, while the column density can vary separately for each individual level. Only the strongest transitions show well distinguishable absorptions, since the noise wipes the weaker transition signatures away.

In VM17, we have observed for the whole 2003-2015 period that v Fe I Exc =20.41 +0.03 -0.05 km s -1 , and b Fe I Exc =1.01±0.06 km s -1 . From Table 5 we can see that in accordance to VM17, both the v and b of excited levels component remain stable in time about 20.39 km s -1 and 0.96 km s -1 respectively, except after 2014 where the velocity is more poorly determined. Conversely, the column densities from the excited levels present a time behaviour similar to the ground level with an important drop after 2011.

To have a better look at the column density variations of the excited levels, we plotted in Fig. 3 all excited levels values (and upper limits), compared to the ground level N Total FeI 0 variations. The cleanest Fe I 416 and Fe I 6928 levels and the total column density in all excited levels are highlighted. All levels column densities are normalized to their corresponding median value before the drop, over the 2003 -2011 period. To calculate the total column density and their uncertainties, we drew at each epoch 10 4 series of estimations of the column density at all excited levels according to their measurements distribution, then calculated the sum leading to 10 4 estimations of the total column density, and determined the final measurement as the median of the sample with errorbars as the 1-σ percentiles.

The drop observed on the total column density of the excited levels is significant at the 6-σ level, with an amplitude of 37±4%. It is larger for the excited levels than for the ground level, for which we measure a 31±2% relative decrease in the column density, leading to a 2-σ significant difference in amplitude. This suggests again that only part of the ground level is undergoing the same drop than the excited levels. 4 are shown as a solid red line.

Revisiting the ground level variations with a 2 components model

It has been proposed by VM17 that the absorption lines of the ground level can be divided into 2 components, one of which, at about 20.4 km s -1 , is common with excited levels transition lines, and a second one lying at about 20.0 km s 1 .

In the rest of the paper, we will refer to these 2 hypothesized components as the red component and the blue component respectively. Besides the variations observed in the excited levels, additional clues suggest two components might be indeed present in the Fe I ground level lines. First, as observed in section 3.1, the velocity variations of the one-component fit of the Fe I 0 absorption lines show that simultaneously to the column density drop there is a blueward shift of the centroid wavelength, suggesting that only the red part of the lines undergoes a drop. Second, the amplitude of the drop in ground level column density is 2-sigma lower than the excited levels column density drop suggesting that only a part of the total amount of Fe I in ground level is vanishing. Revisiting the analysis of the Fe I 0 absorption lines using a 2 components model should confirm these assertions.

From the fit of the excited levels absorption lines in Table 5, the radial velocity of the red component fluctuates about the average value v 2 =20.39 km s -1 , without any trend. We will thus assume that the red component radial velocity is constant and fix it to this value. We then proceed to a 2-components fit of the ground level absorption line, adding a new component and letting all parameters free except v 2 . The results are given in Table 6.

We find that the derived radial velocity of the blue component is weakly fluctuating around the average value v 1 =19.77 km s -1 . However, the derived turbulence parameters have strong scatters with values lower than 0.05 km s -1 for b 1 and as high as 1.5 km s -1 for b 2 . This is not surprising since we are fitting strongly blended features. Other parameters should be fixed to lower such overfitting effects.

We thus fix both radial velocities v 1 and v 2 to respectively 19.77 km s -1 and 20.39 km s -1 . This time the values of the turbulent parameters are better behaved, with b 1 ∼0.11±0.02 km s -1 and b 2 ∼0.77±0.09 km s -1 . The two periods 2015-2016 and 2016-2017 stands aside: as for the excited levels the transition line is not well fit with the common model (for excited levels we measured v∼20.20 km s -1 ). This shift is likely to be imputed to the upgrade of the instrument done in June 2015 1 . Fortunately, it does not impact the measurement of the column density, so the 2015-2017 period remains valuable for the present analysis.

The measured ground level column density variations in each component are plotted in Fig. 4. The column density of the blue component is found monotonically decreasing, while the red component undergoes a strong drop. This difference is especially pronounced between 2011 and 2013 during the drop, with the red component column density divided by a factor of 2, and the blue component remaining essentially stable. Interestingly, the red variations follow well the excited levels variarions with a slight increase of column density between 2003 and 2011.

A Pearson's R test shows that the total excited levels column density calculated in Table 5 explains the variations of the red component with R=0.87 (null-hypothesis rejection probability p=9.8 10 -4 ), while it only explains the variations of the blue component with R=0.59 (p=0.074). This means that the red component measurements, having also smaller errorbars (∼0.02) than the blue component column density (∼0.06), are much better explained by the excited levels variations. However it is difficult to firmly conclude on the compatibility of the blue component column density variations with the excited levels, because although they have larger scatter, they also have larger measurement uncertainties.

Conducting another Pearson's R test on linear relationship of the components column density with time shows that the blue component is better explained by a continuous decrease through the different epochs, with R=-0.90 (p=3.7 10 -4 ), while the red component has only R=-0.56 (p=0.093).

The red and the blue are thus most likely uncorrelated, and the drop in the ground level column density is better explained, as initially suspected, by only the variation of a single component centered on 20.4 km s -1 . Observing this red component in the absorption lines of both excited and ground levels, and keeping in mind the measured temperature of this medium by VM17 (1300 K), leads to infer that the dropping component is located at close distance (∼38 R ⋆ ) to the star and varies from a yet unknown process, perhaps exocomets activity drop, as proposed by [START_REF] Welsh | [END_REF] and studied in more details in Section 4.

Since there is no evidence for a blue component in the excited levels lines, it should thus be located at larger dis-tance to the star, certainly several AU where temperatures are much lower than 1000 K. This would explain the absence of a correlation with the inner red component. It is moreover strongly pushed-out in the anti-stellar direction, and slowly dissipating. This component might be part of the distant expanding circumstellar gas identified by Brandeker et al. (2004Brandeker et al. ( ,2011)).

Exploring the link with β Pictoris circumstellar environnement

4.1. Exocomets activity in the Ca II doublet

It has been suggested by [START_REF] Welsh | [END_REF] and VM17 that the circumstellar (CS) Fe I originates from the numerous exocomets observed in the system of β Pictoris. One possible way to test this conjecture would be to determine if variations in the Fe I absorption lines of the circumstellar gas correspond to variations in the cometary activity, or the quantity of particles evaporated from these exocomets.

In the same HARPS spectra as those used here to analyse Fe I lines, there are the Ca II doublet lines that were used in Kiefer et al. (2014) to show that the β Pic's exocomets separate into 2 families. The D-family would be composed of strongly evaporating comets about a common orbit, while the S-family would be composed of older comets with smaller amounts of gas released in the circumstellar medium. The D-family absorption signatures are all located within the -10 to 50 km s -1 range in the β Pic rest frame, while the S-familly signatures are scattered on a wider velocity range, spanning from -100 to 150 km s -1 .

In order to quantify the cometary activity around β Pictoris, we can calculate the average absorption depth in different velocity domains of the Ca II normalized spectrum. In the small region about the tip of the circumstellar line that reaches almost zero, there could be deep features strongly blended with the circumstellar line; we thus first exclude that region from the analysis, within the range bounded by the instrument resolution (±2.6 km s -1 ) about 21.57 km s -1 , the tip of the CS line close to the β Pic systemic velocity. We fixed the velocity domain for the Dfamily to be +5-25 km s -1 and for the S-family to be 50-100 km s -1 . These two domains are not overlapping and are centered on the core regions of each family detection statistics, as found in Kiefer et al. (2014).

