© ESO, 2016

1. Introduction

The interaction between the central star and its surrounding disk in young stellar objects (YSOs) could be one the most important processes in the evolution of young stars, proto-planetary disks, and planetary system formation but, paradoxically, one of the least understood. Ultraviolet and X-ray irradiation from the star affects the dispersal and evolution of its surroundings (Owen et al. 2010), and the magnetic activity of the star has an important role in the mass-accretion rate from the disk onto the central object. The X-ray emission from the central star should photo-ionize the circumstellar material (Gorti & Hollenbach 2009), affecting its chemical composition, accreting processes (Alexander et al. 2014), outflows, and potential planetary atmospheres.

T Tauri stars present X-ray luminosities (L_X) near the saturation limit (log(L_X/L_bol) = −3) found for main-sequence (MS) stars, L_X/L_bol ~ 10^-3.5, i.e., sometimes orders of magnitude higher than more evolved stars. For MS stars the X-ray activity is highly related with the rotation period, a relation given by the power law L_X/${\mathit{L}}_{\mathrm{bol}}\mathrm{\propto }{\mathit{P}}_{\mathrm{rot}}^{-2.6}$ (Pizzolato et al. 2003). But this relation has not been found for T Tauri stars (Preibisch et al. 2005). Several reasons have been postulated: the totally convective nature of young stars could be generating a different magnetic activity than that of MS stars (solar-like dynamo); a possible star magnetic field that is coupling with its surrounding disk; or the X-ray emission from accretion shocks could be altering the total amount of X-ray luminosity (Preibisch et al. 2005).

In the accretion process, material from the disk falls onto the stellar photosphere, generating a characteristic shock spectrum and an excess emission (L_acc), which can be measured with spectroscopic or photometric methods (Calvet & Gullbring 1998). This accretion luminosity can be linked to the mass accretion rate, Ṁ_acc, through the relation: Ṁ_acc = L_accR_∗/0.8GM_∗, with R_∗, and M_∗ being the radius and the mass of the star, respectively, and 0.8 being the factor that accounts for the assumption that the infall originates at a magnetospheric radius of R_m = 5 (Gullbring et al. 1998). The excess emission is mostly seen in the blue part of the spectrum (U-band excess) and in the emission lines (Hα equivalent width) (Hartmann 1998).

The accretion processes were thought to play an important role in the X-ray activity of these stars, although several studies have found that strong accretors present lower L_X (Preibisch et al. 2005). Different explanations have been elaborated, such as disk opaqueness to certain L_X energies (Güdel et al. 2007b), thermalization and absorption of the soft component of the X-ray luminosity (~5 keV) (Calvet & Gullbring 1998) or changes in the coronal magnetic field activity provoked by the accretion processes (Telleschi et al. 2007). Also, a higher magnetic activity of the young star would result in highly energetic flares, showing large enough peaks in the X-ray measurements to even connect the inner disk to the star’s photosphere (Aarnio et al. 2010).

Several studies have been carried out regarding the relation between mass accretion rates and X-ray emission. One of these is the anti-correlation found between the residual L_X and the Ṁ_acc by Telleschi et al. (2007), using data part of the XMM-Newton Extended Survey of the Taurus molecular cloud (XEST). Our main objective is to compare the mass accretion rates – X-ray emission relation found in that article (Telleschi et al. 2007) for the low mass T-association of the Taurus Molecular Cloud (TMC) with data on the Orion Nebula Cluster (ONC), and to look for any possible environmental effect. We used the X-ray emission data from the Chandra Orion Ultra-deep Project (COUP; Getman et al. 2005b; Preibisch et al. 2005) and the accretion measurements from Manara et al. (2012), which use data from the Hubble Space Telescope (HST) Treasury Program on the ONC (Robberto et al. 2013).

This article is organized as follows: Sect. 2 describes the different datasets we use in our study and the cross-matching procedure. Section 3 illustrates the selection of the sub-samples we use. In Sect. 4 we explain the relation between X-ray emission and accretion processes we want to analyze and the correlation results we obtained, which are fully discussed in Sect. 5. In Sect. 6, we summarize the conclusions of this work.

2. X-rays and accretion in the ONC

2.1. Taurus and Orion comparison

The TMC is the nearest largest (distance ~140 pc, Loinard et al. 2005) star-forming region known. It is composed of several loosely associated molecular clouds, each of them producing small numbers of YSOs. Its small star density (1–10 stars pc^-2, Gomez et al. 1993) prevents a notable influence from gravitational effects, outflows, or strong UV radiation fields, which creates a calm evolutionary environment, compared to other star-forming regions.

