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Physical parameters of helium-rich subdwarf B stars from spectral energy distributions
A. Ahmad and C. S. Jeffery
Armagh Observatory, College Hill, Armagh BT61 9DG. N. Ireland. UK Received 15 July 2003 / Accepted 02 October 2003
Abstract. We present effective temperatures and angular radii for eleven helium-rich subdwarf B stars. These are measured

using spectral energy distributions from archival IUE spectra and existing optical and infrared photometry. The data have been analysed using a grid of high-gravity helium-rich LTE model atmospheres and a 2 -minimization procedure. The parameters derived here allow for independent verification of the parameters derived from the analysis of optical spectra.
Key words. stars: chemically peculiar - stars: early-type - subdwarfs - stars: atmospheres - stars: fundamental parameters

1. Introduction
Helium-rich subdwarf B stars (He-sdB) stars are rare faint blue stars first identified as sdOD stars in the Palomar-Green (PG) survey of faint blue objects (Green et al. 1986). They are found both in our Galaxy (PG survey) as well as in globular clusters (Moehler et al. 1997; 2002). The optical spectra of He-sdB stars, by definition show strong HeI and in some cases HeII absorption lines. Some of them also show strong carbon lines. The evolution of these stars has been under much debate. Initially it was suggested that they might be the products of merged white dwarfs (Iben & Tutukov 1986). More recently Brown et al. (2001) have suggested that these stars might be the product of late flash-mixing in single star evolution. Analysis of optical spectra (Ahmad & Jeffery 2003 ­ Paper I) of a sample of fifteen He-sdB stars indicate that they have effective temperatures (T eff ) in the range 30 000 ­ 40 000 K, surface gravities (log g) in the range 5.0 ­ 6.0 (cgs) and helium abundances (nHe ) ranging from 0.10 ­ 0.99. Although He-sdB stars exhibit a range of helium abundance, most of them are extremely helium-rich, having nHe 0.90. Misclassification of He-sdB stars is a known problem (Paper I). The PG catalogue classified cooler subdwarfs having "pure" HeI spectra with weak or absent hydrogen Balmer lines as sdOD stars implying that He-sdB stars should be extremely helium-rich. Other authors have identified sdB stars showing significantly more helium than "normal" to be He-sdB stars, eg. JL 87 (nHe 0.17, Schulz et al. 1991) and LS IV­14116 (nHe 0.21, Paper I). Such stars have also been analysed in this paper although they are not "typical" He-sdB stars. This paper aims to measure the fundamental parameters ­ effective temperature (T eff ), interstellar reddening (E B-V ) and
Send offprint requests to: A. Ahmad, e-mail: amir@star.arm.ac.uk Based on INES data from the IUE satellite

angular diameter () of a sample of He-sdB stars by studying their flux distribution using a grid of helium-rich model atmospheres and a 2 -minimization procedure. Stars selected for this study include all He-sdB stars from the literature which have been observed with the International Ultraviolet Explorer (IUE) satellite. These observations were supplemented with optical photometric measurements from the literature and from the recently released 2MASS infrared measurements. The parameters derived by this method are independent from those obtained from the analysis of optical spectra (Paper I), thus providing an independent verification.

2. IUE observations
IUE observations for eleven He-sdB stars, shown in Fig. 1, have been collected from the IUE Final Archive at MAST as "IUE Newly Extracted Spectra" (INES, Nichols & Linsky 1996). The observations listed in Table 1 were made at low resolution ( 6 å) with the Short Wavelength Prime (SWP : 1150 ­ 1980 å) and the Long Wavelength Prime and Redundant (LWP and LWR : 1850 ­ 3350 å) cameras. The short wavelength cameras on the IUE were more sensitive than the long wavelength cameras and hence the SW and LW observations were merged in the overlap region (1850 ­ 1980 å) using weights of 100:1 with the Starlink package DIPSO (Howarth et al. 1998). For the analysis the IUE spectra were trimmed at the long and short wave limits to remove noisy data. We found that two stars originally classified as He-sdB stars by Beers et al. (1992) and observed with the IUE are actually white dwarfs; BPS CS 29517­0049 is a DB white dwarf (Wegner & Nelan 1987) and BPS CS 22968­0019 is a DB4 white dwarf (Wesemael et al. 1993). These two stars were not analysed.


