arXiv subjects

B. Freytag

Publications and source records attributed to B. Freytag.

At least 19 recordsLinked to original sources

arXiv2026

VLTI-GRAVITY measurements of cool evolved stars: II. Pulsation properties and mass-loss process of the Mira star R Car and the red supergiant VX Sgr

The mass-loss process of red supergiant (RSG) and asymptotic giant branch (AGB) stars and its relation to variability are poorly constrained. We study two evolved stars, the Mira-type AGB star R Car and the extreme RSG VX Sgr. Our sample comprises 54 VLTI-GRAVITY snapshots taken over 7 years, being the largest VLTI time-series dataset to date. We determine the angular diameter as a function of time. The radii of the photosphere ($R_{\star}$) and atomic atmospheric layers are variable and relate to the light curve with phase shifts, showing a maximum radius near visual brightness minima. The more extended CO layers show longer, irregular periods and maximum extensions of $\sim 1.3-1.7 \: R_{\star}$ for R Car, and of $\sim 1.5-2.2 \: R_{\star}$ for VX Sgr. Comparison with CO5BOLD simulations revealed a similar behavior. Furthermore, during 2020-2021, VX Sgr exhibited an extreme mass-loss event similar to that of Betelgeuse, preceded by two strong shocks and culminating with the extreme expansion of H$_2$O and CO layers, both up to $\sim 2.2 \: R_{\star}$. During this event, we detected Brackett $\gamma$ and Balmer emission lines, both of which are signatures of a shock propagating through the atmosphere. The Mira R Car showed a photospheric radius $R_{\star} = 280 \pm 25 \: \rm R_\odot$, with a fundamental mode (FM) pulsation amplitude $\sim13 \%$ of $R_{\star} $. During its active cycle, the RSG VX Sgr showed $R_{\star} = 1556 \pm 110 \: \rm R_\odot$ with FM amplitude $ \sim13 \%$ of $R_{\star} $, the same as R Car. During its quiescent cycle, it showed $R_{\star}= 1456 \pm 108 \: \rm R_\odot$ and low-amplitude pulsations near the first overtone, only $\sim4 \%$ of $R_{\star} $. This supports a steady mass loss for Miras related to stable, large-amplitude FM pulsation, whereas the mass-loss process for RSGs may be dominated by extreme events connected to changes in the pulsation mode.

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arXiv2024

Retrieving stellar parameters and dynamics of AGB stars with Gaia parallax measurements and CO5BOLD RHD simulations

Context. The complex dynamics of asymptotic giant branch (AGB) stars and the resulting stellar winds have a significant impact on the measurements of stellar parameters and amplify their uncertainties. Three-dimensional (3D) radiative hydrodynamic (RHD) simulations of convection suggest that convection-related structures at the surface of AGB star affect the photocentre displacement and the parallax uncertainty measured by Gaia. Aims. We explore the impact of the convection on the photocentre variability and aim to establish analytical laws between the photocentre displacement and stellar parameters to retrieve such parameters from the parallax uncertainty. Methods. We used a selection of 31 RHD simulations with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the Gaia G band [320-1050 nm]. From these maps, we calculated the photocentre position and temporal fluctuations. We then compared the synthetic standard deviation to the parallax uncertainty of a sample of 53 Mira stars observed with Gaia. Results. The simulations show a displacement of the photocentre across the surface ranging from 4 to 13 % of the corresponding stellar radius, in agreement with previous studies. We provide an analytical law relating the pulsation period of the simulations and the photocentre displacement as well as the pulsation period and stellar parameters. By combining these laws, we retrieve the surface gravity, the effective temperature, and the radius for the stars in our sample. Conclusions. Our analysis highlights an original procedure to retrieve stellar parameters by using both state-of-the-art 3D numerical simulations of AGB stellar convection and parallax observations of AGB stars. This will help us refine our understanding of these giants.

