Pre-Main Sequence Ap Star LkHα 324/B in LDN 988 Star Forming Region

Abstract

We present results of the investigation of the star LkHα 324/B, which belongs to the starforming dark cloud LDN 988. Based on high resolution spectroscopy, we determined its fundamental parameters as $T_{\mathrm{eff}}=\mathrm{11,175}\pm 130$ K, $\log (L_{*}/L_{\odot })=1.87\pm 0.07$. According to these parameters, we found that LkHα 324/B is a pre-main sequence star with mass $M\approx 3M_{\odot }$ and age $t\approx 2.9$ Myr. Recently, it underwent the phase of actively accreting the Herbig Ae/Be star, but accretion has now ceased in the LkHα 324/B system. This is consistent with the fact that the star is surrounded by a circumstellar disk with an inner cavity, as was determined from its spectral energy distribution. Our analysis revealed the peculiar abundance pattern of LkHα 324/B typical to those of magnetic Ap stars. It possesses mild underabundance of the light elements and excess up to ∼2–4 dex (in comparison to the Sun) of the iron peak and rare earth elements. We found no evidence for abrupt vertical abundances gradients in the lines forming the region of the LkHα 324/B atmosphere, in agreement with the results of the theoretical diffusion calculations in this temperature domain. From the intensification of the magnetically sensitive lines, we deduced that LkHα 324/B probably hosts a global magnetic field of $⟨B⟩\approx 3.5$ kG strength. We suppose that the stabilizing role of this field favored the elements’ separation by diffusion before the star reached the main sequence.

1. Introduction

Among chemically peculiar (CP) stars of the upper main sequence (MS), magnetic Ap/Bp stars exhibit the most striking abundance of anomalies, with some elements being by ∼3–5 dex overabundant than in the solar composition [1,2]. Modern theory successfully explains the development of the peculiar surface composition in Ap/Bp stars under the action of selective atomic diffusion [3,4]. In a stabilized atmosphere, competing processes of radiative acceleration and gravitational settling leads to the effective vertical separation of elements, depending on the character of their interaction with the radiation field. An important condition for the effective diffusion is the unperturbed atmosphere, where the turbulent mixing as well as any types of macroscopic circulation are inhibited by slow axial rotation and strong magnetic fields.

This paradigm is generally consistent with observational data and allows for quantitative modeling of the spectra of MS Ap/Bp stars (e.g., [5,6]). However, a number of unresolved questions still remain, particularly concerning the evolutionary aspect of this scenario. What is the exact moment in stellar life of the manifestation of Ap/Bp type peculiarity? The vast majority of known Ap/Bp stars lies on the MS [7]. Investigation of the frequency of the Ap/Bp stars in open clusters with different ages revealed the gradual increasing of their number with age in the $6.7\lesssim logt\lesssim 8.5$ Myr range [8,9]. At the youngest ages, the occurrence of Ap stars in this statistics drops down to the zero threshold at $logt\approx 5.7$ Myr—the age of the Orion Nebula cluster. At first glance, this is consistent with the expectations that the Ap/Bp peculiarity manifests after the star passed the perturbed Herbig Ae/Be (HAeBe) phase: very close to, or immediately on, the Zero Age Main Sequence (ZAMS).

HAeBe stars are the ∼0.1–10 Myr old stars of intermediate mass contracting toward ZAMS via the radiative parts of the pre-main sequence (PMS) evolutionary tracks (see Brittain et al. [10] for a review). Accretion of the matter from the surrounding protoplanetary disks provides a wide range of activity phenomena observed in HAeBe stars. However, details of this process are still unclear and depends strongly on the existence of organized stellar magnetic fields, which can control the flows of infalling matter. Indeed, such fields, although statistically weaker than those of early-type magnetic stars on MS, have been discovered in the ∼10% of HAe stars [11]. It is believed that HAe stars interact with the disk in the magnetospheric accretion regime, while more massive HBe stars possibly accrete through the boundary layer [12,13]. In any case, accretion from the disk should sustain the primordial surface composition at least until the accretion fades, which roughly coincides with the moment of arrival of the star to ZAMS. However, recent discoveries of a few accreting HAeBe stars with magnetic fields and abundance patterns resembling Ap/Bp ones [14,15], non-accreting young intermediate-mass CP stars [16,17,18], as well as refinement of ages and statistics of CP stars in subgroups of the Orion star forming complex [19] clearly show that in some cases, the development of anomalies of the surface chemical composition can occur as early as the PMS phase. It is very important to understand exactly what mechanism or specific conditions lead to the formation of surface chemical inhomogeneities at such early phases of evolution.

The application of diffusion theory to explain the abundance patterns of young Ap/Bp stars faces a number of challenges. The most serious of them is accounting for accretion of undepleted gas with primordial composition from circumstellar disks during the HAeBe phase. Calculations by Turcotte and Charbonneau [20] show that accretion rates $\dot{M}\gtrsim {10}^{-12}{M}_{\odot }·$yr${}^{-1}$ erase the signatures of vertical elements separation in the upper atmospheric layers and the surface chemical composition appears to be the same as in the accreted gas. According to their estimates, it takes ∼1 Myr after the end of accretion for shaping the surface chemical composition by diffusion. More recent calculations by Vick et al. [21], accounting for the mass loss due to wind, extended this time to ∼2–25 Myr, depending on stellar mass. As suggested by Wade et al. [22], HAeBe stars and MS Ap/Bp stars constitute the uniform evolutionary sequence. Hence, adoption of the above-mentioned numerical results leads to considerable inconsistency in the characteristic time scales. HAeBe stars are known to accrete matter from their disks with typical rates of $\dot{M}\sim {10}^{-6}-{10}^{-8}{M}_{\odot }·$yr${}^{-1}$, which are several orders of magnitude larger than the diffusion predominance limit derived by Turcotte and Charbonneau. The age dependence of mass accretion rates [13,23] indicates that accretion with rates of $\dot{M}\gtrsim {10}^{-9}{M}_{\odot }·$yr${}^{-1}$ lasts during the major fraction of the PMS evolution of 2–5$M_{\odot }$ stars (see also Figure 5 in Wichittanakom et al. [13]). It takes ∼10 and 1 Myr, respectively, for the mentioned stellar masses to reach ZAMS. Comparing these data with timescales by Turcotte and Charbonneau and, especially, Vick et al., it turns out that the PMS star generally could not have enough time to shape the surface chemical composition due to diffusion after the end of the active accretion and before settling on the ZAMS.

