Post-AGB candidate IRAS 02143+5852: Cepheid-like variability, three-layer circumstellar dust envelope and spectral features

We present the results of multicolour $UBVR_{\text{C}}I_{\text{C}}JHK$ photometry, spectroscopic analysis and spectral energy distribution (SED) modelling for the post-AGB candidate IRAS 02143+5852. We detected Cepheid-like light variations with the full peak-to-peak amplitude $\Delta V\sim0.9$ mag and the pulsation period of about 24.9 d. The phased light curves appeared typical for the W Vir Cepheids. The period-luminosity relation for the Type II Cepheids yielded the luminosity $\log L/L_{\odot}\sim2.95$. From a low-resolution spectrum, obtained at maximum brightness, the following atmospheric parameters were determined: $T_\text{eff}\sim7400$ K and $\log g\sim1.38$. This spectrum contains the emission lines H$\alpha$, BaII $\lambda$6496.9, HeI $\lambda$10830 and Pa$\beta$. Spectral monitoring performed in 2019-2021 showed a significant change in the H$\alpha$ profile and appearance of CH and CN molecular bands with pulsation phase. The metal lines are weak. Unlike typical W Vir variables, the star shows a strong excess of infrared radiation associated with the presence of a heavy dust envelope around the star. We modelled the SED using our photometry and archival data from different catalogues and determined the parameters of the circumstellar dust envelope. We conclude that IRAS~02143+5852 is a low-luminosity analogue of dusty RV Tau stars.


INTRODUCTION
IRAS 02143+5852 (02 h 17 m 57.s 8, +59 • 05 ′ 52 ′′ , 2000) is an infrared (IR) source mentioned for the first time by Manchado et al. (1989) as an object with the far-IR colours similar to those of planetary nebulae.These authors suggested that the object is in the post-AGB stage of evolution.From this point on, the star began to be studied together with other post-AGB candidates.Omont et al. (1993) considered it as a carbon-rich proto-planetary nebula (PPN).Observations in the near-IR were carried out by García-Lario et al. (1990), Fujii et al. (2002), Ueta et al. (2003) and Cooper et al. (2013).Ueta et al. (2003) pointed out that the H and K ′ magnitudes showed a slight variation compared to previous observations.Extended dust shells ⋆ E-mail: ikonnikova@sai.msu.ruhave been found in a number of post-AGB stars, however IRAS 02143+5852 is unresolved at 11 µm (Meixner et al. 1999).Gledhill (2005) did not detect polarization within errors in the J-band.No H2O maser emission was detected by Suárez et al. (2007).Fujii et al. (2002) were the first to obtain optical magnitudes for the star: B = 14.96 mag and V = 13.74 mag.The authors assumed the star to be of F5Ib spectral type with corresponding temperature T eff = 6900 K, intrinsic colour (B−V )0 = 0.33 mag and colour excess E(B−V ) = 0.89 mag.Fujii et al. (2002) analysed the SED spanning the optical to far-IR wavelengths and obtained an estimate for the dust shell temperature T dust = 205 K.
The spectral type of the object is not clear.Kelly & Hrivnak (2005) classified the IRAS 02143+5852 spectrum as an Ae one.Based on a low-resolution spectrum, Suárez et al. (2006) stated an F7Ie spectral type.
Analysing the spectrum presented in the appendix of the above paper, Molina (2018) found T eff = 7967 ± 91 K. Sivarani & Parthasarathy (2004) noted that the optical spectrum showed strong Balmer lines in absorption and no helium lines.
The light variability of the star was discovered based on the All Sky Automated Survey for SuperNovae (ASAS-SN) data (Shappee et al. 2014;Kochanek et al. 2017).In the ASAS-SN catalogue of variable stars (Jayasinghe et al. 2019), it has the designation ASASSN-V J021757.82+590552.0, a period of 50.18 d and an YSO (Young Stellar Object) variability type.The star is also contained in the ZTF catalogue of periodic variable stars (Chen et al. 2020), where it is designated as ZTFJ021757.80+590552.1, has period 25.1385074 d, and is classified as CepII (Cepheid variable).
In this paper, we present new photometric and spectroscopic observations of IRAS 02143+5852 obtained in 2017-2021.These data allowed us to detect light variability and to study its character, as well as to determine the parameters (T eff , log g) of the star and to investigate spectrum change.
We have used all currently available IR photometric data to perform the SED modelling aiming to probe the properties of the circumstellar material.
The paper is organized as follows.Photometric and spectroscopic observations and data reduction procedures are described in Section 2. In Section 3 we analyse photometric data.Section 4 presents the results of low-resolution spectroscopy.In Section 5 we discuss the evolutionary status of the star.Section 6 is devoted to the SED modelling.In Section 7 we discuss the obtained results and the star's similarity to known objects.Section 8 presents our conclusions.

U BV RCIC photometry
The photometric observations of IRAS 02143+5852 were carried out with the FLI ML3041 CCD (2048×2048 pixels, the pixel size 15 µm) mounted on the 0.6-m telescope of the Stará Lesná Observatory of the Astronomical Institute of Slovak Academy of Science (Sl600) in 2018-2019 and with the Andor iKon-L BV camera (2048×2048 pixels, the pixel size 13.5 µm) mounted on the new 0.6-m telescope (RC600) installed at the Caucasian Mountain Observatory (CMO) of the Sternberg Astronomical Institute of the Moscow State University (for more details see Berdnikov et al. (2020)) in 2019-2021.Each detector was equipped with a set of Johnson-Cousins U BV RCIC filters.Standard data reduction procedures (debiasing, flat-fielding, darking) and aperture photometry were performed using the maxim dl5 package and self-developed python scripts.The mean photometric uncertainty is about 0.005-0.010mag for the B, V , RC, IC bands and up to 0.05 for the U band.
Information on the comparison stars, used for differential photometry, is presented in Table 1.The magnitudes for the comparison stars were acquired via referencing to photometric standards in the S23-246 and S23-436 fields (Landolt 2013).The RC image of IRAS 02143+5852 and comparison stars is shown in Fig. 1.The U BV RC IC-photometry is presented in Table A1 where for every night we list the mean time of observation and magnitudes in each of photometric bands averaged over 2â€"3 frames.

