Hydrogen Emission from Accretion and Outflow in T Tauri Stars

The progenitors of Sun-like stars are the T Tauri stars. They are low mass $\lesssim 2~\textrm{M}_{\odot}$, young pre-main sequence stars known for their variability, strong magnetic fields, accretion disc, and mass outflows (Johns-Krull, 2007; Hartmann et al., 2016). Classical T Tauri stars (CTTS) have observed excess ultraviolet and infrared continuum; their emission lines can be strong and have complex kinematic profiles (Reipurth et al., 1996). However, the origin of the radiation is not fully understood. By modelling the T Tauri emission, insight can be gained into the accretion, outflow, and the processes of angular momentum transfer present in these stars.

Koenigl (1991) proposed that the accretion mechanism is similar to that of neutrons stars developed by Ghosh et al. (1977). In this formalism, known as magnetospheric accretion, the magnetic field truncates the disc at a radius $R_{\rm T}$, where the magnetic and material stresses are of the same order. The accreting material free-falls from the disc to the stellar surface along the magnetic field, creating an accretion column or funnel. The in-falling matter thermalises the kinetic energy as it impacts the stellar surface forming a shock zone or “hot-spots”. The large energy release heats the gas to $\approx 10^{6}{\rm~K}$ and could be responsible for the high blue and UV excesses observed from T Tauri stars (Hartmann et al., 2016). The presence of an extended magnetosphere allows for angular momentum transport, which that may help explain the observed slow T Tauri rotation (Bouvier et al., 2014). Furthermore, the magnetospheric accretion can explain the red-shifted sub-continuum absorption, known as inverse P-Cygni (IPC) profiles, seen (e.g. Reipurth et al., 1996; Folha & Emerson, 2001; Edwards et al., 1994) in some T Tauri spectra.

Complex radiative transfer models were first employed to study magnetospheric accretion in T Tauri stars by Hartmann et al. (1994). They used a two-level hydrogen model to show that magnetospheric accretion could explain the strong emission lines and blue excess of several T Tauri stars. Muzerolle et al. (1998) further built on the T Tauri model by using a 2D radiative transfer code that performed a multilevel statistical equilibrium calculation for eight hydrogen levels. They concluded that the Br $\gamma$ line profiles could be reproduced for embedded objects, and the Balmer line flux agreed with observations. Muzerolle et al. (1998) and Muzerolle et al. (2001) constrained the accretion column temperature to be between $6000$–$10000{\rm~K}$ and determined that Stark broadening may contribute to the observed broad H $\alpha$ wings ($\pm 500{\rm~kms}^{-1}$). Bouvier et al. (2007) firmly established funnel-flow magnetospheric accretion paradigm, and it is now the generally accepted model for accretion in Classical T Tauri stars.

Blue-shifted sub-continuum absorption (the classical P-Cygni profile) is also observed and interpreted as evidence of the presence of mass outflow (e.g. Edwards et al., 2006; Kwan et al., 2006). Kurosawa et al. (2006) introduced a disc wind and a polar stellar winds into their T Tauri radiative transfer simulations and were able to produce all seven classical line profile classes defined by Reipurth et al. (1996) for H $\alpha$. Kurosawa et al. (2011) showed that a bipolar stellar wind could produce a broad P-Cygni absorption, whereas a narrow P-Cygni absorption was the product of a slow disc wind. Although, it is not clear in which physical paradigms these outflow mechanisms are dominant or whether they coexist.

Another consideration for magnetospheric accretion is that the magnetic fields of T Tauri stars are rarely aligned with their poles (e.g. McGinnis et al., 2020). A magnetic obliquity will cause the accretion funnel to favour specific longitudes of the ascending nodes preferentially (Espaillat et al., 2021). A non-axisymmetric accretion funnel is likely to reduce the frequency of the observed IPC profiles, an effect that has been explored in several studies. For instance, Alencar et al. (2012) successfully used a non-axisymmetric accretion model, based on a magnetohydrodynamic simulation, to perform a radiative transfer simulation of V2129 Oph* in H $\alpha$ and H$\beta$. However, they were unable to reproduce the red-shifted absorption accurately.

