Shrinking or expanding the size of the ROI also changes the height of the peak, while preserving a “bump”-like spectrum that rises steeply at low energies and peaks around ∼ 2 GeV. In general, larger ROIs give rise to lower normalizations for the signal. This effect appears to be driven by a higher normalization of the diffuse back- ground model for larger ROIs; when the fit is confined to the inner Galaxy, the diffuse model prefers a lower coef- ficient than when fitted over the full sky, suggesting that the Pass 6 model has a tendency to overpredict the data in this region. This may also explain why larger ROIs prefer a somewhat steeper slope for the profile (higher γ); subtracting a larger background will lead to a greater relative decrease inthe signal at large radii, where it is fainter. We also find evidence for substantial oversub- traction of the Galactic plane in larger ROIs, consistent with this hypothesis, as we will discuss in Appendix A 3. In Fig. 20, we show the regions of the dark matter mass-annihilation cross section plane favored by our fit, for several choices of the ROI (for annihilations to b¯ b and an inner slope of 1.18). The degree of variation shown in this figure provides a measure of the systematic un- certainties involved in this determination; we see that the cross section is always very close to the thermal relic value, but the best-fit mass can shift substantially (from ∼ 35 − 60 GeV). As previously, the contours are based on statistical errors only.
The ISM evolution is determined by the complex interplay between the magneto-hydrodynamics laws, which describe how the gas flows inthe galaxy, gravity and self-gravity, which contribute to shaping and compressing the gas at all scales, as well as a number of processes related to stellar evolution, like the propagation of supernova shock waves, the gas heating by photoelec- tric e ffect on dust grains or gas ionization by stellar ultra-violet (UV) flux. The ISM represents a significant portion of the mass of theMilkyway, equivalent to around 10 to 15% of the to- tal stellar mass. This is known to be the matter from which stars form as explained in detail, for example, by McKee & Ostriker ( 2007 ), Kennicutt & Evans ( 2012 ), and references therein, and described briefly here. From the proportions reported above, it is visible that the MW has already converted most of its gas into stars. Under the combined e ffects of dynamics and grav- ity the interstellar medium will contract hierarchically creating dense clouds. At some point they will become optically thick and their inside will get cooler by preventing the ambient UV light from stars to penetrate the cloud deeply. The low temperatures enable a complex chem- istry catalyzed by dust grains that allows the creation of larger molecules and lets dust grain themselves grow in size, which changes the optical properties of the densest structures. The definition threshold of a dense cloud is a tricky question that is often solved using a certain amount of CO emission or by the dust reddening amount that is much higher in dense clouds. If the cloud is massive enough so that gravity is stronger than the gas support (kinetic energy, turbulence, magnetic field), it will collapse gravitationally, starting the formation of a protostar. It ultimately leads to the formation of a star that is supported by nuclear fusion in its core, i.e. a main-sequence star. The steps of star-formation, from the gravitational collapse to the main- sequence star are described where they are useful in Section 3.1 .
Abstract. Motivated by the strong evidence that the state
of the northern hemisphere vortex in boreal winter influ- ences tropospheric variability, teleconnection patterns over theNorth Atlantic are defined separately for winter episodes wherethe zonal wind at 50 hPa and 65 ◦ N is above or below the critical velocity for vertical propagation of zonal plane- tary wave 1. We argue that the teleconnection structure inthe middle and upper troposphere differs considerably between the two regimes of thepolar vortex, while this is not the case at sea level. If thepolar vortex is strong, there exists one meridional dipole structure of geopotential height inthe up- per and middle troposphere, which is situated inthe central North Atlantic. If thepolar vortex is weak, there exist two such dipoles, one over the western and one over the eastern North Atlantic. Storm tracks (and precipitation related with these) are determined by mid and upper tropospheric condi- tions and we find significant differences of these parameters between the stratospheric regimes. For the strong polar vor- tex regime, in case of a negative upper tropospheric “NAO” index we find a blocking height situation over the Northeast Atlantic and the strongest storm track of all. It is reaching far north into the Arctic Ocean and has a secondary maximum over the Denmark Strait. Such storm track is not found in composites based on a classic NAO defined by surface pres- sure differences between the Icelandic Low and the Azores High. Our results suggest that it is important to include the state of thepolar vortex strength in any study of the variabil- ity over theNorth Atlantic.
inthe surrounding IceCube strings causally connected with that point. This filter reduces the passing event rate by nearly a factor of 10.