Fig. 1. Flux distribution of He-sdB stars with the model fits. Table 1. IUE observations of He-sdB stars. LW Image LWP18452 LWP31664 LWR06514 LWP31781 PG 1127+019 LWP10994 PG 1413+114 LWP10989 EC 14316­1908 LWP23384 PG 1544+488 LWP10992 PG 1559+222 LWP10993 LS IV­14 116 LWP10814 JL 87 LWP09467 PG 2321+214 LWP18329 Star PG 0240+046 LB 1766 PG 0902+057 Exp [s] 2699 399 3599 1499 1199 8999 1320 899 6899 759 419 1445 SW Image SWP39307 SWP56159 SWP56259 - - SWP31135 SWP45020 SWP31142 SWP31143 SWP31029 SWP29594 SWP39208 Exp [s] 2099 299 999 - - 14999 660 899 5999 759 299 1019

3. Photometry
Photometric measurements of He-sdB stars were collected from published photometry. The optical photometry includes Johnson U BV and Stromgren uvby measurements and these are ¨ listed in Table 2. Infrared Johnson J H K measurements, listed in Table 3 were collected from the 2MASS All-Sky Catalogue of Point Sources (Cutri et al. 2003). For some of the stars there are no published y or V measurements; in such cases the V magnitude has been calculated from the Bpg magnitude using the transformation equation given by Thejll et al. (1994), V = 6.628 â 10
0.024 B
pg

.

(1)

The transformed V magnitudes have a standard deviation of 0.3 mag. The errors in the photometric measurements listed in Tables 2 and 3 are derived from the source papers.


Table 2. Visible light photometry of of He-sdB stars. Star PG 0240+046 LB 1766 PG 0902+057 PG 1127+019 PG 1413+114 EC 14316­1908 PG 1544+488 PG 1559+222 LS IV­14 116 JL 87 PG 2321+214 u 13.785 ± 0.021 11.906 ± 0.112 - - - - 12.500 ± 0.120 - 12.629 ± 0.025 12.082 ± 0.056 - v 14.034 ± 0.018 12.158 ± 0.053 - - - - - - 12.847 ± 0.011 12.095 ± 0.032 - b 14.037 ± 0.016 12.223 ± 0.023 - - - - 12.770 ± 0.070 - 12.882 ± 0.003 12.034 ± 0.026 13.530 ± 0.364 U - - - - 14.580 ± 0.3604 11.860 ± 0.0405 - - - - - B - - - - 15.710 ± 0.024 12.990 ± 0.020 - - - - - y/V 14.142 ± 0.014 12.343 ± 0.012 14.415 ± 0.300 13.603 ± 0.300 16.070 ± 0.015 13.210 ± 0.010 12.800 ± 0.050 14.786 ± 0.300 13.029 ± 0.001 12.049 ± 0.022 13.560 ± 0.324

1 2

1 2

1 2

1 2 3 3 4 5 6 3 2 7 8

4 5

6

6

2 7

2 7

2 7 8

References : 1 Wesemael et al. (1992); 2 Kilkenny & Busse (1992); 3 V calculated using Eq. 1; 4 Beers et al. (1992); 5 Kilkenny et al. (1997); 6 Green (1980); 7 Hauck & Mermilliod (1998); 8 Bixler et al. (1991) Table 3. Infrared photometry of He-sdB stars from the 2MASS survey (Cutri et al. 2003). Star PG 0240+046 LB 1766 PG 0902+057 PG 1127+019 PG 1413+114 EC 14316­1908 PG 1544+488 PG 1559+222 LS IV­14 116 JL 87 PG 2321+214 J ± ± ± ± ± ± ± ± ± ± ± H 14.936 ± 13.181 ± 14.789 ± 14.751 ± 16.701 ± 13.848 ± 13.561 ± 15.482 ± 13.799 ± 12.388 ± 14.430 ± K 14.844 ± 13.248 ± 15.116 ± 14.688 ± - 13.933 ± 13.666 ± 15.555 ± 13.898 ± 12.410 ± 14.434 ±

14.755 13.062 14.742 14.498 16.609 13.773 13.460 15.398 13.638 12.308 14.289

0.033 0.027 0.036 0.029 0.138 0.026 0.022 0.054 0.027 0.026 0.024

0.052 0.031 0.049 0.062 0.316 0.045 0.030 0.112 0.031 0.027 0.038

0.100 0.038 0.162 0.111 0.060 0.046 0.219 0.051 0.026 0.075

The photometric magnitudes used in the energy distribution analysis were converted into fluxes using F = 10
0.4 (C -m )

.

(2)

The scale factors C used for converting the magnitudes to fluxes are taken from Heber et al. (1984) for the ¨ Stromgren uvby filters and from Johnson (1966) for the Johnson U BV J H K filters.

by fitting model fluxes using a 2 minimisation procedure (cf. Aznar Cuadrado & Jeffery 2001). The best fit parameters for each star correspond to the minimum in the 2 surface. Aznar Cuadrado & Jeffery (2001) had noted that these surfaces should be treated carefully as they may have more than one minimum and FFIT can find wrong parameters if it ends up in a local minimum instead of the global minimum. We examined the quality of each final solution (Fig. 1) to ensure that it looked reasonable and to check whether it was consistent with previous measurements.

