P Lampens

J.-L Prieur

⋆⋆ R W Argyle

J Cuypers

Relative astrometry and near-infrared differential photometry of nearby southern orbital binaries with adaptive optics ⋆

Keywords: Astrometry -Photometry -Stars, Binaries, close -Binaries, visual

We present relative astrometry and differential photometry measurements for a sample of nearby southern orbital binaries making use of the technique of Adaptive Optics. The observations were made in December 2000, with the ADONIS camera mounted at the 3.6m ESO telescope from La Silla Observatory, equipped with the broad-band near-infrared filters (J-, H-, K-passbands). Our sample contains stars which do not fit very well the empirical mean mass-luminosity relation (according to our previous study), but for which accurate parallaxes (determined by the Hipparcos satellite) and high-quality orbits were available thanks to many previous efforts. We derived accurate positions and J, H, K magnitudes of the individual components of those binaries. The individual stellar components have near-infrared colour indices well grouped in those plots and are comparable to standard single stars. The data reduction procedure used for deriving those results is described in detail. It is based on a leastsquares fit of Moffat-Lorentz profiles in direct imaging for well-resolved systems and on Fourier analysis for very close pairs.

Introduction

Binaries with significant orbital motions deserve to be observed and studied because they are essential in deriving stellar masses in a fundamental and direct way. New stellar mass determinations are still much needed to enable detailed comparisons with models of stellar structure and evolution. The required accuracy for this purpose is of the order of 1-2% at least on the individual stellar mass (Andersen, 1991). This requirement is much more difficult to meet for the visual binaries (VB's) which are on the lower part of the Main Sequence than for the eclipsing binaries (EB's) due to the much longer orbital periods and the need for high-angular resolution to resolve the closest pairs. This is why the empirical Mass-Luminosity Relation (noted hereafter as MLR) remains poorly determined for masses M less than 1 M ⊙ [START_REF] Henry | [END_REF]Henry et al., 1999;Delfosse et al., 2000 -for M ≤ 0.6 M ⊙ ; Henry 2004 -from end to end with a special emphasis for M ≤ 0.2 M ⊙ ). However, the class of visual binaries (including the "speckle" or interferometric binaries) is important for various reasons:

visual binaries have non-interacting components in general. They thus represent better the evolutionary scenario of single stars;

⋆⋆ Corresponding author: jean-louis.prieur@irap.omp.eu -they carry a lot of angular momentum and therefore represent a different fraction of the binary population than eclipsing binaries whose masses can be very accurately determined; -they are the only objects which allow calibration of the MLR in the mass range from 0.2 to 1.0 M ⊙ ; -the distributions of their dynamical characteristics (orbital elements such as the period P orb , the true semi major axis A and eccentricity e) are directly connected to the mechanisms of their formation (Halbwachs et al., 2005, Patience et al., 1998).

Often, the limiting factor in the precise determination of the stellar mass is the poor knowledge of the distance of the system. Thanks to the astrometric satellite mission Hipparcos [START_REF] Esa | The Hipparchos and Tycho Catalogues[END_REF], many of the parallax uncertainties have been reduced by a factor of 2 to 5. However, this improvement is generally not sufficient: after the Hipparcos mission, the principal error contribution on the mass determination of binary systems still comes from the error on the parallax. Indeed, according to Kepler's laws, the relative error on the total mass M of the two components is given by ε M = ε 2 a 3 /P 2 + 9 ε 2 π , where a is the semi-major axis in AU, P the period in yr, M the sum of the masses in M ⊙ , and π the parallax in arcseconds, and where ε designates a relative rms error (see for example, [START_REF] Lampens | Proc. JD 14, IAU GA XXIII[END_REF].

In an early review on the determination of stellar masses, Popper (1980) listed only 8 V B's with a relative error on the sum of masses less than 3%. Twenty years later, thanks to the improvement of the parallax determination obtained by Hipparcos, Ruymaekers (1999) listed 30 V B's with a relative error on the ratio a 3 /P 2 < 3%, while Söderhjelm (1999) reported only 10 V B's with a relative error on the sum of masses smaller than 5% (cf. his tables 1 & 2). This illustrates the difficulty for improving our knowledge on stellar masses in specific mass intervals (Xia et al. 2008 -for masses from 0.07 M ⊙ to 0.2 M ⊙ ).

But for a fully consistent picture of the system, the total mass determination is insufficient. Fractional masses as well as absolute luminosities are needed too. The relative error ε M of the component absolute luminosity M again depends (largely) on the parallax accuracy ε π , but also on the error of the component magnitude ε m according to ε M = [(5. log 10 e) ε π ] 2 + ε 2 m (where e is the base of the Napierian logarithm).

Accurate component magnitudes and colours are thus further needed to derive reliable physical properties of the components. The Hipparcos Catalogue provided for the first time a precise differential magnitude, ∆H p for many visual binaries of sub-arcsecond separation [START_REF] Esa | The Hipparchos and Tycho Catalogues[END_REF]Martin & Mignard, 1998), and the complementary Tycho Double Star Catalogue [START_REF] Fabricius | [END_REF] also gave ∆B T and ∆V T for systems with ρ > 0 ′′ .5 and ∆m < 3. Unfortunately, many nearby visual binaries were too close to be fully resolved by Hipparcos/Tycho and still lack precise component colours. Existing spectral classifications generally refer to the system as a whole: when component spectral types are reported, these usually rely on a visual estimation of the magnitude difference, with a typical error of the order of ±0.2 mag (Christy & Walker, 1969;Edwards, 1976). Therefore, the situation is such that the (rare) precise stellar masses of visual binary systems are generally attributed to components with unknown or uncertain colours.

This point is well-illustrated in the study by Delfosse et al. (2000) on M-dwarf binaries with masses accurate to within 10%. Their table 2 in which they collected basic information for 18 pairs, i.e. 3 EBs and 15 VBs, is lacking accurate magnitude differences in several cases: the flux ratios in the near-IR bands were not determined for 7 systems (3 EBs + 4 VBs), while 6 systems had spectroscopically derived magnitude differences, inferred from the relative line depths of doublelined spectra (1 EBs + 5 VBs), and 6 had large errors (0.1 mag or larger) on the visual magnitude difference ∆m V (2 EBs + 4 VBs).

The aim of the present study is to determine differential near-infrared magnitudes and colours for a sample of nearby close visual binaries from a single observation with the technique of adaptive optics (AO). This technique offers high-angular resolution and allows to derive reliable differential photometry between the components (ten Brummelaar et al. 1996;[START_REF] Roberts | Poster Proceedings on Fundamental Stellar Properties[END_REF]Roberts et al. 2005). In addition, it provides relative astrometric data useful for the computation of improved orbits.

