BD+30$\degr$549: young helium-weak silicon star in NGC 1333 star-forming region

The absorption line-spectrum of BD+30$\degr$549 generally corresponds to the mid- to late B photosphere. No hydrogen or metallic lines emissions indicative for the accretion activity were detected. Hence BD+30$\degr$549 cannot be classified as typical Herbig Ae/Be star at least on the base of the spectrogram at our disposal. Its comparison with the spectra³³3High resolution ($R$=42000) spectra were retrieved from the ELODIE archive (Moultaka et al., 2004) of two late-B MK standards (Gray & Corbally, 2009), namely HR1029 (sp:B7V) and 134 Tau (sp:B9IV) revealed the striking absence of the He i lines, even the strongest ones at 4471 and 5876 Å . The strong Mg ii 4481 Å  line visible in spectrum of of BD+30$\degr$549 seems to be somewhat shallow comparing to that in 134 Tau spectrum. At the same time the Si ii lines at 4621, 5041, 5055, 5466, 6347, 6371 Å  are abnormally enhanced. The Si iii triplet at 4552, 4567, 4574 Å  which is almost absent in the spectra of standards clearly seen in the spectrum of BD+30$\degr$549. The notable sharpness of the absorption lines of different metals indicates very slow rotation. Qualitatively it is possible to classify BD+30$\degr$549 as helium-weak Bp star with silicon peculiarity.

Rich interstellar spectrum which contains both atomic and molecular features as well as numerous DIBs is superimposed on the photospheric ones. Measurements of the radial velocity of the CH at 4300 Å , Na i D interstellar features and few most symmetric DIBs including those at 5780, 5797, 6380, 6614 Å  provide average value $RV_{h}\approx$+14 km s^-1 which is close to the heliocentric radial velocity $RV_{h}$=+16.45 km s^-1of BD+30$\degr$549 measured by cross-correlation of the photospheric absorption lines with the template spectrum in several spectral windows.

The Gaia EDR3 (Gaia Collaboration et al., 2021) provides the parallax $\pi=3.48\pm 0.0237$ for BD+30$\degr$549 with Renormalised Unit Weight Error parameter $RUWE=1.14$. This value of RUWE is well below the recommended 1.4 upper threshold⁴⁴4https://dms.cosmos.esa.int/COSMOS/doc_fetch.php?id=3757412 and indicates the "good behaved"  astrometric solution. The parallax of the star can be converted into distance $D=287\pm 2$ pc which is in the perfect agreement with the average distance to the NGC 1333 cluster. Both the spatial position and coincidence of the radial velocity of the star with the mean velocity of molecular material in NGC 1333 region $RV_{h}\approx+15.7$ km$\cdot$s^-1 determined from the ¹³CO (3-2) and C¹⁸O (3-2) transitions (Curtis et al., 2010) confirms that location of BD+30$\degr$549 inside the reflection nebula is not due to the projection effect. The star is bona fide member of NGC 1333 star forming region and still intimately connected with its parental molecular material.

Embeddedness inside the reflection nebula implies the non-negligible effects of interstellar reddening which affect the observed photometry of BD+30$\degr$549. The variations of the ratio of total to selective absorption $R_{V}$ within NGC 1333 was investigated by Cernis (1990) who found that in direction toward BD+30$\degr$549 it deviates significantly from the interstellar one and equals to $R_{V}=4.7\pm 0.1$. In order to determine the value of the interstellar extinction $A_{V}$ we used the color excess $E(B-V)=+0.59^{m}$ calculated from the observed color index $(B-V)$=+0.48^m (Henden et al., 2016) and the intrinsic colors interpolated from the Pecaut & Mamajek (2013) tables for our best-fit effective temperature $T_{\rm eff}$=13100 K (Sect. 3.3). As a result we obtained visual extinction $A_{V}=2.8^{m}$. The observed spectrophotometry of BD+30$\degr$549 was dereddened using this value and Fitzpatrick et al. (2019) extinction curve. The bolometric absolute magnitude $M_{\mathrm{bol}}^{*}=-0.5^{m}$ was found for BD+30$\degr$549 adopting 287 pc distance and using this extinction value as well as the bolometric correction $BC_{V}=-0.9^{m}$ (Pecaut & Mamajek, 2013). Finally, the absolute magnitude was converted to luminosity: $\log(L_{*}/L_{\odot})=0.4(M_{\mathrm{bol}}^{\odot}-M_{\mathrm{bol}}^{*})=2.1\pm 0.1$.

With the obtained values of luminosity and effective temperature the star was placed on HR diagram (Fig. 1). Comparison with the evolutionary tracks and isochrones from the PARSEC model grid (Bressan et al., 2012) calculated for solar metallicity $Z=0.017$ revealed that BD+30$\degr$549 lies near the end of the $3.2M_{\odot}$ PMS track, close to ZAMS. The stellar radius inferred from the model track is $R=2.2R_{\odot}$. The age of the star was determined from the closest theoretical isochrone as $t\approx$2.7 Myr.