Although several other X-ray studies have been carried out in the region, the XEST project provided the most sensitive and complete sample of X-ray detections (Telleschi et al. 2007; Güdel et al. 2007a). The X-ray emission of TTS is usually between L_X ~ 10²⁹−10³¹ erg s^-1, clearly higher than the instrument detection limit of L_X ~ 10²⁸ erg s^-1, for typical integration times. In fact, the XEST presents X-ray detection statistics consistent with near-completeness: 126 out of 152 TMC members are detected in X-rays (Güdel et al. 2007a). Out of a this sample, 55 are classified as strong accretors (or classical T Tauri stars) and 45 as weak accretors (or weak-line T Tauri stars), a classification that is based on the equivalent width of the Hα line. We refer to Telleschi et al. (2007) for a complete description of their sample selection and analyses.

In contrast, the ONC presents a much denser picture, with a distance of ~414 pc (Menten et al. 2007). This massive cluster of young stars (~10⁶ yr) located in the Orion Molecular Cloud is illuminated by two O-type stars (Θ¹ Ori C and Θ² Ori A), has a star population of ~1600 optically visible sources, and is recognized as a benchmark laboratory for star and planet formation, and the closest massive cluster to the Sun. It represents a coherent and homogeneous group of pre-main sequence (PMS) stars (Hillenbrand 1997; Da Rio et al. 2010, 2012), and a perfect bench test for a comparison with the TMC. Table 1 summarizes some key characteristics of both regions.

2.2. X-ray emission in the ONC – COUP

We use the data available from the COUP (Preibisch et al. 2005; Feigelson 2005; Getman et al. 2005a), or more precisely, from the Chandra Orion Ultra-deep Point Source Catalog¹.

The COUP was a deep observation of the ONC using the Advanced CCD Imaging Spectrometer (ACIS) mounted on the Chandra X-ray telescope. This was a continuous 838 ks exposure program over a period of 13.2 days in January 2003. It detected 1 616 individual X-ray sources, with typical positional uncertainties of <. This observation of the ONC (Getman et al. 2005b) resulted in the detection of ~1400 X-ray-emitting PMS and is the richest source of X-ray data ever obtained for the ONC. We refer to Getman et al. (2005a,b) for a full review of the program.

2.3. Accretion data

For the accretion measurements, we used the data of Manara et al. (2012) on the ONC, in which they use the photometric catalog from the HST Treasury Program of Robberto et al. (2013). This program observed the ONC for 104 HST orbits of HST time with the Advanced Camera for Surveys (ACS), the Wide-Field/Planetary Camera 2 (WFCP2), and the Near-Infrared Camera and Multi-Object Spectrograph (NICMOS), using 11 filters in total that range from the U to the H-band. With the data obtained from WFPC2, Manara et al. (2012) calculate the mass accretion rates of almost ~600 PMS stars. Here we summarize the key aspects of their work and briefly discuss the two methodologies they use to determine the accretion rates. In the following, we divide the discussion on this dataset using two subsamples that were created by the method used to determine the accretion rates: the U-band excess and the Hα line flux. For a complete analysis of the data selection and procedure, we refer to their article.

Manara et al. (2012) construct a two-color diagram (2CD) with the UBI photometric measurements, and simultaneously obtain an estimate of the extinction, A_V, and accretion luminosity, L_acc/L_tot. They assume that the displacement of the observed sources from the theoretical isochrone on the 2CD is caused by a combination of these two processes. They assume spectral types from the literature for all their targets.

U-band excess – From the 2CD that they converted they derive L_acc/L_tot into L_acc/L_⊙, taking into consideration the stellar luminosities with the relation L_acc/L_⊙ = (L_acc/L_tot)/(1−L_acc/L_tot)* L_∗/L_⊙ (L_∗ being the stellar luminosity).

Hα line – Manara et al. (2012) also use the Hα luminosity as an accretion tracer. With the Hα photometry available from the WFPC2 catalog (more precisely, the photometry from the F656N filter), they measure the excess with respect to the photospheric (Hα - I) color for each star, which is dependent on T_eff. They then convert this Hα excess into equivalent width. They consider the sources that fulfill the condition 3 Å <EW_Hα< 1000 Å as accretors. Finally, they derive the accretion luminosity L_acc from the Hα luminosity L_Hα with the relation log(L_acc/L_⊙) = (1.31 ± 0.03)log(L_Hα/L_⊙) + (2.63 ± 0.13). The L_acc−L_Hα relation was calibrated using the U-excess data. The masses of the stars were computed with an evolutionary model interpolation of the position of them on the Hertzprung-Russel diagram (HRD).

Manara et al. (2012) obtain accretion rates for 244 objects using the U-excess method, and for 486 using the Hα one. These subsamples are independent of one another. The excess in the U-band is a direct proxy of accretion, while the L_Hα is an indirect one. Thus, the accretion rate measurements of the U-excess subsample are more reliable than those of the Hα one.

