ISSN 1063-7737, Astronomy Letters, 2009, Vol. 35, No. 11, pp. 780–790. c Pleiades Publishing, Inc., 2009. Original Russian Text c G.A. Gontcharov, 2009, published in Pis’ma v Astronomicheski˘ı Zhurnal, 2009, Vol. 35, No. 11, pp. 862–872.
Influence of the Gould Belt on Interstellar Extinction G. A. Gontcharov* Pulkovo Astronomical Observatory, Russian Academy of Sciences, Pulkovskoe sh. 65, St. Petersburg, 196140 Russia Received December 19, 2008
Abstract—A new analytical 3D model of interstellar extinction within 500 pc of the Sun as a function of the Galactic spherical coordinates is suggested. This model is physically more justified than the widely used Arenou model, since it takes into account the presence of absorbing matter both in the layer along the equatorial Galactic plane and in the Gould Belt. The extinction in the equatorial layer varies as the sine of the Galactic longitude and in the Gould Belt as the sine of twice the longitude in the Belt plane. The extinction across the layers varies according to a barometric law. It has been found that the absorbing layers intersect at an angle of 17◦ and that the Sun is located near the axial plane of the absorbing layer of the Gould Belt and is probably several parsecs below the axial plane of the equatorial absorbing layer but above the Galactic plane. The model has been tested using the extinction of real stars from three catalogs.
PACS num b e r s : 97.20.-w; 97.10.Zr; 78.20.Ci; 97.20.-w; 97.10.Zr DOI: 10.1134/S106377370911005X Key words: Galaxy (Milky Way), spiral arms.
INTRODUCTION by Arenou et al. (1992) for a distance of 500 pc and Galactic latitudes +15◦
780 INFLUENCE OF THE GOULD BELT 781 extinction within the nearest kiloparsec with a relative rotation of the highest point of the Gould Belt relative accuracy higher than that of the model by Arenou to the X axis, i.e., the angle between the Y axis and et al. (1992) is unlikely to be possible. To achieve a the line of intersection between the axial plane of the high accuracy of the extinction correction, it is more equatorial layer and the axial plane of the Gould Belt, preferable to reveal specific absorbing clouds or to as λ0. determine the individual extinction for each star from The longitude λ and latitude β of a star relative to its highly accurate multiband photometry. However, the axial plane of the Gould Belt can be calculated a physically justified analytical model is important for from its Galactic coordinates: analyzing large-scale structures within the nearest − kiloparsec. sin β =cosγ sin b sin γ cos b cos l, (1) A Galactic structure, the Gould Belt, that lies − outside the Galactic plane in the regions of the tan(λ λ0)=cosb sin l/(sin γ sin b (2) sky where an enhanced extinction is observed and +cosγ cos b cos l). that has a suitable size, several hundred parsecs, exists in the neighborhood of the Solar system. The observed extinction A is approximated by the The Gould Belt and related Galactic structures, the sum of two functions: Local Bubble and the Great Tunnel, were described by Gontcharov and Vityazev (2005 and references A = A(r, l, b)+A(r, λ, β); (3) therein), Bobylev (2006 and references therein), each of them is represented by a barometric law and Perryman (2009, pp. 324–328 and references (Parenago 1954, p. 265). The extinction in the equa- therein). The Gould Belt contains young stars and their associations. Stars are also formed here at torial layer is present. The accompanying interstellar clouds can A(r, l, b)=(A0 + A1 sin(l + A2)) (4) cause extinction. The extinction in the Gould Belt −r| sin b|/ZA was first pointed out by Vergely et al. (1998). × ZA(1 − e )/| sin b|, In this paper, we tested the hypothesis that the interstellar extinction in the Gould Belt supplements where A0, A1,andA2 are the free extinction term, the extinction along the Galactic plane and con- amplitude, and phase in the sinusoidal dependence tributes significantly to the 3D pattern of extinction on l, and the extinction in the Gould Belt is within the nearest kiloparsec. A(r, λ, β)=(Λ0 +Λ1 sin(2λ +Λ2)) (5)
