Blue Supergiants: The Flux-Weighted Gravity-Luminosity Relationship (FGLR)

Big and Blue

Blue Supergiants are among the hottest and most luminous stars in the universe, falling in spectral class O, B, or A and luminosity class I. They have surface temperatures ranging from 10,000 K – 50,000 K. This places them in the upper left of a standard Hertzsprung-Russell (HR) diagram.

FGLR

The last few years have given rise to newfound studies relating the bolometric magnitude of blue supergiants with their flux-weighted gravity, g_F, defined as g/T_EFF^4.

Urbaneja et al. (2017) describes this relationship by the linear formula:

M_BOL= a(log g_F − 1.5) + b

where a is the slope and b is the y-intercept of bolometric magnitude vs the logarithmic form of flux-weighted gravity. Should consistent values for a and b be found, this relationship would allow blue supergiants to be used as standard candles.

Break in the Slope

Urbaneja et al. predicts a change in the slope of the FGLR around 1.29 dex, as indicated by the vertical dashed line in the scatterplot below, which was published in the 2017 paper.

The slope and intercept found in Urbaneja et al. below their breakpoint were a = 3.20 ± 0.08 and b = -7.90 ± 0.02 mag. In addition, the parameters found by Kudritzki et al. (2008) were a = 3.41 ± 0.16 and b = -8.02 ± 0.04 mag.

Extension to Our Galaxy

Urbaneja et al. investigated the Large Magellanic Cloud (LMC) while another paper, Kudritzki et al., extended the FGLR to galaxies outside the Local Group. With the publication of Gaia’s Second Data Release, my team and I were able to study galactic blue supergiants. Our findings indicate that the FGLR is a promising distance indicator not only for the extragalactic but also the galactic regime.

After running a simple linear regression 100 times, we generated an average slope of a = 3.55 ± 0.35 and an average y-intercept of b = -7.98 ± 0.13 mag. These values did not account for a potential break in the slope of the FGLR. Due to the scale of our errors in the logarithm of the flux-weighted gravity, we could not accurately define a break.

The orange line in the scatterplot below represents a linear regression of our data, while the green indicates a piecewise linear regression, assuming a break at around 1.5 dex.

While within the derived errors, the slope of our simple linear regression is slightly greater than the values derived by both Kudritzki and Urbaneja. This is indicative of an increase in the slope above the potential breakpoint, which would influence the overall slope of the line.

Necessary Improvements

The lack of spectroscopy data for our supergiants forced us to rely on surface gravity and effective temperature values provided in the literature. This increased the error in our calibration and made it difficult to identify a clear break in the slope, as proposed by Urbaneja et al.

Furthermore, the lack of metallicity data for our BSGs made it impossible to analytically compute bolometric correction values, forcing us to rely on the empirical bolometric correction values compiled by Schmidt-Kaler (1982). Further improvements to our work should be based on precise stellar parameters from spectroscopic surveys targeted toward blue supergiants, which remain of great importance to extragalactic astronomy.