Despite the relative success of radiative transfer studies, the T Tauri models still have multiple free parameters and chronic degeneracy. It is unclear how to disentangle the effects of geometry, accretion, and mass loss on the observed spectra. Consequently, although evidence supports the magnetospheric paradigm, the radiative transfer models need development before they can be comprehensively used as a diagnostic tool for T Tauri spectra. For example, Folha & Emerson (2001) noted that the current radiative transfer magnetospheric accretion models produced infrared lines (Paschen and Brackett) that were narrower than their observations by $\approx 100{\rm~kms}^{-1}$.

The focus of this work is to present an initial comparison of synthetic and observed hydrogen line profiles, using the radiative transfer code TORUS (Harries et al., 2019). Our primary focus is on the model development and morphology of the synthetic spectra. This paper is structured as follows: initially, we introduce the T Tauri observations and data reduction in § 2. We then describe in § 3 the T Tauri model and the radiative transfer method. This section also outlines the parameters for our grid of synthetic hydrogen line profiles. The results of our parameter study, the comparison of the observations with the ensemble of synthetic profiles, and possible model modifications are presented in § 4. Finally, we discuss the results and their implications in § 5 and conclude in § 6.

We selected 29 T Tauri stars from the ESO programme 084.C-1095(A) observed on 2010 January 18, 19, and 20 (PI G. Herczeg, see Manara et al. 2016, Rugel et al. 2018, Schneider et al. 2018, and Liu et al. 2016). The observed targets were selected to have a broad range of accretion rates of four orders of magnitude, the full list can be seen in Table 1. The observations were made using VLT’s X-Shooter instrument (Vernet et al., 2011) providing medium-resolution ($R~11600-18400$) spectra. The spectral range is $300-2480{\rm~nm}$ divided into three parts, UVB, VIS, and NIR corresponding to the three independent cross-dispersed echelle spectrographs on X-Shooter, which are observed simultaneously. The spectra were obtained by nodding the telescope parallel to the slit. A slit width of 0.4” was used for all stars apart from DG Tau, which used a width of 1.2”. The spectra were flux calibrated during their initial reduction using the spectrophotometric standard star GD-71 Manara et al. (2016).

Telluric corrections were applied using ESO’s Molecfit pipeline (Smette et al., 2015; Kausch et al., 2015). The hydrogen lines H $\alpha$ (2-3, $6562$ Å), Pa $\beta$ (3-5, $12818$ Å), Pa $\gamma$ (3-6, $10938$ Å) and Br $\gamma$ (4-7, $21655$ Å) were extracted from the full X-Shooter spectra. The profiles were normalised by fitting a third order polynomial to the nearby continuum. Veiling is expected to influence the equivalent widths of the optical and infrared lines due to excess emission from the accretion and warm dust in the disc. Although the profiles are presented in continuum normalized space, the ISM extinction will influence the unnormalised fluxes. The star’s Cardelli et al. (1989) extinction law reddening corrections are given in Table 1. However, the effects of veiling and extinction are not addressed in this work and are left to a future paper. Instead, the focus is on the line morphology and width, characteristics independent of the veiling and extinction.

The hydrogen line profiles from X-Shooter can be seen in Fig. 1. The figure shows the continuum normalised line profiles for the target stars arranged in order of H $\alpha$ intensity. Each column displays the spectra for the individual objects listed in Table 1 at four different wavelengths, centred on H $\alpha$, Pa $\gamma$, Pa $\beta$, and Br $\gamma$. Some stars with strong H $\alpha$ emission, e.g. Cha Ha 6, CID 0223980048 (ESO-HA 442), and Ass Cha T 2-33 have undetected emission in the Paschen and Brackett lines.

Following the scheme set out by Reipurth et al. (1996), the emission-line profiles were classified as follows.

• •

  Type I symmetric profiles with little or no features.

• •

  Type II two peaks, the second being greater than half the strength of the primary.

• •

  Type III two peaks, the second being less than half the strength of the primary.

