JSTOR

1. INTRODUCTION

L and T dwarfs have unusual spectral energy distributions (SEDs), with most of their flux emitted through windows in the near‐IR. Normalized spectra of an L5 and T4.5 dwarf (Geballe et al. 2002) are shown in Figure 1 to illustrate how absorption bands of , CO, and regulate the near‐IR emission and create the flux windows. The bands are the same features responsible for the telluric absorption that defines the conventional J (1.1–1.4 ), H (1.5–1.8 ), and K (2.0–2.4 ) bandpasses. Thus, the presence of in the atmospheres of the L and T dwarfs forces much of their flux to be emitted within these bands, resulting in the extreme far‐optical and near‐IR colors that are used to identify L and T dwarf candidates from photometric surveys like the Two Micron All Sky Survey (2MASS; Beichman et al. 1998) and the Sloan Digital Sky Survey (SDSS; York et al. 2000).

(80 KB)

Fig. 1.— Normalized observed spectra for an L5 and a T4.5 dwarf from Geballe et al. (2002). The principal absorption bands in the dwarf spectra are identified, and the bandpasses for the MKO J, H, and K filters (left to right) are shown as dashed lines.

Open New Window

There are now hundreds of L and T dwarfs with near‐IR magnitudes published in various photometric systems. To maximize the science potential of these observations and their impact on brown dwarf theory, transformation equations are desirable to convert these and any future magnitudes to a common photometric system. Because the J, H, and K bandpasses include , CO, and absorption features, any variation in the width of the filters will lead to system‐dependent magnitudes. Therefore, transformation equations need to be derived as a function of near‐IR spectral type, or, less desirably, color (see discussion in § 4) to correctly account for the presence of the molecular bands.

Figure 2 shows J−K color as a function of spectral type for typical main‐sequence stars (A0–M5) in the Bruzual‐Persson‐Gunn‐Stryker Spectrophotometry Atlas,1 and late M, L, and T dwarfs reported in Leggett et al. (2002). Important features to note, all of which are explained more fully in other works (e.g., Leggett et al. 2002) are: the intrinsic spread in J−K for the L dwarfs, which may be produced by variations in the extent and location of the condensed grain layer in the photosphere; the increasingly bluer J−K color for the late L dwarfs and T dwarfs, which is mostly due to the appearance of the band at 2.2 μm; and the scatter in J−K for the latest T dwarfs, likely due to gravity‐dependent opacity. Although T dwarfs can have the same value of J−K as A through M stars, convolving a T dwarf spectrum with its strong molecular absorption bands (Fig. 1) with any JHK bandpass will produce a very different result from the convolution of, e.g., the Rayleigh‐Jeans curve of an A0 star with the bandpass. Consequently, transformations based on the colors of hotter stars are not valid for L and T dwarfs, and photometric transformations must be derived directly from observations of these ultracool dwarfs.

(41 KB)

Fig. 2.— Observed MKO J−K colors for several late M (squares), L (triangles), and T dwarfs (circles) as a function of spectral type (Leggett et al. 2002). Synthetic J−K values generated for the standard main‐sequence stars in the Bruzual‐Persson‐Gunn‐Stryker spectral atlas are also shown for comparison (pentagons).

Open New Window

In this paper we present synthesized J, H, and K magnitudes using near‐IR spectroscopic observations of L and T dwarfs from each spectral subtype, for the photometric systems in which L and T dwarf photometry has most frequently been published and for established systems in which future observations may occur. The photometric systems presented are: 2MASS (Carpenter 2001), Caltech (CIT; Elias et al. 1982), the Deep Near‐Infrared Survey (DENIS; Fouqué et al. 2000), Las Campanas Observatory (LCO; Persson et al. 1998), Mauna Kea Observatory (MKO; Simons & Tokunaga 2002; Tokunaga, Simons, & Vacca 2002), the U.S. Naval Observatory Flagstaff Station (NOFS; Dahn et al. 2002; Guetter et al. 2003), and the United Kingdom Infrared Telescope (UKIRT; Hawarden et al. 2001). We also generate equations to transform J, H, and K magnitudes between the other systems and the MKO system. The MKO photometric system was chosen as the reference point because MKO filters are narrower than classical J, H, and K filters, thus avoiding the telluric absorption bands that can vary with time and observing location (see discussion in Simons & Tokunaga 2002; Tokunaga et al. 2002). As a result, MKO magnitudes have little dependence on local observing conditions, and their use produces transformation equations with less uncertainty than would be obtained using another photometric system. In addition, the MKO filters have been widely adopted, and the system is endorsed by the IAU Working Group on Infrared Astronomy as the preferred photometric system for ground‐based near‐IR observations.

