A white dwarf with an oxygen atmosphere

S.O. Kepler, Detlev Koester, Gustavo Ourique

Supporting online material

S1: Observational data

Some basic information on the observational data is summarized in Table 1. The most obvious lines in the SDSS spectrum are those of oxygen and magnesium, both in the neutral and ionized state (MgI, MgII, OI, OII). Closer inspection also reveals a few lines of SiII and NeI. No other elements could be identified. Table 2 lists the vacuum wavelengths in Å and the ion identifications.

S2: Theoretical models

The spectrum was analyzed using theoretical atmosphere models and synthetic spectra for white dwarfs. The details of the methods and data used are described in []. Test calculations showed that the strengths of the lines from the ionized states can only be explained by an effective temperature (Teff) above 20 000 K. At these temperatures most white dwarfs show either very strong hydrogen or helium lines. The total absence of these lines in SDSS J124043.01+671034.68 could only mean that none of these elements dominates the atmosphere; instead oxygen must be the dominating element. The only calculation of a pure oxygen atmosphere we are aware of is shown in [] in their Figure 5, but the authors did not have observations to compare. It was necessary for us to include new atomic data into the models. We used 183 photoionization cross sections of OI, OII, MgI, MgII, NeI, and NeII obtained from the TOPBASE database [,,]. Data for all observed spectral lines were already included in our models; they are obtained using the Vienna Atomic Line Data VALD [] and National Institute of Standards databases NIST [].

S3: Determination of atmospheric parameters

In DA and DB white dwarfs the hydrogen and helium lines in the range of Teff=20000 K are very broad and dominate the whole optical spectrum. Since the pioneering work of [] and [] it is standard practice to use large regions around these lines and fit a theoretical line profile using the Χ² fitting method. With this method not only the total strength (equivalent width, EW) of the feature is used, but also its detailed shape. However, the oxygen and magnesium lines in our object are much weaker and the profiles in most cases dominated by the resolution of the spectrograph of approximately 2.5 Å. The line shape is thus just a reflection of the instrumental profile and only the EW contains information. We therefore decided to use in this case a comparison of observed and theoretical EWs instead of the fitting of large regions or the whole spectrum.

Some preliminary test calculations showed that the effective temperature must be near 22 000 K, the logarithmic number abundance ratio log N(Mg)/N(O) (henceforth abbreviated as [Mg/O]) around -1.8, [Si/O] ~ -3.5, [Ne/O] ~ -1.4. We therefore calculated a two-dimensional grid with the variables Teff from 18 000 to 25 000 K in steps of 1000 K, and [Mg/O] from -1.35 to -2.10, with steps 0.15. We started the analysis assuming a value of logg, the typical value for most white dwarfs (13). The abundances of Si and Ne, which have no significant influence on the equivalent widths of O and Mg, where kept fixed. After the final parameters were determined, we confirmed (below) that the abundances used are the correct final values.

Equivalent widths for the strongest features in the observed spectrum were measured using the intervals given in Table 3 for the continuum definition. The EWs were measured by fitting a Lorentzian profile or using direct numerical integration depending on whether the absorption feature is a well defined line or a more complicated blend. The EWs and their errors are also given in Table 3. The same intervals were used to define the theoretical EWs in the models; they are also given in Table 3 for loggand [Mg/O] = -1.80. The last row gives the χ² values from the comparison of observed and theoretical EWs. These are reduced χ² values, i.e. divided by the number of degrees of freedom n_free (24 = 26 EWs - 2 parameters, Teff and [Mg/O]).

Similar comparisons were made for the other abundance ratios and Table 4 shows the complete χ² table for the whole grid. These values χ²(Teff,[Mg/O]) were then fit with a second order parabolic surface, which determined the location of the minimum and the 90% confidence intervals from the confidence ellipse defined by χ² = χ²_m + 2.71/n_free []. The final result for the best fitting parameters at fixed loggis

Teff= 21700±620 K, [Mg/O] = -1.69±0.11, χ²_m = 1.302

We calculated similar grids for other logg values and repeated the whole procedure for loggto 8.50, with step width 0.25. The corresponding χ² tables are Table 5-8, in the same format as Table 4. The best fitting minimum χ² solutions for all logg values are collected in Table 9.