JHK-photometry
The JHK-photometry was obtained from 2017 November 6 to 2021 February 18 (73 nights in total) with the ASTROnomical Near-InfraRed CAMera (ASTRONIRCAM) (Nadjip et al. 2017) mounted on the 2.5-m telescope of CMO.We used the dithering mode to obtain images in the JHK bands of the MKO-NIR system (Mauna Kea Observatories Near-InfraRed (Simons and Tokunaga 2002)).Each frame was automatically reduced and calibrated using the pipeline described in detail in Tatarnikov et al. (2023).The standard reduction procedures were performed including the correction for non-linearity and bad pixels, dark subtraction, flatfielding and background subtraction.The instrumental magnitudes for the star were derived using differential aperturebased photometry with respect to 2MASS stars (Fig. 1, Table 2) which magnitudes were converted to the MKO-NIR system following the equations from Leggett et al. (2006).
The JHK-photometry in the MKO-NIR and 2MASS systems is presented in Table B1.
As we obtained several frames for each filter during each pointing, uncertainties were calculated as standard deviations.The average uncertainties are ∆J = 0.011 mag, ∆H = 0.010 mag, ∆K = 0.012 mag.

Spectroscopy
A low-resolution optical and near-IR spectrum of IRAS 02143+5852 was obtained on the 3-m telescope of the Lick Observatory (USA) with the Aerospace Corporation's Visible and Near Infrared Imaging Spectrograph (VNIRIS) (Rudy et al. 2021) (0.46-2.5 µm, R ∼ 700) on 2018 October 20 (JD 2458412.5).The spectra were calibrated using the solar-type standard star HIP 9829.Low-resolution spectra were acquired on the 2.5-m telescope of CMO via the Transient Double-beam Spectrograph (TDS) equipped with two Andor Newton 940P cameras using E2V CCD42-10 detectors, and volume phase holographic gratings (see Potanin et al. (2020)).A 1. ′′ 0 slit was used.The log of observations is given in Table 3.The data reduction procedures including dark and flat-field correction, cosmic ray removal, two-dimensional wavelength linearization, background subtraction, and relative flux calibration using spectrophotometric standards listed in Table 3 were performed using python scripts.

PHOTOMETRIC ANALYSIS
In Fig. 2 we present the U BV RC IC light and colour curves for the period from 2019 August to 2020 March which was best covered by observations.A periodic variation is clearly seen both in light and colour curves.The shape of light curve differs from band to band being sawtooth in the U band while the RC and IC light rapidly rises to a flat and longlasting maximum.There is a bump on the declining branch of the B and V light curves.One can also see that deeper minima alternate with shallower ones and this effect is most pronounced in the U and B bands and in the B − V colour.The BV RC IC light curves of IRAS 02143+5852 are very sim-ilar to those of W Vir which is the Type II Cepheid prototype (Templeton & Henden 2007).
The near-IR light curves spanning the whole observational period are shown in Fig. 3.As can be seen, the JHKbrightness varies with a peak-to-peak amplitude of about 1 mag.

Periodicity analysis
In order to study the periodicities, we have used the winefk code developed by V.P. Goranskii1 .This code implements the well-known method of minimizing the phase dispersion (Lafler & Kinman 1965) and the discrete Fourier transform for arbitrarily distributed time series (Deeming 1975).
The Fourier spectra of our V -band data presented in Table A1 is shown in Fig 4 .In the frequency spectrum obtained by the Deeming method a peak corresponding to a period of 24.885 d is dominant (Fig. 4 (a)).There are two weaker peaks on both sides of the primary one which turn out its one-year aliases.Taking into consideration all our U BV RC IC data for the 2018-2021 interval we derived P = 24.885± 0.150 d.
Analysing the times of maxima allowed us to revise the ephemeris to be: where 'maximum' is defined as a peak at the end of the rising branch.
The Lafler-Kinman method gives a frequency spectrum that contains peaks corresponding to the period of 24.885 d, and its multiples of 49.736 and 74.635 d (Fig 4 (b)).
The light curves folded on the 24.885 d period show a significant scatter (>0.1 mag) at phase 0.6-1.0 which is much larger than observation errors indicating that there are cycleto-cycle variations.Folding on twice the above period reveals some details in light curves, particularly, the alteration of deep and shallow minima.The U BV RCIC light curves folded on periods of 24.885 and 49.736 d are shown in Fig. 5.
The near-IR data are less numerous than the optical data, so, it is harder to determine reliable period.The power spectrum derived by the Lafler-Kinman method for periods in the range 10-100 d is dominated by the peaks which correspond to the periods of 24.819 d and 49.690 d (J-band), 24.793 d and 49.690 d (H and K bands).The JHK light and J − H colour curves folded on the period P =24.819 d and on nearly twice the period P =49.690 d are shown in Fig. 6.
The JHK phase curves are similar in shape showing a rapid rise to maximum and gentle slope.The phase curves folded on twice the period demonstrate the pattern of minima alternating in depth which is typical for the RV Tau type variables.The J − H colour reaches maximum at maximum light, so, the star is redder when brighter.
A brief summary of characteristics yielded from the photometric study, namely, the periods derived for different photometric bands as well as maximum brightness, peak-to-peak amplitudes, and the number of observations (N ), is given in Table 4.
The data presented in Table 4 and Fig. 7 indicates that the oscillation amplitude is the largest in the U -band, decreases with increasing wavelength in the optical range up to the   IC-band, and then begins to increase in the near-IR range from J to K. The ratio of A(K) to A(V ) is 1.08.This is an unexpected result, since in pulsating variables the amplitudes of oscillations in the near-IR range are usually lower than in the optical.For example, in classical Cepheids with periods P > 20 d, the ratios of the amplitudes A(J), A(H) and A(K) to A(V ) are approximately 0.4 (Inno et al. 2015).As we show below, IRAS 02143+5852 exhibits a significant excess of near-IR emission.As almost half of the H-band emission arises from dust and pulsations do affect the emission from the dust envelope, it seems credible to relate the observed near-IRamplitude-wavelength dependence to the presence of dust.