In § 2 we present the observed differences in the 2MASS and MKO magnitudes that have been measured for several L and T dwarfs, showing that system transformations cannot be reliably derived empirically because of significant uncertainty in the observational data. Section 3 discusses the inputs for synthesizing magnitudes: filter transmission profiles, telluric absorption bands, instrument optics, and observed spectra. Our results are presented in § 4 and our conclusions given in § 5.

2. OBSERVED MAGNITUDES IN DIFFERENT SYSTEMS

Figures 3 and 4 compare the J, H, and K magnitudes, and J−H, H−K, and J−K colors for a sample of L and T dwarfs that have been observed in both the 2MASS and MKO photometric systems. These are the only systems with a large enough number of L and T dwarfs in common to make a meaningful observational comparison. 2MASS magnitudes for these objects were taken from the 2MASS L dwarf archive Web page2 and A. Burgasser’s T dwarf Web page.3 The MKO magnitudes are reported in Leggett et al. (2002). Figure 3 plots δmag as a function of spectral type, and Figure 4 plots δmag as a function of J−K (on the MKO system), which provides the largest baseline.

(82 KB)

Fig. 3.— Observed , , , δ(J−H), δ(H−K), and δ(J−K) mag as a function of spectral type for the 2MASS and MKO systems. L dwarfs are shown as triangles, and T dwarfs as circles. Error bars are omitted in the lower plot for clarity.

Open New Window

(73 KB)

Fig. 4.— Observed , , , δ(J−H), δ(H−K), and δ(J−K) mag as a function of color for the 2MASS and MKO systems. L dwarfs are shown as triangles, and T dwarfs as circles. Error bars are omitted in the lower plot for clarity.

Open New Window

Spectral type is taken from Geballe et al. (2002), who define a classification scheme for both L and T dwarfs based on the strength of the near‐IR absorption bands. This classification gives results very similar to the scheme presented for the T dwarfs by Burgasser et al. (2002). However, the scheme for L dwarfs presented by Kirkpatrick et al. (2000), which is based on red spectra, can assign L dwarf spectral types that differ by up to 2.5 subclasses from the Geballe classification. For the samples shown in Figures 3 and 4, the average difference in L dwarf classification is only 1.0 subclass. Therefore, given the size of the observational uncertainty (see the figures) the choice of classification scheme is not significant.

Despite the large observational uncertainty in Figures 3 and 4, it can be seen that there are significant differences in the magnitudes, especially at J, and that general trends in δmag with type do exist. The difference between systems can be understood with reference to the spectra shown in Figure 1. The 2MASS J filter is wider than the MKO J, and 2MASS K is narrower than MKO K (§ 3.1); the wider filters include more of the absorption bands of and without increasing the signal, and hence, with reference to the calibrator, L and T dwarfs appear to be fainter in the systems with wider filters. As these features become stronger with later spectral type, the effect is more pronounced, and trends appear, with 2MASS J becoming increasingly fainter than MKO J, and MKO K fainter than 2MASS K. Although these trends can be seen, the considerable uncertainty in the data prevents the determination of reliable system transformations from direct observations. In the following sections we derive and discuss theoretical transformations between these and other systems.

