Hot subdwarf wind models with accurate abundances I. Hydrogen dominated stars HD 49798 and BD+18 ∘ 2647
J. Krticka, J. Janik, I. Krtickova, S. Mereghetti, F. Pintore, P. Nemeth, J. Kubat, M. Vuckovic
aa r X i v : . [ a s t r o - ph . S R ] S e p Astronomy & Astrophysicsmanuscript no. esosubwind c (cid:13)
ESO 2019September 30, 2019
Hot subdwarf wind models with accurate abundances
I. Hydrogen dominated stars HD 49798 and BD+18 ◦ ⋆ J. Krtiˇcka , J. Janík , I. Krtiˇcková , S. Mereghetti , F. Pintore , P. Németh , J. Kubát , and M. Vuˇckovi´c Ústav teoretické fyziky a astrofyziky, Masarykova univerzita, Kotláˇrská 2, CZ-611 37 Brno, Czech Republic Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Alfonso Corti 12, 20133, Milano, Italy Astronomický ústav, Akademie vˇed ˇCeské republiky, Friˇcova 298, CZ-251 65 Ondˇrejov, Czech Republic Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Gran Bretaña 1111, Playa Ancha, 2360102,Valparaíso, ChileReceived
ABSTRACT
Context.
Hot subdwarfs are helium burning objects in late stages of their evolution. These subluminous stars can develop winds drivenby light absorption in the lines of heavier elements. The wind strength depends on chemical composition which can significantly varyfrom star to star.
Aims.
We aim to understand the influence of metallicity on the strength of the winds of the hot hydrogen-rich subdwarfs HD 49798and BD + ◦ Methods.
We used high-resolution UV and optical spectra to derive stellar parameters and abundances using the TLUSTY andSYNSPEC codes. For derived stellar parameters, we predicted wind structure (including mass-loss rates and terminal velocities) withour METUJE code.
Results.
We derived e ff ective temperature T e ff =
45 900 K and mass M = . M ⊙ for HD 49798 and T e ff =
73 000 K and M = . M ⊙ for BD + ◦ ff usion. The subdwarf HD 49798 has a strong wind that does not allow for chemical separation and consequently the star showssolar chemical composition modified by hydrogen burning. On the other hand, we did not find any wind in BD + ◦ ff ected by radiative di ff usion. Accurate abundances do not lead to a significant modification ofwind mass-loss rate for HD 49798, because the increase of the contribution of iron and nickel to the radiative force is compensated bythe decrease of the radiative force due to other elements. The resulting wind mass-loss rate ˙ M = . × − M ⊙ yr − predicts an X-raylight curve during the eclipse which closely agrees with observations. On the other hand, the absence of the wind in BD + ◦ Conclusions.
Wind models with accurate abundances provide more reliable wind parameters, but the influence of abundances on thewind parameters is limited in many cases.
Key words. stars: winds, outflows – stars: mass-loss – stars: early-type – subdwarfs – X-rays: binaries
1. Introduction
The stellar winds of hot stars are driven by the radiative force dueto light absorption in the lines of heavy elements (Castor et al.1975; Puls et al. 2008). Consequently, metallicity, in additionto stellar luminosity, is one of the key parameters that deter-mine the properties of hot star winds. Thanks to a relativelylow metallicity gradient in our Galaxy (e.g. Netopil et al. 2016),wind studies of Galactic main sequence and supergiant massivestars may safely assume solar chemical composition in mostcases. Moreover, although the mixing induced by stellar rota-tion may alter the surface chemical composition during stellarevolution (Meynet & Maeder 2000), corresponding variations ofwind parameters are typically negligible for solar metallicitystars whose surfaces are enriched by hydrogen burning products(Krtiˇcka & Kubát 2014). This further justifies the assumption ofsolar metallicity for studies of main sequence and supergiant hotstars. ⋆ Based on observations collected at the European Southern Obser-vatory, Paranal, Chile (ESO programme 097.D-0540(A)).
With the advent of 8m class telescopes and the HubbleSpace Telescope (HST) it became possible to spectroscopicallystudy winds from individual hot stars residing in the LocalGroup of galaxies (e.g. Massey et al. 2005; Bouret et al. 2015;Sabín-Sanjulián et al. 2017). Although these stars have non-solarabundances, a simple assumption of scaled solar chemical com-position seems to be su ffi cient for the study of their winds(Vink et al. 2001; Krtiˇcka & Kubát 2018).However, the assumption of scaled solar chemical compo-sition drops at late evolutionary phases of massive stars dur-ing the Wolf-Rayet phase when the envelope is stripped inthe course of single or binary star evolution (Vanbeveren et al.2007; Ekström et al. 2012). In these late evolutionary phases,products of hydrogen and helium burning appear on the stel-lar surface. This results in strong deviations from solar chemi-cal composition, which has severe consequences for mass-loss(Gräfener & Hamann 2008).The e ff ects of deviations from solar chemical composi-tion on stellar winds can also be expected in hot subdwarfs.These stars, stripped of their envelope, are low-mass counter-parts to Wolf-Rayet stars (Götberg et al. 2018) and therefore also Article number, page 1 of 11 & Aproofs: manuscript no. esosubwind
Table 1.
Spectra used for the analysis.