The reference spectrum that is divided out of the spectra contains the stellar lines and the stable circumstellar and interstellar components. Thus, in the normalized spectra, only flux variations due to exocomet absorption or circumstellar disk fluctuations remain.

The average absorption depth (AAD, hereafter) is measured by averaging each normalized spectrum over the specified spectral band. It is thus proportional to the equivalent width, by a factor ∆λ, the wavelength width of the calculation window. Therefore, as long as the absorbing medium is optically thin, this quantity reflects the amount of materials released in the circumstellar medium by transiting exocomets. It also provides information on the typical depth of signatures that are present in the spectrum within the velocity bounds. The marker size is proportionnal to the number of nights where β Pic was observed by HARPS in each period (see Table 1).

The errorbars indicate the scatter of average absorption depth during each period. See text for explanations.

Most of the time, several spectra are observed on the same night; this allows us to obtain an average AAD per night, a measure of exocometary activity during a single night. Averaging these night-based AAD over each of the periods considered in this paper (Table 1) we get a measure of how much the exocometary activity varies through time from one period to the other. It could then be compared to the Fe I variations in Fig. 4. Using the night-based AAD for this computation, rather than averaging over all spectra of a given period, makes more sense, because it prevents nights with many collected spectra to dominate the period-based AAD. These average absorption depth are plotted for each exocomet familly on Figure 5.

As can be seen, there is no obvious long-term variations or sudden drop in the exocomet activity. On the contrary, the measurements scatter and the errorbars show that the total quantity of particles evaporated from the many transiting exocomets is variable even within a given period. Thus we see no evidence here for any correlation between exocomet activity and Fe I disk column densities.

Variability in the core of the Ca II CS line

We first excluded the strongly blended CS line region (0±5 km s -1 ), since we were initially interested in exocomet absorption. However, the CS line region incorporates cir- 4. The marker size is proportionnal to the number of nights where β Pic was observed by HARPS in each period (see Table 1). For the sake of comparison, the Fe I column densities are scaled to the Ca II AAD median.

cumstellar disk variations, as well as exocomets transit signatures. It is interesting to see if significant Ca II variations show up in that region, even though we are not able to know their origin. We plotted the AAD variation in this domain in Fig. 6.

This time, we observe a neat decrease in average absorption depth. The varying blended features in that region have an average depth of about 0.68±0.03 in 2003-2011 and decrease to 0.50±0.04 in 2013-2017, for a total 3.6σ drop of 26% along the 14 years of observations. This is comparable to the measured drop of column density of Fe I. This variation is confirmed by measuring a flux increase in the 5 pixels at the tip of the K-line from 0.0096±0.0012 to 0.0196±0.0021 in arbitrary unit, and from 0.0166±0.0019 to 0.037±0.0064 at the tip of the H-line.

Given that the average absorption depth is directly proportional to equivalent width, and thus at first approximation to average column density in the absorbing medium, we see that both Ca II medium and Fe I medium varied in about the same proportions. This has implications on the Fe and Ca relative abundance in the circumstellar medium close to the star, that we will explore in more details in the next section.

In conclusion, the variations experienced by the Fe I components column density are likely connected to Ca II variations in the circumstellar medium. Ca and Fe are thus part of a common reservoir that suddenly dissipated between 2011 and 2013. We cannot firmly identify the origin of these variations, which could be either large low-velocity exocomets or local gas disk inhomogeneities. The exocomets scenario is however less likely as they would have to be disconnected to the already known exocomets which families show no sign of long-term or sudden variations.

W K,H = AAD × 10 km s -1 c × λ K,H (1)
The lower limit from simple linear relation between equivalent width and column density in the K and H lines gives that the variation of the column density of Ca II should be ∆N Ca II >4.5 10 11 cm -2 . Using Somerville (1988) equivalent width ratio method, best to use in close-tosaturated cases, we find a range of possible column density for a ratio of 1.2:

∆N Ca II ∼ 1 -4 10 12 cm -2 (2)
This should be compared to the ∆N Fe I =(7.5±0.9) 10 11 cm -2 lost during the 2011-2013 drop in the ground level column density. Assuming that Ca is fully ionized below 1 au (Fernandez et al. 2006), we can obtain an estimation of the abundance of Ca with respect to Fe in this medium, by calculating ∆N Ca II /∆N Fe I . We find a ratio of about Ca II/Fe I ∼ 1 -5

(3) Therefore, Ca II and Fe I are almost as abundant in this medium. If it follows β Pic standard abundances (Roberge et al. 2006), with Fe/Ca∼15, then we must have Fe II/Fe I∼15-75, implying a low ionization rate for Fe. This is in fairly good agreement with the results of VM17, proposing that Fe I/Fe II 1 in the 20.4 km s -1 component at 1300 K.

Ca I line variations

In the HARPS spectra, we also found a Ca I circumstellar absorption line about 4226.728 Å, as plotted on Fig. 7. Measuring its variation allow comparing Ca I and Fe I and determining independently the Ca/Fe abundance ratio. We thus analysed as for Fe I the variation of the column density in this line using Owens.f. The results are given in Table 8, and compared to Fe I and Ca II variations in Fig. 8.

Again we found a 2-σ significant drop of column density compatible with 30% between 2011 and 2013. The measured column density variation is ∆N Ca I =(1.54±0.70) × 10 8 cm -1 . This means that Ca I, Ca II and Fe I variations are all compatible and most likely originate from a common medium.

First comparing the column density variation of Ca I, to the one estimated above for Ca II, we find that indeed Ca is almost fully ionized with a ratio Ca II/Ca I∼10 4 , much higher than what primarily found by Hobbs et al. (1985) but closer to the theoretical estimations of Fernandez et al. (2006). Second, comparing this Ca I variation to ∆N Fe I we find that Fe I is ∼5000 (±2400) times more abundant than 8. The median of all datasets was shifted to 0. The size is proportional to the number of observed nights for Ca II, while it is proportional to SNR for Fe I and Ca I, as given in Tables 7, 4 and 8 respectively.

Ca I. If originating from a common medium, then according to photoionisation-recombination balance (Lagrange et al. 1995), Ca and Fe should follow, at a given distance to the central star, a one-to-one correspondance in first ionization ratio

N Fe I /N Fe II = 200 × N Ca I /N Ca II (4)
Assuming that N Fe ∼N Fe II and N Ca ∼N Ca II is a fairly good approximation even if Fe II/Fe I∼10. In this case, we derive an abundance ratio Fe/Ca of about 25 (±12). It is compatible with the solar value for this ratio ∼15 (Lodders 2003, Lodders 2010) and the value found in β Pic by Roberge et al. (2006), 15±10.

We can also confirm that Fe ionisation ratio is low with the direct measurement of Fe II/Fe I∼30-100, using the above formula and the estimation of N Ca I /N Ca II .

Conclusion

To summarize the reported results, we observed in the circumstellar gas disk of β Pictoris that -The Fe I ground level column density drop of 2011-2013 is also observed in the Fe I excited levels absorption lines centered around velocity 20.4 km s -1 , -The blue and red components of Fe I 0 absorption lines have different variability, with the 20.4 km s -1 more compatible with a sudden drop, while the blue component seems to have an independent behavior, -We identified a varying Ca II component in the circumstellar line region, which equivalent width is dropping in average with an amplitude comparable to that of Fe I.

-The Ca I circumstellar line also experiences a drop between 2011 and 2013. This drop is compatible with β Pic-like relative abundances for Ca and Fe,

-The varying component of Fe has a low ionisation ratio, in agreement with VM17 results.