Manara et al. (2012) discard close binaries and visual proplyds (Ricci et al. 2008) from their sample. Thus, our subsamples are cleansed of these objects too. Consequently, our catalogs are only composed of young accreting stars. We will refer to these catalogs as the U-excess and the Hα subsamples, respectively.

2.4. Cross-matching

The first step in our analysis was to find the COUP X-ray counterparts for the sources in the HST sub-samples. Using the nearest neighbors method, we made a first cross-match with the sky positions of the sources of the COUP catalog and those of the Manara2012 subsamples, using a matching distance of 1′′ as a first approximation. We chose this distance taking into account the astrometric accuracy of Chandra: the 99% limit on positional accuracy is 0.8′′, in the worst case being an offset of 1.1′′². With this matching distance, we obtained 170 pairings with the U-excess group, and 322 pairings with the Hα one.

Fig. 1 Right ascension and declination offsets between the HST Hα sources and the COUP sample, before and after correction.

We wanted to check if a systematic offset in the positions of both catalogs was present. Thus, we calculated the median differences in the right ascension and declination of this first set. As can be seen in Fig. 1, we found δRA_U−excess = + 0.274′′ and δDEC_U−excess = + 0.036′′, and δRA_Hα = + 0.228′′, and δDEC_Hα = + 0.026′′. We then corrected the COUP sources’ right ascension and declination with these median offset values to refine the search of HST counterparts, and did a new cross-match with these new coordinates. For the U-excess sub-sample we found one less source, obtaining a sub-sample of 169 matches, whereas for the Hα sub-sample we gained two more, obtaining 324 pairings.

As an extra control measure, we also performed the cross-match with the possibility of various pairings instead of just the nearest one. Not one of the HST sources in our Manara2012 subsamples had more than one COUP counterpart nearby. Table 2 shows the parameters from this procedure.

3. Sample selection

3.1. Spectral type and low mass

To study the mass accretion rates and the X-ray luminosities as a function of T_eff, we only kept sources with a known spectral type. This left us with 281 sources in the case of the Hα subsample, and 164 in the U-excess one. Spectral types were derived from Hillenbrand (1997), Luhman et al. (2000), and Lucas et al. (2001). For some sources, the spectral type was recalculated in Hillenbrand et al. (2013). In these cases, we use the latest spectral type available.

The X-ray emission of high-mass stars is non-coronal in origin, or comes from a different kind of corona, or originates in unresolved lower mass companions (Flaccomio et al. 2012). Because of this, we limited our study to stars with M_∗< 2 M_⊙. With this selection, the numbers decreased to 277 sources for the Hα subsample and 163 for the U-excess subsample.

Some sources did not have defined uncertainties for the mass accretion rates. We only used sources with valid mass accretion values and uncertainties, discarding the invalid ones. Thus, the U-excess subsample was reduced to 154 sources. The Hα remained the same. This selection criteria is similar to that in Telleschi et al. (2007).

3.2. Classical T Tauri stars and weak-line T Tauri stars

The T Tauri family is divided into classical T Tauri stars (CTTS) and weak-line T Tauri stars (WTTS). This division takes into account the value of some accretion tracers to classify the objects into accretors or non-accretors. Several studies use this classification when studying the accretion properties of star-forming regions. For example, Preibisch et al. (2005) and Flaccomio et al. (2003) use the Ca_II infrared triplet lines (λ = 8542 Å) equivalent width to classify their sample, as do Hillenbrand et al. (1998); and in Telleschi et al. (2007) they use the Hα line (λ = 6563 Å), as in Güdel et al. (2007a).

In our case, different classifications were possible. From the COUP data we accessed the values of the Ca_II line for both of our subsamples. Furthermore, for the Hα subsample, the Hα line equivalent width was also available. Thus, a second classification analysis could be carried out for this subsample.

Table 3 shows the mean accretion values for both subsamples. We note that, although both subsamples were classified using the Ca_II method, not every object in them was included in the analysis. The classification method only selects objects with EW(Ca_II) < −1 Å (CTTS) and EW(Ca_II) > 1 Å (WTTS) (Preibisch et al. 2005). Thus, objects with −1 Å <EW(Ca_II) < 1 Å are not included in the classification. In the case of the Hα subsample, we used 108 sources for these analyses, and for the U-excess subsample we used 56 sources.

Several objects that we classified as WTTS have stronger accretion rate measurements than the mean value of the total CTTS, and several CTTS have lower accretion rate values than the mean WTTS value. As a result, the mean Ṁ_acc values of the WTTS and CTTS sources for both subsamples differ by less than 3σ.

