Laboratory hydrogen-beta emission spectroscopy for analysis of astrophysical white dwarf spectra

This work communicates a review on Balmer series hydrogen beta line measurements and applications for analysis of white dwarf stars. Laser-induced plasma investigations explore electron density and temperature ranges comparable to white dwarf star signatures such as Sirius B, the companion to the brightest star observable from the earth. Spectral line shape characteristics of the hydrogen beta line include width, peak separation, and central dip-shift, thereby providing three indicators for electron density measurements. The hydrogen alpha line shows two primary line-profile parameters for electron density determination, namely, width and shift. Both Boltzmann plot and line-to-continuum ratios yield temperature. The line-shifts recorded with temporallyand spatiallyresolved optical emission spectroscopy of hydrogen plasma in laboratory settings can be larger than gravitational redshifts that occur in absorption spectra from radiating white dwarfs. Published astrophysical spectra display significantly diminished Stark or pressure broadening contributions to red-shifted atomic lines. Gravitational redshifts allow one to assess the ratio of mass and radius of these stars, and subsequently, the mass from cooling models.


Introduction
The investigation of spectral characteristics from stellar objects leads to an understanding of their characteristics.Measurement of sun spectra allows one to infer surface temperature.Hydrogen Balmer series absorption spectra are communicated in Rowland tables [1,2] that map the sun.The equivalent widths [3] of the hydrogen alpha line, H α , hydrogen beta line, H β , and hydrogen gamma line, H γ from the sun amount to 0.402 nm, 0.368 nm, and 0.286 nm, respectively.White dwarf spectra that show hydrogen lines are designated as DA stars.The white dwarf (WD) companion to Sirius A, designated as Alpha Canis Majoris B (α CMa B) [4], reveals significant hydrogen spectra at a temperature of 26 kK [5].For comparison with the sun spectra, H γ of Sirius B shows an equivalent width [6] of 3.1 nm.
Laboratory measurements with so-called optical emission spectroscopy in a high-current arc [7,8] suggest that observed gravitational redshifts in WD spectra [9,10] may require corrections due to contributions from Stark-effect caused redshifts [11].Radiative-transfer considerations [12] however confirm that the Stark or pressure shifts have no material or substantial effect on the measurement of gravitational redshifts.With an observed redshift uncertainty between 5 and 10 km/s [12], the pressure shifts are smaller than the error margins.A recent discussion [13] elaborates on the computation of Stark line profiles in successive layers of an WD atmosphere, and concludes that the Stark effect does not cause substantial redshifts.
Extensive hydrogen modeling [20] and detailed analysis of Balmer series lines including the H β peak separation [21,22] reflect the level of knowledge about laboratory plasma, including recent systematic experimental efforts [18,19].In view of astrophysical WD absorption data [5], laboratory spectra and analysis are essential for determination of astrophysical WD characterization.Experiments utilize frequently other macroscopic measurement methods including photography [23].H β is of interest due to providing better accuracy [24][25][26] than H α for an electron density of the order of 10 17 cm −3 .
A generally accepted method for the determination of the mass of WD's is based on gravitational redshifts [10].In this approach [38], the mean gravitational redshift, v g , is determined first to find the mass-radius ratio, where c and G are the speed of light and gravitational constant, respectively.The symbols M and R indicate respectively the mass and radius of the WD.The redshift, ∆λ, at the wavelength, λ, of the selected line is usually extracted by fitting a line shape to recorded absorption profiles.
The gravitational redshift is commonly expressed in units of km/s, with M and R in solar units, From effective temperature and from evolutionary cooling models [39], the average mass of 449 non-binary DA stars [38] equals 0.65 times the mass of the sun.Details of WD spectra are further investigated by utilizing sufficiently bright light sources for direct measurement of plasma absorption spectra [40,41].
Regarding Sirius B, analysis of extreme ultraviolet explorer data [42] concludes with a set of parameters to describe this white dwarf Sirius A companion.Table 1 displays the inferred [42] important characteristics, namely, temperature, gravity, mass, and radius.Knowledge of the WD mass of course is important in order to determine whether the mass is close to the Chandrasekhar limit of 1.44 × solar mass [44].Additionally, a WD in a binary star configuration that exists within the Roche limit [45] of the larger companion may contribute sufficient mass to lead to a supernova.
Typical sizes of WD's are comparable to the earth but with a mass similar to that of the sun.
Investigations of H β widths, peak separations, and central dip-shifts in the laboratory further elucidate an understanding of white dwarf stars.This work focuses on various aspects of hydrogen Balmer series measurements of laser-induced plasma, including recently communicated findings in the laboratory [18,19] for conditions encountered for DA type WD's.Laser-induced plasma experiments consistently confirm H β central dip-shifts.

