Be profiles An amateur contribution to Be stars study

Transcription

1 Be profiles An amateur contribution to Be stars study M. Bonnement1, F. Cochard1;2, and V. Desnoux1 1Aras Amateur Ring for Astronomical Spectroscopy, 2Shelyak Instruments, France - Abstract. Since 2003, the amateur astronomical community has decided, in collaboration with the Paris-Meudon Observatory (GEPI) to coordinate their observations to get the best spectral survey of Be stars as possible. A database for amateur and professional Be star spectra, BeSS, has been created. This study is a first analysis of collected data, mainly focused on Be profiles classification. We're doing here only descriptive analysis, with no assumption on the physical phenomena causing these profiles. We've defined a profile list, which covers all Be cases encountered... Keywords. stars: Be, stars: emission-line, techniques: spectroscopic, stars: activity, surveys 1. Amateurs, spectroscopy and Be stars Be stars are easy targets for small instruments (300 stars up to magnitude 8, Northern hemisphere). Amateur observations are very complementary to professional ones, because we can have a much better time coverage for a high number of stars. The amateur community has developed several tools to contribute to Be spectroscopic Observations among which ArasBeam, a web based tool to coordinate Be observations. 2. BeSS : the Be stars database BeSS is available at ArasBeam is a website developed and administrated by amateurs, available at 3. ArasBeam : Be observing program by amateurs (work in progress) 4. Former works Different classifications of Be stars spectra have been proposed. Hanuschik s classification is a currently used one (in Astronomy and Astrophysics 302, ). It defines four principal classes, closely related to the inclination angle (i.e. between the line of sight from the observers position and the stars rotation axis) : P pole on (i = 0), L low, H high and E edge on (i > 80). An index is added : 1 if the profile is symmetrical, 2 if asymmetrical. This classification is thus exclusively connected to a parameter unrelated to the star s own physics. Some later works have tried linking the observed profile to the stars own physical features (Hummel and Vranken in Astronomy and Astrophysics 359, April 2000, Porter and Rivinus in Publications of the Astronomical Society of the Pacific, 115 : , 2003 October), even have set up theoretical

2 4 M. Bonnement, F. Cochard & V. Desnoux models being later compared to a large set of really observed Be stars spectra with the aim of reproducing their global characteristics. (Silaj et Al. in The Astronomical Journal Supplement Series, 187 : , 2010 March). Be it as it may, Hanuschik s P, L, H, E typology is still regularly used. We have to admit that if the shape of the H alpha line is strongly impacted by the inclination angle, a classification entirely based upon this parameter is on one hand deeply simplistic and on the other hand, does not take into account all the observed profile types. Our approach has consisted in classifying the H alpha line profiles of the 419 stars of BeSS database, whose magnitude is inferior or equal to 9 and of which at least one usable spectrum is available in the database, on a strictly topological basis. It appeared right away that only a part of them could take place in Hanuschik s categories, an important proportion of stars showing profiles which escape this typology. We must insist on that point, that our work has been exclusively descriptive, our condition of amateurs forbidding us any astrophysical interpretation of the profiles we met. This is why we have defined a priori a set of 21 possible profiles (as far as topology is concerned, we shall see later on that some of them have never been encountered), and a 22nd unclassified case, those type-profiles being obtained by a combination of 1, 2, 3 or 4 gaussian-type curves, characterised by the number of their extrema (minima and maxima) and their relative positions. Besides the extrema are also noticed the inflexion points, which are at least 2, the first one where the profile leaves the continuum line, the second one where it returns to that line. The set of extrema + inflexion points gives the number of characteristic points of the profile (always uneven, from 3 to 9). Those profile types are designated by a figure which is the number of characteristic points, followed by a letter attributed arbitrarily. And so the 3A profile shows a simple emission, while the 3B in which the extremum is a minimum, shows a simple absorption. (See in appendix A the table of the profile types and the GnuPlot formulas used to draw them, this drawing having just a qualitative, descriptive, typological value and not a quantitative one). 7. Method The spectra of 419 studied stars have been loaded from the BeSS database by order of increasing magnitude, thus beginning by the brightest stars. Each one is loaded in Valérie Desnoux s VisualSpec software, and scripts automating the process perform the following operations : computation of the local continuum line in the area surrounding the H alpha line (between 6491 and 6671 Å) with reference to a list of 22 points avoiding atmospheric lines; this computation is not critical as far as the continuum on such a short interval is quasi linear, division of the raw profile by this continuum in order to obtain a normalised and rectified profile,