The event sample is further reduced by requiring a mini- mum number of eight hits inthe event distributed in at least four strings. This ensures that the remaining events can be well reconstructed. The events are then processed through a series of reconstructions aimed at determining their type (cas- cade or track), arrival direction and energy. In a first stage, two first-guess reconstructions are applied; fits for a track hypoth- esis and for a cascade hypothesis are performed in order to obtain a quick characterization of the events and perform a first event selection. These fits are based on the position and time of the hits inthe detector, but do not include information about the optical properties of the ice, in order to speed up the computation. The track hypothesis performs a χ 2 fit of a straight line to the hit pattern of the event, returning a vertex and a velocity [ 35 ]. The cascade hypothesis is based on deter- mining the amplitude-weighted centre of gravity of the hits inthe event and its associated time. The algorithm calculates the three principal axes of the ellipsoid spanned by the spacial distribution of hits, and the longest principal axis is selected to determine the generic direction of the event. Since the spe- cific incoming direction along the selected axis is ambiguous, the hit times are projected onto this axis, from latest to earli- est, to characterize the time-development of the track so that it points towards wherethe incident particle originated. The tensor of inertia reconstruction is generally only suitable as a first guess of the direction for track-like events, since for cascade-like events the three principal axes of the ellipsoid will be close to equal in size. This property, however, can be used to discriminate between tracks and cascades. Addi- tionally, a series of cuts based on variables derived from the geometrical distribution of hits, as well as from information
inner halo (e.g. Haywood et al. 2018 ; Fernández-Alvar et al. 2019 ;
Belokurov et al. 2020 ).
In that respect, retrograde stars intheMilkyWay hold a key place in our understanding of the assembly history of our Galaxy because there is no clear mechanism that could form them exclu- sively in situ. Counter-rotating stars inthe halo have been dis- cussed since Majewski ( 1992 ), Carney et al. ( 1996 ), Carollo et al. ( 2007 ), Nissen & Schuster ( 2010 ), Majewski et al. ( 2012 ). In particular, Majewski ( 1992 ) identified, via an investigation of proper motions and a multi-colour analysis of a sample of few hundred stars towards thenorth Galactic pole, a retrograde rota- tion among stars reaching 5 kpc from the plane. Majewski ( 1992 ) reports that they exhibit no radial metallicity gradient, while also stating that this population may be younger, on average, than the dynamically hot metal-poor stars that are closer to the plane. This result was later confirmed by Carney et al. ( 1996 ) using a kinematically biased sample of 1500 stars and by Carollo et al.
s ¼ sL j s2L j; ð2Þ
and where s L and s 2L are the slopes of baselines of length L
and 2L, respectively, centered at the point of interest. The slope of each baseline is defined as the slope of the line connecting the two baseline endpoints (Figure 4). For this study, we explored slopes for which L was 0.8, 3.2, or 5.6 km (i.e., 2L was 1.6, 6.4, or 11.2 km). Subtracting the longer- baseline slope from the shorter-baseline slope inthe expres- sion for differential slope in equation (2) tends to remove the influence of large-scale topographic trends, and calculating the differential slope over several length scales permits an exploration of roughness versus horizontal wavelength. The absolute value operator is applied to the slope difference in equation (2) because a negative differential slope and a pos- itive equivalent contribute similar information to the char- acterization and comparison of surface roughness on crater floors. We have taken the roughness for a particular crater floor to be the median value of all the differential slopes for that floor.
For Galactocentric distances greater than 8 kpc, the metal- licity gradient flattens as one moves further from the plane, regardless of whether we correct for the zero-point o ffset on the parallaxes (see also Tables A.1 and A.2 ). For the distances derived without the zero-point correction, the metallicity gradi- ent eventually reverts from a negative one to a slightly positive one at distances wherethe thick disc dominates (i.e. |Z| > 2 kpc). This result, first reported in Boeche et al. ( 2013 ) using RAVE- DR4 data ( Kordopatis et al. 2013a ), is not due to small num- ber statistics (as approximately 5 · 10 4 targets are still available at those distances) nor to the non-homogeneity of the consid- ered samples, as the metallicity gradient can also be measured when using LAMOST, APOGEE, RAVE-DR5, and GALAH separately (see top-left panel of Fig. 7 ). The inversion of the gra- dient (or the flattening) can be interpreted as a thick disc that is more centrally concentrated and more metal-poor than the thin disc combined with a thin disc that exhibits a flare at large radii. This result has also been suggested in studies in which the discs have been defined chemically ([α/Fe]-high population for the thick disc and [α/Fe]-low population for the thin disc), such as in Bensby et al. ( 2011 ), Hayden et al. ( 2015 ), Kordopatis et al.