Star Instrument Spectrum Domain [Å] JD − / GHRS z0x60606t 1248–1270 48733.94266z0x60607t 1300–1335 48733.94516z0x60608t 1602–1637 48733.94818z0x60609t 1650–1684 48733.95195z0x6060at 1800–1834 48733.95564z0x6060ct 1840–1874 48733.97662BD + ◦ / SWP 20488 1150–1975 45536.48785FUSE m1080701000 900–1190 51664.15527show non-solar chemical composition. Moreover, the processesof radiative di ff usion and gravitational settling may a ff ect thesurface chemical composition of subdwarfs (Unglaub & Bues2000; VandenBerg et al. 2002; Michaud et al. 2011a; Hu et al.2011).Subdwarfs share with Wolf-Rayet stars not only non-solarchemical composition but probably also similar origin. Thereare several possible evolutionary channels that can lead to theappearance of subdwarfs. Helium low-luminosity subdwarfsmay originate as a result of merging of two white dwarfs(Iben & Tutukov 1984; Saio & Je ff ery 2000; Zhang & Je ff ery2012) or due to helium core flashes while descending on thewhite dwarf cooling track directly after the departure from thered giant branch (‘hot flasher’ scenario, e.g. Brown et al. 2001;Battich et al. 2018). Subluminous stars may also be products ofred giants stripped of their envelopes most likely during theirbinary evolution (e.g. Han et al. 2007).Despite their likely non-solar chemical composition, stel-lar winds of hot subdwarfs were studied assuming either so-lar or scaled solar chemical composition (Vink & Cassisi 2002;Unglaub 2008; Krtiˇcka et al. 2016). This is likely not the mostsuitable approach to late evolutionary stages, when the as-sumption of scaled solar composition does not provide a pre-cise estimate of wind structure. Moreover, some hot subdwarfsemit X-rays, which are supposed to originate in their winds(La Palombara et al. 2014). The non-solar chemical compositioncould explain why some hot subdwarfs are located far away fromthe canonical relationship between X-ray luminosity and bolo-metric luminosity (Krtiˇcka et al. 2016).To understand the role of non-solar chemical composition,we initiated an observing campaign, during which we plan toderive detailed photospheric properties of selected hot subdwarfsand to simulate their winds with accurate chemical composition.We selected subdwarfs that emit lower amounts of X-rays thanexpected from the mean relationship between X-ray luminosityand bolometric luminosity (Krtiˇcka et al. 2016, Fig. 5). Here wepresent the results of such a study for two hydrogen-dominatedsubdwarfs.
2. Spectroscopy
The spectral analysis presented here of hydrogen-dominatedsubdwarfs is based on our own optical spectroscopy and onarchival ultraviolet (UV) data. We obtained observational timewith the high-resolution spectrograph UVES ( R =
80 000) lo-cated at the Nasmyth B focus of VLT-UT2 (Kueyen) via ESOproposal 097.D-0540(A). The spectrum of the star BD + ◦ routines(bias, flat, and wavelength calibration). Both spectra cover thespectral region of 3732 − . The list of all used observations is given inTable 1.
3. Analysis of spectra
The spectroscopic analysis of subdwarf spectra was based on thehydrostatic NLTE model atmosphere code TLUSTY (Hubeny1988) version 200. The hydrostatic model atmospheres give re-liable stellar parameters even for stars with winds (Bouret et al.2003; Heap et al. 2006), provided the mass-loss rates are low,as in the case of subdwarfs. The atomic data used for the atmo-sphere modelling are the same as in Lanz & Hubeny (2003). Thedata were mostly calculated within the Opacity and Iron Projects(Seaton et al. 1992; Hummer et al. 1993). Synthetic spectra werecalculated from the model atmospheres using the SYNSPECcode (Hubeny & Lanz 2011) version 45. We also measured theradial velocity from each UVES spectrum by means of a cross-correlation function using the theoretical spectrum as a template(Zverko et al. 2007).The stellar parameters were determined using the χ minimi-sation of the di ff erence between observed and predicted spectrausing the simplex method (Krtiˇcka & Štefl 1999). We derivedstellar e ff ective temperature T e ff , surface gravity log g , and abun-dances of individual elements ε el for each star. The elementalabundances are given as number density ratios relative to hydro-gen, that is, ε el = N el / N H . The minimisation proceeded in threesteps:1. We calculated a model atmosphere and a synthetic spec-trum grid in T e ff , log g , and ε He . At the beginning of it-erations we used a relatively broad range of stellar pa-rameters, which was subsequently made narrower as theparameters approached the final value. We assumed afixed number density ratio N el / ( N H + N He ) of heavier el-ements with respect to hydrogen and helium for elementswhose abundances were derived from spectra. For other el-ements we used solar (Asplund et al. 2009) density ratio m el N el / ( m H N H + m He N He ), where m el is the atomic mass, as-suming that the abundance of these elements was not a ff ectedby nuclear reactions or by di ff usion. IRAF is distributed by NOAO, which is operated by AURA, Inc.,under cooperative agreement with the National Science Foundation. Mikulski Archive for Space Telescopes, http: // archive.stsci.eduArticle number, page 2 of 11. Krtiˇcka et al.: Hot subdwarf wind models with accurate abundances: I. HD 49798 and BD + ◦
2. We minimised the χ di ff erences between the observed spec-trum and the predicted spectrum interpolated from the gridto derive T e ff , log g , and ε He .3. We calculated a model atmosphere with T e ff , log g , and ε He derived in step 2 and based on this model atmosphere weminimised the χ di ff erences between the observed spectrumand the predicted spectrum calculated for actual abundancesof heavier elements.The steps 1 – 3 were repeated until the changes of parameterswere lower than 1%. The derived parameters are given in Ta-ble 2. The uncertainties on T e ff , log g , and ε He were estimatedfrom fits of individual H and He lines. The uncertainties of otherelemental abundances were estimated from the abundances de-rived from individual spectral regions.We encountered some numerical di ffi culties during the com-putation of model atmospheres. To resolve these di ffi culties, wefollowed general recommendations (Hubeny & Lanz 2017); thatis, we typically started with the LTE model and treated lowerlevels assuming detailed radiative balance (using the ILVLINparameter). The model becomes more realistic with lower val-ues of ILVLIN. It is usually e ff ective to start with high values ofILVLIN =
100 for the models that have di ffi culties in converging.After the successful calculation of the model with a high valueof ILVLIN, we used the result as an input for a following mod-elling and progressively decreased the value of this parameterin subsequent steps. In some cases, we successively decreasedthis parameter separately for individual elements to obtain a pureNLTE model. We gradually included individual elements to cal-culate more detailed models. Moreover, in some cases during thecalculation of an intermediate NLTE model we fixed the temper-ature in the outer layers to achieve convergence. We relaxed thisassumption during the calculation of final NLTE models.