Description of the sample

The following criteria were used for selecting the target binaries:

nearby visual binaries (i.e., located within a distance ≤ 67 pc) for which the combination of accurate Hipparcos parallaxes (for which the relative error is well below 5%) with high-quality orbits allows to derive component masses with an accuracy, ε M better than 10-15%. This latter information is based on the catalogue of orbital parameters with realistic errors computed by means of the Bootstrap technique (Ruymaekers, 1999); -with predicted angular separations between 0 ′′ .1 and 1 ′′ at epoch 2001.0 and with declination less than +10 • ; -having orbital periods from 2 to 700 yr and total masses from 0.4 to 8 M ⊙; -which do not fit well the mean empirical MLR derived from the new Hipparcos parallaxes [START_REF] Lampens | Proc. JD 14, IAU GA XXIII[END_REF] To this list we also added some 18 binaries from table 1 of Söderhjelm (1999), with orbital periods less than 29 yr and with new astrometric mass ratios but which were not always consistent with the previous determination (Martin & Mignard, 1998).

This selection led to a list of some 50 bright, close southern visual binaries. The sub-sample of the objects from this list that we could observe is presented in Table 1 and described in the next section.

Observations

The observations were performed with the ESO 3.6-m telescope of La Silla, during two nights (13-14 and 14-15 December 2000). The telescope was equipped with ADONIS ('ADaptive Optics Near Infrared System') and the Sharp II+ infrared camera.

We employed a lens scale of ∼ 0 ′′ .050/pixel (see Sect. 4) and the ESO broad-band filters J (λ c =1.253 µm, ∆λ=0.296 µm), H (λ c =1.643 µm, ∆λ=0.353 µm) and K (λ c =2.177 µm, ∆λ= 0.378 µm). Exposure times ranged from 40 ms (shutter mode) to 500 ms (normal mode). We used the standard configuration with chopping mode between star and sky in order to optimize the number of exposures per star. In this way, for each filter, the observational data consisted of four sets of 20 exposures each: 2 × 20 exposures with the target binary on quadrant 1, and 2 × 20 exposures with the target on quadrant 3. The sky level was estimated on the quadrants 2 and 4, opposite to the quadrants used for the target. In nearly half of the cases, a single reference star was observed immediately after the binary to calibrate its point-spread-function (PSF).

Some 36 close visual binaries, most of them belonging to the all-sky sample described in Sect. 2, were observed during the allocated nights. They are listed in Table 1 with basic information including various identifiers (Cols. 1, 2, and 6), Hipparcos magnitude Hp (Col. 3), spectral type (Col. 4), Hipparcos parallax (Col. 5), orbital period (Col. 6), (in years) and additional notes in Col. 8 (e.g. SB-VB: spectroscopic-visual binary). Unless specified in Col. 2, they all refer to AB couples. Among those, 11 targets were taken from table 1 from Söderhjelm (1999) and 9 are outliers from the empirical MLR with ε M < 15%. We also added a few targets needed for the astrometric calibration.

Because some of our main targets were not accessible during these nights, we completed the observations by inserting additional problematic targets though they had ε M > 15%. For example, we included HIP 7254 which is a new Hipparcos discovery and HIP 2237 for which "two orbital solutions fit the available data equally well: in the case of the higheccentricity, half-period solution a too high mass-sum is derived" (Söderhjelm, 1999). Unluckily, the latter remained unresolved.

On average the seeing was about 1-2 ′′ , but the atmospheric conditions were more stable during the first night. This explains why ADONIS performed better and faster, resulting into a higher detection rate on the first night than on the second night. We were able to resolve 17 objects of the 20 binary systems observed on Dec. 13th 2000 whereas only 11 objects of the 17 observed on Dec. 14th 2000 (see Tables 2 and3 in Sect. 5).

Data reduction

The reduction steps were performed in the following order:

-Preprocessing: bad pixel correction (darks), skysubtraction, flat-field division (using sky flats taken at twilight) were done using the excellent ESO Eclipse software package (Devillard, 1997).

-a) When the components were clearly resolved, we used a profile-fitting algorithm on each single frame. It is based on the fitting of twodimensional Moffat-Lorentz profiles (see Fig. 1 and Sect. 4.1). b) When the binaries were not well-resolved, we performed a Fourier analysis of the power spectrum of the AO images. We calibrated the transfer function of the imaging system with observations of (unresolved) PSF reference stars located within ∼5 • from the binary targets. The ratio of the corresponding power spectra exhibited fringes when two stars were detected (e.g. Fig. 2). The determination of the position angle (θ 0 ) and period (d 0 ) of those fringes then led to the astrometric parameters of the binary: ρ = n/d 0 (with n×n the size of the images), and θ = θ 0 + π/2. In this case, the position angle θ was determined with a 180 • ambiguity, which could sometimes be solved by direct inspection of the AO images. -We used the astrometric calibration from Berthier et al. (2002) based on observations of the Trapezium cluster in the nights preceding and following our observations (since too few of our calibration double stars fitted the available field). We thus adopted the scale of 0 ′′ .0496/pixel and the orientation of 269 • .609 and 179 • .619 for the X and Y axes, respectively (In Figs. 1 and2, North is to the bottom, East to the left).

Fitting procedure of Moffat profiles to long exposures

Experience has shown that the point spread function of long exposure images is generally well represented by the semi-empirical Moffat-Lorentz profile [START_REF] Moffat | [END_REF]:

I 1 (x, y) = h 1 (1 + b r 2
1 ) q where (x, y) are the Cartesian coordinates of the image, q is a real value, generally in the range [1, 2] (it is a Lorentz profile when q = 2), and r 1 is the distance of the current point (x, y) to the centre of the profile (x 1 , y 1 ). The parameter b is used to take into account the profile width. It is related to s, the full width at half maximum of the profile (FWHM or "seeing") with:

s = 2 √ 2 1/q -1 b
This profile was originally proposed by Moffat to model stellar profiles of photographic plates, to take into account the diffusion of light inside photographic emulsions. It was then widely used for many other applications and appeared to be well suited to images obtained with electronic detectors. In particular, we used this model for extracting the relative positions and differential magnitudes of CCD images of binary stars when profiles of the components overlap [START_REF] Oblak | Proc of the ESA symposium "Hipparcos-Venice 97[END_REF][START_REF] Lampens | [END_REF], Lampens et al., 2001, Strigachev & Lampens, 2004, and Lampens et al., 2007).

To obtain the differential photometry and relative astrometry measurements presented in Table 2, we have fitted the following brightness function corresponding to the sum of two Moffat two-dimensional profiles, to the ADONIS images:

I(x, y) = 2 m=1 I m (x, y) + n(x, y) with I m (x, y) = h m [1 + (b r m ) 2 ] q
where m = 1, 2 are the indices of the two stellar components. For each profile, h m is the central intensity and r m is the distance of the current point to the centre (x m , y m ) of the profile. The function n(x, y) is a two dimensional polynomial that is used to model the sky background. For our application, a first order polynomial was sufficient:

n(x, y) = n 0 + n 1 x + n 2 y + n 3 x y
For the images where the profile isophotes of many frames were not circular, we took their ellipticity into account by changing the expression of r m :

r m = (x -x m ) 2 + e (x -x m ) (y -y m ) + (1 + k) (y -y m ) 2
where e and k are two additional parameters.