− | | × ζ (1 − e r sin β /ζA )/| sin β|, THE MODEL A where Λ , Λ ,andΛ are the free extinction term, Figure 3 presents the relative positions of two 0 1 2 amplitude, and phase in the sinusoidal dependence layers of absorbing matter, the layer with half- on 2λ. The assumption that the extinction in the thickness Z near the equatorial Galactic plane A Gould Belt has two maxima in the dependence on (below referred to as the equatorial layer) and the layer longitude λ was confirmed in our subsequent study. with half-thickness ζ in the Gould Belt. Denote the A The extinction maxima in the Gould Belt are observed inclination of the Gould Belt to the Galactic plane near the directions where the distance of the Belt from by γ. The working coordinate system is defined by the Galactic plane is at a maximum, i.e., approxi- the observed coordinates of stars: the heliocentric mately in the directions of the Galactic center and distance r and the Galactic longitude l and latitude b. anticenter. The Sun is at the origin of the working coordinate system and we do not consider its displacement Given the displacement of the Sun relative to the relative to the Galactic plane, because it cannot absorbing layers, Eqs. (4) and (5) transform to be determined in the model under consideration. A(r, l, Z)=(A0 + A1 sin(l + A2)) (6) However, we consider the displacement of the axial −| − | plane of the equatorial layer relative to the Sun, Z0, × r(1 − e Z Z0 /ZA )Z /|Z − Z | and the analogous displacement for the absorbing A 0 layer of the Gould Belt, ζ0. For clarity and comparison and with the standard Galactic coordinate system, Fig. 3 A(r, λ, ζ)=(Λ0 +Λ1 sin(2λ +Λ2)) (7) shows the X and Y axes—the axes of a rectangular −| − | coordinate system in the axial plane of the equatorial × r(1 − e ζ ζ0 /ζA )ζ /|ζ − ζ |. layer. The X axis is parallel to the direction toward A 0 the Galactic center and the Y axis is parallel to the The quantities |Z − Z0|/ZA and |ζ − ζ0|/ζA that are direction of Galactic rotation. We will designate the encountered in these formulas twice characterize the
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6 6 (a) (b) 8 8
10 10
12 12
14 14 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 s
K 6 6 (c) (d) 8 8
10 10
12 12
14 14 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 J Ð Ks
◦ ◦ ◦ Fig. 1. (J−Ks)–Ks diagram for 2MASS stars with accurate photometry: (a) near b =+15 , l = 180 ;(b)nearb =+15 , l =0◦;(c)nearb = −15◦, l = 180◦;(d)nearb = −15◦, l =0◦. stellar position in the absorbing layers displaced rela- this would be quite noticeable in the observational tive to the Sun. We do not consider the displacement data. The combined mean extinction in the equatorial of the Sun relative to the center of the Gould Belt layer A0 and the Gould Belt Λ0 cannot differ too much along the X and Y axes, because the accuracy of the from the universally accepted extinction in the near data used is insufficient for this purpose. part of the Galaxy, 1m. 5 kpc−1. As a result, we have the system of equations (3), one equation for each star. The observed extinction A COMPARISON OF THE MODELS is on the left-hand sides and the function of three observed quantities—r, l,andb—is on the right-hand Given the large scatter of individual extinctions sides. The solution gives 12 unknowns: γ, λ0, ZA, for stars within the nearest kiloparsec noted above, ζA, Z0, ζ0, A0, A1, A2, Λ0, Λ1,andΛ2. These are one might expect better agrement of the suggested chosen so as to minimize the sum of the squares of analytical model and the model by Arenou et al. the residuals of the left-hand and right-hand sides of (1992) between themselves than with observations. Eqs. (3). Therefore, comparing the extinctions calculated us- We can estimate some of the unknowns in ad- ing these models for the same stars is of great vance. The inclination γ of the Gould Belt to the importance. In this case, the accuracy of the Galactic Galactic plane has been estimated by different re- coordinates of stars is important. Consequently, searchers to be in the range 10◦–25◦.Sincethemax- the best data are the coordinates of stars from the imum height of the Gould Belt above the Galactic Hipparcos catalog (ESA 1997). plane approximately coincides with the direction of The model by Arenou et al. was used to calculate the Galactic center, λ ≈ 0◦. The half-thickness of the extinctions for 89 470 Hipparcos stars with paral- 0 the absorbing layer ZA is close to 100 pc (Parena- laxes