Inclination Bias in Techniques Used to Identify Be Star Candidates

TL;DR

This study quantifies how inclination affects the identification of Be star candidates, using 20,000 synthetic Be stars generated with Bedisk/Beray to test spectroscopic and photometric methods. The spectroscopic peak-finding approach exhibits strong bias against high inclinations ($i>80^{\circ}$), while two photometric H\alpha diagnostics show opposite inclinations biases, with a surplus of detections at moderate inclinations ($50^{\circ}<i<80^{\circ}$) and varying sensitivity to low and very high inclinations. The results demonstrate method-dependent biases that can distort inferred spin-axis distributions in clusters, underscoring the need to account for inclination effects when using Be stars as tracers of cluster dynamics or stellar rotation. The authors propose combining methods and extending analyses to time-series photometry to mitigate biases and enable more reliable inferences about Be-star populations and their underlying spin distributions.

Abstract

Several methods for identifying Be star candidates are reviewed for observational bias with respect to system inclination, that is the angle between the stellar/disk rotation axis and the observer's line of sight, with focus on two photometric methods that leverage narrow-band filters centred on H$α$ and a spectroscopic method using a H$α$ peak-finding algorithm. Tests for bias were performed using a sample of 20,000 synthetic Be stars drawn from a Salpeter initial mass function and computed libraries of spectral energy distributions and H$α$ profiles. The spectroscopic method showed substantial bias against high inclinations ($i > 80^\circ$). Both photometric methods were biased against low inclinations, with one also biased against inclinations above $80^\circ$, resulting in a surplus in the Be star candidate detection rate for moderate inclinations ($ 50^\circ < i < 80^\circ$). Inclination probability distributions, including the random $\sin i$ factor, are given for the three methods that can be applied to observational samples.

Figures (18)

• Figure 1: Change in the visual magnitude (star+disk minus star alone) of an $M=7\,M_\odot$ Be star as the viewing inclination ranges from $i=0^\circ$ (pole-on star, face-on disk) to $i=90^\circ$ (equator-on star, edge-on disk). The solid lines with symbols are Bedisk/Beray calculations (see Section \ref{['synthBestars']} for computational details). Here the star is surrounded by a disk with parameters $\rho_0=2.35\times 10^{-11}\,\rm g\,cm^{-3}$ and $n=2.25$, and several disk radii are considered (see legend). The red line is the prediction of Equation \ref{['eq:dmv']} with $R_c=1.3$ stellar radii.
• Figure 2: Change in H$\alpha$ equivalent width as a function of viewing inclination. Positive equivalent widths represent net emission. The same Be star model of Figure \ref{['fig:VIcorr']} was used, except that $R_d$ was fixed at 25 and the power-law index was varied with the values given in the legend.
• Figure 3: A random sample of 1000 discarded disks in the density ($\rho_0)$ versus power-law index ($n$) plane. The disk size ($\rm r_d$) is represented by the symbol size as indicated in the legend.
• Figure 4: Histograms of the number of accepted (top panel) and discarded (bottom panel) synthetic Be stars. The dashed blue line in the top panel shows the expected number if the distribution was perfectly uniform ($\approx1,538$ stars per inclination). Note the large change in the y-axis scale from the top to bottom panel.
• Figure 5: Top: A violin plot of $\Delta\,M_{\beta}$ for the Be star sample in several colours $\beta=\rm BVRI$ and H$\alpha$. White circle shows the median of each distribution, and thick black lines show the first and third quartiles, respectively. Bottom: The corresponding CDFs of the $\Delta\,M_{\beta}$ in the top panel as identified in the legend.