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We correct our measurement of the surface density of the disk of the Milky Way in the solar neighborhood, Korchagin et al. 2003 (hereafter K03). In K03, a sample of old, red-giant stars was extracted from the Hipparcos Catalog to serve as a set of kinematic test particles with which to measure the underlying gravitational matter distribution. The sample was constructed using a theoretical 3 Gyr isochrone as a blueward boundary within the HR diagram. A previously undetected coding error applied the wrong sign to the stars' B − V color corrections, resulting in a sample that was improperly formed. Note that while our color corrections were in error, the extinction corrections (and thus absolute magnitudes) were calculated properly. Upon correcting the error, and thus the composition of the sample, our estimate of the disk surface density becomes 40 ± 6 M⊙ pc−2.
Figure 1 shows the corrected HR diagram and location of the boundaries of the RG2 sample of old red-giant stars. The corrected sample contains 1049 stars, compared to the flawed sample's 1476 stars. As one would expect, the difference in the samples is preferentially at low latitude where reddening is larger. This can be seen in Figure 2, a plot of individual star absorption values as a function of distance from the Galactic plane, z.
Figure 1. Corrected version of Figure 2 in K03; HR diagram constructed from the Hipparcos catalog for the survey stars satisfying the apparent-magnitude completeness criteria. Dotted lines show the superimposed Yale-Yonsei isochrones for solar metallicity stars with ages 1 Gyr and 3 Gyr. The surface density is determined from the sample of stars that falls within the region labeled RG2. These are presumed to be old, bright red giants with ages greater than 3 Gyr. The absolute magnitudes of stars have been corrected for extinction and colors are now properly corrected for reddening.
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Figure 2. Corrected version of Figure 4 in K03; calculated visual absorption corrections for each of the bright red giant stars in our RG2 sample as a function of distance from the plane, z. The blue curve shows the mean trend for the properly color-corrected sample, while the red curve shows the erroneous mean curve from K03.
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Standard image High-resolution imageIn addition to the effects of extinction and a geometric correction for the non-cylindrical shape of the sample volume (see K03), the sample's z distribution must also be corrected for Lutz-Kelker bias, which is caused by the finite relative errors of the measured trigonometric parallaxes. Figure 3 shows the final z distribution of the corrected RG2 sample after these corrections are made (thick blue curve). For comparison, the distribution of the earlier, flawed sample is also shown (thick red curve).
Figure 3. Corrected version of Figure 7 in K03; the upper panel shows the z distribution of red giant stars older than ∼3 Gyr in the Hipparcos catalog (dashed line) compared with the extinction-corrected distribution of Hipparcos red giants (thin blue line), and that distribution adjusted for individual parallax measurement errors (heavy blue line). To illustrate the effect of our original color-correction error, the thin and heavy red lines show the comparable but erroneous curves presented in K03. The bottom panel shows the parallax error correction factor calculated for the exponential and sech2 distributions of stars (black curves) together with the relative parallax error σπ/π as a function of z (blue dots) for the properly color-corrected sample.
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Standard image High-resolution imageAnalytical fits to the adjusted z distribution are made, using functions of z that are exponential, sech, and sech2 in form. Figure 4 shows the best-fit functions to the observed z distribution of the corrected RG2 sample. As in K03, the fits are made over the range 0.05 kpc < 
< 0.35 kpc. The best-fit scale height for each functional form is listed in the second line of Table 1. Uncertainties are those from K03, scaled by the respective increases in scale-height value. The functional form that is adopted for the purpose of surface-density calculation is that of sech2, for which the best-fit scale height is 357 pc compared to 280 pc for the original, flawed RG2 sample.
Figure 4. Corrected version of Figure 8 in K03; extinction and distance-error corrected z distribution of old red giants represented by the RG2 sample (blue curve). Also shown are functional fits—exponential (dashed black curve), and sech and sech2 (solid black curves). The fits were made over the interval 0.05 kpc < 
< 0.35 kpc. The z distribution derived from the original, flawed sample is shown in red.
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| Sample | exp(z/H) | sech(z/H) | sech2(z/H) |
|---|---|---|---|
| Flawed (K03) | 283 ± 27 | 185 ± 15 | 280 ± 15 pc |
| Corrected | 415 ± 40 | 241 ± 20 | 357 ± 19 pc |
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As shown by Equation (6) in K03, the integrated surface density within +/−zout depends inversely on the scale height of the test particles and is proportional to the square of their vertical velocity dispersion, σz. A second sample, designated RG2RV, is constructed that consists of old, red-giant stars with measured radial velocities. This sample is used to estimate σz. With proper color correction, this sample consists of 1227 stars, compared to 1868 stars in the RG2RV sample of K03. Figure 5 shows the normalized distribution in vertical velocity, vz, for the new sample (blue histogram) compared to that of the flawed sample of K03 (red histogram). The dispersions of the full and core portions of the corrected distribution are 16.4 km s−1 and 14.9 km s−1, respectively, after adjustment for the estimated velocity measurement errors. A final adjustment for inflation of the observed dispersion by an expected binary fraction and its associated orbital motion (see K03) brings the "true" full and core dispersion values to 15.9 km s−1 and 14.3 km s−1. These values are roughly 4% larger than the equivalent determinations in K03.
Figure 5. Normalized histogram of the vertical velocities of the corrected RG2RV sample (blue line) compared to that of the flawed sample from K03 (red). The distributions are roughly similar, with that of the corrected sample being slightly wider. (Compare to Figure 14 of K03.)
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Using the revised determinations of the sech2 scale height and core vertical-velocity dispersion, as in K03, we make a corrected estimate of the Milky Way surface density within +/−350 pc of the plane. Adding in the small ∼1 M⊙ pc−2 contribution from the second term in Equation (6) of K03, the enclosed surface density is 33 ± 6 M⊙ pc−2. (The stated uncertainty is a combination of the propagated statistical errors and a somewhat larger systematic component, the latter being deduced from the difference in surface density value from a trial solution employing the sech fit to the z distribution, as opposed to the sech2 fit.) Alternatively, if one were to adopt the full distribution's intrinsic dispersion of 15.9 km s−1, the resulting value of surface density within +/−350 pc of the plane becomes 40 ± 6 M⊙ pc−2. In retrospect, there is little justification for adopting a "core" velocity dispersion and, thus, we feel a surface density of 40 ± 6 M⊙ pc−2, based on the dispersion of the full RV sample, is the preferred value.
We are grateful to Eric Kramer for discovering and bringing to our attention the discrepancy that led to our finding the coding error in our original study.