4. Wind modelling
We used the global wind code METUJE for the prediction ofwind parameters (Krtiˇcka & Kubát 2017). METUJE providesglobal (unified) models of the stellar photosphere and radiativelydriven wind. The code solves the comoving frame (CMF) radia-tive transfer equation, the kinetic (statistical) equilibrium equa-tions (often denoted as NLTE equations), and hydrodynamicequations from an almost hydrostatic photosphere to a superson-ically expanding wind. The hydrodynamical equations containthe CMF radiative force calculated using NLTE level popula-tions. Therefore, the code predicts basic wind parameters includ-ing the mass-loss rates ˙ M and the terminal velocities v ∞ simplyfrom the stellar parameters. The code assumes a stationary (time-independent) and spherically symmetric wind.We calculated wind models for the stellar parameters ( T e ff , R , and M ) given in Table 2 for both subdwarfs studied here. Tounderstand the role of specific chemical composition in the driv-ing of wind, we calculated two sets of wind models. One set wascalculated for derived stellar chemical composition (yielding ˙ M and v ∞ ) and the second set for solar (Asplund et al. 2009) chem-ical composition (giving ˙ M ⊙ and v ⊙∞ ). These values are providedin Table 2. We assumed solar chemical composition for the ele-ments whose abundances were not derived from spectra.
5. HD 49798
The binary HD 49798 (CD-44 2920, α = .
70 s , δ = − ◦ ′ . ′′ , J2000) consists of a hot subdwarf and a com-pact companion (Thackeray 1970). The nature of the compact Table 2.
Derived parameters of studied stars.
Parameter HD 49798 BD + ◦ T e ff [K] 45 900 ±
800 73 000 ± g/ − ) 4 . ± .
08 5 . ± . R [ R ⊙ ] 1 . ± .
06 0 . ± . M [ M ⊙ ] 1 . ± .
32 0 . ± . ε He . ± .
07 0 . ± .
010 0 . ε C < − . < − . − . ε N − . ± . − . ± . − . ε O − . ± . − . ± . − . ε F < − . − . ε Ne < − . − . ε Mg − . − . ε Al − . ± . − . ε Si − . ± . − . ± . − . ε S − . ± . − . ε Fe − . ± . − . ± . − . ε Ni − . ± . − . ± . − . v rad [km s − ] 107 . ± . ∗ . ± . ∗ v rot sin i [km s − ] 40 ± ± d [pc] 508 ±
17 307 ± M [ M ⊙ yr − ] 2 . × − < − v ∞ [km s − ] 1570˙ M ⊙ [ M ⊙ yr − ] 2 . × − . × − v ⊙∞ [km s − ] 1550 1800 Notes.
Solar abundances were taken from Asplund et al. (2009). Blankitems denote values that were not determined. ( ∗ ) The radial velocity was derived from the UVES spectrum.
Table 3.
Wavelengths of the strongest lines (in Å) used for abundancedetermination in HD 49798. C iii iii , iv iii ii iii iv M > . M ⊙ (Mereghetti et al. 2009).HD 49798 is one of the few hot subdwarfs that has been de-tected in the X-ray range (see Mereghetti & La Palombara 2016,for a review on X-ray emission from hot subdwarfs). Most of theX-ray emission seen from this binary is emitted by the compactcompanion of HD 49798, which must be either a neutron star ora white dwarf, as evidenced by the presence of a significant pe-riodicity at 13.2 s in the X-ray emission (Mereghetti et al. 2009,2016; Popov et al. 2018). However, a significant X-ray flux witha thermal spectrum and X-ray luminosity 3 × erg s − is alsoclearly detected when the compact companion is eclipsed by HD49798, and can be associated to the X-ray emission in the windof the hot subdwarf itself (Mereghetti et al. 2013). We used UVES and HST / GHRS spectra for the determina-tion of the stellar parameters of HD 49798. All stellar param-eters (see Table 2) were derived from UVES spectra except forabundances of Al, Fe, and Ni, for which we used HST / GHRS
Article number, page 3 of 11 & Aproofs: manuscript no. esosubwind
He I observedfit 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 4080 4085 4090 4095 4100 4105 4110 4115 4120 H δ observedfit 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 4320 4325 4330 4335 4340 4345 4350 4355 4360 H γ observedfit 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 4466 4468 4470 4472 4474 He I observedfit 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 4675 4680 4685 4690 4695 4700
He II observedfit 0.7 0.75 0.8 0.85 0.9 0.95 1 3955 3960 3965 3970 3975 3980 3985 H ε observedfit 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 4840 4845 4850 4855 4860 4865 4870 4875 4880 H β observedfit 0.75 0.8 0.85 0.9 0.95 1 1.05 4180 4185 4190 4195 4200 4205 4210 4215 4220 He II observedfit 0.9 0.95 1 1.05 4385 4386 4387 4388 4389 4390 4391
He I observedfit 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 4520 4525 4530 4535 4540 4545 4550 4555 4560
He II observedfit 0.8 0.85 0.9 0.95 1 3825 3830 3835 3840 3845 H η observedfit 0.7 0.75 0.8 0.85 0.9 0.95 1 3875 3880 3885 3890 3895 3900 3905 H ζ , He I observedfit 0.85 0.9 0.95 1 1.05 3910 3915 3920 3925 3930 He II observedfit 0.85 0.9 0.95 1 1.05 4710 4711 4712 4713 4714 4715
He I observedfit 0.9 0.95 1 1.05 4917 4918 4919 4920 4921 4922 4923 4924 4925
He I observedfit
Fig. 1.