The atmospheric parameters of BD+30$\degr$549 were determined using the self-consistent iterative procedure based on spectral synthesis technique. As an initial guess, we used the effective temperature and surface gravity of a B8 star from the MK system calibrations (Gray & Corbally, 2009; Schmidt-Kaler, 1982). In the next step, the grid of the helium-weak atmospheric models with hydrogen abundance $N_{H}/N_{tot}=0.99$ was calculated using the LLmodels code (Shulyak et al., 2004), which accurately accounts the influence of anomalies in chemical composition on the opacity distribution in the atmosphere. Hereafter, we use the models with the temperature structure calculated for the homogeneous abundance distribution as the best approximation to date (see Sect. 3.6 for discussion). Using these model atmospheres and atomic data extracted from the VALD3 database (Piskunov et al., 1995; Ryabchikova et al., 2015; Pakhomov et al., 2019) the synthetic spectra were calculated with the Synth3 code (Kochukhov, 2007). The $T_{\rm eff}$, $\log{g}$  parameters had been refining by the comparison of the synthetic spectrum with the observed one in the region of the wings of hydrogen H$\alpha$, H$\beta$ and H$\gamma$ lines. Since in late-B stars the hydrogen lines are both temperature- and gravity-sensitive we used the observed SED as the independent temperature constraint. The observed spectrophotomery was dereddened using Fitzpatrick et al. (2019) extinction curve adopting $R_{V}=4.7$. The dereddened SED was compared with the synthetic fluxes computed on each iteration with LLmodels code for a given model atmosphere. The theoretical fluxes were dilluted assuming the 287 pc distance and the stellar radius $R=2.2R_{\odot}$. The microturbulent velocity $\xi_{\rm t}$  was determined by the classical method of minimizing the slope of the dependence of the elemental abundance on the equivalent widths. We used a set of unblended Fe ii/ iii lines further employed for stratification analysis (see Sect. 3.5 and Tab. 4). The calculations were performed with a version of the Kurucz’s Width code modified by V. Tsymbal (priv.com.). The procedure of spectrum and SED fitting was repeated in a few iterations. The uncertainties of derived parameters were estimated from the dispersion of few last iterations around the best-fit solution.

As a result the following set of parameters was determined: the effective temperature $T_{\rm eff}$=13100$\pm$100 K, the surface gravity $\log{g}$=4.2$\pm 0.1$, the microturbulent velocity $\xi_{\rm t}$=0 km s^-1. The stellar parameters are also summarised in Table 1. The comparison of the observed and synthetic Balmer lines profiles calculated with this final set of parameters is shown in Fig. 4. One can see the reasonable agreement between synthetic spectrum and observations for H$\beta$ and H$\gamma$ lines. The prominent discrepancy between the observations and synthetic spectrum in the core of the H$\alpha$ line is caused by unaccounted non-LTE effects, while a little mismatch in the red wing could be due to the spectrum reduction faults. At the same time, the theoretical SED reproduces well the magnitude of the Balmer discontinuity and the slope of the Paschen continuum (Fig. 2), that confirms the reliability of our effective temperature determination.

The macroscopic broadening parameters: rotational broadening $v\sin{i}$ and macroturbulence $\zeta_{\rm RT}$ were found by fitting the metallic lines profiles in several spectral windows (e.g. 4590-4650 Å , 5045-5115 Å ) with the BinMag6 tool (Kochukhov, 2018). In agreement with the visual impression of the lines sharpness, neither rotational nor macroturbulence broadening was detected. Given the spectral resolution and instrumental profile width we can set the upper limit for rotational velocity as $v\sin{i}$$\lesssim$1-2 km s^-1 .

Despite the sharpness of absorption lines and the evidence for highly stabilized atmosphere no sign of Zeeman splitting or sufficient magnetic intensification was detected in the magnetically-sensitive spectral lines like Fe ii $\lambda\lambda$4303, 4385, 4520, 6149 Å . Within the measurement error we also were unable to detect the differential magnetic intensification in the Fe ii 6147/6149 Å  pair of lines which often is considered as an indication of the magnetic field presence (Mathys & Lanz, 1992; Kochukhov et al., 2013). These lines have identical intensity in normal stars without magnetic fields but possess a different Zeeman spitting that produces a difference in the observed equivalent widths when the magnetic field is presented. We estimate the normalized equivalent width difference of these lines as $\Delta W_{\lambda}/\overline{W_{\lambda}}\lesssim 0.03$. Unfortunately, there is no accurate experimental transition probabilities for these lines. Non-magnetic spectrum synthesis results in $\Delta W_{\lambda}/\overline{W_{\lambda}}$=0.026 with the theoretical transition probabilities from Raassen & Uylings (1998) while $\Delta W_{\lambda}/\overline{W_{\lambda}}$=0.003 with the theoretical transition probabilities from Kurucz’s 2013 line list⁵⁵5http://kurucz.harvard.edu/atoms/2601/gfemq2601.pos. Magnetic spectrum syntesis of this pair with the help of SYNMAST code (Kochukhov, 2007) showed that a global magnetic field $\langle B\rangle>$1 kG produced too wide synthetic line profiles. Therefore, we set an upper limit on the strength of the mean magnetic field as $\langle B\rangle\lesssim$1 kG. Although based on single-epoch spectroscopy, we cannot rule out the possible existence of a stronger magnetic field in BD+30$\degr$549, which could be detected in another rotational phase, or, more confidently, with the spectropolarimetric observations.