The excess emission in Hα (and probably in U-band) present in WTTS may be due to cromospheric emission and not only to accretion. There have been studies that measure how strong this effect is and, in general, it is below the observed accretion rates (Ingleby et al. 2011; Stelzer et al. 2013; Manara et al. 2013a). Accreting PMS with values of logL_acc ≤ −3 logL_⊙ should be treated with caution because the line emission may be dominated by the contribution of chromospheric activity (Manara et al. 2013b). In our case, none of the WTTS with strong accretion measurements had logL_acc values lower than −3 logL_⊙, so we assume no significant cromospheric dependence for their accretion-rate measurements.

Our data do not allow us to classify our subsamples between CTTS and WTTS clearly. Medium-high resolution spectra would be needed for that analysis. Thus, in this work, we do not use the classical and weak-lined T Tauri division.

4. Relations between X-ray luminosity, stellar mass, and accretion rate

For the characterization of the X-ray properties, we used the following data from the COUP catalog: the total X-ray luminosity L_X (corrected for interstellar absorption), which corresponds to the total 0.5–8.0 keV energy band, with units of erg s^-1, and the equivalent width values of the Ca_II line for the T Tauri classification, in units of Å (see previous section). Importantly, Manara et al. (2012) formulate their analyses using a distance of 414 pc to the ONC, while the data in the COUP catalog assumes a distance of 450 pc. We corrected the latter with the distance of the former, using the equation used in the COUP catalog: L = 4πD²F, with F being the X-ray flux and D being the distance in parsecs. We used a value of 0.39 dex for the uncertainty of L_X.

These X-ray parameters are selected as in Preibisch et al. (2005). The main difference with that work is the spectral type classification (we updated the spectral types of several objects with the information from Hillenbrand et al. 2013) and the sample selection (we used only objects with M_∗< 2 M_⊙).

The rest of the stellar parameters were gathered from Manara et al. (2012): the stellar masses M_∗, in units of M_⊙, were obtained from D’Antona & Mazzitelli (1994) models and the accretion rates, with units of M_⊙ yr^-1, were derived from that paper, using photometric data from the HST Treasury Program (see Sect. 2).

In Table 4 we present the final catalog with all these parameters for both subsamples.

4.1. Least-square fit and outlier rejection study

In this work the regression analyses were carried out using two methods: a least-square approximation and an outlier rejection fit.

For the first, we used a classical ordinary least square (OLS) algorithm using the scipy’s orthogonal distance regression (ODR) package on Python (Jones et al. 2001; Boggs et al. 1988). The ODR package allowed us to feed the uncertainties of our parameters into the analysis and take them into account to acquire the fit. Moreover, it also produced the errors of the fitted coefficients, which we used to compute the uncertainties in our results.

Because of the large spread of our data, we decided to include a Bayesian outlier rejection algorithm with Monte Carlo Markov chain (MCMC), using the astroML package of Python (Vanderplas et al. 2012). The points, which are identified by this method as not part of the fit with a probability greater than 99.7% (3σ confidence), are selected as outliers. This method uses models that marginalizes over the probability that each point is an outlier. The MCMC is used for this marginalization process. Then, from the sets of maximum a posteriori likelihoods for the slope and intercept values, we selected the median values for both parameters as the best-fit results.

This method relies heavily on the measurement uncertainty. A few good points might have been rejected if their uncertainties were underestimated. But since the sample and measurements come from the same homogeneous survey, these errors should not bias our result significantly.

The Spearman correlation analysis was used to test the relation between the parameters in our study, because it is less sensitive to outliers than other correlation analyses, such as Kendall τ or Pearson ρ.

Fig. 2 Stellar mass vs. mass accretion rates for both subsamples. The plot on the left corresponds to the Hα subsample, and the one on the right to the U-excess subsample. Regression lines (straight) are plotted with their respective errors in the slope (shaded areas) for the OLS regression analysis (black) and the outlier rejection regression method (red).

4.2. Stellar mass dependencies

Many studies have shown that there is an inherent relation between the mass of the young star and its X-ray emission (Flaccomio et al. 2003; Preibisch et al. 2005; Telleschi et al. 2007; Ercolano et al. 2014) and between the stellar mass and the mass accretion rates (Calvet et al. 2004; Muzerolle et al. 2003, 2005; Mohanty et al. 2005; Natta et al. 2006; Manara et al. 2012; Alcalá et al. 2014). We want to test these results with our data.

Stellar mass and accretion rates – Fig. 2 and Table 5 show the correlation study between the mass of the star and its mass accretion rate. Important differences can be found for both subsamples. Strong correlation coefficients are found for the U-excess subsample, with a relation of logṀ = (1.94 ± 0.23) × log M_∗− (7.95 ± 0.12) using the minimum-square fit analysis. This result is consistent with previous studies, logṀ = 2 × log M_∗−7.5, which is used in the Telleschi et al. (2007) study of the TMC. But we can see how this is not the case for the Hα subsample. The relation for this subsample is logṀ = (1.57 ± 0.23) × log M_∗− (7.60 ± 0.15), but with weaker correlation coefficients. This discrepancy suggests that U-band excess is a better accretion tracer than the Hα line equivalent width (Venuti et al. 2014), and calls for a word of caution when using Hα to derive accretion rates. In the case of the outlier rejection analysis, a steeper slope is found for the U-excess subsample, logṀ = (3.29 ± 0.25) × log M_∗− (7.37 ± 0.15), as well as for the Hα subsample, (3.19 ± 0.21) × log M_∗− (7.09 ± 0.16). In Sect. 5 we address this difference.