The lowest overall minimum is near loggFitting a parabola to find the minimum we obtain the final adopted solution

Teff = 21590±620 K, logg = 7.93±0.17, [Mg/O] = -1.70±0.13, χ²_m = 1.287

We note that the minimum χ² value is slightly larger than 1.0. The reason is that we included only statistical errors from the EW measurements. Systematic errors from the reduction of the observations, the models, the atomic data, and possibly other sources are impossible to quantify. This underestimate of the errors leads to smaller errors of the final parameters. We correct for that effect by dividing the χ² values with the minimum value χ²_m - equivalent to increasing all errors by a constant factor - and repeat the determination of the error ellipse. This does not change the location of the minimum, but results in slightly larger and more realistic errors. This has been used in all error determinations.

Using the mass-radius relation of the Montreal group for white dwarfs without outer hydrogen layer [,,,], we can determine the mass and radius for the object

M = 0.56±0.09 M_\odot R = 0.01348±0.00317 R_\odot

For the cool oxygen-rich white dwarfs in (10) it has been impossible to determine masses from the spectra. It is surprising that in this case a fairly accurate determination is possible. How robust is the determination of the surface gravity and the relatively low mass? This is certainly the most important question raised by our analysis. Theory predicts that carbon burning (the most likely origin of the abundances) should only occur after the stellar C/O core has reached a mass larger than 1 M_\odot. The uncertainty of the surface gravity, logg = 7.93±0.17, is formally the 90% confidence interval from the χ² fitting. Using the 99% confidence interval would increase the uncertainty to 0.24. A value of logg = 8.75, which corresponds to 1.06 M_\odot, the theoretical minimum for the start of carbon burning, is therefore excluded with very high confidence. This, however, assumes that the errors are purely statistical in the observations and that the models are correct.

In contrast to the cool oxygen-rich white dwarfs we observe ions of different ionization. The equilibria for MgI/MgII and OI/OII, and therefore the ratios of line strengths between neutral atoms and ions, depend on temperature and surface gravity (through the pressure in the Saha equation). On the other hand, the ratio of line strengths within one ionization stage depends (apart from the fixed atomic data) only on temperature through the difference in the excitation potentials of the lower levels, which for OI, e.g., range from approximately 9-14 eV. This combination allows for the determination of the surface gravity.

Possible sources of uncertainties of the parameters, and especially the mass, are the atomic data. We used the VALD database and compared wavelengths and oscillator strengths for all important lines against the critically evaluated data in the NIST database. Line broadening constants for Stark broadening were obtained from VALD. The lines in this object are weak and at this temperature dominated by impact broadening through the Stark effect. This is much less complicated than in the case of the extremely strong H and He lines, where the broad wings depend on the exact nature of the interaction potential. It is also much better understood than the neutral broadening in the cooler oxygen-rich stars. To our knowledge we are using the most accurate atomic data available. While future measurements or calculations might bring some changes, a significant change of our results is unlikely.

S4: Other elements

The abundances for Si and Ne were determined less formally. With Teff and logg fixed at the final values, we calculated models with the Si and Ne abundance changing in steps of 0.1 dex until the best fit, as well as upper and lower limits, were found by visual inspection. The lines 4129.219, 4132.037, 4132.059 Å (SiII) and 6404.016, 6600.776, 6680.120, 6718.897 Å (NeI) were used, with the results given in Table 10. The best fitting values were still the ones used already in the grid calculation, confirming the consistency of the analysis. The NeI lines are weak and individually not convincing detections. However, all the strongest lines and several more of the weaker ones coincide with absorption features, and the non-detections of the remaining ones are consistent with the model predictions. We are thus convinced that the Ne detection is real. For upper limits of the elements most often observed in polluted white dwarfs (H, He, C, Ca, Fe) we similarly increased the abundances until the strongest lines became clearly detectable. These upper limits are also given in Table 10.

These elements had not been included in the grid models. In particular the high upper limit for He could possibly change the fit results, if these elements were indeed present in the object. We have therefore repeated the whole procedure, including all the above elements with their maximum possible abundance. The final result with these models is

Teff = 21640±640, logg = 7.98±0.16, [Mg/O] = -1.74±0.12, χ²_m = 1.268 .

The final atmosphere model has a convection zone from Rosseland optical depth t = 0.2 down to the bottom of our model at t = 1000. Our envelope code currently is not suited for oxygen-rich matter, and we do not know the total extent of the convection zones and the total H and He masses. Because of the atmospheric convection it is plausible that all observed elements remain mixed with the oxygen, which is the lightest of these elements. If a large amount of hydrogen would be present we would expect this to diffuse out of the top of this zone and form a hydrogen layer, which at this temperature would not be convective. This is analogous to the usual assumption that heavy metals diffuse out of a H or He convection zone at the bottom. Helium, however, would have an outer convection zone and thus very likely stay mixed with the oxygen zone. Since even with the maximum possible abundances of H and He the final result agrees within the errors with the analysis using only observed elements, we prefer to retain the results from the latter.