Comparison of the best-fit synthetic spectra (red line) and UVES spectra (black line) of HD 49798 in the visual region. Here we plot thenormalised spectrum as a function of wavelength in Å. F λ [ − e r g s − Å − c m − ] λ [Å] Fe IV Fe IV Fe IV Fe IV S IV S IV, Fe IV observed spectrumfit 2.5 3 3.5 4 4.5 5 5.5 6 1650 1655 1660 1665 1670 1675 1680 1685 F λ [ − e r g s − Å − c m − ] λ [Å] Fe IV Fe IV, V Fe, Ni IV Fe IV Fe IV Fe IV observed spectrumfit
Fig. 2.
Comparison of the best-fit synthetic spectra (red line) and HST / GHRS spectra (black line) of HD 49798 in the UV region. spectra. The model atmosphere grid for the stellar parame-ter determination, T e ff ∈ [44 , ,
48] kK, log( g/ − ) ∈ [4 . , . , . , . ε He ∈ [0 . , . , . T e ff =
47 500 ± g/ − ) = . ± .
2, and ε He = . ± .
1. Af-ter the determination of the helium abundance and the values of T e ff and log g from this grid, we determined the abundances ofother elements using a model with fixed ε He , T e ff , and log g . Weiterated the process until convergence.We adopted a slightly lower value of projected rotational ve-locity than Kudritzki & Simon (1978) v sin i =
40 km s − thatprovides a better fit of metallic lines. Figures 1 and 2 comparethe observed UVES and HST / GHRS spectra with the best-fitsynthetic spectra. The strongest lines used for the abundance de-termination are summarised in Table 3. We have not listed the UV lines of Fe and Ni, which are too numerous. The derived at-mosphere parameters given in Table 2 agree with the results ofKudritzki & Simon (1978) within errors except the derived sur-face gravity, which is slightly higher. The nitrogen abundance israther uncertain, because di ff erent nitrogen lines give very dif-ferent abundances. The derived chemical composition deviatessignificantly from the solar composition (see Table 2). Whilecarbon and oxygen are depleted, the abundances of nitrogen,iron, and nickel are a factor of a few higher than the solar value(Asplund et al. 2009).The distance of HD 49798 was derived using GAIA DR2data (Gaia Collaboration et al. 2016, 2018). With V = . ± .
003 mag (Landolt & Uomoto 2007) this gives the absolutemagnitude M V = − . ± .
07 mag and with the bolomet-ric correction BC = . − .
80 log T e ff (Martins et al. 2005) Article number, page 4 of 11. Krtiˇcka et al.: Hot subdwarf wind models with accurate abundances: I. HD 49798 and BD + ◦
28 28.5 29 29.5 30 30.5 31 31.5 32 10 100 1000 10000 100000 l og ( L x / e r g s - ) L [ L ⊙ ] HD 49798BD+18˚ 2647O starsbinary detectedsingle detectedbinary upper limitsingle upper limit Fig. 3.
Relation between observed X-ray luminosity and the stellar lu-minosity for subdwarfs (adopted from Krtiˇcka et al. 2016). Blue sym-bols refer to individual subdwarfs: circles denote X-ray-detected sub-dwarfs, while triangles denote available upper X-ray detection limits,filled symbols denote subdwarfs in binaries, and empty symbols corre-spond to single objects. Overplotted is the extrapolation of the observedmean relation for O stars (Nazé 2009, solid red line). The shift of thestellar parameters with respect to previous determinations is denotedusing the black arrow. the estimated luminosity is L = ± L ⊙ (Martins et al.2005, Eq. (5)). From this latter value, we derive a stellar radiusof R = . R ⊙ ± . R ⊙ . With spectroscopic surface gravity,this gives the mass M = . ± . M ⊙ , which nicely agreeswith the mass of 1 . ± . M ⊙ derived from the orbital so-lution (Mereghetti et al. 2009). With i = ◦ and the radius, and v rot sin i from Table 2, we derive a rotational period of 1 . ± . × erg s − , Mereghetti et al.2013). Consequently, in this case the o ff set of the position ofthe star from the mean relationship was due to imprecise stellarparameters. We used our wind code to predict the structure of the stellar windof HD 49798. The subdwarf lies well above the wind boundaryin the T e ff versus log g diagram (see Fig. 4), and consequently thepredicted mass-loss rate is relatively large, 2 . × − M ⊙ yr − (see Table 2). Although iron and nickel are significantly over-abundant with respect to the ratio of abundances of these ele-ments relative to hydrogen, the predicted wind mass-loss rateis slightly lower than the value derived assuming solar chemi-cal composition, 2 . × − M ⊙ yr − . This is because (for solarchemical composition) the contribution of iron and nickel to the l og g [ c g s ] T eff [kK]Dorman et al. (1993)Hall et al. (2013)UV linesX-rays HD 49798BD+18˚ 2647 ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Fig. 4.