First we conclude that the VM17 1300 K medium at 20.4 km s -1 contains not only Fe, but also Ca, and both stands at photoelectric equilibrium. It is located at close distance to the star ∼38 R ⋆ to sustain the 1300 K temperature and the high ionisation ratio of Ca. The Fe I blue component is likely not connected to this inner disk and belongs to a colder outer location with different photoionization conditions, possibly from recombination of Fe II beyond 100 AU, as described by Brandeker et al. (2004Brandeker et al. ( ,2011)).

Second, although the Ca II absorptions due to exocomets in the β Pictoris spectrum have a strong variability, they do not show any long term or sudden variations as in the column density of the 20.4 km s -1 component of Fe I. On the other hand, depth variations in the core of the Ca II circumstellar line have a stronger compatibility with the Fe I drop. Large and slow transiting exocomets could be at the origin of such absorptions, blended within the circumstellar line, such as members of the D-family, as suggested by [START_REF] Welsh | [END_REF]. However, the absence of correlated variations at larger velocity (up to +30 km s -1 in β Pic rest frame) where most D-family objects lie does not support this hypothesis.

Small scale disk inhomogeneities with yearly density variations are another alternative scenario. Such variations could be triggered by an outer planet, through direct gravitational interaction or indirectly by changing the flux of incoming dust within an inner disk at 0.3 au. However in that case a periodic behaviour would be expected. The baseline is not long enough to confirm or exclude periodicity, but a slight increase of the Fe I column density is already observed. The continuation of the monitoring of β Pic optical spectrum with high resolution spectrograph such as HARPS will allow testing this scenario.

Fig. 1 .

 1 Fig. 1. The time distribution of the HARPS observing nights used in our study. The horizontal dotted lines show the limits of the selected observing periods.

  2004

Fig. 3 .

 3 Fig.3. The spread and evolution of the (log) Fe I column density among the 12 excited levels over time. The black circles refer to each excited level's column density relative to its median value as observed from 2003 to 2017. The grey triangles are upper limits derived from weaker absorptions. A few points outside the plot window are figured by arrows next to the axis. The black solid line shows how the total column density of excited Fe I varies over time. The cyan and green solid lines show the evolution of the column densities derived respectively for the Fe I416 and Fe I6928 excited levels. The Fe I0 variations derived in Table4are shown as a solid red line.

Fig. 4 .

 4 Fig. 4. Column density variations measured in the Fe I ground level absorption lines. Top panel: blue component at 19.80 km/s. The solid black line is a linear model fit of the data. Bottom panel: red component at 20.4 km/s. The coloured solid lines are the variations observed in excited levels column densities of Fe I416 (cyan), Fe I6928 (green) and total excited Fe I (black), as given in Table5. They are scaled up to ground level column density.

Fig. 5 .

 5 Fig.5. Average absorption depth variations in the co-added Ca II K and H absorption spectra. Top: S-familly, between 50 and 100 km s -1 . Bottom: D-familly, between 5 and 25 km s -1 . The marker size is proportionnal to the number of nights where β Pic was observed by HARPS in each period (see Table1). The errorbars indicate the scatter of average absorption depth during each period. See text for explanations.

Fig. 6 .

 6 Fig.6. Average absorption depth (AAD) variations in the Ca II circumstellar line region 0±5 km s -1 . In blue, the K-line AAD and in red the H-line. They are compared to the total Fe I ground level column density variations in Table4. The marker size is proportionnal to the number of nights where β Pic was observed by HARPS in each period (see Table1). For the sake of comparison, the Fe I column densities are scaled to the Ca II AAD median.

Fig. 7 .

 7 Fig. 7. Ca I absorption line at 4226.728 Å with a shift of 20 km s -1 . All HARPS spectra from 2003 to 2017 are here coadded.

Fig. 8 .

 8 Fig. 8. Scaled-to-median Ca I column density variations at 4226.728 Å, in green, compared to Ca II-K (in blue), Ca II-H (in red) and Fe I variations (black). Absolute values for Ca I column densities are reported in Table8. The median of all datasets was shifted to 0. The size is proportional to the number of observed nights for Ca II, while it is proportional to SNR for Fe I and Ca I, as given in Tables 7, 4 and 8 respectively.

Table 1 .

 1 The repartition of the 2946 HARPS observations. The signal-to-noise is calculated next to the main Fe I line between 3859.30 Å and 3859.70 Å.

	Periods (year) 2003-2004 2004-2007 2007-2008 2008-2009 2009-2010 2010-2011 2013-2014 2014-2015 2015-2016 2016-2017 1080 N obs N night ∆t span (day) (3860 Å) SNR 255 53 127 42 14 651 198 12 108 417 12 196 54 1 1 207 4 159 453 19 250 60 4 4 190 4 162 11 109	Average Epoch 2004.025 2006.235 2008.203 2009.070 2009.847 2011.081 2013.929 2015.091 2016.063 2017.041

Table 2 .

 2 Transition parameters for the detected FeI lines, (i lower level, k upper level. A is the transition probability in s -1 , f is the oscillator strength, and E is the energy in cm -1 .

Table 3 .

 3 Fe I initial levels of the 32 electronic transitions detected in absorption in the HARPS spectrum of β Pictoris.

	12.5
	Total Fe I column density
	12.45
	12.4
						29 %
	12.35
	12.3
	12.25
	12.2
	2006	2008	2010	2012	2014	2016	2018
	Fig. 2. Column density variations in the ground state of the circumstellar Fe I of β Pic. Left: Temporal variations of the total Fe I0 column density showing a 30 % drop after year 2011. Middle and right: Sum of the Fe I HARPS fluxes, over the two separate periods, from 2003 to 2011 (solid) and after 2011 (dashed) at the ground state Fe I transition lines wavelengths, 3860 Å(middle) and 3824 Å(right).
	Energy level Energy level J Number (cm -1 ) (K) of lines 0 0 4 2 416 598 3 3 704 1013 2 3 888 1278 1 3 978 1407 0 1 6928 9968 5 1 7377 10614 4 1 7728 11120 3 3 7986 11490 2 2 8155 11733 1 2 11976 17232 4 4 12561 18073 3 4 12969 18660 2 3

Table 4 .

 4 Properties of the FeI gas over the different epochs of observations, evaluated by fitting simultaneously the two absorption lines from the ground state (3859.30 Å and 3859.70 Å) with a single component.

	Periods (year) 2003-2004 215 20.15±0.01 0.73±0.02 12.418±0.002 Nb. v b logN FeI Obs. (km/s) (km/s) (cm -2 ) 2004-2007 42 20.16±0.02 0.81±0.06 12.398±0.005 2007-2008 198 20.20±0.01 0.84±0.04 12.383±0.004 2008-2009 417 20.21±0.01 0.77±0.02 12.427±0.002 2009-2010 54 20.22±0.02 0.58±0.13 12.408±0.020 2010-2011 207 20.24±0.02 0.93±0.05 12.401±0.005 2013-2014 453 20.14±0.01 0.87±0.03 12.258±0.004 2014-2015 60 20.18±0.02 0.85±0.07 12.253±0.007 2015-2016 190 20.16±0.02 0.47±0.08 12.215±0.010 2016-2017 1080 20.20±0.01 0.40±0.05 12.328±0.015

Table 6 .