Line identification in BD+30$\degr$549 spectrum was performed using a synthetic spectrum calculated in the entire range $\lambda\lambda$4240-6710 Å  covered by the spectrogram at our disposal, we also used the line lists from Fossati et al. (2009) for guidance. Due to relatively high effective temperature most of the elements in BD+30$\degr$549 spectrum are presented by the moderate number of lines of the first ions. Only iron and silicon possess lines originated from two different ionization stages. The negligible rotational broadening simplified the task of lines selection. We were able to select a reasonable number of lines for abundance analysis, although for some light elements e.g. C  and O  the sampling was incomplete due to the limited spectral coverage and decrease of S/N ratio in the blue spectral region. The atomic data for abundance analysis were taken from the VALD3 database. For the light elements Mg  and Si  the oscillator strengths $gf$, excitation energies and damping constants retrieved from the VALD were checked against critically selected data from Alexeeva et al. (2018); Mashonkina (2020) and if necessary replaced by the latter values. We compiled a list of Fe ii/ iii with excitation energies ranged from 2.8 to 18.2 eV for the abundance determination and subsequent stratification analysis (see Tab. 4). Hyperfine splitting was taken into account for Al ii and Ti ii using the facilities of VALD3 database (Pakhomov et al., 2019).

Abundances, $\log(A)_{X}=\log(N_{X}/N_{H})$, were determined under LTE assumption as the mean of measurements of several lines of a given element $X$. Individual abundances were deduced from the fitting of observed line profiles by synthetic one with BinMag6 tool. The error in abundance determinations was estimated as a standard deviation of individual measurement from the mean.

We derived LTE abundances of 13 elements. The results of the abundance analysis are summarised in Table 2 and are also shown in Fig. 5. In the latter plot we compare the derived abundances with the solar ones as [X/H]=$\log(N_{X}/N_{H})-\log(N_{X}/N_{H})_{\odot}$. The reference solar abundances were taken from Scott et al. (2015a); Scott et al. (2015b) for elements from Na  to Ni  while the rest were adopted from Asplund et al. (2009). Most of the studied elements in BD+30$\degr$549 show depletion up to $\approx 1$ dex with respect to the solar atmosphere. We were unable to detect any traces of absorption due to He i at 4471, 5015, 5876 Å  and hence put the upper limit for helium abundance as $\log(A)_{\text{He\,{}}}\leq-3.5$ dex, which is 2.4 dex lower than the solar value. Contrary, Si , Ca , P  and Fe  display the overabundance. For silicon and iron, we found substantial abundance differences of 0.8 dex and 1.2 dex, respectively, between the lines of the first and second ions. Also for the strongest lines of Si ii (5055/5056, 6347, 6371 Å) and Mg ii 4481 Å, their wings and cores cannot be fitted with a single value of abundance. In such cases, the element abundance that fits the entire profile in the best way was adopted as a final value. The found discrepancies inspired us to check an influence of the departures from LTE on line formation for Si ii-iii, Mg ii, and Ca ii and to determine the non-local thermodynamic equilibrium (non-LTE) abundances (Sect. 3.4).

Despite the mild phosphorus overabundance in BD+30$\degr$549 atmosphere, we were unable to detect any gallium lines which could be also enhanced in spectra of the phosphorus-gallium subgroup of the helium-weak stars. We also did not find any strontium lines, because the strongest of them, Sr ii 4077Å and 4215 Å, were not covered by our spectrogram.

Lines of Si ii and Si iii in BD+30$\degr$549 reveal the largest deviations from the classical line-formation scenario that is based on the assumptions of LTE and a chemical homogeneity of the atmosphere. In this section, we check an influence of the departures from LTE on the statistical equilibrium (SE) of silicon and the element abundances derived from different Si lines. The non-LTE calculations were performed with the model atom treated by Mashonkina (2020). It includes levels of the first three ionization stages (Si i, Si ii, and Si iii) and the ground state of Si iv and implements the most up-to-date atomic data on transition probabilities, photoionization cross-sections, and electron-impact excitation rates. One of the stars studied by Mashonkina (2020), namely, HD 17081 ($\pi$ Cet), has atmospheric parameters ($T_{\rm eff}$ = 12800 K and log $g$ = 3.75) close to that of our star. The LTE analysis of $\pi$ Cet found an abundance difference of 0.23 dex between the two ionization stages, Si ii and Si iii, while consistent within 0.03 dex abundances were obtained in the non-LTE calculations. Compared with $\pi$ Cet, BD+30$\degr$549 reveals substantially larger LTE abundance discrepancies between Si ii and Si iii and high Si abundance, which exceeds the solar one by more than 1.3 dex. In the atmosphere enhanced with silicon, the Si line-formation depths shift to the upper atmospheric layers that can result in the stronger non-LTE effects compared with those for $\pi$ Cet.