3. CALCULATION OF SYNTHETIC MAGNITUDES

3.1. Filters

Figure 5 shows the filter profiles for the 2MASS, CIT, DENIS, LCO, MKO, NOFS, and UKIRT JHK filters at instrument temperatures. The 2MASS filter profiles were obtained from the 2MASS Web pages,4 the MKO filter profiles were obtained from the UKIRT Web pages,5 and the UKIRT profiles from Hawarden et al. (2001). The LCO profiles were generated with tables obtained from Persson et al. (1998), the DENIS profiles were obtained from P. Fouqué (2002, private communication), and the NOFS profiles were obtained from F. Vrba (2003, private communication). The CIT H and K profiles measured at operating temperature were obtained from the Cerro Tololo Inter‐American Observatory (CTIO) infrared instrumentation Web page,6 where they are identified as 25 mm OCLI H and K filters. We selected these filters for CIT H and K because they match the documented CIT bandpasses (Elias et al. 1982). The CIT J profile measured at ambient temperature was also obtained from the CTIO Web site, where it is identified as CIT J. A shift to bluer wavelengths was required to correct this profile to values appropriate for operating temperatures.

(159 KB)

Fig. 5.— Filter bandpasses for the systems considered here (solid line) and with atmospheric absorption (dotted line). The Elias J bandpass is drawn in the same box as the CIT J bandpass, both without atmospheric absorption (dash‐dotted line) and with (dashed line).

Open New Window

We attempted to determine the appropriate shift for the CIT J band from the literature; however, there is a discrepancy between the cold transmission profile measured for CIT J by H. Jones (1994, private communication between E. Persson and H. Jones; see also Jones et al. 1994) and the bandpass given by Elias et al. (1982). Therefore, two independent shifts were made to the CIT J bandpass, producing two different transmission profiles. The first shift moved the bandpass ∼0.015 μm and was chosen to produce a bandpass identical to the one determined for the CIT system by H. Jones. We refer to this filter bandpass as CIT J throughout the rest of the paper (solid line in Fig. 5). The second J bandpass was created by shifting the ambient J profile ∼0.04 μm to match the CIT J bandpass specified by Elias et al. (1982). In determining this shift, we assume that the Elias et al. (1982) bandpass limits do not include atmosphere (see § 3.2), and we refer to this bandpass in the paper as Elias J (dash‐dotted line in Fig. 5).

Since the original 1980s‐era CIT filter profiles no longer exist (J. Elias & E. Persson 2003, private communication), it is not clear which transmission profile represents the original CIT J filter. The Elias J bandpass involves a ∼3% shift in wavelength of the Web page listed ambient profile, which is about twice the value seen for the UKIRT filters on a cool‐down from ambient to 77 K. In this regard, the bandpass measured by Jones seems more reasonable. However, we present both profiles in this work, as the bluer bandpass is specified in the defining work by Elias et al. (1982). Note that the red cutoff of each filter is effectively defined by the atmosphere, but the differences in the blue cut‐on produces significant systematic differences in the J magnitudes, as we show in § 4. The H and K magnitudes are well determined, as these profiles agree with the Elias et al. (1982) bandpasses and are identical to the CIT profiles measured by H. Jones (1994, private communication; see also Jones et al. 1994).

4. RESULTS

Tables 1, 2, and 3 list the synthesized J, H, and K magnitudes, respectively, in the various systems for the sample of 24 L dwarfs and 17 T dwarfs. The magnitudes are given to the millimag level, despite the 0.03–0.05 mag uncertainty in these derived magnitudes, because we wish to avoid introducing errors in the transformations by rounding off the synthetic magnitudes to too low a level of significance. The transformations are given by the difference in magnitudes from each system, and as systematic errors in the flux calibration cancel out, the uncertainty in this difference is smaller than that in the original photometry. The uncertainty in the transformation is determined only by the weighting of the noise in the spectra by each bandpass, and also by any uncertainty in the definition of the bandpass (see §§ 3.1, 3.2, 3.4, and further discussion below).

