LS IV-14^{\circ}116: radial velocities

Radial velocity measurements of the pulsating zirconium star: LS IV1

Abstract

The helium-rich hot subdwarf LS IV  shows remarkably high surface abundances of zirconium, yttrium, strontium, and germanium, indicative of strong chemical stratification in the photosphere. It also shows photometric behaviour indicative of non-radial g-mode pulsations, despite having surface properties inconsistent with any known pulsational instability zone. We have conducted a search for radial velocity variability. This has demonstrated that at least one photometric period is observable in several absorption lines as a radial velocity variation with a semi-amplitude in excess of 5 . A correlation between line strength and pulsation amplitude provides evidence that the photosphere pulsates differentially. The ratio of light to velocity amplitude is too small to permit the largest amplitude oscillation to be radial.

keywords:
asteroseismology,, stars: chemically peculiar, stars: subdwarf, stars: individual (LS IV), stars: pulsation
36

1 Introduction

The helium-rich hot subdwarf LS IV  is remarkable for several reasons. Its peculiarity was first recognised in a spectroscopic follow-up of UV-excess objects (Viton et al., 1991). Subsequent analyses confirmed the excess helium abundance and high effective temperature ( T), making it one of relatively few such stars (Ahmad & Jeffery, 2003, 2004), and the only one to show photometric variability (Ahmad & Jeffery, 2005). Follow-up photometry confirmed the star to be a multi-periodic variable, almost certainly a non-radial g-mode oscillator (Jeffery, 2011; Green et al., 2011) with a dominant pulsation signal at 1953 s (=0.022 d) and weaker signals at 2620, 2872, 3582, 4260 and 5084 s. However LS IV  presents a problem in that its effective temperature and gravity are deemed inconsistent with domains known to be unstable to g-mode oscillations (Jeffery & Saio, 2006, 2007; Green et al., 2011). A further surprise came with the discovery of superabundances (by dex) of zirconium, yttrium, strontium, and, to a lesser extent, germanium (Naslim et al., 2011). It has been argued that these could be associated with a dynamical self-stratification of the photosphere as a young subdwarf contracts towards the extreme horizontal branch (Naslim et al., 2013), suggesting that LS IV  is a proto-sdB star which will eventually develop a helium-poor atmosphere, and prompting speculation that the oscillations might represent the first known case of driven7 pulsation (Miller Bertolami et al., 2011, 2012). Meanwhile, the exotic surface chemistry suggested that, as in some Bp(He) stars (Townsend et al., 2005), magnetic activity might be responsible for the variability (Naslim et al., 2011), a speculation quite delicately dismantled by Green et al. (2011).

Whilst LS IV  presents conundra in terms of the driving mechanism for the pulsation, its surface composition and its actual effective temperature (Green et al., 2011), more basic data are also required. First, many hot subdwarfs are known to be members of binaries, providing at least three mechanisms for the removal of surface layers necessary for evolution to the extreme horizontal branch. LS IV  is a very slow rotator (Naslim et al., 2011); would radial-velocity measurements show it to be a binary? Second, if light variations are due to pulsation (and not magnetic activity), surface motion should be detectable in radial-velocity data at periods equal to the light variations. Such measurements could ultimately provide direct radius measurements or mode identifications using techniques similar to the Baade-Wesselink method (Stamford & Watson, 1981). Third, Naslim et al. (2011) suggested that, if the photosphere of LS IV  is chemically stratified and pulsating, differential motion could be detected by comparing the radial velocity curves due to different elements. As a consequence, we have attempted over several years to resolve the surface motion of LS IV . This paper describes the observations attempted and the ultimate detection of surface motion associated with the principal photometric oscillation at a period of  s.