The coupled radiative transfer and statistical equilibrium equations were solved with the code detail (Giddings, 1981; Butler, 1984), where the opacity package was updated as presented by Mashonkina et al. (2011). Figure 6 displays the departure coefficients, b${}_{i}=n_{i}^{\rm NLTE}/n_{i}^{\rm LTE}$, of the selected levels of Si ii and Si iii involved in the transitions, where the Si ii 5041, 5055, 5056 Å ($4p\,^{2}{\rm P}^{\circ}$ – $4d\,^{2}{\rm D}$) and Si iii 4552 Å ($4s\,^{3}{\rm S}$ – $4p\,^{3}{\rm P}^{\circ}$) lines arise. Here, $n_{i}^{\rm NLTE}$ and $n_{i}^{\rm LTE}$ are the SE and thermal (Saha-Boltzmann) number densities, respectively. Si ii is subject to overionization in the line-formation layers, above log $\tau_{5000}$ = 0, resulting in depleted populations of the ground state and the excited levels up to $4p\,^{2}{\rm P}^{\circ}$ ($E_{i}$ = 10.1 eV). The upper level of the Si ii $4p\,^{2}{\rm P}^{\circ}$ – $4d\,^{2}{\rm D}$ transition is depopulated to a lesser extent than is the lower level in the atmospheric layers up to log $\tau_{5000}\simeq-3$ and, in contrary, to a greater extent in the higher layers. Such a behavior of $4d\,^{2}{\rm D}$ is explained by a competition of the pumping UV transition from the ground state and spontaneous transitions to the levels below $4d\,^{2}{\rm D}$. As a result, the Si ii 5041 Å line, which forms downwards log $\tau_{5000}\simeq-3$, is weakened compared with its LTE strength (Fig. 7, middle panel) due to b($4p\,^{2}{\rm P}^{\circ}$) $<1$ and the line source function, $S_{\nu}$, greater than the Planck function, $B_{\nu}(T)$. The core of Si ii 5055.98 Å forms around log $\tau_{5000}\simeq-3.4$, where $S_{\nu}<B_{\nu}(T)$, and this prevails over b($4p\,^{2}{\rm P}^{\circ}$) $<1$, resulting in strengthened line core (Fig. 7, top panel). The wings of Si ii 5055.98 Å form in deeper layers and are weakened compared with the LTE case. Note that, in Fig. 7, the non-LTE profile of Si ii 5055.98 Å was computed with a higher Si abundance than that for the LTE profile.

The Si iii levels have enhanced populations in the line-formation layers, resulting in strengthened Si iii lines compared with their LTE strengths, as shown in Fig. 7 for Si iii 4552 Å.

The LTE and non-LTE synthetic spectra were calculated with the SynthV_NLTE code (Tsymbal et al., 2019), which implements the pre-computed departure coefficients from the DETAIL code. The best fit to the observed spectrum was obtained automatically using the IDL BinMag6 tool. In the fitting procedure, $\xi_{t}$ = 0, $V\sin i$ = 0, and $R$ = 48 000 were fixed, while the Si abundance and macroturbulent velocity were allowed to vary.

We found that profiles of the Si ii 4621.4, 4621.7, 5041.0, 5466.8 Å lines are well fitted in non-LTE (see Fig. 7 for Si ii 5041 Å) and the obtained non-LTE abundances are higher than the LTE ones, by 0.12 to 0.21 dex (Tab. 3). For the Si ii 5056 Å blend, the non-LTE profile reproduces the observed one better than the LTE profile, however, fails to fit to the observed line core (Fig. 7). The non-LTE abundance obtained from the line wings beyond the relative flux of $r\simeq 0.6$ is only about 0.1 dex lower compared with that for the well-fitted Si ii lines. The strongest Si ii 6347.1 and 6371.3 Å lines, with their cores formed in the uppermost atmospheric layers (log $\tau\simeq-4.2$), can only be fitted in their outer wings ($r\gtrsim 0.9$).