Colour-colour diagrams
The location of IRAS 02143+5852 in the U−B, B−V colourcolour diagram is shown in Fig. 8 along with the sequence of supergiants from Straižys (1982).The observed colours vary from the reddest in minimum light to the bluest in maxima which is common to temperature oscillations related to pulsations.Analysing spectroscopic data (see Section 4), we found that at light maximum the star has a spectral class of approximately F0I, for which the normal colour index is (B − V )0 = 0.20 mag (Straižys 1982).The observed colour at light maximum is B − V = 1.03 ± 0.02 mag, and therefore the colour excess can be estimated as E(B−V ) = 0.83±0.02mag.In the colour-colour diagram (Fig. 8), the dereddened colours are located above the sequence of supergiants, indicating that the star has some ultraviolet excess, which is typical of W Vir stars and may be due to low metallicity (Straižys 1982).As we discuss below, IRAS 02143+5852 also has low metal content.
The star demonstrates a significant near-IR excess.In Fig. 9 we plot the J − H, H − K colour-colour diagram for IRAS 02143+5852, the supergiant sequence from A5 to M5 and a blackbody with temperature in the range from 1200 to 2000 K.The J − H and H − K colours for supergiants were taken from Koornneef (1983) and converted to the 2MASS system using equations from Carpenter (2001) and then to the MKO-NIR system using equations from Leggett et al. (2006).The star's colours dereddened with E(B − V ) = 0.83 mag occupy the location which can be attributed to a sum of radiation from a ∼F5 supergiant and hot dust with T dust ∼ 1300 K.Note that the dust contribution is bigger in maximum light than in minimum.
The star also has a considerable excess of far-IR radiation  related to cold dust.We present the circumstellar dust shell modelling in Section 6.

SPECTRAL FEATURES AND STELLAR PARAMETERS
The flux-calibrated spectrum obtained on 2018 October 20 near the maximum brightness (φ = 0.07) is shown in Fig. 10.Because of low resolution in the short wavelength region most of lines are blended, which makes the analysis difficult.The most prominent details in the spectrum are the emission lines: Hα, Ba ii λ6496.9,He i λ10830 and Paβ.The Hβ line has also an emission component.
The main absorption features are D Na i, diffusion interstellar bands (DIBs) at λ5780 and λ6280, the O i triplet at λλ7771-74, the Ca ii triplet (λλ8498, 8542, 8662), the Paschen hydrogen lines, in particular P12, P14, P17, and the Brackett hydrogen lines.
The equivalent widths (EWs) of the most prominent lines are presented in Table 5.We consider EW negative for absorption and positive for emission.The measurement error is estimated to be about 10 per cent.
We have estimated T eff and log g of the star, using empirical relations from Molina (2018) and Mantegazza (1991).Molina  (2018) proposed a functional relationship to assess the value of log g: where EW (O i) is the equivalent width of the O i triplet lines at λλ7771-74.For IRAS 02143+5852 we have derived log g = 1.38 ± 0.38 which corresponds to the Iab luminosity class according to the calibration of Straižys (1982).But it is necessary to keep in mind that the strength of the O i  triplet lines also depends on other atmospheric parameters (Kovtyukh et al. 2011), particularly on metallicity, which can be defined reliably only via the analysis of high-resolution spectra.
As was shown by Mantegazza (1991), the ratio Ca/P where Ca is the sum of EWs of the Ca ii IR triplet lines and P is the sum of EWs of P12, P14, and P17, can be used to estimate the effective temperature of a star.Just as was reported by Mantegazza (1991) for the spectra of RV Tau stars, the components of the Ca ii IR triplet are blended with P13, P15, and P16 in our spectra.Table 5 reports the measured EWs of P12, P14, P17 and Ca ii triplet lines.In accordance with eq. 1 from Mantegazza (1991), log T eff = 3.90 − 0.20 log(Ca/P) ± 0.07, (3) we derived T eff = 7400 +1248 −1152 K.The calibration of Flower (1996) ascribes the intrinsic colour (B − V )0 = 0.20 mag to a supergiant with T eff = 7400 K. Our spectrum was obtained near maximum light when the mean value of B−V is about 1.03 mag, so, the colour excess can be estimated as 0.83 mag.The spectrum dereddened with E(B −V ) = 0.83 mag is shown in Fig. 11 together with the synthetic spectrum of an F5I star taken from the stellar spectral flux library presented by Pickles (1998).As one can see, the 5000-7500 Å spectrum of IRAS 02143+5852 corresponds well to an F5I type spectrum, whereas at longer wavelengths there is a significant excess of radiation compared to a standard star.According to the calibration of Flower (1977), an F5I star has the temperature T eff = 7000 K which falls within the range of temperatures inferred from the Ca/P ratio.
We were interested to study spectral changes depending on the pulsation phase.So, we obtained 12 spectra in the 3500-7500 Å range at different pulsation phases on the 2.5-m telescope of CMO with TDS (Table 3).The main characteristics of the IRAS 02143+5852 spectrum are the following: • The optical spectrum is dominated by the Balmer lines.Hα and Hβ have emission components which vary with pulsation phase.The Hα emission appears near minimum light, persists on the rising branch until maximum and then weakens rapidly on the declining branch and becomes double- The numbers in parentheses indicate the order number of spectra as it is defined in Table 3.
peaked with a peak-to-peak separation of about 3.6 Å or 164 km s −1 .Strong hydrogen emission lines observed during rising light are characteristic of population II Cepheids and their appearance is explained by the propagation of a shock wave through the expanding outer layers of stellar atmosphere (Abt 1954;Whitney 1956;Wallerstein 1959).
• In the blue part of the spectrum there are molecular bands of CH (λ4261, λ4280, λ44323) and CN (λ4197, λ4214, λ4216).The strength of the bands varies with pulsation phase and is the largest near the middle of the declining branch.Fig. 13 shows the blue spectral region with the molecular bands mentioned above.IRAS 02143+5852 is found to have weaker metal lines in its spectrum compared to stars of normal metallicity.In order to illustrate this fact, we show the spectra of IRAS 02143+5852 obtained near minimum and maximum light as well as the spectra of HD 17971 (F5Ib) and SAO 37370 (F0Ib) obtained with TDS, so, all of them have the same spectral resolution.
We have also compared the spectrum of IRAS 02143+5852 with that of the star CC Lyr, which is a Type II Cepheid (Harris 1985).It has the pulsation period P = 24.01d (Berdnikov et al. 2020) which is close to that of IRAS 02143+5852.In Fig. 14 we present the spectrum of CC Lyr which we obtained on 2020 March 8 when the star was on the ascending branch of light curve (φ = 0.76).The spectrum has much in common with that of IRAS 02143+5852: the appearance of the Balmer series is nearly the same, the metal lines are also weak.Like IRAS 02143+5852, CC Lyr displays strong Hα emission and the CH band at λ4280.Harris and Wallerstein (1984) noted that 'because of their peculiarities, the spectra of Type II Cepheids are difficult to classify by direct comparison with MK standards'.Based on HI lines Harris and Wallerstein (1984) ascribed an F4- to the order number of spectra as it is defined in Table 3.
F8 spectral type to CC Lyr depending on the pulsation phase; from metal lines they deduced an A type and also pointed to the presence of the CH band.So, according to Harris and Wallerstein (1984) the spectral classification of CC Lyr at maximum light is hF4mA:CH+1.We can state that the spectra of IRAS 02143+5852 and CC Lyr are similar in their peculiarity.