The best fitting model (convolved with a 2.5 Å Gaussian to account for the resolution) is provided as (wavelength, flux) table with a simple header.

S5: Photometry

From the model grid with the abundances close to the final values, we calculated theoretical magnitudes in the SDSS and GALEX filters. These were used to fit the observed magnitudes. The surface gravity has to be kept fixed, since the photometry is almost independent of logg, as is evident from the first 3 rows in Table 11. Since the distance above the Galactic plane z for the final result is larger than 250 pc, the maximum reddening value of E(B-V) = 0.018 from the dust maps of [] was used. The distance is calculated from the solid angle of the star (the factor between theoretical and observed magnitudes) and the radius of the white dwarf. The effective temperatures are consistently lower than the spectroscopic result. Possible explanations are a larger reddening than indicated by the dust map, or some (unknown) differences between observed and theoretical spectra in the UV, which could affect the slope in the optical region. The lower Teff obtained when including the GALEX photometry indicates that some UV absorption might be missing in our models. Generally, the photometry at these relatively high temperatures is not very sensitive to temperature, and even in much better studied DA white dwarfs differences up to 2000 K between spectroscopic and photometric solutions are found []. We therefore prefer the spectroscopic solution. The best distance estimate is then obtained with Teff and logg fixed at the spectroscopic results and only distance as variable (last row in Table 11).

Table 1: Basic information on observational data


object name	SDSS J124043.01+671034.68
coordinates (J2000)	RA = 12:40:43.01, d = 67:10:34.68
spectrum	P-M-F 7120-56720-0894, S/N = 23
SDSS ugriz	17.880, 18.244, 18.587, 18.875, 19.096
ugriz errors	0.025, 0.022, 0.017, 0.020, 0.062
GALEX FUV, NUV	17.93,17.52
FUV, NUV errors	0.08, 0.04
proper motion	201.7 mas/yr

The spectrum can be downloaded at

http://dr12.sdss3.org/sas/dr12/sdss/spectro/redux/v5_7_0/spectra/7120/spec-7120-56720-0894.fits and the SDSS photometry from

http://skyserver.sdss.org/dr7/en/tools/explore/obj.asp?ra=12%2040%2043.01&dec=+67%2010%2034.68.

Table 2: Line identifications ordered by vacuum wavelength in Å. Uncertain detections are indicated with a colon.


l[Å]	atom or ion

3830.441, 3833.386, 3833.391, 3839.381,3839.384	MgI
3849.302, 3849.432, 3851.478	MgII :
3857.112, 3863.690	SiII :
3893.009, 3896.676	MgI
3948.410, 3948.598, 3948.703	OI
4070.770, 4071.030, 4073.300, 4077.010	OII :
4129.219, 4132.037, 4132.059	SiII
4346.780, 4350.650	OII :
4369.486	OI
4385.869, 4391.748, 4391.806	MgII
4429.238, 4435.232, 4437.838	MgII
4482.383, 4482.407, 4482.583	MgII
4640.150, 4643.110, 4650.440, 4652.140, 4662.940	OII
4740.918, 4852.425, 4852.455	MgII
5042.430, 5057.394, 5057.727	SiII
5168.761, 5174.125, 5185.047	MgI
5330.578 -5332.224	OI
5403.022, 5403.058	MgII
5436.689, 5437.286, 5438.370	OI
5690.396, 5702.952	SiII
5854.110	NeI :
6076.019, 6097.851	NeI :
6107.956	OI :
6158.482, 6159.891	OI
6263.279, 6268.625	OI :
6268.228	NeI :
6348.498, 6348.509, 6348.719	MgII
6373.132	SiII
6384.756, 6404.016	NeI
6455.386, 6456.228, 6457.761	OI
6547.750, 6547.803	MgII
6600.776	NeI
6680.120	NeI
6718.897	NeI
6931.378	NeI
7003.853,7004.161	OI
7034.352	NeI :
7158.670, 7256.150, 7256.447	OI
7774.083, 7776.305, 7777.528	OI
7879.222, 7898.539	MgII
7949.354, 7949.734, 7952.991, 7954.347	OI
8216.245, 8225.166, 8225.207, 8235.456	MgII
8448.568, 8448.680, 8449.079	OI

Table 3: Wavelength intervals and measured EWs in Å (estimated 1s errors in parentheses), and theoretical EWs for different effective temperatures of the model. Surface gravity was fixed at logg, [Mg/O] = -1.80. The final row gives the reduced χ² for each column.