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arXiv2024

A new dimension in the variability of AGB stars: convection patterns size changes with pulsation

Stellar convection plays an important role in atmospheric dynamics, wind formation and the mass-loss processes in Asymptotic Giant Branch (AGB) stars. However, a direct characterization of convective surface structures in terms of size, contrast, and life-span is quite challenging. Spatially resolving these features requires the highest angular resolution. In this work, we aim at characterizing the size of convective structures on the surface of the O-rich AGB star R Car to test different theoretical predictions, based on mixing-length theory from solar models. We used infrared low-spectral resolution (R~35) interferometric data in the H-band (~1.76 $\mu$m) with the instrument PIONIER at the Very Large Telescope Interferometer (VLTI) to image the star's surface at two epochs separated by ~6 years. Using a power spectrum analysis, we estimate the horizontal size of the structures on the surface of R Car. The sizes of the stellar disk, at different phases of a pulsation cycle, were obtained using parametric model-fitting in the Fourier domain. Our analysis supports that the sizes of the structures in R Car are correlated with variations of the pressure scale height in the atmosphere of the target, as predicted by theoretical models based on solar convective processes. We observe that these structures grow in size when the star expands within a pulsation cycle. While the information is still scarce, this observational finding highlights the role of convection in the dynamics of those objects. New interferometric imaging campaigns with the renewed capabilities of the VLTI are envisioned to expand our analysis to a larger sample of objects.

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arXiv2022

Probing Red Supergiant dynamics through photo-center displacements measured by Gaia

Red supergiant (RSGs) are cool massive stars in a late phase of their evolution when the stellar envelope becomes fully convective. They are the brightest stars in the universe at infrared light and can be detected in galaxies far beyond the Local Group, allowing for accurate determination of chemical composition of galaxies. The study of their physical properties is extremely important for various phenomena including the final fate of massive stars as type II supernovae and gravitational wave progenitors. We explore the well-studied nearby young stellar cluster chi Per. Using Gaia EDR3 data, we find the distance of the cluster (d = 2.260+-0.020 kpc). We then investigate the variability of the convection-related surface structure as a source for parallax measurement uncertainty. We use state-of-the-art 3D radiative hydrodynamics simulations with CO5BOLD and the post-processing radiative transfer code OPTIM3D to compute intensity maps in the Gaia G photometric system. We calculate the variabiltiy, as a function of time, of the intensity-weighted mean from the synthetic maps. We then select the RSG stars in the cluster and compare their uncertainty on parallaxes to the predictions of photocentre displacements. The synthetic maps of RSG show extremely irregular and temporal variable surfaces due to convection-related dynamics. Consequentially, the position of the photo-center varies during Gaia measurements between 0.033 and 0.130 AU (up to 5% of the corresponding simulation stellar radius). We argue that the variability of the convection-related surface structures accounts for a substantial part of the Gaia EDR3 parallax error of the RSG sample. We suggest that the variation of the uncertainty on Gaia parallax could be exploited quantitatively using appropriate 3D simulations to extract, in a unique way, important information about the stellar dynamics and parameters of RSG stars.

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arXiv2021

The extended atmosphere and circumstellar environment of the cool evolved star VX Sagittarii as seen by MATISSE

Context. VX Sgr is a cool, evolved, and luminous red star whose stellar parameters are difficult to determine, which affects its classification. Aims. We aim to spatially resolve the photospheric extent as well as the circumstellar environment. Methods. We used interferometric observations obtained with the MATISSE instrument in the L (3 to 4 μm), M (4.5 to 5 μm), and N (8 to 13 μm) bands. We reconstructed monochromatic images using the MIRA software. We used 3D radiation-hydrodynamics (RHD) simulations carried out with CO5BOLD and a uniform disc model to estimate the apparent diameter and interpret the stellar surface structures. Moreover, we employed the radiative transfer codes Optim3D and Radmc3D to compute the spectral energy distribution for the L, M, and N bands, respectively. Results. MATISSE observations unveil, for the first time, the morphology of VX Sgr across the L, M, and N bands. The reconstructed images show a complex morphology with brighter areas whose characteristics depend on the wavelength probed. We measured the angular diameter as a function of the wavelength and showed that the photospheric extent in the L and M bands depends on the opacity through the atmosphere. In addition to this, we also concluded that the observed photospheric inhomogeneities can be interpreted as convection-related surface structures. The comparison in the N band yielded a qualitative agreement between the N band spectrum and simple dust radiative transfer simulations. However, it is not possible to firmly conclude on the interpretation of the current data because of the difficulty in constraing the model parameters using the limited accuracy of our absolute flux calibration. Conclusions. MATISSE observations and the derived reconstructed images unveil the appearance of the stellar surface and circumstellar environment across a very large spectral domain for the first time.