 6 Table of fitting parameters, modelizing the Fe I ground level absorption lines with 2 components.

	Periods Nb. Obs.	2003-2004 215	2004-2007 42	2007-2008 198	2008-2009 417	2009-2010 54	2010-2011 207	2013-2014 453	2014-2015 60	2015-2016 190	2016-2017 1080
	Comp 2 fixed to v=20.39 km s -1
	V comp,1, FeI 0 b comp,1, FeI 0 b comp,2, FeI 0 log N comp 1, FeI 0 12.02±0.03 12.36±0.06 12.07 +0.06 19.48 +0.11 -0.05 20.08 +0.05 -0.11 19.72±0.20 19.73 +0.15 -0.06 0.04 +0.02 -0.01 0.16±0.05 <0.07 0.06±0.02 0.55 +0.08 -0.04 1.50 +0.55 -0.28 0.87 +0.38 -0.10 0.77±0.03 -0.12 12.01±0.04 12.20 +0.09 19.84 +0.15 -0.40 <0.09 0.65 +0.48 -0.20 -0.30 log N comp 2, FeI 0 12.28 +0.01 -0.03 11.94 +0.15 -0.11 12.24 +0.03 -0.16 12.29 +0.01 -0.06 12.25 +0.02 -0.08 χ 2 (DOF=137) 142.86 143.03 142.63 154.14 139.22	19.81 +0.04 -0.17 <0.06 0.99±0.08 12.03 +0.07 -0.12 12.29±0.02 12.12±0.02 12.00 +0.07 19.48±0.10 19.96±0.11 19.85±0.20 19.78 +0.20 -0.11 <0.05 0.09 +0.06 -0.04 <0.14 0.20 +0.23 -0.14 0.76 +0.05 -0.08 1.17 +0.40 -0.20 0.43 +0.17 -0.13 0.19 +0.09 -0.03 11.86±0.07 12.04 +0.05 -0.15 11.95 +0.05 11.79±0.09 -0.15 -0.14 11.96±0.10 12.20 +0.04 -0.11 140.21 144.99 142.70 138.39 137.85
	Comp. 1 fixed to v=19.77 km s -1
	Comp. 2 fixed to v=20.39 km s -1
	b comp,1, FeI 0 b comp,2, FeI 0	0.14±0.02 0.81±0.03	0.06±0.02 0.90±0.08	0.05±0.03 0.91±0.05	0.08±0.02 0.82±0.03	<0.04 0.63±0.13	<0.04 1.00±0.05	0.08 +0.04 -0.02 1.01±0.05	<0.12 0.98±0.10	0.06 +0.06 -0.03 0.43±0.15	0.28±0.15 0.20 +0.09 -0.03
	χ 2 (DOF=138)	153.79	147.04	143.11	156.63	139.24	140.23	149.60	143.93	138.39	137.87	03

log N comp 1, FeI 0 12.16±0.02 12.19±0.05 12.09±0.06 12.05±0.03 12.19±0.10 12.04±0.06 11.99±0.04 11.94±0.09 11.92±0.06 11.82±0.03 log N comp 2, FeI 0 12.18±0.01 12.21±0.02 12.23±0.02 12.27±0.01 12.25±0.03 12.29±0.02 12.04±0.02 12.08±0.03 11.99±0.03 12.19±0.

Table 7 .

 7 The variation of the Ca II average absorption depth and average flux around Ca II K and H circumstellar lines. Average absorption depths are calculated from the normalized spectra, either separating K and H spectra, either co-adding the K and H absorption lines. Average fluxes are calculated from the raw spectra. Their continuum is scaled to an arbitrary level that is common to all spectra. With only 1 night observed it is not possible to evaluate uncertainties.5. Discussing the relation between Ca and Fe5.1. Implication for the Fe II/Fe I ionization ratioIndependently in both K and H line of the Ca II doublet, we measure an average absorption depth drop of about 0.36±0.04. The average K/H-line ratio of the dropped Ca II component is therefore about 1±0.2. Comparing the individuals AAD of K and H lines in Table7leads to a refined K/H ratio closer to 1.2. Thus, the Ca II varying medium is likely not fully saturated. In terms of equivalent width, with the core of the variation concentrated within ±5 km s 1 of β Pictoris velocity, we can estimate that

	Periods	K only	Average absorption depth CS-line D-family H only K & H coadded S-family	Average flux [arb. unit] tip of CS-line K only H only	blue wing K only
	2003-2004 2004-2007 2007-2008 2008-2009	±5 km s -1 0.704±0.014 0.61597±0.010 0.276±0.028 0.0495±0.0045 ±5 km s -1 5 -25 km s -1 50 -100 km s -1 0.753±0.029 0.68788±0.027 0.152±0.024 0.0580±0.0088 0.701±0.013 0.61683±0.013 0.283±0.064 0.134±0.027 0.828±0.020 0.75697±0.026 0.336±0.040 0.061±0.011	0±2 km s -1 0.01118±0.00063 0.01843±0.00062 0.3881±0.0010 0±2 km s -1 -150±5 km s -1 0.0105±0.0016 0.0162±0.0024 0.3864±0.0024 0.01146±0.00074 0.01679±0.00080 0.3768±0.0038 0.00437±0.00059 0.00801±0.00091 0.3810±0.0017
	† 2009-2010 2010-2011 2013-2014 2014-2015 2015-2016 2016-2017	0.72174 0.610±0.036 0.54054±0.037 0.114±0.022 0.0265±0.0069 0.64518 0.135 0.081 0.531±0.012 0.48492±0.012 0.234±0.020 0.104±0.014 0.634±0.016 0.52135±0.015 0.242±0.045 0.0170±0.0041 0.46±0.11 0.34875±0.12 0.099±0.035 0.0294±0.0048 0.602±0.034 0.4145±0.026 0.200±0.024 0.0450±0.0054	0.0079 0.0124±0.0022 0.02185±0.00060 0.02788±0.00065 0.3820±0.0024 0.0204 0.3869 0.0198±0.0029 0.39563±0.00057 0.01436±0.00060 0.0233±0.0011 0.3949±0.0014 0.0241±0.0060 0.049±0.012 0.3950±0.0021 0.0182±0.0012 0.04530±0.00092 0.3858±0.0013
	†

Table 8 .

 8 The variation of the Ca I velocity shift, b value and column density evaluated by fitting the ground base line at 4226.728 Å. Upper-limits for b-values are given at 1-sigma.

	Periods (year) 2003-2004 2120 19.80±0.25 SNR v (km s -1 )	b (km s -1 ) <2.0	logN FeI (cm -2 ) 8.48±0.08
	2004-2007 870 21.29±0.42	<1.4	8.60 +0.10

https://www.eso.org/sci/publications/messenger/archive/no.162-dec15/messenger-no162-9-15.pdf.

Article number, page 8 of 10 Kiefer et al.: Fe I in the Beta Pictoris circumstellar gas disk

Acknowledgements. We thank the anonymous referee for his help on greatly improving the quality of the article. We warmly thank T. Lanz for fruitful discussions on the subject of the present article. F.K. acknowledge support by a CNES fellowship grant. A.L.E, A.V-M and F.K thank the CNES for financial support. This work has been partly carried out thanks to an award from the Fondation Simone et Cino Del Duca. P.A.W. acknowledge support from the European Research Council under the European Unions Horizon 2020 research and innovation programme under grant agreement No. 694513. V. B. and D. E. acknowledge support by the Swiss National Science Foundation (SNSF) in the frame of the National Centre for Competence in Research PlanetS, and has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (project Four Aces; grant agreement No 724427). HARPS data were obtained at ESO 3.6m telescope from 2003 to 2017, with Program IDs, 60.A-9036, 072.C-0636, 075.C-0234, 076.C-0073, 076.C-0279, 078.C-0209, 079.C-0170, 080.C-0032, 080.C-0664, 080.C-0712, 081.C-0034, 082.C-0308, 082.C-0412, 084.C-1039,

A&A proofs: manuscript no. FeI_HARPS_paper_2_arxiv


D Borodin

A Schori

J.-P Rueff

J Ablett

S Shwartz
email: sharon.shwartz@biu.ac.il

Evidence for collective nonlinear interactions in x ray into ultraviolet parametric down-conversion

We present the observation of peculiar non-monotonic photon energy dependencies of the count rates and of the rocking curves of parametric down-conversion of x rays into ultraviolet far from any atomic resonances. The observations cannot be explained by models that consider only atomic or bond charge responses and suggest that collective phenomena contribute to the effect. We propose an interpretation that includes nonlinear interactions with plasmons, which can explain the existence of peaks in this energy range.