LUMINOSITY, DISTANCE AND EVOLUTIONARY STATUS
IRAS 02143+5852 shows many important similarities to longperiod Type II Cepheids, e.g., the shape of light curves, the pulsation period, the emergence of Balmer emission, among other observed photometric and spectroscopic properties.We therefore decided to estimate the star's luminosity from the period-luminosity relation established for this type of pulsating variables.We applied the relation MV = −0.61− 2.95 log P + 5.49(V − R)0 proposed by Alcock et al. (1998) for the long-period (0.9 < log P < 1.75) Type II Cepheids.
As IRAS 02143+5852 is positioned as a post-AGB star, let us compare the parameters of the star with the predictions inferred from the evolution models for post-AGB objects presented by Miller Bertolami (2016).Typical post-AGB objects with initial masses on the Zero Age Main Sequence (ZAMS) between 0.8 and 8.0 M ⊙ at the stage after shedding their shells on AGB have final masses of 0.52-0.85M ⊙ and luminosities log L/L ⊙ ranging from 3.4 to 4.2, respectively, which is significantly higher than that obtained for IRAS 02143+5852.
Taking into account the new data presented here and our presumption of IRAS 02143+5852 being a W Vir star, we have turned to the evolutionary models of W Vir pulsating variables.The evolutionary status of these stars was discussed more than once, e.g., by Gingold (1974Gingold ( , 1976)).Gingold (1985) and Fadeyev (2020) summarized the previous work done in this area.On the basis of self-consistent stellar evolution models and nonlinear stellar pulsation calculations, Fadeyev (2020) concluded that W Vir pulsating variables are the low-mass post-AGB stars that experience the final helium flash.He found that a set of evolutionary models with masses M = 0.536M ⊙ , 0.530M ⊙ and 0.526M ⊙ that experience the loop in the Hertzsprung-Russel diagram, due to the final helium flash, can provide a solution of hydrodynamic equations which describes radial oscillations of W Vir stars.The log L/L ⊙ = 2.95 found for IRAS 02143+5852 falls into the range of luminosities predicted for the above masses.
The results of the Gaia mission for IRAS 02143+5852 are confusing.The parallax of the star listed in the Gaia DR2 turned out negative (π = −0.8487± 0.4583 mas; Gaia Collaboration ( 2018 (Bailer-Joneset et al. 2021).At this distance, the star would have had a luminosity of about 16L ⊙ , however, which contradicts its evolutionary status.