The problem to be solved consists therefore in minimizing a function f (p) where the vector p belongs to R 14 . The corresponding 14 coordinates are (x m , y m , h m ) (for m = 1, 2), b, q, k, e, n 0 , n 1 , n 2 and n 3 :

f (p) = (x,y)∈A z(x, y) -I p (x, y) 2
In this expression, z(x, y) is the value of the brightness function as measured on the detector and A is the image domain within which the minimisation is performed. This method was first implemented by one of us (JC) as a procedure in the ESO/MIDAS software, using a Newton-Raphson minimisation algorithm (J. Cuypers, 1997). For this application, we also developed a new stand-alone program fit moffat.cpp, with the bound constrained LBFGS minimisation algorithm (Byrd et al, 1995). Both programs require the knowledge of the gradient vector g of f (p), whose components g i are given by:

g i = (x,y)∈A -2 z(x, y) -I p (x, y) ∂I p (x, y) ∂p i
In appendix, we provide the expression of the gradient ∂I p (x, y) ∂p i that may be useful for the readers who want to create their own fitting program.

Main results

The relative astrometric and differential near-infrared photometric measurements obtained with the method of Moffat profile fitting for 32 components of 29 binary and multiple systems are listed in , the number N of quadrants used for the astrometric measurements in Col. 4, the average relative astrometric measurements ρ all (Col. 5) , θ all (Col. 7), and their corresponding errors σ ρall (Col. 6) and σ θall (Col. 8). The subscript 'all' is added to indicate that the current measurement corresponds to the average of all the measurements obtained with the three filters J, H, and K. In the next columns we report the differential photometric measurements ∆m J , ∆m H , and ∆m K with their corresponding errors σ ∆mJ , σ ∆mH , and σ ∆mK , and the numbers of quadrants used for those photometric measurements: N J , N H , and N K , respectively. Table 3 lists the values we obtained using the method of Fourier analysis, i.e., for 8 resolved components of 6 multiple systems. For each system we indicate its HIP number in Col. 1, the component names in Col. 2, the fractional Besselian epoch of observation and the relative astrometric measurements ρ, θ and their corresponding errors σ ρ , σ θ for each filter J, H, and K. The subscript 'all' indicates that the current measurement corresponds to the average of the measurements in the different filters.

Analysis of astrometric data

The distribution of the angular separations ρ all reported in Tables 2 and3 is plotted in Fig. 3. The average rms errors for (ρ all ,θ all ) are (0 ′′ .008, 0 • .8) and (0 ′′ .010, 2 • .3) for Moffat profile fitting and Fourier analysis, respectively. In the case of Fourier analysis, the larger error on θ all is due to the difficulty of determining the direction of the fringes accurately (see Sect. 4).

We detected a new candidate binary star among our (supposed single) reference stars, HIP 19233, which was resolved in all the direct images obtained with the J H and K filters (see Table 2). This object (also known as HR 9233) is also the high proper-motion nearby star LTT 1877 (parallax 42.3 mas). This new pair has a magnitude difference close to 3 mag (in J H and K), which may explain why it was not previously resolved. Further observations are needed to confirm its nature.

The technique of Fourier analysis (see Sect. 4) allowed the measurement of angular separations close to the diffraction limit of the 3.6 m telescope (which is 0. ′′ 069 in J, i.e., λ/D). In particular, this analysis revealed the presence of possible components Ab, Ac and Ad around HIP 20087Aa that could not be measured with the Moffat profile fitting procedure. Components Ac and Ad would be newly-discovered components, located very close to the primary star, nearly at the theoretical diffraction limit (see Fig 2). Further confirmation is needed, especially for the Ad component which was only detected with the J filter. The latter could be an artifact caused by a bad estimation of the PSF (let us recall that the PSF could only be calibrated by observations of single stars before or after the observation of our targets, see Sect. 4). The existence of the Ac component is more secure since it was detected at the same location, both in H and K.

Table 4 illustrates the comparison of our relative positions with the positions computed at the given Besselian epoch (B 2000.95) for those systems which have a published orbit. For each measurement taken from Tables 2 and3, we report the HIP number in Col. 1, the component names in Col. 2, the astrometric measurements ρ all , θ all in Cols. 4 and 6, with their corresponding errors σ ρall , σ θall in Cols. 5 and 7, and the numbers of quadrants used for those measurements in Col. 3. We write the HD number in italic in Col. 1 when the measurement was taken from Table 3, else it was taken from Table 2. In Cols. 8 and 9, we report the computed positions ρ c , θ c at the epoch of observation, from the orbit whose bibliographic reference is indicated in Processing example of the image of HIP 20087 in H. The AO correction leads to integrated frames (left panel) which only show a single bright patch. When dividing the corresponding power spectrum with that of a calibration star, we obtain a "restored" power spectrum (right panel) which exhibits two systems of fringes betraying the presence of two companions 'Ab' and 'Ac' around the primary star (named 'Aa'). The inner disk that clearly appears in this power spectrum is bounded by the circle corresponding to the maximum resolution that can be reached with the 3.6-m telescope in H. The structure of the noise which is present outside of this disk also perturbs the "useful" signal inside of this disk.

Fig. 3

Distribution of the angular separations reported in Tables 2 and3 Col. 14. The corresponding residuals for ρ, θ are given in Col. 10 and 11, respectively. The position difference in Cartesian coordinates ∆Pos is indicated in arcseconds in Col. 12, and the percentual ratio ∆Pos/ρ all is displayed in Col. 13. Most of the orbits used here were taken from the "Sixth Catalog of Orbits of Visual Binary Stars" (Hartkopf et al, 2012b), but we also added some orbits computed by Ruymaekers (1999) and a few more found from in the recent literature.

The residuals in the form ρ.∆θ O-C versus ∆ρ O-C /ρ are plotted in Fig. 4. The largest residuals are noticeable for HIP 7372 AC and HIP 46404, indicating that their orbits are only preliminary. When using the criterion ∆Pos/ρ all > 13% (see Col. 13 of Table 4, two more objects appear with large residuals: HIP 20087 and HIP 27901, indicating that a revision of the orbit will also be needed in the future. In all other cases, the residuals are smaller than 13%, which is an indication that our measurements agree rather well with the adopted ephemeris. (1) new candidate binary star.