Our work implies that nonlinear interactions between x rays and either ultraviolet or visible radiation can be utilized as a powerful atomic scale probe for collective effects in solids.

The field of nonlinear interactions between x rays and longer wavelengths has made a major progress in recent years [1][2][3][4][5][6][7][8][9]. These processes are interesting, since they present novel physics involving fundamental aspects of light-matter interactions arising from the large diversity of the involved wavelengths, and since they can be used to probe phenomena related to valence electrons at the atomic scale resolution [9,10]. This is because the long optical wavelengths interact with the valence electrons and the x rays provide the high spatial resolution. This effect can be viewed as x-ray scattering from the optically induced valence charge variations. The photon energy of the scattered x rays is shifted by the amount that is equal to the photon energy of the longer wavelength wave to conserve energy. In a typical experiment, the requirement for momentum conservation (phase matching) is fulfilled by using one of the reciprocal lattice vectors of the nonlinear crystal. Consequently, the efficiency of the effect is propositional to the absolute square of the Fourier component of the induced valence charge density corresponding to the selected reciprocal lattice vector. A series of measurements of these coefficients can be used for the reconstruction of the microscopic optical response of the valence charges of materials [3].

Most of the valence electronic resonances of materials are in the ultraviolet (UV) range. Since materials are opaque at those wavelengths, nonlinear interactions between x rays and longer wavelengths have been observed by using the effect of x ray into UV parametric down-conversion (PDC) [1-3, 6-8, 11]. This is a second-order nonlinear process in which a pump photon interacts with the vacuum field in a nonlinear medium, which in turn leads to the generation of a photon pair, where one photon is an x-ray photon and the other is a UV photon. The convention is to denote the x-ray photon as the signal and the UV photon as the idler. The sum of the photon energies of the generated photons is equal to the photon energy of the pump photon. Since the photon pairs are generated simultaneously at the same position, the count rates of the emerging x-ray photons depend on the generation rate of the UV photons. Consequently, although the UV photons are absorbed in the material, the information on phenomena that are associated with energies that correspond to UV wavelengths is retrieved by measuring the x-ray photons. The measurements of the x-ray photons also provide the atomic scale resolution, which is an inherent property of x-rays arising from their short wavelengths. Hence, PDC of x-rays into UV can be used as a probe for the microscopic optical response at extremely high resolution as has been demonstrated by Tamasaku and his colleagues [3].

However, the authors of all the previous papers on x ray and either UV or optical nonlinear interactions have considered only local responses [1][2][3][4][5][6][7][8][9][10][11]. The interactions have been viewed as inelastic x-ray scattering from local charge excitations where both atomic and bond charge responses have been considered [1][2][3][4][5][6][7]. In some of the papers the results have been interpreted as Fano interference between the PDC and Compton scattering [1][2][3].

In this Letter, we extend the study on nonlinear x-ray optics to include the interactions with plasmons. We explore the effect of PDC of x rays into UV in a diamond crystal by measuring the x-ray signal that corresponds to idler photons in the energy range of 28 -54 eV where our model predicts peaks in the frequency dependence of the efficiency of the effect far from any atomic resonances (the binding energies of electrons in carbon are 12, 16, and 280 eV). We measure the non-monotonic dependencies of the count rate and of the angular peak positions of the rocking curves on the signal photon energy, which include the predicted peaks but also show more unexplained structures.

The photons that are generated via the PDC process obey energy and momentum conservation (phase matching). The energy conservation equation can be written in the form of

p s i     h h h
, where p, s, and i refer to the pump, the signal, and the idler respectively. Since the x-ray wavelengths are comparable to the interatomic distances, phase matching is achieved by using the reciprocal lattice vector G r [12]. The k-vectors of the pump, signal, and idler waves satisfy the phase-matching equation

p s i k G k k    r r r r ,
where k denotes the wave vector of the corresponding photon.

We first describe a simple theory that includes the interactions with plasmons and that predicts the existence of peaks far from atomic resonances. We consider a classical model for the nonlinearity that includes excitations of plasmons in the nonlinear medium.

The nonlinear signal can be calculated by solving the wave equation with the nonlinear current density as the source term. Consequently, the efficiency of the PDC process is proportional to the absolute square of the nonlinear current density and the information that is encoded in the nonlinear current density can be reconstructed from the measurement of the efficiency of the PDC.

The nonlinear current density can be found as a second-order perturbation of electron motion [13]:

(2) (1) (1) (1) (1) 0 NL s s p i i p J v v v        r r r r , (1)
where 0  is the unperturbed charged density,

(1) j  is the charge density modulated by the j-th frequency, and

() n j v
is the n-th order velocity at the j-th frequency. The model consists the equation of motion of an electron with the restoring force and the equation of continuity for the signal and idler waves [4,[START_REF] Shen | The Principles of Nonlinear Optics[END_REF]:

2 0 ( ) ( )
( ) 0 j e j j j j j j e j jj v q v v r E v B tm v t                   r rr r r r r r , (2)
where e m is the effective electron mass, e q is the electron electric charge,

j B is the magnetic field, j E
is the electric field strength of the corresponding wave, and 0  denotes the resonance frequency. We assume that the motions of electrons at the signal and pump frequencies are free, since their photon energies are well above any electronic binding energy in the nonlinear medium. At the idler frequency we include the restoring force term, since its corresponding photon energy is on the order of the binding energies of the valence electrons. We solve the system of Eq. 2 together with the Maxwell equations [15]. Note, that we take the Gauss's law in the form

e G i i p i p s NL s p plasma oi q E E G e e e J m                      r , (3) where (1)
()

G i



is the Fourier component of the linear electric susceptibility that correspond to the reciprocal lattice vector r G at the idler frequency, and ê is the polarization vector of the corresponding wave. We estimate eV for diamond. In our calculations we use the plasma resonance energy of 34 eV due to the dispersion of plasmons in the [110] direction [18]. The expression in Eq. 3 predicts a nonlinear resonance at a frequency, which is equal to

22 0 i NL plasma       
. In Ref. 4 the authors took 0

 to be equal to the band transition of a diamond crystal for the correction of the nonlinear current density. Since in real crystals there is more than one resonance associated with band transitions, we use the resultant nonlinear current density in the following form

1 1 2 2
... Figure 1 shows calculations of the spectrum of the resultant nonlinear current density calculated by using Eq. 4 and include resonances at 5.5 eV, 7.4 eV, 12 eV, 14.4

NL NL NL tot s s J W J W J    , (4)
eV, 16 eV, 20 eV, and 24 eV, which are associated with band transitions in a diamond crystal as described in the literature [20,21]. The simulation shows that the PDC signal depends strongly on the photon energy of the idler when it is near NL  . Each spectral feature represents nonlinear interactions between the band transitions and bulk plasmons [19]. This dependence cannot be explained by any theory that does not include non-local interactions. We note that a recent work by Lucchini and colleagues the measurements of absorption on a polycrystalline diamond sample shows the absence of resonant transitions in this photon energy range [22]. The arrows point at the spectral regions where the peaks were experimentally observed. The discussion on that will be provided later in the text.

