---
abstract: |
    We performed a spectral analysis of the EUVE spectrum and ROSAT data of the unique object , which is an extremely hot post-AGB star entering the white dwarf cooling sequence. It is the only pre-white dwarf known, whose surface is free of hydrogen and helium, hence, it represents the bare core of a former AGB star. The EUV spectrum (75–150Å) is dominated by strong lines and we can identify a number of lines.

    EUVE and ROSAT data can be fitted with models between =170000K and 200000K. We derive an extraordinarily high neon abundance (2%–5% by mass, i.e. 20–50 times solar) which we confirm by an optical line detected in a Keck HIRES echelle spectrum. This abundance is expected for $3\alpha$ processed matter and corroborates our understanding of  as a C-O stellar core which has lost its entire H- and He-rich envelopes.
author:
- Klaus Werner
- Burkhard Wolff
date: 'Received date; accepted date'
title: The EUV spectrum of the unique bare stellar core H1504+65
---

Introduction
============

The optical counterpart of the soft X-ray source  was detected by Nousek (1986) and spectroscopy revealed the unique nature of this object. From the spectroscopic signatures it belongs to the PG1159 stars, which are very hot (=75000–180000K) hydrogen-deficient pre-white dwarfs (=5.5–8, cgs-units). But in contrast to all other PG1159 stars it appeared to be also helium-deficient, which was later confirmed by model atmosphere analyses of optical spectra (Werner 1991) and FUV spectroscopy with the [*Hopkins Ultraviolet Telescope*]{} (Kruk & Werner 1998). Detailed NLTE line profile fitting revealed that  is the most massive PG1159 star, having the highest surface gravity, and that it is among the hottest of this group (M/M$_{\sun}=0.86\pm 0.15$, =$8.0\pm 0.5$, =170000K$\pm$ 20000K; Werner 1991).

 is one of the brightest sources in the EUV and an early attempt to understand its spectrum recorded with the [*Extreme Ultraviolet Explorer*]{} (EUVE) failed in several respects, particularly the model flux was overestimated by an order of magnitude, however, it became obvious that the spectral appearance is dominated by strong lines of (Barstow 1995). Since that time considerable progress was made in NLTE modeling of stellar atmospheres so that a new attempt to analyze these data together with soft X-ray ROSAT observations and new optical Keck spectra seemed promising.

Observations and data reduction
===============================

The EUVE spectrum of  was retrieved from the public archive. The exposure lasted 38000 seconds, starting on Dec.5, 1993. It was reduced (including flux calibration and subtraction of higher order contributions) with the standard procedures of the IRAF/EUV software package (Version 1.6.2).  is only detected in the EUVE short wavelength spectrometer because of its relatively high interstellar column density. The observed spectrum covers the range 75–150Å at a resolution of 0.5Å.

A useful complement are X-ray ROSAT PSPC data, which were retrieved from the public archive. The observation lasted 4882 seconds, beginning on July 18, 1990. A pulse height distribution was extracted by using the MIDAS-EXSAS software. Source flux is detected in the range 30–120Å (100–420eV).

We have performed optical spectroscopy of  at the 10m Keck I telescope on July 20, 1998, under excellent weather conditions. We have taken two spectra, which were later co-added, with a total of 6000 seconds exposure time, using the high resolution echelle spectrograph (HIRES) and the blue cross disperser. For details on data reduction see Zuckerman & Reid (1998). The spectrum covers the full wavelength region between 3600Å and 5100Å at a resolution of 35000.

Model atmospheres and spectral fitting
======================================

We have computed a grid of non-LTE model atmospheres with different input parameters (, , element abundances). The models include the most abundant elements, C and O, as well as Ne and He self-consistently and they are plane-parallel and in radiative and hydrostatic equilibrium. The computer code is based on the Accelerated Lambda Iteration method and is described in detail by Werner & Dreizler (1999).

Let us present the atomic input data at some length, because this is the first detailed analysis of an EUV spectrum of a PG1159 star with data of this good quality. We note in passing that similar models were applied only in the case of one other PG1159 star (PG1520+525; Werner 1996a) from which a useful spectrum could be taken by EUVE. However, the S/N was much worse in that case.

Potential spectral lines and absorption edges in the EUVE spectrum of 
----------------------------------------------------------------------

No features of and are located in the 75–150Åspectral range, however, absorption edges at longer wavelengths are important because they contribute strongly to the background opacity in the EUVE region. Although is the dominant ionization stage of carbon we do not expect to see any of its spectral lines because temperatures are too low to populate excited levels. On the other hand, we know from previous studies that the ground state edge (31.6Å) almost completely blocks the flux (Werner 1996b) in a PG1159 stellar atmosphere. This has no observable influence for the EUVE range, but is important in order to interpret correctly the ROSAT PSPC data.