Position of studied stars in the T e ff versus log g diagram. Red re-gion denotes the parameter area with no predicted wind (Krtiˇcka et al.2016). Overplotted are the evolutionary tracks of Dorman et al. (1993),post-RGB tracks of Hall et al. (2013) and the positions of subdwarfswith known mass-loss rates derived from observed UV wind-line pro-files (blue circles) and subdwarfs with X-ray emission (black crosses).Adapted from Krtiˇcka et al. (2016). radiative force is surpassed by that of oxygen, which is depletedon the surface of HD 49798 by more than one order of mag-nitude with respect to the solar value. Moreover, the total massfraction of heavier elements is close to the solar value. Similarresults were derived for the influence of CNO cycle abundanceson mass-loss rate for O stars (Krtiˇcka & Kubát 2014).The derived mass-loss rate is in close agreement with thevalue 2 . × − M ⊙ yr − derived from the fitting formula forsubdwarfs (Krtiˇcka et al. 2016) assuming solar chemical com-position. The mass-loss rates derived using the formula for tentimes higher and ten times lower abundances of heavier elementsare 8 . × − M ⊙ yr − and 8 . × − M ⊙ yr − , respectively.The moderate di ff erence between these values and the predictedmass-loss rate further demonstrates that the mass-loss rate is notparticularly sensitive to abundances for HD 49798 parameters.The X-ray luminosity of HD 49798 outside eclipses stemsfrom the release of the gravitational potential energy duringwind accretion on the compact companion. Within the clas-sical Bondi-Hoyle-Lyttleton theory (Hoyle & Lyttleton 1941;Bondi & Hoyle 1944) the accretion luminosity is L X = η G M R X D v ˙ M , (1)where M X and R X are the mass and radius of the compact com-panion, D is binary separation, v is relative velocity, and η ise ffi ciency. If the wind velocity is much larger than the orbitalvelocity and is not a ff ected by X-ray ionisation (Krtiˇcka et al.2018; Sander et al. 2018), the wind terminal velocity can be in-serted instead of the relative velocity v = v ∞ . Using wind param-eters derived here (Table 2) in conjunction with M X = . M ⊙ and D = . R ⊙ (Mereghetti et al. 2009), with η = L X = . × erg s − for typical parameters of a white dwarfand L X = × erg s − for a neutron star. The observed X-ray luminosity, with the updated distance provided by GAIA, is ∼ erg s − (Mereghetti et al. 2016). Consequently, to explain Article number, page 5 of 11 & Aproofs: manuscript no. esosubwind C o un t s s - Fig. 5.
X-ray light curve of HD 49798 plotted during the eclipse. Thered line shows the simulated eclipse light curve predicted assuming de-rived wind and stellar parameters. For a comparison, we also plot thelight curve calculated assuming solar chemical composition (blue line). this luminosity in the case of a white dwarf, a decrease of thewind velocity due to X-ray ionisation is required. Instead, in thecase of a neutron star, the predicted luminosity is higher than theobserved one, requiring a low e ffi ciency. X-ray observations with the XMM-Newton satellite showed thatthe eclipse ingress and egress are not sharp, suggesting that theX-rays emitted by the compact object are gradually absorbed inthe wind of the sdO star. Using the wind model and surface com-position derived in this work, we computed the absorption coef-ficient at di ff erent X-ray energies χ ν ( r ) and derived the expectedprofile for the resulting light curve around the time of the eclipseas an integral F ( ϕ ) = F e − τ ( ϕ ) , τ ( ϕ ) = Z ∞ z c ( ϕ ) χ ν ( r ( z )) d z . (2)Here, F is the X-ray flux from the companion and the integral iscalculated numerically along the phase ϕ -dependent ray betweenthe companion (located at z = z c ) and observer. We assumed acircular orbit with an inclination of 85 ◦ that fits the length of theeclipse.The calculation is compared to the observations in Fig. 5.The data were obtained from nine XMM-Newton observationscovering the orbital phase of the eclipse (2008 May 10; 2011May 02; August 18, 20, 25; September 3, 8; 2013 November9; 2018 November 8). The figure shows the net light curve inthe 0.15-0.5 keV energy range as measured with the EPIC pn in-strument (the emission from HD 49798, as derived in the 4300 sof complete eclipse, has been subtracted). The red line showsthe expected profile of the eclipse as computed with the windabundances of HD 49798 derived in Sect. 5.2. For comparison,the blue line shows the profile that would be caused by a stel-lar wind with solar abundances. Although the statistical qualityof the current X-ray data does not allow us to directly estimatethe wind parameters, it is clear that the model derived with theproper abundances provides a good description of the X-ray data. Table 4.
Surface abundances of HD 49798 expressed relative to the totalnumber density of baryons.
HD 49798 Sunlog ˜ ε CNO − . ± . − . ε Mg − . ± . − . ε Al − . ± . − . ε Si − . ± . − . ε Fe − . ± . − . ε Ni − . ± . − . Bisscheroux et al. (1997) propose that the progenitor ofHD 49798 was a star with an initial mass of 4 − M ⊙ whichduring the asymptotic giant branch phase lost its envelope dueto the common envelope event. This would imply that the staris in the phase of shell-helium burning with a degenerate C-Ocore. However, stars with C-O core mass implied by this scenariowould instead ignite carbon (Siess 2007, 2010). Moreover, mas-sive post-AGB objects evolve on an extremely fast evolution-ary timescale of the order of years (Vassiliadis & Wood 1994;Miller Bertolami 2016) and are therefore unlikely to be spottedin this stage. Alternatively, massive subdwarfs could be formedby the merger of white dwarfs, but this would likely lead to hy-drogen deficient objects (Saio & Je ff ery 2002).Popov et al. (2018) suggested that the subdwarf originatesfrom an object with a helium-burning core. The compan-ion could be either a white dwarf or a neutron star, butthe white dwarf is preferred on the basis of known proper-ties of X-rays and on evolutionary grounds (Bisscheroux et al.1997). Moreover, the detected spin-up of the compact com-panion (Mereghetti et al. 2016) could be naturally explained asthe consequence of cooling and contraction of a white dwarf(Popov et al. 2018).HD 49798 shows very unusual chemical composition (seeTable 2). Chemical peculiarities in blue horizontal branch starsare typically attributed to radiative di ff usion (Hui-Bon-Hoa et al.2000; Michaud et al. 2008; LeBlanc et al. 2009). A mass-lossrate of the order of 10 − M ⊙ yr − is required to explain theobserved abundance anomalies in sdB stars (Unglaub & Bues2001). Higher mass-loss rates would not allow for the abun-dance separation in the atmosphere, while weaker wind wouldlead to a complete absence of helium (Unglaub & Bues 2001;Michaud et al. 2015). Given the relatively high mass-loss ratefound in HD 49798, the detected abundance anomalies are likelyof evolutionary origin.The high abundance of helium likely results from the strip-ping of the stellar envelope which led to the exposition of thestellar core, whose chemical composition was a ff ected by hy-drogen burning. A typical abundance ratio resulting from hy-drogen burning by CNO cycles is log( ε O /ε N ) ≈ − ε O /ε N ) = − . ± .
