Hubble Space Telescope spectroscopy of hot helium rich white dwarfs: metal abundances along the cooling sequence

Astron. Astrophys. 5, 6 644 (999) Hubble Space Telescope spectroscopy of hot helium rich white dwarfs: metal abundances along the cooling sequence S. Dreizler Institut für Astronomie und Astrophysik, Universität Tübingen, Waldhäuser Strasse 64, 776 Tübingen, Germany (dreizler@astro.uni-tuebingen.de) Received 9 July 999 / Accepted October 999 ASTRONOMY AND ASTROPHYSICS Abstract. Metal abundances are the indicators of the chemical evolution in white dwarfs, which is dominated by the element separation due to the strong gravitational field. A reliable analysis and interpretation requires high resolution and high signalto-noise UV spectroscopy. For hot helium rich DO white dwarfs this is currently only feasible with the Hubble Space Telescope. In this paper I report on our HST spectroscopy of DO white dwarfs and describe our model atmospheres employed for the analysis. This includes an introduction to our new selfconsistent, chemically stratified non-lte model atmospheres, which take into account gravitational sedimentation and radiative levitation. The results of the analysis shows that DO white dwarfs can best be fitted with chemically homogeneous models, whereas stratified models show significant deviations. Several possible reasons for this unexpected result are discussed. At the current stage, weak mass loss is the most plausible explanation. Key words: stars: abundances stars: atmospheres stars: evolution stars: AGB and post-agb stars: white dwarfs ultraviolet: stars. Introduction DO white dwarfs are hot helium rich white dwarfs which populate the white dwarf cooling sequence from the hot beginning (T eff = K) down to 45 K. At this temperature the helium rich cooling sequence is interrupted by the DB gap (Liebert et al. 986) where no helium rich white dwarfs are found down to K. Recently, Dreizler & Werner (996 [DW], 997) determined effective temperatures and surface gravities of all 8 known DO white dwarfs. Since they summarized the cur- Based on observations obtained with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-6555 Only those DO white dwarfs are counted here that do not show the phenomenon of an extremely hot and fast wind (Werner et al. 995b, Dreizler et al. 995). Up to now, no suitable model atmospheres exist for these stars. Recently, we also identified KUV -8 as member of this group. rent stage of our knowledge about these stars in detail I will concentrate on the points important for this work. DO white dwarfs have a nearly pure helium atmosphere, with only a few hot DOs showing weak metal lines. Their chemical composition is in general interpreted as the product of the interaction of gravitational settling and radiative levitation. The basic mechanism responsible for this nearly monoelemental composition of white dwarf atmospheres was identified by Schatzman (949, 958). As described below, the time scales for the diffusion processes are much shorter than the evolutionary time scales of white dwarfs so that models for the outer layers can be calculated time independently. First results for white dwarfs were obtained by Fontaine & Michaud (979) and Vauclair et al. (979) taking into account radiative levitation. These processes are also invoked to explain the transition from the possible progenitors, the hydrogen deficient, C and O rich PG 59 stars (see Dreizler & Heber 998 for an introduction to these objects) during which heavier elements in the atmosphere are depleted and only traces of metals can be kept in the helium rich atmosphere as long as the radiative levitation is sufficiently strong due to high effective temperatures. Finally, at the hot end of the DB gap, enough of the remaining traces of hydrogen floats up to cover the helium rich envelope with a thin hydrogen rich layer. Even though this scenario is able to explain the evolution of hot helium rich white dwarfs qualitatively, these processes are far from being understood quantitatively. Observed metal abundances do not fit theoretical predictions (Chayer et al. 995; DW, Dreizler & Werner 997, Dreizler et al. 997). Whether this is due to the rather poor