The Effect of Dust Extinction on the Observed Properties of Galaxies in the Near-Infrared

Galaxies behind the Milky Way suffer size reduction and dimming due to their obscuration by dust in the disk of our Galaxy. The degree of obscuration is wavelength dependent. It decreases towards longer wavelengths. Compared to the optical, the Near InfraRed (NIR) $K_s$ band extinction is only $\approx10%$ that of the $B$ band. This makes NIR surveys well suited for galaxy surveys close to the Galactic Plane where extinction is severe. While Galactic obscuration is less prominent in the NIR it is not negligible. In this paper we derive empirical relations to correct isophotal radii and magnitudes of galaxies observed in the NIR for foreground absorption. We simulate extinction in the $J$, $H$ and $K_s$ bands on 64 (unobscured) galaxies from the 2MASS Large Galaxy Atlas \citep{jarrett}. We propose two methods for the extinction correction, the first is optimized to provide the most accurate correction and the second provides a convenient statistical correction that works adequately in lower extinction regions. The optimized correction utilizes the galaxy surface brightness, either the disk central surface brightness, $\mu_0$, or the combined disk plus bulge central surface brightness, elliptical and disk/spiral Hubble types. A detailed comparison between the different methods and their accuracy is provided.

are severe, we initiated a study of the effect of Galactic extinction on galaxies imaged in the J (1.2 μm), H (1.6 μm) and K s (2.2 μm) bands. This will allow us to correct their observed isophotal-radii and magnitudes for extinction. In our current ZOA survey along the Norma wall (Riad et al., in preparation), we noted that ≈85 per cent of the galaxies in our sample were found in regions with an extinction A J 1.0 mag, while ≈14 per cent were found in regions with an extinction 1.0 A J 3.0 mag. Only 1 per cent of the galaxies were found in regions with an extinction A J > 3.0 mag. For the H and K s band ≈94 and 98 per cent, respectively, of the galaxies were found in regions with A H ,Ks 1.0 mag, while ≈5 and 1 per cent of the galaxies were obscured by 1.0 A H ,Ks 3.0 mag. Only a handfull of the galaxies were found in regions with A H ,Ks > 3.0 mag. We therefore limited the simulation to the extinction range A J ,H ,Ks = 0.0-3.0 mag. In this work and for the purpose of estimating the extinction suffered by galaxies in our ZOA survey, we used the general extinction law, Where E(B − V ) is the colour reddening derived from the Schlegel, Finkbeiner & Davis (1998) reddening maps and A V is the extinction in the optical V band. A typical value for R V is 3.1 (Cardelli, Clayton & Mathis 1989). Extinction in the NIR J, H and K s passbands was derived using the parametrization given by Cardelli et al. (1989), see equations (1)-(3).
In this paper, we derive NIR corrections to isophotal magnitudes and radii for galaxies obscured by the Milky Way. Section 2 describes the data set and method. We describe two methods to apply the corrections (Sections 2.2 and 2.3). In Section 3, we provide a brief comparison between the different methods, and discuss their respective reliability.