The enhanced UV darkness inthe images presented here inside the auroral oval compared to outside sug- gests much of the newly formed material travels poleward at the higher altitudes, 900 –1,400 km above the 1 bar level, wherethe aurora occurs (Gérard et al., 2009, their Figure 3) at pressures of 1 –0.01 microbars. This poleward transport is supported by Global Circulation Modeling studies (Müller ‐Wodarg et al., 2006, 2012) that ﬁnds both poleward and equatorward meridional transport away from auroral latitudes at auroral altitudes. These models also ﬁnd vertical upwelling at the auroral latitudes and downwelling near the pole, tending to move the newly forming haze particles down inside the auroral ovals. The hexagon's jet may act as a barrier to equatorward transport of polar aerosols, leading to different haze particle populations at tropo- spheric levels inside and outside of the jet (Sanz ‐Requena et al., 2018). Cassini ISS images at 935 nm taken with polarizers also show structural differences inside and outside of the hexagon (West et al., 2015). The range of pressures sensed by the UVIS images (Figure 6d) is estimated by calculating the pressure level of the vertical one ‐way optical depth one level for Rayleigh scattering in Saturn's hydrogen and helium polar atmosphere which occurs at ~30 mbar at 180 nm (using cross sections from Chan and Dalgarno (1965) and Ford and Browne (1973), and pressure values adapted from Pryor (1989)). Slant path effects reduce this pres- sure: in Saturn's northpolar region, the Sun is always low inthe sky, making the typical slant scattering opti- cal depth one level closer to ~10 –20 mbar. Even a black object would be much less visible seen through
Proper motion studies of satellite systems, such as the glob- ular clusters and dwarf galaxies of theMilkyWay, have a long history, starting from the use of photographic plates that were sometimes taken with a time baseline longer than 100 years (see Meylan & Heggie 1997 and van Leeuwen et al. 2000 for interesting and thorough historical reviews on the determina- tion of PM of stars in globular clusters). More recently, the space missions H IPPARCOS and the Hubble Space Telescope (HST), and of course the Gaia mission in its first data release ( Gaia Collaboration 2016 ), have demonstrated the enormous power of space-based astrometry. H IPPARCOS data ( Perryman et al. 1997 ) have been used for many purposes, and in partic- ular, for studying the dynamics of nearby open clusters (e.g. van Leeuwen 1999 , 2009 ), and although H IPPARCOS did not observe stars in globular clusters, it provided an absolute ref- erence frame that was used to derive the orbits of 15 globular clusters from photographic plates, for example ( Odenkirchen et al. 1997 ). On the other hand, the HST has carried out several large (legacy) surveys (e.g. Soto et al. 2017 ) that have allowed studies of the dynamics of globular clusters and of theMilkyWay satellites, and it has even constrained the motions of our largest neighbouring galaxy M31 ( Sohn et al. 2012 ). In all these cases, relative astrometry is done using background quasars and distant galaxies to define a reference frame, and typically, a time baseline of 5–10 yr is used. This has been a highly successful approach, and has, for example, allowed researchers to develop the idea that the Magellanic Clouds may be on their first infall ( Kallivayalil et al. 2006b ; Besla et al. 2007 ), to place constraints on the mass of theMilkyWay from its most distant satellite Leo I ( Boylan-Kolchin et al. 2013 ), and also to argue in support of the conjecture that dwarf galaxy satellites may lie on a vast polar plane based on the first constraints on their orbits ( Pawlowski & Kroupa 2013 ).
