Zmass Ks epoch 1999.855 *

Figure 6.8. e Indi Bab, the binary T dwarf companion to the nearby K5 dwarf, e Indi A. The separation between the two components is 7 arcminutes (courtesy of R. Scholz and Astronomy & Astrophysics).

colours change with decreasing absolute magnitude through the L and T regime. Those diagrams only include systems with accurate distance measurements. Although trigonometric parallax data are available for over 50 systems ([Dl], [V2]), those objects still represent a small subset of known L and T dwarfs.

An alternative way of tracking changes is to consider the variation with spectral type, since almost all known L and T dwarfs have types that are tied to the standard systems [K5], [G7], [B12], and spectral type serves as a reasonable surrogate for effective temperature. Hawley et al. [H7] have averaged results for M, L and T dwarfs with SDSS and 2MASS photometry, and Figure 6.9 plots the mean colour as a function of spectral type for several combinations of these passbands. Among the more notable features are the reversal in (r-i) at ~M9 (due to weakening TiO absorption) and the turnaround in (z-K) and (J-K) at ~T0 (due to the increasing strength of methane bands in the K passband). The (i-z), (i-J) and (z-J) sequences are all close to monotonic with spectral type. Of these three, (z-J) generally offers the best prospects for extending ground-based surveys, since T dwarfs are brightest at J and, allowing for the extremely red colours, the z passband is the most sensitive optical passband for ultracool dwarfs.

The onset of methane absorption has a significant effect on the luminosities of cool dwarfs at near-infrared wavelengths. The impact at H and K is obvious, but the J passband is also affected, in the opposite sense. Figure 6.10 shows the run of MJ and MK with spectral type. With the acquisition of more parallax measurements, it became clear that the mid-type T dwarfs (T3-T5) are actually brighter in MJ than late-type L and early-type T dwarfs (L6-T2). This is at least partly due to the presence of higher opacities at longer and shorter wavelengths in T dwarfs, which force a higher proportion of the total flux into the relatively transparent 1.2-^m window. Note, however, that the effect is also present, to a lesser extent, in the K passband, which includes strong CH4 absorption. We consider this behaviour further in the discussion of the L/T transition in Section 6.7.3.

Many of the brighter L and T dwarfs have ground-based observations in the L and, in a few cases, M passbands (3 and 5 ^m). Figure 6.11 shows the colours as a function of spectral type. The (K-L) colour increases monotonically with increasing spectral type, with significant dispersion at later types, as is the case with (J-K). The (L-M) colour becomes increasingly negative from M0 to L5, but that trend reverses at later types. The negative colours imply that there is more flux at 5 ^m than predicted by a black-body extrapolation from 3 ^m. Spitzer is providing more extensive mid-infrared observations of a much larger sample of ultracool dwarfs, generally confirming these results.

6.7.2 Bolometric corrections and the temperature scale

Section 2.3 emphasised the importance of observations at infrared wavelengths in mapping out the spectral energy distribution of cool dwarfs. Mid-infrared data are particularly important for ultracool dwarfs, since the cooler temperatures and the more diverse range of opacity sources leads to significant deviations from the simple Rayleigh-Jeans flux distribution at these wavelengths (Figure 6.11). Recent high-quality L and M photometry [G8], coupled with flux-calibrated near-infrared spectra, enable reliable measurement of bolometric magnitudes for a large sample of M, L and T dwarfs (Figure 6.12(a)), and those results, in turn, allow a closer examination of the likely temperature range spanned by spectral classes L and T.

Given a measurement of bolometric luminosity, the effective temperature can be derived using Equation (1.28), provided that one has an estimate of the radius.

Figure 6.9. Far-red and near-infrared colours for late-type dwarfs as a function of spectral type (from [H7], courtesy of the Astronomical Journal). Note that the optical colours are on the SDSS/Gunn system (Table 1.1) and represents preliminary SDSS processing, as indicated by the * (see [H7]).
Figure 6.10. MJ and MK as a function of spectral type for L and T dwarfs with accurate trigonometric parallax measurements (from [V2], courtesy of the Astronomical Journal).
Figure 6.11. 3-5 ^m colours of M, L and T dwarfs (from [G8], courtesy of the Astronomical Journal).

Lacking direct measurements, the radius is usually taken from evolutionary models (e.g., [Bl], [B7]). For brown dwarfs, this demands an age estimate - at a given luminosity, young, low-mass brown dwarfs have larger radii than older, more massive objects. Since all of the calibrating sources are isolated brown dwarfs in the immediate Solar Neighbourhood, most studies adopt ages of 3-5 Gyr, corresponding to the average age of the local stellar population. Fortunately, the brown dwarf radius is not a very strong function of mass, varying by at most 30% (see Section 3.5.3). This corresponds to an upper limit of ~300K in the uncertainty of the temperature estimates.