In Table 5, we report some measurements of our selected targets made by other observers. For each target, we indicate the concerned pair in Col. 2, and display our measurements ρ all , θ all ) in Cols. 3 and 4, the measurements ρ d , θ d ) from other sources in Cols. 5 and 6, and the corresponding position differences in Cols. 7, 8, 9 in polar (ρ all -ρ d , θ all -θ d ) and Cartesian coordinates (∆Pos), with the epoch of observation of those measurements in Col. 7 and their bibliographic reference in Col. 8. The mention "WDS" is used when the data come from the Washington Double Star Catalog [START_REF] Mason | The Washington Double Star Catalogue[END_REF]. Note that this comparison is meaningful only when the epoch of the other measurements is close to 2000.95, the epoch of our observations, or when the couples have a very long orbital period.

There is a fair agreement, with ∆Pos < 0.1 ′′ in general. The largest discrepancy concerns HIP 27901 (FIN 382). This is also the object having the second largest O -C residual reported in Table 4. Our new measurement of HIP 27901 appears to be inconsistent both with orbits of Cvetkovic (2008) and Hartkopf et al. (2012a). We still think that our measurements are valid and discard an identification error, because they are in close agreement with those made by Hipparcos for the epoch 1991.25 (see Table 5). The situation is not at all clear, the more that some older measurements too were discarded by Cvetkovic (2008) in his orbit computation because they were found to be incompatible with the proposed 32-yr period (e.g. the measurement from 1979). Clearly more observations are needed for this system.

The case of HIP 25037 (STT 105) is also particularly interesting since the companion had not been measured for nearly thirty years and high-angular res- olution data obtained from speckle or AO measurements were deemed necessary. Our measurement is the first direct observation made since 1971 and perfectly matches the model of a linear motion of component A. This target is thus likely to be a (close) optical pair with an apparent closest approach during the interval 1980-1990 (see Fig. 5 where we plotted the apparent motion of B relative to A). This (recti)linear motion is also compatible with the proper motion of component A measured by Hipparcos (µ α ( * ) = 5.67 mas/yr; µ δ = -29.35 mas/yr [START_REF] Esa | The Hipparchos and Tycho Catalogues[END_REF], indicating a proper motion in the direction of 169 • . It seems that the B star has no significant proper motion and was still relative to the celestial sphere in the period [1980][1981][1982][1983][1984][1985][1986][1987][1988][1989][1990].

Table 4

Comparison between observations and predicted relative positions. a : The HIP identifier is in italic font when the corresponding measurement was derived by Fourier analysis.

HIP a Cp N ρ all σρ θ all σ θ ρc θc ∆ρ (O-C) ∆θ (O-C) ∆Pos ∆Pos /ρ 0rbit ( ′′ ) ( ′′ ) ( • ) ( • ) ( ′′ ) ( • ) ( ′′ ) ( • ) ( ′′ ) (%)
Q : This symbol is used when a quadrant correction of 180 • has been applied.

Analysis of photometric measurements

Another important piece of information derived from Moffat profile fitting is the differential photometry between the two stellar components The values we obtained are reported in Table 2, in Cols. 10, 13 and 16, for the filters J, H and K, respectively, with the corresponding errors in Cols. 11, 14 and 17. As shown in Figs. 6 and7, we were able to measure large differences of magnitudes, up to 3 mag. The average rms photometric errors for σ ∆mJ , σ ∆mH , and σ ∆mK are 0.06, 0.06 and 0.07 mag, respectively.

We next made use of archived information from the 2MASS Catalogue (a survey operated by IPAC Infrared Science Archive (IRSA), Caltech/JPL) to extract to-tal magnitudes in the near-infrared passbands for the observed systems. We also searched through the bibliographic data base of SIMBAD (CDS, Strasbourg). Table 6 lists the total magnitudes in the J-, H-and K-bands with their respective errors collected in this way. The 2MASS JHK photometric system is very close to the ADONIS ESO JHK filter system we used (see Bouchet, 1991, andBessel, 2005).

In combination with the measured differential magnitudes (see Table 2), we then derived the component magnitudes from the above-mentioned data for 27 binary and multiple systems. This enabled us to also derive the component colours for most of these systems. These results are reported in Table 7 and plotted in Fig. 8. In this figure, we also plotted the average val- a : For a given identifier in italic font, the measurement was derived by Fourier analysis.

Q : This symbol is used when a quadrant correction of 180 • has been applied.

Fig. 6

Distributions of the magnitude differences between the two components ∆mJ (blue solid line), ∆mH (green dotted line) and ∆mK (red dashed line), reported in Table 2.

ues obtained on sample of about 200 standard stars by other observers at ESO (Bouchet et al. (1991). Those standard stars were apparently single stars. Some of the spectral types are indicated close to the corresponding data points.

The individual stellar components have nearinfrared colour indices rather well grouped along the line formed by the ESO standard stars. The dispersion is rather small. The only possible outlier is the B component of HIP 15382 AB (whose primary is indicated to be a K0-III star), which has an H -K index slightly smaller from the other stars of our sample. However our sample is very small which makes any conclusion on this object too premature.

Conclusion

We obtained relative astrometric and differential photometric data for a sample of nearby southern orbital binaries for which high-quality Hipparcos parallaxes and supposed well-known orbits were already available, but for which accurate component magnitudes and/or colour indices were lacking. This lack of information may explain why some of these binaries did not fit well the empirical mean mass-luminosity relation first derived with the new Hipparcos parallaxes [START_REF] Lampens | Proc. JD 14, IAU GA XXIII[END_REF]). For about 30 binary systems of the sample, we additionally derived the component magnitudes and colour indices by combining existing total J-, H-, and K-magnitudes with our measurements of differential colours in the near-infrared J-, H-, K-passbands. Among these 30 observed systems, 2). Bouchet et al., 1991) are plotted as black filled squares for main sequence stars and red filled circles for giant stars. seven targets pertain to the list of systems used by Xia & Fu (2010), though sometimes without information on the secondary component. We thus provide original data for the secondary (in casu tertiary) components of HIP 2941, HIP 7372, HIP 20087 and HIP 40167.

(J-H)1 (J-K)1 (H-K)1 (J-H)2 (J-K)2 (H-K)2 (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag
Our study took advantage of Adaptive Optics observations on a large telescope, that allowed us to derive relative astrometric and differential photometric measurements of the individual components of close binaries. We explained in detail the data reduction procedure that we used, in particular the Moffat profile fitting and the Fourier analysis. The Moffat profile method was very efficient in deriving accurate position and differential magnitude measurements. Fourier analysis was a useful complement for very close binaries, but a major problem was the difficulty to estimate accurately the PSF, since this PSF could not be calibrated simultaneously with the observations of the targets.

Based on a study of the astrometric O -C residuals, we concluded that the orbits of HIP 7372 AC and HIP 46404 as well as those of HIP 21280 and HIP 41261 will need revision in the near future. The measurement we obtained for HIP 27901 is incompatible with the recently proposed orbit(s) and some previous measurements. However, it fits well the Hipparcos data. We suggest that this system needs more follow-up data before any reliable conclusion on its orbit can be drawn. For HIP 25037 AB, we showed that component A follows a rectilinear path on the sky which is also compatible with its proper motion. The system is an optical visual double star.