The strongest opacity source is oxygen. is most important: In the spectral range in question we find two absorption line series arising from the ground state and the first excited state. The respective absorption edges are located at 89.8Å and 98.3Å (see Fig.\[euve\], top panel), the latter one causes the flux to drop at $\lambda<100$Å. Absorption edges of are weaker (because is more populated), but they are more numerous so that their combined opacity is important for the overall flux distribution (Fig.\[euve\]). These edges arise from the six lowest levels, where we have accounted for the possibility that from any 2s2p configuration either the 2p or 2s electron can be ionized, leaving behind an ion in the ground state or first excited state, respectively; therefore two edges appear at different locations in the spectrum. Spectral lines of are less important because of the weak population of this ion and because the line profiles are intrinsically less broad than those of the lines (quadratic vs. linear Stark effect, see below).

Many lines from are located in the 80-140Å range, as well as numerous absorption edges from to . The edges turned out to be very weak as compared to oxygen, which is of course a consequence of the lower Ne abundance.

Primary source for the used level energies is Bashkin & Stoner (1975). Carbon and oxygen oscillator strengths for spectral lines as well as bound-free cross-sections for photon and electron collisional ionization were largely provided by K. Butler (priv.comm.). Oscillator strengths for lines were retrieved from the Opacity Project data base (Seaton 1994), and bound-free cross-sections were computed hydrogen-like (the Ne model atom is essentially identical to that of Werner & Rauch 1994). Alternatively we have also used Opacity Project photon ionization cross-sections for all species, but the consequences are not relevant for our present study.

Finally we note that helium, for which an upper limit of 1% by mass was derived, does not at all affect the EUV spectrum.

Line broadening and pressure ionization
---------------------------------------

Line broadening is a problem which can be tackled only approximately at best, particularly in the most important case, the lines. is a hydrogenic ion. Its energy levels with equal principal quantum number are closely spaced but not degenerate. As a consequence, line broadening ranges between the linear and quadratic Stark regimes. We faced the same problem for optical lines in previous analyses and we refer to Werner (1991) for details on the approximative approach which we apply here, too. For and lines we assume quadratic Stark broadening, which is reasonable except for the highest members of the line series in our synthetic spectra, because linear Stark effects could become important here, too.

Another problem is posed by the numerical treatment of the bound-free photon cross-sections. It is clear from the outset that absorption edges in a stellar spectrum are not really sharp. Pressure effects lower the atomic ionization potential and tend to smear them out (see Fig.\[euve\], top panel). We account for this effect by an occupation probability formalism (Hummer & Mihalas 1988) which was generalized to NLTE conditions by Hubeny (1994). We use essentially their numerical treatment, but two details demand special attention in our case. First, the perturber particles, which impose an electric microfield at the location of the radiating atom, are not protons (as it is the case in atmospheres with solar composition), but highly charged particles (mostly and ). Consequently the critical field strength $\beta_{\rm c}$ as given in Hubeny (1994; their eq.A.2) needs to be scaled by C$^{1/3}$, where C is the ratio of the total ion density to the electron density, $n_{\rm Ion}/n_{\rm e}$. And second, the plasma correlation parameter $a$, which is defined as the ratio of the mean distance of ions to the Debye length, needs to be scaled, so that we have instead of their eq.A.4: $$a =
 0.09 \frac{n_{\rm e}^{1/6}}{\sqrt{T}} {\left(1 + \sum_i Z_{\rm i}^2 N_{\rm i}/n_{\rm e} \right)^{1/2}
\left( \sum_i N_{\rm i}/n_{\rm e}  \right)^{-1/3} }$$ where $N_{\rm i}$ and $Z_{\rm i}$ are the number density and charge of the i-th ion, respectively, and $n_{\rm e}$ and $T$ are the electron density and temperature. This procedure is formulated strictly for hydrogenic ions only and, hence, applicable for , but we also treat the edges in this way, because we lack any better approach. But since the edges are weak, this uncertainty is not important for our analysis.

To summarize, the most severe uncertainty in the synthetic spectrum calculations is the lack of a satisfactory treatment of line broadening, because strong line merging has a significant effect on the overall shape of the EUV spectrum. Theoretical line broadening data exist for only few of the lines relevant here, but these do not account for linear Stark effects (Dimitrijevic & Sahal-Brechot 1992).

Iron group elements
-------------------

EUVE spectra of hot hydrogen-rich white dwarfs are completely dominated by iron and nickel lines and bound-free continua (e.g. Wolff 1998), hence, it was felt mandatory to check the relevance of these opacities in the case of . Model calculations show that effects of the iron group elements (with a solar abundance fraction) are not detectable at the resolution and S/N level of the present EUVE spectrum. Continuous opacities of the Fe group are negligibly small compared to the dominant species. On the other hand, our model predicts that a large number of lines should be detectable in future observations with the Chandra X-ray observatory, which will be able to provide spectra with higher resolution and better S/N.