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arXiv2021

Atmosphere of Betelgeuse before and during the Great Dimming event revealed by tomography

Despite being the best studied red supergiant star in our Galaxy, the physics behind the photometric variability and mass loss of Betelgeuse is poorly understood. Moreover, recently the star has experienced an unusual fading with its visual magnitude reaching a historical minimum. We investigate the nature of this event with the help of a recently developed tomographic technique. Tomography allows us to probe different depths in the stellar atmosphere and to recover the corresponding disk-averaged velocity field. We apply the tomographic method to a few-year time-series high-resolution spectroscopic observations of Betelgeuse in order to relate its atmospheric dynamics to the photometric variability. Our results show that a sudden increase of the molecular opacity in the cooler upper atmosphere of Betelgeuse is likely the reason of the observed unusual decrease of the star's brightness.

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arXiv2020

Optical interferometry and Gaia measurement uncertainties reveal the physics of asymptotic giant branch stars

Context. Asymptotic giant branch stars are cool luminous evolved stars that are well observable across the Galaxy and populating Gaia data. They have complex stellar surface dynamics Aims. On the AGB star CL Lac, it has been shown that the convection-related variability accounts for a substantial part of the Gaia DR2 parallax error. We observed this star with the MIRC-X beam combiner installed at the CHARA interferometer to detect the presence of stellar surface inhomogeneities. Methods. We performed the reconstruction of aperture synthesis images from the interferometric observations at different wavelengths. Then, we used 3D radiative hydrodynamics simulations of stellar convection with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the spectral channels of MIRC-X observations. Then, we determined the stellar radius and compared the 3D synthetic maps to the reconstructed ones focusing on matching the intensity contrast, the morphology of stellar surface structures, and the photocentre position at two different spectral channels, 1.52 and 1.70 micron, simultaneously. Results. We measured the apparent diameter of CL Lac at two wavelengths and recovered the radius using a Gaia parallax. In addition to this, the reconstructed images are characterised by the presence of a brighter area that largely affects the position of the photocentre. The comparison with 3D simulation shows good agreement with the observations both in terms of contrast and surface structure morphology, meaning that our model is adequate for explaining the observed inhomogenities. Conclusions. This work confirms the presence of convection-related surface structures on an AGB star of Gaia DR2. Our result will help us to take a step forward in exploiting Gaia measurement uncertainties to extract the fundamental properties of AGB stars using appropriate RHD simulations.

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arXiv2020

VLTI-PIONIER imaging of the red supergiant V602 Carinae

Context. Red supergiant stars possess surface features and extended molecular atmospheres. Photospheric convection may be a crucial factor of the levitation of the outer atmospheric layers. However, the mechanism responsible is still poorly understood. Aims. We image the stellar surface of V602 Carinae (V602 Car) to constrain the morphology and contrast of the surface features and of the extended atmospheric layers. Methods. We observed V602 Car with the Very Large Telescope Interferometer (VLTI) PIONIER instrument (1.53-1.78 $\mathrmμ$m) between May and July 2016, and April and July 2019 with different telescope configurations. We compared the image reconstructions with 81 temporal snapshots of 3D radiative-hydrodynamics (RHD) CO$^5$BOLD simulations in terms of contrast and morphology, using the Structural Similarity Index. Results. The interferometric data are compatible with an overall spherical disk of angular diameter 4.4$\pm$0.2 mas, and an extended molecular layer. In 2016, the reconstructed image reveals a bright arc-like feature toward the northern rim of the photospheric surface. In 2019, an arc-like feature is seen at a different orientation and a new peak of emission is detected on the opposite side. The contrasts of the reconstructed surface images are 11%$\pm$2% and 9%$\pm$2% for 2016 and 2019, respectively. The morphology and contrast of the two images are consistent with 3D RHD simulations, within our achieved spatial resolution and dynamic range. The extended molecular layer contributes 10--13% of the total flux with an angular diameter of 6--8 mas. It is present but not clearly visible in the reconstructed images because it is close to the limits of the achieved dynamic range. The presence of the molecular layer is not reproduced by the 3D RHD simulations. Conclusions...