observational data, due to a lack of adequate models, or a problem of the comparison itself could not be decided at that stage. In the recent years we therefore investigated the problem in all these directions. In the following I will describe our observations (Sect. ). These observations are analyzed with chemically homogeneous and, for the first time, with self-consistent stratified non LTE model atmospheres which are introduced in Sect.. Finally, I present and discuss the results in Sect. 4.. Observations Metal abundances in white dwarfs are difficult to derive because the heavier elements are in most cases reduced due to gravita-

S. Dreizler: HST spectroscopy of DO white dwarfs 6 Table. Log of HST GHRS observations. All stars were observed with the G6M grating. Parameters are those determined by DW and WDW. The flux at λ cent is given in erg/(cm s Å ). star T eff [kk] log g t exp [s] flux λ cent [Å] PG 4+ 7.5 88. 55.7.6 576. 47. 7.9 88. 8. 87.6 88.. 549.7 88. 5.9 64. PG 8+ 95 7.5 5.4.5 45.8 849.6.7 56.7 RE 5-89 7 7.5 76.6. 45.8 76.6 7.6 56.7 HS + 65 7.8 4569.6 4.9 45.8 HZ 5 7.8 5.4 8.7 45.8 958.4 6.8 56.7 HD 49499 B 5 8. 45. 4. 45.8 45.. 56.7 544. 46.8 76.9 tional sedimentation. As a result, the optical spectra of DO white dwarfs are nearly pure helium spectra. Only a few show weak C iv lines, which have been analysed by DW. UV spectra are much better suited for this purpose since several lines of C, N, O, Fe, and Ni can be detected there. However, high resolution and high signal-to-noise are required. For most DO white dwarfs these requirements could not be met by the IUE satellite. Existing determinations of metal abundances, summarized by DW, are therefore not sufficient to provide reliable constraints for the understanding of the settling process. To improve the situation we selected five DOs for HST observations (Cycle 6, P.I. Werner PEP ID 6455), which together with two DOs with existing HST spectra, represent the whole cooling sequence from the hot end down to the DB gap. These spectra serve as the observational basis for our analysis. The observations are summarized in Table. All spectra were obtained with the G6M grating of the GHRS spectrograph resulting in a spectral resolution of or. Å/pixel covering 5 Å each. We used the pipeline extraction and co-added each four spectra obtained in fp-split mode. Finally, we normalized the spectra since the pipeline flux calibration leaves bumps in the continuum. The analysis of the bright DO RE 5-89 was separated from this work. The spectrum of this star is covered over a broad wavelength range with EUVE, several high resolution IUE spectra, additional HST GHRS spectra and high resolution optical spectra. It has been therefore treated in a detailed multi-frequency analysis by Barstow et al. (999). The results from this analysis are adopted here. We also employ the results for PG 4+ (Werner et al. 995a, [WDW]) which was observed earlier (P.I. Shipman PEP ID 59). In Table the main stellar and interstellar lines visible in the spectra are identified. In the following figures, these lines are indicated at the top (interstellar) and at the bottom (stellar). While the low ionization stages can be identified as interstellar lines, this is not immediately clear for the N v resonance doublet, which can be either stellar or interstellar. Comparing the radial velocities of other stellar and interstellar lines reveals that, except for PG 8+, N v is undoubtedly of stellar origin. All stellar lines in HZ and HD 49499 B as well as Fe and Ni lines in HS + are so weak that the identification is very uncertain. In all these cases I will only determine upper limits. There are more numerous Fe v and Ni v lines in this spectral range which are, however, near or below the detection limit. Therefore only the strongest lines of Fe and Ni are listed in Table.. Model atmospheres For spectral analysis we applied plane-parallel model atmospheres in radiative and hydrostatic equilibrium. Despite of high gravity, the ionization and excitation of the plasma is dominated by the intense radiation field making non-lte calculations necessary as demonstrated by DW. Since the modeling technique (Dreizler & Werner 99; Werner & Dreizler 