Due to the low Earth orbit, the duration of the Swift observations are about 1 ks, which is short compared to the flare observed durations (from some hundred of seconds to more than 10 ks). I test the effect of this short exposure on the detection probability of the flares with the Bayesian blocks algorithm. I first simulate two non- flaring event lists with a typical exposure of 1 ks and a Poisson flux with a non-flaring level of 0.027 counts s −1 inthe 2–10 keV energy range. I then simulate a third event list with a Gaussian flare above this non-flaring level using for the sampling 30 mean count rates from 0.035 to 0.1 counts s −1 and 30 durations from 300 s to 10 ks in logarithmic scale. I finally extract a time range of 1 ks from different part of the simulated flare (the center of the time range is defined to divide the flare duration in ten time ranges) to create a typical Swift event list of a flare. I apply the Bayesian block algorithm on the three concatenated event lists (non-flaring, flaring and non-flaring) and compute how many times the algorithm found two change points. The flares mean count rates are converted to mean unabsorbed fluxes using the averaged conversion factor between the mean count-rates and mean unabsorbed-flux inthe 2–10 keV energy band of 293.5 × 10 −12 erg s −1 cm −2 /count s −1 computed for N H = 14.3 × 10 22 cm −2 and Γ = 2. The resulting detection probability, shown inthe left panel of Fig. 6.2 , has two different regimes with a small mean-unabsorbed-flux range wherethe detection probability jumps from 20% to 100%. For flare durations longer than 800 s, the X-ray flares are either nearly undetected (detection probability lower than 20%) or always detected with a mean unabsorbed flux limit of about 0.044 counts s −1 (corresponding to 13.2 × 10 −12 erg s −1 cm −2 ). For flare durations shorter than 800 s, the flare detection efficiency decreases with the decay of the flare duration with a 100% detection probability at 0.044 counts s −1 for a flare duration of 800 s and 0.065 counts s −1 for a flare duration of 300 s. The Bayesian blocks algorithm is thus less efficient for observations with exposures shorter than the flare duration and detects only flares with a mean unabsorbed flux larger than 13.2 × 10 −12 erg s −1 cm −2 when the flare duration is larger than the observation exposure. Therefore, I use the GTI-binned method of Degenaar et al. ( 2013 ) which is optimized to detect the X-ray flares for the Swift observing setup.
Some objections can be pointed out here: long integration time, star creation in an interarm or spur, and the Local Arm not being a long density wave arm. At optical wavelengths, there are almost no open star clusters younger than 5 Myr (Dias & L´epine 2005 ); hence, the backward integration time must use older star clusters that may have diverged from the pure circular orbit, thus increasing the final position errors. Radio masers are much younger (<1 Myr). A typical lifetime of an O5.3 III star is only 3 Myr (Weidner & Vink 2010 ). Using longer time-scale only adds to the error bars when integrating backward along an orbit. Their use of young open star clusters employs stars already above 10 Myr, up to 50 Myr, and thus quite scattered away from their birthplaces (see fig. 2 in Dias & L´epine 2005 for stellar ages above 30 Myr). The critical value for the young cluster age is model dependent; different models can be found to get the cluster ages, such as the adopted theoretical isochrones fitting to the photometric data, the adopted reddening, and the adopted spectral type of the stars.
We present the chemical distribution of theMilkyWay, based on 2900 deg 2 of u-band photometry taken as part of the Canada–France Imaging Survey. When complete, this survey will cover 10,000 deg 2 of the northern sky. By combing the CFHT u-band photometry together with Sloan Digital Sky Survey and Pan-STARRS g r , , and i, we demonstrate that we are able to reliably measure the metallicities of individual stars to ∼0.2dex, and hence additionally obtain good photometric distance estimates. This survey thus permits the measurement of metallicities and distances of the dominant main-sequence (MS) population out to approximately 30 kpc, and provides a much higher number of stars at large extraplanar distances than have been available from previous surveys. We develop a non-parametric distance–metallicity decomposition algorithm and apply it to the sky at 30 < ∣ ∣ b < 70 and to theNorth Galactic Cap. We ﬁnd that the metallicity–distance distribution is well-represented by three populations whose metallicity distributions do not vary signiﬁcantly with vertical height above the disk. As traced in MS stars, the stellar halo component shows a vertical density proﬁle that is close to exponential, with a scale height of around 3 kpc. This may indicate that the inner halo was formed partly from disk stars ejected in an ancient minor merger. Key words: galaxies: formation – Galaxy: halo – Galaxy: stellar content – Galaxy: structure – surveys
Zoccali et al. 2017 ). At variance, inthe GC region the MR /MP number ratio significantly increases up to a value of about 3.6, indicating a dominance of the MR component. Figure 5 shows the map of the MR /MP number ratio inthe innermost bulge region while in Table 3 we list the fraction of MR /MP stars for each field. For comparison we also show the ratio of MR to MP stars from Zoccali et al. ( 2018 ) based on the GIBS data (see their Table 1) but confined to |b| ≤ 3 ◦ . The distribution is rather flat, with values ranging between 0.8 and 1.2 with a spike inthe GC region. In Fig. 5 , we superimpose the stellar mass dis- tribution of the nuclear disk from Launhardt et al. ( 2002 ) where our metallicity peak corresponds with the concentration of the mass within the nuclear disk /NSC. Subsequent studies all con- firm the extreme concentration of stellar mass inthe nuclear disk and the NSC (e.g., Fritz et al. 2016 ). Interestingly enough, the individual samples and the merged ones (i.e., FK17 +R17 inthe GC region, N18 +Za19+Zo17 inthe b = ±1 and b = ±2 fields, and N18 +Za19 inthe b = ±3 field) show similar MR/MP number ratios, despite their different spectral resolution, line diagnostics, and statistical significance. This suggests that the merged samples, meaning those with the highest statistical significance, can be safely used to trace possible metallicity vari- ations. Our finding that di fferent spectral resolution and line diagnostics provide similar results is not surprising, given that we are simply considering two broad metallicity categories (i.e., MR and MP).