4. Models and 2 minimization
A grid of LTE model atmospheres was computed assuming plane-parallel geometry and hydrostatic equilibrium using the code STERNE (Jeffery & Heber 1992). The grid points were defined by T eff = 20 000 (5 000) 40 000, 50 000, log g = 5.0 (0.5) 6.0 and nHe = 0.100, 0.300, 0.699, 0.997. Solar metal abundances were assumed. Another model grid was used to study the effect of carbon enhancement in the model atmospheres, these comprised T eff = 28 000 (2 000) 40 000, log g = 5.0 (0.5) 6.0 and abundance (nHe + nC ) = 0.960+0.030, 0.990+0.010, 1.000+0.003. The FORTRAN90 program FFIT (Jeffery et al. 2001) was used to calculate the effective temperature (T eff ), reddening (E B-V ) and angular diameter () from the observed flux distribution

5. Errors
Aznar Cuadrado & Jeffery (2001) have shown that the T eff is not very sensitive to log g in the range of 5.0 ­ 6.0 (cgs). We have therefore assumed a value for log g for our stars based on Paper I and previous analyses. The results do not change if log g is varied by ±0.3 dex. Also, nHe does not affect the parameters if it is varied by ±0.1. The best model fits were calculated without any interpolation in log g and nHe . For some stars in this study there are no previous analyses for surface gravity and helium abundance, in such cases we have assumed log g = 5.5 and n He = 0.99, which are the typical values for He-sdB stars (Paper I). It is clear from optical and IUE spectra that some He-sdB stars are carbon-rich while others are carbon-poor. Hence we


Table 4. Physical parameters of of He-sdB stars along with previous measurements from the literature. Values in square brackets are assumed. Star PG 0240+046 [carbon-rich] E
B-V

LB 1766 [carbon-poor] PG 0902+057 [carbon-poor] PG 1127+019 [carbon-rich] PG 1413+114 [carbon-rich] EC 14316­1908 [carbon-poor] PG 1544+488 [carbon-rich]

PG 1559+222 [carbon-poor] LS IV­14 116 [carbon-poor]

JL 87 [carbon-rich]

PG 2321+214 [carbon-poor]

0.07 ± 0.01 - - 0.06 - 0.02 ± 0.01 - 0.08 ± 0.01 - - 0.03 ± 0.01 - 0.12 ± 0.02 0.00 0.12 ± 0.02 0.12 0.08 0.01 ± 0.01 - - - 0.09 ± 0.02 - 0.03 ± 0.01 - - 0.01 0.16 ± 0.01 - - 0.15 0.13 ± 0.02 - 0.10±0.03

[rad] â10-12 4.08 ± 0.09 - - - - 7.98 ± 0.17 - 3.37 ± 0.10 - - 3.82 ± 0.16 - 1.74 ± 0.07 - 6.06 ± 0.22 - - 7.51 ± 0.12 - - - 2.92 ± 0.13 - 6.90 ± 0.10 - - - 15.00 ± 0.36 - - - 4.93 ± 0.22 - -

T

eff

[K]

log g [cgs] [5.5] 5.40 ± 0.10 6.25 ± 0.10 - 5.30 ± 0.30 [6.0] 6.30 ± 0.30 [6.0] - 6.00 ± 0.10 [5.0] 5.00 ± 0.10 [5.5] - [5.5] - - [5.0] 6.00 ± 0.30 5.10 ± 0.10 5.10 [5.5] - [5.5] 5.40 ± 0.10 - 5.80 ± 0.20 [5.0] 5.50 ± 0.30 5.00 5.20 ± 0.30 [5.5] 5.30 ± 0.10 -

n

He

Reference FFIT Paper I Aznar Cuadrado & Jeffery (2002) Aznar Cuadrado & Jeffery (2001) Thejll et al. (1994) FFIT Lanz et al. (2003) FFIT Paper I Thejll et al. (1994) FFIT Paper I FFIT Beers et al. (1992) FFIT Drilling & Beers (1995) Beers et al. (1992) FFIT Lanz et al. (2003) Paper I Heber et al. (1988) FFIT - FFIT Paper I Ulla & Thejll (1998) Viton et al. (1991) FFIT Lanz et al. (2003) Magee et al. (1998) Schulz et al. (1991) FFIT Paper I Ulla & Thejll (1998)

34 600 ± 1 700 34 000 ± 150 36 200 ± 400 34 800 ± 1 850 37 000 ± 2 000 40 400 ± 1 300 40 000 ± 2 000 47 000 ± 3 000 > 40 000 44 000 ± 2 000 42 100 ± 2 000 39 900 ± 200 40 300 ± 2 500 31 600 42 000 ± 3 000 77 000 33 900 32 100 ± 1 000 36 000 ± 2 000 34 000 ± 300 31 000 38 700 ± 2 100 - 32 500 ± 700 32 500 ± 150 35 000 33 000 ± 1 000 28 100 ± 1 100 29 000 ± 2 000 30 000 28 000 ± 1 000 38 400 ± 3 000 39 600 ± 150 43 0001