999) as well as the model atoms are identical to those employed by Dreizler & Heber (998) we again emphasize only the points relevant for this work. In addition to H, He, C, N, and O we included Fe and Ni in the same way as treated e.g. by WDW. In the first set of models we assumed chemically homogeneous atmospheres. In the case of white dwarfs this may be too coarse an approximation since the diffusion process tends to produce steep abundance gradients. Fitting chemically homogeneous model atmospheres to stratified stars can therefore lead to large systematic errors which might be responsible for the poor agreement (DW) between previous metal abundance determinations in DOs and predictions from diffusion calculations (Chayer et al. 995). Another reason for this discrepancy might be the fact that Chayer et al. determine the equilibrium abundances between gravitational settling and radiative levitation without treating the reaction on the atmospheric structure and the radiation field. Both potentially severe handicaps have been overcome with our new set of model atmospheres which for the first time solve the equilibrium abundances self-consistently together with the model atmosphere structure in full non-lte. These models shall be described in the following in more detail. Our approach is very similar to that of Chayer et al. (995) and earlier work of this group, however, we perform these calculations for the first time under non-lte conditions. Assuming the absence of concurring processes like convection and mass loss the short diffusion time scale justifies to determine the abundances at each depth point from the balance of gravitational, radiative and electrical forces. For a trace element (i) in a plasma mainly composed of element () this can be written as: m F m i F i =(A i A )m p g (Z i Z )ee A i m p g rad,i =. A i are the atomic weights, Z i the mean electrical charges, m p is the proton mass, and g rad,i is the radiative acceleration acting on element (i). Neglecting the radiative forces on element () assumes that the main constituent of the plasma is homogeneously ()

64 S. Dreizler: HST spectroscopy of DO white dwarfs Table. Line identifications of the ID 6455 run. Wavelengths are given in Å, radial velocities in km s. The typical errors is 5 km s. A : denotes uncertain measurement either due to broad lines of C iv or line strengths near the detection limit. Line identifications of PG 4+ are given by WDW. PG 8+ RE 5-89 HS + HZ HD 49499 B λ lab Ion λ obs v rad λ obs v rad λ obs v rad λ obs v rad λ obs v rad Interstellar lines 8.8 N v 8.8 -.4 8.94 9. 8.9: 6.6 4.8 N v 4.8. 4.9. 4.9: 6.5 5.58 S ii 5.57 -.4 5.49 -.6 5.56-4.8 5.56-4.8 5.8 S ii 5.79-4.8 5.79-4.8 5.79-4.8 5.74-6.8 59.5 S ii 59.5.4 59.5-4.8 59.49-7. 59.44-9. 6.4 Si ii 6.4.4 6.49 6.6 6.4. 6.9-7. 6.7 -.9 Stellar lines.4 C iv.: -.4.9:..: 9..49 C iv.5: 4.9.66: 4.4.69: 48.7.477 Fe vi.5:.4 8.8 N v 8.8-4.8 8.94 9. 8.9: 6.6 4.8 N v 4.8. 4.9 8.9 4.9: 4. 44.74 Ni v 44.9.9 44. 7.6 44. 7.6 45.74 Ni v 45.:.8 47.8 C iii 47.9.4 47.5. 47.54 8.5 49.5 Ni v 49.5 -.9 49.65.7 5.8 Ni v 5.97 7.8 5.8 Ni v 5.8. 5.4 7.6 5.789 Fe vi 5.9.4 56.55 C iii 56.5-4.8 56.64.5 56.68. 57.66 Ni v 57.66 8. 57.77 4. 57.7: -.4 8.6 O iv 8.66 4.5 8.75 9. 4.99 O iv 4. 4.5 4.5 5.7 4.5 O iv 4.55 6.7 4.65. 5.5 C iv 5.:. 5.4:. 5.98 C iv 5.97:.4 5.: 6.6 6.86 Fe v 6.84. 6.864 Fe v 6.89 5.7 7.9 O v 7. 6.5 7.46 5. 7.589 Fe v 7.65:. possible blend with stellar N v possible blend with interstellar N v possible blend with Fe vi distributed over the atmosphere (however, still hydrostatically stratified). The radiative acceleration is given by g rad,i = 4π κ ν,i H ν dν () ρ i c where ρ i is the mass fraction of the element (i), κ ν,i is the frequency dependent mass absorption coefficient which includes all contributions of this element at the frequency ν, and H ν is the Eddington flux. The electric field E can be obtained from charge conservation: Pj Z j = P e () where P j and P e denote the partial pressures of the elements (j) and of the electrons, respectively. Differentiating Eq. () with respect to r and inserting the partial pressures P i as given by: dp i P i dr = A im p g + Z iee kt kt results after some simplifications in ee = A m p g Z +. With this expression Eq. () reads ( ) m F m i F i = m p g A i A ZiA Z + ZA + Z + A i m(( p g rad ) ) = A i m p A(Zi+) A i(z +) g g rad,i =. With g eff,i := ( A ) (Z i +) g A i (Z +) (4)