• •

  Type IV sub-continuum absorption with no further significant emission beyond the absorption.

The types are subdivided into B or R, depending on if the absorption feature is blue-shifted or red-shifted relative to the primary peak. Types IVB and IVR are analogous to P-Cygni and IPC profiles, respectively.

Fig. 2 shows the Reipurth classification for the observations and the synthetic profiles. The latter are discussed in § 4. The line profiles were classified by eye. The seven types of profile morphology defined by Reipurth et al. (1996) are seen in the data. For spectra where the Reipurth type was not easily determined due to the noise levels, the profiles were not classified and excluded from the results of this paper. Therefore, these unclassified spectra introduce an uncertainty into the Reipurth distribution. The number of unclassified spectra are: 0 H $\alpha$, 10 Pa $\beta$, 14 Pa $\gamma$, and 18 Br $\gamma$. The sample of T Tauri stars is comparatively small and a significant proportion of the infrared lines could not be classified. Consequently, the statistical significance of the distribution is ambiguous; however, it exhibits a similar distribution of morphologies as those seen in previous T Tauri studies (e.g. Folha & Emerson, 2001; Reipurth et al., 1996). The distribution concurs with the previous results in showing that the majority ($\approx 43$ per cent) of profiles are type I and the second highest population of Reipurth types for the infrared lines are type IVR.

There are several cases of IPC profiles in our data, the majority of which are seen for Pa $\beta$. There are two notable stars that contain prominent IPC signatures across all the infrared lines. Ass Cha T 2-35 has strong IPC absorption in all the infrared lines. Whereas, the H $\alpha$ line only displays a red-shifted secondary peak. Ass Cha T 2-49 has a narrow IPC absorption in the infrared lines and no significant H $\alpha$ red-shifted absorption. Blue-shifted absorption is even more rare in our data. For instance, Ass Cha T 2-52 has a narrow H $\alpha$ P-Cygni absorption profile consistent with a disc wind (Kurosawa et al., 2011). None of the infrared lines exhibit discernible blue-shifted absorption.

Four of the observed stars are classified as weak line T Tauri stars, according to the classification scheme of White & Basri (2003), because their half widths at 10 percent maximum (HW10%) are less than $135{\rm~kms}^{-1}$. The stars are RECX-6, Ass Cha T 2-45a, Ass Cha T 2-4, and RECX-12. In this work, we adopt the HW10% criterion because White & Basri (2003) showed it to be a reliable method of distinguishing between classical and weak line T Tauri stars and the HW10% criterion is unaffected by veiling.

To create synthetic T Tauri hydrogen emission lines, we used the radiative transfer code TORUS (Harries et al., 2019). The code uses an analytic model as an input that approximates the expected geometry, density, temperature, velocity, emission and absorption sources in a 3D space. These include the disc, star, magnetospheric accretion, and stellar wind. TORUS then uses this model to calculate the expected population levels and create synthetic spectra.

The general trends seen in the grid of synthetic line profiles are outlined as follows. Higher accretion rates increase the line width and intensity. A high accretion rate of $\log{\dot{M}_{\rm acc}}=-6$ produced structured H $\alpha$ absorption superposed on broad ($\pm 1000{\rm~kms}^{-1}$) emission profiles. Only a limited number of models with an accretion rate of $\log{\dot{M}_{\rm acc}}=-6$ were run and the profiles are not included in this paper. The line profile intensity increases with magnetospheric temperature. The H $\alpha$ lines are dominated by Stark broadening for accretion flow temperatures of at least $7500{\rm~K}$ at accretion rates of $\log{\dot{M}_{\rm acc}}\geq-8$. The Stark broadening significantly increases the line widths and is highly dependent on the magnetospheric temperature and density. For a temperature of $9500{\rm~K}$ and an accretion rate of $\log{\dot{M}_{\rm acc}}=-7$, the H $\alpha$ profiles are Stark broadened to have wings of over $\pm 1000{\rm~kms}^{-1}$. Conversely, the infrared lines are almost completely unaffected by Stark broadening. The intensity and equivalent width of the infrared lines increase significantly with greater accretion rates and temperature. Whereas, the full widths at half maximum (FWHM) of the profiles are less strongly affected by the rate and temperature of the accretion flow.