Stellar mass and X-ray emission – Fig. 3 shows the relations between the stellar mass and L_X, for both subsamples. The regression and correlation parameters of the different subsamples are summarized in Table 5. For the U-excess subsample, stronger correlations are present between these parameters than those found for the Hα one, a similar result to that on the Ṁ_acc−M_∗ study. In Sect. 5 we explain this critical difference.

Fig. 3 X-ray luminosities vs. the mass of the sources. The plot on the left corresponds to the Hα subsample, and the one on the right to the U-excess subsample. Regression lines (straight) are plotted with their respective errors in the slope (shaded areas) for the OLS regression analysis (black) and the outlier rejection regression method (red).

4.2.1. Selection bias

Ercolano et al. (2014) study whether the Ṁ_acc−M_∗ relation found for different samples of YSO can be a consequence of a selection bias or detection threshold. Apart for finding similar relations to our subsamples, they find that it is not affected by a selection bias.

The Manara2012 sample we used is almost complete down to the hydrogen-burning limit. Thus, we conclude that selection effects are not present in our Ṁ_acc−M relations. And given the X-ray detection limit of the Chandra telescope, which is lower than our lowest X-ray luminosity value, we also deduce that our L_X−M relations are also not affected by a selection bias owing to undetected sources.

4.3. Accretion rate and X-ray luminosity

We now focus on our primary objective: study the accretion processes of the PMS objects in the ONC and their relation with the X-ray emissions of the central stars. This interaction has also been studied in different works, such as Preibisch et al. (2005) and Drake et al. (2009) in Orion, or Telleschi et al. (2007) in Taurus. Here we want to reformulate the results obtained in these works, using different accretor tracers and measurements. In particular, we want to compare the analysis of Telleschi et al. (2007) in the TMC with our results in the ONC, and see if similar relations can be inferred.

In our work we are not interested in studying the differences between accretors and non-accretors. That classification is no longer appropriate for our study, as seen in Sect. 3. This is why we study the direct dependences and relations of the measured mass accretion rates and the X-ray luminosities. We take an approach similar to that of Telleschi et al. (2007). Here they study the L_X−Ṁ_acc relation, taking into account the inherent dependences of these properties with the mass of the star. Class II objects show a direct relation between Ṁ_acc and M. Using different evolutionary tracks, Muzerolle et al. (2003, 2005) found Ṁ ∝ M² and Ṁ ∝ M^2.1, respectively, so in Telleschi et al. (2007) they adopted the relation log Ṁ ≈ 2log M− 7.5. They also compute a relation between logL_X and logM with their data. Finally, they relate the L_X with the Ṁ_acc with the equation logL_X(Ṁ) = 0.85 × log (Ṁ) + 36.67.

Taking the same approach, we used the Ṁ_acc−M_∗ and the L_X−M_∗ relations we found for both our subsamples and derived L_X as a function of Ṁ_acc. By using both the OLS and the outlier detection and rejection methods, different regression results and, consequently, L_X(Ṁ_acc) equations, are obtained for each subsample. These results are shown in Table 6. With them, we computed the expected L_X given the Ṁ_acc of the sources in our catalog. We called this our theoretical L_X(Ṁ_acc). This relation could define the L_X - Ṁ_acc in Orion if both parameters were to only depend on the stellar mass.

Fig. 4 Residual X-ray luminosity, after normalization with the M – LX and M – Ṁ relations, as a function of the mass accretion rate. Left figures correspond to the Hα subsample. Right figures correspond to the U-excess subsample. The top plots present the results using the OLS method for the initial regression analyses between M∗, LX and Ṁacc. The bottom ones when using the outlier rejection method for those same analyses. Regression lines (straight), with their respective errors in the slope (shaded areas), are shown for the OLS (black) and outlier rejection (red) final regression results.

Finally, we computed what we called the residual L_X. This parameter was obtained by dividing the observed L_X by the theorethical L_X, given by our derived equations, for a given Ṁ_acc. In Table 4 we include the different residual L_X values of each source that has been computed this way, for both subsamples. This residual X-ray luminosity compares the observed L_X with the expected value if both the L_X and the Ṁ_acc were to only depend on the stellar mass. It represents the excess (or deficit) of X-ray luminosities that are dependent on the Ṁ_acc. In Fig. 4 we plot this value against the Ṁ_acc. If this ratio were determined only by the L_X−M_∗ and Ṁ_acc−M_∗ relations, then the values would scatter around a constant. As can be seen in the figure, they present a large scatter, pointing towards more dependencies, in addition to the stellar mass, for L_X and Ṁ_acc.