Eq. (4) yields: g rad,i = g eff,i (5) which is exactly what Chayer et al. (995) derived. Eq. (5) defines the mass fraction of element (i) at each depth point through the dependence of the radiative acceleration on ρ i (Eq. ). In contrast to homogeneous model atmospheres, the opacity in the stratified models has to be determined accounting for Stark broadening of every line. Additionally, the model atoms have to be very detailed in order to provide a realistic amount of radiative acceleration. At the current stage, we ignore possible effects from redistribution of the transferred momentum over the ionization stages. We also assume that a bound-free transition transfers the momentum completely to the ion ignoring a momentum transfer to the electron. Since the equilibrium condition (5) is coupled to the structure of the model atmosphere via the opacity and the Eddington flux, it must be solved self-consistently with our usual set of equations necessary for the construction of non LTE model atmospheres. We perform this in the most simple way by an iterative scheme. Starting with a homogeneous atmosphere we use its radiation field, density and temperature stratification as well as the occupation numbers of all atomic energy levels to calculate the radiative acceleration of all elements at all depth points. Solving Eq. (5) yields a chemical stratification for all trace elements. Keeping this fixed, we re-determine the structure and the radiation field for the next iteration step. Alternatively the equilibrium condition could be included as an additional constraint equation in the construction of the model atmosphere which in principle would result in a faster convergence. Then, however, starting from the chemically homogeneous models would be nearly impossible, due to large initial changes in the abundances and therefore in the atmospheric structure. The emergent spectrum of such a chemically stratified atmosphere only depends on the effective temperature and the surface gravity, which define the structure and the radiation field of the atmosphere and therefore self-consistently also the chemical composition in all depths through the equilibrium condition (5). As demonstrated in Fig. the general trend is a reduced equilibrium abundance with decreasing effective temperatures due to a less efficient radiative levitation. In some depths this trend can be modified by the fact that the radiative forces are also dependent on the degree of ionization since lower ionization stages have more line transitions. Compared to chemically homogeneous atmospheres, the composition is no longer a free parameter. In principle, knowledge of T eff and log g is sufficient to reproduce an observed spectrum of a white dwarf. 4. Results and discussion Previous analyses by DW, based on the He line profiles, provide reliable effective temperatures and surface gravities. This is also true if the atmospheres of the stars are chemically stratified. Since helium is the dominating element the stratification of the trace elements does not influence the chemical abundance of helium. In the following, I will therefore use the previously S. Dreizler: HST spectroscopy of DO white dwarfs 65 log C log O log Fe -5 - -5 - -5 - -4 - -4 - -4 - log τ ross log N log Si log Ni -5 - -5 - -5 - -4 - -4 - -4 - log τ ross Fig.. Equilibrium abundances within stratified model atmospheres for DO white dwarfs given in logarithmic number ratios. Solid line: T eff = 95 K, log g = 7.5; long dashed line: T eff = 7 K, log g = 7.5; short dashed line: T eff = 65 K, log g = 7.8; dash-dotted line: T eff = 5 K, log g = 7.8. Si, Fe, and Ni are not included in the coolest model. determined effective temperatures and surface gravities and concentrate on the abundance determinations. 