DATA A N D M E T H O D
We selected 64 galaxies from the 2MASS Large Galaxy Atlas (LGA) (Jarrett et al. 2003) to simulate the effect of extinction on isophotal-radii and magnitude for galaxies observed in the NIR. 2MASS is an All-Sky NIR survey in the bands J (1.2 μm), H (1.6 μm) and K s (2.2 μm). Galaxies were selected in such a way that they are minimally affected by contamination from neighbouring sources, and give a fair representation of all morphological types. The sample includes 25 elliptical and lenticular (E/S0), and 39 spiral (S) galaxies. Half of the galaxies in the spiral galaxy sample are barred with some of them having ring features. The selected galaxies cover a wide range in galaxy size and brightness. The apparent radii range between r 20 = 34-1614 arcsec where r 20 is the isophotal radius at the surface brightness level μ K = 20 mag arcsec −2 . The apparent isophotal magnitude range covered by our sample is K 20 = 1.04-10.77 mag, where K 20 is the integrated magnitude within r 20 . The galaxies in our sample suffered minimal obscuration ranging between A Ks = 0.01-0.07 mag, see last column in Table 1.The list of selected galaxies is given in Table 1. This table lists the most common name of the galaxy, followed by the morphological type, r 20 , K 20 , inclination (b/a) and position angle (PA) in the K s band. All the data are taken from Jarrett et al. (2003). In the table, we also give the disc central surface brightness μ 0 (Freeman 1970) and the central surface brightness μ c in the K s band. The last column lists the mean extinction A Ks . Extinction in the K s band was derived from the Schlegel et al. (1998) reddening maps and equation (3). The surface brightness profiles for the galaxies are taken from the LGA 1 (given in tabular format).
The method we implement here for simulating the effect of extinction on galaxies closely follows the precepts of earlier work done by Cameron (1990) in the B band.
It is difficult to define a reliable total radius and magnitude for a galaxy (Jarrett et al. 2003), but more straightforward to work with isophotal radii and magnitudes out to a given radius. For this reason, we only consider here corrections to isophotal radii and the flux within that respective radius. In this paper, we define the limiting isophotal radius R as the radii to an isophote of 21.4 mag arcsec −2 in the J, 20.6 mag arcsec −2 in the H and 20 mag arcsec −2 in the K s band. Those values are approximately the 1σ NIR sky background (Jarrett et al. 2003). We also define the integrated isophotal magnitude m iso as the integrated magnitude out to this radius R.

Simulating extinction
The simulation of the effect of Galactic extinction on the apparent properties of a galaxy was achieved by the inward displacement of the limiting isophote along the surface brightness profile. The limiting isophote was shifted in non-uniform steps along the galaxy light profile with each step being equivalent to a certain extinction level in the investigated band. As an example, the left-hand panel of Fig. 1 shows the effect of extinction on the surface brightness profile of the spiral galaxy M88 in the K s band. The panel indicates increasing levels of extinction at A Ks = 0.0, 0.7, 1.4, 1.7, 1.9, 2.2, 2.6 mag and A Ks = 3.0 mag applied to the galaxy. The extinction levels are represented as horizontal lines on the plots. For each of the horizontal lines, the part of the profile lying below the line represents the obscured part of the galaxy while the part above is what remains visible at a given extinction. The intercept of the line with the ordinate gives the apparent limiting isophote, while the intercept of the light profile on the abscissa shows the size of the obscured galaxy that remains visible. The projection of the point of intercept of the line representing A Ks = 0.0 mag with the light profile on the abscissa gives the intrinsic radius R • . The additional dimming caused by the loss of the faint outer region is demonstrated by the integrated isophotal magnitude profile m iso shown in Fig. 1 The reduced radii and magnitudes were calculated for each step and compared to the original values. The quantities calculated as a function of extinction were f (R) and m iso , defined as where m • iso , m iso , R • and R are the intrinsic and absorbed magnitudes and radii, respectively. The different values of f (R) and m iso corresponding to the simulated extinction values were then calculated, and fitted to the empirical relations following the formalism  The table lists the morphological type, r 20 , K 20 , (b/a) and PA, values are taken from the LGA (Jarrett et al. 2003). The table also lists the K s band μ 0 and μ c . Extinction in the K s band is also listed. Galaxies marked with are those showing the deviated correction trend explained in the next section.  given by Cameron (1990), where F , v, a, b are the fitting parameters, and A λ the extinction. This parameter fitting was done for all galaxies in our sample. It was performed separately for all three J , H , K s bands. The resulting corrections show very comparable trends in the three bands, due to the similarity of the light profiles of the galaxy in the three bands. To demonstrate the effectiveness of our procedure we therefore reduce the discussion to the results of the K s band only. Fig. 2 displays the calculated values of f (R), and m iso as a function of A Ks , with their fitted relations for the galaxy M88 in the K s band. The ability of equations (4) and (5) to fit the simulated data varies among the galaxies. Some galaxies show tighter fits compared to M88, while others show more dispersion. The variation in the quality of the fitting is expected due to the different structures imprinted on the surface brightness profile of the galaxies.