Treatment of interstellar absorption in synthetic spectra
---------------------------------------------------------

EUV and soft X-ray spectra are very sensitive to absorption from interstellar hydrogen and helium. For the EUVE spectrum this attenuation was calculated according to the model of Rumph (1994). The interstellar column density of neutral hydrogen ($N({\rm {\mbox{H\ {\scriptsize I}}}})$) enters as a free parameter. It was chosen so that the observed flux could be reproduced at $\lambda \ga 130$Å. The column densities of and were fixed relative to hydrogen using the mean values of ${\rm {\mbox{He\ {\scriptsize I}}}}/{\rm {\mbox{H\ {\scriptsize I}}}} = 0.068$ and ${\rm {\mbox{He\ {\scriptsize II}}}}/{\rm {\mbox{H\ {\scriptsize I}}}} = 0.052$ from Wolff (1999).

For the ROSAT PSPC pulse height distribution we have also used fixed relative abundances for helium (see Jordan (1994) for details of the analysis). Since different spectral regions are used to determine the interstellar absorption the $N({\rm {\mbox{H\ {\scriptsize I}}}})$ values from the ROSAT and EUVE analyses differ.

Results and discussion
======================

In the top panel of Fig.\[euve\] we display a model spectrum for . The numerous O and Ne lines are identified and close inspection shows that the lines are strongest. Line blending with and occurs at many locations and the degraded spectrum (shifted upward in the Figure) which simulates the EUVE resolution of 0.5Ådemonstrates that disentangling of single lines becomes difficult. However, it is possible to identify a few isolated lines or line cores of and which are indicated by arrows in the lower panel of Fig.\[euve\]. The roll-over of the flux towards shorter wavelengths is caused by the strong absorption edge of the first excited level of at 98Å, which can be seen by the dashed line in the top panel of Fig.\[euve\] which represents the continuum flux of the model. As already mentioned, the sharp absorption edge is strongly smoothed out by pressure effects as well as the converging absorption line series. For the same reason all other absorption edges which are indicated in Fig.\[euve\] cannot be recognized in the final model spectrum.

Effective temperature
---------------------

The best fitting model was found by taking models with different  and keeping fixed =8 and the abundance ratio C/O=1. The latter two parameters, when varied within the limits of the optical line analysis, affect the model spectrum much less than . The model flux is normalized to the observed visual magnitude (V=16.24, Nousek 1986) and the interstellar column density, which is responsible for the roll-off at the long wavelength end of the spectrum, is treated as a free parameter. The neon abundance can be estimated from the line near 106Å which is observed to have a deeper core than the blending lines near 107Å.

The best fit is displayed in the bottom panel of Fig.\[euve\], with model parameters as indicated. The overall fit is satisfactory. The strongest and line features can be identified and the model can fit them. The absolute flux level at the flux maximum and at longer wavelengths is matched by the model with =175000K. Models with  less than 170000K can be clearly ruled out, because the absorption edges become too strong. On the other hand,  higher than 180000K causes a strong flux excess in the region of the observed flux maximum.

However, in one respect this model fails to fit the observation. Its flux is distinctly too low at $\lambda<100$Å. This could in principle be improved with a hotter model (200000K, along with a higher column density to fit the spectrum at long wavelengths), but the flux exceeds the maximum by a factor of two in the range 100–120Å (Fig.\[euve\_hot\]). This is the range where strong line merging occurs and it is conceivable that, in case that we underestimate the line broadening, stronger line wings can effectively block more flux in this region. Alternatively, yet unidentified opacity sources of other light metals may be responsible (e.g. Mg might be as abundant as Ne, and many and lines are located in the EUV), but any progress must await data with better spectral resolution.

Another argument that speaks for  slightly higher than 175000K is the strength of the optical  3644Å line (the very strong EUV lines of Ne are much less temperature sensitive). A better fit is obtained at 200000K, although still, the equivalent width is too weak (Fig.\[keck\]). This can be improved by reducing  to 7.5 and/or increasing the Ne abundance (see below).

As one can expect from the EUVE flux below 100Å, the ROSAT PSPC pulse height distribution (120–30Å) cannot be matched by the “cool” 175000K model (Fig.\[rosat\]). A model with =200000K is needed to obtain a satisfactory fit (where we accept a model flux excess at the softest energies, which might be caused by the underestimated flux blocking in the 100-120Årange as mentioned above).