Fourier analysis furthermore revealed the presence of possibly two new components around HIP 20087, both of which are very close to the diffraction limit of the telescope. We also found another possible new binary star, HIP 19233, with a large magnitude difference. Those two possible serendipitous discoveries need confirming observations. The newly presented photometric measurements show that most of the stellar components have nearinfrared colour indices comparable to those of normal (apparently single) standard stars. The results are reported in Table 8.

The function I m (x, y) can be also written as: All the gradient components computed in this appendix are reported in Table 8.

I m (
Table 8 Expression of the components of the gradient of Im(x, y), as a function of the parameters Am = 1 + (brm) 2 and Bm = 2 Im(x, y) q rm b/Am. The symbol log designates the Napierian logarithm.

  Fig. 1 Example of a Moffat-Lorentz profile fitted to the profile of the ADONIS image of calibration star HR 8658 obtained in K: raw image (a), residual image (b) and comparison of the corresponding profiles (c), with the raw image profile (solid line) and the Moffat-Lorentz profile (dashed line).

Fig. 2

 2 Fig. 2Processing example of the image of HIP 20087 in H. The AO correction leads to integrated frames (left panel) which only show a single bright patch. When dividing the corresponding power spectrum with that of a calibration star, we obtain a "restored" power spectrum (right panel) which exhibits two systems of fringes betraying the presence of two companions 'Ab' and 'Ac' around the primary star (named 'Aa'). The inner disk that clearly appears in this power spectrum is bounded by the circle corresponding to the maximum resolution that can be reached with the 3.6-m telescope in H. The structure of the noise which is present outside of this disk also perturbs the "useful" signal inside of this disk.

Fig. 4

 4 Fig. 4Illustration of the (O-C) residuals from Table4: ρ∆θ (O-C) versus ∆ρ (O-C) /ρ. The units used here are arcseconds for ρ and ∆ρO-C, and radians for ∆θO-C.

  Fig.5HIP 25037 (STT 105): relative motion of component B versus component A in the period 1980-1990. In fact A has a proper motion in the direction of 169 • , whereas B seems still relative to the celestial sphere. North is to the bottom and East to the right.

Fig. 7

 7 Fig.7Magnitude difference between the two components plotted versus their angular separation. Those parameters were obtained by fitting Moffat profiles to the AO images (see Table2).

Fig. 8

 8 Fig. 8 Near-infrared colour indices of the individual stellar components derived from Table 7. Used symbols are blue open circles for the primary components and blue open squares for the secondary components. Standard stars (fromBouchet et al., 1991) are plotted as black filled squares for main sequence stars and red filled circles for giant stars.

7

  Appendix: computation of the gradient of the Moffat profileIn this appendix, we derive the gradient of our model (see Eq. 4.1 presented in Sect. 4):I(x, y) = m=1,2 I m (x, y) + n 0 + n 1 x + n 2 y + n 3 xy with I m (x, y) = h m [1 + (b r m ) 2 ] q

  x, y) = h m exp(-q log A m ) with A m = 1+(br m ) 2It comes:∂I m (x, y) ∂h m = exp(-q log A m ) = I m (x, y) h mand:∂I m (x, y) ∂q = -(log A m ) I m (x, y) Since ∂A m (x, y)/∂b = 2 r 2 m b, it comes: ∂I m (x, y) ∂b = -q I m (x, y)This can also be written as:∂I m (x, y) ∂b = -B m r m with: B m = 2 I m (x, y) q r m b A mLet us now consider the parameters e and k that are used in the expression of r m . Since ∂A m (x, y)/∂r m = 2 r m b 2 , we deduce:∂I m (x, y) ∂e = -q I m (x, y) (2 r m b 2 ) xx m ) 2 + e (xx m )(yy m ) + (1 + k) (yy m ) 2(3) Let us differentiate with respect to e and k:2r m ∂r m = (xx m )(yy m ) ∂e + (yy m ) 2 ∂k It comes: ∂r m ∂e = (xx m )(yy m ) 2 r m and ∂r m ∂k = (yy m ) 2 2 r mWhen substituting in (1) and (2), we obtain:∂I m (x, y) ∂e = -B m b 2 r m (xx m )(yy m ) and ∂I m (x, y) ∂k = -B m b 2 r m (yy m ) 2Let us now consider the last parameters, which are x m and y m . The partial derivative of I m (x, y) relative to those variables are equal to: ∂I m (x, expression of the partial derivatives of r m relative to x m and y m , let us develop the expression (3):r 2 m = [x 2 + e x y + (1 + k) y 2 m ] -x m (2 x + e y) +x 2 m + e x m y m -y m [x e + 2y (1 + k)] +y 2 m (1 + k)(6)Let us differentiate (6) with respect to x m : 2r m ∂r m = -(2 x + e y) ∂x m + 2 x m ∂x m + e y m ∂x m It comes: ∂r m ∂x m = -2 xe y + 2 x m + e y m 2r m After substitution in (5), we finally obtain: ∂I m (x, y) ∂x m = -B m b 2 r m (-2 xe y + 2 x m + e y m ) Similarly, when differentiating the expression (6) with respect to y m , we obtain: 2r m ∂r m = -[e x + 2 y(1 + k)] ∂y m +2 y m (1 + k) ∂y m + e x m ∂y m Hence: ∂r m ∂y m = -e x -2 y (1 + k) + 2 y m (1 + k) + e x m 2 r m Let us substitute in (5): ∂I m (x, y) ∂y m = -B m b 2 r m [-e x-2 y (1+k)+2 y m (1+k)+e x m ]

  x -2 y (1 + k) +2 ym (1 + k) + e xm]

Table 2

 2

	. For each
	couple we indicate its HIP number in Col. 1, and the
	component names in Col. 2, the Besselian epoch of ob-
	servation in Col. 3 (in Besselian years, after subtraction
	from 2000)

Table 2

 2 Relative astrometry and differential photometry obtained with Moffat profile fitting. all σ θall NJ ∆mJ σ∆m J NH ∆mH σ∆m H NK ∆mK σ∆m K