Variation among galaxies (optimized corrections)
In Fig. 3, we show the magnitudes and radii corrections for all the E/ S0 (top) and S galaxies (bottom). The curves in the plots clearly show that the Cameron (1990) relations in their present form can not fully account for the variation among the galaxies in the two respective groups.
We investigated the origin of these discrepancies by looking at trends with, for example, inclination, central surface brightness μ c , and the disc central surface brightness μ 0 extrapolated from the fainter outer disc. No significant trend was found between the corrections and the variation among galaxies inclinations. Most probably a much larger sample than the current one is needed to investigate the correlation. A clear correlation between μ 0 and μ c with the corrections was noted, however.
It was noted that galaxies with a low central surface brightness μ c ≥ 17.0 mag arcsec −2 in the K s band, and low surface brightness galaxies in general require larger corrections. This is expected as those galaxies become obscured much more quickly. Galaxies that required larger corrections in our sample are M33, NGC 24, NGC 247, NGC 1073, NGC 55, NGC 4244; they are labelled in Fig. 3 Even though the corrections were found to depend on μ c , it was in fact found that μ 0 shows the better correlation with the corrections.
In this section we describe the method to optimize the corrections using either μ 0 or μ c . Optimizing the corrections using μ 0 gives tighter estimates to the corrections than using μ c . On the other hand, optimizing the corrections using μ c is convenient since it is easily measured and is typically found in large catalogues including 2MASX. A further point to note is that the NIR μ c can be used to roughly classify the galaxies as early or late-type galaxies (Jarrett 2000). In Section 2.3, we derive a more general correction which can be applied when only the galaxies are classified as early or late type but neither μ 0 nor μ c is available.

Optimized correction based on μ 0
It was realized that the derived quantity, μ 0 , defined as the disc central surface brightness extrapolated from the fainter outer regions of the galaxy correlates well with the deviation among the galaxies. The definition of μ 0 corresponds to the disc central surface brightness for spirals as defined by Freeman (1970). The better correlation of the corrections with μ 0 rather than μ c is expected since it is always the fainter outer regions of the galaxy that suffer most from extinction. To accommodate μ 0 into the corrections, equations (4) and (5) were rewritten as with Using the parameter products (a × b), (F × v) for each galaxy, and analysing how they vary with μ 0 , we derived these parameters (a • , b • , F • , v • , a 1 , b 1 , F 1 and v 1 ). The values are listed in Table 2. For each galaxy, the value of μ 0 was found from a linear fitting to the disc part of the light profile of the galaxy with μ λ 17.0 mag arcsec −2 . The intercept of the straight line fitted to the disc  part of the light profile with the surface brightness axis was then μ 0 . The disc part of the light profile was identified by visual inspection.
The goodness of f (R, μ 0 ) and m iso in describing the correction curves for the different galaxies accurately was found to be very sensitive to the value of μ 0 . This shows the importance of having an accurate light profile of the galaxies, and hence μ 0 , to be able to use the μ 0 optimized correction.

Optimized correction based on μ c
For optimizing the extinction corrections using the central surface brightness μ c we used the same methodology as for the μ 0 optimization. To incorporate μ c in the corrections we rewrote equations (4) and (5) as with a(μ c ) = a • exp(μ c · a 1 ), Again we determine the products (a × b) and (F × v) and how they vary with μ c and hence derived the parameters (a F 1 and v 1 ). The values of these parameters are given in Table 3.
To quantify the performance of the two optimization corrections, we computed the difference between the corrections as given by the simulated data and as given by the optimized corrections using both the parametrization f (R, μ 0 ), m iso (μ 0 ) and using f (R, μ c ), m iso (μ c ). The comparison was made for all galaxies in the K s band in the extinction range A Ks = 0.0-3.0 mag. A summary of the comparisons is listed in Table 4, and displayed in Fig. 4 for the μ 0 optimization, and Table 5  The μ 0 optimized corrections were calculated using equations (6) and (7). The value of μ 0 for each galaxy was found by performing a linear regression to fainter outer region of the galaxy light profile with μ λ 17.0 mag arcsec −2 and measuring its intercept with the ordinate. The plots and tables show that the accuracy of the corrections are extinction dependent, showing smaller deviations and less dispersion at low levels of extinction. It is also evident that spiral galaxies show larger deviations and more dispersion than elliptical and lenticular galaxies. The relatively larger errors for the spiral galaxies can be attributed to the more structural features like spiral arms, bars traced by their light profiles. The comparison also shows that the corrections parametrized using the disc central surface brightness show less systematic shifts and tighter dispersion than the corrections using the central surface brightness optimization. The better performance of μ c in describing the corrections results from the fact that it is the outer galaxy disc that suffers more of the obscuration. It is also worth noting that ≈85, 94 and 98 per cent of the galaxies in the J, H and K s bands in our ZOA survey are in regions with an extinction A J ,H ,Ks 1.0 mag where the corrections show very little dispersion.