The Si iii line profiles in BD+30$\degr$549 are well fitted in the non-LTE calculations. Their non-LTE abundance corrections, $\Delta_{\rm NLTE}=\log A_{\rm non-LTE}-\log A_{\rm LTE}$, are negative and amount to $-0.24$ dex to $-0.11$ dex (Tab. 3). Thus, non-LTE reduces an abundance discrepancy between Si iii and Si ii, however, it is still substantial, $\log A$(Si iii – Si ii) = 0.53 dex. The non-LTE calculations confirm a strong enhancement of silicon in the atmosphere of BD+30$\degr$549, with [Si/H] = 1.45 and 1.98 from lines of Si ii and Si iii, respectively.

Our spectrum of BD+30$\degr$549 covers only weak Ca ii lines listed in Table 3. They all form in deep atmospheric layers and, in the LTE analysis, indicate an enhanced Ca abundance. We performed the non-LTE calculations using the model atom treated by Mashonkina et al. (2007). It was successfully applied by Sitnova et al. (2018) to achieve the Ca i/Ca ii ionization equilibrium in the sample of A-B type stars, including the star $\pi$ Cet with $T_{\rm eff}$ and log $g$ close to the corresponding parameters of BD+30$\degr$549.

We obtained that, in the line-formation layers of BD+30$\degr$549, Ca ii is subject to overionization, resulting in depleted level populations, weakened spectral lines, and positive non-LTE abundance corrections. The lines under investigation have very similar $\Delta_{\rm NLTE}$ = 0.46 and 0.47 dex (Tab. 3). Thus, the derived Ca abundance is pushed up to [Ca/H] = 1.11.

The non-LTE calculations were also performed for Mg i-Mg ii using the non-LTE method treated by Alexeeva et al. (2018). In contrast to Si and Ca, Mg is underabundant in the atmosphere of BD+30$\degr$549, with [Mg/H] $\sim-1$ from the LTE analysis. Therefore, compared with the Si ii lines of similar excitation energy and $gf$-value, the Mg ii lines form deeper in the atmosphere, and the non-LTE effects are expected to be smaller. The core of the strongest of the used lines, Mg ii 4481 Å, forms around log $\tau_{5000}=-1.8$ and the remaining Mg ii lines listed in Table 4 form close to log $\tau_{5000}=0$. Similarly to Si ii and Ca ii, Mg ii is subject to overionization in the atmosphere of BD+30$\degr$549. The non-LTE effects are minor, with $\Delta_{\rm NLTE}<$ 0.01 dex, for all the Mg ii lines except Mg ii 4481 Å. For the latter, non-LTE leads to the strengthened line core, but the weakened line wings and $\Delta_{\rm NLTE}=-0.06$ dex.

In summary, accounting for the non-LTE effects leads to much better representation of those silicon lines, which are formed at intermediate optical depths (log $\tau_{5000}>-3$), but fails to reproduce profiles of the strongest Si ii 5056, 6347, 6371 Å lines. Non-LTE reduces, but does not remove the abundance discrepancy between Si ii and Si iii. The obtained results lead us to suspect a presence of a vertical abundance gradient for silicon, with increasing abundance towards deeper layers. We consider the chemical stratification in the next section.

Abundance analysis of BD+30$\degr$549 under assumption of a chemically homogeneous atmosphere led to the following discrepancies, which are canonical signatures of a vertical abundance gradients (Ryabchikova et al., 2003):

• •

  Strong Si  and Mg  lines require different abundances to fit their wings and cores.
  

• •

  The abundances obtained from the lines of the same ion, e.g. Fe ii show a dependence on the excitation energies. The strong Fe ii lines which are formed in the upper layers indicate a lower abundance than the weaker ones, forming deeper in the atmosphere.
  

• •

  The lines of the second ions Fe iii and Si iii are abnormally strong and could not be fitted with the same abundances as for the first ions of iron and silicon.

Therefore we performed the stratification analysis using the approximation of the vertical abundance distribution in the atmosphere by the step-like function (see e.g Ryabchikova et al., 2005; Kochukhov et al., 2006, for validation of the method). Stratification calculations were made for three elements Fe , Si  and Mg  with DDAFit code (Kochukhov et al., 2006). The automatic procedure is based on the least-square fitting of the observed line profiles varying the four parameters which characterize the stratification profile: lower and upper abundances, position and width of the abundance jump in the $\log\tau_{5000}$ scale. Selection of spectral lines and atomic data for analysis is of critical importance for reliable reconstruction of stratification profile. The employed linelist should include lines with different excitation energy of the lower level, $E_{i}$, and formed at different optical depths, which are uniformly distributed through the atmospheric layers contributing to the line absorption.