3 ArasBeam 5 correction of the atmospheric lines (division by a synthetic H 2 O spectrum), mouse-clicking the characteristic points : inflexions at the beginning and the end of the line, minima and maxima; VisualSpec then returns in a text file the pairs of X,Y coordinates (resp. lambda / intensity) of those points. Figure 1. Mouse-clicking the characteristic points It is very important to notice at this point that all those operations do not, for this first study, aim at bringing in quantitative results (e.g. the equivalent width of the line, the maximum peak(s) intensity, the width at half maximum etc) It is just about locating each characteristic point in respect with another to obtain a topological description of the observed profile and thus classify it by comparison with the profile-types. For each star, the list of the (λ, i) pairs is analysed with an algorithm allowing to automatically determine to which of our profile-types the analysed one relates to. (see in appendix B the descriptive table of the algorithm). The text file data are opened in a spreadsheet program in which the algorithm is implemented. A graphical thumbnail is also edited by VisualSpec, allowing the operator to check the conformity of the automatically determined profile to the one ensued from his own judgement. This double-check automatic/visual, allows to eliminate at the same time the odds of a wrong visual estimation (relative height of the points difficult to appreciate, visual fatigue, confusion) and those of a wrong automatic analysis (in fact, the only discordances which have been noticed because of the algorithm found their cause in a wrong original mouse-clicking of the characteristic points, so actually in an operatorrelated mistake, corrected during the final examination: 16 occurrences out of 419 cases, and 10 cases of unclassified profiles, because strongly asymmetrical or P Cygni types). A systematic study of the whole lot of spectra (4000) of the BeSS database has been considered. It could include the measurement and the quantitative analysis of those parameters. For feasibility reasons, we have decided in a first step to limit our work to undertaking a qualitative classification of the latest recorded spectrum of each star.

4 6 M. Bonnement, F. Cochard & V. Desnoux 8. Results The list of the 419 stars and their types determined by this method is shown in appendix 4. The table below gives the statistical distribution by types of the 419 stars: Observed profile Number % 5C % 3B % 3A % 7J % 7L % 5A % 7D % 5E % 7F % 5B % 7H 9 2.1% 9A 9 2.1% NR asym 9 2.1% 7B 6 1.4% 7K 3 0.7% 5F 2 0.5% P Cygni 1 0.2% 5D 1 0.2% Total %

5 ArasBeam 7 A second table gives the distribution of the 347 profiles of other types than 3B (pure absorption) Observed profile Number % 5C % 3A % 7J % 7L % 5A % 7D % 5E % 7F % 5B % 7H 9 2.6% 9A 9 2.6% NR asym 9 2.6% 7B 6 1.7% 7K 3 0.9% 5F 2 0.6% P Cygni 1 0.3% 5D 1 0.3% Total % The whole set of thumbnail images which illustrates the spectra of those 419 stars is shown in appendices C to S. They are sorted by category and inside each category, by decreasing brightness. The reader can refer to it to follow visually the following comments. Hanuschik s classification being currently used but being, in our opinion, incomplete to cover all the types actually observed, our comment will centre around two main parts: the types possibly related to P, L, H and E types, and those not taken into account by this classification The stars matching Hanuschik s types The type we call 5C (appendix G) is the most common: it is found in 25% of the stars of the whole sample and in 30% of those showing an emission. It matches, for a part of them, the H type in Hanuschik s classification, which some stars illustrate perfectly: HD54309, 25 Ori, 228 Eri, HD224559, V558 Lyr are examples of the symmetric variety of this type (H1). Our method leads to include in this category stars showing a more or less obvious asymmetry, which would match the H2 type. We can name for example 228 Eri, HD38010, HD162428, HD The topological character of the classification (two peaks, the central minimum remaining above the continuum line) induces that a part of the E type in Hanuschik s classification We shall see at point 8.3 that some 10 type 3B spectra car actually show an emission of a peculiar profile.