l region	EW(obs)	EW(th) for Teff [K]
		18000	19000	20000	21000	22000	23000	24000	25000
MgI 3811 - 3874	9.07 (0.80)	12.93	11.77	10.58	9.41	8.30	7.25	6.26	5.33
MgI 3883 - 3908	0.98 (0.40)	2.45	1.96	1.43	0.91	0.39	0.00	0.00	0.00
MgI 5164 - 5195	1.45 (0.30)	3.75	3.02	2.39	1.89	1.51	1.23	1.04	0.91
MgII 4376 - 4413	3.64 (0.35)	3.73	3.71	3.62	3.46	3.26	3.02	2.78	2.50
MgII 4420 - 4450	2.16 (0.35)	2.02	2.00	1.92	1.78	1.60	1.38	1.13	0.86
MgII 4449 - 4552	11.35 (0.50)	12.79	12.34	11.84	11.31	10.78	10.27	9.79	9.30
MgII 4825 - 4878	1.55 (0.35)	1.49	1.59	1.64	1.62	1.54	1.45	1.35	1.24
MgII 5376 - 5423	1.75 (0.60)	1.26	1.46	1.59	1.67	1.66	1.64	1.59	1.53
MgII 6312 - 6395	5.49 (1.20)	4.63	4.84	4.97	4.99	4.91	4.80	4.66	4.51
MgII 6504 - 6575	5.39 (0.50)	4.60	4.68	4.66	4.57	4.45	4.33	4.19	4.10
MgII 7839 - 7924	7.52 (0.80)	6.74	6.68	6.59	6.47	6.37	6.28	6.22	6.18
MgII 8188 - 8280	6.41 (1.50)	8.47	8.23	7.96	7.70	7.47	7.27	7.12	7.01
OI 3937 - 3963	1.57 (0.35)	2.81	2.64	2.47	2.34	2.24	2.18	2.15	2.14
OI 4360 - 4377	0.59 (0.20)	0.98	0.88	0.78	0.72	0.67	0.64	0.63	0.63
OI 5301 - 5370	3.47 (0.40)	5.17	4.78	4.33	3.91	3.52	3.21	2.93	2.69
OI 5421 - 5472	2.25 (0.30)	3.04	2.79	2.51	2.24	2.01	1.81	1.64	1.50
OI 6125 - 6230	6.67 (0.50)	9.37	9.00	8.57	8.18	7.84	7.55	7.33	7.16
OI 6237 - 6294	1.71 (0.50)	0.17	0.28	0.39	0.49	0.59	0.67	0.72	0.75
OI 6425 - 6503	3.73 (0.80)	5.48	5.05	4.58	4.11	3.71	3.38	3.10	2.91
OI 6970 - 7082	6.77 (1.00)	5.84	5.61	5.36	5.13	4.98	4.83	4.71	4.60
OI 7120 - 7184	1.65 (0.40)	2.36	2.28	2.19	2.10	2.03	1.98	1.94	1.92
OI 7231 - 7294	2.65 (0.60)	3.25	3.08	2.89	2.72	2.58	2.48	2.39	2.32
OI 7720 - 7818	6.90 (1.00)	7.62	7.22	6.80	6.42	6.11	5.87	5.68	5.55
OI 7930 - 7976	3.04 (0.50)	2.76	2.66	2.57	2.49	2.43	2.42	2.45	2.47
OI 8406 - 8513	7.42 (2.00)	8.81	8.44	8.05	7.72	7.42	7.23	7.04	6.92
OII 4632 - 4672	1.26 (0.50)	0.33	0.57	0.88	1.21	1.57	1.94	2.29	2.62
χ²		8.550	4.971	2.580	1.517	1.505	2.327	3.771	5.698

Table 4: χ² table for logg the two-dimensional grid with Teff and [Mg/O] as parameters.


[Mg/O]	Teff[K]
	18000	19000	20000	21000	22000	23000	24000	25000
-2.100	9.145	5.984	4.019	3.340	3.738	4.965	6.847	9.236
-1.950	8.623	5.185	3.008	2.114	2.299	3.317	4.992	7.112
-1.800	8.550	4.971	2.580	1.517	1.505	2.327	3.771	5.698
-1.650	8.896	5.201	2.710	1.503	1.347	1.988	3.244	4.905
-1.500	9.610	5.903	3.353	2.038	1.743	2.244	3.310	4.783
-1.350	10.759	7.033	4.456	3.059	2.646	3.006	3.934	5.202

Table 5: χ² table for logg the two-dimensional grid with Teff and [Mg/O] as parameters.