Results
The laboratory results of the hydrogen beta line, H β , and hydrogen alpha line, H α , of the Balmer series are reviewed first.Selected data from the WD Montreal data base [5] are communicated along with approaches that are common in the astrophysics communities.However, considering the vast variety of scientific papers devoted to the study of astrophysical objects in the optical region, this review presents aspects of laboratory H β spectroscopy and its application to white dwarf stars.

Laboratory experiments
Line-of-sight and radially resolved data, obtained by Abel inversion, are modeled using computed asymmetric profiles [31].Detailed experiments on H β emission spectroscopy [19] explore the radial distribution of laser-induced plasma in hydrogen gas.
The determination of electron density, N e , from the hydrogen beta line frequently employs well-established empirical identities [20][21][22], N e [cm −3 ] = ∆w Hβ 4.8 1.46808 or utilizes results from generalized line shape theory [16] in analysis of laser-induced laboratory plasma [17].The fitted asymmetric H β profiles indicate central dip-shifts.A systematic study [18] confirms H β central wavelength shifts and relates the central dip-shift [18,46,47]    The line shape of the hydrogen beta line, H β , due to the Stark effect [48] is described by a Holtsmark profile when considering ion broadening only [49].But when accounting for various line broadening phenomena [50] such as Debye shielding, ion and electron broadening, and ion-ion correlations [24,25], the hydrogen beta line profile shows modified central dip and Lorentz line shape    Spectra recorded with resolving powers of 800 to 1800 (spectral resolution of 0.61 to 0.27 nm at the H β 486.14-nm wavelength) rarely if at all show evidence of the hydrogen beta central peak separation.At N e of 1 × 10 17 cm −3 , the peak separation and central dip-shift in the laboratory micro-plasma would respectively amount to 1.3 nm and 0.14 nm, but again, radiative transfer considerations (e.g., see Ref. [13]) indicate that the astrophysical WD spectra do not show significant Stark shifts.
Selected data records of the Sloan digital sky survey [55,56] presents 9316 spectroscopically confirmed white dwarfs, and several WD stars are further analyzed [57].As an example of a magnetic DA type star (DAH), the Zeeman triplets are nicely recognizable in Fig. 5. Magnetic white dwarfs pose challenges [58] in the modeling of the recorded absorption spectra.Figure 5    The H β and H α profiles in Fig. 5 indicate Zeeman-split blue-and red-peak separations respectively of σ β = 14.6 nm and σ α = 26.6 nm.The ratio of the H α peak separation, σ α , and H β peak separation, σ β , is equal to the square of the ratio of H α and H β wavelengths, as expected, although the line shapes appear asymmetric due to Stark broadening.For H α and H β , the Zeeman-splits amount to an energy shift 0.038 eV on each side of line center.The shifts in Fig. 5 imply magnetic fields of the order of 500 Tesla, also indicated in the computed H α Zeeman triplet [58] for a magnetic field of 500 Tesla.The electron density estimate equals 3.1 × 10 17 cm −3 , determined from FWHM of the central absorption of H β , ∆w Hβ = 10 ± 1 nm, and H α , ∆w Hα = 2.7 ± 0.5 nm.
Several of the previously discussed white dwarf spectra show a spectral resolution of the order of 1000.However, it would be not unusual to achieve resolving powers of 40,000 (or 0.012 nm at the H β wavelength) with Echelle spectrometers, for instance, when using the so-called HIRES Echelle spectrometer [59].The analysis utilizes readily available software, or already extracted sections of an Echelle spectrum.The overall spectral record is composed of parts from different spectral order.
Figure 6 shows data for HG 7-85 from the Hyades cluster.The data displayed in Figure 6 are available at KOA [60] following observations [61] on October suggest that the spectrum is composed of broad and narrow H β components.The narrow component would imply an electron density that is over two orders of magnitude smaller than that for the broad component.
The gravitational shift of HG 7-85 [61] is 44.3 km/s.Using Equation ( 1), the corresponding wavelength shift at 486.14 nm amounts to ∆λ = 0.072 nm.Note that the center wavelength of the broad Lorentzian fit is at 486.22 nm, or shifted by 0.08 nm .Clearly, further modeling of the atmosphere condition for this Hyades WD would be needed to evaluate the accuracy of this inference.However, the appearance of the H β spectrum from HG 7-85 could very well indicate absorption from a dense and two orders of magnitude less dense WD atmosphere, as perhaps suggested for other WD's by including carbon, nitrogen, and oxygen in WD atmospheres models [36].