Telescope / Date UT – UT S/N Observer
Instrument nm s
WHT/ISIS 2005 May 27 03:30 – 05:00 436–507 10 000 300 8 100 Ahmad
WHT/ISIS 2005 May 28 04:20 – 05:00 376–452 9 000 45 32 15–40 Ahmad
AAT/UCLES 2005 Aug 27 11:41 – 13:30 382–521 30 000 1800 3 40 Ahmad
SAAO 1.9/CGS 2007 June 29 01:03 – 04:15 380–560 2 000 300 36 20–30 Ahmad
SAAO 1.9/CGS 2007 June 29–30 23:43 – 02:54 2 000 36 Ahmad
SAAO 1.9/CGS 2007 July 02–03 23:39 – 03:56 2 000 48 Ahmad
SAAO 1.9/CGS 2007 July 03–04 23:46 – 04:03 2 000 48 Ahmad
ANU 2.3/WiFES 2010 June 18 12:42 – 14:33 418–552 5 000 480 9 100 Kerzendorf
VLT/UVES 2011 Sept 07 02:31 – 06:20 330–680 100 000 300 39 30–40 Service
1: Naslim et al. (2011)
Table 1: Observing log.

2 Observations

Spectroscopic time-series observations of LS IV  were obtained in 2005 with the Intermediate dispersion Spectrograph and Imaging System (ISIS) on the William Herschel Telescope (WHT), in 2005 with the University College Echelle Spectrograph (UCLES) of the Anglo-Australian Telescope (AAT), in 2007 with the Cassegrain Grating Spectrograph (CGS) on the 1.9 m telescope of the South African Astronomical Observatory (SAAO 1.9), in 2010 with the Wide-Field Spectrograph (WiFeS) on the Australian National University 2.3 m telescope (ANU 2.3), and in 2011 with the Ultraviolet and Visual Echelle Spectrograph (UVES) on the Very Large Telescope (VLT) of the European Southern Observatory (ESO). Details of dates observed, duration of observations in UT, wavelength range covered , spectral resolution , exposure times , numbers of exposures , and average signal-to-noise ratio per exposure S/N are given in Table 1. The spectra were reduced using standard procedures, including bias-subtraction, flat-fielding, sky-subtraction, wavelength-calibration, and rectification. For UVES, the ESO pipeline reduced data were recovered from the ESO archive.

Figure 1: Relative radial velocities for LS IV  obtained with WHT/ISIS on 2005 May 27 and 28.
Figure 2: Relative radial velocities for LS IV  obtained with SAAO 1.9/CGS on 2007 June 29 - July 04.
Figure 3: Relative radial velocities for LS IV  obtained with ANU 2.3/WiFES on 2010 June 18 (blue ’’ 420–488 nm, red ’’ 490–550 nm – offset by   d for clarity).
Figure 4: Relative radial velocities for LS IV  obtained with VLT/UVES from 2011 Sept 07 for three different wavelength regions. Top:  He i 501.6 nm. Middle: ‘metal’ absorption lines. Bottom: 627.0–632.5 nm telluric absorption lines. Since the sampling rate is quite low, data points are connected in order to guide the eye.

3 Velocity Measurements

Radial velocities were measured by cross-correlating each spectrum with a template defined to be a mean of all spectra for a given observing sequence. For this purpose, each spectrum was normalised to an approximate continuum, which was then subtracted. Cross-correlation was carried out in log wavelength space. Velocities were measured by fitting a parabola to a region around the maximum of the cross-correlation function (ccf) and customized to each wavelength region studied. The formal error in the position of the parabola apex was adopted as representative of the velocity error.

The observer’s frame radial velocity of the template was obtained by cross-correlation with a theoretical spectrum computed for a hot subdwarf with atmospheric abundances of hydrogen and helium being 70% and 30% by number, solar abundances of other elements, effective temperature  K, surface gravity , and microturbulent velocity (Behara & Jeffery, 2006). This is not a perfect match to the observed spectrum, but completely satisfactory for the purpose of velocity measurement by cross correlation. Corrections to the heliocentric frame were then applied. These template velocities () are shown in Table 1. Becasue of uncertainty in the absolute wavelength calibration, the template velocities for the low-resolution data () are untrustworthy and are shown in parentheses. The relative velocities are much more reliable.

3.1 Radial Velocities

Relative velocities for the three individual AAT observations are not shown since the exposure times were long compared with the photometric variation.

The short duration of the WHT observations and the resolution of the SAAO observations were inadequate to offer any prospect of detecting the pulsation at 0.022 d, and show no evidence for longer-period variations (Figs. 1,2). Periodograms for these data showed no evidence of periodicity.