2.2. A Survey of the Properties of M-dwarfs 11 Despite their extreme faintness (10 −2 −10 −5 L
⊙ ) in V bandpass, M-dwarfs yield spectroscopic
features which can still provide us with information about basic atmospheric properties such as luminosity, metallicity and temperature. For example i) The CaOH bands around 0.54-0.556 µm in dwarfs later than M3 are a very good temperature indicator and a good discriminant between M-dwarfs and backgrounds red giant stars (Gizis 1997; Reid & Gizis 2005; Martin et al. 1996). ii) An atomic spectral feature such as that of Ca I (6162 Å) can possibly be used to distinguish subdwarfs from dwarfs. iii) Hydride bands such as those of CaH at 6380 Å and 6880 Å decreases in strength with decreasing temperature, whereas the NaI doublet at 8183 Å and 8195 Å is relatively strong for earlier type M-dwarfs but relatively weaker for later type. iv) The KI doublet at 7665 Å and 7699 Å is very strong and is useful for making gravity determination. v) The saturation of the TiO band strength in M-dwarfs later than M5 and the introduction of the VO to TiO band strength index is now used to classify M-dwarfs and substellar candidates later than M5 (Henry et al. 1994; Kirkpatrick et al. 1995; Martin et al. 1996). Figure 2.2 shows the optical to red SED of M-dwarfs from M0 to M9.5, observed at Siding Spring Observatory (SSO) at a spectral resolution of 1.4 Å (Rajpurohit et al. 2013). Molecular band spectra are much more complex than atomic spectra and dominate the spectral regions in which they are located. TiO has an especially distributed and complex spectrum and it dominates M dwarf spectra inthe spectral regions traditionally used to determine the chemical compositions of solar-type stars. This can be seen in fig. 2.2, wherethe M dwarf spectra show a significant deviation, primarily due to TiO absorption, from the predominantly smooth continuum spectra of earlier type stars.
What we are likely seeing isthe mixing of two stellar pop- ulations coming from different locations: the high-[Mg/Fe] se- quence, which formed inthe inner Galaxy where star formation rates were significantly higher than the low-[Mg /Fe] sequence, which formed stars at much lower rates and had a more gradual build up of metallicity. Stars belonging to the high-[Mg /Fe] se- quence are observed inthe solar neighborhood via radial mixing, wherein the older stars are primarily blurred to the solar cylin- der, while those of higher metallicity and lower [Mg /Fe] come from both blurring and churning mechanisms. The idea that the solar neighborhood isthe juxtaposition of the inner and outer disk is not new. Haywood et al. ( 2013 ) argued that this is a po- tential explanation for the observations of the two sequences inthe solar neighborhood, and the potential mixing of the high- [Mg /Fe] sequence with a more in situ population was initially seen in Fig. 20 of Edvardsson et al. ( 1993 ), who found that stars coming from the inner disk were often metal poor and [Mg/Fe] enhanced, while more in situ stars generally had so- lar type abundances. Qualitatively, our results are very similar to those of Edvardsson et al. ( 1993 ) with respect to the inner disk being dominated by high-[Mg /Fe] populations. With the addi- tion of extremely precise kinematics and distances from Gaia and a larger sample size of stars with reliable ages, we find that the high-[Mg /Fe] sequence was likely not a completely separate phase of disk evolution but indeed formed stars for many Gyr and was coeval with thethe low-[Mg /Fe] sequence of popula- tions. This inner disk origin for the bulk of the high-[Mg/Fe] se- quence explains the relative similarity of the high-[Mg /Fe] se- quence with radius (e.g., Nidever et al. 2014 ), as radially mixing of the high-[Mg /Fe] population out to larger radii preserves its appearance inthe chemical plane.