The linelist with atomic parameters used in our calculations is presented in Table 4. Thanks to the large number of observed lines, including those from the second ionization stage, these line selection criteria are easily fulfilled for the iron. For iron we performed calculations with two sets of atomic data. First was based on Kurucz’s 2010 and 2013 lists for Fe iii and Fe ii respectively, while in second one we used primarily Raassen & Uylings (1998) data for Fe ii. Both datasets resulted in the fairly close parameters of the stratification profile, but linelist based entirely on the Kurucz’s data made it possible to fit the observed line profiles more accurately. The silicon lines we used also originate from the two ionization states and are more or less evenly distributed in the 8-19 eV energy range. In contrast, most of the available magnesium transitions are in the narrow range of excitation energies. However, the strong Mg ii 4481Å  line is formed over a wide range of optical depths $-1.7\lesssim\log\tau_{5000}\lesssim 0.8$ and allows to account for the contribution of different atmospheric layers.

The resulting abundance stratification for Mg  and Fe  are shown in Fig. 8. The iron and magnesium possess the step abundance gradient in the narrow range of optical depths near $\log\tau_{5000}\approx-0.3$. Both elements show tendency to increase abundance in the deeper atmosphere. Iron is mildly depleted in the upper atmosphere and increased its concentration with depth up to $\sim 1.5$ dex excess relative to the Sun. Magnesium is significantly underabundant by 1.9 dex in the upper atmospheric layers, reaches the solar value at $\log\tau_{5000}\approx 0$ and experiences a mild overabundance in the deepest layers contributing to line absorption. Comparison between observed lines profiles and synthetic ones calculated with stratified abundances shows a reasonable agreement in case of Fe  and Mg . Compared with the homogeneous distribution, accounting for stratification allows to adequately reproduce the line core depths for Fe  lines arising from both ionization stages (Fig. 9), as well as the profiles of magnesium lines including wings of the Mg ii 4481Å  line (Fig. 10).

In contrast, the jump of stratification profile for silicon turned out to be very gradual, distributed over the wide range of optical depths. Resulting fit of the observed lines profiles is poor and can reproduce neither the enhanced absorption in the Si iii lines, nor the wings of the strong Si ii lines.

Qualitatively, depth-dependence of iron and magnesium abundance as well as the depletion of helium in the upper atmosphere of BD+30$\degr$549, is consistent with the results of theoretical calculations (LeBlanc et al., 2009) and points to selective diffusion as the reason for the vertical stratification of these elements. However, exact position and magnitude of the abundance jumps in the BD+30$\degr$549 atmosphere deviates from the model predictions. First, these parameters depend on the physical conditions in a given atmosphere, and, second, the calculations represent the equilibrium solution while equilibrium could not yet be reached in the young BD+30$\degr$549 atmosphere. It is interesting to note that the results of the LeBlanc et al. (2009) calculations show a flattening of the stratification profiles as the $T_{\rm eff}$ rises from 8000 K to 12000 K. The latter value is the maximum effective temperature used in their calculations, and the resulting abundance gradients are overplotted in our Fig. 8. It is evident that the stratification profiles in the hotter atmosphere of BD+30$\degr$549 are steeper, in contrast to the theoretical predictions. This can be due to the star’s young age and non-equilibrium diffusion processes.

Our abundance analysis revealed that both silicon and iron are substantially overabundant in BD+30$\degr$549 atmosphere (Sect. 3.3) and also these elements possess both vertical and probably lateral abundance gradients (Sect. 3.5; 3.2.2). These metals play the important role in the opacity distribution throughout the atmosphere due to bound-free transitions and consequently affect its thermal balance (e.g. Khan & Shulyak, 2007). Indeed, as far back as Strom & Strom (1969) it was shown that $\approx$1.5 dex silicon enhancement affects the structure of the atmosphere in the same way as a $\sim$1000 K increase in $T_{\rm eff}$  and also causes a flux redistribution in the UV.

We performed a preliminary series of calculations to check how the vertical and horizontal stratification of the silicon affects the atmospheric model structure and emergent spectrum in case of BD+30$\degr$549. First, we calculated with LLmodel code the atmospheric model taking into account the individual abundances determined in BD+30$\degr$549 atmosphere as well as the vertical stratification for Si , Fe  and Mg . For iron and magnesium we applied stratification profiles derived from our analysis (see Fig. 8). For silicon profile was set manually. The abundance $\log(N_{\text{Si\,{}}}/N_{H})=-2.33$ dex deduced from the LTE determination using Si iii lines was adopted for the deep atmospheric layers, while as the upper limit we took $\log(N_{\text{Si\,{}}}/N_{H})=-3.76$ dex obtained from our fitting procedure with DDAFit. The location of the abundance jump was set at the same optical depths as for iron. Results of calculations are shown in Fig. 11. One can see that the temperature structure of the model changed noticeably both in the regions of lines and continuum formation. In the line forming region, we obtained a trend of decreasing temperature with depth compared to the homogeneous model (also helium-weak and silicon-rich). The difference reaches $\Delta T\approx$3$\%$ at $\log\tau_{5000}=-1$. The change in the electron pressure was less pronounced and occured predominantly in the deep atmospheric layers with $\log\tau_{5000}\gtrsim 0$. The joint effect of these changes on the SED and line profiles appeared to be significant. The stratified model provides the larger Balmer discontinuity and steeper Balmer continuum in UV. The latter resulted in better fit of the observed fluxes in the XMM-OM $UVW2$ and $UVM2$ filters than in case of homogeneous model (see Fig. 2). The magnitude of the Balmer jump produced with stratified model is less consistent with the observations, but this can be compensated by small variations in extinction and increasing $T_{\rm eff}$  within $\sim$300 K. Nevertheless, in the synthetic spectrum calculated with the stratified model, the Balmer lines became much broader. Fitting the theoretical profiles to the observed ones requires significant temperature correction, conflicting with the SED fitting. We conclude that current calculations with the homogeneous provide better simultaneous representation of the SED and line absorption spectrum of BD+30$\degr$549.