The WiFES data are divided into two wavelength regions (418 – 488 nm and 490 – 552 nm). Each was studied separately. Results are shown in Fig. 3. In general the two sets of velocities agree to within , where . There is little evidence for variability in excess of on a timescale of 0.1 d

The UVES data were recorded in three wavelength regions (330–452, 480–575, and 583–680 nm). These regions include broad Balmer,  He i and  He ii lines. They include sharp stellar absorption lines from both light and heavy ions. They also include sharp interstellar and telluric absorption lines; there may also be residual instrumental artefacts. The latter all produce a sharp and stationary component in the ccf. The telluric absorption lines give an essentially flat velocity curve with a maximum deviation of () (Fig. 4). These velocities are consistent with small drifts in the instrumental calibration. The stellar absorption behaves quite differently and shows significant variability with a full amplitude of up to 15  (Fig. 4). Although there are differences between velocities measured in different spectral regions and from different lines, the shape of the velocity curve is maintained. Therefore we conclude the velocity curve to be real and due to variable motion of the stellar surface in the line of sight.

The mean heliocentric radial velocity of LS IV  is . This is large, but not unusual for a hot subdwarf in the thick disk. We see no evidence for long-period or large-amplitude variability that might suggest motion within a binary system.

Figure 5: Classical power spectrum for radial velocities obtained from the  He i 501.6 nm line observed with VLT/UVES on 2011 Sept 07.
Figure 6: Radial velocity curve for LS IV  obtained from the  He i 501.6 nm line phased to the principal period of 1978 s with a semi-amplitude of 5.5 .
Figure 7:  Zr iv line profiles for LS IV  obtained from the mean spectrum (solid – black), around minimum (dot-dot-dot-dashed – blue: ), mean (dashed – green: ) and maximum (dot-dashed – red: ) relative radial velocity.
Lines
nm nm d
metals 415.5 – 430.0 43.8 4.6
many 490.5 – 570.0 43.7 4.1
many 332.0 – 452.0 43.7 2.7
 Sr ii 407.8 407.5 – 407.8 43.8 3.4 0.90 0.33
 Sr ii 421.5 421.2 – 421.6 43.8 4.3 0.88 0.32
 Ge ii 417.9 417.5 – 417.9 43.8 5.2 0.86 0.33
 Ge ii 426.1 425.7 – 426.0 43.8 3.7 0.89 0.32
 Ge ii 429.1 428.6 – 429.2 43.8 1.7 0.95 0.37
 Y iii 404.0 403.6 – 4.3.9 43.8 3.4 0.89 0.31
 Zr iv 413.7 413.4 – 413.7 45.4 2.8 0.89 0.43
 Zr iv 419.8 419.5 – 419.7 43.8 5.4 0.79 0.16
 Zr iv 431.7 431.3 – 431.7 43.8 4.4 0.82 0.23
 C ii 426.7 426.0 – 427.0 43.8 4.2 0.74 0.25
 C iii 406.3 – 407.0 43.8 3.9 0.87 0.25
 N ii 399.5 399.1 – 399.5 43.8 4.5 0.85 0.28
 He i 386.7 386.3 – 386.8 43.8 3.7 0.87 079
 He i 388.8 388.5 – 389.0 43.8 1.5 0.60 0.34
 He i 396.3 396.0 – 396.5 43.8 1.3 0.68 0.22
 He i 412.1 411.6 – 412.2 43.8 5.1 0.75 0.77
 He i 438.8 438.0 – 439.3 43.8 5.2 0.74 1.63
 He i 447.1 445.0 – 449.0 43.8 3.8 0.55 1.41
 He i 501.6 500.0 – 502.5 43.8 5.5 0.66 0.20
 He i 667.8 666.0 – 669.0 43.8 5.0 0.59 0.47
H 655.5 – 656.5 45.3 1.4 0.69 1.63
H 484.0 – 488.0 43.7 4.9 0.61 1.12
H 432.0 – 435.5 43.7 2.7 0.60 1.77
telluric 627.0 – 632.5 34 0.3 0.75
6.5 0.1 0.01
Table 2: Frequencies (), velocity amplitudes () and residual intensity at line centre () for various wavelength windows ().