3.3. Axisymmetric approach 11
2014 ; Czekaj et al. , 2014 ) is not computed everywhere in space to allow computation of stellar orbits.
Some improvements have been recently examined by Bienaymé et al. ( 2015 ) using Stäckel potentials fitting, which adopt simple expressions for the integral of motions. This method provides a good local approximation of axisymmetric potentials in disk galaxies as has been pointed out in Bienaymé et al. ( 2015 ). However, such a Stäckel potential fit fails at low galactic radius closer to the Galactic bulge, and beyond when non-axisymmetric structures are considered, wherethe integrals of motions are not straightforwardly con- served. In this work we therefore improve this picture, and we employ an axisymmetric plus non-axisymmetric gravitational model, which is valid everywhere intheMilkyWay. A point to be emphasized is that here we employ the gravitational potential associated to each thin disk component as the sum of "homogeneous oblate spheroid" wherethe functional expressions are numerically solved (see Schmidt , 1956 ), and whose density laws approximate the density model of Robin et al. ( 2003 ) with a step-stair function. Each stair-step function represents a homogeneous spheroid component (see, for example, the Fig. 10 in Pichardo et al. , 2004 ). The basic idea to compute the three-dimensional potential of the thin disk consists in considering that the mass density distribution can be approximated locally in a linear form, i.e, by a succession of linear segments.
A special line list and continuum files were used, in which many features, including the Ca ii K and Ca ii IR triplet were la- belled as 26.00, thus treating them as if they were iron. We de- liberately exclude the features due to C-bearing molecules from our estimate (G-band and Swan band), although the C abun- dance is estimated from them. This was done because the reso- lution and S/N of the SDSS spectra are not sufficient for a multi- element analysis, especially at low metallicity; in many spectra, the only measurable feature isthe Ca ii K line. So what MyGIs- FOS provides in this case is an overall ‘metallicity’ that is essen- tially a mean of Mg, Ca, Ti, Mn, and Fe. The choice of [α/Fe] only impacts the lower metallicities, wherethe metallicity esti- mate is dominated by the Ca ii line. At higher metallicities, the Fe feature holds more weight, and our estimate is not biased. We verified this by looking at our estimates based on the SDSS spec- tra for a sample of seven stars from Ca ffau et al. (2018) with low [α/Fe]. At low metallicity, there is a large scatter, but at metallic- ity > −1.0 there is a tight correlation with no o ffset. Throughout this paper, we refer to this quantity as metallicity, and it should not be confused with Z, the mass fraction of metals. Our metal- licity estimate is closer to [Fe /H] than to Z, and the difference can be very large inthe case of CEMP stars, which, as discussed below, we cannot detect in a complete and reliable manner.
J. Kn¨odlseder: Cygnus OB2 – a young globular cluster intheMilkyWay 543
elliptical shape of Cyg OB2 inthe DSS data is produced by an elongated region of rather low extinction that is enclosed by two dust lanes running from south-east to north-west. Several local maxima that appear like extensions from the Cyg OB2 associa- tion are simply areas of reduced absorption, wherethe number of background stars is locally enhanced. A massive system of molecular clouds below δ = +40 ◦ 30 0 provides an efficient bar- rier for visible light, pushing the apparent centroid of Cyg OB2 towards thenorth. Hence DSS star counts are apparently not very suitable for the determination of the morphology of Cyg OB2. In contrast, a comparison with Fig. 1, and the above dis- cussion of the completeness of the PSC sample, suggest that the 2MASS stellar density distribution is basically unaffected by absorption, hence it reveals indeed the true morphology of Cygnus OB2.
model and the “McMillan”  proﬁle. The parameters for these models are taken from  and  and are shown in Table 1 . The McMillan proﬁle is a variant of the Zhao proﬁle  , which treats one of the shape parameters, γ , as a free parameter and therefore is also referred to as the “ γ free” model. The optimum value of γ for this model is 0 . 79 ± 0 . 32. The uncertainties on the halo proﬁle parameters are not used in this analysis. In Fig. 1 the integrated J-Factors for the three models are shown. The NFW pro- ﬁle gives a larger total amount of dark matter that is also more concentrated inthe core of the source than for the Burkert proﬁle. This is due to the fact that the NFW proﬁle is a so-called cuspy proﬁle and diverges at the centre of the source, in contrast to the cored Burkert proﬁle.