exceeding 0.0025 (i.e., located approximately in go 1954). If the absorbing layer of the Gould Belt the Gould Belt). Based on these data, we obtained a was produced by some “deformation” of the equa- solution to the system of equations (3) that is in best torial layer, then we can also assume the same half- agreement with the model by Arenou et al. (1992). It thickness for it, i.e., ζA ≈ 100 pc. The displacements is presented in the table as the HIP solution. Figure 4 of the Sun relative to the absorbing layers Z0 and shows how well the extinctions calculated from this ζ0 are unlikely to exceed several parsecs; otherwise, solution agree with those inferred from the model
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2.5 2.5 +15° < b < +30° +15° < b < +30° 2.0 (a) 2.0 (b) 1.5 1.5 1.0 1.0 0.5 0.5 0 0 2.5 2.5 2.0 +5° < b < +15° 2.0 +5° < b < +15° 1.5 1.5 1.0 1.0 0.5 0.5 0 0 2.5 2.5 2.0 –5° < b < +5° 2.0 –5° < b < +5° 1.5 1.5
V 1.0 1.0 A 0.5 0.5 0 0 2.5 2.5 2.0 –15° < b < –5° 2.0 –15° < b < –5° 1.5 1.5 1.0 1.0 0.5 0.5 0 0 2.5 2.5 2.0 –30° < b < –15° 2.0 –30° < b < –15° 1.5 1.5 1.0 1.0 0.5 0.5 0 0 0 45 90 135 180 225 270 315 360 0 45 90 135 180 225 270 315 360 l, deg
Fig. 2. Extinction AV versus Galactic longitude at a distance of 500 pc from the Sun for various Galactic latitudes: (a) according to the model by Arenou et al. (1992); (b) according to the model suggested here. The dashes indicate the dependence 0.8+0.5sin(l +20◦). The vertical bars indicate the accuracy of the model by Arenou et al. (1992) and a relative accuracy of 40% for the suggested model. by Arenou et al. (1992): (a) for 89 470 Hipparcos expression with two sine waves. In this case, the stars with parallaxes exceeding 0.0025 and (b) for orientation of the Gould Belt, the thickness of the absorbing layers, the displacement of the Sun, and 111 444 stars with parallaxes exceeding 0.0005. the total extinction correspond to the expected ones. The standard deviation of the differences between the extinctions calculated using the two models is COMPARISON OF THE MODELS m designated in the table as σ(AG − AArenou).Itis0 . 13. WITH OBSERVATIONS This confirms that the parabolas of the model by Are- Having ascertained that the two extinction mod- nou et al. can be replaced by the suggested analytical els agree for a large number of Hipparcos stars, let
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Solutions of the system of equations (3)
HIP GCS V86 OBhip OBrpm OBph
γ,deg 14 ± 2 17 ± 2 17 ± 2 17 ± 2 15 ± 2 19 ± 2
λ0,deg −10 ± 2 −2 ± 7 −10 ± 3 −8 ± 3 −8 ± 3 −10 ± 3
ZA,pc 70 ± 20 63 ± 14 100 ± 30 90 ± 20 60 ± 20 50 ± 20
ζA,pc 60 ± 20 26 ± 10 30 ± 30 50 ± 20 60 ± 20 45 ± 20
Z0,pc 15 ± 3 4 ± 11 −7 ± 10 16 ± 6 10 ± 6 0 ± 10
ζ0,pc 3 ± 3 0 ± 7 0 ± 10 6 ± 3 0 ± 3 0 ± 10
−1 A0,mag.pc 1.2 ± 0.1 0.8 ± 0.1 2.0 ± 0.3 2.2 ± 0.1 1.9 ± 0.2 2.1 ± 0.2
−1 A1,mag.pc 0.6 ± 0.1 0.3 ± 0.1 0.4 ± 0.3 0.6 ± 0.2 0.7 ± 0.1 0.9 ± 0.2
A2,deg 45 ± 5 39 ± 7 35 ± 10 37 ± 3 30 ± 4 32 ± 5
−1 Λ0,mag.pc 1.0 ± 0.1 0.0 ± 0.1 0.2 ± 0.2 0.1 ± 0.1 0.5 ± 0.2 0.2 ± 0.2
−1 Λ1,mag.pc 0.9 ± 0.1 0.4 ± 0.1 1.2 ± 0.4 1.0 ± 0.1 1.0 ± 0.1 0.8 ± 0.2
Λ2,deg 130 ± 5 129 ± 8 130 ± 10 131 ± 5 140 ± 5 133 ± 5
σ(AG − AArenou),mag. 0.13
σ(Aobs − AArenou),mag. 0.11 0.27 0.26 0.37 0.35
σ(Aobs − AG),mag. 0.06 0.28 0.22 0.38 0.35 us compare the models with the extinction data for racy, irrespective of the method of its determination. real stars. Unfortunately, the extinction is low within Consequently, there are few accurate extinction es- 500 pc of the Sun, where the Gould Belt is located. timates for this region of space. In this paper, we Therefore, it is determined with a low relative accu- consider three catalogs of stars with fairly accurate individual extinctions: for OB stars from the Hip- parcos and Tycho-2 catalogs (Høg et al. 2000), the
extinctions were determined from multiband photom- etry by Gontcharov (2008a; hereafter OB stars); for F Y' ζ A and G dwarfs from the Geneva–Copenhagen sur- ZA vey of the solar neighborhood, the extinctions were estimated from Stromgren¨ photometry (Nordstrom¨ et al. 2004; hereafter GCS); and for various stars, ζ Z 0 0 γ the extinctions were derived from UBV photome- λ try and spectral classification (Guarinos 1992; here- 0 after the V86 catalog, according to the Strasbourg X' database). We selected stars with Hipparcos paral- laxes π>0.002 from GCS and V86. For OB stars, we calculated the distances from their Hipparcos par- allaxes as well as the photometric and photoastro- metric distances (from reduced proper motions). Ap- Fig. 3. Relative positions of two absorbing layers. plying the extinction model to OB stars is also a