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arXiv2019

Tomography of cool giant and supergiant star atmospheres II. Signature of convection in the atmosphere of the red supergiant star $μ$ Cep

Red supergiants are cool massive stars and are the largest and the most luminous stars in the universe. They are characterized by irregular or semi-regular photometric variations, the physics of which is not clearly understood. The paper aims at deriving the velocity field in the red supergiant star $μ$ Cep and relating it to the photometric variability with the help of the tomographic method. The tomographic method allows to recover the line-of-sight velocity distribution over the stellar disk and within different optical-depth slices. The method is applied to a series of high-resolution spectra of $μ$ Cep, and these results are compared to those obtained from 3D radiative-hydrodynamics CO5BOLD simulations of red supergiants. Fluctuations in the velocity field are compared with photometric and spectroscopic variations, the latter being derived from the TiO band strength and serving (at least partly) a proxy of the variations in effective temperature. The tomographic method reveals a phase shift between the velocity and spectroscopic/photometric variations. This phase shift results in a hysteresis loop in the temperature - velocity plane, with a timescale of a few hundred days, similar to the photometric one. The similarity between the hysteresis loop timescale measured in $μ$ Cep and the timescale of acoustic waves disturbing the convective pattern suggests that such waves play an important role in triggering the hysteresis loops.

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arXiv2019

Calibration of the mixing length theory for structures of helium-dominated atmosphere white dwarfs

We perform a calibration of the mixing length parameter at the bottom boundary of the convection zone for helium-dominated atmospheres of white dwarfs. This calibration is based on a grid of 3D DB (pure-helium) and DBA (helium-dominated with traces of hydrogen) model atmospheres computed with the CO5BOLD code, and a grid of 1D DB and DBA envelope structures. The 3D models span a parameter space of hydrogen-to-helium abundances between -10.0 and -2.0, surface gravities between 7.5 and 9.0 and effective temperatures between 12000 K and 34000 K. The 1D envelopes cover a similar atmospheric parameter range, but are also calculated with different values of the mixing length parameter, namely ML2/alpha between 0.4 and 1.4. The calibration is performed based on two definitions of the bottom boundary of the convection zone, the Schwarzschild and the zero convective flux boundaries. Thus, our calibration is relevant for applications involving the bulk properties of the convection zone including its total mass, which excludes the spectroscopic technique. Overall, the calibrated ML2/alpha is smaller than what is commonly used in evolutionary models and theoretical determinations of the blue edge of the instability strip for pulsating DB and DBA stars. With calibrated ML2/alpha we are able to deduce more accurate convection zone sizes needed for studies of planetary debris mixing and dredge-up of carbon from the core. We highlight this by calculating examples of metal-rich 3D DBAZ models and finding their convection zone masses. Mixing length calibration represents the first step of in-depth investigations of convective overshoot in white dwarfs with helium-dominated atmospheres.

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arXiv2018

Tomography of the red supergiant star μ Cep

A tomographic method, aiming at probing velocity fields at depth in stellar atmospheres, is applied to the red supergiant star μ Cep and to snapshots of 3D radiative-hydrodynamics simulation in order to constrain atmospheric motions and relate them to photometric variability.

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arXiv2018

Pure-helium 3D model atmospheres of white dwarfs

We present the first grid of 3D simulations for the pure-helium atmospheres of DB white dwarfs. The simulations were computed with the CO5BOLD radiation-hydrodynamics code and cover effective temperatures and surface gravities between 12000 K < Teff < 34000 K and 7.5 < log(g) (cgs units) < 9.0, respectively. In this introductory work, synthetic spectra calculated from the 3D simulations are compared to appropriate 1D model spectra under a differential approach. This results in the derivation of 3D corrections for the spectroscopically derived atmospheric parameters of DB stars with respect to the 1D ML2/alpha = 1.25 mixing-length parameterisation. No significant Teff corrections are found for the V777 Her instability strip region, and therefore no 3D revision is expected for the empirical blue and red edges of the strip. However, large log(g) corrections are found in the range 12000 K < Teff < 23000 K for all log(g) values covered by the 3D grid. These corrections indicate that 1D model atmospheres overpredict log(g), reminiscent of the results found from 3D simulations of pure-hydrogen white dwarfs. The next step will be to compute 3D simulations with mixed helium and hydrogen atmospheres to comprehend the full implications for the stellar parameters of DB and DBA white dwarfs.