Average behaviour (average correction)
The application of the optimized method to estimate the obscuration corrections for galaxies requires the knowledge of the value of μ 0 and hence the galaxy light profile. In many cases, that information is not available, or hard to obtain, like trying to correct isophotal radii or magnitudes for galaxies in a galaxy catalogue such as the 2MASX. For such cases, an average correction independent of the The μ c optimized corrections were calculated using equations (9)  galaxy light profile is required. In this section, we derive such an average correction. A comparison between the application of the optimized and average corrections is given later in Section 3. The all elliptical galaxies and the majority of the spiral galaxies (85 per cent of the spirals) show comparable trends (see Fig. 3), while only a few galaxies (M33, NGC 24, NGC 247, NGC 1073, NGC 55, NGC 4244, marked on the plots) deviate from the average behaviour. To produce an average correction for each galaxy family E/S0 or S, we excluded the strongly deviating galaxies. For the ones showing the similar behaviour (25 E/S0 and 33 S galaxies), their simulated corrections were binned, resulting in an average correction curve for each family in each of the three bands. These average curves for the J, H and K s bands are displayed in Fig. 6. For comparison, the B-band corrections are displayed as well. The latter are taken from Cameron (1990).
As expected, the error bars grow with increasing extinction. It should be noted that the error bars are biased with our selection of galaxies representing the average behaviour. If we would include the strongly deviating galaxies, the error bars would obviously be larger. But given that the majority of the galaxies follow the general behaviour it would be unreasonable to include those outliers for the correction. It is also obvious from Fig. 6 that our correction curves are similar to those given by Cameron for the B band, especially the shorter J and H bands. The average correction curves were then fitted with equations (4) and (5). The respective fitting parameters are given in Table 6.
To gain more insight on the variation of the average correction among the galaxies, we calculated the difference between the simulated corrections and the average corrections for each galaxy at A Ks = 1.0 mag. The average correction was calculated using equations (4) and (5) and the parameters in Table 6. In Fig. 7, we plot these differences against the value of μ 0 for the galaxy in the K s band. We find that E/S0 galaxies with μ 0 ≥ 16.2 mag arcsec −2 and S galaxies with μ 0 ≥ 16.6 mag arcsec −2 are generally underestimated by the average correction, while brighter galaxies are overestimated by the correction.
To assess the accuracy of the average correction as a function of extinction, we made a comparison between the simulated corrections and those derived from the average correction in the extinction range A Ks = 0.0-3.0 mag. The results are plotted in Fig. 8. A summary is given in Table 7, where we list the mean difference between the simulated data and the average correction value at the extinction levels A Ks = 0.5, 1.0, 2.0 and 3.0 mag, as well as their scatter.  Similar to the optimized corrections, the average correction method performs better for lower levels of extinction. Comparing Figs 4, 5 and 8, Tables 4, 5 and 7, we note that the optimized corrections are more accurate than the average correction method.