ASTRONOMY LETTERS Vol. 35 No. 11 2009 INFLUENCE OF THE GOULD BELT 785
3 3 (a) (b)
2 2 V A 1 1
0 1 2 3 0 1 2 3 AVArenou
Fig. 4. Correspondence between the extinctions calculated here and those inferred from the model by Arenou et al. (1992) for 89 470 Hipparcos stars with parallaxes exceeding 0 .0025 (a) and for 111 444 stars with parallaxes exceeding 0.0005 (b).
check of how accurate the extinctions and distances AArenou) and σ(Aobs − AG) given in the table confirm calculated for them are. the crucial role of the natural scatter of stellar char- Below, we will denote the observed extinction by acteristics. The mean observed extinction is AV = 0m. 28, the extinction from the model by Arenou et al. Aobs, the extinction from the model by Arenou et al. 0m. 25 (1992) by AArenou, and the extinction from our ana- is , and the extinction from the suggested model m lytical model by AG. is 0 . 38. GCS. The extinctions for GCS stars were deter- OB stars. In this study, we are interested not in mined from multiband Stromgren¨ photometry. The the spatial distribution of stars and other statistical solution of Eqs. (3) for 9996 of these stars with π> characteristics of the sample of OB stars from Gon- 0.002 from Hipparcos is presented in the table as the charov (2008a) but in the extinction, whose accuracy GCS solution. Here, the standard deviations of the depends primarily on the accuracy of the multiband Aobs − AArenou and Aobs − AG differences are denoted photometry used. Therefore, for this study, the stars m by σ(Aobs − AArenou) and σ(Aobs − AG), respectively. with photometry less accurate than 0 . 05 at least in We see that the suggested analytical model agrees one of the Tycho-2 and 2MASS bands under con- better with the data than the model by Arenou et al. sideration were excluded from our sample: BT, VT, J, Unfortunately, the high accuracy of the extinctions H, Ks. This should provide an accuracy of determin- determined from Stromgren¨ photometry is compen- ing the reddening E(B–V ) at a level of 0m. 1 when sated for by the closeness of the stars under con- four photometric quantities are used for this pur- sideration and, accordingly, by the low value of the pose. However, Gontcharov (2008a) calculated the extinction itself. In addition, the observed extinction extinction coefficient R = AV /E(B–V ) not for each is systematically lower than that calculated from both m star but for a region of space and, as Wegner (2003) models: the mean observed extinction is AV =0. 04, showed, the standard deviation (natural scatter) of the while the extinctions from the models by Arenou et al. coefficient R for OB stars in the same region of space and the suggested model are 0m. 12 and 0m. 17, respec- is typically more than 0m. 3. Consequently, this is the tively. This may be the result of selection in favor of expected accuracy of determining the extinctions for stars with lower extinctions in the GCS catalog. the OB stars considered here. V86. We determined the extinctions for V86 stars, which represent the entire variety of stellar types, Instead of the relation R =2.8+0.18 sin(l + ◦ from UBV photometry and spectral classification. 115 ) adopted by Gontcharov (2008a), here we use The solution of Eqs. (3) for 9319 V86 stars with π> an apparently more plausible relation, R =2.65 + ◦ 0.002 from Hipparcos is presented in the table as the 0.2sin(l +75 ). Like the previous one, it was de- V86 solution. Contrary to popular belief, the present- rived by extrapolating the extinction law from the day spectral type–color index calibrations have an (BT–VT)–(VT–Ks) relation based on Tycho-2 and accuracy of no better than ±0m. 3 (or even 1m–2m) 2MASS photometry and is valid as an approxima- due to the natural scatter of stellar characteristics tion at low Galactic latitudes. Obviously, a separate (Perryman 2009, p. 215). The values of σ(Aobs − detailed study of the variations in R will be necessary.
