3 Photometric results

   
3.1 Radial colour gradient

During the process of calibration we realised that a strong colour gradient is present in the Arches field. In Fig. 5, the $H - K^\prime$ colour is plotted against radial distance from the cluster center. As the extinction law has not yet been derived for HST filters, we have used the colour transformations in BGB to transform NICMOS into 2MASS magnitudes. Though the 2MASS filters deviate slightly from the standard Johnson JHK filters used to determine the extinction law (Rieke & Lebofsky 1985), we will be able to estimate the approximate amount of change in visual extinction across the field. The extinction parameters from Rieke & Lebofsky (1985) are given by

$$A_J/A_V = 0.282 \ \ \ A_H/A_V = 0.175 \ \ \ A_K/A_V = 0.112,$$

where $A_{\rm Filter}$ is the extinction in the given filter. For a change in extinction of $\Delta A_V$ this leads to

$$\Delta A_V = \Delta (A_J - A_H) / 0.107$$

$$\Delta A_V = \Delta (A_H - A_K) / 0.063$$

$$\Delta A_V = \Delta (A_J - A_K) / 0.170.$$

We are able to measure the right-hand side of each expression from the transformed HST/NICMOS $JHK_{\rm s}$ photometry. The resulting $\Delta A_V$ is given in each plot in Fig. 6, together with the fitting uncertainty from the rms scatter in the colour.

From the linear fits in Fig. 6 we see that A_V increases by about one order of magnitude over the entire field when moving outwards from the cluster center. The effect is most pronounced in the HST $J-K_{\rm s}$ vs. radius diagram (Fig. 6, bottom), where the longest colour baseline is used. We derive a change in visual extinction of $\Delta A_V = 10.71 \pm 2.47$ mag over the Gemini field (1000 pixels $\hat{=}$ 0.8 pc). Notably, if only the innermost 5 $^{\prime \prime }$ (250 pixels, 0.2 pc) are fitted, no variation in A_V is observed. When fitting the core separately, we get $\Delta A_V = 0.77 \pm 1.12$ mag for $R < 5\hbox{$^{\prime\prime}$ }$ (250 pixels) versus $\Delta A_V = 7.87 \pm 2.85$ mag for $5\hbox{$^{\prime\prime}$ }< R < 20\hbox{$^{\prime\prime}$ }$ ( 250 < R < 1000 pixels). The latter value corresponds to $\Delta A_V = 10.5\ {\rm mag}/1000\ {\rm pix}^{-1}$, consistent with the trend over the entire field. The small radial trend and low extinction value in the cluster center indicates the local depletion of dust. This could be either due to winds from massive stars or due to photo-evaporation of dust grains caused by the intense UV-radiation field.

A change in A_V of $\sim$ $10\ {\rm mag}/1000\ {\rm pix^{-1}}$ is also consistent with the result found in J-H, $8.8~\pm~2.1\ {\rm mag}/1000\ {\rm pix^{-1}}$, while a larger value of $\Delta A_V = 14.9\pm 3.2$ mag is derived from the $H-K_{\rm s}$ plot. Due to the uncertainties we conclude that the extinction varies by $\Delta A_V \sim 9 {-} 15$ mag across the Arches field of 20 $^{\prime \prime }$ or 0.8 pc, most likely closer to the lower value. This is in any case a tremendous change in the dust column density along the line of sight, with strong implications on limiting magnitudes and the potential detection of faint objects.

We have used a linear fit to the colour variation with radius for $R > 5\hbox{$^{\prime\prime}$ }$ to correct for the strong change in reddening observed in the outer cluster field. The values for cluster center stars ( $R < 5\hbox{$^{\prime\prime}$ }$) have been left unchanged, due to the large scatter and the very small trend found. Thus, these adjusted colours are scaled to the cluster center, where A_V is lowest. From the Rieke & Lebofsky (1985) extinction law, the change in K-band magnitude with radius corresponding to the change in colour can be derived as $\Delta A_K = 0.112/0.063 \cdot \Delta A_{H-K}$. We have used this relation to adjust the K-band magnitudes accordingly. The "dereddened'' colour-magnitude diagrams will be shown in direct comparison with the observed CMDs in Sect. 3.3 (cf. Fig. 9).

Figure 5: Colour variation across the Gemini field, as observed in instrumental Gemini magnitudes and HST/NICMOS data. As a trend of increasing colour excess with increasing distance from the Arches cluster center is observed in the two independent datasets, an instrumental effect as the cause for this variation is highly improbable.