THE MODEL OF THE CIRCUMSTELLAR DUST ENVELOPE AND MODELLING ASPECTS
The SED of the object demonstrates a prominent IR excess.Thus, assuming that the excess is caused by the radiation from heated dust, we estimated the circumstellar dust envelope parameters via the simulations with radmc-3d (Dullemond et al. 2012).
Our modelling was based on the following sets of observational data: • U BV RcIcJHK photometry.We used the absolute flux calibrations from Straižys (1992) for the U , B, V bands, Bessell (1979) for the Rc, Ic bands and Tokunaga & Vacca (2005) for the J, H, K bands.
• The observed fluxes at 65 and 90 µm from the AKARI/FIS Bright Source Catalogue.The data at 140 and 160 µm were omitted because of their low quality.
• The observations at 9 and 18 µm from the AKARI/IRC Point Source Catalogue.
• The flux densities in the A, C, D, and E bands of the Midcourse Space Experiment (MSXC6).
• The average non-colour corrected flux densities at 12, 25 and 60 µm from the IRAS Point Source Catalog v2.1 (PSC).The data at 100 µm were excluded as only the upper limit is presented.
We modelled the SED of the star using our U BV RCICJHK data for maximum light and the data available from different catalogues listed in Table 6.We used the initial model atmosphere parameters T eff = 7460 K and log g=1.38 found in this study which correspond to an F5I star from Pickles (1998).An example of the fitting SED derived for IRAS 02143+5852 is shown in Fig. 15.
The object is situated close to the galactic plane with the galactic latitude of about −2 • .According to Bailer-Jones et al. ( 2018) the distance to the object is within the confidence interval of about 2272-5636 pc.These two facts lead to large interstellar extinction which distorts the spectral energy distribution of the object.A distance estimation error causes an uncertainty in the SED corrected for interstellar extinction.We decided to use the period-luminosity relation for W Vir variables (Alcock et al. 1998) to estimate the distance to the object.Our approach to this problem allowed us to reconcile the luminosity derived from this relation, distance to the star and the luminosity calculated by integrating the SED corrected for interstellar extinction.
This method is as follows.The period-luminosity relation, when averaged over the period, gives a bolometric magnitude of −2.65 mag, corresponding to a luminosity of 910 L ⊙ .Comparing the bolometric magnitude to the actual observations yields a distance of 2470 pc.
To take into account interstellar extinction we used dust maps by Green et al. (2019) and the interstellar extinction law from Cardelli et al. (1989) andO'Donnell (1994) assuming RV = 3.1 as a mean for the Galaxy.
To estimate the distance we applied the photometry averaged over the period and assumed that the fluxes corresponding to the AKARI, WISE, MSX and IRAS data did not change essentially during the pulsation cycle.This assumption needs to be explained.It was shown by Fedoteva et al. (2020) for a Mira-type star V CrB that the main parameters of the model dust shell (τ , Rin, Rout and dust properties) do not depend on whether the maximum or minimum light SED is fitted.V CrB varies with an amplitude of > 4 mag in B and ∼ 0.8 mag in KLM and a period of 355.2 d, so, even if the case of such large-scale variations does not require different dust shell models for minimum and maximum light, we can assume the constancy of IR fluxes during the pulsation cycle for IRAS 02143+5852.
The temperature of the internal star is of great importance for simulating.Since we have the spectrum at maximum light obtained at the Lick Observatory we were able to evaluate the corresponding temperature.The value turned out to be 7400 K. Thus, the SED modelling was carried out for the phase of the maximum brightness.This means that unlike the case of determining the distance when we considered the average SED, for the modelling we applied the photometry obtained at maximum light.We corrected these data for interstellar extinction using the distance estimated as was described above.As mentioned earlier, we presume that the fluxes corresponding to the AKARI, WISE, MSX and IRAS data do not change significantly during the pulsation So, we let ourselves adopt these observational data not only for the average brightness but also for the maximum light.
The SED of IRAS 02143+5852 has a non-trivial profile, such that the flat SED in the IR domain can not be explained by the presence of only one dusty spherical shell with a simple dust density distribution ρ ∝ r −α .A series of simulations showed that in order to reproduce the observed SED we should consider at least three nested spherical layers that correspond to the different stages of mass loss.The idea of multiple shells has been supported by observational evidence for AGB stars (see, for example, the studies on CW Leo by Mauron & Huggins (2000) or Cernicharo et al. (2015)).Thereby, following the law of parsimony, we considered three shells (three components of the composite dust envelope) in further modelling, which was carried out under the following assumptions: • The SED of the star is assumed to be that of an F5I star.
• The components of the circumstellar dust envelope are spherical layers located symmetrically about the star.
• α = 2 for each spherical shell, since this describes the simplest case of the constant mass-loss rate and expansion velocity.
• Dust grains are spherical.Hence, the opacity coefficients were calculated in accordance with the Mie theory.
• Since there is no indication of the chemical composition, we used amorphous carbon dust grains to avoid additional ambiguity.The corresponding optical constants were taken from Suh (2000).The parameters of the corresponding model dust shells, namely, the distance from the stellar center to the inner and outer boundaries, the radius of dust grains, the optical depth, the dust mass and the mass-loss rate, are listed in Table 7.
Our estimates of the mass-loss rate were derived under the assumption that the expansion velocity and the gasto-dust ratio are equal by the order of magnitude to the typical values found for the circumstellar envelopes of AGB stars: ve=10 km s −1 and ρg/ρ d =100.Our mass-loss rate estimates are in agreement with the values that were derived for AGB stars from observations and fall within the interval ∼ 10 −8 − 10 −5 M ⊙ yr −1 (see Ramstedt et al. (2009)).Fig. 16 demonstrates the model density distribution in the dust envelope.The discontinuities coincide with the boundaries between different components of the dust envelope.

Verification of unambiguity
To judge whether a two or three-shell model fits the observed data better, we used the F -test to select the most appropriate model at a significance level of α = 5%.We could not construct a model consisting of one or two dust shells which could reproduce the observed SED, for no combination of parameters did we get the F value less than critical.
Our simulation is not based on analytical formulae, so, it is rather problematic to claim the confidence intervals of the obtained model parameters.If we consider a three-shell model, then, in our case, for a limited sample of independent parameters and observed data points the critical value of F -test statistics is F (5%) = 2.5.Our best model has F = 1.25.We used the F -test to estimate the interval for each parameter where F < 2.5.So, we successively varied each of model parameters with the others being fixed until F was less than 2.5.Then we considered the range between derived extreme values as a confident interval for that parameter.The corresponding F values for each variation are shown in Fig. 17.The derived intervals for all model parameters are listed in Table 7.One can see that the most strictly constrained parameters are r2 and r3, in the sense that a slight relative variation significantly affects the shape of SED, whereas r4, the outer radius of dust envelope, has the least effect: even a three time increase keeps F < 2.5.This can be understood if we turn to the aspects of modelling: with τ3 being fixed, an increase in r4 leads to a decrease in the dust temperature at the outer radius (r4) and to some redistribution of matter inside the outer shell, so, that the dust density at its inner radius r3 declines only slightly, thus barely affecting the shape of SED.An increase of far-IR emission produced by cold dust at a new larger r4 is partially compensated by a decrease of dust density at the previous distance r4.
The variation of model parameters affects the total mass of the dust envelope differently.We calculated the total dust mass for each model that satisfied the criterion F < 2.5.Fig. 18 visualizes how the F value changes with the change of the outer dust shell mass caused by the variation of one of model parameters, namely those corresponding to the outer shell: r3, r4 -its inner and outer radii, τV .It is clearly seen that the dust mass strongly depends only on the outer radius.Other parameters modify the but barely affect the total dust mass.
Our calculations show that the shell radius does not affect the derived mass-loss rate, even though it does affect the resulting mass.It is due to the fact that the lifetime of the  7 where the model parameters are listed.shell and its mass grow linearly with radius, if we assume ρ(r) ∼ r −2 .