3. TheCNO equilibrium carbon-to-nitrogen ratio is log( ε C /ε N ) ≈ − . ε C /ε N ) < − .
1. To ac-count for the enhanced abundance of helium, we scaled the de-rived elemental abundances relative to the baryonic number den-sity ˜ ε el = ε el / ( ε H + ε He ). From Table 4 it follows that the scaledabundances of most elements are consistent with solar chemicalcomposition.According to the evolutionary models, the helium-shell-burning subdwarf will fill its Roche lobe in approximately40 000 – 65 000 yr (Brooks et al. 2017; Wang et al. 2017). Onthis evolutionary time-scale, the current mass loss as predicted Article number, page 6 of 11. Krtiˇcka et al.: Hot subdwarf wind models with accurate abundances: I. HD 49798 and BD + ◦ Table 5.
Wavelengths of the strongest lines (in Å) used for abundancedetermination in BD + ◦ C iii iv iv (923), (924), (955), 1719N v iv iv v iv v vi v vi v vi Notes.
Lines of N iv given in parentheses, which point to a higher ni-trogen abundance than given in Table 2, were heavily contaminated byinterstellar lines and were not used to determine abundances. here will not significantly contribute to mass transfer. The sub-dwarf lifetime is of the order of 1 Myr if the subdwarf is in-deed burning its core helium (Paczy´nski 1971), implying a largercontribution of the wind to the mass transfer. Mereghetti et al.(2009) showed that the further evolution of the system could leadto a second phase of mass transfer, which could ignite a SN Iaexplosion. An alternative outcome of the evolution could be adouble degenerate binary consisting of a neutron star (originat-ing from the collapse of the compact companion) and a whitedwarf (Brooks et al. 2017; Wang et al. 2017).
6. BD+18 ◦ Subdwarf BD + ◦ + α =
12 h 41 m 51 .
79 s , δ = + ◦ ′ . ′′ , J2000) is a helium-poorstar, which does not show any signs of a secondary compan-ion (Latour et al. 2018). The subdwarf does not show any de-tectable X-ray emission with the upper limit of X-ray luminosity3 . × erg s − (La Palombara et al. 2014). We used UVES, IUE, and FUSE spectra for the determina-tion of the stellar parameters of BD + ◦ T e ff , log g ,and helium abundance were determined from the fit of op-tical and Lyman lines. The cores of predicted optical linesshow emission and the cores of Lyman lines are a ff ectedby interstellar absorption. Therefore we fitted only the wingsin the case of hydrogen Lyman lines and Balmer lines withcentral emission. The wings originate in the lower parts ofthe photosphere and are not severely a ff ected by NLTE ef-fects. For the determination of BD + ◦ T e ff ∈ [55 , , , , , , ,
90] kK, log( g/ − ) ∈ [4 . , . , . , . ε He ∈ [0 . , . , . T e ff ∈ [65 , ,
75] kK, log( g/ − ) ∈ [5 . , . , . ε He ∈ [0 . , . , . T e ff , log g , and ε He listed in Table 2. The abundancesof heavy elements were determined from the fit of UV spectra with a model calculated for derived values of stellar parameters.These steps were repeated until convergence was achieved.The strongest lines used for abundance determination aregiven in Table 5. The comparison of the observed UVES andFUSE spectra and the best-fit synthetic spectra is given in Figs. 6and 7. The derived atmosphere parameters and abundances givenin Table 2 agree with the results of Latour et al. (2018) within er-rors, except for the derived e ff ective temperature which is higherby about 12 kK. Latour et al. (2018) used optical spectra withlower resolution, consequently the problems with line centreemission could be one of the reasons for the di ff erence in the de-rived temperatures. We were able to obtain a reasonable fit of hy-drogen lines for lower T e ff , but this led to overly strong He i lines.Our derived e ff ective temperature is lower than T e ff =
75 000 Kderived by Bauer & Husfeld (1995).To test the origin of the di ff erence between the e ff ectivetemperature derived by Latour et al. (2018) and our results, wesmoothed the observed spectra by a Gaussian filter with 1 . ff ective tem-perature was lower by about 6 kK. This shows that the adoptedspectral resolution in combination with a di ff erent way of fittingcould be one of the causes of the di ff erence between the results.A higher abundance of iron, as derived by Latour et al. (2018),could be another reason for the di ff erence. For some stars, theuse of UV and optical observations may lead to discrepant re-sults (Dixon et al. 2017), however in our case the UV spectrahelped us mainly to constrain the grid of possible stellar param-eters.Because the derived e ff ective temperature is higher than thatderived by Latour et al. (2018), we further compared the pre-dicted flux distribution with that derived using the VOSA tool(Bayo et al. 2008). The observed flux distribution in Fig. 8 is inclose agreement with predictions with E ( B − V ) = . ± .
02 andassuming the Fitzpatrick & Massa (2007) extinction law. The de-rived reddening agrees with E ( B − V ) = . ± .
02 (Green et al.2018), which corresponds to BD + ◦ V = . ± .
12 mag (Høg et al. 2000) this gives the absolutemagnitude M V = . ± .
15 mag (with E ( B − V ) = . ± . = . − .