[Mg/O]	Teff[K]
	18000	19000	20000	21000	22000	23000	24000	25000
-2.100	6.863	4.847	4.012	4.187	5.149	6.673	8.703	11.111
-1.950	6.147	3.932	2.932	2.927	3.710	5.050	6.876	9.054
-1.800	6.041	3.661	2.481	2.318	2.960	4.130	5.738	7.713
-1.650	6.482	3.935	2.598	2.302	2.778	3.809	5.254	7.003
-1.500	7.391	4.683	3.204	2.793	3.162	4.059	5.348	6.936
-1.350	8.742	5.835	4.223	3.672	3.956	4.753	5.902	7.350

Table 6: χ² table for logg the two-dimensional grid with Teff and [Mg/O] as parameters.


[Mg/O]	Teff[K]
	18000	19000	20000	21000	22000	23000	24000	25000
-2.100	7.683	5.069	3.687	3.434	4.104	5.526	7.478	9.874
-1.950	7.024	4.183	2.603	2.184	2.701	3.895	5.657	7.810
-1.800	6.922	3.906	2.160	1.558	1.918	2.962	4.505	6.443
-1.650	7.317	4.178	2.291	1.574	1.777	2.646	4.009	5.715
-1.500	8.191	4.945	2.954	2.107	2.188	2.929	4.112	5.646
-1.350	9.496	6.146	4.052	3.104	3.075	3.682	4.730	6.100

Table 7: χ² table for logg the two-dimensional grid with Teff and [Mg/O] as parameters.


[Mg/O]	Teff[K]
	18000	19000	20000	21000	22000	23000	24000	25000
-2.100	11.363	7.907	5.394	4.213	4.232	5.194	6.949	9.205
-1.950	10.936	7.217	4.445	3.010	2.777	3.494	5.004	7.046
-1.800	10.844	6.994	4.058	2.408	1.938	2.476	3.718	5.527
-1.650	11.096	7.229	4.186	2.375	1.739	2.068	3.098	4.673
-1.500	11.637	7.806	4.741	2.842	2.101	2.239	3.055	4.418
-1.350	11.386	8.751	5.716	3.781	2.938	2.910	3.558	4.709

Table 8: χ ² table for logg the two-dimensional grid with Teff and [Mg/O] as parameters.


[Mg/O]	Teff[K]
	18000	19000	20000	21000	22000	23000	24000	25000
-2.100	14.320	10.920	8.010	6.236	5.734	6.313	7.770	9.901
-1.950	13.877	10.328	7.109	5.050	4.265	4.562	5.784	7.644
-1.800	13.769	10.064	6.738	4.456	3.404	3.460	4.399	6.007
-1.650	13.902	10.191	6.788	4.375	3.108	2.954	3.645	4.988
-1.500	14.203	10.609	7.205	4.725	3.360	3.031	3.499	4.578
-1.350	14.748	11.238	7.960	5.469	4.045	3.546	3.835	4.714

Table 9: Best fitting solutions (Teff, [Mg/O]) for different surface gravities. Numbers in parentheses are the errors from the determinations at fixed logg.

logg

Teff[K]

[Mg/O]

χ²_m

7.50

20864 (821)

-1.719 (0.154)

2.249

7.75

21274 (605)

-1.710 (0.113)

1.449

8.00

21703 (617)

-1.687 (0.111)

1.302

8.25

22201 (662)

-1.652 (0.131)

1.725

8.50

22824 (921)

-1.591 (0.172)

2.889

Table 10: Logarithmic number abundance ratio to oxygen or upper limits for elements other than oxygen and magnesium. The errors are not formally derived, but correspond rougly to 2s errors.


element	abundance
[Ne/O]	-1.40 ± 0.30
[Si/O]	-3.50 ± 0.20
[H/O]	< -3.00
[He/O]	< -1.50
[C/O]	< -2.30
[Ca/O]	< -5.50
[Fe/O]	< -2.90

Table 11: Fitting observed photometry with theoretical magnitudes. In the first 5 rows the surface gravity is kept fixed. In the last row temperature and surface gravity are kept fixed at the spectroscopic solution. The distance is d, the height above the Galactic plane z. For our adopted spectroscopic solution (last row) the distance error is 50 pc, if the atmospheric parameters are allowed to vary within their errors.


method	Teff[K]	logg	d[pc]	z[pc]
fixed logg, SDSS photometry	20067 (322)	7.500	451	345
	19930 (278)	8.000	321	246
	19803 (243)	8.500	222	170
spectroscopic logg fixed	19957 (290)	7.930	337	258
SDSS+GALEX photometry, logg fixed	19747 (240)	8.000	319	244
spectroscopic Teff,logg fixed	21590	7.930	361	276