TABLE 1 Synthesized J‐Band Photometry

Open New Window

TABLE 2 Synthesized H‐Band Photometry

Open New Window

TABLE 3 Synthesized K‐Band Photometry

Open New Window

Figure 6 shows the calculated differences in JHK for the various photometric systems as a function of spectral type, and Figure 7 the difference in the colors as a function of type. Figures 8 and 9 also show δmag and δcolor, this time as a function of J−K_MKO. The trends in δ(2MASS−MKO) agree well with the observed trends shown in Figures 3 and 4. Other observational comparisons are very limited. Only three L dwarfs have independently measured J and K in both the DENIS and MKO systems, and for these the agreement with Figure 6 is reasonable, but the observational uncertainties are large. No data currently exist in the LCO system for L and T dwarfs. Data have been published for some dwarfs in both the UKIRT and MKO systems, but these are not independent measurements; instead, one data set has been synthesized from the other, as we have done here. Photometry for several L and T dwarfs obtained with the NOFS filters has been published by Dahn et al. (2002) and calibrated using Elias et al. (1982) standards (Guetter et al. 2003). Comparison of the NOFS‐system magnitudes with MKO data for 15 L dwarfs and 2 T dwarfs in common produces δmags that agree well with our derived sequences at J and H, but that differ at K for the two T dwarfs by ∼0.2 mag (compared to the measurement uncertainty of ∼0.1 mag). These results will be investigated further when more data from this group are available.

(131 KB)

Fig. 6.— Synthesized , , and mag as a function of spectral type for all the systems considered here. L dwarfs are shown as triangles, and T dwarfs as circles. Synthesized δmags using the Elias J filter are shown as open symbols. The solid lines show the cubic fits given in Table 4.

Open New Window

(129 KB)

Fig. 7.— Synthesized δ(J−H), δ(H−K), and δ(J−K) mag as a function of spectral type for all the systems considered here. Symbols are as in Fig. 6.

Open New Window

(130 KB)

Fig. 8.— Synthesized , , and mag as a function of color for all the systems considered here. Symbols are as in Fig. 6. The solid lines show the fits given in Tables 5 and 6.

Open New Window

(132 KB)

Fig. 9.— Synthesized δ(J−H), δ(H−K), and δ(J−K) mag as a function of color for all the systems considered here. Symbols are as in Fig. 6.

Open New Window

In Figures 6 and 7 spectral type is given on the infrared typing scheme of Geballe et al. (2002). As discussed in § 2, the optically‐based L dwarf classification scheme of Kirkpatrick et al. (2000) can lead to differences in spectral classification of up to 2.5 subclasses, although the average difference for this sample is only 1.0 subclass. The uncertainty in the Geballe classification is typically 0.5 subclasses, and, given the slow change in δmag with type for L dwarfs, the sequences shown in Figures 6 and 7 should be effectively independent of the classification scheme. We tested this by fitting δmag values using both the Geballe and Kirkpatrick classifications, and the difference for a given L type was always substantially less than the standard deviation of the fit.

As an additional check, we determined the difference in δmag that would occur if spectral type was allowed to vary by two L sub‐classes, simulating the difference in classification that can occur between the visible and near‐IR classification systems. For the case of the 2MASS J filter, which is a relatively steep function of type, the difference in δmag between L6 and L8 types is 0.017 mag. The sensitivity to type for earlier L spectral types is <0.01 mag, and the H and K filters are insensitive to L dwarf type, as can be seen in Figure 6. Hence, uncertainties in L spectral type lead to uncertainties in δmag of <0.01 mag, except for late‐L dwarfs at J, for which large uncertainties could lead to an uncertainty of ∼0.02 mag. Note that for determining near‐IR photometric system dependencies, an infrared scheme is more appropriate than an optical scheme and should give a tighter relationship between δmag and type.

The δmag/type sequences can be well fitted mathematically. Table 4 gives the results of cubic fits to , , and as a function of type, all with respect to the MKO system, and the standard error of the fit in magnitudes (colors can be calculated by differencing the relations). The accuracy of the derived transformations are quite good—the standard error is better than 0.01 mag. The fits to δmag with type can be seen as solid lines in Figure 6. The scatter around the fits is small, 0.005–0.020 mag, which is consistent with the noise in the spectra.

