Lyα DOMINANCE OF THE CLASSICAL T TAURI FAR-ULTRAVIOLET RADIATION FIELD

We employed a multi-Gaussian IDL line-fitting code, optimized for COS emission line spectra, to measure the total flux from Lyα-pumped H₂. This code assumes a Gaussian line shape convolved with a wavelength-dependent line spread function, then uses the MPFIT routine to minimize χ² between the fit and data (Markwardt 2009). An unconvolved Gaussian was used for TW Hya observed with the Space Telescope Imaging Spectrograph (STIS). To reconstruct the local Lyα profile incident upon the molecular disk surface, we measured the total flux from 12 fluorescent progressions excited by Lyα. We chose to restrict the emission line analysis to the 1395–1640 Å range to mitigate the effects of H₂ self-absorption, which are strongest at λ ≲ 1400 Å (Herczeg et al. 2004). The brightest, unblended lines from 12 progressions in the 1395–1640 Å bandpass (up to 38 lines) were fitted. We refer the reader to France et al. (2012) for additional information on the H₂ emission characteristics of our sample, including progression IDs for all lines measured.

The total flux from progression m is given by

where F_mn is the reddening corrected, integrated H₂ emission line flux (in units of ergs cm⁻² s⁻¹) from rovibrational state m (=[, ]) in the B¹Σ⁺ _u electronic state to n (= [,]) in the ground electronic state, X¹Σ⁺ _g . B_mn is the branching ratio for each transition in a progression, defined as the ratio of the Einstein A-value for a given transition m → n () to the total transition rate out of state m, including transitions to bound states and the vibrational continuum (Stecher & Williams 1967; Wood & Karovska 2004; France et al. 2011b). N is the number of emission lines measured from a given progression.

We take the error to be the standard deviation of the individual measurements of F_m (H₂), as this is the relative uncertainty in H₂ fluxes in most cases. These standard deviations are typically less than 10% for bright progressions, and as high as 20%–30% in weaker progressions. The primary uncertainty in H₂ luminosities relates to the extinction correction (see A_V in Table 1), although to zeroth order this would affect all progressions similarly as they have been chosen from a narrow range of wavelengths. Upper limits on the H₂ emission line fluxes of undetectable progressions were determined from the standard deviation in a ±50 km s⁻¹ region surrounding the laboratory wavelength of the transition.

The flux incident on the H₂ (I_inc(λ_m ), in units of ergs cm⁻² s⁻¹ Å⁻¹) at each H₂ absorbing transition wavelength λ_m was then assumed to be the total progression flux divided by the equivalent width (W_λ) of the absorbing H₂ transition:

where each [v, J] state of the ground electronic level is populated by a single rotational temperature () and column density (). Non-thermal populations can result from dust heating and photoexcitation by the strong X-ray and UV radiation fields (Nomura et al. 2007; Gorti & Hollenbach 2009). However, a degeneracy exists between and in our model, discussed further in Section 3.2. As a first-order approximation to simplify this degeneracy we assume a thermal population. To determine W_λ, we used a grid of in 100 K increments from 1000 K to 5000 K, and in 0.1 dex increments from 10¹⁶ to 10²² cm⁻². Models with < 1000 K produce a negligible population in the v = 2 level of the ground electronic state and are therefore not considered. For each of the 12 transitions, we calculated a set of I_inc for each pair of and . Each pair of and therefore creates 12 unique values of I_inc.

Our reconstruction technique finds the set of outflow-absorbed Lyα profiles (I_ab, in units of ergs cm⁻² s⁻¹ Å⁻¹) that best fit the variety of I_inc values. The model assumes that Lyα emission is created near the stellar surface. Some amount of H i lies in between the Lyα source and the H₂, absorbing some of the Lyα photons before they reach the H₂. For each target, we create a grid of I_ab profiles, each with its own single Gaussian emission component and single outflow H i absorber:

C_Lyα is the average continuum flux per Angstrom near Lyα. I_Lyα is the accretion/magnetospheric-generated Gaussian emission profile, centered at the stellar radial velocity and parameterized by amplitude I₀ and FWHM (in units of ergs cm⁻² s⁻¹ Å⁻¹ and km s⁻¹, respectively). The optical depth τ_out is determined with a Voigt profile for the H i Lyα transition, characterized by an outflow velocity v_out and column density N_out (in units of km s⁻¹ and cm⁻², respectively). This outflow absorption component is essential to adequately fitting the I_inc values.

For each I_ab model profile, a χ² is calculated with each set of [, ]-dependent I_inc. We then exclude any sets of and which yield a χ² greater than 95.4% (2σ) from the peak of the χ² probability distribution. The H₂ progressions for which only upper limits are calculated provide additional constraints on the Lyα profile; we reject any Lyα profile with a flux greater than an upper limit value at that wavelength. Given the various combinations of I₀, FWHM, v_out, N_out, , and , a variety of Lyα profiles adequately fit the I_inc values. This is demonstrated in Figure 1, where several combinations of I_Lyα, I_ab, and I_inc are shown. We quantify the overall distribution of I_Lyα profiles for each target by integrating each I_Lyα profile from 1210 Å to 1222 Å, resulting in fluxes F_Lyα (in units of ergs cm⁻² s⁻¹) which form an approximately Gaussian distribution.

