3 Analysis of high resolution spectra and results

The main aim of this paper is to present a quick-look physical interpretation, very similar in philosophy and implementation to the pipeline reduction of the data at ESO. The intention of the project is of course to search for double degenerates, and in the beginning we did not expect the spectra to be useful for a detailed spectral analysis. That turned out to be wrong, and one purpose of this work is to alert the community to the data of this project, which will all be available very soon in the VLT archive. It is important to note that a significant fraction of the objects - and an even larger one in the following papers - are new white dwarf identifications, mainly from the Hamburg ESO Quasar Survey (HE). We do not have the manpower to really exploit all the information in these data. Several of the objects show metal lines, some of them probably stellar - this is interesting material for the study of the accretion/diffusion scenario in DA white dwarfs. A more careful analysis could be done, adapting the spectral fitting for each individual spectrum to the highest quality spectral range of the observations, to get an accurate mass distribution. In the near term a study of the white dwarf kinematics is carried out in Bamberg, which will use the masses from this work to determine the velocity correction corresponding to the gravitational redshift. For all these reasons and constraints we have decided to use the data almost exactly as they come from the UVES reduction pipeline and implement the analysis in an analogous way: the original data go into the input end of the analysis pipeline, are merged, rebinned, rescaled, fitted with models and the fits plotted without human intervention. At the end, however, the final plots are visually inspected, any peculiarities noted, and spectra, which are not useful, are taken out of the queue, before a repeated run of the software produces the final results and output. This is all very similar to the philosophy of the reduction pipeline for the data at ESO.

Let us look at this analysis pipeline in some detail. As a first step for the spectral analysis the three different spectral ranges are further binned to approximately 1 Å resolution and combined to one file per observation. This serves to improve the signal-to-noise ratio, but also to decrease the large amount of data to a more manageable size. The spectra are then fitted with theoretical spectra from a large grid of LTE DA and DB models, using a $\chi ^2$ technique based on the Levenberg-Marquardt algorithm (Press et al. 1992). The input physics for our models is similar to the description in Finley et al. (1997); some details on the fitting method can also be found in Homeier et al. (1998).

Figure 1 shows four rather arbitrarily selected examples of this procedure. Theoretical spectra are fitted to the continuum on both sides of the Balmer lines and the best fit is then determined from the line profiles. The figure shows in the upper panels two DA spectra with good S/N; the right spectrum also has a CaII K line in absorption. The star in the lower left panel shows clear Zeeman splitting in the lower Balmer lines and is thus a magnetic DA. The lower right panel finally is an example for spectra with lower S/N.

Because the strength of the Balmer lines in white dwarfs reaches a maximum around $T_{\rm eff}$ = 12000 K, it is often possible to find two minima with the $\chi ^2$ minimization. We have always used two starting values for the iterative solution (9000 K and 15000 K). If the solutions did not converge to a single value, we preferred the one with the lower $\chi ^2$ value, which was further confirmed by a visual inspection.

Several of the DA, for which the LTE fit resulted in a temperature hotter than 40000 K were reanalyzed using a NLTE DA grid, to check the dependence of the results on possible NLTE effects. The models and fit procedure are described in Napiwotzki et al. (1999). The differences compared to the LTE fits were minor as expected; the tables in the following nevertheless give the NLTE results in these cases. One of the DA in this range (EC13123-2523) shows the so-called "Balmer line problem'' (see Napiwotzki & Rauch 1994): higher Balmer lines point to higher effective temperatures than the low lines and the overall fit with pure hydrogen models is poor. The problem has been traced back to the influence of EUV metal line blanketing (Werner 1996).

Figure 4: Comparison of DA echelle spectra (thin line) with single-order spectra of lower resolution (thick line) from various telescopes and instruments.

Figure 5: Comparison of echelle and single-order spectra for 3 more DA.

 

 

Table 1: Comparison of echelle spectra with single-order spectra. The first line for each object gives the fit result from the echelle spectra of this work (in the case of two available echelle spectra the better one was used). The second line is a fit to lower resolution single-order spectra, using the same line intervals for fitting, except for H$\alpha$, which is not available for the single-order spectra.

object	$\mbox{$T_{\rm eff}$ }$	$\mbox{$\log g$ }$
WD0133-116	11768	7.84
	12301	8.03
WD0302+027	36158	7.66
	38352	7.68
WD1422+095	12700	7.95
	12847	7.84
WD1544-377	10613	8.12
	11023	8.19
WD1736+052	9064	8.24
	8783	8.19
WD2014-575	28013	7.80
	28264	7.93
WD2326+049	11515	7.97
	11969	8.20

3.1 White dwarfs of spectral type DA

Table A.1 (Appendix, only available online) gives the results for the normal DA spectra. The objects are sorted by right ascension; the table gives the WD numbers from the white dwarf catalog (McCook & Sion 1999), where further information can be found. For objects not in the catalog we attempt to give the designation from the discovery survey: HE for the Hamburg/ESO Quasar survey, EC for the Edinburgh-Cape Survey, and MCT for the Montreal-Cambridge-Tololo Survey; these papers are also the sources for the magnitudes. All coordinates were measured on the DSS (Digital Sky Survey) frames, and in many cases corrected for proper motion to epoch 2000.