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the photometric distance for Galactic latitudes −5◦ < 3.0 (‡) b<+5◦ in the first(a),fourth(b),andsixth(c) Galactic octants, which differ significantly by the 2.0 pattern of extinction. We see a large natural scatter of individual extinctions in the first octant (more 1.0 than 0m. 5), a much “quieter” picture in the fourth octant, and a low extinction and a standard deviation of less than 0m. 3 in the sixth octant. The mean 0 deviation of the individual stellar extinction from the analytical model also changes accordingly. In Fig. 6, the extinction is plotted against the 3.0 (b) Galactic longitude. This dependence corresponds to the data of the model by Arenou et al. (1992) shown 2.0 in Fig. 2a. For 2472 Hipparcos OB stars with parallaxes ex- V ceeding 0.0025, we obtained a solution presented in
A 1.0 the table as the OBhip solution. 0 Figure 7 shows the correspondence between the various extinctions for these 2472 OB stars: (a) Aobs and AArenou;(b)Aobs and AG calculated from the analytical model using photoastrometric distances; 3.0 (c) (c) AArenou and AG calculated from the analytical model using Hipparcos parallaxes; and (d) Aobs and 2.0 AG calculated from the analytical model using Hip- parcos parallaxes. On the whole, we see good agree- 1.0 ment. The group of stars deviates from the bisector in 0 Fig. 7c due to the asymmetry of the model by Arenou et al. (1992) in the Gould Belt, which is also seen in ◦ ◦ 0 500 1000 1500 2000 Fig. 2a: in the region with l ≈ 180 and b ≈−15 ,the m rph, pc extinction is AV ≈ 2 , i.e., approximately twice that in the symmetric region with l ≈ 0◦ and b ≈ +15◦, m where AV ≈ 1 . Our new analytical model gives ap- Fig. 5. Extinction versus photometric distance for the proximately equal extinctions for these regions. OB stars under consideration in the region −5◦ ASTRONOMY LETTERS Vol. 35 No. 11 2009 INFLUENCE OF THE GOULD BELT 787 2.5 1.5 V A 0.5 –0.5 0 90 180 270 360 l, deg Fig. 6. Extinction versus Galactic longitude for the OB stars under consideration. are no accurate extinction determinations for a large considerations that A0 and Λ0 must be approximately m number of stars. equal. Therefore, we finally adopted A0 =1. 2 and m (2) The acceptable accuracy of the OBrpm and Λ0 =1. 1. OBph solutionsaswellastheir agreement with the The final formulas to calculate the extinction from remaining solutions suggest that the photoastromet- the suggested model with the best values of the un- ric and photometric distances can be used for an ap- knowns found here are ◦ proximate calculation of the extinctions of stars based (1.2+0.6sin(l +35 )) on the suggested analytical model if more accurate distances are unavailable. × r(1 − e−|Z−0.01|/0.07)0.07/|Z − 0.01| (3) Comparison of σ(A − A ) and σ(A − obs Arenou obs and A ) shows that the suggested model agrees with the G ◦ −|ζ|/0.05 observational data no more poorly than the model by (1.1+0.9sin(2λ + 135 ))r(1 − e )0.05/|ζ|, Arenou et al. (1992). where the longitudes l and λ are given in degrees; (4) As expected, the two models under considera- the distances r, Z,andζ are given in kpc, and the tion are closer to each other than to the observational resulting extinction is given in magnitudes. Figure 2b data due to the natural scatter of extinctions for indi- shows the dependence of extinction AV on the Galac- vidual stars. tic longitude calculated from the suggested model for (5) The values found for 10 unknowns (except A0 a distance of 500 pc and various Galactic latitudes. and Λ0) agree in all solutions. The vertical bars indicate a relative accuracy of 40%. (6) A0 and Λ0 vary from one solution to another, In Figs. 2a and 2b, we see good agreement between but their sum, along with the total calculated extinc- the models under consideration. tion, are approximately the same in all of the solu- The extinction in the Gould Belt must hide the tions except the GCS one. Only the total constant more distant stars. Indeed, analysis of the number extinction rather than the