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ASTR 5610, Majewski [SPRING 2020]. Lecture Notes

ASTR 5610 (Majewski) Lecture Notes



Definition of "metallicity":

Abundances by weight:

Effects of Line Strengths on Broadband Colors: UBV Example

Metallicity effects play an important role on how the stars in a stellar population are distributed in a color-magnitude diagram (CMD).

  • Here is the same thing for actually observed stars in globular clusters of different metallicities, but presumably similar ages.

    Combined color-absolute magnitude diagrams for 14 globular clusters of similar age from Gaia DR2 data, with stars color-coded by metallicity. From .

  • Obviously, if we want to use CMDs to interpret the age/metallicity characteristics of a population, we need to understand how these metallicity effects change the colors and magnitudes of stars.

    I will focus initially on one particular example, metallicity effects in the UBV system, not only to give flavor of how the CMD changes, but because this particular example has played an important role in Galactic astronomy/stellar populations studies.

    • A nice, lucid discussion of the UBV case is given in Mihalas & Binney, Section 3.6; by extrapolation, the same basic phenomena apply to other filter systems covering similar wavelengths (see below).
    • Another version of this is given in the original paper on UV-excess by Wildey, Burbidge, Sandage & Burbidge (1962, ApJ, 135, 94).
    In the following figure is shown the variation of the line-blocking coefficient (LBC) with wavelength for various types of stars.

    You can think of the LBC as something like (1-emissivity), with the emissivity of a source defined as the ratio of true flux to that from a BB of same temperature.

    Line blocking as a function of stellar type in top three panels. Bottom two panels shows change in the LBC for two stars of same spectral type but different metallicity. From Mihalas & Binney (1980).
    Here is another, more modern example of a comparison of two stars of the same nominal spectral type but vastly different metallicities:
    Two early K giants differing by almost two orders of magnitude in metallicity, showing the spectral differences that result. The strongest variation comes in the ultraviolet. Figure from Gregg et al. (2005, "The HST/STIS Next Generation Spectral Library", The 2005 HST Calibration Workshop, Space Telescope Science Institute, 2005, A. M. Koekemoer, P. Goudfrooij, and L. L. Dressel, eds.).
    From the above figures notice that:

    What is happening in above diagram?

    • If we start with stars of no metallicity and therefore no metal lines, and then gradually increase abundances to solar type, the star should become redder in B-V, but even redder in U-B, simply on the basis of the line blanketing effect.

    • But this is not the entire story. We also have several competing effects.

      One of these compensating effects that comes into play to interpret the relative color changes is backwarming:

      • All other things being equal, the same amount of energy still has to leave the star.
      • Can only do so between lines in spectrum.
      • Thus, the continuum emission levels become elevated, and make the star (in continuum) appear as if it is a star of hotter BB temperature.
    • Backwarming effect mitigates and competes with the line blanketing effect.

      • U band: (line blanketing) >> (backwarming)
      • B band: (line blanketing) >~ (backwarming)
      • V band: (line blanketing) <~ (backwarming)
      These effects are obvious in the K giant spectra shown above.

      Thus, in the (B-V,U-B) two-color diagram, the line blanketing vectors are nearly vertical -- showing that Δ(U-B) is more strongly changed than Δ(B-V) for given change in metals.
    • Blanketing vectors for stars of different temperatures from line-free colors (shown by crosses) to solar metallicity locus (shown by the curve). From Wildey et al. (1962).
    • We say that metal-poor stars show an "Ultraviolet Excess" or "UVX'' (comparatively more UV flux) than metal-rich stars - which have a lot more UV absorption lines
    • Now here is a more modern version of the same plot, shown in the Sloan filter system (two versions of the same plot are shown, with one inverted for comparison to the UBV versions of the plot shown elsewhere on this webpage).

      Theoretical models and observed stellar spectra from SDSS/SEGUE DR8. Colors indicate metalllcity for both the models and the actually observed stars. The panels from left to right in each version of the figure show stars that are approximately giants, subgiants, and dwarfs, respectively. From Casagrane & VandenBerg (2014, MNRAS, 444, 392).

    • Quantifying "Ultraviolet Excess":
      • Traditionally adopt the locus of stars in the Hyades open star cluster to represent "solar metallicity" .
        • Note, however, actual Hyades [Fe/H] ~ +0.25 (i.e., a bit more metal rich than the Sun...)!
      • The UVX, written as:

        is the difference of a star's (U-B) color from that of a Hyades star of the same (B-V) color.

        Modified from Wildey et al. (1962) and Mihalas & Binney (1980).

      • Wildey et al. (1962; Table 4) tabulate blanketing vectors Δ(U-B), Δ(B-V), and corresponding δ(U-B) for each B-V.

    • Connection between δ(U-B) and [Fe/H]...

      • ... unfortunately, the connection of the size of δ(U-B) to the size of [Fe/H] is a function of B-V!!
      • Isometallicity lines from Sandage (1969). Note that the "guillotine'' represents the limit of UVX for stars with no metals.
      • To bring some uniformity to the translation of δ(U-B) to [Fe/H], Sandage (1969, ApJ, 158, 1115 ) invented a normalization of δ(U-B) for different B-V.