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arXiv2018

Atmospheres and wind properties of non-spherical AGB stars

The wind-driving mechanism of asymptotic giant branch (AGB) stars is commonly attributed to a two-step process: first, gas in the stellar atmosphere is levitated by shockwaves caused by stellar pulsation, then accelerated outwards by radiative pressure on newly formed dust, inducing a wind. Dynamical modelling of such winds usually assumes a spherically symmetric star. We explore the potential consequences of complex stellar surface structures, as predicted by three-dimensional (3D) star-in-a-box modelling of M-type AGB stars, on the resulting wind properties with the aim to improve the current wind models. Two different modelling approaches are used; the CO$^5$BOLD 3D star-in-a-box code to simulate the convective, pulsating interior and lower atmosphere of the star, and the DARWIN one-dimensional (1D) code to describe the dynamical atmosphere where the wind is accelerated. The gas dynamics of the inner atmosphere region at distances of $R\sim1-2R_\star$, which both modelling approaches simulate, are compared. Dynamical properties and luminosity variations derived from CO$^5$BOLD interior models are used as input for the inner boundary in DARWIN wind models in order to emulate the effects of giant convection cells and pulsation, and explore their influence on the dynamical properties. The CO$^5$BOLD models are inherently anisotropic, with non-uniform shock fronts and varying luminosity amplitudes, in contrast to the spherically symmetrical DARWIN wind models. DARWIN wind models with CO$^5$BOLD-derived inner boundary conditions produced wind velocities and mass-loss rates comparable to the standard DARWIN models, however the winds show large density variations on time-scales of 10-20 years.

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arXiv2018

Heading Gaia to measure atmospheric dynamics in AGB stars

Context. Asymptotic Giant Branch stars are characterised by complex stellar surface dynamics that affect the measurements and amplify the uncertainties on stellar parameters. The resulting motion of the stellar photo-center could have adverse effects on the parallax determination with Gaia. Aims. We explore the impact of the convection-related surface structure in AGBs on the photocentric variability. We quantify these effects to characterise the observed parallax errors and estimate fundamental stellar parameters and dynamical properties. Methods. We use 3D radiative-hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the Gaia G band. From those maps, we calculate the intensity-weighted mean of all emitting points tiling the visible stellar surface and evaluate its motion as a function of time. We extract the parallax error from Gaia DR2 for a sample of semiregular variables in the solar neighbourhood and compare it to the synthetic predictions of photo-center displacements. Results. AGB stars show a complex surface morphology characterised by the presence of few large scale long-lived convective cells accompanied by short-lived and small scale structures. As a consequence, the position of the photo-center displays temporal excursions between 0.077 to 0.198 AU (5 to 11% of the corresponding stellar radius), depending on the simulation considered. We show that the convection-related variability accounts for a substantial part to the Gaia DR2 parallax error of our sample of semiregular variables. Finally, we put in evidence for a correlation between the mean photo-center displacement and the stellar fundamental parameters: surface gravity, radius, and pulsation. We denote that parallax variations could be exploited quantitatively using appropriate RHD simulations corresponding to the observed star.

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arXiv2018

Using the CIFIST grid of CO5BOLD 3D model atmospheres to study the effects of stellar granulation on photometric colours. I. Grids of 3D corrections in the UBVRI, 2MASS, Hipparcos, Gaia, and SDSS systems

The atmospheres of cool stars are temporally and spatially inhomogeneous due to the effects of convection.The influence of this inhomogeneity, referred to as granulation, on colours has never been investigated over a large range of effective temperatures and gravities. We aim to study, in a quantitative way, the impact of granulation on colours. We use the CIFIST grid of CO5BOLD hydrodynamical models to compute emerging fluxes. These in turn are used to compute theoretical colours in the UBVRI,2MASS,Hipparcos,Gaia and SDSS systems. Every CO5BOLD model has a corresponding one dimensional (1D) plane-parallel LHD model computed for the same atmospheric parameters, which we used to define a "3D correction" that can be applied to colours computed from fluxes computed from any 1D model atmosphere code. The 3D corrections on colours are generally small, of the order of a few hundredths of a magnitude, yet they are far from negligible. We find that ignoring granulation effects can lead to underestimation of Teff by up to 200K and overestimation of gravity by up to 0.5dex, when using colours as diagnostics. We have identified a major shortcoming in how scattering is treated in the current version of the CIFIST grid, which could lead to offsets of the order 0.01mag, especially for colours involving blue and UV bands.We have investigated the Gaia and Hipparcos photometric systems and found that the (G-H_p),(BP-RP) diagram is immune to the effects of granulation. In addition, we point to the potential of the RVS photometry as a metallicity diagnostic. Our investigation shows that the effects of granulation should not be neglected if one wants to use colours as diagnostics of the stellar parameters of F,G,K stars. A limitation is that scattering is treated as true absorption in our current computations, thus our 3D corrections are likely an upper limit to the true effect. (Abridged)

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arXiv2017

Spectroscopic properties of a two-dimensional time-dependent Cepheid model II. Determination of stellar parameters and abundances