H $\alpha$ exhibits IPC profiles for accretion rates of $\log{\dot{M_{\rm acc}}}=-8$ when $T_{\rm acc}\leq 7500{~\rm K}$ and for $\log{\dot{M}_{\rm acc}}=-9$ when $T_{\rm acc}\leq 8500{~\rm K}$. For accretion rates and temperatures above this, the Stark broadening smooths over the absorption features. For the infrared lines, the IPC profiles are exhibited irrespective of inclination, accretion rate, or temperature.

Strong P-Cygni profiles are seen when the wind outflow rate is $\geq 0.01\dot{M}_{\rm acc}$ and the inclination is within the stellar wind opening angle. The continuum relative depth of the blue-shifted absorption increases with the wind temperature. The line intensity is inversely correlated with the wind temperatures. This is particularly apparent for the infrared lines, because the higher energy levels, 5, 6, and 7, become depopulated before the upper H $\alpha$ level. However, this inverse relationship does not hold at a high wind temperature ($2\times 10^{4}{\rm~K}$), where emission from the wind dominates when the mass loss rate is $\geq 0.01\dot{M}_{\rm acc}$.

The frequency of P-Cygni profiles is correlated with the ratio $\dot{M}_{\rm sw}/\dot{M}_{\rm acc}$ and not $\dot{M}_{\rm sw}$ alone. For example, at a high accretion rate of $\log{\dot{M}_{\rm acc}}=-7$, P-Cygni profiles are only seen at mass-loss rates of $\log{\dot{M}_{\rm sw}}=-8$ and $-9$. Whereas, for an acretion rate of $\log{\dot{M}_{\rm acc}}=-8$, P-Cygni profiles are seen for mass-loss rates of $\log{\dot{M}_{\rm sw}}=-9$, $-10$ and $-11$ with decreasing frequency. Similar results are seen for an accretion rate of $\log{\dot{M}_{\rm acc}}=-9$. P-Cygni profiles were produced for mass-loss rates as low as $10^{-12}~{\rm M_{\odot}yr}^{-1}$. At higher accretion rates, the emission from the magnetosphere more commonly dominates, overwhelming the blue-shifted absorption.

The synthetic line profiles were calculated for velocity increments of $\Delta v=12.04{\rm~kms}^{-1}$, which corresponds to a spectral resolution of $R=24900$. The observations are observed at resolutions of $R=18400$ ($16{\rm~kms}^{-1}$) for H $\alpha$ and $R=11600$ ($26{\rm~kms}^{-1}$) for the infrared lines. We explored the effect of applying a Gaussian convolution to the synthetic spectra to reduce their resolution to the resolution of the observed spectra. However, the change in line profile morphology, in particular the FWHM and HW10%, was negligible when the synthetic spectra were convolved. Therefore, convolution was not considered a significant factor and not included in our analysis.

Although, our model grid was not set up to fit any particular star, it is informative to directly compare the synthetic line profiles to the observed line profiles. As an example, we show the spectra of three stars (Sz 22, DG Tau, and Ass Cha T 2-52) in Fig. 7 and a corresponding model selected to match the H $\alpha$ line profiles. The models were chosen using a $\chi^{2}$ fit test to find the closest H $\alpha$ profiles from the grid. The parameters of the chosen models are shown in Table 3. The models use our fiducial values of $T_{\rm eff}=4000{\rm~K}$ and $M_{\ast}=0.5{\rm M}_{\odot}$, whereas the effective photospheric temperature for Sz 22 is $4350{\rm~K}$, for DG Tau it is $4350{\rm~K}$, and for Ass Cha T 2-52 it is $5110{\rm~K}$ (Manara et al., 2016; Nguyen et al., 2012). The stellar masses for Sz 22, DG Tau and Ass Cha T 2-52 are $1.09$, $1.4$, and $1.4{\rm~M}_{\odot}$, respectively (Manara et al., 2016).