Although our spectrum allowed to put only an upper limit on the strength of the magnetic field of BD+30$\degr$549 at the date of observation, generally helium-weak silicon stars belongs to the magnetic sequence of CP stars (Romanyuk, 2007). Therefore, if BD+30$\degr$549 hosts a large-scale magnetic field, it could also lead to the patchy horizontal distribution of elements, i.e. existence of elemental spots with an altered temperature structure. The detected photometric variability of BD+30$\degr$549 preliminary confirms this assumption.

To take into account the influence of the silicon spot on the emergent spectrum, we used approach similar to that applied for another silicon star CU Vir (Krivoseina et al., 1980). A grid of simple models in which $\sim$50% of the stellar surface is occupied by a spot with enhanced silicon abundance and the rest of the surface being with the solar abundance has been computed. The temperature structure of the spot was recomputed with the LLmodel code, taking into account the opacity due to the increased silicon abundance. Varying the spot area and silicon abundance within reasonable limits, we were able to reproduce the profiles of individual silicon lines. However, the attempt to simultaneously reproduce Si ii and Si iii lines with the same abundance in the spot also failed. A simple estimate also shows that presence of such a spot with [Si /H]=+1.8 dex leads to rotational brightness modulation with an amplitude up to $\sim 0.1^{m}$ magnitude in the $V$ filter. This value is less than the observed $\Delta V\approx 0.2^{m}$ amplitude, but it should be taken into account that in reality the temperature structure of the spot could be modified by opacity due to other elements as well as by effects of vertical stratification. Thus, in order to reproduce the emergent spectrum, one needs to know both the distribution of spots on the stellar surface and the elemental abundances within each of them. Such information can be obtained from a subsequent spectroscopic monitoring of BD+30$\degr$549.

Our spectroscopic analysis of BD+30$\degr$549 atmosphere yields the following parameters: $T_{\rm eff}$=13100$\pm$100 K and $\log{g}$= 4.2$\pm$0.1. According to the modern temperature calibrations of MKK system (Gray & Corbally, 2009; Pecaut & Mamajek, 2013) such an effective temperature, as well as the bolometric absolute magnitude $M_{\mathrm{bol}}^{*}=-0.5^{m}$, are in the reasonable agreement with the historical spectral classification of the star as B8. Our analysis revealed the significant depletion of helium in the atmosphere of BD+30$\degr$549 with $\log(A)_{\text{He\,{}}}\leq-3.5$ dex. Other elements on average are also depleted, with the exception of Ca , P , Si  and Fe  which possess mild- to strong overabundance. The helium-weak stars constitute a rather heterogeneous group of hot CP stars and reveal a diversity of the element abundance patterns (see e.g. Ghazaryan et al., 2019). With the obtained element abundance pattern, BD+30$\degr$549 is not an outlier in this group. We attribute BD+30$\degr$549 with a caution to the silicon subgroup of helium-weak stars because of strikingly enhanced lines of Si ii and Si iii in its spectrum.

Except the general enrichment of silicon in BD+30$\degr$549 atmosphere which exceeds more than 1.3 dex with respect to the solar value, the lines corresponding to the two ionization stages yield an abundance difference of about 0.8 dex. In fact, such a discrepancy in abundances deduced from the Si ii and Si iii lines is known for B-type stars (see Bailey & Landstreet, 2013, and references therein). The latter authors studied this "Si ii/ iii-anomaly"  on the representative sample containing normal B-type stars as well as magnetic Bp and HgMn stars. It was shown that both magnetic and non-magnetic stars exhibit $\log A$(Si iii – Si ii) difference, but in case of normal B stars it is less pronounced reaching $\sim 0.3-0.8$ dex. The non-LTE effects and abundance stratification were proposed as possible reasons for this "Si ii/ iii-anomaly" . Indeed the non-LTE calculations by Mashonkina (2020) resulted in agreement between Si iii and Si ii based abundances for normal B7 and B3 stars, i.e. eliminated the difference in LTE abundances of 0.23 and 0.7 dex.