   
3.2 Extinction maps

We can calculate the individual extinction for each object by shifting it along the reddening vector onto the isochrone. If we assume that intrinsic reddening plays only a minor role for most of the stars within the cluster, we can combine the individual reddenings to estimate the spatial extinction variation. In practice, we have applied a reddening of A_V = 15 mag to a 2 Myr isochrone of the Geneva set of models (Lejeune & Schaerer 2001). This choice of reddening ensures that the isochrone serves as a blue envelope for the bulk of the cluster stars, which are significantly more reddened. The choice of the isochrone will be discussed in context with the mass function (Sect. 5), where the physical effects of the population model used are more important. As discussed in Grebel et al. (1996), colours of main-sequence stars also depend on binarity, stellar rotation, and intrinsic infrared excess. We ignore these effects here since we have no means to distinguish them from reddening effects. In the worst case, we will overestimate the reddening for some stars. We have then shifted the stars along the reddening path in colour-magnitude space, again assuming that the relative slopes of the extinction law approximately follow a Rieke & Lebofsky (1985) law. The resulting extinction map for the Gemini photometry is shown in Fig. 7.

Figure 6: Colour trends over the Arches field as observed in the HST/NICMOS data set within the area covered by the Gemini observations. The radial distance from the cluster center is given in pixels on the Gemini scale. For the calculation of $\Delta A_V$, the Rieke & Lebofsky (1985) reddening law has been assumed.

Since the original HST/NICMOS field has twice the area of the Gemini central Arches field, we have also calculated the extinction map for the entire NICMOS field following the same procedure. The corresponding map is shown in Fig. 8.

The extinction measured with this procedure in the K-band lies in the range 1.9 < A_K < 4.1 mag, with an average value of 3.1 mag, corresponding to 16 < A_V < 37 mag, $<\!\!A_V\!\!> ~= 27.7$ mag. Cotera et al. (2000) derive a near-infrared extinction of 2.8 < A_K < 4.2 mag, with an average value of $<\!\!A_K\!\!>\ = 3.3$ mag for 15 lines of sight towards several Galactic Center regions, corresponding to an average visual extinction of $<\!\!A_V\!\!>\ = 29.5$ mag (transformed using Rieke & Lebofsky 1985). They obtain the highest extinction towards a field close to the Arches cluster, A_V = 37.5 mag. This is very close to our highest extinction value. The average value determined from individual dereddening here is the same as the average extinction obtained by Figer et al. (1999), $<\!\!A_V\!\!>\ = 27.7$ mag. Note that the typical random scatter $\sigma(A_K)$ from foreground dust density fluctuations found in GC fields is linearly related to the average extinction within a field. The relation determined by Frogel et al. (1999) from giant branch stars in 22 pointings towards fields within 4$^\circ$ from the GC is given by $\sigma(A_K) = 0.056 (\pm 0.005)<\!\!A_K\!\!>~+ 0.043 (\pm 0.005)$. This yields an expected natural scatter from GC clouds of only $\sigma(A_K) = 0.22$ mag for $<\!\!A_K\!\!>~= 3.1$ mag, much below the difference in reddening observed in the Arches field. Thus, the change in extinction cannot be explained by the natural fluctuations of the dust distribution in the GC region.

Comparison of the cluster center main sequence population with the main sequence colour of a theoretical 2 Myr isochrone from the Geneva set of models (Lejeune & Schaerer 2001), later-on used for the derivation of the mass function, yields an average extinction of $A_V = 24.1 \pm 0.8$ mag in the cluster center. This extinction value has been used to transform isochrone magnitudes and colours into the cluster magnitude system. It has been suggested that the brightest and most massive stars in Arches are Wolf-Rayet stars of type WN7 (Cotera et al. 1996; Blum et al. 2001). Fundamental parameters of Wolf-Rayet stars are compiled in Crowther et al. (1995). For stars of subtype WN7 they find typical colours of $(H - K) \sim 0.2$ mag, leading to an extinction of $A_V = 24.9 \pm 2.4$ mag with an observed H - K colour of $\sim$1.77 mag for the WN7 stars, which were identified by comparison with the Blum et al. (2001) narrow band photometry. This value is in very good agreement with the A_V determined from the main sequence colour in the cluster center.

Figure 7: AK extinction map, binned in the same manner as the residual map in Fig. 3 (North is up, East is to the right). White spots are positions without stars for evaluation. The individual extinction has been calculated by shifting the stars in the K vs. H - K colour-magnitude diagram to a 2 Myr isochrone offset bluewards of the main sequence. Transformation to AK = 0 mag has been performed afterwards, to avoid large errors in the shifting procedure. This results in a minimum AK of 1.86 mag, and a maximum of 4.08 mag, assuming a Rieke & Lebofsky (1985) extinction law.