The experiment was conducted on the GALAXIES beamline at the SOLEIL synchrotron facility [23,24]. The experimental setup is shown in Fig. 2. We use a monochromatic beam of 9.995 keV using the Si(111) reflection of the beamline double crystal monochromator. We use the reciprocal lattice vector normal to the C(220) atomic planes of a diamond crystal for the phase matching in reflection (Bragg) geometry. We select the photon energy of the signal by using the beamline Rowland circle RIXS spectrometer. The instrument consist of a spherically bent Si(555) crystal analyzer with a curvature radius of one meter and a hybrid-type pixelated 2D MERLIN detector. We estimate that the photon energy resolution of the receiving optics is about 0.5 eV. We use an adjustable iris in front of the analyzer to reduce the background radiation along with spatial filtering of the detector image. Typical iris diameter during the measurements was about 5 mm.

The first experimental step is to verify that we observe PDC by confirming that the phase-matching conditions are satisfied. We measure the rocking curves of the x-ray signal that correspond to various idler photon energies as we show in Fig. 3. The peak positions of the rocking curves are slightly shifted from the solutions of the kinematic phasematching equation as we observe also in the simulations. This is because the rocking curves include a large number of the vacuum fluctuation modes with different weights that are determined by the strength of the nonlinearity and the boundary conditions at the various modes as discussed in Ref. 7. The inset in Fig. 3 shows the comparison between the experimentally observed peaks and that obtained in the simulations. The difference between the estimated offset from Bragg and measured is about 0.01 deg. We note that the difference between the calculated and measured shifts is smaller than the width of the curves (about 0.02-0.03 deg). The phase mismatch z abs kL  , where abs L is the absorption length, at all measured peaks of the PDC rocking curves is about 0.1, which is much smaller than 2π. As we expect, the peak position shifts farther apart from the Bragg angle as the idler photon energy increases. These are clear indications that the rocking curves in Fig. 3 constitute conclusive evidence that we observe PDC.

Next, we explore the dependencies of the signal count rates and the rocking curve peak positions on the photon energy of the idler and show that as predicted by our theory, the dependencies are not monotonic in the energy range of 28-54 eV, which is far from any atomic resonances. For this purpose we measure rocking curves similar to those shown in we plot the measured count rates at the peaks of the rocking curves (power spectrum) and relative positions of rocking curve peaks with respect to the angle of elastic scattering as a function of the photon energy of the idler. In the measured power spectrum we see two spectral features above the monotonic decrease of the signal intensity around 36 eV and around 42 eV as predicted by the model we described above. The existence of this nonmonotonic dependence of the power spectrum on the idler photon energy, indicates that the underlying physical mechanism for the nonlinear interactions must include origin that is not from atomic interactions since the structures are obtained far from any atomic resonances. According to the theory we have derived above, it can be explained by including interactions with plasmons. A marginal feature around 47 eV is not present in the simulations. This might indicate the contribution of interband transitions in the diamond crystal with higher energies. The corresponding energy of this transition should be around 32-33 eV. Since the feature is very small, the weight coefficients from Eq. ( 4)

corresponding to that transition should be also very small.

While the experimental observed structures of the power spectrum indicate clearly on the nonlinear interactions with the plasmons, the detailed comparison with the theory requires the full simulation of the PDC process since the count rate of the signal depends not just on the nonlinearity but also on the refractive index and the absorption, which are also photon energy dependent. We simulate the PDC process by solving the coupled slowly varying envelope wave equations in the Heisenberg-Langevin model [25] together with the model for the nonlinearity described above. The count rate is calculated by integration the solution for the signal over the photon energies and the solid angle of the experimental detection system. The results of the simulation are shown in the inset of the Fig. 4(a) where the arrows point at the positions of the measured spectral features. We note that most of the features from the calculated nonlinear current density appear in the measured power spectrum. The measured features are wider than predicted by the simulations and some of the spectral features that are predicted by our model are not resolved in the experiment due to the measurement resolution. The simulation also predicts a much higher enhancement of the PDC efficiency near NL  than the efficiency that we observe in the experiment. This is probably because of losses that are associated with the plasmon interactions and that we do not consider in our simulation. The selection rules for the nonlinear interactions are also needed to take into account to improve the agreement between the experiment and the theory. In addition, we believe that a comprehensive model that includes a band structure calculation is required for a better description of the effect.

In Fig. 4(b) there is a distinct sharp change in the curve at 45 eV, which is also seen in the inset that shows the rocking curves of the signal at the corresponding points.

Interestingly, the comparison with Fig. 4(a) indicates that at the same photon energy there is a small dip in power spectrum. Such a feature does not appear in the simulation and requires further investigations.

In

  . 14. Our calculations result in the following expression for the envelope of the nonlinear current density

  below 35 eV from the experimental data[START_REF] Phillip | [END_REF] and for higher idler energies we use the values calculated by Henke et al.[17]. The plasma resonance plasma  h is calculated by using the well-known expression for the plasma frequency

W

  where j are weight coefficients and NL sj J are the nonlinear current densities from Eq. 3 that corresponds to the j-th resonance [19]. Weight coefficients indicate the contribution of the corresponding resonance to the resultant process. In the current calculation the best fit with the experimental result is obtained when the weight coefficients are equal. The reason for this is still an open question that should be addressed with a more comprehensive theory.

Fig. 3

 3 Fig. 3 for photon energies of the signal in this range in steps of 1 eV. In Figs. 4(a) and 4(b)

  FIG. 2. (Color online) (a) Phase-matching scheme where the indices p, s, and i stand for pump, signal, and idler respectively. The dashed line indicates the Bragg diffraction direction. (b) Experimental setup. The synchrotron radiation (SR) illuminates a diamond crystal, which is tuned to an angle satisfying the phase-matching conditions. The PDC signal is collected by a bent crystal analyzer, which images the beam at the selected energy onto a two-dimensional detector.

FIG. 3 .

 3 FIG. 3. (Color online) Rocking curves of the PDC signal for corresponding idler photon energies at 25 eV, 28 eV, 30 eV, and 32 eV. The dashed lines are guides for the eye. The inset shows the comparison between the experimental data and simulations.

position of the measured spectral peaks. In (b) the inset shows the rocking curves of the PDC at the photon energies near the sharp change in the peak position as a function of the idler photon energy.


Demet Yesiltepe

Ruth Dalton

Ayse Ozbil

Nick Dalton

Sam Noble

Michael Hornberger

Antoine Coutrot

Hugo Spiers

USAGE OF LANDMARKS IN VIRTUAL ENVIRONMENTS FOR WAYFINDING: Research on the influence of global landmarks

Keywords: Wayfinding, Local Landmarks, Global Landmarks, Virtual Environments

. Thus, in this paper, we aim to better understand the effect of global landmarks on wayfinding. We used different virtual game-environments and compared two different conditions: the presence of local landmarks versus the presence of both global and local landmark conditions. Participants from all around the world (n=1.3 million) contributed to the study and were asked to view maps of environments first, then navigate a boat to find specific destinations that had been indicated on the maps. Environments were analyzed using axial and segment based integration, choice and intelligibility as well as visual connectivity and integration. In addition, segment lengths and the number of decision points in the map's layout were also analyzed. Levels with similar spatial values were chosen to compare the different landmark conditions. Preliminary findings indicate that global landmarks do not appear to have a significant impact on wayfinding. The large dataset underpinning this study contributes to our knowledge of the effect of landmarks by clarifying a gap in the literature -whether global and local landmarks or only one type of landmark are more influential on wayfinding.