4.. Analysis with homogeneous model atmospheres In the first step I applied our usual procedure, namely fitting the spectra with chemically homogeneous model atmospheres by varying the C, N, O, Fe, and Ni abundances. Since C and O are detected in two ionization stages (C iii/iv; O iv/v) we can check these parameters through a comparison of the line strength in both ionization stages. As obvious from the final fits (Fig. ) the previously determined parameters T eff and log g provide consistent fits confirming our previous parameters. The metal lines in the three hotter DOs can be excellently fitted with our theoretical spectra. As demonstrated in Fig., the typical error is a factor of two. In the case of HS + we did not observe the 5 Å range which prevents the determination of the O abundance. In two cooler objects no stellar lines apart from the N v doublet in HZ can be identified. In these cases only upper limits for C, N (for HD 49499 B), and O are determined. Upper limits for Fe and Ni are not meaningful in these cases since no

66 S. Dreizler: HST spectroscopy of DO white dwarfs PG 8+ HS + HZ HD 49499B 4 5 6 PG 8+ HZ HD 49499B 4 5 6 7 wavelength / A o Fig.. HST GHRS spectra (thick line) of our program stars (smoothed by. Å) compared with theoretical spectra (thin line) from homogeneous model atmospheres. The parameters for the models are summarized in Table. Interstellar lines are marked at the top, stellar lines (long C, N, or O lines; medium Fe vi, short lines Ni v; very short lines Fe v) at the bottom. See also Table.

S. Dreizler: HST spectroscopy of DO white dwarfs 67 factor. factor. factor.5 4 5 6 factor. factor. factor.5 4 5 6 7 wavelength / A o Fig.. Change of theoretical spectra (thin line) by the variation of the abundances by a factor two up and down compared to PG 8+ (thick line). Interstellar lines are marked at the top, stellar lines (long C, N, or O lines; medium Fe vi, short lines Ni v; very short lines Fe v)at the bottom. See also Table. lines from populated ionization stages are within this spectral range. The resulting abundances are summarized in Table and illustrated in Fig. 4. In general, the abundances decrease with the effective temperature as expected from the scenario of equilibrium between gravitational settling and radiative levitation. We therefore also list the equilibrium abundances as determined by Chayer et al. (995, priv. comm.). From this comparison it is obvious that our spectroscopically derived abundances can not be reproduced by these equilibrium models as already noted previously by DW. The only agreement is the general trend towards lower abundances with decreasing effective temperature. However, this result is now based on high quality spectra covering DO white dwarfs over the whole parameter range. The problem therefore needs further investigation since it directly affects our understanding of the evolution of hydrogen deficient post AGB stars. There are several possible reasons for this large discrepancy: The abundances are derived with homogeneous model atmospheres. As demonstrated in Fig., atmospheres of these stars are non homogeneous if an equilibrium between gravitational settling and radiative levitation is achieved. Our homogeneous models might therefore be severely affected by systematic errors. Second, the equilibrium abundances of Chayer et al. (995, priv. comm.) are representative abundances obtained at τ ross =/. In highly stratified atmospheres such representative abundances can also be very misleading. Additionally, these equilibrium abundances are determined with radiation fields from homogeneous LTE model atmospheres, and the feedback of the stratification on the atmospheric structure is not taken into account. 4.. Analysis with stratified model atmospheres All these drawbacks can be overcome with our new selfconsistent, chemically stratified non-lte model atmospheres (Sect. ). In a second step, I therefore calculated a grid of such models where the emergent spectra are uniquely determined by T eff and log g alone. As can be seen from Fig. 5, the fit is much less convincing than in the case of homogeneous models. While N and Ni are predicted too strong, C is too weak, though Fe and O are reproduced reasonably. We are therefore still far from understanding the abundances of DO white dwarfs in the framework of gravitational settling. However, before we can draw any conclusions we have to check several possibilities for this failure.