6 8 M. Bonnement, F. Cochard & V. Desnoux also gets into type 5C. Among those whose profile is symmetrical which would match E1, let us name Psi Per, HD34959, HD50658, HD49888, HD13669, HD Some others, whose profiles show a more or less obvious asymmetry, would match E2: Phi Per, HD217050, HD50138, HD51480, HD45910, HD37806, HD45667, HD39340, HD50209, HD The type we called 5A (appendix E - 6% of the stars in emission) matches Hanuschik s E type, in which the central minimum is so marked that it extends below continuum (shell stars). Hanuschik only describes this case as an asymmetrical variant (E2). Nevertheless, we notice that if this topological case is actually observed in asymmetrical profiles such as HD142983, Zet Tau, Eps Cas, HL Lib, V923 Aql, it is also observed in perfectly symmetrical profiles such as those of HD179343, HD162732, HD197434, HD Type 5E (appendix I - 5% of the stars in emission) matches Hanuschik s P type: the single peak is very strong and shows winebottle-type shoulders giving it its characteristic shape. Several cases of asymmetry are noticed: 120 Tau, V764 Cas, HD One can consider that type 3A (appendix C - 15% of the stars in emission) also matches type P, in which the shoulders would not be strong enough to be noticed in the spectra of our database. Lets name for example Chi Oph for which the operator has hesitated to mouse-click a weak side-inflexion. Finally, our type 7L (appendix Q - 7% of the stars in emission) completely matches Hanuschik s L type and shows both a weak central reversal as in type H and winebottletype shoulders as in type P. All in all, among the 419 studied stars, only 218, i.e. 62.9% of the whole set, or 52% of those showing an emission, really match one of the types described by Hanuschik. The table below gives a correspondence between Hanuschik s types and those determined by our classification method: Hanuschik P L H E Our classification 5E / 3A 7L 5C 5C / 5A Example 8.2. The stars not matching Hanuschik s types They can be split up into three main categories and an intermediate one. (a) The profiles related to a Hanuschik type whose emission line would be surrounded

7 by a broader shallow depression shaped like a basin. ArasBeam 9 Type 7J (appendix O - 12% of the spectra showing an emission) tallies with a 5C type (which, as we have seen, itself matches type H and sometimes type E of Hanuschiks classification) whose central two-peaked emission would be surrounded by a basin shaped depression on both sides. Type 7K (appendix P - 3 cases, i.e. 1% of the stars showing emission signs) tallies with type 5E surrounded by a basin. Thus it is related to Hanuschiks type P surrounded by a depression. Type 5B (appendix F - 4% of the spectra showing an emission) is the equivalent of type 3A, also surrounded by a depression. We have seen above that type 3A could, like type 5E, be matched with Hanuschiks type P if we consider that the shoulders are simply not strong enough to be noticed. We can thus consider that type 5B is also related to type P surrounded by a depression. Type 9A (appendix R - 3% of the spectra showing an emission) is the equivalent of type 7L, thus also of Hanuschiks type L, surrounded by a depression. In the four cases, we ignore the - a priori - paradoxical meaning of that lateral depression (the emission being caused by the stars disk, shouldnt it normally always be more widely spread out by the Doppler effect, and thus broader, than the absorption generated by the star, whose Doppler widening is less wide?) Type 7H (appendix N) could be described here like a type E whose central absorption extends below the continuum, the whole thing being surrounded by a depression. Save the spectrum of HD44783, which matches this description, the other spectra of this type (numbered 8) can be better described like an intermediate type which will be described at point 4 below. The table below gives a correspondence between Hanuschik s types surrounded by a depression and those determined by our classification method: Hanuschik + depression P L H E Our classification 7K / 5B 9A 7J (7J?) Example (b) The profiles showing a broad absorption in the centre of which peeks out an emission line, more or less strong, but not reaching the continuum level:

8 10 M. Bonnement, F. Cochard & V. Desnoux Type 5D (appendix H) matches this description in which a weak central emission shows a single peak. This type has however been observed only one time out of 317 showing emission signs, among 419 studied. Type 7B (appendix K) also tallies with this description, with a two-peaked central emission not going past the continuum and jutting out a broad absorption basin. Six cases of this type have been observed, i.e. 2% of the stars showing emission signs. 1 peak 2 peak Emission in the centre of a broad absorption 5D 7B Example (c) A thin absorption line surrounded with a more or less strong two-peak emission. These three types are characterised by a thin absorption line, flanked with shoulders (5F) or real local maxima (7D and 7F). Type 5F (appendix J) distinct from Voigt type absorption profiles (see type 3B below) by the fact that the shoulders mark not only a break in the slope, but also an inversion of the curvature: the concave side always looking downwards in the case of Voigt profiles, belonging among type 3B (pure absorption), while the concave side is turned upwards in this type 5F, which could mean a trace of emission. This type has however been observed only twice among the studied spectra and it seems difficult to conclude that these shoulders unambiguously mark a sign of emission. It is no so for the following types. Type 7D (appendix L - 6% of the stars showing emission) shows on both sides of the absorption line, very strong shoulders characterised by a local maximum whose intensity however does not reach the continuum line. In type 7F (appendix M - 4% of the spectra showing emission), these shoulders are still stronger as they are characterised by a local maximum going past the continuum line. In one star (Nu Gem), we come close to a Hanuschik type E surrounded by a shallow depression. Barely visible Not reaching Going past continuum the continuum Thin absorption surrounded 5F 7D 7F by emission shoulders Example (d) There is finally an intermediate type already mentioned above (7H, appendix N -

9 ArasBeam 11 3% of the stars showing emission) which can be described either like a two peak emission surrounded by a shallow depression or like a central thin absorption surrounded by a strong two-peak emission The stars showing no obvious sign of emission. The BeSS database contains all stars listed as Be, meaning that they have at some point shown an emitting activity. Our method consisting in taking into account for each star, only the latest available spectrum (or one of the latest three, when the last one has not a satisfying quality), leads to establish that some 72 stars (17% of the whole lot) show no obvious sign of emission on the spectrum which has been examined. We have already observed that some absorption profiles (Voigt type) could be confused with our 5F profiles whose shoulders on both sides of the absorption line could be understood like a trace of emission. This case has however been rarely met. Finally, we have found some ten 3B profiles in which the absorption line looks like a very rounded basin (Zet Oph, Lam Eri, 69 Ori, HD24479, 19 Mon, V1040 Sco, HD208682, NW Ser, HD17505, HD190864). Our method brings to classify them as showing no obvious emission; nevertheless, we have noticed in Silaj s work that this type of profile could match a very particular set of parameters in the circumstellar disk (low base-disk density g cm-3, decreasing law R n with n 2,5). Those profiles wrongly considered as in absorption should therefore constitute an emitting type of their own Theoretical profiles having never been observed (7A, 7C, 7E, 7G, 7I) Five of our theoretical profiles, computed by a combination of gaussian curves, among those showing 7 characteristic points, have never been actually observed (see in appendix A their theoretical shapes). One can be surprised that type 7C was never met; it would be a three-peaked profile, the central peak being stronger than the side ones. Indeed, Hanuschik describes it as an extreme case of P type in which the shoulders would be so strong that they would form this triple peak. Only one star, Chi Oph, matches this description among those of his 77 stars set. The spectrum of this same star, which we have examined, did however not show this triple peak; on the contrary, the shoulders were so weak that we have classified it as type 3A. Type 7A would be a triple peak with side peaks stronger than the central one. Type 7E would also be a triple peak in which the inversions between peaks would extend below the continuum line, and type 7G would be the same situation, with a central peak less high than the side ones. Finally the 7I type would describe as an absorption line surrounded by emitting

10 12 M. Bonnement, F. Cochard & V. Desnoux shoulders with an emission not reaching the continuum in its centre. So it seems the last named four profiles do not tally any physical reality. 9. Temporary conclusions. As we have seen, we have decided for this study to classify the observed spectra on a strictly descriptive basis, leading to categories which we refused to link to any physical interpretation. It seems to us that the study could lead to the conclusion that a classification such as Hanuschik s one could be somehow extended: it covers only about half of the stars showing emission, it takes into account only one parameter (the inclination angle in respect with the line of sight), unconnected to the stars own physics. We come to think that the latter could explain the former and that the observed profiles (almost half of the whole lot) which do not match Hanuschik s classification, either because they are surrounded by a basin shaped depression or because they match a completely different description, are impacted by intrinsic physical phenomena so strong that they overwhelm the line of sight effect. Leaving aside multiple systems, showing by nature peculiar spectral types and evolutions, we have been particularly interested by the work of Silaj et al. of march 2010, presenting a set of theoretical H alpha emission line profiles, computed by a systematic variation of different parameters (inclination angle, but also spectral type and thus surface temperature, stellar disk-base density and its decreasing power law with the radius); the work clearly shows that the profile type is far from being uniquely and unambiguously determined by the line of sight angle. Moreover we find among the theoretical models created by Silaj, the types we have described at point 8.2 above, particularly those surrounded by a basin shaped depression. Would the point 8.1 Hanuschik compatible spectra be the ones for which the impact of the stars own physical parameters would be, for any reason, overwhelmed by the inclination angle effect, while in those of point 8.2 non-hanuschik the intrinsic physical parameters would override the simple geometry of Earth-star alignment? There too, one will find explanatory elements in Silaj s article. It could be also that stars with spectra perfectly matching the P, L, H, E typology, thus dominated by geometry factors unconnected with their own physics, show therefore an apparent stability in their emission characteristics, while those not matching it (or at least part of them) would be more likely to show evolutions connected with their own physics. Would the latter in particular have a stronger potential en terms of variability (or even outbursts) observation?