To summarize, we estimate =170000–200000K from the EUV and X-ray data, which compares reasonably well with the range obtained previously from the optical spectra (=150000–190000K). This indicates that approaches or even exceeds the temperature of the hottest known PG1159 star (=180000$\pm$20000K; RXJ0122.9$-$7521; Werner 1996b).

Neon abundance
--------------

The EUV spectrum indicates a high neon abundance (2%), which is a factor of 20 higher than the solar value. We estimate a possible error of a factor of three, which is caused by the S/N of the data and the fact that the strong lines are saturated. Our first detection of the  3644Å line in the Keck spectrum of  (a previous attempt with the 3.5m Calar Alto telescope failed) indicates, that the actual abundance might be even higher. Fig.\[keck\] shows several model fits to this line. Even under the assumption of a lower gravity (=7.5), which represents the lower limit of the optical analysis and which results in a stronger line, the relatively strong observed profile suggests an abundance of the order 5%. We successfully detected this line earlier in three other PG1159 stars (Werner & Rauch 1994) and, as discussed in detail in that paper, the derived Ne abundance (2%) can be expected in matter processed by 3$\alpha$ burning. This high abundance can be rated as an indication that the stars have lost their H- and He-rich envelopes, with  being the most extreme case.

We have already speculated that the He-deficiency in  points at the possibility that the star has burned carbon in previous evolutionary stages (Werner 1991). Hence, it might have been one of the “heavyweight” intermediate-mass stars (8M$_{\sun}{\raisebox{-0.4ex}{${\stackrel{<}{\scriptstyle \sim}}$}}$ M ${\raisebox{-0.4ex}{${\stackrel{<}{\scriptstyle \sim}}$}}$ 10M$_{\sun}$) which form white dwarfs with electron-degenerate O-Ne-Mg cores resulting from carbon burning. The extraordinarily high Ne abundance found in the present study and the unusually high mass of  corroborate this speculation. In any case, the Mg and Na abundances can be as high as the Ne abundance (Iben 1997), so that better EUV spectra, which can be provided by the future Chandra mission, should be used for further studies in this direction with a possible identification of other metal lines.

Keck data were taken in collaborative observations with I.N.Reid. A travel grant from the DFG (We1312/21-1) to the Keck Observatory is gratefully acknowledged. ROSAT data analysis in Tübingen and Kiel is supported by the DLR under grants 50OR97055 and 50OR96173, respectively. Correspondence with I.Hubeny on occupation probabilities was helpful.

Barstow M.A., Holberg J.B., Koester D., Nousek J.A., Werner K. 1995, in White Dwarfs, eds. D. Koester and K. Werner, Lecture Notes in Physics 443, Springer, Berlin, p. 302

Bashkin S., Stoner J.O., Jr. 1975, Atomic Energy Levels & Grotrian Diagrams, Vol. 1, Amsterdam, North Holland

Dimitrijevic M.S., Sahal-Brechot S. 1992, A&AS 93, 359

Hubeny I., Hummer D.G., Lanz T. 1994, A&A 282, 157

Hummer D.G., Mihalas D. 1988, ApJ 331, 794

Iben I. Jr., Ritossa C., Garcia-Berro E. 1997, ApJ 489, 772

Jordan S., Wolff B., Koester D., Napiwotzki R. 1994, A&A 290, 834

Kruk J.W., Werner K. 1998, ApJ 502, 858

Nousek J.A., Shipman H.L., Holberg J.B., Liebert J., Pravdo S.H., White N.E., Giommi P. 1986, ApJ 309, 230

Rumph T., Bowyer S., Vennes S. 1994, AJ 107, 2108

Seaton M.J., Yan Y., Mihalas D., Pradhan A.K. 1994, MNRAS 266, 805

Werner K. 1991, A&A 251, 147

Werner K., Rauch T. 1994, A&A 284, L5

Werner K., Dreizler S. 1999, in Computational Astrophysics, eds. H. Riffert and K. Werner, Journal of Computational and Applied Mathematics, Elsevier, in press

Werner K., Heber U., Hunger K. 1991, A&A 244, 437

Werner K., Dreizler S., Heber U., Rauch T. 1996a, in Astrophysics in the Extreme Ultraviolet, IAU Colloquium 152, eds. S. Bowyer and R.F. Malina, Kluwer, p. 229

Werner K., Wolff B., Pakull M., Cowley A.P., Schmidtke P.C., Hutchings J.B., Crampton D. 1996b, in Supersoft X-ray Sources, ed. J. Greiner, Lecture Notes in Physics 472, Springer, Berlin, p. 131

Wolff B., Koester D., Dreizler S., Haas S. 1998, A&A 329, 1045

Wolff B., Koester D., Lallement R. 1999, A&A in press

Zuckerman B., Reid I.N. 1998, ApJ 505, L143