68 S. Dreizler: HST spectroscopy of DO white dwarfs log C log N log O log Fe log Ni - HS + RE 5-89 PG 8+ PG 4+ -4-6 - -4-6 - -4-6 - -4-6 - HZ -4-6 - HD 49499 B -4-6 -4 - -4 - -4 - log τ ross Fig. 4. Results of the HST data analysis: Abundances from homogeneous models (dashed line), representative abundances from stratified models as defined in Sect. 4.. (solid line), and the equilibrium abundances at τ ross =/ as calculated by Chayer (priv. comm.; dasheddotted line). Abundances are log of number ratios relative to He. See also Table.. 4... Representative abundances of stratified models In order to investigate the difference between our stratified models and the observation as well as between the stratified and homogeneous models, representative abundances of the stratified models are required. Due to the steep abundance gradients it is not obvious how to derive reliable representative abundances from the stratified model atmospheres. A possible definition would be the abundance at τ ross =/ as used by Chayer et al. (995), a more reliable procedure seems to be a fit of the stratified model spectra with homogeneous model spectra as demonstrated in Fig. 6. The abundances of the best fitting homogeneous model are then taken as representative abundances for the stratified model. These abundances are also listed in Table. It has to be noted that the fit is not perfect. Most clearly, this can be seen in the O iv/v lines (8, 4, and 7 Å). The homogeneous spectra cannot reproduce the lines of both ionization stages of the stratified model simultaneously at the fixed effective temperature and surface gravity. This is, however, not surprising since this directly reflects the influence of the stratification on the atmospheric structure. The reliability of this procedure is therefore also checked by scaling the abundances in the stratified models of each element with the ratio between the homogeneous and the representative stratified abundances. The

S. Dreizler: HST spectroscopy of DO white dwarfs 69 PG 4+ 4 PG 8+ RE 5-89 HS + HZ HD 49499B 4 5 6 PG 4+ 4 PG 8+ RE 5-89 HZ HD 49499B 4 5 6 7 wavelength / A o Fig. 5. HST GHRS spectra (thick line) of our program stars compared with theoretical spectra (thin line) from stratified model atmospheres. The parameters are summarized in Table. Interstellar lines are marked at the top, stellar lines (long C, N, or O lines; medium Fe vi, short lines Ni v; very short lines Fe v) at the bottom. See also Table.

64 S. Dreizler: HST spectroscopy of DO white dwarfs stratified homogeneous 4 5 6 7 wavelength / A o Fig. 6. Comparison between a theoretical spectrum from a stratified model atmosphere with one from a homogeneous model atmosphere with the representative abundances from the stratified model. See text for details. Table. Results of the HST data analysis: Abundances from homogeneous models (top line in each column), representative abundances from stratified models as defined in Sect. 4.. (middle line in each column), and the equilibrium abundances at τ ross =/ as calculated by Chayer (priv. comm.; bottom line in each column). Abundances are log of number ratios relative to He. See Fig. 4 for an illustration. star log C log N log O log Fe log Ni PG 4+ -5. -. -4. -5. <-5. T eff = kk -.7-4.5-4. -4. -. log g=7.5 -.7 -. -.8 -. PG 8+ -. <-7. -. -4. -4. T eff = 95kK -.7-4.5-4. -4. -. log g=7.5 -.7 -. -.9 -.4 RE 5-89 -. -4.8 -. <-6. -5. T eff = 7kK -.5-4.5-4. -4. -.5 log g=7.5 -.5 -. -. -.6 HS + -. <-8.5 <-6. <-6. T eff = 65kK -4. -5.5-5.5-5.5 log g=7.8 -.8 -.9-4. HZ <-6. -5. <-6. T eff = 5kK -4.7-4.7-5. log g=7.8 -.8-4. -4. HD 49499 B <-6. <-6. <-6. T eff = 5kK -4.7-5.7-5.7 log g=8. -.9-4. -4. result is presented in Fig. 7. Now, the spectra can be reproduced much better, demonstrating that our representative abundances are well chosen. However, the discrepancies are still slightly larger than in the fit with homogeneous models (Fig. ). This is visible in the N v resonance doublet (8/4 Å) as well as in the oxygen lines (8/4/7 Å). 