D I S C U S S I O N
In this paper, we present two methods to correct the isophotal magnitudes and radii for galaxies observed in the NIR obscured by foreground extinction. The optimized correction requires knowledge of the galaxy's light profile. The use of μ c to estimate the corrections is useful as it can also be independently used to roughly categorize the galaxies as early or late type. The average correc-tion method is more straightforward. It gives average corrections at each extinction level in the J , H , K s observed wavebands, and only requires the classification of a galaxy as early or late type.
To compare the accuracy of the average and the μ 0 method, we used their comparison with the simulated corrections, see Figs 4 and  8 and Tables 4 and 7. For spiral galaxies estimating the magnitude corrections using μ 0 optimization, m iso (μ 0 ) shows a systematic shift = −0.01 mag with a SDE = 0.0 mag for an obscuration level of A Ks = 0.5 mag. Meanwhile using the average correction shows a = 0.04 mag with SDE = 0.02 mag at the same level of extinction. At A Ks = 1.0 mag, m iso (μ 0 ) has a systematic shift of = −0.01 mag and a SDE = 0.02 mag, while the average correction has a = 0.09 mag with a SDE = 0.05 mag. Radius corrections for spiral galaxies revealed a similar trend for the two methods, (see Tables 4 and 7). The comparisons for the elliptical galaxies are also given in Tables 4 and 7.
Figs 4 and 8 and Tables 4 and 7 give the comparison between the optimized and average corrections as compared to the simulated corrections for the extinction values A Ks = 0.5, 1.0, 2.0 and 3.0 mag. They clearly emphasize that the μ 0 optimized correction is more accurate compared to the average correction method. But the average correction remains more useful when applying the corrections to galaxy parameters from a galaxy catalogue.
The μ c optimized correction shows larger shifts and more dispersion than the μ 0 optimized correction, but smaller shifts and tighter dispersion compared to the average correction.
In the following, we give some average correction values to correct magnitudes and radii of obscured galaxies. The average correction estimates a 0.13 mag correction to the isophotal magnitude of elliptical galaxies at A Ks = 1.0 mag. This magnitude correction is over and above the A Ks = 1.0 mag correction. The magnitude correction shows a systematic shift of = 0.01 mag with a SDE = 0.01 mag at A Ks = 1.0 mag. As a function of radius, ellipticals are estimated to be 28.3 per cent smaller in radius at A Ks = 1.0 mag, when using the average correction. The radius correction shows a = 0.6 per cent and SDE = 0.9 per cent at the same extinction level (see Table 8).  (4) and (5), and the parameters in Table 6. The isophotal magnitudes of spiral galaxies at A Ks = 1.0 mag are expected to be 0.20 mag brighter when applying the average correction. They show a systematic shift of = 0.09 mag with a SDE = 0.05 mag at A Ks = 1.0 mag. The average corrections predict that spiral galaxies appear 28.4 per cent smaller at A Ks = 1.0 mag. The corrections show a systematic shift of = 4.4 per cent with a SDE = 2.6 per cent at the same obscuration level (see Table 8). The table also lists the expected magnitudes and radii corrections, respectively, at the extinction levels A Ks = 0.5, 1.0 and 2.0 mag. The table also lists the systematic shifts and the SDE. The magnitude values listed in Table 8 give the additional dimming, the galaxy size reduction, the systematic shift when using the average correction and their respective SDE. The positive systematic shifts indicate that the average correction under estimates the obscuration corrections.
It is worth mentioning that our corrections agree well with corrections given by Nagayama et al. (2004) for galaxies in the K s band obscured by A Ks 1.0 mag. In their work, they estimated the extra dimming to elliptical galaxies to be m iso = 0.15 mag compared to m iso = 0.13 mag as expected by our average correction. For spiral galaxies, they estimated the correction to be m iso = 0.18 mag which also agree well with our expected correction of m iso = 0.20 mag. Compared to Nagayama et al. (2004) corrections, our results are useful for higher extinction levels in the three NIR bands J, H and K s , that is A J ,H ,Ks ≤ 3.0 mag.

C O N C L U S I O N
We present two methods to correct galaxies for extinction in the J, H and K s bands. The optimized correction methods are more accurate than the average correction. However, the average correction method is more straightforward to apply as it requires no knowledge of the light profile of the galaxy but only the classification of galaxies as early or late types. The extinction corrections that we present here are considered as a NIR extension to those for the B band derived before by Cameron (1990).
These corrections will be invaluable to the analysis of largescale structures in the ongoing NIR galaxy survey along the Norma Wall in the ZOA. It will also be applicable to other galaxy surveys e.g. 2MASX or prospective European Southern Observatory (ESO) galaxy surveys e.g. VISTA Kilo-Degree Infrared Galaxy Survey (VIKING 2 ) using the VISTA telescope.