        The normalization is such that we correct all δ(U-B) to the δ(U-B) of a star with the same metallicity but (B-V)=0.6.

        This table from Sandage (1969) gives the corrections for interpolation to the "standard" δ(U-B)0.6.
      • See also Box 5.4 in Binney & Merrifield for a description of this correction.

    • Armed with normalized δ(U-B)0.6, we may now estimate the [Fe/H] for any star.

      Several schemes have been given:

      • Mihalas & Binney (1980, eqn. 3-42) give the simple relation "for modest values of δ(U-B)0.6":

        [Fe/H] = [Fe/H]Hyades - 5δ(U-B)0.6

      • Laird et al. (1988, AJ, 95, 1843) gives (see Binney & Merrifield Box 5.4):

        δ(U-B)0.6 ~ -0.0776 + (0.01191-0.05353[Fe/H])1/2

    Why Are There "Subdwarfs"?

    It was noticed in the 1950s (perhaps earlier?), that stars with an ultraviolet excess also appeared to be subluminous with respect to normal Population I type stars.

    • For example: figures from Eggen & Sandage (1962, ApJ, 136, 735) showing the color-absolute magnitude diagram for stars of measured parallax sorted by their ultraviolet excess.

      These panels show a correlation of δ(U-B) with subluminosity compared to, say, the Hyades.

      Figures from Eggen & Sandage (1962).

    • Note that the above figures are very hard to make (properly) because it requires having trigonometric parallaxes for these subdwarfs.

      • Because subdwarfs are associated with Population II there are very few of them near the Sun, where reliable parallaxes can be obtained!
      • This is a continuing problem in astronomy, and the situation is only marginally better after HIPPARCOS, which contributed only a few more parallaxes for subdwarfs.
      • Figure from Reid (1999, ARAA, p.203) showing the current state of the art after HIPPARCOS obtained parallaxes for a few more subdwarfs. A concerted effort by the US Naval Observatory to do CCD parallaxes of subdwarfs has also contributed to this endeavor.

      • Traditionally this problem has been greatly affected by a statistical bias (called the Lutz-Kelker bias) inherent to creating a figure like the above out of the few subdwarfs we had managed to be able to get parallaxes for (a problem that also affects Gaia, but not to the same degree --- we will return to in the distance scale section of the course).
      • Now that Gaia is out, we can finally get large numbers of metal-poor stars that can be used to calibrate our subdwarf sequences "once and for all". We show here again one version of this, the globular cluster sequences we already showed above.

        Combined color-absolute magnitude diagrams for 14 globular clusters of similar age from Gaia DR2 data, with stars color-coded by metallicity. From .

        (Note that wwe already saw on the previous web lecture that Gaia shows a sorting of high velocity stars to "subdwarf" areas of the absolute magnitude CMD for nearby stars).
      • Figures like those above are critical components to the distance scale problem, because they are used to get distances to globular clusters from main sequence fitting.

    • What is the origin of the subdwarf effect?

      • Recall that in the V band, backwarming dominates line blanketing as we add metallicity to a star.
      • Thus, as we make a star more metal-poor (i.e., as we deblanket it), by the backwarming effect one would think that not only does the star become bluer in (B-V) [and (U-B)], but it also should get fainter in V:
      • Color-magnitude vector for subdwarfness by Wildey et al. (1962).

        So, from the combination of stellar atmospheric blanketing/backwarming effects one would think that the main sequence locus, for increasingly metal poor populations moves left (blueward) and slightly down (fainter) in the CMD, something like this:

      • But there is also a competing stellar interiors effect that as one decreases the metallicity of a star, the opacity is reduced. This makes the overall energy output at the surface greater and the luminosity of the star increases.

      • Thus, ironically, "subdwarfs" are actually more luminous than their higher metallicity counterparts of same mass, and so "subdwarfs" is therefore a misnomer!

        • The truth of the matter is that while the subdwarf "sequence" lies below the high metallicity main sequence, subdwarf and solar metallicity stars at the same color have different mass, and subdwarfs of the same mass are bluer and brighter than their more metal rich counterparts.

      • Similar atmosphere/interior effects manifest themselves along other stellar loci in the CMD, for example, the reason why red giant branches vary for clusters of different abundance (see the Gaia globular cluster plot above, and the MIST isochrones, repeated here:
      • A more up to date version of the same from the MIST isocrhones (unfortunately, age of this set unknown -- sorry). From
  • Connection between δ(U-B)0.6 and δMV

    • One can use the Wildey et al. (or other) calibrations of blanketing effects and make the direct connection between ultraviolet excess and subdwarfness.
    • One calibration of the relation by Laird et al. (1988, AJ, 95, 1843) gives (see Binney & Merrifield, P. 277):

      δMV = 0.862 [-0.6888 δ(U-B)0.6 + 53.14 δ(U-B)0.62 - 97.004 δ(U-B)0.63]
    • Approximate relation in terms of [Fe/H], by Reid & Majewski (1993, ApJ, 409, 635):

      δMV ~ -0.87 δ[Fe/H]

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    Filter curves taken from All other material copyright © 2003, 2006, 2008, 2010, 2012, 2014, 2016, 2018, 2020 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 551 and Astronomy 5610 at the University of Virginia.