Again, we used both the OLS and the outlier detection and rejection methods for these final plots. Table 5 summarizes all the regression results obtained for all the possible combinations of data and methods. The values under “Least square algorithm” in Table 5 correspond to the regression results that were obtained using the OLS methodology, whilst the ones under “Outlier rejection algorithm” correspond to the results obtained using the named method. The four top rows present the results of the regressions that were found directly from the data, whilst the bottom four show the regression results from the derived residual X-ray luminosity. This last parameter is computed using what we defined here as the theoretical X-ray luminosity, L_X(Ṁ), which in turn depends on the first relations. Thus, depending on the methodology used to derive the first relations on the top four rows (OLS or outlier rejection), different L_X(Ṁ) are obtained. This is represented in the four bottom rows. The top two present the results from the L_X(Ṁ) derived from the OLS methodology, while the bottom two represent the L_X(Ṁ) derived from the outlier rejection analysis.

5. Discussion

We will now discuss the correlations and trends found in the previous section. The main objective is to compare the residual X-ray luminosity – mass accretion rate relations from both Taurus, obtained in Telleschi et al. (2007), and Orion, obtained in this work, which we do in Sect. 5.1. Different methods yield different results, which we address in Sects. 5.2 and 5.3. In Sect. 5.4, we interpret these results.

5.1. Comparing Taurus and Orion – OLS method regression results

Telleschi et al. (2007) find the following results when studying the X-ray emission differences between CTTS and WTTS: i) CTTS present smaller L_X than WTTS, on average; ii) they also present smaller L_X/L_∗; iii) and a correlation is found between the electron temperature and the total L_X for WTTS, but not for CTTS (where the temperatures are higher than those in the WTTS). Their results point towards a magnetic coronal source for the X-ray emissions in TTS. Also, they suggest that the lower L_X emission from CTTS is caused by coronal heating from an accretion disk and accretion processes. Denser accreting material from CTTS would cause a decreased heated plasma from the reconnection events, accounting for the lower measurements of L_X in accreting systems than in WTTS. The cool plasma may also reorganize the magnetic loops after entering them, stretching and causing them not to reconnect (diminishing the X-ray emission therefore); or by just lowering their temperature because they are colder than them; or inducing radiative losses and more rapid cooling.

One of their main results regarding the accretion processes and the L_X luminosities was the relation between the residual L_X and the Ṁ_acc they they found for their CTTS sample. The main difference to their work can be found in the subsamples we gathered for the Orion YSOs, which yield different results in each case.

5.2. OLS method regression results

As can be seen in Figs. 2 and 3, the spread in the data is considerable, over orders of magnitude. For the Hα subsample, in fact, this spread is large enough to produce ineffective correlation results as can be seen in the low Spearman ρ coefficient for the Ṁ_acc−M_∗ relation in Table 5. This spread may be caused by hidden variables that affect our data.

The U-excess subsample presents a stronger correlation between these parameters, pointing towards more coherent measurement of the mass accretion rates of the sources (Venuti et al. 2014). The process to derive the accretion rate, which uses the equivalent width of the Hα line, is more complex than the one with the excess emission of the U-band. More factors enter into play in the former, leading to more uncertainties in the final data, which maybe explains the larger spread in the plots for this subsample.

This is why we cannot assert the reliability of the rest of the results from the Hα sample from this conclusion onward. The low ρ coefficient in the Ṁ_acc−M_∗ relation means the derived L_X−Ṁ_acc one is not sufficiently reliable. Therefore, our analyses will focus on the U-excess subsample from now on. Nevertheless, we report the results from the other subsample as a reference and when making a comparison with the U-excess data.

The U-excess subsample presents moderate/strong correlations between our four main parameters, M_∗, Ṁ_acc, L_X, and the residual L_X. In fact, this is very similar to those found in Telleschi et al. (2007). The relation between M_∗ and Ṁ_acc, $\mathit{Ṁ}{}_{\mathrm{acc}}\mathrm{\propto }{\mathit{M}}_{\mathrm{\ast }}^{\mathrm{1.94}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}\mathrm{0.23}}$ given by the least-square method is totally compatible with that found in many previous studies. Also, the ${\mathit{L}}_{\mathrm{X}}\mathrm{\propto }{\mathit{M}}_{\mathrm{\ast }}^{\mathrm{1.72}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}\mathrm{0.17}}$ relation is compatible with that found in Preibisch et al. (2005) for the same region. We still find considerable spreads in the data but the results we find are consistent with those on Taurus in Telleschi et al. (2007).