4... Influence of T eff and log g As already indicated by the comparison between stratified and homogeneous model spectra (Fig. 6) we might encounter systematic differences in the effective temperatures and surface gravities. As mentioned, however, at the beginning of Sect., we do not expect large uncertainties in these parameters which have been determined independently from fits to the optical helium lines. Nevertheless, the next step is an investigation of the influence of a change of T eff and log g on the stratified model atmospheres (Fig. 8). As expected, reasonable changes cannot account for the discrepancies between stratified model spectra, since it is difficult to correct on the one hand the underabundance of e.g. C and on the other hand on the overabundance of e.g. Ni. From Fig. and the equilibrium condition (Eq. 5) it is obvious that a change in one of these parameters acts nearly equally on all abundances. 4... Influence of model atoms A further possible explanation might be found in the treatment of the model atoms. Even though they are very elaborated, several sources of uncertainty remain. The model atoms of the lighter elements (e.g. C, N, O) are constructed by a direct transformation of the atomic levels into model levels. This procedure, however, prohibits a treatment of the fine structure splitting since this would result in far too many model levels. In previous calculations this was no problem, because the fine structure splitting

S. Dreizler: HST spectroscopy of DO white dwarfs 64 PG 4+ 4 PG 8+ RE 5-89 HS + HZ HD 49499B 4 5 6 PG 4+ 4 PG 8+ RE 5-89 HZ HD 49499B 4 5 6 7 wavelength / A o Fig. 7. HST GHRS spectra (thick line) of our program stars compared with theoretical spectra (thin line) from scaled stratified model atmospheres. The parameters are summarized in Table. Interstellar lines are marked at the top, stellar lines (long C, N, or O lines; medium Fe vi, short lines Ni v; very short lines Fe v) at the bottom. See also Table.

64 S. Dreizler: HST spectroscopy of DO white dwarfs 4 95 K/7.8 95 K/7.5 K/7.5 8 K/7.5 4 5 6 4 95 K/7.8 95 K/7.5 K/7.5 8 K/7.5 4 5 6 7 wavelength / A o Fig. 8. Influence of T eff and log g on the spectra of stratified model atmospheres. Interstellar lines are marked at the top, stellar lines (long C, N, or O lines; medium Fe vi, short lines Ni v; very short lines Fe v) at the bottom. See also Table.

S. Dreizler: HST spectroscopy of DO white dwarfs 64 is small enough to treat them as combined levels with combined transitions. Only for the spectrum synthesis these levels are split, e.g. the O iv triplet at 8/4 Å. For the calculation of the radiation pressure this might, however, be a severe drawback. The self absorption is higher in the combined, i.e. stronger, than it would be in the split, i.e. weaker, transition and therefore the radiation pressure is underestimated. This does not automatically result in higher abundances because the reaction of the model atmosphere is highly non linear. The general trend will, however, be toward an underestimation of the equilibrium abundances. The model atoms of the iron group elements (e.g. Fe and Ni) are not affected by this problem. Due to the huge number of levels the direct mapping of atomic levels onto model levels even fails with the above approximation. Such complex atoms can be handled in non-lte only with a statistical approach (Dreizler & Werner 99). For the calculation of the radiation pressure this approach has the advantage that it accounts for the fine structure splitting. However, in the case of DO white dwarfs, the Fe abundances are not significantly better reproduced than e.g. the oxygen abundances. Nevertheless, this is a point which will be investigated in the future, because in the case of the hydrogen rich DA white dwarf G 9-BB the Fe abundance can be fitted perfectly with a stratified model atmosphere while the lighter elements show discrepancies up to a factor of ten (see also below). Other sources of uncertainties in the model atoms come from the uncertainty of bound free transitions. This is especially the case for Ni, where no detailed theoretical cross sections exist. 