constant extinction in each ofstarsandtheextinctionfortheOBstarsunder layer is reliably determined probably because of the consideration with photometric distances from 400 to low inclination of the Gould Belt to the Galactic 800 pc shows that the number of stars is considerably plane and, accordingly, the narrow range of longi- larger in the southern (relative to the Sun and not tudes where the absorbing layers are separated. Since relative to the Galactic equator!) hemisphere: 3841 the extinction for GCS stars is low, we could not versus 3415, while the extinction is higher in the m m correctly estimate A0 and Λ0. It is clear from physical northern hemisphere: 0 . 76 versus 0 . 66.Figure8 ASTRONOMY LETTERS Vol. 35 No. 11 2009 788 GONTCHAROV 2.0 2.0 (‡) (b) 1.5 1.5 1.0 1.0 G A Arenou A 0.5 0.5 0 0 –0.5 –0.5 0 0.5 1.0 1.5 2.0 0 0.5 1.0 1.5 2.0 AObs AObs 2.0 2.0 (c) (d) 1.5 1.5 1.0 1.0 G G A A 0.5 0.5 0 0 –0.5 –0.5 0 0.5 1.0 1.5 2.0 0 0.5 1.0 1.5 2.0 AArenou AObs Fig. 7. Correspondence between the various extinctions for 2472 Hipparcos stars: (a) the observed extinctions and those from Arenou et al. (1992); (b) the observed extinctions and those calculated using photoastrometric distances; (c) the extinctions from Arenou et al. (1992) and those calculated using astrometric distances; (d) the observed extinctions and those calculated using astrometric distances. shows smoothed contour maps for the stars under The height of the Sun above the Galactic equa- ◦ consideration within 400–800 pc and −36 ASTRONOMY LETTERS Vol. 35 No. 11 2009 INFLUENCE OF THE GOULD BELT 789 (‡) 20 0 –20 , deg b (b) 20 0 –20 090 180 270 360 l, deg Fig. 8. Smoothed contour maps for the OB stars under consideration within 400–800 pc and −36◦ CONCLUSIONS going to construct an extinction model for much of the Galaxy using 2MASS photometry, which, as is This study has shown that there is absorbing mat- shown Fig. 1, allows the reddening of stars in different ter both in the Galactic plane and in the plane of directions and at different distances to be estimated. the Gould Belt. For this reason, the Gould Belt con- tributes significantly to the extinction for stars at moderate Galactic latitudes, especially toward the 1. ACKNOWLEDGMENTS Galactic center (at positive latitudes) and anticenter (at negative latitudes). The 3D model by Arenou et al. In this study, we used various results from the Hip- (1992) that represents the extinction as a parabola parcos project and data from 2MASS (Two Micron depending on the distance with various coefficients All Sky Survey), a joint project of the Massachusetts for 199 regions of the sky can be replaced by the University and the IR Data Reduction and Analy- sum of two sine waves that describe the extinction sis Center of the California Institute of Technology in the Galactic plane and in the plane of the Gould financed by NASA and the National Science Foun- Belt. The absorbing layers were found to intersect at dation. We also used resources from the Strasbourg an angle of about 17◦. This angle may be considered Data Center (France) (http://cdsweb.u-strasbg.fr/). as the inclination of the Gould Belt to the Galactic This study was supported in part by the Russian equator. The angle between the line of intersection of Foundation for Basic Research (http://www.rfbr.ru) the Gould Belt with the Galactic plane and the Y axis (project no. 08-02-00400) and in part by the “Origin is about −10◦. The Sun is probably several parsecs and Evolution of Stars and Galaxies” Program of the below the axial plane of the equatorial absorbing layer Presidium of the Russian Academy of Sciences. but above the Galactic plane. The suggested analytical 3D extinction model REFERENCES agrees with the observed extinction for stars from the three catalogs considered and gives an extinction 1. F.Arenou, M. Grenon, and A. Gomez, Astron. Astro- phys. 258, 104 (1992). estimate for any star within 500 pc of the Sun (and 2 . V. V. B o b y l e v, P i s ’ m a A s t r o n . 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