**4. The Humphreys–Davidson Limit**

The original HR Diagrams from the Humphreys and Davidson 1979 paper are reproduced here in Figures 2 and 3, with the upper boundary shown as a solid line. The original eyeball fit was first drawn to approximate the upper boundary of the supergiant luminosities in the Milky Way. The same line was then transferred to the LMC Diagram, which also matched the observed upper envelope to the LMC luminosities. The upper boundary for both galaxies is an envelope of declining luminosity and decreasing temperature for the hottest stars and a relatively tight upper limit to the luminosities of the cooler stars (less than ≈10,000 K) near M*Bol* ≈ −9.5 Mag.

*Galaxies* **2019**, *7*, 75

**Figure 2.** The HR Diagram, M*Bol*vs. log T, for the luminous stars in the Milky Way from [25].

**Figure 3.** The HR Diagram, M*Bol* vs. log T, for the luminous stars in the LMC from [25].

This empirical boundary is often referred to in the literature as the "Humphreys–Davidson" Limit. It was not predicted by theory or the stellar structure models and evolutionary tracks at that time. The lack of evolved stars, post main sequence stars, above a certain luminosity implies an upper limit to the masses of stars that can evolve to become red supergiants thus altering the previously expected evolution of the most massive stars across the HR Diagram. In the original study, this limit corresponded to an initial mass near 60 M. Improved models with mass loss and rotation sugges<sup>t</sup> a mass more like 40–50 M today.

Spectroscopy of luminous star candidates in other Local Group galaxies confirmed the upper luminosity boundary in galaxies of different types, but, in most cases, surveys and population studies were minimal: M31 [26], IC 1613 and NGC 6822 [27]. Humphreys & Sandage [28] completed a major survey for the brightest blue and red stars in M33, that provided the basis for spectroscopy and identification of the most luminous supergiants in that nearby spiral [29], and in subsequent studies. Similar HR Diagrams for

the massive stars in the SMC were published a few years later by Humphreys [30] based on a combination of previous work and new observations.

At the time the Humphreys–Davidson paper was published, it was apparent that significant mass loss occurred in both the blue and red supergiants and there was increasing interest in the role that mass loss may have on their evolution. The lack of evolved cooler counterparts to the most massive evolved hot stars in both galaxies suggested that their post main sequence evolution was of special interest. A few high luminosity stars were known for their instabilities, variability and evidence for high mass loss such as eta Car and P Cyg in the Milky Way and S Dor in the LMC. Several luminous blue variables, spectroscopically similar to eta Car and P Cyg, were now recognized in other galaxies [31,32]. As a group, they were known as S Doradus Variables or as Hubble–Sandage Variables in M31 and M33. Several of these stars were included on the HR Diagrams. They were increasing evidence that the phenomena of high mass loss and instabilities, as observed in eta Car and P Cyg, were more common. Humphreys and Davidson thus suggested that the most massive hot stars could not evolve to cooler temperatures because of their instabilities resulting in high mass loss. The temperature dependence of the luminosity limit for the hottest stars was evidence that the instability was mass dependent. This mass loss could be unsteady and much greater at times resulting in high mass loss events. The relatively tight upper luminosity boundary for the cooler stars represented the upper limit to the initial masses of stars that could evolve across the HR Diagram in a stable way to become red supergiants (RSGs).

Some of the first evolutionary tracks with mass loss were also being published at that time [33–36]. It was shown that high mass loss (higher than observed) would cause the tracks to reverse and the stars evolve back to warmer temperatures.

### **5. Surveys and More Surveys**

We emphasize the importance of spectroscopy for the identification and analysis of the most luminous stars, but surveys are essential for identifying candidates. Beginning in the 1980s, astronomers began to add multi-wavelength surveys, primarily in the near-infrared, to complement the traditional optical photometry. Elias, Frogel, & Humphreys [37] obtained near IR photometry for known and candidate red supergiants in the LMC and SMC for a comparison with the Galactic population. The all-sky near-infrared 2MASS survey from 1.2 to 2.2 μm [38] reached the brightest stars in M31 and M33 as well as the Clouds. The infrared observations allowed astronomers to look for free-free emission from the stellar winds and the presence of circumstellar dust, another indicator of mass loss, and to correct the luminosites for possible additional extinction due to circumstellar dust.

Space-based telescopes such as UIT and later GALEX added FUV and NUV imaging and photometry for more complete SEDS at the shorter wavelengths and more accurate estimates of the total luminosities for the hottest supergiants. The mid-infrared surveys with Spitzer/IRAC of the Magellanic Clouds [39,40] and M31 [41] and M33 [42] added fluxes from 3 to 8 μm and even longer wavelengths to search for colder dust, thus allowing us to investigate their mass loss histories.

With the advent of the wide-field CCD mosaic cameras, ground-based, multi-wavelength optical surveys, such as the Local Group (LGGS) by Massey et al. [43], added to the fundamental data. These ground-based surveys however are seeing-limited and lack spatial resolution, thus the images are often multiple. Here, again, spectroscopy or higher resolution imaging with Adaptive Optics on large telescopes can identify and even separate the stars. These ground-based surveys are enhanced by observations with the Hubble Space Telescope such as the PHAT surveys in M31 and M33 [44]. Numerous imaging programs of other galaxies intended for other purposes with HST have provided lists of resolved stars for further observation in, for example, M101 [45] and NGC 2403 and M81 [46,47].