Discussion
Broadly speaking, laboratory measurements of the hydrogen Balmer series in the optical region of the electromagnetic spectrum show significant applications in the study of white dwarfs.The research efforts on modeling line shapes extend over several decades if not centuries.At an electron density of 10

Materials and Methods
The experimental arrangement for the laboratory studies include a pulsed, Q-switched, Nd:YAG laser device operated at pulse-widths of 6 to 13 ns using different models.Figure 7 illustrates the schematic for laser-induced plasma experiments inside a laboratory cell.Laser-induced optical breakdown is accomplished by focusing 150 mJ per pulse of fundamental 1064-nm radiation to achieve of the order of 1000 GW/cm 2 in a cell containing hydrogen gas.Typically, crossed Czerny-Turner spectrometers of 0.25-nm or 0.64-nm focal length disperse the hydrogen lines.
In addition, studies of plasma in air or following laser ablation contribute to the set of investigations.
A photomultiplier, linear intensified diode array or an intensified charge-coupled device record spectrometer-dispersed light.
Usual sensitivity correction, wavelength calibration, and detector background subtraction deliver data records suitable for analysis that includes de-convolution from the detection system transfer function.An overview video [63] of the measurement protocol provides sufficient detail for laser-induced breakdown spectroscopy for atomic and diatomic molecular analysis [64].
Spectral resolutions for linear diode arrays or ICCD's of the order of 0. the H α spectral resolution of 0.02 nm is realized, or a resolving power of 33,000 at 656.28 nm.For H β , spectral resolving powers of the order of 50,000 at 486.14 nm or a resolution of 0.01 nm with the JY spectrometer would in principle be available when using a photomultiplier that preferably would need to be gated for accurate measurements at longer time delays of say 175 ns, in order to block the early and intense plasma radiation as the line emerges from the free electron background radiation.
The analysis of the recorded line profiles, over and above the evaluation of the FWHM, includes fitting of tabulated profiles [24,25], fitting to Voigt profiles or Lorentz profiles, and recently, fitting to asymmetric hydrogen beta profiles [31].The latter approach allows one to efficiently analyze Abel-inverted data sets in investigations of radial plasma expansion phenomena.

Conclusions
The laboratory laser-induced plasma investigations using temporally-and spatially-resolved spectroscopy clearly indicate direct application to determination of astrophysical white dwarf parameters.Data collection with a resolving power of the order of 50,000 to 75,000 or better appears to be desirable for astrophysical and laboratory spectra in order to determine accurate hydrogen beta line profile parameters for the encountered white dwarf spectral redshifts and electron densities.
Moreover, the line shape of especially the hydrogen beta line deserves further theoretical attention in order to exactly reconcile asymmetries and shifts noticeable in laboratory optical emission spectroscopy and in part discernible in recorded astrophysical absorption spectra.Previous laser-induced plasma work [17] addresses determination of electron density from full widths at half-maximum of the Balmer series hydrogen-beta line, H β , peak-separation of H β , and comparisons with hydrogen-alpha line, H α , results.Re-analysis in view of the central dip-shifts in Figs. 1 (a) and 1 (b) of Ref. [17] shows values of (0.5 ± 0.025) nm and (0.33 ± 0.025) nm, respectively, that lead to N e of (6.7 ± 0.5) × 10 17 cm −3 and (3.6 ± 0.4) × 10 17 cm −3 .These values are consistent with the determined N e from in the last column of Table 2 in Ref. [17].