We find that the final relation between the residual X-ray luminosity and the mass accretion rate for the U-excess subsample, L_X/L_X(Ṁ) ∝Ṁ^{− 0.53 ± 0.05}, is very compatible with the relation found in Taurus in Telleschi et al. (2007), L_X/L_X(Ṁ) ∝Ṁ^{− 0.48 ± 0.15}.

5.3. Outlier method regression results

To test the robustness of our fits, we used an outlier detection algorithm. The problem with this method, as stated before, is that it is very sensitive to uncertainties in the dependent variable, in this case, Ṁ_acc, L_X, and L_X/L_X(Ṁ). Several sources present sufficiently small errors as to be selected as outliers, although their position in the plot is consistent with the best-regression fit. Thus, the results obtained using this method should be taken cautiously.

The parameters we are working with (stellar mass, mass accretion rate, and X-ray luminosity) are not measured directly, but obtained indirectly from other measurements (i.e., the equivalent width of the Hα line or the excess in the U-band for the Ṁ_acc, or the flux of the objects, which is obtained by measuring the photons that arrive to the X-ray detector, for the L_X). Consequently, the uncertainties should represent this process.

As mentioned in the previous section, the relation obtained between the residual X-ray luminosity and the mass accretion rate using the OLS method for the U-excess subsample agrees considerably well with the results found by Telleschi et al. (2007) in Taurus. On the other hand, using the outliers detection method, the results on Orion differ considerably from those in Taurus.

The relations obtained with the outliers detection method between M_∗ and Ṁ_acc in both subsamples have considerably steeper slopes compared to those found in the literature: $\mathit{Ṁ}{}_{\mathrm{acc}}\mathrm{\propto }{\mathit{M}}_{\mathrm{\ast }}^{\mathrm{3.19}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}\mathrm{0.21}}$ for the Hα subsample and $\mathit{Ṁ}{}_{\mathrm{acc}}\mathrm{\propto }{\mathit{M}}_{\mathrm{\ast }}^{\mathrm{3.29}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}\mathrm{0.25}}$ for the U-excess one. This represents a difference of more than 3σ from the ones obtained using the OLS method. In the case of the L_X−M_∗ relation, the results differ from one subsample to another. The U-excess subsample presents compatible regression results between both methods, and between the relation found in Preibisch et al. (2005). But the ones found for the Hα subsample are considerably different, by a factor larger than 3σ.

In Table 5 all the final L_X/L_X(Ṁ_acc) – Ṁ_acc relations are shown, and Fig. 4 presents the final plots. Using both methods, we obtain eight different results: two plots for the Hα subsample, each with two different regression results, depending on whether we used the OLS or the outliers detection method to derive the regressions between L_X or Ṁ_acc and M_∗ and between L_X/L_X(Ṁ_acc)−Ṁ_acc; and the same in the case of the U-excess subsample.

Out of these eight results, and taking into account the aforementioned issues with each subsample and methodology, we decided that only two of them were compatible with Taurus: the one from the U-excess subsample that uses the OLS method between the M_∗−L_X and M_∗−Ṁ_acc relations and between the L_X/L_X(Ṁ_acc)−Ṁ_acc final relation, and the one from the Hα subsample that uses the outliers detection method for the initial relations and the OLS analysis for the L_X/L_X(Ṁ_acc)−Ṁ_acc final relation.

The uncertainties shown in Table 5 for Orion are far narrower than those found in Telleschi et al. (2007) for Taurus. The 1σ range for the slope from Telleschi et al. (2007) is −0.33 to −0.63, which is compatible with three more results from our analysis if we add the uncertainties from them (slopes −0.35 ± 0.07, −0.67 ± 0.06, and −0.68 ± 0.13). With these, our final interpretation of the results, as stated in Sect. 5.4, becomes stronger. Nevertheless, we urge caution, given the issues we explained before.

One important result to point out is that the regression results obtained using the OLS method are recovered using the outliers detection method when the uncertainties on the dependent variables are increased sufficiently (1σ, 2σ, 3σ...).

The accretion processes present an important variability in time, which we disregard. Applying an outliers detection and rejection method to these kind of data, without taking this characteristic into account may seem risky, as some sources could be an order of magnitude off its quiescent value and be selected as outliers when, in fact, they are not. This is another reason why the results of the outliers analysis must be taken with caution. Nevertheless, given the numbers in our data, this issue is not so critical.

5.4. Results

Our main result is the anti-correlation found between the residual L_X and the Ṁ_acc. We deduce two interpretations from these results.

The first is that for higher accretion rates there is a deficit in the observed L_X, compared with the theoretical one. This implies that, for stronger accretors, the observed L_X is weaker. That is, the accretion processes seem to “cover” the emission of X-ray radiation from the YSOs. This result is also found in (Telleschi et al. 2007).