Thus, to explain the existence of Ap/Bp stars at the PMS phase, either special conditions leading to faster-than-average disruption of the inner disk and termination of accretion (e.g., effects of a strong magnetic field, tidal interaction with a companion) should be invoked, or the current models need to be modified. In any case, there is an obvious reason to expand the present sample of very young Ap/Bp stars and carefully study their characteristics in order to reconstruct the complete evolutionary sequence of Ap/Bp phenomenon. One possibility is to identify such objects not only in clusters but in younger star-forming regions, which also allows for accurate tagging to absolute age. The aim of this work is to investigate quantitatively the atmospheric parameters and chemical composition and to determine the evolutionary status of the peculiar star LkH$\alpha$ 324/B, located in the star-forming cloud LDN 988.

2. LDN 988 Cloud and Peculiar Star LkH$\alpha$ 324/B

The dark cloud LDN 988 [24] is a part of the giant complex of molecular clouds TGU 541 [25] in the northern region of the Cygnus constellation. The most recent and comprehensive study of the young stellar population in the vicinity of LDN 988 was made by Herbig and Dahm [26]. They examined the eastern part of the LDN 988 cloud, dominated by few early-type stars, including emission-line stars LkH$\alpha$ 324 and LkH$\alpha$ 324SE. LkH$\alpha$ 324 is surrounded by the rich compact cluster of low-mass stars with an age $\overline{t}\sim$0.7–1.5 Myr. It was proposed that the “LkH$\alpha$ 324-cluster” is visible thanks to its location in the cavity excavated in the molecular material by the radiation and winds of the aforementioned two luminous stars, while the entire LDN 988 is also encompassed by an active star formation shielded by heavy extinction. Indeed, radio CO observations [27] and narrow-band optical imaging [28] revealed the presence of numerous molecular outflows and Herbig-Aro (HH) objects in this region.

At optical wavelengths, early-type star LkH$\alpha$ 324/B coinciding with point source IRAS 21014+5001 (RA = 21${}^h$03${}^m$03${}^s$.25, DEC = +50${}^{\circ }$13${}^{\prime }$13″.05) lies in the region of highest obscuration near the center of LDN 988. The star illuminates reflection nebula DG 169 and is surrounded by a group of faint and heavily reddened stars, indicating that it probably belongs to a PMS population of LDN 988. LkH$\alpha$ 324/B was classified by Chavarria-K [29] as A0 Vp star with enhanced Si II lines. Herbig and Dahm also noticed enhanced Cr II, Mn II lines as well as an absence of absorption due to He I in the high-resolution spectrogram of the star. They concluded that LkH$\alpha$ 324/B is a very young CP star which still locates within its natal material. Remarkably, Clark [27] identified the high-velocity blueshifted molecular outflow close to position of LkH$\alpha$ 324/B (IRAS 21014+5001). This outflow is likely bipolar, but its symmetrical receding lobe is misidentified due to overlapping with redshifted gas associated with other sources. Follow-up optical ($H\alpha$ and [SII]) searches led to the identification of numerous shocks from protostellar outflows within the LDN 988 cloud [28]. Several of them, namely HH objects HH1046, 1049, 1053, and HH1060, 1063, are aligned along the axis crossing LkH$\alpha$ 324/B and roughly coincide in the western part with the northern contour of Clark’s CO outflow. If the alignment of these shocks is not the result of the accidental projection in the crowded region and they actually trace the same outflow driven by LkH$\alpha$ 324/B, then its full length is ∼4.6 pc, as Walawender et al. [28] concluded.

3. Observations and Data Reduction

3.1. High-Resolution Spectroscopy

The high-resolution spectrum of LkH$\alpha$ 324/B was retrieved from the Keck Observatory Archive1. Observations were obtained by G. Herbig with a 10 m Keck I telescope and High-Resolution Echelle Spectrometer (HIRES) on the night of 6 July 2003. The instrument configuration was used with the 0.86 × 7 arcsec C1 decker, which provided a resolving power of $R\approx$ 48,000. The spectrogram covers the $\lambda \lambda$4350–6690 Å wavelength range with some gaps between echelle orders in the red region. With a 1200${}^s$ integration time, a signal-to-noise ratio (S/N) of ∼180–200 was achieved in the red orders of the LkH$\alpha$ 324/B spectrogram.

The HIRES observations were processed with the MAKEE (MAuna Kea Echelle Extraction) pipeline written by T. Barlow and available via the webpage2. The standard reduction procedure including the bias subtraction, flatfielding with the spectrum of quartz lamp and cosmic rays correction was applied to the scientific frame. Tracing of the echelle orders and defining the background region was made in the interactive regime in order to correctly account for the contribution of the underlying nebula. Manual determination of the orders boundaries succeeded in a quality extraction of the one-dimensional spectrum. The 1D target spectrum was wavelength-calibrated using the reference Th-Ar lamp spectra. The heliocentric velocity correction was applied to the science data. The normalization of the echelle orders to the continuum level was performed using approximation by the low-degree cubic spline. Orders containing hydrogen lines with broad Stark wings were normalized by interpolating the continuum level between two adjacent orders.