INTRODUCTION

Landmarks are essential elements for wayfinding tasks [START_REF] Ruddle | Navigating buildings in desk-top'' virtual environments: Experimental investigations using extended navigational experience[END_REF][START_REF] Stülpnagel | Active route learning in virtual environments: disentangling movement control from intention, instruction specificity, and navigation control[END_REF]. Depending on their location during a wayfinding process, landmarks can be divided into two categories as global and local landmarks. Distant landmarks such as mountains and towers, which can be seen from a large area, are accepted as global landmarks [START_REF] Steck | The role of global and local landmarks in virtual environment navigation[END_REF]. [START_REF] Lynch | The image of the city[END_REF] describes global (distant) landmarks as elements seen from many angles and distances, and/or seen over the top of lower elements.

In contrast to global landmarks, local landmarks are visible just from a small distance [START_REF] Steck | The role of global and local landmarks in virtual environment navigation[END_REF]; they are visible only in a limited area and only from certain approaches Proceedings of the 12 th Space Syntax Symposium [START_REF] Lynch | The image of the city[END_REF]. Local landmarks can be trees, storefronts or innumerable signs [START_REF] Lynch | The image of the city[END_REF]. [START_REF] Lynch | The image of the city[END_REF] determined that people tend to use global landmarks only if they are unfamiliar with an environment. In his study (within a real environment), he observed that people used global landmarks only for very general orientation and they used local landmarks more frequently. In their study on environmental cognition, Evans and others (1984) focused on the effect of stress, landmarks and path configuration on environmental cognition. They discovered no significant differences between internal and external landmark conditions. However, they observed that there was a trend for internal landmarks to be more helpful than external ones. Lately, Ruddle and others (2011) hypothesized that adding both global and local landmarks in an environment would reduce the number of errors people make when they travel in virtual environments. They observed that although local landmarks did reduce participants' errors, global landmarks did not influence the overall number of errors. Therefore, contrary to their hypothesis, local and global landmarks interfered with each other and so they observed that participants who were provided both kinds of landmarks made more errors. Thus, in all these studies researchers observed that local landmarks were more effective on wayfinding. Similarly, Meilinger and others (2015) tested whether global landmarks improve spatial performance or not. For their study in a large-scale virtual environment, 33 participants were selected, and they were randomly assigned to three conditions: self-movement cues, self-movement and orientation cues and finally self-movement, orientation and distance cues. Results of this study showed that global landmarks did not have any dramatic influence on orientation. Researchers concluded the study by saying that proprioceptive information was sufficient to keep participants oriented. Moreover, in their previous study, Meilinger and his colleagues (2014) Participants of this study first completed the learning phase, and then they were asked to walk in an immersive virtual environment and point to seven learned targets. Results of this study also showed that participants relied on local reference frames rather than global reference frames or orientation free representations. They mentioned that survey tasks can be solved by the usage of interconnected local reference systems. Hence, these studies also pointed to the idea that global landmarks are not effective on wayfinding. Schwering and others (2013), on the other hand, attempted to determine types of information that support orientation during wayfinding. Researchers discovered that in both tasks they organised (verbal instructions and sketch maps), participants provided both global and local information to help orientation. Furthermore, they suggested that including landmarks not only decision points but also along routes and off routes can make route orientation more Proceedings of the 12 th Space Syntax Symposium efficient. In addition, in their study on virtual environments, [START_REF] Steck | The role of global and local landmarks in virtual environment navigation[END_REF] hypothesized that people use different strategies; they may rely on only local landmarks, or global landmarks, or they may use some global and some local landmarks or they may use both kind of landmarks. They created visual environments to test their hypothesis and they discovered that some participants used only local landmarks for decisions when others used only global landmarks. In addition, they observed that some participants used local landmarks at one position and global landmarks at another. As a result of this study, they asked a new question: "how do participants select a landmark for a certain decision?" and they concluded the study by mentioning landmark saliency and by saying that functions of landmarks could also be effective on people`s preference. These studies gained importance to show that both landmark types can have an influence on wayfinding behaviours. Finally Schwering and others (2014) aimed to explore the use of landmarks in verbal descriptions for routes at different scales and different transportation modes. Findings of this study suggest that local landmarks are mostly used in the verbal descriptions whereas global landmarks are used for wayfinding and spatial orientation in new environments. They also discovered an increase in the usage of global landmarks (particularly regional global landmarks) for orientation as the distance increased. Results of this study was essential as it suggested that global landmarks might be more useful in new environments, which also supported Lynch's idea (1960) for how global landmarks are used in real environments.

Other studies also pointed to the importance of the existence of both global and local landmark conditions [START_REF] Schwering | The use of local and global landmarks across scales and modes of transportation in verbal route instructions[END_REF][START_REF] Li | The effects of different verbal route instructions on spatial orientation[END_REF]. Lin and others (2012) assessed gender differences in wayfinding in virtual environments.

Researchers discovered that participants travelled longer paths in an environment with local landmark than in an environment with global landmarks. They explained this result by describing the 'anchor-point'1 usage of global landmarks in orientation and the time that participants spent finding local landmarks. Hence, this study also gained importance by mentioning the importance of global landmarks within virtual environments.

Proceedings of the 12 th Space Syntax Symposium

Based on the different results within the literature, this study aims to explore the effect of location of landmarks on wayfinding performance. By using a large dataset, we aim to have accurate results on the impact of global and local landmarks on wayfinding performance.

Our hypothesis is that, in environments with global landmarks the time taken to complete the levels will decrease as participants will use the global landmarks as environmental clues.

METHODS

To test the influences of landmarks on wayfinding a game produced by an independent games design company, Glitchers Ltd. [START_REF] Hyde | Sea Hero Quest: the World's first mobile game anyone can help scientists fight dementia[END_REF], for smart phones and tablets is used. The game "Sea Hero Quest" (SHQ) [START_REF] Coutrot | Global determinants of navigation ability[END_REF] was released in 2016 and 3,7 million participants completed at least the first level of the game.

Wayfinding in the game environments (for layouts of some levels see Figure 1) is controlled by three moves; tap right to turn right, tap left to turn left and swipe up (boost) to accelerate.

There are 75 levels and mainly three kinds of tasks required to complete the game. In the wayfinding levels (44 levels), which are used in this study, participants first are asked to look at a map that includes their current location and goal locations they should reach. Then the map disappears, and they are asked to navigate a boat in a virtual environment and look for the goal locations. In order to play next levels, participants are first asked to complete the previous levels.

2016))

The first wayfinding level, which was also the first level of the game, was excluded from the analysis because this level was designed as a training phase. The data which is used in this study includes results of 1.3 million people (for the second level) who volunteered information about their age and gender (participants aged between 18-99; 769,556 male, 551,295 female and 326 other).

In order to explain the effect of landmarks first the spatial structure of levels was compared and then the levels which include similar theme (different environments were created in the game, only two of them were used in this paper: Arctic Rivers and High Rollers), type (three Proceedings of the 12 th Space Syntax Symposium different tasks, only checkpoint levels were selected), weather conditions, variety of landmarks and existence of global landmarks were grouped. In order to analyse the spatial characteristics of levels, average values of axial and segment-based2 choice (radius r: n, 3), visual integration and choice as well as average axial intelligibility, segment length, number of decision points and number of destinations of levels were measured in Depthmap X 0.50.

Results of the levels were clustered in statistical software JMP with hierarchical clustering method (Figure 2). As it can be seen in figure 2, 5 clusters were automatically produced, represented with different colours and shapes. As a second step of the analysis, conditions of levels were compared. Table 1 demonstrates different theme, type, landmark (categorised based on the saliency of landmarks and accessibility of their positions), existence of global landmarks and weather conditions of 4 selected levels. Levels 11 and 13 as well as level 63 and 73, which are located in the same clusters, were analysed separately based on the time taken by participants. Care was taken to ensure that all attributes, apart from the presence of global landmarks, were matched.

