Luminous Blue Variables (LBVs)

In quiescence an LBV or S Doradus variable is a moderately evolved hot star, with a B-type supergiant or Of-type/late-WN spectral classification. During the "eruption" or maximum visible light stage, increased mass loss causes the wind to become optically thick, sometimes called a pseudo-photosphere, at T~7000-9000 K with an absorption line spectrum resembling an F-type supergiant. Since this alters the bolometric correction, the visual brightness increases by 1--2 magnitudes while the total luminosity remains approximately constant [, ] and numerous early references therein) or may decrease []. Such an event can last for several years or even decades. Basic causes of the instability remain somewhat mysterious; most proposed explanations invoke an opacity-modified Eddington limit, subphotospheric gravity-mode instabilities, and super-Eddington winds (see [, , ]).

Two interesting examples SN2002kg and the historic SN1954J both in the nearby spiral galaxy NGC 2403 illustrate the differences among the LBVs and the giant eruptions []. Both received a supernova designation. SN2002kg's eruption was sub-luminous and it was quickly reognized as a non-supernova. It was identified with the "irregular blue variable" V37 in NGC2403 [], a known LBV/S Dor variable in its maximum light stage [,]. V37's pre-eruption luminosity and its luminosity near maximum was approximately M_Bol -10.4 mag or 10⁶ L_⊙ and possible initial mass of 60 - 80 M_⊙. Like other LBVs/S Dor variables, V37s outburst was an apparent transit on the HR Diagram, at nearly constant luminosity due to increased mass loss and the formation of a cooler, dense wind. Its high mass loss stage lasted about 13 years

SN1954J, also known as V12 in NGC2403, is a giant eruption. Based on its peculiar light curve (Figure 1) and its resemblance to eta Car and SN1961V, it was also considered another possible example of Zwicky's Type V supernovae. Its pre-eruption light curve is remarkable for the rapid variations in its apparent magnitude in the years 1950 -1954 prior to its giant eruption, sometimes a half magnitude or more in only a few days. These erratic fluctuations are most likely due to a short term surface instability distinct from the LBV/S Dor long-term eruptions which have different characteristics. It increased by five magnitudes in apparent brightness and its absolute magnitude at maximum was at least - 13 or ≈ 10⁷ L_⊙. Its actual maximum lasted about a year. Its maximum luminosity and its pre-maximum outbursts are similar to other SN impostors or giant eruptions. HST imaging ([]) resolved V12 into four stars, one of which is very bright in Halpha, and is the likely survivor. But this likely survivor is 2.5 - 3 mag or about 10 times fainter than the progenitor star with a peculiar energy distribution. The mystery was solved when spectra obtained with the Large Binocular Telescope showed that the survivor is actually two stars, a hot supergiant with a cooler companion G supergiant, and the fading could be explained by large grains of circumstellar dust formed during the eruption [].

One of the most distinguishing characteristics of LBV/S Dor variability is that during quiescence or minimum light, the stars lie on the S Dor instability strip first introduced by Wolf [] and illustrated here in Figures 2 and 3 for confirmed LBVs in the nearby spirals M31 and M33 and in the Large and Small Magellanic Clouds [].

The more luminous, classical LBVs above the upper luminosity boundary have not been red supergiants, while those below are post-red supergiant candidates. Thus LBVs with very different initial masses and different evolutionary histories occupy the same locus in the HR Diagram.

Normal mass losing supergiants are found in the S Dor instability strip. Thus some factor must distinguish LBVs from the far more numerous ordinary stars with similar T_eff and L, and L/M is the most evident parameter. LBVs have larger L/M ratios than other stars in the same part of the HR Diagram. Their Eddington factors Γ = L/L_Edd are around 0.5 or possibly higher. This is not surprising for the very massive classical LBVs. But how can the less luminous LBVs have such large L/M ratios? The simplest explanation is that they have passed through a red supergiant stage and moved back to the left in the HR diagram []. show that stars in the 22 -- 45 M_⊙ initial mass range, evolving back to warmer temperatures, will pass through the LBV stage, and recent evolutionary tracks, with mass loss and rotation [], show that these stars will have shed about half of their initial mass. Having lost much of their mass, they are now fairly close to (L/M)_Edd. Although empirical mass estimates are uncertain, the low luminosity LBVs are close to their Eddington limit with Γ ≈ 0.6 []. Hence the evolutionary state of less-luminous LBVs is fundamentally different from the classical LBVs.

To illustrate this, in Figure 4 we show the evolution of L/M for two differen t masses representing the two LBV/S Dor classes. It shows a simplified Eddington factor, Γ_s=(L/L_⊙)/(43000 M/M_⊙), as a function of time in four evolution models reported by [] for rotating and non-rotating stars with M_ZAMS= 32 and 60 M_⊙. The 32 and 60 M_⊙ models have log L ~ 5.6 and 6.0, respectively, when they are in the LBV instability strip (see Figs.\ 2 and 3). Three critical evolution points are marked in the figure: (1) The end of central H burning, (2) the farthest major excursion to the red side of the HR Diagram, and (3) the end of central He burning. For the 60 M_⊙ star, Γ_s ≳ 0.5 as it leaves the main sequence, but the 32 M_⊙ star must pass through yellow and/or red supergiant stages before its Γ_s reaches 0.5.