3.2. Low-Resolution Spectroscopy

The low-resolution optical spectrum of LkH$\alpha$ 324/B was obtained with the ADAM spectrograph [30] attached to the 1.6 m telescope AZT-33IK at the Sayan Solar Observatory (SSO) operating in the Institute of Solar Terrestrial Physics. Observations were carried out on the night of 8 November 2021. The $\lambda \lambda$3600–10,000 Å wavelength range was covered by two spectrograms dispersed with the VPGH600G and VPGH600R grisms. Data were recorded by the 1024 × 256 px E2V CCD detector with 26 $\mathsf{\mu }$m pixel size. Since the seeing conditions at SSO were typically ≈1.5–2.0 arcsec during observational runs, the 1.5 arcsec slit was used, which resulted in nominal resolving power $R\approx 1200$. The total integration time was 360${}^s$ in each blue and red arm. A complete set of calibration frames was obtained, including bias frames, spectra of flat field quartz lamp, as well as spectra of hollow-cathode Ne-Ar lamp for wavelength calibration. Spectra of a few spectrophotometric standards, i.e., BD+25${}^{\circ }$4655, EG139, EG247, were obtained quasi-simultaneously with the same setup configuration.

The low-resolution spectroscopic data were processed using the standard reduction scheme with the tool longslit of the IRAF package [31]. The science spectra were flux-calibrated using the extinction-corrected sensitivity curve determined from the observations of the standard stars.

3.3. Photometry

The $UBVRI$ photometry of LkH$\alpha$ 324/B was obtained on two nights in July 2022 (JD 2459788 and 2459789). The observations were made with 2048 × 2048 BI AIMO CCD mounted on the 1.25 m telescope AZT-11 of the Crimean Astrophysical Observatory (CrAO). For extinction corrections and reduction to the standard photometric system, the quasi-simultaneous observations of Landolt’s standard area 41 [32] were also obtained.

Primary reduction of frames and aperture photometry was performed with the standard IRAF routines. The procedure included accounting for bias and dark frames, flat fielding, and extraction of fluxes of target, control, and comparison stars. Transformation of the instrumental magnitudes to the standard Jonson-Cousins photometric system were made with the software written by K.N. Grankin (priv. comm.), accounting for the air mass, extinction, and instrumental coefficients. Star SA41-171 was used as a comparison. The standard deviation of V magnitudes and color indexes B–V, V–R, and V–I was less or equal to 0.01 mag, while the standard deviation for U–B is about 0.2 mag.

4. Results

4.1. Distance, Extinction, and Stellar Parameters

The low-resolution spectrum of LkH$\alpha$ 324/B definitely indicates that the star belongs to the CP class. A comparison with spectra of several A7–B7 chemically normal stars retrieved from the MILES library [33] revealed an enhanced Si II 4128/4132 Å doublet near $H\delta$ as well as another one at 3856/3862 Å. Lines of ionized chromium, such as Cr II 3866, 4077, and 4172 Å are also abnormally strong in LkH$\alpha$ 324/B, while lines due to He I were undetectable in our low-resolution spectrum. Based on these criteria [34], we attribute the star to the Ap Si subgroup, consistent with previous classifications [26,29]. Another important feature visible in the flux-calibrated spectrum of LkH$\alpha$ 324/B is the extended “$\lambda$5200-depression” caused by strong blending due to Fe II and Cr II absorptions, which is often served as an indicator of magnetic Ap stars [35,36].

According to the GAIA EDR3 [37] catalog, the parallax of LkH$\alpha$ 324/B equals to $\pi =1.591\pm 0.014$ mas. The corresponding Renormalized Unit Weight Error (RUWE) parameter $RUWE=0.965$ is less than the recommended 1.4 threshold and indicates a secure astrometric solution. Hence, this parallax can be directly converted to distance $D=628.5\pm 5.5$ pc, which agrees very well with the 600 pc distance previously adopted for the PMS population in the L988 region (e.g., [26,28]). As was pointed out by Herbig and Dahm [26], heliocentric radial velocities (RVs) of bright stars in L988 regions are close to the cloud velocity measured from molecular lines. Indeed, the $R{V}_h=-16.2$ km/s of LkH$\alpha$ 324/B within a few kilometers per second coincides with $R{V}_h=-14$ km/s3 measured at this direction from ${}^{12}$CO$(J=1-0)$ transition [39]. The coincidence of both the distance and kinematics of LkH$\alpha$ 324/B with those of the cloud material reinforce the conclusion about their genetic relationship.

The location within the region of heavy obscuration, as well as the rich interstellar spectrum containing atomic absorption lines and numerous diffuse interstellar bands (DIBs), implies that LkH$\alpha$ 324/B suffers significant interstellar extinction. In order to estimate its amount, we first measured equivalent widths ($EW$s) of few DIBs at 5780, 5797, 6380, 6614 Å in our HIRES spectrogram and then employed empirical calibrations [40,41], relating the $EW$s of DIBs with extinction $A_V$. The average value was found to be $A_V\backsimeq 2.5$ mag. This value was used as the first guess during the procedure of atmospheric parameters determination. We used the method of simultaneous fitting the observed spectral energy distribution (SED) and hydrogen Balmer lines in order to obtain effective temperature $T_{\mathrm{eff}}$, stellar radius $R_{*}$, and visual extinction $A_V$ (see Section 4.2).

The SED of LkH$\alpha$ 324/B was constructed in the ∼0.36–100 $\mathsf{\mu }$m range using the original CrAO $UBVRI$ photometry and flux-calibrated SSO low-resolution spectrum, as well as the archival data from the Two Micron All Sky Survey (2MASS, [42]), Wide Field Infrared Explorer (WISE, [43]), and Infrared Astronomical Satellite (IRAS, [44]) point source catalog. We fitted the observed SED by the grid of pre-computed theoretical fluxes for an appropriate range of $T_{\mathrm{eff}}$ values and stellar radii. Simultaneously, the interstellar extinction was also fitted using the Fitzpatrick et al. [45] extinction curve and the total-to-selective absorption ratio $R_V=3.1$. As a result, we determined extinction $A_V=2.2$ mag, which is close enough to the value initially determined from DIBs.