However, in case of BD+30$\degr$549 even after accounting for the non-LTE effects the $\approx$0.5 dex difference still persists between abundances deduced from the Si ii and Si iii lines. Intuitively, the discrepancy in the silicon lines after accounting for the non-LTE effects suggest its depletion in the upper atmosphere with increasing abundance in the deepest layers. Indeed, we found clear observational evidence of vertical abundance stratification in BD+30$\degr$549 manifested in the lines of some other elements, e.g. Fe  and Mg . However, in our analysis we were unable to construct such a stratification profile to equalize the abundances determined from the silicon lines forming at significantly different optical depths. Although at present state we cannot fully explain the "Si ii/ iii-anomaly"  observed in BD+30$\degr$549 spectrum, our results clearly indicate that combination of the effects of abundance stratification as well as departures from LTE in the silicon’s line formation region contributes to its appearance, in agreement with suggestion by Bailey & Landstreet (2013).

Another important factor which have to be accounted is inhomogeneous lateral distribution of elements over the stellar surface (chemical spots), which is typical for Ap/Bp stars. In the case of BD+30$\degr$549, the spots manifest in the rotationally-modulated period, detected in photometric variability of the star. Our preliminary calculations have shown that both silicon overabundance and vertical gradient of its abundance also affects significantly the temperature structure of the atmosphere. Thus, we reinforce the conclusion by Kochukhov & Ryabchikova (2018) that sophisticated interpretation of the observed spectra of CP stars generally requires taking into account the 3D distribution of abundances and subsequent recalculation of the atmospheric structure.

CP helium stars are abundant among the young stellar population in OB associations and Galactic star forming regions. For a long time numerous helium-weak stars are known in young Orion and Scorpius-Centaurus OB associations (see review in Smith, 1996). The existence of helium-weak stars in Ori OB1c ($\sim 2-6$ Myr old, Bally (2008)) subgroup (Romanyuk et al., 2013), as well as recent finding of the helium-weak silicon star in the Orion’s Trapezium region (Costero et al., 2021) (although without unambiguous attribution to $\sim 1$ Myr old Trapezium cluster) indicate that the onset of this type of peculiarity is either a very rapid process, or it can be triggered long before star’s settling on the ZAMS, during the PMS phase. The target of the present study, BD+30$\degr$549, is the member of active NGC 1333 star forming region and still embedded in the reflection nebula. Its isochronal age $t\approx 2.7$ Myr is slightly larger than the median cluster age $\sim 1.5$ Myr (Luhman et al., 2016) but is well within age dispersion found by Aspin (2003). In the HR diagram, BD+30$\degr$549 lies at the end of its PMS track, very close to the ZAMS.

Results of modern time-dependent diffusion calculations show that the diffusion timescale in the typical Ap/Bp atmosphere is of order $\sim 10^{1}-10^{3}$ yr (Alecian et al., 2011; Alecian & Stift, 2019), and hence development of the surface chemical inhomogeneities can occurs rapidly when the favorable conditions for an effective atomic diffusion have been achieved. Basically, such conditions are set up by slow axial rotation and hence ineffective meridional circulation as well as by suppressing of the microturbulence.

Indeed, our spectroscopic analysis revealed zero turbulence in the atmosphere of BD+30$\degr$549 and undetectable rotational broadening of the absorption lines with the upper limit on projected rotational velocity $V\sin i\lesssim 2$ km$\cdot$s^-1. Is BD+30$\degr$549 a really slow rotator or it is observed pole-on? If the photometric variability of the star is rotationally-modulated, then the $\approx$123^d.3 period corresponds to the equatorial rotation velocity $V_{*}\lesssim 1$ km$\cdot$s^-1, adopting the stellar radius $R_{*}=2.2R_{\odot}$. This velocity is in good agreement with our spectroscopic determination and implies that the star is observed close to equator-on. If we assume that during the PMS phase, BD+30$\degr$549 followed the evolutionary path of a typical Herbig Ae/Be star, then after the main protostellar mass-accretion phase it should gained the angular momentum resulted in typical equatorial rotational velocity of order $V_{*}\approx$150 km$\cdot$s^-1 (corresponding rotational period $\approx 0.7^{d}$ for $R_{*}\approx 2R_{\odot}$). Comparing this value with the present day rotational period we conclude that that BD+30$\degr$549 has lost (or not gained) a significant fraction of its angular momentum during the PMS phase.

The main agent in various macroscopic mechanisms of rotational braking (see Bouvier, 2013, for review) is believed to be the magnetic field, which is also effectively suppresses the turbulence and various types of circulation in the outer layers of the atmosphere (Mestel & Moss, 1977). Another possibility sometimes invoked to explain the loss of the angular momentum by Ap/Bp stars is synchronization in a binary system. Below we will examine both of these scenarios to see if they can explain an increase the rotational period of BD+30$\degr$549 from $\approx 0.7^{d}$ to about $123^{d}$ during the lifetime of the star, i.e $\approx 2.7$ Myr.