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Astron. Astrophys. 332, 71-76 (1998)

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3. Results

To isolate the contribution from the Local Arm, it is necessary to subtract the background emission, which is mainly due to the exponential component of the disc. It is very important to take into account the north warp, for which the maximum deviation is near the direction of interest here. Moreover, both the warp and the optical Local Arm are observed over the mean galactic plane. It is therefore necessary to use a model of the exponential component of the warped disc.

In a recent paper, Porcel et al. (1997) developed a model of the warped disc, which was used to interpret the data from DIRBE ("Diffuse Infrared Background Experiment ") (Freudenreich et al. 1994) on board COBE ("Cosmic Background Experiment"). They have shown that either the stellar disc is noticeably less warped than the gas, or a truncation of the stellar disc, taking place not far from the Sun, prevents comparison between the stellar and the gaseous warps. In this latter case, the truncation radius cannot be larger than 13 kpc.

We will now use the same model to undertake the subtraction. First of all, we must adjust the parameters of this model for a better fit to the COBE observations. Suppose that we adopt the first interpretation, i.e. that the stellar warp is smaller than the gas one. Suppose that both warps are related at all galactocentric radii by a constant. In other words, let [FORMULA] be the stellar warp curve and [FORMULA] the gaseous warp curve: then, we assume [FORMULA], where [FORMULA] is less than unity and is one of our adjustable parameters.

The other two adjustable parameters are [FORMULA], the Sun's height over the mean plane and [FORMULA], the galactocentric azimuth of the maximum deviation from the mean plane due to the warp. After comparison of the COBE results with a family of our three-parametric models, we deduced that the best fit is obtained for the following set of parameters: [FORMULA], [FORMULA], [FORMULA]. To obtain this family of parameters we benefited from the fact that they can be in principle obtained independently. The value of the mean z depends on [FORMULA] and not on the others parameters. The value of [FORMULA] similarly is obtainable from a displacement of the [FORMULA] origin alone, independent of the other parameters. These facts provided a very limited range of possible values, which were, on the other hand, similar to current values typically adopted in other papers. What was considered a main object of this paper, and therefore with much more detail, was the obtention of the value of [FORMULA], considered implicitly to be one in most previous papers. A numerical least squares method provided the value of [FORMULA]. After trials with different close values we estimated the error to be about 0.1.

The first two values for [FORMULA] and [FORMULA] are typical, just confirming those found by various authors, and lie close to currently adopted values. The value of [FORMULA], on the other hand, is striking, as unity is an implicitly assumed value in most gravitational models of the warp (see Binney 1992 and Combes 1994, for a review). Under this interpretation, the stellar warp is roughly half the gas warp.

We have not included the extinction in our computations. Being the infrared extinction coefficient so small, it was demonstrated in the previous model by Porcel et al.(1997) that the results are noticeably insensitive to extinction, even when studying so distant features as warps. The effect of extinction is clearly much less important for a very close feature, as the Local Arm.

Within the region of the Local Arm, we now subtract the data of the best fit model with [FORMULA], [FORMULA] and [FORMULA] from the near-infrared data obtained by the ground-based telescope at Tenerife to obtain a clear map of the Local Arm. The mean latitude of the L-band flux predicted by the best fit model is reproduced in Fig. 2, together with the same data from DIRBE. The fitting cannot account for the observational values in galactic latitudes [FORMULA], i.e. the region of the Local Arm.

[FIGURE] Fig. 2. Open circles stand for mean latitude of DIRBE data in the L band. The solid line shows the model's prediction with the parameters that best fit the observational data, i.e. [FORMULA], [FORMULA], [FORMULA].

Of course, the Local Arm is necessarily present in the DIRBE data. This is clear in Fig. 3, where we show the 12 µm flux contour maps obtained from DIRBE data for the region of interest.

[FIGURE] Fig. 3. Contour map of the brightness of the Galaxy DIRBE map in 12 µm in the longitude range [FORMULA]. The contour levels are in MJy/sr from 17 to 33. The difference between successive contour levels is 2 MJy/sr.

Our procedure is correct because of the very different angular extent of the warp and the Local Arm. We used [FORMULA] data to deduce the best fit model using DIRBE, and then applied this model to study a small feature, as the Local Arm is only [FORMULA] in longitude. Fortunately for us, the Local Arm is larger (see for instance, Becker & Fenkart, 1970) but is angularly small because it passes through the Sun. To obtain the fitting parameters the zone outside the Local Arm was considered with a greater weight.

Suppose, on the other hand, that we adopt the second interpretation of the apparent smallness of the stellar warp, i.e. that it is due to a truncation of the stellar disc, which therefore does not reach the zone of highest warp. Though this explanation is plausible and physically very different in the interpretation of warps, the distinction is not important for our present purposes, because the truncated disc produces the same map to be subtracted from the ground-based data.

In Fig. 4 we plot the contour maps corresponding to the Tenerife observations, for the number of stars with [FORMULA].

[FIGURE] Fig. 4. Contour map of star counts up to 10 magnitude. The value between successive contour levels is 100 [FORMULA] from 600 to 1800.

Fig. 5 shows the same plot for stars with [FORMULA]. The first map includes nearly all observed stars; the second map may be more interesting for our purposes, as nearly all [FORMULA] stars belong to the Local Arm. Some [FORMULA] bright stars may not belong to the Local Arm, but the number of [FORMULA] distant stars must be so scarce, that the distribution of [FORMULA] in the expected region of the Local Arm is the best way to define its geometry. Latitude profiles for four longitudes, [FORMULA], [FORMULA], [FORMULA] and [FORMULA] are very illustrative to see how the contribution of the Local Arm is apparent over the emission of the rest of the disc (Figs. 6 a-d). These profiles reasonably match what is to be expected from the model outside the Local Arm region. This fact is appreciated at longitude [FORMULA] where the arm lies outside, but in the Local Arm the profile varies from the model. At [FORMULA], the great extension in latitude is noticeable, as observational data do not show any clear dependence on latitude.

[FIGURE] Fig. 5. Contour map of star counts up to 8 magnitude. The value between successive contour levels is 20 [FORMULA] from 100 to 440.

[FIGURE] Fig. 6. Latitude profile of the star counts up to 10 magnitude. Solid line shows the observational data and dashed line the model prediction: [FORMULA], [FORMULA], [FORMULA]. a for [FORMULA], b for [FORMULA] c for [FORMULA] d for [FORMULA].

Fig. 7 is the final objective of this work, which is clear contour maps of the Local Arm without contamination from the exponential component of the warped thin disc. The Arm is clearly seen with values of [FORMULA] stars per square degree higher than 130, at a longitude of [FORMULA] in the North. There is also visible a large extension in latitude at longitudes between [FORMULA] and [FORMULA]. This thickening of the disc is produced by the proximity of the Local Arm to the Sun. We then see two properties of the Arm. It is oriented towards the Sun with a net elevation above the disc and is (angularly) very thick.

[FIGURE] Fig. 7. Contour map of star counts up to 8 magnitude due to the Local Arm, after subtracting the contribution of the exponential component of the disc. The value between successive contour levels is 20 [FORMULA] from -30 to 170.

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© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998