The necessity of large dust grains
The main peculiarity of this model is the presence of large dust grains with a radius of 5 µm in the third shell.The usage of such large particles is dictated by the necessity to reproduce the SED in the 25 µm region.Carbon dust grains with a radius of ∼ 1 µm have a larger absorption opacity coefficient at 25 µm than the smaller ones with agr ∼ 0.1 µm.At the same time, the absorption opacity coefficient of the larger grains with agr ∼ 1 µm is much smaller in the optical region than that of the smaller ones with agr ∼ 0.1 µm.Hence, when we try to reproduce the  SED in the 25 µm region using the dust grains with the radius smaller than 5 µm, a large mass of dust that is required for this will cause too much absorption in the optical range.But in the case of the particles with a radius of 5 µm the values of absorption and reradiation caused by the third dust shell component are consistent with the observed SED.The absorption opacity coefficients for dust grains of different sizes are depicted in Fig. 19.

A short discussion on the dust grain sizes
As a result of our research two populations of dust grains were found: smaller grains with agr = 0.3 µm and larger ones with agr = 5 µm.
The radius of small grains we found here coincides, in order of magnitude, with the sizes of dust particles claimed by the recent observational and theoretical studies.Dust grains of the similar radii were detected by Norris et al. (2012) (agr ∼ 0.3 µm) for several O-rich AGB stars and by Ohnaka et al. (2017) for W Hya (agr is about 0.1 µm at minimum light and 0.5 µm at maximum light).These results are in agreement with the theoretical models of Hofner (2008) who deduced that silicate dust grains of M-type AGB stars should have radii in the range of about 0.1-1 µm to drive the stellar outflow.In the case of C-type AGB stars where carbon species dominate, the modelling presented by Mattsson et al. (2010) shows that the dust with agr ∼ 0.1 µm may be common for stellar winds.
As for the large dust grains, there are some studies that The calculation was performed according to the Mie theory with the optical constants for amorphous carbon adopted from Suh (2000).
have found evidence for the presence of rather big dust particles in the circumstellar discs around the stars more evolved than IRAS 02143+5852.Jura (1997) proposed that there is an orbiting, long-lived gravitationally bound disk of dust grains with radii 0.02 cm surrounding a carbonrich AGB star in the Red Rectangle nebula.Shenton et al. (1995) analysed the IRAS-millimetre flux distributions of the two post-AGB stars AC Her and 89 Her and suggested the existence of large grains (agr 1 µm) in their dusty discs.De Ruyter et al. (2006) explored a sample of post-AGB stars and found the emission from large ( 0.1 mm) grains.They assumed that the presence of such large grains may be the indication of Keplerian discs around binary systems, where the grain growth is facilitated.Hence, according to these papers large dust grains around IRAS 02143+5852 is a possible indication of the second component which has not been discovered yet and the dusty disc surrounding the possible binary system.

DISCUSSION
Our photometric study has produced evidence that IRAS 02143+5852 is a pulsating variable with a period of about 25 d and light curves typical for W Vir stars.The star also demonstrates some similarity to the RV Tau stars, namely, a pattern of alternating minima observed in the U IRAS 02143 13 and JHK phase light curves.The double wave of alternating deep and shallow minima in the light curve of the RV Tau variables is their main characteristic.Gerasimovič (1929) proposed that the recurring feature of alternating minima represents two pulsation modes simultaneously excited in a ratio of 2:1 resonance.A detailed description of this and other explanations for this phenomenon is presented by Pollard et al. (1996).It should be mentioned that much less pronounced period doubling behaviour has recently been discovered in some W Vir (Plachy et al. 2018), BL Her (Smolec 2012) and RR Lyr (Szabo et al. 2010) type stars.
We have found that hydrogen emission is present in the spectrum of of IRAS 02143+5852 at certain phases of the pulsation cycle with Hα being the most prominent.We have also detected the Ba ii and He i λ10830 emissions in the spectrum obtained close to maximum light.Schmidt et al. (2004b) studied the Hα and helium emissions in long-period (with periods longer than 8 days) Type II Cepheids.Kovtyukh et al. (2011) detected and investigated the behaviour of emission and line doubling of many metallic lines, in particular, Ba ii, in the spectrum of the Type II Cepheid W Vir. Strong metallic emissions were observed in the spectra of the RV Tau stars U Mon and AC Her (Bopp 1984).Pollard et al. (1997) reviewed the previous spectroscopic studies of the RV Tau variables and presented the results of a long-term photometric and spectroscopic study of eleven stars classified as RV Tau.In particular, they concluded that line emission originates within the de-excitation zone of the shock wave that propagates through the stellar atmosphere.The fact that Hα is observed in emission for much of the pulsation cycle is due to a large range of atmospheric layers where this line forms.On the contrary, the metallic emissions appear only when the shock wave crosses the region where these lines originate.Thus, IRAS 02143+5852 with emission lines of hydrogen, helium, and metals in the spectrum is representative of W Vir and RV Tau stars.
Significant excesses of near, medium and far-IR radiation are distinguishing features of IRAS 02143+5852.These are due to multiple circumstellar envelope, which according to our simulations, has a complicated structure and was formed during three episodes of mass loss.
Many RV Tau stars have an IR-excess which indicates the presence of circumstellar material and for some of them a disc-like structure was proved.Moreover, as the discs are found around binaries, RV Tau stars are likely to be binary systems, too (Manick et al. 2017).
The near-IR excess is rare among W Vir stars.Using published data on periods and SEDs for the Galactic Type II Cepheids, Saario et al. (2018) found that only 43 objects of 1307 have a near-IR excess and only 8 of these 43 have periods less than 30 d.
Besides, IRAS 02143+5852 stands out among typical W Vir stars because of its location in the Galaxy.Whereas W Vir stars are low-mass pulsating variables of the intermediate disc or halo population, IRAS 02143+5852 lies near the Galactic plane (b = −1.• 93).