A comparison of the dereddened observations with theoretical flux calculated for the best-fit set of parameters is shown in Figure 1. One can see from the figure that the synthetic flux perfectly matches the observations in the visual and near-infrared (NIR) spectral regions, while longward from ∼12 $\mathsf{\mu }$m ($W3$ band), there is a significant IR emission above the photospheric level. The mid-IR part of this excess is reasonably well-fitted by $T_{bb}\sim 300$ K blackbody and can be attributed to the thermal radiation of the dust orbiting in the circumstellar disk around LkH$\alpha$ 324/B. The absence of $JHK$ excess as well as signatures of the accretion activity indicate the presence of the inner cavity in the disk, probably formed due to photoevaporation and/or planet formation. The far-IR radiation traced by 60 $\mathsf{\mu }$m and 100 $\mathsf{\mu }$m IRAS points is most probably related to the population of the cold dust in the outer regions of the disk or dust in reflection nebula. We estimated fractional IR luminosity as $L_{IR}/L_{bol}\approx 0.13$ integrating flux density under the SED. This value lies within the range observed in HAeBe stars with optically thick disks (e.g., [46,47]). However, this should be taken as the upper limit with caution, since the contribution of the reflection nebula in the FIR region has not been isolated. Further investigation of the structure and optical properties of LkH$\alpha$ 324/B disk and estimation of its mass using sophisticated SED modeling is desirable.

Using the temperature and stellar radius derived from SED fitting, which are $T_{\mathrm{eff}}$ = 11,175 ± 130 K and $R_{*}=2.3\pm 0.15R_{\odot }$, respectively, (Section 4.2), it is possible to calculate stellar luminosity as:

$$L_{*}/L_{\odot }={(R_{*}/R_{\odot })}^2{(T_{*}/T_{\odot })}^4\approx 74$$

and plot LkH$\alpha$ 324/B in the Hertzsprung–Russell (HR) diagram (Figure 2). A comparison with the theoretical evolutionary tracks and isochrones from the PARSEC grid [48] calculated for the metallicity $Z=0.017$ reveals that LkH$\alpha$ 324/B is a $\approx 3M_{\odot }$ star with an age of $\approx 2.9$ Myr. It still lies above ZAMS on the PMS evolutionary track and recently passed the penultimate luminosity minimum caused by the rearrangement of the central structure after ignition of the first two proton capture reactions in the C${}^{12}$→N${}^{14}$ chains of CNO cycle [49]. The star is now on the ascending part of the evolutionary track due to enhanced release of the gravitational energy. It is interesting to note that although LkH$\alpha$ 324/B lies close (≲0.05 dex by $T_{\mathrm{eff}}$ ) to ZAMS on the ($T_{\mathrm{eff}}$, L)-plane, it will take a non-negligible time to reach it. The star has so far completed only ∼78% of its entire 3.7-Myr PMS evolution.

4.2. Atmospheric Parameters

In order to determine the atmospheric parameters of LkH$\alpha$ 324/B, we used the self-consistent method based on spectral synthesis of the Balmer $H\alpha$ and $H\beta$ lines and simultaneous fitting of the observed SED by theoretical flux. Exclusive usage of hydrogen lines, which are sensitive to both $T_{\mathrm{eff}}$ and surface gravity $logg$ in the given temperature domain, could result in degeneracy of the solution. To avoid this, we employed fitting of the SED as an independent temperature constraint and also adjusted the stellar radius $R_{*}$ and extinction $A_V$ during this procedure.

Atmospheric parameter determination was an iterative procedure for finding a model that yields the best match between synthetic spectrum and observations. As the starting parameters $T_{\mathrm{eff}}$ and $logg$, we used those of ∼A0– B9 stars obtained from the calibrations of the MKK system [34,50]. Then, within reasonable limits around these parameters, we have calculated the initial grid of helium-weak (Section 4.4) models with a hydrogen abundance of $N_H/N_{tot}=0.99$. The atmospheric model and the emergent flux were calculated with the LLmodels code [51], which employed line-by-line opacity treatment, and hence, allows to effectively account the specific opacity distribution in the chemically peculiar atmospheres. The corresponding synthetic spectra were calculated with these models using Synth3 code [52] and with the atomic data retrieved from the VALD3 database [53,54,55]. The iterative procedure also involved estimation the abundances of the few elements (e.g., He, Si, Fe, and Cr) mostly contributing to opacity, and hence, the temperature structure of the atmosphere. At each iteration, the atmospheric model and the emergent flux were recalculated, taking into account the current approximation of the chemical composition.

The best representation of the observed hydrogen lines profiles as well as SED was achieved with $T_{\mathrm{eff}}$ = 11,175 ± 130 K, $logg$ = 4.2 ± 0.15. One can see from Figure 3 that, with the given parameters, the theoretical spectrum describes well the observed wings of the Balmer lines, excluding the non-LTE cores and the wing-to-core transition in the $H\alpha$ line. The latter is a well-known feature of magnetic CP stars named “core to wing anomaly” [56,57]. Theoretical flux calculations represent the magnitude of the Balmer jump in the SED and the slope of the Paschen continuum as well, which confirms the obtained value of $T_{\mathrm{eff}}$ (Figure 1). The uncertainties of parameters were estimated from the variance around the final values at the last few iterations. In the atmospheres of Ap stars, the microturbulent velocity ${\xi }_{\mathrm{t}}$ is typically suppressed to a zero value. Indeed, in the atmosphere of LkH$\alpha$ 324/B, we found a lack of dependence of the abundance on $EW$s of three dozen of Fe II lines, assuming ${\xi }_{\mathrm{t}}$ = 0 ± 0.2 km s${}^{-1}$. The projected rotational velocity was found to be $vsini$ = 24 ± 1.5 km s${}^{-1}$ from fitting of the numerous metallic lines profiles in several spectral windows, e.g., 4516–4583, 5037–5106, 5970–6058 Å with the BinMag6 tool [58]. The radial velocity $RV=-16.2\pm 0.2$ km s${}^{-1}$ found by cross-correlation with the synthetic template in the same spectral windows proved to be in excellent agreement with the Herbig and Dahm [26] measurement. The final set of the parameters of LkH$\alpha$ 324/B is summarized in

Table 1. Parameters of LkH$\alpha$ 324/B.