11 ArasBeam 13 Perhaps would they deserve a particular survey among the amateur community? From this point of view, one could imagine a systematic low resolution survey programme in which the activity of those stars would be monitored as frequently as possible on the basis of a quantitative criterion i.e. the lines equivalent width. If preliminary trials in our study have shown that the precise computation of this parameter and above all its comparability between spectra taken in different conditions of instrumentation was difficult, its low resolution measurement would nevertheless constitute a warning signal bringing to light variations justifying to trigger a particular high resolution monitoring by amateur or professional means. 10. Next steps As explained above, the present study is just a first qualitative step on a reduced field, of a further study which we would like to be more thorough (examining all spectra in BeSS and not only the latest of each star) and quantitative, i.e. consisting in measurements, for each spectrum, of parameters such as the lines equivalent width, its barycentre, its spreading (base and half-maximum widths), its maximum intensity, the spacing between double peaks, their V/R ratio, each of these parameters having a physical signification (see on this principle the study of D. Ballereau et al. in Rev. Mexicana Astro. Astrof. 15, ). The study would cover all of BeSS life extent (existing since 2003 and containing some spectra dated 1999) and thus bring to light time lapse variations, periodicities... We meet for now two difficulties to undertake this task. On the one hand, the heterogeneity of the available data (BeSS holds both amateur and professional spectra taken in extremely varied conditions of instrumentation) makes difficult to work out a systematic treatment process able to produce homogeneous measurements in a sufficient quality. On the other hand, we have a limited work force (if the present qualitative study on about 400 spectra required about two months of an amateur free time, a study implying quantitative measurements on over 4000 spectra would imply the collaboration of a real team of highly motivated and skilled amateurs, having available sturdy calibrated routines to yield reliable results). We have not yet come to this point Special thanks We wish to thank the authors of the spectra upon which this study has been based. Most of them are particularly regular and highly skilled amateur observers, among which Christian Buil, Valérie Desnoux, José Ribeiro, Thierry Garrel, José Guarro Fló (to be completed). See footnote

12 14 M. Bonnement, F. Cochard & V. Desnoux Appendix A. Profile types

13 ArasBeam 15 Tracing the reference curves (GNUPlot) # Definition of a gaussian curve gauss(x, m, s) = exp(-0.5*((x-m)/s)**2)/sqrt(2*pi*s**2) # Definition of 21 topological profile types Profil3A(x) = (1 + 3*gauss(x, 0, 0.5)) Profil3B(x) = (1-3*gauss(x, 0, 0.5)) Profil5A(x) = (1 + 2*gauss(x, 0, 1)-gauss(x, 0, 0.2)) Profil5B(x) = (1-2*gauss(x, 0, 1) + gauss(x, 0, 0.2)) Profil5C(x) = (1 + 6 * gauss(x, 0, 1)- 0.5 * gauss(x, 0, 0.2)) Profil5D(x) = (1-6 * gauss(x, 0, 1) * gauss(x, 0, 0.2)) Profil5E(x) = (1 + 6 * gauss(x, 0, 1)- 0.5 * gauss(x, 0, 0.4) * gauss(x, 0, 0.2)) Profil5F(x) = (1-6 * gauss(x, 0, 1) * gauss(x, 0, 0.4) * gauss(x, 0, 0.2)) Profil7A(x) = ( * gauss(x, 0, 1)- 10 * gauss(x, 0, 0.6) * gauss(x, 0, 0.2)) Profil7B(x) = (1-19 * gauss(x, 0, 1) + 10 * gauss(x, 0, * gauss(x, 0, 0.2)) Profil7C(x) = ( * gauss(x, 0, 1)- 7 * gauss(x, 0, 0.6) * gauss(x, 0, 0.2)) Profil7D(x) = (1-12 * gauss(x, 0, 1) + 7 * gauss(x, 0, 0.6) * gauss(x, 0, 0.2)) Profil7E(x) = ( * gauss(x, 0, 1) * gauss(x, 0, 0.6) * gauss(x, 0, 0.2)) Profil7F(x) = (1-12 * gauss(x, 0, 1) * gauss(x, 0, 0.6) * gauss(x, 0, 0.2)) Profil7G(x) = ( * gauss(x, 0, 1)- 11 * gauss(x, 0, 0.6) * gauss(x, 0, 0.2)) Profil7H(x) = (1-12 * gauss(x, 0, 1) + 11 * gauss(x, 0, 0.6) * gauss(x, 0, 0.2))