	HIP	Cp	Epoch N ρ all θ (2000.) σ ρall ( ′′ ) ( ′′ ) ( • )	( • )		(mag) (mag)		(mag) (mag)		(mag) (mag)
	730	AB	.953	0.281 0.022 59.6 5.0	4	2.39 0.03	4	2.75 0.10	3	2.92 0.11
	2941	AB	.956	0.554 0.003 292.5 0.4	4	0.26 0.02	4	0.24 0.02	4	0.25 0.04
	5165	AB	.956	0.241 0.002 238.3 0.6	-	-	-	-	-	-	4	0.32 0.04
	5842	CD	.956	0.947 0.011 275.8 0.2	-	-	-	-	-	-	4	0.29 0.02
	7254	AB	.953	0.157 0.003 182.8 1.3	4	1.07 0.15	4	0.56 0.10	4	0.52 0.08
	7372	AB	.953	0.111 0.005 276.9 3.0	4	0.24 0.13	3	0.47 0.23	4	0.28 0.15
	7372	AC	.953	1.794 0.004 333.5 0.2	4	2.87 0.04	4	2.72 0.14	4	2.46 0.02
	7580	AB	.953	0.263 0.006 147.4 0.5	4	0.99 0.03	4	0.91 0.07	4	0.85 0.05
	15382	AB	.956	0.366 0.044 273.6 4.8	3	2.10 0.24	4	2.11 0.11	4	2.45 0.31
	19233 (1) AB	.953	0.415 0.016 294.3 1.1	4	2.86 0.12	4	2.85 0.07	4	2.83 0.08
	21280	AB	.956	0.170 0.003 232.4 2.1	4	1.15 0.15	4	0.68 0.02	4	0.66 0.06
	22550	AB	.953	0.210 0.003 274.1 0.5	4	0.08 0.02	4	0.10 0.02	4	0.13 0.02
	22573	AB	.953	0.206 0.005 31.6 0.3	4	0.40 0.02	4	0.29 0.03	4	0.29 0.04
	22607	AB	.953	0.527 0.005 228.8 0.2	4	1.25 0.02	4	1.12 0.02	4	1.11 0.02
	25037	AB	.956	0.177 0.006 301.7 1.3	-	-	-	4	0.67 0.09	4	0.67 0.05
	25119	AB	.953	1.225 0.002 171.4 0.2	4	1.52 0.02	4	1.12 0.03	4	1.07 0.02
	27901	AB	.953	0.177 0.004 176.2 0.8	-	-	-	4	1.10 0.17	4	1.06 0.04
	29234	AB	.953	0.178 0.003 294.1 0.7	4 -0.03 0.04	4	0.09 0.08	4	0.12 0.04
	30920	AB	.956	0.562 0.007 339.1 0.8	5	1.63 0.04	-	-	-	-	-	-
	30953	AB	.956	0.732 0.001 265.8 0.2	4	0.05 0.02	4	0.07 0.02	4	0.05 0.02
	33451	AB	.953	0.265 0.013 185.2 0.6	4	0.29 0.03	4	0.24 0.04	4	0.28 0.03
	40167	AB	.956	0.859	-	78.2	-	-	-	-	-	-	-	1	0.18	-
	40167 A,Ca	.956	6.220	-	73.2	-	-	-	-	-	-	-	1	0.56	-
	40167 A,Cb	.956	6.546	-	72.9	-	-	-	-	-	-	-	1	1.61	-
	41261	AB	.953	0.199 0.003 355.4 0.4	4	0.34 0.06	4	0.30 0.02	4	0.30 0.02
	42075	AB	.953	0.190 0.007 96.4 1.5	4	0.99 0.16	4	0.98 0.07	4	0.97 0.12
	45170 Aa,Ab	.953	0.117 0.007 296.1 3.5	4	0.26 0.28	4	0.09 0.10	4	0.03 0.03
	46404	AB	.956	0.372 0.026 153.4 0.9	4	1.30 0.04	4	1.62 0.03	4	1.71 0.12
	46454	AB	.956	0.591 0.004 86.3 0.3	4	0.64 0.02	4	0.76 0.03	4	0.84 0.02
	47479	AB	.953	0.161 0.004 71.2 0.8	4	0.10 0.03	4	0.13 0.02	4	0.13 0.02
	53840	AB	.953	0.165 0.002 285.4 0.6	4	0.18 0.04	4	0.25 0.04	4	0.30 0.02
	114576	AB	.953	0.243 0.007 113.3 0.9	4	0.23 0.02	4	0.25 0.03	4	0.18 0.01

Table 5

 5 Comparison between some of our measurements (ρ all , θ all ) made in 2000.95 and other published data (ρ d , θ d ).

	HIP a	Cp	ρ all	θ all	ρ d	θ d ρ all -ρ d θ all -θ d ∆Pos Epoch Reference
			( ′′ )	( • )	( ′′ )	( • )	( ′′ )	( • )	( ′′ )
	7254	AB	0.157 182.8	0.1 185.	0.057	-2.2 0.057 1991.25 ESA, 1997
	7254	AB	0.150 182.0	0.1 185.	0.050	-3.0 0.050 1991.25 ESA, 1997
	27901	AB	0.177 176.2 0.165 179.	0.012	-2.8 0.015 1991.25 ESA, 1997
	"	"	"	"	0.1 142.	0.077	34.2 0.110 1993.10 Hartkopf et al., 2000
	40167	AC	6.22 73.2 6.17 73.5	0.050	-0.3 0.062 2001.24 Mason et al., 2002
	40167 Ca,Cb 0.327 67.7 0.317 84.5	0.010	-16.8 0.096 2000.14 Hutchings et al., 2000
	"	"	"	"	0.338 62.1	-0.011	5.6 0.034 2001.27 Balega et al., 2006
	53840	AB	0.165 285.4	0.1 304. Q	0.065	18.7 0.077 1994.31 Hartkopf et al., 1996b

Table 7

 7 Derived infrared component magnitudes and colours.

	HIP Cp Ntot	J1	J2	H1	H2	K1	K2

www.an-journal.org

Acknowledgements

We thank the ESO staff in Chile for their technical support during the observations. This work has made use of the following data base facilities: 2MASS/IPAC Infrared Science Archive (IRSA), Caltech/JPL; SIM-BAD, CDS, Strasbourg; the Washington Double Star Catalog (WDS) maintained at the U.S. Naval Observatory; and the Catalogue of Components of Double and Multiple Stars (CCDM) (Dommanget J. & Nys O., 2002). We are very grateful to the staff of those scientific institutes. Finally, we would like to thank the referee, W.I. Hartkopf (U.S. Naval Obs.), for his useful comments.

Table

Relative astrometry obtained by Fourier analysis. In col. 6, the asterisk indicates a possible 180 • -ambiguity on θ.

HIP Cp

Epoch ρ all σ ρall θ all σ θall ρJ σρJ θJ σ θJ ρH σρH θH σ θH ρK σρK θK σ θK (2000.)


Kurt Englmeier1
email: kurtenglmeier@acm.org

Josiane Mothe2
email: josiane.mothe@irit.fr

Application-Oriented Approach

Keywords: Hate Speech Detection, Named-Entity Recognition, Social Anchor, Storyline

Introduction

Detection of cyber-aggression and hate speech is still a complex task. It requires the careful analysis of a variety of human factors in language that reach beyond the words used in hate speech itself. Here, we give an impression to what extend named-entity recognition can be used in order to identify and classify regions of aggressive utterances in statements and to discriminate them against regions of profane utterances. In general, there is an actor creating aggressive statements that address a target person (prominent person or victim of cyberbullying, etc.) or group (refugees, Jewish people, Muslims, etc.). We discuss our approach based on a collection of German tweets, mainly related to the topic "refugees". We also explain the role and importance of an analysis along the storyline of tweets and of including information about social anchors as roots of storylines. The work presented here, including the prototype used for demonstration purposes. Nevertheless, it demonstrates the potential of named-entity recognition for hate speech detection. All in all, we see our approach as useful complement for partof-speech-or ontology-based strategies.

