Ultraviolet Spectropolarimetry: on the origin of rapidly rotating B stars

Abstract

UV spectroscopy and spectropolarimetry hold the key to understanding certain aspects of massive stars that are largely inaccessible (or exceptionally difficult) with optical or longer wavelength observations. As we demonstrate, this is especially true for the rapidly-rotating Be and Bn stars, owing to their high temperatures, geometric asymmetries, binary properties, evolutionary history, as well as mass ejection and disks (in the case of Be stars). UV spectropolarimetric observations are extremely sensitive to the photospheric consequences of rapid rotation (i.e. oblateness, temperature, and surface gravity gradients), far beyond the reach of optical wavelengths. Our polarized radiative-transfer modelling predicts that with low-resolution UV spectropolarimetry covering 120–300 nm, and with a reasonable SNR, the inclination angle of a rapid rotator can be determined to within 5 degrees, and the rotation rate to within 1%. The origin of rapid rotation in Be/n stars can be explained by either single-star or binary evolution, but their relative importance is largely unknown. Some Be stars have hot sub-luminous (sdO) companions, which at an earlier phase transferred their envelope (and with it mass and angular momentum) to the present-day rapid rotator. Although sdO stars are small and relatively faint, their flux peaks in the UV making this the optimal observational wavelength regime. Through spectral modelling of a wide range of simulated Be/n+sdO configurations, we demonstrate that high-resolution high-signal-to-noise ratio UV spectroscopy can detect an sdO star even when ∼1,000 times fainter in the UV than its Be/n star companion. This degree of sensitivity is needed to more fully explore the parameter space of Be/n+sdO binaries, which so far has been limited to about a dozen systems with relatively luminous sdO stars. We suggest that a UV spectropolarimetric survey of Be/n stars is the next step forward in understanding this population. Such a dataset would, when combined with population synthesis models, allow for the determination of the relative importance of the possible evolutionary pathways traversed by these stars, which is also crucial for understanding their future evolution and fate.

Appendices

Appendix A: Target list

Table 1 Target list. The listed UV flux values (at 1500 Å and 2500 Å) are in units of erg/s/cm²/Å$\times 10^{-10}$, and are estimated from IUE data whenever possible. If not observed by IUE, these flux values are interpolated based on the V_mag and the spectral type. The ‘Class’ column describes the type of system as follows. ‘sdO’ systems are confirmed Be+sdO binaries where the sdO stars has been directly detected. ‘gCas’ are the X-ray emitting $\gamma$ Cas analogs. All ‘sdO’ and ‘gCas’ systems are also Be stars. The table is sorted by class, and then by V_mag within each class. Spectral types are from the literature. The ‘ch. 1 $t_{\exp}$’ is the exposure time, in seconds, for one full Polstar observation (made up of six sub-exposures) and the corresponding SNR. The ‘ch. 2 $t_{\exp}$’ is the exposure time needed in channel 2 to deliver the polarization precision given in the next column (‘ch. 2 prec.’)

Appendix B: Detectability of faint sdO companions

Further details are described here concerning the methods used to determine the channel 1 spectroscopic SNR needed to adequately explore the parameter space of Be/Bn+sdO binaries. It is worth keeping in mind that while in the known Be+sdO binaries the sdO star contributes about 2% – 10% of the total flux in the UV, these cases were discovered primarily through analysis of low-SNR archival spectra which were not sensitive enough to detect fainter systems. In order to determine the binary fraction and properties of the Be/n population in general, while discovering and characterizing potential Be/n+sdO systems, observations should be sufficiently sensitive as to detect hot sub-luminous companions even when they contribute only ∼0.1% (or a few times this) of the total UV flux. This is justified in Sect. 5.1.2 and further examined here.

2.1 B.1 Methodology

Synthetic composite spectra were used to emulate Polstar observations of Be/n+sdO binaries using the non-LTE radiative code CMFGEN (Hillier and Miller 1998). For the (O)B star component, models were generated for $\log{g}$ = 4.0 and five values of $T_{\mathit{eff}}$ (13, 18, 20, 25, and 35 kK), roughly corresponding to spectral types of B8, B6, B4, B1, and O9. These spectra were convolved with a Gaussian so that absorption lines were broadened to correspond approximately to $v\sin{i}$ = 250 km s⁻¹. Ten sdO model spectra were generated for $\log{g}$ = 4.5 and 5.0, and $T_{\mathit{eff}}$ = 30, 35, 40, 45, and 50 kK, broadened to correspond to $v\sin{i}$ = 15 km s⁻¹. The B and sdO spectra were then co-added over a range of luminosity ($L_{\mathit{sdO}}$ = 0.1 – 1,000 $L_{\odot}$) and noise levels (SNR between 10 – 1,000) for a given B star model spectrum. For testing the relatively luminous O star, $L_{\mathit{sdO}}$ was extended to 10,000 $L_{\odot}$, although such high sdO luminosities are not realistic.