Figure 8: AK extinction map derived from HST m205 photometry. See Fig. 7 for details. The coordinate transformed HST/NICMOS F205W image is also shown for comparison. Note the different scales (HST/NICMOS: $40\hbox {$^{\prime \prime }$ }\times 40 \hbox {$^{\prime \prime }$ }$, Gemini/Hokupa'a: $20\hbox {$^{\prime \prime }$ }\times 20 \hbox {$^{\prime \prime }$ }$).

   
3.3 Colour-magnitude diagrams

The resulting colour-magnitude diagrams for Gemini and HST are presented in Fig. 9 (upper panel). Two important differences are seen when inspecting the CMDs. First, the scatter in the main sequence is significantly larger in the ground-based photometry. While the HST/NICMOS CMD reveals a narrow main sequence in the cluster center (circles in Fig. 9), the same stars display a much larger colour range in the Gemini CMD. The poor Strehl ratio in the Gemini/Hokupa'a data as compared to the HST/NICMOS data (see Sect. 2.1.5) causes a high, non-uniform additional background due to uncompensated seeing halos around bright stars, which decreases photometric accuracy. In the dense regions of the cluster center, where crowding problems are most severe, the photometry is most affected. The number of faint, unresolved companion stars that merge into the high stellar background underneath the bright cluster population is very high. As discussed in Sect. 2.1.4, the halos of the bright stars hinder the detection of faint objects despite the principally high spatial resolution seen in individual PSF kernels. Operating at the diffraction limit, NICMOS is not restricted by these effects, yielding a better effective resolution especially in the dense regions. A tighter main sequence and less scatter is the consequence. In Fig. 9, the innermost 5 $^{\prime \prime }$ of the Arches cluster are marked by open circles. It is clearly seen that most massive (bright) stars are located in the cluster center.

A second effect observed is the much larger number of faint objects seen in the HST data (cf. Fig. 2). As the limiting magnitude and the measured spatial resolution of the images are similar in both datasets, this, too, has to be a consequence of the low Strehl ratio in the AO data.

Figure 9: Colour-magnitude diagrams. Left: Gemini/Hokupa'a, right: HST/NICMOS. Lower panel: CMDs corrected for radial reddening gradient (Sect. 3.1).

The lower panel of Fig. 9 shows the "dereddened'' CMDs, corrected for the radial colour gradient found and the corresponding change in extinction, $\Delta A_K$ (Sect. 3.1). The colours of stars beyond $R > 5\hbox{$^{\prime\prime}$ }$ have been adjusted to the colour of the cluster center. Comparison with the original CMDs shows that most of the bright, seemingly reddened stars fall onto the same main sequence after correcting for the colour trend. These stars are located at larger distances from the cluster center and thus suffer from more reddening by residual dust. As will be discussed in the context of the mass function (Sect. 5), these stars might have formed close to the cluster at a similar time as the cluster population. At the faint end of the CMD, there are, however, a large number of objects that remain unusually red after the correction has been applied. These objects may either be pre-main sequence stars or faint background sources. Unfortunately, we are not able to disentangle these two possible contributions, and will thus exclude objects significantly reddened relative to the main sequence when deriving the mass function.

   
3.4 HST/NICMOS colour-colour diagram

For comparison with the reddening path and a main sequence in standard colours, the NICMOS filters have been transformed into the 2MASS $JHK_{\rm s}$ system. In Fig. 10, we show the transformed HST/NICMOS colour-colour diagram for the stars bright enough to be observed in all three filters. The A_V values are from the Rieke & Lebofsky (1985) extinction law for standard JHK photometry. Though we are aware of the uncertainties inherent to the transformation of severely reddened stars, the proximity of the reddening path to the data points supports the validity of the equations derived by BGB. Changing the transformation parameters slightly results in a large angle between the data points and the reddening path.

A wide spread population of stars is clearly seen along the reddening path, as expected from the colour trend discussed in Sect. 3.1 (no correction for the varying extinction has been applied in this diagram). Again, the stars with the lowest reddening within the cluster population are the bright stars in the Arches cluster center. Moving along the reddening line towards higher values of A_V mainly means moving radially outwards from the cluster center. As in the CMD, a correction for the observed colour gradient causes the bulk of the stars to fall onto the main sequence with a reddening of A_V = 24 mag, corresponding to the cluster center.

Figure 10: Two-colour diagram from HST observations. The reddening path is shown as a straight line labeled with AV values, and the main sequence is indicated by the thick grey line. The area between the dashed lines marks the region of reddened main sequence stars.