Objects analogous to IRAS 02143+5852
Among the W Vir stars with the longest periods and RV Tau stars with the shortest periods, there are few objects similar to IRAS 02143+5852.
CC Lyr.CC Lyr is classified in the General Catalogue of Variable Stars (GCVS) as a W Vir-type variable with P = 24.16d and a full peak-to-peak amplitude of ∆V = 0.8 mag (Samus et al. 2017).
The light curves of this star, as well as those of IRAS 02143+5852, show alternating minima of different depth, a characteristic of RV Tau variables (Schmidt et al. 2004a).CC Lyr, as well as IRAS 02143+5852, has a IR excess (Schmidt 2015), also invariably a characteristic of RV Tau variables.CC Lyr and IRAS 02143+5852 have similar spectra (see Section 4).Maas et al. (2007) determined the parameters of the star T eff = 6250 K and log g = 1.0 and revealed that refractory elements show large depletion (e.g., [Fe/H]=-3.5).Aoki et al. (2017) confirmed its extremely low metallicity ([Fe/H] < −3.5) and concluded that the abundance anomaly of this star is due to dust depletion.In addition, Aoki et al. (2017) found that the double-peaked Hα emission shows no evident velocity shift which suggests that the emission is forming in the circumstellar matter, presumably the rotating disc around the object.The double-peaked Hα emission is also observed in the spectrum of IRAS 02143+5852 at certain phases of the pulsation cycle.
So, IRAS 02143+5852 and CC Lyr are similar in showing alternating minima and in having close pulsation periods and composite spectra that combine the properties of a hot and a cool star.At the same time, IRAS 02143+5852 demonstrates a significantly larger IR excess than CC Lyr.Besides, they differ in their location in the Galaxy: whereas CC Lyr is a high galactic latitude star (b = +17.• 27), IRAS 02143+5852 lies close to the Galactic plane.
AF Crt = IRAS 11472-0800.According to GCVS it is a SRB-type variable (semiregular late-type giants with poorly defined periodicity) (Samus et al. 2017).Kiss et al. (2007) determined a period of P = 31.5 ± 0.6 d based on the ASAS data and classified the star as a Population II Cepheid.Through analysing the photometric data obtained at the Valparaiso University Observatory (VUO) in 1995-2008(Van Winckel et al. 2012) derived well-determined period values of 31.16±0.01d (V ) and 32.18±0.04d (R) ( Van Winckel et al. 2012).
We have analysed the ASAS-SN data (Shappee et al. 2014;Kochanek et al. 2017) in the V -band obtained from 2012 to 2018 and determined a period of P = 31.7 d and a peak-topeak amplitude of ∆V = 0.8 mag.The light curves look like that of a W Vir star, but the period lies in the range typical for RV Tau stars.Besides, the photometric data folded on twice the period demonstrate the alternation of more and less deep minima as is common for RV Tau.
AF Crt, as well as CC Lyr, is located at high galactic latitude (b = +51.• 56).It is an extremely depleted object with the photospheric abundances of [Fe/H]=-2.7 and [Sc/H]=-4.2( Van Winckel et al. 2012).Van Winckel et al. (2012) also found that besides the variation of radial velocity related to pulsations, there is a long-term systematic change which they attributed to binary motion.
AF Crt is a highly evolved star of spectral type F, with a large IR excess produced by thermal radiation of circumstellar dust.Based on all the data known to date, Van Winckel et al. (2012) concluded that AF Crt is a lowluminosity analogue of the dusty RV Tau stars.GK Car and GZ Nor.GK Car (IRAS 11118-5726) and GZ Nor (IRAS 16278-5526) are two similar objects studied in detail by Gezer et al. (2019).From the ASAS-SN data, they determined the pulsation periods of 27.6 d for GK Car and 36.2 d for GZ Nor.The light curves folded on twice the period demonstrate alternating minima.The refractory elements are depleted in both stars which may indicate their binarity.The luminosities derived from the period-luminosity relation for the Type II Cepheids are significantly lower than the typical values for post-AGB stars.Based on the acquired results, Gezer et al. (2019) concluded that GK Car and GZ Nor are low-luminous, depleted RV Tau stars and have likely evolved off the RGB.GK Car and GZ Nor with the temperatures of 5500 and 4875 K, respectively, are cooler than IRAS 02143+5852.