[0.70] 0.63 ± 0.01 0.66 ± 0.02 - 0.55 ± 0.11 [0.99] 0.99 [0.99] - 0.97 ± 0.19 [0.99] 0.99 ± 0.01 [0.99] - [0.99] - - [0.99] 0.98 0.99 ± 0.01 0.99 [0.99] - [0.30] 0.21 ± 0.01 - 0.20 ± 0.07 [0.10] 0.09 ­ 0.16 - 0.17 ± 0.05 [0.99] 0.99 ± 0.01 -

1

Thejll, Husfeld & Saffer (unpublished) reported by Ulla & Thejll (1998)

studied the effect of carbon enhancement in the atmosphere by adding 3%, 1% and 0.3% carbon in the model atmospheres. The results indicate that increasing the amount of carbon in the atmosphere does not significantly change the flux distribution in the wavelengths under study (1180 ­ 22000 å). The effect of the change in carbon abundance on T eff is 600 K, which is quite small considering the errors associated with T eff in the best model fit are around ±1 500 K. Hence, we have used a solar carbon abundance for this analysis.

6. Results
The IUE spectra of He-sdB stars are shown in Fig. 1 combined with the photometric fluxes and model fits. The best fit parameters derived from FFIT are quoted in Table 4 along with the formal errors. It is interesting to note that some He-sdB stars show strong CIII/CIV lines in their IUE spectrum (see Fig. 1) as well as in the optical spectrum (Paper I) indicating that they are carbon-rich. In other stars these strong carbon lines are absent. This reinforces the view that there are two distinct sub-classes within He-sdB stars, one which consists of stars which are carbonrich and the other which comprises stars which are carbon-poor (Table 4).

It has been established (Kudritzki 1979) that for T eff 35 000 K, departure from local thermodynamic equilibrium (LTE) does not significantly affect measurements of T eff in high-gravity stars. For hotter stars, NLTE effects become increasingly important. However the relative temperature differences obtained from LTE analysis are still useful.

7. Discussion
Some of our He-sdB stars have been analysed previously. For these, most of our results match quite well with those already in the literature (Table 4). PG 1413+114, EC 14316­1908 and


PG 1559+222 do not have previous estimates for log g and n He hence typical values for these parameters were assumed for the analysis. The optical spectra of these three stars show strong HeII lines indicating that they are hot ( 40 000 K) and enriched in helium. PG 1413+114 is a He-sdB star from Jeffery et al. (1996). Beers et al. (1992) have also referred to it as a He-sdB star (BPS CS 22883­0015) and estimated T eff = 31 600 K and E B-V = 0.0. Such a low effective temperature is not consistent with the presence of the strong HeII lines. We derive a much higher effective temperature and interstellar reddening for this star in our analysis. EC 14316­1908 is a He-sdB star from the Edinburgh-Cape survey of blue objects by Kilkenny et al. (1997). Beers et al. (1992) refer to it as a He-sdO star (BPS CS 22871­0019) and estimate T eff = 33 900 K and E B-V = 0.08. This star appears as two different object in SIMBAD. Drilling & Beers (1995) have estimated T eff = 77 000 K and E B-V = 0.12 by analysing the flux distribution of this star. The optical spectrum shows strong HeII but also some HeI which suggests that although this star is quite hot (T eff 40 000 K), it is not as hot as estimated by Drilling & Beers (1995). We derive the same interstellar reddening but a much lower effective temperature (42 000 K).

References
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8. Conclusion
We have analysed a sample of eleven He-sdB stars and derived fundamental parameters from their flux distributions. The results confirm those obtained from analyses of optical spectra. The IUE spectra of He-sdB stars reinforces the idea of two distinct subclasses of these stars. The carbon-rich He-sdB stars which show strong carbon lines in their optical and IUE spectra can be explained by the merger of CO+He white dwarfs (Saio & Jeffery 2002) as well as the flash-mixing model (Brown et al. 2001) whereas carbon-poor He-sdB stars can be explained by He+He white dwarf mergers (Saio & Jeffery 2000). Detailed abundance measurements will be required to determine which of these evolutionary channel(s) are responsible for the formation of these rare faint blue stars.
Acknowledgements. We thank Dr D. Kilkenny, the referee, for useful comments and suggestions. This research is supported by a grant to the Armagh Observatory from the Northern Ireland Department of Culture, Arts and Leisure. The authors acknowledge the data analysis facilities provided by the Starlink Project which is run by CCLRC on behalf of PPARC. This research has made use of NASA's Astrophysics Data System. This research has also made use of the Aladin, Vizier and SIMBAD databases, operated at CDS, Strasbourg, France. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NAG5-7584 and by other grants and contracts.