Appendix B. Typical laboratory spectra of H β and H α
Recent laboratory experiments [18]

For
different time delays, τ, from plasma initiation, Figures1 and 2(a) display recorded and fitted line-of-sight and Abel-inverted spectra for hydrogen gas in a cell at a pressure of 1.06 × 10 5 Pa, and 2(b) shows the center H β portion at a cell pressure of 1.32 × 10 5 Pa.

Figure 3
Figure 3 illustrates spectra from Sirius B and Procyon B, indicating hydrogen Balmer series lines and C 2 Swan molecular spectra in absorption, respectively.The resolving power, R, for the Sirius B spectrum in Fig. 3(a) equals R ∼ 555, or a spectral resolution of 0.88 nm that is too coarse for determination of the expected 0.144-nm redshift.Procyon B (α CMi B) is further evolved [51] in its life time, and it shows a temperature of 8 kK.Procyon B is classified as DQZ type WD and reveals molecular spectra of C 2 due to a carbon-rich and metal-rich atmosphere.Sirius B (α CMa B) reveals a temperature of 26 kK [52] and a typical spectrum for DA white dwarfs.These two stars form the so-called Winter Triangle with Betelgeuse of the constellation Orion.

28 and 29 ,
2012.Fig. 6(a) displays the overlays from Echelle orders, and it shows a broad Lorentzian (dashed) with FWHM of 10 nm, centered at 486.22 nm.Fitting of the composite Echelle spectra is accomplished using publicly available software [62].The width implies an electron density of 3.1 × 10 17 cm −3 .The expanded core of the spectrum indicates a shift of 0.3 nm -coincidentally, if time-resolved emission spectroscopy were applied to characterize laboratory plasma, a shift of 0.3 nm (strictly speaking a dip-shift of resolved H β blue and red peaks) would indicate N e of 3.1 × 10 17 cm −3 as well.Fig. 6(b) illustrates a narrow Lorentzian of width 0.19 nm.A FWHM of 0.19 nm would yield an electron density of 0.012 × 10 17 cm −3 .Comparisons with H β laboratory results however would

Figure 7 .
Figure 7.Typical experimental arrangement for generation and measurement of laser-induced plasma.
Figures B.1 and B.2 show H β and H α pseudo-colored images for a time delay, τ, of 250 ns from laser-plasma initiation.The Figs. also show the corresponding averages along the slit.From the FWHM and using formulae in Appendix A, the average electron density is N e = 2.1 × 10 17 cm −3(see TableA1in Appendix A).The electron temperature, T e , equals 50 kK (4.3 eV) for τ = 250 ns[18], evaluated from line-to-continuum and Boltzmann plots with an error margin of ± 10 kK (0.86 eV).

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 31 May 2018 doi:10.20944/preprints201805.0459.v1
[43]urements from the Hipparcos satellite, operated between 1989 and 1993 by the European Space Agency, indicate slightly different parameters for Sirius B when compared to the data in Table1.Table2summarize the measurements for Sirius B and Procyon B based on Hipparcos parallaxes[43].
also compares H β and H α Zeeman-split and asymmetric Stark-broadened line shapes.

preprints.org) | NOT PEER-REVIEWED | Posted: 31 May 2018 doi:10.20944/preprints201805.0459.v1 Peer
17cm −3 , H β and H α widths are well over one order of magnitude larger than Stark-effect redshifts that are measured in laboratory plasma.However, astrophysical data obtained with increased resolution available at observatories motivate and require accurate measurements of the line shapes and the gravitational redshifts.Accurate laboratory data, modeling and advances in theory are expected to contribute to precise inferences Preprints (www.-reviewedversion available at Atoms 2018, 6, 36; doi:10.3390/atoms6030036about white dwarf stars, especially for WD's with radiation temperatures in excess of the order of 26 kK or that of Sirius B.
× 10 17 cm −3 .However, redshifts for N e of 10 × 10 17 cm −3 are large enough to achieve acceptable error margins.For H β and H α , the ratio of width to central dip-shift and redshift amounts to 32 and 24, respectively, at 1 × 10 17 cm −3 with a weak N e dependency as indicated in Appendix A. Noteworthy, for the experiments with a photomultiplier and moving 3600 grooves/mm grating of the JY spectrometer,

Table A1 .
[18]age H β central dip-shifts, widths, and electron densities, N e , from dip-shifts and widths for selected time delays of optical breakdown in 0.76 × 10 5 Pa hydrogen gas[18].