A caveat to the direct comparison is that the veiling of the observed lines have not been considered. Whereas, the effect of reddening is negated by the continuum normalization, the influence of veiling is not. Nevertheless, Fig. 7 highlights a trend seen in the grid of synthetic spectra. Namely, that while our method selects models with similar strengths and widths in H $\alpha$ to that observed, the models fail to reproduce the observed infrared lines. The synthetic infrared lines are too structured and narrow. This trend is presented in more detail in § 4.2 and § 4.3, and discussed in § 5.

In the following sections, we present an analysis of the structure (§ 4.1) and the width (§ 4.2) of the ensemble of synthetic line profiles. To best compare the synthetic and observed spectra, we use only a subset of our grid. The models are selected to correspond to the observed H $\alpha$ range. Only models that have an H $\alpha$ HW10% in the range of $60-400{\rm~kms}^{-1}$ are included.

A significant caveat to our comparison of the observed and synthetic line profiles is the possibility that our observed data set is incongruous and not representative of the consensus of T Tauri stars. However, our sample of 29 stars appears to be consistent with other observational datasets. For instance, the sample has a similar fraction of Reipurth classes to the distributions reported by Reipurth et al. (1996) for H $\alpha$ and Folha & Emerson (2001) for Pa $\beta$ and Br $\gamma$. Additionally, the Pa $\beta$ and Br $\gamma$ line peaks are slightly blue-shifted in agreement with Folha & Emerson (2001), even though the mean FWHM of our line profiles is smaller than the mean FWHM reported by Folha & Emerson (2001).

A second caveat is that our grid of synthetic line profiles were not adjusted to attain an agreement with any particular observation and a singular stellar mass, radius, and temperature were used. Broadly speaking, the synthetic line profile morphology is determined by the geometry, accretion rate, and temperature of the magnetosphere. Accordingly, our grid was designed to encompass the broad range of parameters predicted for T Tauri accretion and outflow (e.g. Hartmann et al., 1994; Muzerolle et al., 1998, 2001; Kurosawa et al., 2006; Lima et al., 2010; Kurosawa & Romanova, 2012). In turn, our T Tauri sample has an extensive range of accretion rates and stellar parameters, making it an appropriate initial dataset for a comparison with the ensemble of synthetic spectra.

Our models predict a greater number of H $\alpha$ IPC profiles than observed. However, our grid of models can reproduce the observed fraction of H $\alpha$ Reipurth types, after the lines classified as Weak Line T Tauri stars ($\approx 40$ per cent) are removed. By removing the Weak Line T Tauri models, we discard the H $\alpha$ models that contain red-shifted sub-continuum absorption. Hence, for our model grid, IPC profiles are only produced by models that would be classified as Weak Line T Tauri stars. This result is substantiated by Kurosawa et al. (2006) who demonstrated that H $\alpha$ IPC profiles were only produced in $\approx 5$ per cent of their sample. Moreover, in these cases, the accretion rate was low enough that the lines would be consistent with a weak line T Tauri classification.

The same models that correctly reproduce the observed H $\alpha$ Reipurth types predict a very high frequency of IPC profiles for Pa $\beta$, Pa $\gamma$, and Br $\gamma$. For H $\alpha$, Stark broadening smooths out the synthetic spectra, masking absorption features (Muzerolle et al., 2001). However, for the higher lines, the effect of Stark broadening is negligible at the temperatures and densities expected in T Tauri accretion. A possible reason for the dearth of observed IPC profiles is non-axisymmetric accretion flow. A magnetic obliquity from the stellar pole could cause the accretion funnel to form “curtains” that rotate with the star. IPC profiles would then be seen intermittently when the accretion curtain intersects with the line of sight. Observations support this effect; for example, McGinnis et al. (2020) measured a magnetic obliquity of $18^{\circ}{}^{+8}_{-7}$ for DK Tau and observed an IPC profile for two of the eight epochs. Accretion funnel “curtains” have also been explored in radiative transfer studies. For instance, Symington et al. (2005) used a 3D non-axisymmetric model, to reproduce some of the observed variability seen in T Tauri stars, but in general, the models produced results that were too variable. Esau et al. (2014) successfully modelled variable Balmer emission from AA Tau with a non-axisymmetric accretion model and Alencar et al. (2012) reproduced Balmer lines from V2129 Oph over several stellar rotational cycles. Further analysis of T Tauri time-series spectroscopic surveys would be helpful in better quantifying the variability of IPC profiles across multiple wavelengths.