80 log T e ff (Martins et al. 2005) the estimated luminosity is L = ± L ⊙ (Martins et al. 2005, Eq. (5)). From this, the stellar radius is R = . ± . R ⊙ . With spectroscopic surface gravity thisgives a mass of M = . ± . M ⊙ .The adopted bolometric correction fit (Martins et al. 2005)was derived for O stars with significantly lower e ff ective tem-perature ( T e ff <
45 kK) than derived here. To estimate theerror connected with extrapolation of the bolometric correc-tion, we calculated bolometric correction from our models us-ing Eq. (1) of Lanz & Hubeny (2003) and the V filter responsecurve from Mikulášek (private communication). The derived BC = − . ± .
08 mag is only slightly lower than estimatedfrom the fit of Martins et al. (2005), and therefore the resultingstellar parameters ( L = ± L ⊙ , R = . ± . R ⊙ ,and M = . ± . M ⊙ ) only di ff er within the derived uncer-tainties. We also note that the application of the frequently usedbolometric corrections of Flower (1996, see also Torres 2010,)to BD + ◦ T e ff <
53 kK. Further-more, Flower (1996) used high-order polynomial approxima-tion, which may give erroneous results during extrapolation. Inour case, the formula predicts bolometric correction which is
Article number, page 7 of 11 & Aproofs: manuscript no. esosubwind H ελ [Å] observedfit 0.970.980.991.001.01 4180 4185 4190 4195 4200 4205 4210 4215 4220 He II λ [Å] observedfit 0.950.960.970.980.991.00 4520 4525 4530 4535 4540 4545 4550 4555 4560 He II λ [Å] observedfit0.700.750.800.850.900.951.00 4320 4325 4330 4335 4340 4345 4350 4355 4360 H γ observedfit 0.650.700.750.800.850.900.951.001.05 4675 4680 4685 4690 4695 4700 He II observedfit0.650.700.750.800.850.900.951.00 4840 4845 4850 4855 4860 4865 4870 4875 4880 H βλ [Å] observedfit0.860.880.900.920.940.960.981.00 3870 3875 3880 3885 3890 3895 3900 3905 H ζ r e l a t i v e f l u x observedfit 0.750.800.850.900.951.00 4080 4085 4090 4095 4100 4105 4110 4115 4120 H δ observedfit0.980.991.001.01 4015 4020 4025 4030 4035 4040 He I, II observedfit
Fig. 6.
Comparison of synthetic spectra calculated for the derived parameters and UVES spectra of BD + ◦ F λ [ − e r g c m − s − Å − ] L γ L δ L ε L L Fe V,VI S VI S VI Fe V,VI Ni V,VI Fe V,VI Fe V,VI Fe V He II He II He II observedfit0.00.51.01.52.02.5 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 F λ [ − e r g c m − s − Å − ] L β Ni VI Fe V,VI Ni V,VI Fe V,VI Ni V,VI Fe V,VI Ni V,VI Fe VI,VII He II observedfit0.00.51.01.52.0 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 F λ [ − e r g c m − s − Å − ] Ni V,VI Fe V,VI Ni V,VI Fe V,VI Ni V,VI Fe V,VI Ni V,VI Fe VI λ [Å] observedfit Fig. 7.
Comparison of synthetic spectra calculated for the derived parameters and FUSE spectra of BD + ◦ Article number, page 8 of 11. Krtiˇcka et al.: Hot subdwarf wind models with accurate abundances: I. HD 49798 and BD + ◦ −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 F λ [ e r g s − Å − c m − ] λ [Å]FUSE, IUEmodelVOSA Fig. 8.
Comparison of predicted (red line) and observed flux distribu-tion. The predicted flux was taken from the best-fit model and smoothedusing a Gaussian filter. The observed flux distribution was taken fromFUSE and IUE observations (grey lines) and from the optical and in-ferred photometry available in the VOSA database (squares with errorbars).
On the other hand, the structure of model atmosphere couldbe influenced by elements not included in our analysis. Thiscould be connected with the possible appearance of weak linesin the optical spectrum which is not explained by the predictedspectrum. To test this, we calculated additional model atmo-spheres with ten times higher abundance of selected elementswhose abundances were not determined from spectroscopy (Mg,Al, P, and Cr). However, we did not find any significant influenceof these elements on hydrogen line profiles. Moreover, classi-cal chemically peculiar stars show vertical abundance stratifica-tion (Stift & Alecian 2012; Nesvacil et al. 2013), which may bepresent also in subdwarf atmospheres and a ff ect the observedspectra (as suggested, e.g. by Geier 2013). Also, BD + ◦ T e ff ver-sus log g diagram (Fig. 4, see also Krtiˇcka et al. 2016), howeverthe mass-loss rate 7 . × − M ⊙ yr − predicted using Eq. (1) ofKrtiˇcka et al. (2016) for BD + ◦ . × − M ⊙ yr − derived from globalmodels and solar chemical composition.Due to its low mass-loss rate, the solar abundance windof BD + ◦ + ◦ + ◦ + ◦ g rad with the mag-nitude of the gravitational acceleration g . The winds are only possible if g rad > g. (3)The wind condition of Eq. (3) was tested using artificial windmodels with fixed density and velocity structure and with mass-loss rate as a parameter. We assumed a linear velocity profileand the density profile was derived from the assumed mass-lossrate using the continuity equation. The application of Eq. (3) tothese artificial models led to an upper limit of the mass-loss rateof BD + ◦ − M ⊙ yr − , while the wind condition isfulfilled for a mass-loss rate of 10 − M ⊙ yr − .Nevertheless, Eq. (3) gives a simply necessary but not suf-ficient condition for the presence of wind, because it does notcompare the radiative and gravitational acceleration for a consis-tent wind solution. This likely explains why our global modelsfailed to provide consistent wind models, although Eq. (3) wouldallow for a wind, albeit with a low mass-loss rate. To better un-derstand this issue, we calculated additional simplified (but con-sistent) wind models that use the model atmosphere flux as an in-put for the calculation of the radiative force. Our tests with thesesimplified models showed that they are unable to pass throughthe sonic point with consistently calculated radiative force. Closeinspection of the results revealed that the models are able to pro-vide a converged solution with a first estimate of the radiativeforce, but further iterations failed. This corresponds to the factthat the models fulfilled the necessary condition for the presenceof