14 16 M. Bonnement, F. Cochard & V. Desnoux Profil7I(x) = ( * gauss(x, 0, 1)- 12 * gauss(x, 0, 0.6) + gauss(x, 0, 0.2)) Profil7J(x) = (1-12 * gauss(x, 0, 1) + 12 * gauss(x, 0, 0.6) - gauss(x, 0, 0.2)) Profil7K(x) = (1-3 * gauss(x, 0, 1.2) + 5 * gauss(x, 0, 0.6) * gauss(x, 0, 0.05)) Profil7L(x) = (1 + 6 * gauss(x, 0, 1)- 0.5 * gauss(x, 0, 0.4) * gauss(x, 0, 0.2) * gauss(x, 0, 0.05)) Profil9A(x) = (1-3 * gauss(x, 0, 1.2) + 5 * gauss(x, 0, 0.6) * gauss(x, 0, 0.3) * gauss(x, 0, 0.15) * gauss(x, 0, 0.05))

15 Appendix B. Type determination algorithm ArasBeam 17

16 18 M. Bonnement, F. Cochard & V. Desnoux Appendix C. Type 3A

17 ArasBeam 19

18 20 M. Bonnement, F. Cochard & V. Desnoux

19 ArasBeam 21

20 22 M. Bonnement, F. Cochard & V. Desnoux Appendix D. Type 3B

21 ArasBeam 23

22 24 M. Bonnement, F. Cochard & V. Desnoux

23 ArasBeam 25

24 26 M. Bonnement, F. Cochard & V. Desnoux

25 Appendix E. Type 5A ArasBeam 27

26 28 M. Bonnement, F. Cochard & V. Desnoux

27 Appendix F. Type 5B ArasBeam 29

28 30 M. Bonnement, F. Cochard & V. Desnoux Appendix G. Type 5C

29 ArasBeam 31

30 32 M. Bonnement, F. Cochard & V. Desnoux

31 ArasBeam 33

32 34 M. Bonnement, F. Cochard & V. Desnoux

33 ArasBeam 35

34 36 M. Bonnement, F. Cochard & V. Desnoux

35 Appendix H. Type 5D ArasBeam 37

36 38 M. Bonnement, F. Cochard & V. Desnoux Appendix I. Type 5E

37 ArasBeam 39

38 40 M. Bonnement, F. Cochard & V. Desnoux Appendix J. Type 5F

39 Appendix K. Type 7B ArasBeam 41

40 42 M. Bonnement, F. Cochard & V. Desnoux Appendix L. Type 7D

41 ArasBeam 43

42 44 M. Bonnement, F. Cochard & V. Desnoux Appendix M. Type 7F

43 Appendix N. Type 7H ArasBeam 45

44 46 M. Bonnement, F. Cochard & V. Desnoux Appendix O. Type 7J

45 ArasBeam 47

46 48 M. Bonnement, F. Cochard & V. Desnoux

47 Appendix P. Type 7K ArasBeam 49

48 50 M. Bonnement, F. Cochard & V. Desnoux Appendix Q. Type 7L

49 ArasBeam 51

50 52 M. Bonnement, F. Cochard & V. Desnoux Appendix R. Type 9A

51 Appendix S. Type NR ArasBeam 53