For objects, which already have two independent observations, we give both spectral fit results. The errors for the effective temperature and surface gravity are formal errors from the $\chi ^2$ fitting routine, they do not include systematic errors and therefore usually underestimate the true error. A detailed discussion of realistic error limits for state-of-the-art analysis of DA white dwarfs is provided in Napiwotzki et al. (1999). The $\chi ^2$ value for the best fit should not be over-interpreted, but only used as a relative measure of the fit quality; it depends on the noise of the spectrum, which is determined by filtering the continuum between the lines with a Savitzki-Golay filter and comparing the spectrum with the smoothed continuum. A spectrum with high S/N may thus often have very small errors ($\sigma$); if there are systematic differences between model and observation (as opposed to statistical), the minimum $\chi ^2$ value will be large. The same is true, if e.g. imperfect background subtraction leaves large residuals of night sky lines or other artefacts. On the other hand, if the noise of the spectrum is large, the minimum $\chi ^2$ may be fairly small and less influenced by systematic errors.

Detailed inspection of the fits shows that typically a $\chi ^2$ value larger than about 2.5 indicates that the fit is not very good. This may be due to calibration problems, artefacts in the spectra that were introduced - or not removed - by the pipeline reduction, or the presence of e.g. He lines in the observations,

Figure 6: Mass distribution of the DA white dwarfs in Table A.1.

which are of course not included in the models of our DA grid.

 

 

Table 2: Peculiar objects with H lines. Columns contain from left to right the object name, right ascension and declination, a magnitude (usually V, B stands for photographic B magnitude, v for multichannel v magnitude), effective temperature and its formal error, surface gravity and formal error, and a remark.

object	$\alpha(2000)$	$\delta(2000)$	V	$\mbox{$T_{\rm eff}$ }$	$\Delta\mbox{$T_{\rm eff}$ }$	$\mbox{$\log g$ }$	$\Delta\mbox{$\log g$ }$	Rem
WD0058-044	01:01:02.3	-04:11:11	15.38	16700	62	8.07	0.01	1
WD0128-387	01:30:28.0	-38:30:39	15.32	27909	135	8.54	0.02	2
WD0131-163	01:34:24.1	-16:07:08	13.98	57508	1014	8.17	0.05	3
WD0239+109	02:42:08.5	+11:12:32	16.18	46859	569	7.69	0.05	4
HE0331-3541	03:33:52.5	-35:31:19	14.8B	31372	343	7.70	0.08	5
WD0347-137	03:50:14.6	-13:35:14	14.00B	21296	331	8.27	0.05	5
HE1103-0049	11:06:27.7	-01:05:15	16.2	30607	186	7.37	0.04	6
WD1247-176	12:50:22.1	-17:54:48	16.19	20922	317	8.06	0.05	5
WD1319-288	13:22:40.5	-29:05:35	15.99	18012	212	7.77	0.04	5
EC13349-3237	13:37:50.8	-32:52:23	16.34	48116	1353	6.99	0.10	5
HE1346-0632	13:48:48.3	-06:47:21	16.2	30194	301	6.94	0.06	7
WD1350-090	13:53:15.6	-09:16:33	14.55v	23794	140	7.34	0.02	8
WD2211-495	22:14:11.9	-49:19:27	11.70	63983	891	7.06	0.04	9

Remarks: 1: new magnetic DA: Zeeman triplet H$\alpha$: 6556.827/6563.044/6569.301 Å, H$\beta$ also with triplet; 2: DAB (McCook & Sion 1999); 3: several Balmer line cores with emission, H$\alpha$ possibly multiple peaks; 4: G4-34, called "probable DA+DB unresolved binary'' by Bergeron et al. (1990); it is clearly magnetic with Zeeman splitting in H$\alpha$ to H$\delta$; H$\alpha$: 6548.215/6562.455/6576.422; splitting may be variable; 5: Balmer lines with emission cores; red continuum; DA+dM binary; 6: H$\alpha$ with emission core, CaII in emission; 7: redshifted emission component in Balmer lines; 8: known magnetic (Schmidt & Smith 1994); triplet in all Balmer lines; H$\alpha$ 6555.514/6564.646/6573.778 Å; 9: emission core in H$\alpha$ and H$\beta$.