CONCLUSIONS
The results of the photometric and spectroscopic observations of the post-AGB candidate IRAS 02143+5852 have been reported.
Based on our observational data we have found the star to vary in brightness with a period of 25 d and a V -band amplitude of 0.9 mag.The shape of light curves is typical for the Type II Cepheids.Its spectral properties, in particular the presence of the strong Hα emission at certain phases of the pulsation cycle, are also characteristic for the Type II Cepheids.
IRAS 02143+5852 has a significant IR excess which is not usual for the W Vir stars, but is common among the RV Tau variables and is a determining feature of post-AGB objects.Modelling the SED in a wide wavelength range 0.44-160 µm allowed us to derive the parameters of the dust circumstellar envelope.We show that it has a complicated structure and was produced by three episodes of mass loss (see Section 6).
Comparing IRAS 02143+5852 with similar objects leads to a conclusion that this star may be considered as a lowluminosity analogue of the dusty RV Tau stars.In order to clarify its evolutionary status it is highly necessary to obtain high-resolution spectra which can provide abundances and stellar parameters (T eff , log g).
Long-term high-resolution spectroscopic monitoring is also highly desirable to derive the radial velocity curve and possibly get evidence for the second component, as binarity is considered related to the existence of a powerful dust envelope.As was mentioned above, the presence of excess near-IR radiation is characteristic of post-AGB binary stars, and those of RV Tau type in particular ( Van Winckel 2017).
In addition, it is necessary to continue the photometric monitoring to derive the so-called observed minus calculated (O-C) diagrams to be able to detect the possible light-time travel effect owing to the presence of a binary.Using the method proposed by Hajdu et al. (2015), Groenewegen and Jurkovic (2017) revealed 20 new possible binary systems among 335 Type II and anomalous Cepheids in the Small and Large Magellanic Clouds.

Figure 1 .
Figure 1.The R C -band image of the IRAS 02143+5852 (var) field with the comparison stars marked.This CCD-frame was obtained with RC600 on February 15, 2020.

Figure 2 .
Figure 2. The U BV R C I C -band light and colour curves covering the period from August 2019 to March 2020.

Figure 3 .
Figure 3.The JHK-band light curves covering the period from 2017 November to 2021 February.

Figure 4 .
Figure 4. Frequency spectra for V data obtained by the Deeming (a) and Lafler-Kinman (b) methods.n the bottom panel, Parameter = 1/θ is plotted along the ordinate axis, where θ is the normalised sum of the squares of the deviations of each subsequent point from the previous point in the light curve with a trial period.

Figure 5 .Figure 6 .
Figure 5.The U BV R C I C light curves folded on the periods of 24.885 d (left panel) and 49.736 d (right panel).Filled circles represent the CMO data, crosses -the data obtained in Slovakia.

Figure 7 .
Figure 7.The ratio of the amplitude in U BV R C I C JHK-bands to the amplitude in the V -band.

Figure 8 .
Figure 8. U-B, B-V colour-colour diagram.Red and blue dots are observed and dereddened with E(B − V )=0.83 mag data, respectively.The supergiant theoretical sequence is plotted with black dots connected by dotted line.In the inset, the data for one pulsation cycle (JD2458870.2-2458896.2) are shown.

Figure 9 .Figure 10 .
Figure9.J-H, H-K colour-colour diagram.Red and blue dots are observed and dereddened with E(B − V ) = 0.83 mag data, respectively.The solid black line shows the loci of a blackbody with temperature ranging from 1200 to 2000 K.The dotted black line shows the supergiant sequence.The grey squares connected by a thick grey line correspond to a combination of an F8I star and a 1350 K blackbody, where each square is calculated with a step of 0.1 in terms of the fractions of contributions from individual components to the total emission in the H-band.

Figure 11 .
Figure 11.The Lick Observatory spectrum dereddened with E(B − V ) = 0.83 mag (black line) and the synthetic spectrum of an F5I star taken from Pickles (1998) (grey line).

Figure 12 .
Figure12.The evolution of the Hα profile with pulsation phase.The numbers in parentheses indicate the order number of spectra as it is defined in Table3.

Figure 13 .
Figure13.The spectrum in the 3750-4450 Å wavelength range at different pulsation phase.The numbers in parentheses correspond to the order number of spectra as it is defined in Table3.

Figure 14 .
Figure14.The spectra of IRAS 02143+5852 at two phases of pulsation cycle -near the minimum (6) and near the maximum (12) light -and the spectra of HD 17971 (F5Ib), SAO 37370 (F0Ib) and CC Lyr.The spectra are normalised to continuum and arbitrarily shifted along the vertical axis.
)).The distance based on these data is d = 3606 +2032 −1331 pc (Bailer-Jones et al. 2018).The parallax π = 1.3637 ± 0.2892 mas introduced in the Gaia DR3 (Gaia Collaboration 2022) brings the star much closer to us.The distance estimate for this parallax is d = 854 +276 −175 pc Figure 15.T he SED of IRAS 02143+5852.The blue curve represents the resulting fit corresponding to the model described in the text, the orange one -the SED of the central star reprocessed by the dust, the green one is the radiation from the circumstellar dust shell.The symbols depict the observational data points.For some data the error bars are smaller than the size of the symbols.

Fig. 15
Fig.15represents the best-fitting model SED with minimal normalized deviations from the observed data.The parameters of the corresponding model dust shells,

Figure 16 .
Figure 16.The model dust density distribution in the envelope plotted on logarithmic scale.The values r 1 , r 2 , r 3 and r 4 -the boundary positions of the dust envelope components.r 1 = 2.5 au, r 2 = 110 au, r 3 = 146 au and r 4 = 1750 au according to Table7where the model parameters are listed.

Figure 17 .
Figure 17.The plot illustrating the process of deriving confidence intervals for model parameters.Each panel shows how the F value changes with one single parameter being varied and the others being fixed.The red line indicates the critical F value.

Figure 18 .
Figure18.The plot illustrating the change of the outer shell mass and corresponding F value due to variation of one of the outer shell parameters τ V , r 3 , r 4 with the rest being fixed.
Figure19.Mass absorption coefficient κ abs for spherical amorphous carbon dust grains with different radii agr.The calculation was performed according to the Mie theory with the optical constants for amorphous carbon adopted fromSuh (2000).

Table 1 .
The comparison stars for U BV RcIc photometry.

Table 2 .
The comparison stars for JHK photometry.

Table 5 .
Equivalent widths of absorption and emission lines in spectrum obtained on 2018 October 20.

Table 6 .
Photometric data used to construct the SED for IRAS 02143+5852.

Table 7 .
The parameters of the model dust envelope components.