The average F_Lyα (〈F_Lyα〉) of each target is listed in Table 1, along with the 1σ width of the distribution. 〈F_Lyα〉 represents the total Lyα flux at the star and is generally constrained to within 10%–20%. We also include the average emission FWHM and H i absorber properties (N_out and v_out). Integrating I_ab, the H₂-incident Lyα flux, yields 〈F_ab〉. Assuming a thermally populated ground state distribution, typical values are ∼2500 ± 1000 K and log((cm⁻²)) ∼19 ± 1, similar to those found in TW Hya (Herczeg et al. 2004). Strong UV and X-ray irradiation from the central star would act to preferentially populate excited rovibrational levels in excess of the thermal distribution (see, e.g., Nomura et al. 2007). In our simple model, non-thermal excitation would be approximated by higher rotational temperatures, and this increase in rovibrational population will be offset by lower total H₂ column densities. The varying effects of non-thermal excitation most likely contribute to the spread of the observed and values. Lower can require increased Lyα flux, although we expect that this increase will be of the same order of the uncertainty on the derived Lyα emission flux (∼10%–20%). Untangling the effects of non-thermal populations requires more complex modeling, including the effects of H₂ formation on dust grains, and disk modeling efforts that predict the UV fluorescent spectrum of H₂ (and CO) would be very valuable. Regardless, the overall model Lyα properties follow approximately Gaussian distributions. Figure 2 compares 〈F_Lyα〉 and the observed Lyα fluxes (F_obs; summed over the entire profile) with the total H₂ fluxes. F_obs has a Spearman ρ rank correlation coefficient of 0.57 while 〈F_Lyα〉, by design, has a ρ of 0.96.

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Ideally we would compare our model Lyα profiles with the observed Lyα profiles. However, this involves additional parameters and a more complex analysis than presented here. Primarily, the radiative transfer of Lyα photons between the source, the H₂, and Earth must account for the geometric filling fraction η. This fraction represents the solid angle of H₂ illuminated by the Lyα emission, such that η = 1 implies that the H₂ completely surrounds the star. An η other than 1 would enter Equation (2) by multiplying I_inc(λ_m ) by η. Herczeg et al. (2004) found η = 0.25 for TW Hya, implying gas in a disk surface layer. However, Wood et al. (2002) measured η > 2 in Mira B. A filling factor greater than 1 would possibly correspond to preferential scattering of H₂ photons into, or more likely Lyα photons out of, our line of sight (Wood et al. 2002). Future analysis will incorporate η into a more detailed radiative transfer model of our sample targets.

We determine the fraction of the total FUV output from CTTSs that is in the Lyα emission line, adopting a definition of the Lyα fraction, f_Lyα, given by

where F_Lyα is our average model Lyα flux from the star (in units of ergs cm⁻² s⁻¹; Section 3.2) and F_FUV is the total unreddened FUV flux, measured over the 1160–1695 Å bandpass (in units of ergs cm⁻² s⁻¹). The wings of the stellar Lyα can extend to >±1000 km s⁻¹ from line center in some targets (see, e.g., Figure 2 (top) from Yang et al. 2011), therefore we excluded the 1207–1225 Å region from the computation of F_FUV. We also excluded the 1300–1310 Å region to remove contamination by the geocoronal O i multiplet. A 5% error is assumed on F_FUV corresponding to the uncertainty in flux calibration. The restriction of the total FUV band to 1160–1695 Å is mainly driven by the lack of supporting FUSE observations at short wavelengths (912–1160 Å) for all targets and the end of the STIS E140M bandpass at 1700 Å.

Molecular line emission from H₂ (Herczeg et al. 2006; this work) and CO (France et al. 2011a; Schindhelm et al. 2012) contributes to F_FUV. The FUV molecular emission is thought to originate from an inner warm disk surface (a ⩽ 3 AU; Herczeg et al. 2004; France et al. 2012) or outflow (Saucedo et al. 2003; Walter et al. 2003). The total FUV flux also includes a molecular continuum whose excitation mechanism and spatial distribution are not well constrained (Bergin et al. 2004; France et al. 2011b). 〈F_Lyα〉 shows a much better correlation with F_FUV than F_obs (Figure 2). This is consistent with the idea that both the Lyα and FUV continuum emission are produced by related processes.

We also calculate an observed Lyα fraction (f_obs) using F_obs instead of F_Lyα in Equation (5). We compare f_obs and f_Lyα with the total H₂ flux in Figure 3. For our general assumption of η = 1, we find an average 〈f_Lyα〉 of 81% ± 9%, compared with 15⁺²¹ _{− 15}% for 〈f_obs〉. For η = 0.1, 0.25, 0.5, and 2.0, 〈f_Lyα〉 is 97%, 94%, 90%, and 69%, respectively. A slight trend for decreasing 〈f_Lyα〉 with increasing F_FUV is apparent, although this may be inappropriately weighted by BP Tau and TW Hya. Regardless, our calculated 〈f_Lyα〉 values demonstrate the validity of previous assertions that Lyα emission dominates the FUV radiation field from CTTSs (e.g., Bergin et al. 2003).

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