 

 

Table 3: Observed DB and parameters from spectral fitting. The next-to-last column gives the effective temperature obtained assuming $\log g = 8$. See Table 2 for further explanations of the other entries.

object	$\alpha(2000)$	$\delta(2000)$	V	$\mbox{$T_{\rm eff}$ }$	$\Delta\mbox{$T_{\rm eff}$ }$	$\mbox{$\log g$ }$	$\Delta\mbox{$\log g$ }$	$\mbox{$T_{\rm eff}$ }(\log g=8)$	Rem
HE0025-0317	00:27:41.7	-03:00:58	15.7B	19602	280	8.59	0.06	17356	1
WD0119-004	01:21:48.3	-00:10:54	16.00B	16285	85	8.25	0.05	15900
WD0119-004				16375	99	8.24	0.06	16107
WD0300-013	03:02:53.2	-01:08:35	15.56					14930	2
HE0417-5357	04:19:10.0	-53:50:46	15.1B	18785	50	8.13	0.02	18563
HE0417-5357				18773	62	8.24	0.02	17668
HE0420-4748	04:22:11.4	-47:41:42	14.7B	24285	204	8.16	0.02	24641
HE0420-4748				25176	252	8.16	0.03	25436
WD0615-591	06:16:14.5	-59:12:28	14.09	16874	94	8.22	0.04	16885
WD1149-133	11:51:50.6	-13:37:15	16.29	18607	120	8.43	0.04	17207	3
WD1149-133				19542	152	8.45	0.03	17487	3
EC12438-1346	12:46:30.4	-14:02:41	16.39	17640	81	8.28	0.04	17027
WD1336+123	13:39:13.6	+12:08:30	13.90B	16869	70	8.26	0.03	16448
HE1349-2305	13:52:44.3	-23:20:07	16.3	16770	113	7.95	0.05	16939
WD1428-125	14:31:39.6	-12:48:56	15.98	20452	194	8.39	0.03	19205
WD1428-125				20365	196	8.40	0.03	19203
WD1444-096	14:47:37.0	-09:50:06	14.98	17417	100	8.39	0.04	16639
WD2316-173	23:19:35.4	-17:05:29	14.04					11008	4
WD2316-173								12639	4

Remarks: 1: DBA with strong H$\beta$ and H$\gamma$; 2: strong CaII; no fit with variable $\log g$; 3: DBA with weak H$\beta$ 4: DBQA4 according to McCook & Sion (1999).

A more realistic determination of the parameter errors can be obtained using the two independent spectra available for many objects. For 81 normal DA with two independent determinations we find an average difference of 500 K for $T_{\rm eff}$ and 0.08 dex for $\log g$. The absolute error in $T_{\rm eff}$ is larger for the hotter DA, a reasonable estimate for all objects is to assume a one $\sigma$ error for $T_{\rm eff}$ of about 3%.

Another possibility is the comparison with parameter determinations based on long-slit spectra (since the echelle spectra also use a long slit, we will call this single-order spectra further-on) or optical and infrared photometry available in the literature for about 30 of our objects. This comparison is shown in Figs. 2 and 3. For $T_{\rm eff}$ the systematic shift is about 0.6%, for $\log g$ 0.03 dex; given the larger differences between determinations by different authors even using only high quality single-order spectra (Napiwotzki et al. 1999) this is clearly not significant. The scatter in both diagrams confirms the estimates of parameter uncertainties given above.

A more direct comparison of the combination of echelle reduction effects and the analysis is possible for 7 DA, for which we have single-order spectra with lower resolution available from different telescopes and instruments, gathered for various programs over the last 15 years at La Silla and Calar Alto. Figures 4 and 5 display the Balmer line profiles of these objects in a similar way as in Fig. 1, except that the second curve is not a model, but the lower resolution single-order spectrum. The lower resolution is most obvious in the different central line depths; there are also small wavelength shifts, and some noticeable differences also in the line wings. However, in general the agreement between echelle and single-order spectra is remarkably good. This is also demonstrated by a comparison fit to the single-order spectra, using as far as possible the same spectral intervals as for the echelle spectra. Effective temperatures and surface gravities are compared in Table 1; considering the fact that the single-order spectra are from many different sources and not necessarily of better quality than the echelle spectra, the comparison seems satisfactory, and confirms that the reduction and analysis procedures should produce results of an accuracy comparable to that for traditional single-order spectral analysis.

For those readers interested in individual objects from Table A.1 or in a general assessment of the quality of the fits we have provided in Appendix A a graphical representation of the line fits for all objects in Table A.1 (only available in the online version of the paper).