3.2 Period

For each set of velocities measured from the UVES data, we computed the classical Fourier power spectrum and measured the frequency and semi-amplitude (as square root of power) of the highest peak (Fig. 5, Table 2). Owing to the short duration of the data series, ( d), the frequency resolution is low (). However, the frequency of the highest peak is clearly consistent with that of the largest-amplitude oscillation in the photometry of both Green et al. (2011) and Jeffery (2011). All lines for which a good solution was obtained yielded the same frequency (43.8 d). The phases were the same to within cycles.

Figure 6 shows the radial velocities for one line ( He i 501.6 nm) phased on the dominant period (0.023 d). There remains substantial scatter about the best-fit sine curve, in excess of the formal errors on the velocities. Given the agreement between velocities obtained at different wavelengths, and the stability of the telluric velocity data, there is no reason to consider the errors to be seriously underestimated. We posit that there is unresolved motion due to oscillations at other periods as indicated by photometry.

Figure 8: Radial velocity amplitude as a function of line depth. Symbols represent different elements: Sr, Ge, Y and Zr (+), C and N (), He () and H ().

3.3 Amplitude

It became clear that the amplitude of the velocity variation is sensitive to the wavelength window selected for cross-correlation (Table 2). The presence of interstellar lines or instrumental artefacts was indicated by a small sharp peak in the ccf, but by fitting the ccf peak over a large enough window, this was not a significant factor. Large spectral windows including many broad lines (e.g. 332–452 nm) would give small amplitudes, more restricted windows containing only sharp metal lines would give larger amplitudes (e.g. 415–430 nm), whilst some individual lines would yield still larger amplitudes (e.g.  He i 501.6 nm,  Zr iv 419.8 nm).

For these UVES data, the cross-correlation approach yields high quality radial velocity information from individual lines in which the central depth is at least 5% below continuum. Results for selected lines are shown in Table 2, which also includes the mean velocity error () for each line measured. There is a general trend that, for sharp lines, the velocity amplitude increases with line depth (Fig. 8).

For broad lines, especially the Balmer series and the diffuse  He i lines, the amplitudes were frequently much lower (), principally because the ccf peak is also very broad and therefore poorly defined. However, the same period of 0.023 d was generally recovered, except in the case of the Balmer lines.

One interpretation of the increase in velocity amplitude with central depth is that the pulsation amplitude is a function of position in the stellar atmosphere. Strong lines are formed at lower optical depths and, hence, higher in the atmosphere where densities are lower. An outward running wave will increase in amplitude as it propagates into less dense material, exactly as is observed in the sharp metal lines. Similar phenomena are seen, for example, in rapidly-oscillating Ap stars (Kurtz et al., 2007). In the case of LS IV  the situation is complicated by the apparent super-abundances of zirconium, strontium, etc., since it has been argued that the atmosphere must be chemically stratified. More detailed analysis of these and similar data should enable us to establish the relative depth of the chemically stratified layers relative to the velocity gradient in the photosphere.

3.4 Line Profiles

For large-amplitude radially pulsating stars, velocity shifts are usually associated with line-profile shifts; owing to the centre-to-limb contrast in radial velocity, there is usually some absorption at zero-velocity, whilst the line centre shifts back and forth producing asymmetric profiles at minimum and maximum radial velocity (Montañés Rodriguez & Jeffery, 2001; Jeffery et al., 2013). Non-radial pulsations are often associated with line-profile variations, but usually in rapidly-rotating stars where temperature variations across the surface produce more or less flux at different velocities. We checked for line profile changes by coadding spectra around minimum velocity (), mean velocity () and maximum velocity (). No asymmetries were identified (cf. Fig. 7).

The use of a ccf template constructed as a simple mean allows for the possibility of some velocity smearing. In addition, the AAT/UCLES spectra used previously for atmospheric analysis were obtained with long exposures (cf. Naslim et al. (2011)). The question arises whether either the template could be sharpened, or whether previous analyses overlooked pulsation -broadening of the line profiles that led to an overestimate of the rotational broadening. We found no evidence that the spectrum of LS IV  could be further sharpened (Fig. 7), or that the (Naslim et al., 2011) measurement of should be revised downward.

3.5 Light – velocity amplitude ratio

Green et al. (2011); Jeffery (2011) give the amplitude of the light variation in the optical as 0.27% or mmag. Taking the maximum amplitude of the radial velocity amplitude to be , the ratio of the observed light-amplitude to velocity amplitude in mmag km s is thus . This ratio assumes that the amplitude of the 1953 s oscillation does not vary significantly over time.