Standard spectroscopic analyses of variable stars are based on hydrostatic one-dimensional model atmospheres. This quasi-static approach has theoretically not been validated. We aim at investigating the validity of the quasi-static approximation for Cepheid variables. We focus on the spectroscopic determination of the effective temperature $T_\mathrm{eff}$, surface gravity $\log \,g$, microturbulent velocity $ξ_\mathrm{t}$, and a generic metal abundance $\log\,A$ -- here taken as iron. We calculate a grid of 1D hydrostatic plane-parallel models covering the ranges in effective temperature and gravity encountered during the evolution of a two-dimensional time-dependent envelope model of a Cepheid computed with the radiation-hydrodynamics code CO5BOLD. We perform 1D spectral syntheses for artificial iron lines in local thermodynamic equilibrium varying the microturbulent velocity and abundance. We fit the resulting equivalent widths to corresponding values obtained from our dynamical model. For the four-parametric case, the stellar parameters are typically underestimated exhibiting a bias in the iron abundance of $\approx-0.2\,\mbox{dex}$. To avoid biases of this kind it is favourable to restrict the spectroscopic analysis to photometric phases $ϕ_\mathrm{ph}\approx0.3\ldots 0.65$ using additional information to fix effective temperature and surface gravity. Hydrostatic 1D model atmospheres can provide unbiased estimates of stellar parameters and abundances of Cepheid variables for particular phases of their pulsations. We identified convective inhomogeneities as the main driver behind potential biases. For obtaining a complete view on the effects when determining stellar parameters with 1D models, multi-dimensional Cepheid atmosphere models are necessary for variables of longer period than investigated here.

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arXiv2017

Tomography of cool giant and supergiant star atmospheres. I. Validation of the method

Cool giant and supergiant star atmospheres are characterized by complex velocity fields originating from convection and pulsation processes which are not fully understood yet. The velocity fields impact the formation of spectral lines, which thus contain information on the dynamics of stellar atmospheres. The tomographic method allows to recover the distribution of the component of the velocity field projected on the line of sight at different optical depths in the stellar atmosphere. The computation of the contribution function to the line depression aims at correctly identifying the depth of formation of spectral lines in order to construct numerical masks probing spectral lines forming at different optical depths. The tomographic method is applied to 1D model atmospheres and to a realistic 3D radiative hydrodynamics simulation performed with CO5BOLD in order to compare their spectral line formation depths and velocity fields. In 1D model atmospheres, each spectral line forms in a restricted range of optical depths. On the other hand, in 3D simulations, the line formation depths are spread in the atmosphere mainly because of temperature and density inhomogeneities. Comparison of CCF profiles obtained from 3D synthetic spectra with velocities from the 3D simulation shows that the tomographic method correctly recovers the distribution of the velocity component projected on the line of sight in the atmosphere.

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arXiv2017

Spectroscopic properties of a two-dimensional time-dependent Cepheid model I. Description and validation of the model

Standard spectroscopic analyses of Cepheid variables are based on hydrostatic one-dimensional model atmospheres, with convection treated using various formulations of mixing-length theory. This paper aims to carry out an investigation of the validity of the quasi-static approximation in the context of pulsating stars. We check the adequacy of a two-dimensional time-dependent model of a Cepheid-like variable with focus on its spectroscopic properties. With the radiation-hydrodynamics code CO5BOLD, we construct a two-dimensional time-dependent envelope model of a Cepheid with $T_\mathrm{eff}= 5600$ K, $\log g=2.0$, solar metallicity, and a 2.8-day pulsation period. Subsequently, we perform extensive spectral syntheses of a set of artificial iron lines in local thermodynamic equilibrium. The set of lines allows us to systematically study effects of line strength, ionization stage, and excitation potential. We evaluate the microturbulent velocity, line asymmetry, projection factor, and Doppler shifts. The mean Doppler shift is non-zero and negative, -1 km/s, after averaging over several full periods and lines. This residual line-of-sight velocity (related to the "K-term") is primarily caused by horizontal inhomogeneities, and consequently we interpret it as the familiar convective blueshift ubiquitously present in non-pulsating late-type stars. Limited statistics prevent firm conclusions on the line asymmetries. Our two-dimensional model provides a reasonably accurate representation of the spectroscopic properties of a short-period Cepheid-like variable star. Some properties are primarily controlled by convective inhomogeneities rather than by the Cepheid-defining pulsations.

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