3.2 Properties of the DA sample

A statistical analysis of the DA observed in this project will be presented, when the observations of the whole sample ($\sim$1500 objects) is complete. For a very preliminary analysis we have determined individual masses for all "ordinary'' DA in Table A.1 with good determinations of atmospheric parameters, using the evolutionary mass-radius relation of Wood (1995) for "thick'' hydrogen envelope masses (10^-4 of the stellar mass). The values are also given in the table; the resulting mass distribution for 163 DA confirms the expectations based on several large-scale studies of DA white dwarfs during the last decade based on high S/N low-resolution spectra or optical and infrared photometry, e.g. Bergeron et al. (1992; Bragaglia et al. 1995; Finley et al. 1997; Bergeron et al. 1997; Napiwotzki et al. 1999). The average surface gravity is 7.89, with a one $\sigma$ width of the distribution of 0.32. The average mass is 0.59 $M_{\odot}$, with a one $\sigma$ width of 0.15 $M_{\odot}$. The mass distribution is plotted in Fig. 6, it shows the typical structure known from many previous studies: the peak between 0.45 and 0.60 $M_{\odot}$ containing the majority of DA, the secondary peak below 0.45 $M_{\odot}$, that both theory and observation ascribe to helium-core WDs resulting from binary evolution (Bragaglia et al. 1990; Marsh et al. 1995; Yungelson et al. 2000), and a tail at large masses above 1.0 $M_{\odot}$.

3.3 Peculiar spectra with hydrogen lines

A few objects show peculiar line profiles. These are summarized in Table 2. In some cases the Balmer lines have emission cores, which may be due to NLTE effects for $T_{\rm eff}$ larger than 40000 K, or to the presence of a late-type companion. Three objects are magnetic DA and show Zeeman splitting of H$\alpha$ and sometimes higher lines as well.

3.4 White dwarfs of spectral type DB

Our sample also contains a number of white dwarfs of spectral type DB. These were fitted in a way very similar to the DA sample, using a grid of DB model spectra, which employs the recent line broadening calculations of Beauchamp et al. (1997). As in the DA, there are often two solutions possible: one above and one below the temperature of maximum line strengths, which is about 20000 K in DB. We have used two different starting values (15000 and 25000 K) for the iteration. As for the DA, if the routine converged on two different solutions, we have selected the correct one from the $\chi ^2$ value and visual inspection. The results for the parameters are summarized in Table 3, Fig. 7 shows three examples for the spectra and model fits. Similar figures on a smaller scale for all objects in Table 3 are also given in Appendix A (online version only).

Figure 7: Typical spectra and model fits for helium-rich objects. From top to bottom: a DB with high S/N, a DBA with lower quality spectrum and a weak H$\beta$ line, and a DBA with strong H$\beta$ and visible H$\delta$. Over most of the spectral range the models (thinner lines) fit the spectra within the noise and can hardly be distinguished.

Figure 8: Comparison of echelle (thin line) and single-order spectra for the DB white dwarf WD1428-125 in 3 spectral regions, approximately corresponding to regions used for the spectral fitting with models.

It is generally more difficult to determine surface gravities for DB than for DA. Our results seem to be unusually high, with only one value below $\log g$ = 8.0. The average mass - determined with the Wood (1995) relation for "thin layers'', appropriate for DB - is 0.77 $M_{\odot}$, significantly higher than for the DA. This is in contradiction to previous studies (e.g. Oke et al. 1984; Beauchamp et al. 1999). Our model atmospheres use a composition of pure helium; about 20% of the DB show detectable traces of hydrogen and a small admixture of hydrogen cannot be excluded in other DB, which might affect the determination of atmospheric parameters (Beauchamp et al. 1999). We have therefore repeated the fit with a model grid with a H/He ratio of 10^-5, which results in even slightly larger surface gravities.

We have currently no explanation for this result, and do not know, whether it is real or somehow an artefact of the reduction of the echelle spectra, especially the normalization and merging of the orders. The DA spectra seem to give very reasonable results, although the individual lines are broader. However, since in the DB case many lines overlap, the wavelength regions, which are fitted in one piece are broader than for the DA. We have only one classical single-order spectrum for one of the DB (WD1428-125 = HE1428-1235) of our current sample at our disposal. A comparison of the single-order with the echelle spectra is shown in Fig. 8 for 3 wavelength regions. The echelle spectra in this case have been fitted to the single-order spectrum at the continuum points used for fitting the models in our DB analysis procedure. The agreement of the line profiles is similar as for the DA and does not show any obvious discrepancies. This spectrum has been studied in a detailed analysis by Friedrich et al. (2000), who find $T_{\rm eff}$ = 19050 K, $\log g$ = 7.87, as compared to our values of 20450/8.39. While most of the differences in the line profiles in Fig. 8 are due to the very different resolution (15 vs. 1 Å), there are obviously other small differences not compensated for by the $\chi ^2$ fitting routine, which bias the solution towards higher $\log g$ values. Because of this uncertainty, we have included in the table also a fit with surface gravity fixed to 8.00 for all objects.