Selection of levels

Participants

To make a comparison between these two-binary groups only the players who played both levels were used. Before this step, outliers3 (based on the logarithm of the duration of the levels) in the dataset detected and excluded. For levels 11 and 13, the total number of results collected was 1,666,438 with 52,206 outliers. And for levels 63 and 73 it was 41,813 with 2,091 outliers. After the outliers were detected and excluded, the participants who played two levels (level 11 and 13 or level 63 and 73) were analysed to compare the results fairly.

The number of participants who played both levels 11 and 13 was 706,180 (201,872 results belonged to only one level were excluded) and number of participants who played both levels 63 and 73 was 28,414 (11,308 results were excluded).

RESULTS

Before comparing the time taken by participants to complete a level, the shortest realistic routes of the environments were measured in order to consider the effect of the spatial layout and its effect on wayfinding (Carlson et al., 2010). Segment maps were used to measure the shortest realistic route and all goal locations were tracked respectively. Once the shortest realistic routes were measured for all levels, maximum (usage of the speed up command during the game) and minimum (without boost) speed of the boat was used to measure the seconds that would be spent to complete a level and logarithmic transformation was applied Proceedings of the 12 th Space Syntax Symposium to the results (Table 2, heading A and B) in order to have a normal distribution. Real time spent by participants during the game was also measured and mean durations were calculated (Table 2, heading E). By using just the real time duration that was spent by participants, it is first clear that duration increases as the levels change. Between levels 11 and 13, a slight increase in mean duration can be seen. Likewise, mean duration of level 73 is also higher than level 63. This makes sense as the levels are intended to become progressively more difficult the longer the player plays the game. However, when the ratio of mean duration and expected duration is calculated, the results change. Table 2 shows the ratio of real duration to expected duration with boost, meaning assuming the maximum accelerated speed, (C) and without boost (D). In both conditions, with acceleration, or without it, it took more time for participants to complete level 11 than level 13. Similarly, it is also observed that it took more time for the participants to complete level 73 than level 63.

When these results are compared to the attributes of the levels, it can be seen that both levels 11 and 73, where the environments include global landmarks, duration increased slightly.

Hence, it can be stated that it took more time for participants to complete the levels where there were global landmarks (all other things being equal). Thus, as a result of this study, it can be argued that no significant, or even an inverse, effect of global landmarks was observed on wayfinding.

CONCLUSIONS

The primary objective of this study was to investigate whether global and local landmarks or only one type of landmark is more influential on wayfinding performance of people. To achieve this goal, we used forty-four different levels of SHQ and clustered levels based on their syntactical values. Four different virtual environments from the original set of fortyfour were selected to compare, controlling for all other attributes of the levels. Then these levels were investigated based on the time participants spent to complete the levels and the ratio between the real duration (which was taken by participants) and expected duration (that was calculated based on the shortest realistic routes). The results of the analyses showed that there was no significant decrease in completion duration when the environment contained Proceedings of the 12 th Space Syntax Symposium global landmarks. The results of this study support some other studies in the literature which also did not observe any significant influence of the global landmarks on wayfinding performance [START_REF] Ruddle | The effect of landmark and body-based sensory information on route knowledge[END_REF]. Moreover, in levels containing global landmarks, it took more time for participants to complete the tasks. On further scrutiny of the environments (both levels 13 and 63 which did not have any global landmarks), it was observed that these environments had a ringy layout. Thus, it was concluded that in these levels the layout might make it easier for participants to recover from wrong wayfinding decisions made. As mentioned in earlier studies (Carlson et al., 2010), this paper also concluded by saying that the layout of environments are vital to the movement of people and cannot be fully separated from the presence of landmarks: there is always an interaction between the two.

The present study is essential as it consists of the largest dataset in landmark and wayfinding studies in virtual environments generated to date. The total number of participants was 1.3 million and the number of participants whose results were compared in this study was 706,180 (for levels 11 and 13) and 28,414 (for levels 63 and 73) that makes this study an important contribution to the debate on the effect of landmarks, in terms of the potential accuracy of the results.

On the other hand, in this paper only two conditionsthe existence of both global and local landmarks and the existence of only local landmarks -were compared. A no-landmark condition was not included in this study because of the hierarchical clustering. Even though there were levels where there were similar conditions (weather, difficulty and type) and various landmark conditions (existince of no landmarks, only local landmarks, and both global and local landmarks), these levels were not used in this study due to the fact that they located in different clusters.

Another limitation of this study is that classification of whether a landmark was global or local, that were compared in this study, were pre-defined by the designers of the game-levels (Dalton, Hölscher and Wiener-see Dalton, 2016). A further study will aim to identify global and local landmarks for specific levels in order to have a more accurate rating. Finally, logarithmic duration was used in this study to have normal-distributed data. However, in navagational performance it is possible to have long tails. Thus, for future research it is also aimed to use the real duration instead of logarithmic duration.

Anacta, V.J., Schwering, A., Li, R., 2014

  aimed to explain the effects of three factors: global reference frames, multiple local reference frames and orientation-free representations on representation in memory with two experiments.

Figure 1 :

 1 Figure 1: Layouts of the selected game levels (Source: Glitchers Ltd. (Hyde et al.,

Figure 2 :

 2 Figure 2: Constellation plot of all levels through the use of all measures

Table 1 . Attributes of the selected levels

 1

	Level	Theme	Type	Landmarks	Global	Weather
	11 Arctic Rivers	Checkpoint	Easy	Yes	Clear
	13 Arctic Rivers	Checkpoint	Easy	No	Clear
	63 High Rollers	Checkpoint	Hard	No	Waves
	73 High Rollers	Checkpoint	Hard	Yes	Waves

Table 2 : Comparison between real and expected duration

 2

			(B)Duration			(E)Real
		(A)Duration	without	(C)Ratio		Duration
	Levels	with boost	boost	_reald_ b	(D)Ratio_reald_wb	(mean)
	11	1.561	1.769	1.150	1.015	1.796
	13	1.632	1.839	1.125	0.998	1.835
	63	1.680	1.888	1.221	1.087	2.052
	73	1.737	1.944	1.403	1.253	2.437

  . Determining hierarchy of landmarks in spatial descriptions. Eighth International Conference on Geographic Information Science.

Carlson, L.A., Hölscher, C., Shipley, T.F., Conroy Dalton, R., 2010. Getting lost in buildings. Current Directions in Psychological Science 19, 284-289.

"Anchor-points (anchors for short) are closely related to landmarks, both concepts being defined as cognitively salient cues in the environment. However, as represented in the literature, landmarks tend to be collectively as well as individually experienced as such, whereas anchors refer to individual cognitive maps. Although one would expect to find several local landmarks among the anchors in a person's cognitive map, many anchors (such as the location of home and work) would be too personal to have any significance for other, unrelated individuals. Further, landmarks are primarily treated as part of a person's factual knowledge of space, whereas anchor-points are supposed to perform in addition active cognitive functions, such as helping organize spatial knowledge, facilitating navigational tasks, helping estimate distances and directions, etc. Finally, landmarks are concrete, visual cues, whereas anchor-points may be more abstract elements that need not even be point-like"(Couclelis et al., 1987 Page 102).

In order to produce segment maps, first the edges of the moveable spaces were represented with points, and then Voronoi polygons were created in ArcMap 10.3. Segment lines were drawn from the intersections of Voronoi polygons.

Outlier formula: Upper value=upper quartile + (1.5 * (inter quartile range, IQR)) Lower value= lower quartile -(1.5 * (inter quartile range, IQR))