In addition to the red-shifted features from the magnetosphere, some interesting blue-shifted detail are created by the stellar wind. The stellar wind produces the characteristic broad sub-continuum absorption as noted by Kurosawa et al. (2011). P-Cygni features occur in $\approx 13$ per cent of the synthetic profiles, and $\approx 10$ per cent of those do not contain red-shifted sub-continuum absorption. On the other hand, P-Cygni profiles are very rare in our observations, with none exhibited for the infrared lines. The infrared lines are optically thinner than H $\alpha$, and therefore, less sensitive to the lower density wind. P-Cygni profiles were also noted to be rare by Folha & Emerson (2001) and Edwards et al. (2006). Why these mass outflow signatures are scarce in observations could be a matter of geometry, temperature, or mass loss rate. Geometry should significantly reduce the frequency of fast wind absorption, since those winds are likely to be collimated (Edwards et al., 2006). Lima et al. (2010) showed that for H $\alpha$ a mass-loss rate from the inner disc of at least $10^{-9}~M_{\odot}{\rm~yr}^{-1}$ was needed for blue-shifted absorption features to show. However, for a polar stellar wind, our models produced H $\alpha$ blue-shifted sub-continuum absorption for mass-loss rates as low as $10^{-12}~M_{\odot}{\rm~yr}^{-1}$. Additionally, our results suggest that the frequency of synthetic P-Cygni profiles depends on the ratio of the mass loss to mass accretion rate, not the mass loss rate alone, because higher accretion rates increase the magnetospheric and hot-spot emission which masks the absorption from the wind.

Another factor seen in § 4.2, is that the infrared line widths (FWHM and HW10%) of the synthetic and observed data sets do not agree. Models that produce H $\alpha$ profiles that lie within the observed range create Paschen and Brackett spectra that are too narrow by $\approx 84{\rm kms}^{-1}$. Alencar & Basri (2000) suggested that rotation and turbulence may play an important role in the formation of the infrared line profiles. In agreement with Muzerolle et al. (2001) our results demonstrated that stellar rotation has a negligible effect on the line widths at the rotation rates seen in our observed sample. Furthermore, the level of turbulent motion needed to broaden the synthetic lines sufficiently to account for the difference in width of the synthetic infrared and H $\alpha$ lines is high, $\approx 100{~\rm kms}^{-1}$. Not only is there no obvious physical justification for such a large value of turbulence, but the spectra produced are broad and flat-topped, a morphology not seen in observations.

In addition to turbulence and rotation, we attempted to quantify the reduction in the width of the spectra due to red-shifted absorption, by calculating the width using only the blue-shifted emission; an approach similar to that adopted by Alencar et al. (2012) to compensate for poorly fitting red-shifted absorption. As expected (Bouvier et al., 2007; Alencar et al., 2012), our analysis suggested that a significant change in the model geometry that removed the IPC absorption, such as non-axisymmetric accretion, could account for a substantial increase in the infrared line widths. Alone, such a method may not be sufficient to account for the disparity between synthetic and observed hydrogen profiles. However, if the models were to include some combination of stellar rotation, turbulence and non-axisymmetric accretion, the synthetic profiles may be shifted into accord with the observations. Conversely, Folha & Emerson (2001) showed that, for their sample of Pa $\beta$ and Br $\gamma$ T Tauri spectra, the FWHM of Reipurth type I and type IVR profiles were not significantly different. This would indicate that spectra with inverse P-Cyni profiles are generally broader than those without or that the sub-continuum absorption does not significantly narrow the spectra. However, there is not a sufficient population of type IVR’s in our sample to confirm this result.