In nearly all trials, the features in the co-added spectra are dominated by the relatively luminous B star (see top panels of Fig. 15). Since the absorption lines of the rapidly-rotating B star are wide compared to the sdO lines, in effect the sdO spectrum can be isolated by convolving the co-added spectrum with a Gaussian that is wider than the sdO features but more narrow than the B star features, and then dividing the simulated data by the ‘smoothed’ fit. This was done prior to cross-correlating the sdO template spectra. However, in practice, it may be preferable to simultaneously (or iteratively) perform a two-component CCF analysis considering both the B and sdO stars. In these tests, the input model spectrum of the B star (scaled to the correct flux ratio) could have been removed from the co-added noise-added spectrum perfectly, but such an ideal fit of the B star model to the data is not expected to be realized in practice, and simply applying a smoothing kernel is probably closer to a more realistic treatment of observational data.

Fig. 15

CCF analysis for simulated Be/n+sdO spectra. The left panel illustrates a faint sdO system that is marginally detected, and in the right panel the sdO CCF signal is strong. The top panel shows the co-added model spectrum for a B+sdO system (red curve) with noise added (black curve), and also the isolated sdO spectrum (scaled by the factor in the legend). The CCF signal is shown in the lower panel for the correct sdO model (in red) and the other sdO templates (grey) with different values of $T_{\mathit{eff}}$ and $\log{g}$. No velocity shifts were introduced to the input spectra

A CCF analysis was then used to attempt to recover the spectroscopic signature of the sdO star. Figure 15 illustrates part of this procedure for two trials – a threshold case and a strong detection.

Each sdO template was cross-correlated with the (noisy) simulated spectrum (after removing the broad features, as above). The strength of the CCF signal corresponding to the input sdO model is then used as the metric to gauge the degree of detectability of the sdO spectrum for a given combination of the adopted stellar and noise parameters. In this application, a CCF SNR of ≳5 can be considered a (marginal) detection, but a stronger signal is needed to differentiate between different sdO model spectra. In the majority of cases where the CCF SNR ≳10, the templates with the correct $T_{\mathit{eff}}$ typically have noticeably higher signals than the other models (surface gravity was harder to differentiate). However, the details of determining the sdO stellar properties from these simulations were not investigated in detail.

2.2 B.2 Results

Figure 16 gives an overview of the ‘detectability space’ in terms of UV spectroscopic SNR and sdO luminosity. For this family of tests, an sdO model with $\log{g}$ = 4.5 and $T_{\mathit{eff}}$ = 45 kK was added to the five aforementioned (O)B star model spectra over values of $L_{\mathit{sdO}}$ and SNR. Virtually the same detectability thresholds are found when using as input any of the other sdO spectra.

Fig. 16

Simulated detection thresholds for recovering the spectroscopic signature of an sdO star in a Be/n+sdO binary. Each panel represents simulated scenarios with a rapidly-rotating B star (properties in the bottom-left corner) and an sdO star over a range of luminosity for a UV spectrum with $R = 30,000$. The contours between the dark and light regions trace the boundaries for a CCF SNR of 5 to 10, where a CCF SNR = 5 should be sufficient to detect an sdO spectrum, while higher CCF SNR values improve the ability to accurately characterize the sdO star. The green shaded rectangle marks the sdO luminosity range that corresponds to flux ratios of $f_{\mathit{sdO}}/f_{B} = 2 - 10 \%$ (note, however, that this range corresponds to different values of $L_{\mathit{sdO}}$ depending on the B star model used). The plotted range in $L_{\mathit{sdO}}$ for each panel depends on the (O)B star luminosity, which spans over two orders of magnitude

In Fig. 16 the lighter yellow regions (upper right in each panel) represent configurations where the sdO spectrum is detected strongly and the spectroscopic parameters can be readily determined. The dark regions in each panel represent non-detections. At a CCF SNR of ∼5 (in the definitions employed here) the sdO spectrum is marginally detected. At CCF SNRs of around 8 – 10, the fidelity of the recovered spectrum becomes high enough to begin to characterize the sdO stellar properties (e.g., $T_{\mathit{eff}}$ and $\log{g}$). The contours in each panel in Fig. 16 trace the boundaries at CCF SNR = 5, 6, 7, 8, and 9, and thus this strip and above is the region where a given combination of $L_{\mathit{sdO}}$ and spectroscopic SNR should render a detection in a single observation.

These tests show that high SNR (∼300) UV spectroscopy is sensitive enough to detect sdO stars that are ∼1,000 times fainter than their rapidly-rotating B-type companion. And, in the case of non-detections at this degree of precision, stringent constraints can be placed on the nature of an unseen companion (or lack thereof). With Polstar, such observations can be obtained with reasonable exposure times for a significant fraction of the bright sample of Be/n stars listed in Appendix A.