We can simulate the observable light and amplitude ratios for non-radial modes of different radial degree and azimuthal number using the surface codes bruce and kylie (Townsend, 2003; Ramachandran et al., 2004) and a grid of theoretical spectra for a composition appropriate to LS IV  (Behara & Jeffery, 2006; Naslim et al., 2011). Assuming effective temperature  K, surface gravity and equatorial rotation velocity (Naslim et al., 2011), and also assuming the adiabatic approximation, a polar radius of 0.2  (implying a mass ), inclination , pulsation period 1950 s and an arbitrary surface velocity amplitude, we can compute a time series of theoretical spectra for a given mode . These can be analysed in exactly the same way as the UVES spectra to give both the apparent velocity amplitude and, also, the apparent flux amplitude in a given wavelength region. The ratio of surface velocity to apparent velocity amplitude is a function of and , so we cannot infer anything directly from . However, the ratio is relatively invariant to (Stamford & Watson, 1981) and also to the surface velocity amplitude.

We computed theoretical for and for the dominant mode in LS IV , obtaining  mmag km s for the radial mode and  mmag km s for the non-radial and modes. This strongly argues against the 1953 s period being a radial mode, in complete agreement with the argument from pulsation theory given by Green et al. (2011).

4 Conclusions

We have conducted a search for radial velocity variability in the helium-rich hot subdwarf LS IV : the pulsating zirconium star.

We have demonstrated that at least one periodic variation identified photometrically in LS IV  is also observable as a radial velocity variation with a semi-amplitude in excess of 5 . This provides strong evidence that both are due to an oscillatory motion of the surface and are hence most likely due to pulsation. That is a purely empirical conclusion. Additional evidence from the light/velocity amplitude ratio argues that the pulsation cannot be a radial mode, whilst supporting arguments from pulsation theory (Green et al., 2011) confirm that the observed pulsations are due to a non-radial gravity mode.

We have also demonstrated that differential motion within the photosphere can be resolved by studying lines of different depths, as these probe different levels of the photosphere.

To learn more about LS IV  from these oscillations, the radial velocity measurements must be repeated over a longer period of time, and should be supported be multi-wavelength photometry. Higher frequency resolution would allow the relative phases of different lines to be measured and show how the oscillation propagates through the photosphere. Ultraviolet spectrophotometry would help to identify the modes of oscillation, as well as to address the effective temperature question. Theoretical models need to be developed to interpret the spectrum, incorporating the non-radial oscillations, chemical stratification, and including differential vertical motion. In particular, the profiles and behaviour of the  He i and hydrogen Balmer lines deserve further study.

Acknowledgments

The Armagh Observatory is funded by direct grant-in-aid from the Northern Ireland Dept of Culture, Arts and Leisure. Observing travel for AA was funded by a PPARC grant. CSJ is indebted to Suzanna Randall for encouraging him to complete this study.

Footnotes

  1. Based on data collected with the William Herschel Telescope, the Anglo-Australian Telescope, the SAAO 1.9 m telescope, the ANU 2.3 m telescope, and the ESO Very Large Telescope.
  2. email: csj@arm.ac.uk
  3. pagerange: Radial velocity measurements of the pulsating zirconium star: LS IVBased on data collected with the William Herschel Telescope, the Anglo-Australian Telescope, the SAAO 1.9 m telescope, the ANU 2.3 m telescope, and the ESO Very Large Telescope. Radial velocity measurements of the pulsating zirconium star: LS IVBased on data collected with the William Herschel Telescope, the Anglo-Australian Telescope, the SAAO 1.9 m telescope, the ANU 2.3 m telescope, and the ESO Very Large Telescope.
  4. Based on data collected with the William Herschel Telescope, the Anglo-Australian Telescope, the SAAO 1.9 m telescope, the ANU 2.3 m telescope, and the ESO Very Large Telescope.
  5. Based on data collected with the William Herschel Telescope, the Anglo-Australian Telescope, the SAAO 1.9 m telescope, the ANU 2.3 m telescope, and the ESO Very Large Telescope.
  6. pubyear: 2014
  7. i.e. driven by instability in a nuclear burning zone.

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