The second is with regard to the scatter in the values on these plots. If the L_X and Ṁ_acc are only dependent on the stellar mass of the YSOs, as we have assumed, these values would scatter around a constant value of one. But the higher scatter and the negative slope points towards other dependencies for these parameters (e.g., stellar rotation, Rossby number, magnetic field intensity). What is interesting is the similarity between the L_X/L_X(Ṁ_acc)−Ṁ_acc relation on Taurus and Orion. This suggests that the environment where the T Tauri stars are born is not one of the parameters that affects the L_X/L_X(Ṁ_acc)−Ṁ_acc relation.

As a result, we can conclude that this anti-correlation between the residual L_X and the mass accretion rate is independent of the region and environment; its arbitrary appearance both in the TMC and in the ONC, shows reasonably well how it is an inherent property of accreting systems. Similar analyses in other star-forming regions could reinforce this result.

6. Conclusions

We have gathered a sample of T Tauri stars in the ONC with known X-ray detections and mass accretion rates. Using the classification criteria in Telleschi et al. (2007), we have divided our sample in CTTS and WTTS, finding that several WTTS have accretion rates comparable or even higher to those of CTTS. Since our data do not allow us to confirm these classifications and the number of WTTS in this work is small compared to the whole catalog, we have used all the subsamples for our analysis.

Two subsamples have been used in this work, depending on the method used to calculate the accretion rates of the sources. The Hα sample used the equivalent width of this spectral line, and the U-excess subsample, the color excess compared to the nominal values.

Because of the large spread in our data, two regression analyses were carried out. First, we used a least-square regression analysis, using the ODRPACK of Scipy on Python, obtaining results compatible with those in the literature and with Telleschi et al. (2007) for one of our subsamples. Then, we detected and rejected outliers from our samples using the astroML MCMC package of Python. This method is very sensitive to the uncertainties from the dependent variables and some sources were rejected as outliers as a result of too small error values, which thus affect the final regression-fit results. Using this method, only one more result was compatible with that from Taurus in Telleschi et al. (2007). By enlarging the uncertainties in the dependent variables, the OLS regression results were recovered.

We find that a clear anti-correlation between the residual X-ray luminosity and the accretion rates is present in both subsamples, although we cannot assert the reliability of the Hα results because of the weak correlation found between its previous parameters. In the case of the U-excess subsample, our results are consistent with those found in the Taurus Molecular Cloud. This result, independent of the environment studied, points towards an inherent property in these type of YSOs; the accretion processes causes a decrease in the emission of X-rays. Different theories have been postulated for this situation, such as thermalization by the X-rays of the stream being accreted, which causes a reduction in the X-ray measurements.

Acknowledgments

This work has been made possible thanks to the ESAC Science Operations Division research funds, code EXPRO IPL-PSS/GP/gp/44.2014, plus support from the ESAC Space Science Faculty. Pablo Riviere-Marichalar and Carlo Manara acknowledge funding from the ESA Research Fellowship program. H. Bouy is funded by the Spanish Ramn y Cajal fellowship program number RYC-2009- 04497. This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France. This work made extensive use of Topcat (TOPCAT http:// www.star.bristol.ac.uk/~mbt/topcat/ and STILTS, Taylor 2005, 2006). We thank the referee, Manuel Güdel, for his comments and corrections, which help to make this work complete. We would also like to thank Benjamin Montesinos and Nuria Huelamo for their comments and help.

References

All Tables

All Figures

	Fig. 1 Right ascension and declination offsets between the HST Hα sources and the COUP sample, before and after correction.
In the text

	Fig. 2 Stellar mass vs. mass accretion rates for both subsamples. The plot on the left corresponds to the Hα subsample, and the one on the right to the U-excess subsample. Regression lines (straight) are plotted with their respective errors in the slope (shaded areas) for the OLS regression analysis (black) and the outlier rejection regression method (red).
In the text

	Fig. 3 X-ray luminosities vs. the mass of the sources. The plot on the left corresponds to the Hα subsample, and the one on the right to the U-excess subsample. Regression lines (straight) are plotted with their respective errors in the slope (shaded areas) for the OLS regression analysis (black) and the outlier rejection regression method (red).
In the text

Fig. 4 Residual X-ray luminosity, after normalization with the M – LX and M – Ṁ relations, as a function of the mass accretion rate. Left figures correspond to the Hα subsample. Right figures correspond to the U-excess subsample. The top plots present the results using the OLS method for the initial regression analyses between M∗, LX and Ṁacc. The bottom ones when using the outlier rejection method for those same analyses. Regression lines (straight), with their respective errors in the slope (shaded areas), are shown for the OLS (black) and outlier rejection (red) final regression results.

In the text