TABLE 4 Coefficients of Cubic Fit to [δmag, Spectral Type]

Open New Window

The δmag/J−K relationship is more difficult to fit because of the degeneracy in colors between early L and T dwarfs, the degeneracy within the L dwarfs, and the intrinsic spread in JHK colors of L and T dwarfs with the same spectral type (§ 1, Fig. 2). Objects with different spectral morphologies can have the same color but will have different values for δmag. Consequently, transformations based on color alone will combine dwarfs with different spectral characteristics and produce a δmag value that will be less accurate than the value based on spectral type. This is a problem in particular for as a function of J−K, as can be seen in Figure 8. Tables 5 and 6 give the results of fits to , , and as a function of J−K color in each of the photometric systems: Table 5 gives the coefficients for the quadratic fit found for , and Table 6 gives the coefficients for and , which were well fitted with linear equations. These fits are shown as solid lines in Figure 8. The scatter around the fits at J is 0.005–0.070 mag, at H it is 0.003–0.030 mag, and at K 0.015–0.030 mag. Thus, H and K magnitudes can be transformed almost equally well using either spectral type or color, but J magnitudes transformed from color will be much more uncertain than those based on type. Separating the L and T dwarfs can produce better transformations for the J filter; these fits, and fits using other color combinations, can be determined using the synthetic magnitudes given in Tables 1–3.

TABLE 5 Coefficients of Quadratic Fit to [δ , J−K]

Open New Window

TABLE 6 Coefficients of Linear Fit to [δH, δK mag, J−K]

Open New Window

To summarize, if the spectral type of the dwarf is known and the filter can be regarded as well determined, then J, H, and K transformations can be determined to ∼0.01 mag using the equations provided in Table 4. Therefore, for most observations the original measurement uncertainty (typically ≳0.03 mag; see, e.g., Fig. 3) will limit the accuracy of the transformed magnitude. However, other uncertainties do exist that can significantly affect the J magnitudes, or colors involving J. The CIT J bandpass is not well known, and the profiles of the wider J filters are determined by a possibly variable atmosphere; we showed in § 3.2 that a plausible range in water vapor levels can lead to variations in the J magnitudes of 0.05–0.10 mag for T dwarfs for such filters. For late‐L dwarfs, an uncertainty in spectral type of two subclasses can lead to an uncertainty in mag. If the spectral type is not known at all, then transforming based on J−K color leads to an uncertainty in mag. For mid‐L through T types, variations between detectors can result in an additional, but small, uncertainty in mag (§ 3.3). The H and K bandpasses are better behaved. Detector response uncertainty is only expected to impact K, and then only for late‐T dwarfs at the 0.01 mag level. Also, for H and K, transformations can be derived to ∼0.02 mag on the basis of color alone.

5. CONCLUSIONS

To obtain accurate and stable photometry, filter bandpasses should not go into poor regions of the terrestrial atmosphere—most (classical) J filters are poorly defined from this point of view. Variations in the water vapor content change the effective bandpass of such filters, and for objects with extremely structured spectral energy distributions such as T dwarfs these changes produce photometric deviations of ∼0.05–0.10 mag. To measure magnitudes and colors better than this requires use of a filter set that is well matched to the atmosphere, such as the MKO filter set.

JHK magnitudes for L and T dwarfs are highly dependent on the photometric system used for the observation; for T dwarfs, differences between systems can be several tenths of a magnitude. However, we have shown that JHK magnitudes for L and T dwarfs can be transformed between the 2MASS, CIT H and K, DENIS, LCO, NOFS, and UKIRT systems and the MKO system to ∼0.01 mag if the spectral type of the dwarf is known. This is significantly better than the typical measurement uncertainty (i.e., the original uncertainty in the measurement will determine the accuracy of the transformed value). For the CIT system the uncertainty in the J bandpass affects the derived magnitudes by 0.05–0.10 mag for L and T dwarfs. Variations between the optical elements of common infrared instrumentation are expected to impact the measured magnitudes of the late L and T dwarfs at the 0.01 mag level. If spectral type is not known, then J−K color can be used to transform H and K magnitudes measured in different systems with an accuracy of about 0.02 mag, but the J value can only be derived to ∼0.05 mag on the basis of color alone.

The results presented here will be valuable for researchers in the very active field of ultracool dwarf studies, where imaging data are plentiful, and where the data have unfortunately been obtained with a variety of photometric systems. Transformations based on the colors of hotter stars, even if the stars have the same color, cannot be applied to objects with strong molecular absorption bands such as those seen in L and T dwarfs. For these ultracool objects, comparison of photometric data requires knowledge of the filter profiles at instrument temperature and knowledge of the local atmospheric transmission. If JHK photometry is obtained with a well‐understood photometric system, we have shown that such data sets can be accurately combined or compared.