Parameter	Value
$T_{\mathrm{eff}}$	11,175 ± 130 K
$logg$	4.2 ± 0.15 dex
${\xi }_{\mathrm{t}}$	0.0 ± 0.2 km s${}^{-1}$
$vsini$	24 ± 1.5 km s${}^{-1}$
$RV$	−16.2 ± 0.2 km s${}^{-1}$
$\langle B\rangle$	∼3.5 kG
$A_V$	2.2${}^m$
$log(L/L_{\odot })$	1.87 ± 0.07
$M/M_{\odot }$	3.0
$R/R_{\odot }$	2.3 ± 0.15
Age	≈2.9 Myr

.

4.3. Magnetic Field

Silicon Ap stars generally belong to the magnetic sequence of CP stars. Indeed, a number of features observed in the spectrum of LkH$\alpha$ 324/B and typical for Ap stars allow us to suspect that it hosts a large-scale magnetic field. This evidence is listed below:

• Rotationally modulated photometric variability (see Section 4.5);
• $\lambda$5200 continuum depression;
• “Core-to-wing anomaly” in the $H\alpha$ line;
• Indications for the outflow activity in the past.

However, the non-negligible rotational broadening prevents the direct detection of the Zeeman splitting of lines in the spectrum of LkH$\alpha$ 324/B. In case of stars with an unresolved Zeeman pattern, it is possible, however, to estimate the magnetic field strength from the differential broadening of lines with large effective Lande factors relative to the magnetically insensitive ones [59]. The modern implementation of the method using magnetic spectrum synthesis has the advantage that it can be applied to stars not only with narrow lines, but also with moderately blended spectra. We applied this method to estimate the strength of the putative mean surface magnetic field in LkH$\alpha$ 324/B.

In our analysis, we used the pairs of Fe II lines 4491/4520, 6147/6149 Å. The first pair of lines has considerably different effective Lande factors, i.e., z = 0.4 and $z=$ 1.34, respectively. Thus, in the presence of a magnetic field, Fe II 4520 Å shows a magnetic intensification that increases more rapidly than in Fe II 4491 Å. Fe II 6147/6149 Å lines have the same upper level and very close oscillator strengths, but possess different Zeeman patterns, splitting into pseudo-quadruplet and simple doublet, respectively (see, e.g., [60]). Hence, Fe II 6147/6149 Å lines should have identical intensity in non-magnetic stars and possess different intensification and broadening depending on the magnetic field strength. This makes them a widely used tool for diagnostics of the magnetic field in Ap stars [60,61]. As a reference, we also used magnetically insensitive line Fe II 6586 Å (z = 0.03) situated in the wing of the $H\alpha$ line.

Unfortunately, there is no experimental transition probabilities for the lines used in our analysis, although the accurate atomic data are of crucial importance for the relevant measurements. Thus, we had to check and verify the atomic data we used. First, from the VALD3 database, we had collected theoretical oscillator strengths $loggf$s for the lines used in magnetic analysis from the primary sources: Raassen and Uylings calculations [62] and Kurucz’s 2013 line list4.

These atomic data were checked against observations of two stars: 21 Peg and HD 170973, which have well-defined parameters. Both stars are slowly rotating, but while 21 Peg is chemically normal, HD 170973 belongs to Ap stars with the elemental composition close to that in LkH$\alpha$ 324/B (Section 4.4). Parameters of these stars and corresponding references are given in

Table 2. Parameters of comparison stars.

Star	${\mathit{T}}_{\mathbf{eff}}$, K	$log\mathit{g}$, dex	$\mathit{v}sin\mathit{i}$, km s${}^{-1}$	$\langle {\mathit{B}}_{\mathit{l}}\rangle$, Gs	Composition	Obs. Data
21 Peg 1	10,400	3.55	3.8	−4.6 ± 3.1 2	normal	ESPaDOnS, R = 65,000
HD 170973 3	11,000	3.7	8.5	392 ± 5	Ap	ESPaDOnS, R = 65,000

¹ Parameters and abundances of 21 Peg adopted from Fossati et al. [63]; ² Kochukhov et al. [60]; ³ Parameters and abundances of HD 170973 adopted from Ryabchikova et al. [64] and T. Ryabchikova (private communication).

. The overabundance of iron peak elements observed in HD 170973 also allows us to verify the poorly known oscillator strengths of high excitation Fe II and Cr II lines, which are presented in spectrum of LkH$\alpha$ 324/B, and blended lines used in our magnetic analysis. The verification procedure involved calculation of the synthetic spectra with the parameters from Table 2 for different sets of atomic data and a further comparison of the theoretical line profiles to the observed ones. If the theoretical $loggf$s of a given transition resulted in an unsatisfactory fit of the observed line profile and gave an abundance considerably different from the average, the $loggf$ value was fitted empirically for the fixed average abundance of a given element using BinMag6 tool. The results for the lines quoted above and used in the analysis of magnetic intensification in the LkH$\alpha$ 324/B spectrum are summarized in

Table 3. Lines used for the analysis of magnetic broadening in LkH$\alpha$ 324/B.

Line	$log\mathit{gf}{}^{*}$	${\mathit{E}}_{\mathit{i}}$, eV	z, eff.	$log({\mathit{N}}_{\mathit{Fe}}/{\mathit{N}}_{\mathit{H}})$
				$\langle \mathit{B}\rangle =0$ G	$\langle \mathit{B}\rangle =3500$ G
Fe II 4491.397 Å	−2.71 (FMW)	2.85	0.4	−3.27 ± 0.03	−3.45 ± 0.03
Fe II 4520.224 Å	−2.60 (RU)	2.80	1.34	−2.80 ± 0.05	−3.36 ± 0.06
Fe II 6147.734 Å	−2.731 (K13)	3.88	0.83	−2.61 ± 0.05	−3.46 ± 0.03
Fe II 6149.246 Å	−2.732 (K13)	3.88	1.35	−3.01 ± 0.02	−3.41 ± 0.05
Fe II 6586.708 Å	−2.35 (fit)	5.60	0.01	−3.48 ± 0.06	−3.48 ± 0.06
				−3.03 ± 0.31	−3.43 ± 0.04

* Sources for oscillator strengths: RU—Raassen and Uylings [62]; K13—Kurucz, 2013; FMW—Fuhr and Martin and Wiese [65]; fit—fitted value.