4..4. Influence of stellar evolution The nitrogen abundance is the one where the deviation is most severe, at least for PG 8+ and HS +. This, however, could (partially) be a real feature. From the analysis of PG 59 stars we know that the nitrogen abundance varies at least by three orders of magnitude (Dreizler & Heber 998). For the N-poor PG 59 stars only upper limits could be determined and it is well possible that in these stars N is completely destroyed during the -α burning. If the PG 59 stars are indeed the progenitors of the DOs, those with low N abundances could be the successors of the N-poor PG 59 stars. Apart from hydrogen, the stratified models do not take into account that individual elements may be completely absent in the star. 4..5. Conclusion and future work Concluding the discussion, there is no satisfying explanation why the stratified models in general fail to reproduce the UV spectra of DO white dwarfs. DW and Chayer et al. (995) suggested that this could be due to competing processes like mass loss which have not been included in these calculations. There are several direct and indirect observational hints that weak mass loss can be present even in white dwarfs (Fleming et al. 99, Barstow & Sion 994, Sion et al. 997). As detected by Werner et al. (995b) and Dreizler et al. (995) about half of the hot white dwarfs clearly show spectroscopic signatures of a hot and fast wind. These stars were excluded from this investigation, nevertheless, underlining the importance of mass loss in DO white dwarfs. Very recently the effect of mass loss on gravitational settling in white dwarfs was studied by Unglaub & Bues (998). They find that mass loss down to 4 M /yr is sufficient to disturb the equilibrium as defined in (Eq. 5), which is far below the spectroscopic detection limit. Using the luminosity dependence of the mass loss rate of Blöcker (995) reveals that this critical value should be reached at T eff 65 K. Unglaub & Bues demonstrate that in the case of hydrogen rich white dwarfs this border line nicely reproduces the existence of helium traces in hot hydrogen rich atmospheres. Another important result of their calculations is that mass loss above the critical limit efficiently levels out any abundance gradients. In the light of this result the much better fit of the hotter DO white dwarfs with homogeneous model atmospheres becomes clear. According to this picture the abundances of the two cooler DOs (HZ, HD 49499 B) should be reproduced by the stratified models, which is, however, not the case. For these stars we could only determine the N abundance of HZ, which is not sufficient to draw any further conclusions. At the moment, the treatment of the model atoms (see above) for the lighter elements is a reasonable explanation. This is underlined by the analysis of the hydrogen rich white dwarf G 9-BB (Dreizler & Wolff 999). With an effective temperature of 56 K this star lies below the critical mass loss limit. Here the stratified model provides a significantly better overall fit than any homogeneous model, at least for the iron lines. The C, N, and O abundances are affected by similar offsets as in the DO white dwarfs. Future investigations will explore the influence of the model atoms on the equilibrium abundances and we will combine our detailed atmospheric models with the mass loss calculations of Unglaub & Bues (998). 5. Summary In the previous sections I described our UV spectra of hot helium rich white dwarfs obtained with the Hubble Space Telescope. These spectra were analyzed with chemically homogeneous as well as with stratified non-lte model atmospheres. In the simple picture, where the chemical abundance of hot white dwarfs is determined through the interaction between gravitational settling and radiative levitation, the stratified models should result in a better fit. However, the stratified models reveal significant discrepancies whereas homogeneous models can nicely reproduce the observations. There are numerous possibilities to explain the failure of the stratified models in the current stage. The two most urgent ones, the treatment of the model atoms of the light metals and the inclusion of mass loss will be tackled in the future. Acknowledgements. The author would like to thank K. Werner (Tübingen) for useful discussions and comments. This work has been supported by the Deutsches Zentrum für Luft- und Raumfahrt (DLR)

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