a wind Eq. (3) (which uses just one calculation of the radiativeforce), but failed to provide a consistent model.Therefore, it is likely that BD + ◦ + ◦ + ◦ L X < . × erg s − , La Palombara et al.2014). Hot subdwarfs are typically expected to be the products of bi-nary evolution (Han et al. 2002). However, understanding theevolutionary state of BD + ◦ + ◦ Article number, page 9 of 11 & Aproofs: manuscript no. esosubwind binaries with low-mass subdwarfs (Podsiadlowski et al. 2008;Vos et al. 2019). Alternatively, BD + ◦ + ◦ ff usion and gravitational settling in the atmo-sphere of the star (Latour et al. 2018). The upper limit of themass-loss rate for BD + ◦ ff usion mod-els, low abundance of helium is a result of gravitational settling.Chayer et al. (1995) provided equilibrium abundances of whitedwarfs accounting for radiatively supported di ff usion and, inagreement with our results, found enhanced surface abundanceof iron, while carbon, nitrogen, neon, silicon, and sulphur weredepleted at T e ff =
70 kK.It is not clear how is it possible that the star acquired abun-dance anomalies that would not likely develop if the star ap-peared at its current position on the HR diagram with solar abun-dances. Likely, the star initially had solar chemical composi-tion, was located below the wind limit at some previous stageof its evolution, and developed abundance anomalies by di ff u-sion. The abundance anomalies then persisted until the star at-tained the current parameters, although the wind predicted as-suming a solar composition would have wiped out any peculiar-ities (Unglaub & Bues 2001). It is also not clear why heliumis still present in the atmosphere, because with absence of awind, helium should be missing (Unglaub & Bues 2001). Per-haps, some other process (e.g. turbulence, Michaud et al. 2011b)is responsible for this.Despite similar abundance anomalies, in contrast to clas-sical chemically peculiar stars, the subdwarfs and horizontalbranch stars do not show rotationally modulated light variability(Pancino et al. 2012; Marinoni et al. 2016; Paunzen et al. 2019).Light variability in classical chemically peculiar stars typicallyoriginates due to flux redistribution in surface abundance spots(e.g. Prvák et al. 2015), which are supposed to be connected withstrong surface magnetic field. Hot subdwarfs likely do not pos-sess any strong global magnetic fields (Landstreet et al. 2012),which might explain the lack of rotationally modulated lightvariability.
7. Conclusions
We studied the implications of realistic surface abundances forthe hot subdwarf wind mass-loss rates. We determined stellarparameters for two selected hydrogen-rich, hot subdwarfs fromour own optical spectroscopy and from UV spectroscopy us-ing TLUSTY NLTE atmosphere models. We predicted the windmass-loss rates with our global wind model and compared thederived results with those predicted assuming solar chemicalcomposition. For HD 49798, we find an e ff ective temperature in agreementwith previous determinations and a mass that agrees with a bi-nary solution. The chemical composition, with enhanced abun-dances of helium and nitrogen, appears to be a result of a previ-ous process of hydrogen burning. The mass-loss rate predictedusing realistic surface abundances does not significantly di ff erfrom that derived using solar abundances, because the mass frac-tion of heavier elements roughly corresponds to the solar chem-ical composition. The X-ray eclipse light curve can be nicelyreproduced by absorption in the wind with the derived mass-lossrate and abundances, but not by a wind with solar abundances.In the case of BD + ◦ ff ective temperature, which is about 12 kK higherthan the recent determination, but is still in the range of valuesavailable in the literature. The discrepant temperature is prob-ably due to an overly weak dependence of line profiles on thestellar parameters and the appearance of emission in the coresof predicted absorption lines. The subsolar abundance of lightelements and the overabundance of iron can be interpreted as aresult of radiative di ff usion and gravitational settling. As a resultof this, the homogeneous wind is missing for determined abun-dances, while the wind would exist at solar metallicity. On theother hand, a stronger wind would likely have e ff aced all pecu-liarities.Although we used UV and optical spectra to determine theabundances, the lines of some elements that are important fordriving wind are inaccessible in the available spectral regions.From our models it follows that about one-third of the line driv-ing still comes from such elements. This contributes to the un-certainty related to mass-loss rate predictions.We conclude that while the precise abundances are not veryimportant for the strength of the wind in cases where the sur-face abundances are a ff ected by hydrogen burning, abundanceshave a significant e ff ect when di ff usion processes come into play.Therefore, abundance variations and imprecise stellar parame-ters may be one of the reasons for the large scatter of hot subd-warf X-ray luminosity when plotted as a function of bolometricluminosity. Acknowledgements.
This research was supported by grant GA ˇCR 18-05665S.SM acknowledges financial contribution from the agreement ASI-INAF n.2017-14-H.0. This project has received funding from the European Union’s Frame-work Programme for Research and Innovation Horizon 2020 (2014-2020) un-der the Marie Skłodowska-Curie grant Agreement No. 823734. Computationalresources were provided by the CESNET LM2015042 and the CERIT Scien-tific Cloud LM2015085, provided under the programme "Projects of Large Re-search, Development, and Innovations Infrastructures". The Astronomical In-stitute Ondˇrejov is supported by the project RVO:67985815. This publicationmakes use of VOSA, developed under the Spanish Virtual Observatory projectsupported from the Spanish MINECO through grant AyA2017-84089.
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