.

To calculate the magnetic synthetic spectrum, we extracted atomic data for transitions in the vicinity of the line of interest from the VALD3 database. The ”long” —format of data extraction provides the complete configuration of the atomic levels. From these data, using the IDL procedure written by O. Kochukhov, we calculated the Zeeman splitting of the lines, obtaining the relative intensities and wavelength shifts for the components. For lines with unknown Lande factors, Zeeman patterns were calculated on the basis of the LS-coupling theory. If necessary, the $loggf$s were replaced by the values obtained with the above-mentioned procedure. We performed magnetic spectrum synthesis using SYNMAST code [52]. Using the BinMag6 widget for the magnetically sensitive lines employed in our analysis, we fitted the observed line profiles, adjusting simultaneously the strength of the radial magnetic field and the elemental abundance. Our fitting gave an estimate of the magnetic field strengths averaged over the stellar surface $\langle B\rangle$∼3.5 kG, which provided better representation of the observed lines profiles than in the non-magnetic case. One can see from Table 3 that employment of such a field also leads to reducing the scatter of individual measurements, as well as a decrease of the resulting error of iron abundance: from 0.31 dex (in the non-magnetic case) to 0.04 dex. The null-magnetic line Fe II 6586 Å used for the control gave the same abundance in both cases.

4.4. Average Abundances

Abundances, $log{\left(A\right)}_X=log(N_X/N_H)$, were determined under the LTE assumption for 15 elements in LkH$\alpha$ 324/B atmosphere. We used the method of fitting individual lines with synthetic spectrum implemented in the BinMag6 tool. The synthetic spectrum was calculated with adopted atmospheric parameters (Table 1) and assuming 3.5 kG global magnetic field. The primary source of atomic data was the VALD3 database, but the extracted oscillator strengths (especially for numerous Fe and Cr lines) were checked against the spectra of standard stars 21 Peg and HD 170973 according to the procedure described in Section 4.3 and corrected if necessary. The abundance of element X was determined as the average of the measurements of several lines. The error was estimated as the standard deviation around the mean. Most of the elements in the LkH$\alpha$ 324/B spectrum are represented by the lines of the first ions. However, for Si, Fe, and Cr, abundances were determined separately for two ionization stages. The results of the determination of the abundances are shown in Figure 4 and also summarized in

Table 4. Abundances in LkH$\alpha$ 324/B.

Element	${\mathit{N}}_{\mathit{lines}}$	$log({\mathit{N}}_{\mathit{X}}/{\mathit{N}}_{\mathit{H}})$	$log{({\mathit{N}}_{\mathit{X}}/{\mathit{N}}_{\mathit{H}})}_{\odot }$
He I	2	−3.35 ± 0.15	−1.07
C II	2	−4.10 ± 0.15	−3.57
O I	3	−4.00 ± 0.30	−3.31
Mg II	4	−4.56 ± 0.15	−4.41
Al II	1	−6.18 ± 0.5	−5.27
Si II	9	−3.14 ± 0.17	−4.49
Si III	2	−2.98 ± 0.15	−4.49
Ca II	4	−4.37 ± 0.18	−5.68
Ti II	6	−7.17 ± 0.2	−7.07
Cr I	6	−3.44 ± 0.20	−6.38
Cr II	14	−3.64 ± 0.22	−6.38
Mn II	2	−4.82 ± 0.16	−6.58
Fe I	4	−3.24 ± 0.12	−4.53
Fe II	22	−3.24 ± 0.16	−4.53
Ni II	7	−5.20± 0.26	−5.80
Ba II	2	≲9.00	−9.82
Pr III	4	−7.40 ± 0.17	−11.33
Nd III	12	−6.86 ± 0.17	−10.54

. In Figure 4, we use the notation [X/H] = $log{\left(A\right)}_X^{*}-log{\left(A\right)}_X^{\odot }$, which denotes the abundance of element X relative to the solar ones. Solar abundances were compiled from Scott et al. [66,67] for elements from Na to Ni and from Asplund et al. [68] for the remaining elements.

The comparison of the abundance distribution in LkH$\alpha$ 324/B and in HD 170973 overplotted in Figure 4 clearly indicates that the former exhibits a pattern characteristic for the Ap stars. Helium is significantly underabundant in LkH$\alpha$ 324/B atmosphere, up to −2.3 dex relative to the Sun. Its strongest lines at 4471 Å and 5876 Å are very weak but still detectable in the high-resolution HIRES spectrum. The other light elements (C, O, Mg, and Al) are also moderately depleted, possessing a general trend of increasing abundance with the atomic number, up to a subsolar value for magnesium. Metals are overabundant within the [X/H]$\sim +1.3-3$ dex range. Note that the $\approx +1.4$ dex excess of silicon anticorrelates with helium depletion—a well-known feature of the magnetic Ap stars, predicted by diffusion theory (e.g., [69,70]). Among the iron peak elements, chromium displays the greatest excess [Cr/H] $\approx +2.8$ dex, while titanium deviates from the general trend and has a near-solar abundance. Our abundance results for Si II/III, Fe I/II, and Cr I/II provide an evidence for ionization balance in LkH$\alpha$ 324/B atmosphere. It should be noted that the mean Fe abundance in Table 4 obtained from 22 spectral lines of excitation energy $E_i$ in the 2.6–12.7 eV range slightly differ from the mean abundance given in Table 3 and obtained from 5 lines of low excitation energy. Perhaps, we see a trace of the weak Fe stratification.

In the LkH$\alpha$ 324/B atmosphere, the rare-earth elements (REE) are mostly overabundant. The stellar spectrum is rich of the lines from the second ions of praseodimium and neodimium, yielding their abundances [Pr/H] $\approx +3.9$ dex and [Nd/H] $\approx +3.7$ dex. Barium is obviously not overabundant, because we could not detect even the strongest resonance line Ba II 4554 Å, although its position coincides with the unblended region of the continuum. Hence, we can put the upper limit [Ba/H] $\lesssim +0.8$ dex. Barium deficiency (contrary to a general overabundance of metals) is not unusual for Ap stars, e.g., it is also observed in HD 170973. We were unable to detect europium lines, due to technical reasons, because the strongest of them fell into the inter-order gaps.