Figure 6.12 shows the results from the most recent study that uses M^ol to derive temperature estimates. The formal best-fit polynomial relation (from [G8]) is:

Teff = 14,322 - 5,128.7 x SpT + 909.51 x SpT2 - 83.099 x SpT3

+ 4.0323 x SpT4 - 9.8598 x 10-2 x SpT5 + 9.5373 x 10-4 x SpT6 (6.2)

M5 LO L5 TO T5

M5 LO L5 TO T5

M5 LO L5 TO T5

Spectral Type

Figure 6.12. Bolometric corrections and effective temperatures of ultracool dwarfs as a function of spectral type (from [G8], courtesy of the Astronomical Journal). The solid lines plot 4th order and 6th order polynomial fits, respectively (see equation (2.4) for the BC^ calibration).

M5 LO L5 TO T5

Spectral Type

Figure 6.12. Bolometric corrections and effective temperatures of ultracool dwarfs as a function of spectral type (from [G8], courtesy of the Astronomical Journal). The solid lines plot 4th order and 6th order polynomial fits, respectively (see equation (2.4) for the BC^ calibration).

The temperature range spanned by spectral class L is close to prior estimates (e.g., [K5], [R3]; see Section 4.7), with Teff — 2,250 K at LO and Teff — 1,400 K at L8. The variation with temperature is almost linear for —M7-L7 and T4-T8. However, these data suggest that the average temperature is effectively constant at —1,400 K from spectral type L7-T3. Taken at face value, this implies that brown dwarfs spend a very short time evolving through this transition. Appearances may be deceiving, however, as will be discussed further in the following section.

We can match the temperature/spectral type calibration illustrated in Figure 6.12(b) against the theoretical evolutionary tracks shown in Figure 6.1 to estimate the relative mix of stars and brown dwarfs as a function of spectral type. In doing so, we need to bear in mind that brown dwarfs can appear at any temperature below —3,200 K (spectral type —M4), although their residence times are short at higher temperatures. The Tucson models plotted in Figure 6.1 predict that 0.08 M0 stars settle onto the main sequence at a temperature of —2,100 K, corresponding to spectral type L1; 0.075-M0 transition objects spend several Gyr at temperatures above 1,700 K, spectral type ~L4. Thus, hydrogen-burning stars dominate at spectral types earlier than ~L1; there is a mix of stars and brown dwarfs between L1 and L4, with the relative number of stars decreasing with increasing spectral type; and effectively all objects with spectral types L5 and later are brown dwarfs. In the Lyon models, the hydrogen-burning limit falls at a slightly lower mass (0.072 M0), and 0.075-M0 dwarfs are predicted to stabilise at ^2,000 K, but the overall picture is very similar.

6.7.3 Atmospheres, dust and the L/T transition

Temperature is the main parameter that drives spectral variations along the main sequence from O to M, and decreasing temperature also underlies most of the changes from L0 to T8. However, Figure 6.12(b) strongly suggests that some other factor is responsible for spectral evolution from L7 to T3. What are the physical changes that occur in brown dwarf atmospheres during the transition from spectral type M through L to T?

As summarised in Section 4.7, dust formation is an important process that affects spectral evolution in late M and L dwarfs. One of the main consequences is high atmospheric transparency at optical wavelengths, as the principal molecular opacity sources (TiO, VO) are removed to the solid phase [B8], [F1]. The atmospheres of L and T dwarfs are extremely non-grey, with the r = 1 level varying significantly in physical depth (and hence temperature) as a function of wavelength. The 'photosphere' lies at greater physical depth at A < 1 ^m, and the alkali atomic lines acquire increasing prominence due to high column density, high gas pressure (at r = 1) and increased contrast relative to the continuum. As the temperature decreases, those lines increase in strength until the parent elements form molecular species. In the case of the two most abundant elements, sodium ([Na] = 6.31) and potassium ([K] = 5.13), the lowest excitation (resonance) lines achieve white dwarf proportions in the coolest dwarfs, with exceedingly broad Lorentz damping wings caused by the high-pressure van der Waal's broadening. The sodium D lines become a 1,500 A wide bowl-like depression by spectral type L5 (Figure 6.13), while the potassium 7,665/7,699 A doublet broadens to a width of 500 A by L8 and exceeds 1,000 A in the cooler T dwarfs (see further below). These resonance atomic lines become sufficiently strong that they affect the flux emitted in the broadband V and R passbands (Na D lines) and Iji and z passbands (K I doublet), to the extent that those colours can be used to test chemical equilibrium models [M6].

Dust plays a more active role in influencing the flux distribution at near-infrared wavelengths. Backwarming in late-type M dwarfs, where dust first makes its appearance, heats the atmosphere, dissociates H2O, and, as a result, reduces the depth of the water bands [T12]. Dust continues to affect the near-infrared colours through the L dwarf sequence [T14]. Figure 6.14 compares the observed (My, (J-K)) diagram against brown dwarf models with dusty atmospheres, where dust is maintained at its depth of formation, and dust-free atmospheres, where the dust formation is taken into account in the equation of state and in the depletion of chemical species

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