Another factor not taken into account is the line emission from the accretion shock region. This work treats the accretion shock zone as a black body heated by the release of gravitational potential energy that adds to the continuum. However, the accretion regions will also have line emission (e.g. Dodin, 2018) that will contribute to the observed spectra. A complete radiative equilibrium treatment of the shock region and magnetosphere is necessary to constrain this effect fully, which requires the development of a self-consistent theory of the heating and cooling mechanisms in the magnetosphere.

We presented a grid of synthetic T Tauri line profiles, computed using the radiative transfer code TORUS. Our models used the magnetospheric model originally developed by Hartmann et al. (1994) and further developed by Muzerolle et al. (1998, 2001); Symington et al. (2005); Kurosawa et al. (2006); Lima et al. (2010); Kurosawa et al. (2011). Our models also included a polar stellar wind launched from the star’s surface, a more realistic development to stellar wind used by Kurosawa et al. (2011). We compared our ensemble of models to the spectra of 29 T Tauri stars. The medium-resolution spectra covered a broad range of wavelengths that allowed us to simultaneously compare H $\alpha$, Pa $\beta$, Pa $\gamma$, and Br $\gamma$ lines. We drew the following conclusions:

• •

  The observations exhibited similar Reipurth classifications, widths, and mean line centres to those seen in other studies (e.g. Folha & Emerson, 2001; Reipurth et al., 1996; Edwards et al., 2006).

• •

  For H $\alpha$, our grid of synthetic line profiles were able to reproduce the observed distribution of Reipurth classifications and line widths. However, for the same models the infrared lines could not reproduce the observed emission. The modelled lines were too narrow by $\approx 84{~\rm kms}^{-1}$ and the majority ($\approx 90$ per cent) had IPC profiles.

• •

  We explored the effect of rotation and turbulence and determined that they could not sufficiently broaden the synthetic infrared line profiles or remove the IPC features. The red-shifted sub-continuum absorption was determined to narrow the HW10% of the lines by $\approx 49{\rm kms}^{-1}$.

• •

  The polar stellar wind produced the characteristic broad P-Cygni profiles as suggested by Kurosawa et al. (2011). Our models produced blue-shifted sub-continuum absorption with mass loss-rates as low as $10^{-12}~M_{\odot}{\rm~yr}^{-1}$. Furthermore, our results suggested that the frequency of P-Cygni profiles depends on the ratio of the mass loss to mass accretion rate; the increased emission from higher accretion rates masks the blue-shifted absorption.

Looking forward, future radiative transfer models should include 3D non axi-symmetric models and work to obtain a better match to the observed red-shifted absorption and emission features. The radiative transfer models should be compared to higher resolution observational spectra and include a more complete analysis that takes into account for veiling and extinction effects. Furthermore, the radiative transfer models of T Tauri stars contain a plethora of free parameters. The addition of further constraints on the geometry and temperature of these models is vital if radiative transfer models are to be used as a comprehensive diagnostic tool of T Tauri spectra.

The Authors acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 682393; AWESoMeStars: Accretion, Winds, and Evolution of Spins and Magnetism of Stars; http://empslocal.ex.ac.uk/AWESoMeStars).

This research has made use of the services of the ESO Science Archive Facility. Our research is based on observations collected at the European Southern Observatory under ESO programme 084.C-1095(A).

The authors would like to acknowledge the use of the University of Exeter High-Performance Computing (HPC) facility in carrying out this work.

This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France (Wenger et al., 2000)

We thank the developers of the Python packages, Pandas (Reback et al., 2020) and Matplotlib (Hunter, 2007) that were used for data analysis and creating the figures in this work.

We thank the anonymous referee who provided us with comments and suggestions that improved the clarity of the manuscript.

The VLT/X-Shooter observations are available in the ESO Science Archive Facility at https://archive.eso.org/scienceportal/home under the program ID 084.C-1095(A). The radiative transfer data underlying this article was generated using the code TORUS which can be found at http://www.astro.ex.ac.uk/people/th2/torus_html/homepage.html.