It is of interest to compare abundances of a few representative iron peak elements and REEs in LkH$\alpha$ 324/B atmosphere with a general dependence of abundances on the $T_{\mathrm{eff}}$ observed in Ap stars for these elements. Such a comparison with data for Ap stars on the MS is shown in Figure 5 for Fe, Cr, Pr, and Nd. One can see that LkH$\alpha$ 324/B belongs to the high-temperature tail of the Ap stars sequence, and the abundance of a given element agrees well with the trend observed in Ap stars.

4.5. Photometric Variability and Stellar Rotation

We investigated the photometric variability of LkH$\alpha$ 324/B using the data from the All-Sky Automated Survey for Supernovae (ASAS-SN) archive [72]. The light curve for the 2016–2018 period in the V filter was retrieved from the archive. Lomb–Scargle frequency analysis of these data resulted in a well-defined peak on the periodogram, corresponding to the $P=2.{39}^d$ period (Figure 6). The peak exceeds the level corresponding to the false alarm probability (FAP) = 0.001, which confirms the significance of the detected period. FAP was determined using Fisher’s Randomization method [73]. The phase curve convolved with this period is shown in the lower panel in Figure 6 and demonstrates quasi-sinusoidal light changes with $\Delta V\approx 0.04$ amplitude. Such variability is frequently observed in magnetic Ap stars and is caused by the axial rotation of the star with abundance spots on the surface. If we assume that the photometric variability of LkH$\alpha$ 324/B is rotationally modulated, then for the obtained radius $R=2.3R_{\odot }$, the $2.{39}^d$ period corresponds to the equatorial velocity $V_{eq}\approx 49$ km s${}^{-1}$, which is a factor $\sim 3$ lower than the typical rotational velocities of PMS early-type stars (e.g., [74]). Thus, a low $vsini$ value is not due to the projection effect, and the star is indeed a slow rotator. A comparison with the spectroscopically determined $vsini$ = 24 km s${}^{-1}$ yielded the moderate inclination angle $i\approx {27}^{\circ }$ of the stellar rotational axis.

5. Discussion

Fundamental parameters of LkH$\alpha$ 324/B, which define its position in the HR diagram, suggest that with an age of $t\approx$ 2.9 Myr, it still lies on the PMS evolutionary track. It takes another ∼0.8 Myr (∼22% of the total duration of its PMS evolution) before the star will reach the ZAMS. Despite its PMS status, LkH$\alpha$ 324/B does not belong to the group of the HAeBe stars. Although LkH$\alpha$ 324/B hosts the circumstellar disk traced by prominent mid-IR excess attributed to the thermal emission of the warm dust, its spectrum does not exhibit the emission lines indicative for ongoing mass accretion from the disk. Lack of accretion signatures as well as the absence of NIR excess in $JHK$ bands implies that the gas and dust are depleted in the inner regions of the disk and accretion is now ceased in the LkH$\alpha$ 324/B system. Nevertheless, there is some evidence that previously the star experienced the period of accretion/outflow activity. It was identified as the possible source of the parsec-scale collimated outflow detected in both radio and optical wavelengths [27,28]. Such outflows are frequently observed in young T Tauri and HAeBe stars [75] and represent the magnetically controlled outer regions of the accretion-driven winds (e.g., [76]). The mass and luminosity of LkH$\alpha$ 324/B as well as the indication for a global magnetic field of ∼3.5 kG strength revealed in our analysis are supportive for the scenario in which the star previously interacted with its disk in the magnetospheric accretion regime, similar to some other HAe stars. However, independent confirmation of the LkH$\alpha$ 324/B as the driven source of the jet from the proper motions study of its knots is highly desirable. To summarize, the observational data indicate with high probability that during its evolution, LkH$\alpha$ 324/B has recently passed through the HAeBe phase and is now a non-accreting intermediate-mass PMS star approaching the ZAMS.

In an attempt to restore the complete evolutionary sequence of development of the Ap type peculiarity, it is interesting to compare the abundance distribution revealed in the LkH$\alpha$ 324/B atmosphere with those observed in a few known chemically peculiar HAeBe stars as well as with magnetic Ap stars of the MS. Two secure PMS objects—magnetic HAe stars V380 Ori A [14,77] and AK Sco B [15]—are known to possess Ap-like surface chemical composition. Both stars display near-solar abundance of light elements and mild overabundance of some metals. In V380 Ori A, elements of iron peak, i.e., Mn, Fe, and Ni, are in ∼0.5 dex excess relative to the Sun. In AK Sco B, generalized overabundances are weaker and more pronounced in some lanthanoids, reaching ∼0.3–0.4 dex for Sr, Y, La, and Ba. Silicon is in 0.2–0.3 dex excess in both stars. Whether these patterns are built up exclusively by selective diffusion or by some synthetic mechanism that also involves shaping surface abundances by accretion is unknown. The weakness of the metals overabundance in these HAe stars as well as near solar abundance of light (He, C, N, and O) elements is probably caused by the competitive action of the selective diffusion in stellar atmosphere and ongoing enrichment of the surface layers by the gas of primordial composition. Turcotte and Charbonneau [20] showed that in case of episodic accretion even after the signatures of accreted material were erased and the surface composition becomes to be dominated by effects of chemical separation due to diffusion, some “memory” about accretion episode can persists. This causes a delay in the formation of underabundances of elements experiencing gravitational settling and suppresses the rapid growth of overabundances of radiatively supported elements. Indeed, AK Sco B possesses very weak accretion signatures [15], while it is questionable which component of the V380 Ori hierarchical system is an accretor. Thus, it is likely that the proposed mechanism may be relevant to the formation of the abundance pattern in V380 Ori A and AK Sco B, as may alternative scenarios, such as magnetic-selective accretion [78]. Further discussion is beyond the scope of this article, although this important issue deserves special study.