2

The Problem

Today, applied hate speech detection mainly relies on key word analysis. In fact, there are many comments that use outright and clearly visible offensive terms: "Ich bin dafür, dass wir die Gaskammern wieder öffnen und die ganze Brut da reinstecken. (I am in favor of opening the gas chambers again and putting the whole brood in there)." These and similar statements can be located easily in an automatic way. There are clear key words indicating offensive and inciting statements. The correct classification of this statement as hate speech is unquestionable, even if we consider it in isolation. However, hate speech detection is more than just keyword spotting. The features to discover are manifold (type of language, sentiment, actor and target detection, and so on). Hate speech detection must also catch up with the specifics of the language applied in hate speech and the dynamic changes in our everyday language. The evolution of social phenomena and of our language makes it difficult to track all racial, abusive, sexual, and religious insults. The language used in social media also has its own style. Many authors-in particular when emotionally agitated-don't care or cannot care about correct spelling or punctuation. They use sometimes strange abbreviations or deliberately incorrect spelling to express their emotions or (much like in spam mails) to try to cheat automatic hate speech detection. Apart from the (sometimes) poor writing style, tweets also use references to background knowledge that needs to be taken into account in hate speech analysis.

The specifics of hate language start with these syntactic qualities that differ from regular texts such as in newspapers or books. Only in rare cases, the authors use outright offensive expressions. Sometimes, they try to "hide" their opinions and intentions by less obviously offensive terms. In many cases, offensive terms clearly address facets of events or phenomena, such as the holocaust for example, to indicate the author's intention. Words, appearing innocuous in the first place, may reveal a clear act to stir up hate or to incite criminal acts after a closer look.

Our Approach

With our collection of tweets, we made the experience that • outright offensive terms are much less used than we expected,

• tweets can only partly be classified in isolation, and • we have to consider the complete storyline a tweet is embedded in. We analyze storylines that started with a particular news trailing a series of comments reflecting opinions and opposing viewpoints. Only by viewing the whole storyline we are in the position to identify "toxic" words or expressions that look profane in the first place, but may refer to a context that emblematizes an aggressive or offensive act. Sadly, many such contexts reflect practices or methods of the Nazi regime.

Kaggle's Toxic Comment Classification Challenge differentiates six categories of toxicity that can be detected in hate speech: toxic, severe toxic, obscene, insult, identity hate and threat). The categories are not mutually exclusive. We add a further important category: inciting. Statements that incite others or intend to incite others to do a criminal act or to further propagate hate are among the most dangerous utterances in hate speech.

Named-entity recognition usually addresses the problem of extracting and classifying proper names in texts, such as names of people, organizations, or locations. In this context, an entity is an individual person, place, or thing in the world, while a mention is a phrase of text that refers to an entity using a proper name.

In the context of hate speech detection, named-entity recognition at first includes also extracting and classifying proper names of persons that are authors or targets of offense or aggression or names of locations that are focal points of hate inducing events. However, it also has to locate outright or disguised expressions of hate and offense.

In this paper, we concentrate on this aspect of named-entity recognition: We locate toxic terms and investigate their surroundings, their mentions, and classify them. In such a situation, terms like "train" or "stock car" may become toxic! Both words are not offensive in the first place. However, a mention like "We need again long trains for these refugees!" clearly refers to the trains that brought prisoners of all sorts to the concentration camps during the Nazi regime. The same holds for a phrase such as "Are there any stock cars left?" with the mentioning of refugees or supporters of refugees further up the storyline. In both cases, the mentions refer to the trains of extermination and propose the same fate for the target persons which the passengers of those trains met. Both words turn from "toxic" into "threat" or even "inciting" when considering their immediate surrounding and preceding storyline.

A toxic term or a set of toxic terms indicates the potential existence of a mention containing an offensive or aggressive act. However, here we have to be careful. Any sort of close negation can turn this potential into its contrary: "You are a fool!" (insult) vs. "I'm not such a fool and believe this story!" (profane). This is in particular the case in storylines that cover views and opposing viewpoints.

Related Work

Correctly detecting hate speech and discriminating it from humor or simply profane expressions is still a challenging task. Current approaches apply the full range of method established in text analysis, such as part-of-speech (POS), N-grams, dictionaries or bag-of-words (BOW), TF-IDF, sentiment detection, or ontology-based strategies.

In social media, humans use combinations of words, symbols (smiles etc.), and words that do not even exist in dictionaries. It is thus indispensable to learn significant expressions directly from the tweets. We incline our approach to the analysis of word N-grams [START_REF] Ying | Detecting offensive language in social media to protect adolescent online safety[END_REF], key-phrases [START_REF] Mothe | Automatic Keyphrase Extraction Using Graph-based Methods[END_REF], and linguistic features [START_REF] Xu | Learning from bullying traces in social media[END_REF][START_REF] Bollegala | ClassiNet-Predicting Missing Features for Short-Text Classification[END_REF]. Many aggressive or offensive comments or posts originate from a certain event detailed in the news or in newspaper articles. Sometimes these comments are statements directly following a news. We may consider this news as anchor texts. In information retrieval-in particular when analysis targets social media-, anchor texts are used as query replacements or query enhancements when authors refer to these texts by hashtags or links [START_REF] Anh | The role of anchor text in clueweb09 retrieval[END_REF][START_REF] Eiron | Analysis of anchor text for web search[END_REF]. In contrast to traditional media that simply broadcast news, content in social media takes much more the form of a conversation or discourse. Lee and Croft [START_REF] Lee | Incorporating social anchors for ad hoc retrieval[END_REF] expand concept of anchor text further and consider texts that initiate conversation or discourse as social anchors. We believe that taking into account social anchors is indispensable for a correct interpretation of comments.

Example: "author_of_the_tweet: #kandel 8,5 Jahre Jugendstrafe für einen MORD! Wofür gab es die 1,5 Jahre Rabatt??? Ich kann gar nicht soviel fressen, wie ich kotzen möchte (#kandel 8.5 years of young custody for MURDER! What is the 1.5-year discount for??? I can't eat as much as I want to puke."

In this case, we consider "Kandel" as a social anchor. This includes first of all the anchor text, which can be one or even more news about the event and reports that follow up. A social anchor references a social phenomenon or event that is usually broadcasted by the news. In social media, there are one or more hashtags referring to discourses following this anchor event.