The non-accreting LkH$\alpha$ 324/B shows much more extreme pattern comparable to those in magnetic Ap stars on the MS. We detected both the underabundance of He, C, and O as well as ∼2–4 dex overabundance of iron peak elements and REEs. The comparison of abundance distribution in Figure 4 shows it to be very similar to those in strongly peculiar Ap star HD 170973, while for some individual elements (Fe, Cr, Pr, and Nd), it is consistent with the temperature behavior within the generalized sample of MS Ap/Bp stars (Figure 5). This temperature dependence reflects the impact of changes in the stellar internal structure and the radiation field in the atmosphere on the diffusion processes, and it is in a good agreement with the predictions of the diffusion calculations (e.g., [71,79]). Thus, matching LkH$\alpha$ 324/B to this dependence points to selective diffusion as the reason for the formation of its surface chemical composition. Theoretical diffusion calculations by LeBlanc et al. [80] for $T_{\mathrm{eff}}$ = 12,000 K, which is close to the effective temperature of the LkH$\alpha$ 324/B, show that in hot Ap stars, most of the metals possess very smooth vertical abundance gradients. For some metals, abundance jumps decrease in amplitude and their position shift to the upper atmospheric layers, producing an effect of chemically homogeneous atmosphere in the line formation region. Qualitatively, this agrees well with the detection of the ionization balance for Si, Fe, and Cr in the LkH$\alpha$ 324/B atmosphere and suggests that the observed abundances are close to the equilibrium ones (i.e., when diffusion velocity $V_{diff}=0$ for all elements). It is worth noting that another young CP star BD+30${}^{\circ }$549, despite it being hotter ($T_{\mathrm{eff}}$ = 13,100 K), was more evolved and lies closer to ZAMS, showing strongly non-homogeneous vertical distribution of some elements [18], i.e., far from the theoretically predicted equilibrium solution. If this is an evolutionary effect, then in the case of LkH$\alpha$ 324/B, there must be some agent either contributing to boosting diffusion or prolonging the time when it can operates effectively. Probably, the magnetic field is such an agent. Unlike BD+30${}^{\circ }$549, which has no signs for a magnetic field, a strong-ordered field of LkH$\alpha$ 324/B could both favor the radiative acceleration of ions [81] and, by shielding the stellar surface by magnetocentrifugal barrier during the late stages of accretion activity, provide enough time to diffusion for reaching an equilibrium state.

If LkH$\alpha$ 324/B is confirmed as the source of the bipolar jet, this provides a unique opportunity to estimate the accretion cessation time, i.e., the lower constraint on the diffusion timescale and time required to develop its observed Ap pattern. The accurate proper motion study of the optical HH objects within the jet will lead to an estimation of their dynamical age, which should point to the last period of the accretion/outflow activity. However, even without data on the proper motions, we can estimate the lifetime of the observed HH objects. This lifetime can be roughly determined as the radiative cooling time:

$$t_{cool}\approx \frac{kT}{\Lambda \left(T\right)N_e},$$

where T and $N_e$ are the temperature an electron density of the gas in the cooling zone of the HH object, k is the Boltzman constant, and $\Lambda \left(T\right)$ is the radiative cooling function for the optically thin gas. Substituting the typical values for young stellar jets, $T\sim {10}^4$ K, $N_e\sim {10}^3$ cm${}^{-3}$, and using Dalgarno and McCray cooling function [82], we obtain $t_{cool}\approx {10}^2-{10}^3$ yr depending on uncertainty in basic parameters and ionization fraction within the cooling zone. This time is much shorter than the $\gtrsim 1$ Myr required for the vertical separation of elements in the atmosphere after the accretion has ceased [20,21]. However, if the star hosts a strong dipole magnetic field at the late stages of accretion activity with low $\dot{M}$, it could produce the magnetocentrifugal barrier and prevent the matter infall on the star by spreading it into the surrounding space in the magnetic propeller regime (e.g., [83]). In this case, the star had more time for the vertical stratification of elements under the action of diffusion. In such a scenario, the observational signs of the outflow activity are not always accompanied by substantial accretion [84] and the build-up of the surface chemical composition due to selective diffusion may begin long before their disappearance.

6. Conclusions

Our spectroscopic determination of the atmospheric parameters and abundances of the star LkH$\alpha$ 324/B associated with the active star-forming cloud LDN 988 leads to the conclusion that this is a PMS star with pronounced chemical peculiarity of Ap Si type. We have detected manifestation of the large scale magnetic field of $\langle B\rangle \sim$3.5 kG strength based on analysis of magnetically sensitive lines. The slow axial rotation, inhibited microturbulence in the LkH$\alpha$ 324/B atmosphere and rotationally modulated photometric variability is also typical for magnetic Ap stars. Investigation of the LkH$\alpha$ 324/B abundance pattern showed that it is much more similar to those in Ap stars on the MS rather than in known peculiar HAeBe stars. Agreement with the results of diffusion calculations shows that selective diffusion is the reason for the formation of anomalous surface composition in LkH$\alpha$ 324/B.

However, the position of the star in the HR diagram, existence of the circumstellar disk, and footprints of recent accretion/outflow activity suggests that it has recently passed through the phase of the HAe star. Thus, either vertical separation of elements occurred very rapidly after accretion in the system faded, or the strong magnetic field protected its surface from enrichment with infalling matter during the late stages of accretion activity and extended the diffusion-dominated time.

Being one of the youngest Ap stars, LkH$\alpha$ 324/B is a very promising object for the advanced study of the origin of the strong magnetic fields in radiative A type stars as well as the mechanisms and timescale of the development of their surface chemical anomalies. It is strongly desirable to confirm that the star is indeed the source of the observed jet and to study its kinematics in order to put a lower constraint on the accretion cessation time in the system. Confirmation of the global magnetic field with spectropolarimetric methods and study of its structure as well as the surface abundance inhomogeneity is highly needed.