We take "Kandel" as the title of a social anchor that can be summarized, for example, by the key words (extracted from an anchor text) "event: fatal stabbing", "victim: German girl", "culprit: asylum seeker, refugee, charged with murder, jail: 8.5 years", "December 27, 2017", "Kandel, Germany". To achieve this summary, we may simply apply key word identification using TF/IDF or more sophisticated approaches for feature selection [START_REF] Guyon | An introduction to variable and feature selection[END_REF]. The example also shows that we probably have to collect more things than just key words. Much like in ontologies, there are qualities that further specify key items of the text.

A broad range of tweets in our collection indicate that we probably need a broader concept of social anchor. In particular far-right populists often refer indirectly to the cruelties of the Nazis, mainly things and acts related to the murdering in concentration camps. Therefore, words like "gas", "oven", "furnace", "freight train", "chimney", etc. are potentially toxic. Therefore, we need to treat the facets of the Nazi barbarism also as social anchors.

Feature Detection in Storylines

In the end, we want to identify actor, intent, target, and intensity (or polarity) in hate speech utterances: "I really disgust these people". By analyzing the sequence of utterances, we can link "people" with "refugees" if they are mentioned in close context beforehand. Surface features help to indicate the intent of the statement, too. It also helps to detect special stereotypes like (superiority of an actor or actor group) or the type of language (othering or discriminating language, e.g.).

We propose a supervised learning approach to identify the hate speech-related features [START_REF] Chatzakou | Detecting Cyberbulling and Cyberaggression in Social Media[END_REF]. The ultimate goal is the design of a hate speech detection based on a multilayered feature extraction and learning algorithm.

We start with bags of words containing names of persons (including synonyms) and locations. We are aware that there are promising approaches to automatically identify names of persons and locations in texts using conditional random fields, for instance [START_REF] Sutton | An Introduction to Conditional Random Fields[END_REF]. Here, we collect relevant names manually. Further bags of words contain toxic and severe toxic expressions and words indicating negation. Severe toxic words usually stand for insults like "fool", "scumbag", "idiot" and the like. The most interesting bag of words is the one containing words or expressions that reflect obscene or inciting statements or indicate identity hate or threat. It also contains profane expressions that specify otherwise toxic words as expressions of obscenity, inciting, identity hate, or threat. Words like "fire" or "gas", for instance, are considered toxic. Combined with "send to" or "into" the whole expression becomes aggressive and inciting when referring to a target person or group.

Much like many established approaches for hate speech detection we propose a learning process consisting of the following layers:

1. Cleansing obfuscated expressions, misspellings, typos and abbreviations. 2. Identification of toxic words or expressions (including word n-grams and key phrases) in the tweets along the storylines. Investigation of the proximity of these expressions to further specify the toxicity of these expressions. The obtained words can be new ones or synonym expressions. 3. Add suitable candidate words to existing bags of words.

The first step-the cleansing process-addresses toxic words that are intentionally or unintentionally misspelled or strangely abbreviated:

• "@ss", "sh1t", "glch 1ns feu er d@mit", correct spelling: "gleich ins Feuer damit": "[throw him/her/them] immediately into the fire". • "Wie lange darf der Dr*** hier noch morden?": "How long may this sc*** still murder? "Dr***" stands for "Drecksack (scumbag)". • "… die kuropten Politiker die ieben in saus und braus.", correct spelling: "… die korrupten Politiker, die leben in Saus und Braus": "… the corrupt politicians, they live in clover".

We recommend to apply distance metrics or character pattern recognition in this situation and to tag these expressions as named entities in order to achieve transparent forms of obfuscated, misspelled, or abbreviated terms. The example of figure 1 shows a schema that addresses a target ("politicians"), one toxic expression ("corrupt politicians") and one outright threat ("into the fire"). From the style of the tweet, we probably assume that the toxic expression-as a general statement about politicians-is an insult. However, this is hard to determine in an automatic way without further information. In a country with a high level of corruption this statement even might be true. The close proximity of the toxic expression to the threat, that is, with only (presumably) profane expressions in between, clearly indicates an overall statement to incite somebody to do severe harm to politicians. Thus, we can conclude that the tweet has the character of being inciting. This conclusion can be achieved by the system in an automatic way. This schema works also for similar mentions when different targets addressed like a religious group, a minority, or a prominent person in conjunction with a threat. The threat in the example is to throw somebody (indicated by "damit") into the fire. The system will also indicate instances of similar patterns as "inciting" that mention different threats like "[send them] to the furnace".

The tweet of figure 1 can be classified as hate speech even without consideration of the preceding storyline the tweet is part of. However, there are cases when we need background information. Imagine the statement "send them by freight train to …" instead of "into the fire". "Freight train" in the context of hate speech has always a connotation with the holocaust. The cruelties of the Nazi regime provide important background information, we have to take into account in hate speech analysis. Sadly, each facet of these cruelties can be a social anchor, too. With figure 2 we come back to our example of a social anchor "Kandel" as outlined above. The reference to this anchor with all its characteristics (facts) is important to correctly analyze this tweet. The anchor provides information on the crime of a refugee that sparked an intense social dispute the tweet is referring to. One mention of the tweet indicates a clear negative opinion. The close proximity to the fact (conviction) indicates the author's repudiation of the conviction. Multiple question marks are often used to express an opposite opinion to the fact rendered in the related phrase. Therefore, the system marks the expression as toxic.

However, for the system there are also limits: The tweet expresses a strong opposition against the court decision. The vulgar phrase indicates that, but also the sentence with the three question marks. In absence of the negative opinion, the question marks are the only weak signal pointing to the author's dismissive attitude. Of course, the term "discount" ("Rabatt") in the context of a judgment also reveals the author's objection. From the information we have so far, we cannot automatically infer any negative connotation of the word "discount".

Conclusion

In this paper, we gave an impression to what extend named-entity recognition can support automatic classification of hate speech in social media. The examples of offensive statements discussed here are quite typical for the ones we found in our collection of tweets. They also demonstrate that is hard to interpret and classify statements in the absence of social anchors. Even a storyline of a single author is often rooted in one or more social anchors. As long as we can retrieve sufficient information about these anchors, we are in the position to automatically and correctly detect semantic relationships that essentially support our classification process. From a particular author's storyline as series of her or his tweets we can deduce information on her or his However, there are limits. Many, probably important, utterances pass unnoticed the automatic process of hate speech detection if automatic hate speech detection systems lack the necessary context information. However, by indicating toxic terms or expressions we can support humans that fight against hate speech in social media. We can give them weak signals that point to offensive and aggressive language and make their work more efficient.

Fig. 1 .

 1 Fig. 1. Cleansing and tagging of a single tweet containing misspellings and toxic and inciting expressions as discussed in the example above.

Fig. 2 .

 2 Fig. 2. Example of the analysis of a tweet with reference to the social anchor "Kandel".