MAIN-SEQUENCE FITTING DISTANCE TO THE σ Ori CLUSTER

σ Ori A and σ Ori B are the two brightest cluster members. This visual pair, with a separation of 0.25'', lies roughly at the center of the cluster. Horch et al. (2001) used speckle observations to derive a V-band magnitude difference of 125. Similar results were found by Ten Brummelaar et al. (2000), who report ΔV = 124. Given a combined magnitude of V = 38 and an E(B − V) of ∼006 (see Section 2.2), a magnitude difference of 125 indicates that σ Ori A has V₀ ≃ 391 while σ Ori B has V₀≃ 516.

σ Ori A is itself a double-lined spectroscopic binary. Bolton (1974) estimated a ΔV of ∼05 between σ Ori Aa and σ Ori Ab. This would require σ Ori Aa and Ab to have V₀∼44 and ∼49, respectively. There is no measured spectral type for σ Ori Ab yet, so its UBV colors are unknown. Assuming that it is on the zero-age main sequence (ZAMS), the spectral type a star that is 05 fainter than an O9V star should be is B0V.

Edwards (1976) quotes spectral types of O9V and B0.5V for σ Ori A and B, respectively. Assuming an uncertainty of ±0.5 subtypes, we adopt values of (B − V)₀ ≃ −031 ± 0.01 for σ Ori Aa and (B − V)₀ ≃ −028 ± 0.02 for σ Ori B (Kenyon & Hartmann 1995).

The observed B − V for σ Ori AB is −0.24. Assuming an intrinsic color (B − V)₀ = −030 for σ Ori AB, E(B − V) must be ∼006. This is consistent with the observed N(H) column density of 3.3 × 10²⁰ cm⁻² (Fruscione et al. 1994; Bohlin et al. 1983). The uncertainty on the column density is 20%. This value is also consistent with published estimates of the line of sight reddening to σ Ori AB (e.g. Lee 1968) and with the N(H) column density of 3.6 × 10²⁰ cm⁻² measured by Shull & Van Steenberg (1985).

Greenstein & Wallerstein (1958) measured the B and V magnitudes of σ Ori C. They noted that the observed B − V color of σ Ori C, −002, is too blue for its spectral type, A2V, which should have (B − V)₀ = 006 (Kenyon & Hartmann 1995). Greenstein & Wallerstein (1958) account for the exceptionally blue color of σ Ori C as the result of scattered light from σ Ori AB (11'' away) in the aperture of the photometer. The published V magnitude is 879 (Greenstein & Wallerstein 1958), but that measurement was also contaminated by scattered V-band light from σ Ori AB. Greenstein & Wallerstein (1958) estimate that, after correcting for scattered light, the true V magnitude of σ Ori C is ∼92.

W. H. Sherry et al. (2008, in preparation) report recent differential V and I_C photometry for stars within 6' of σ Ori AB. While σ Ori AB is saturated, C, D, and E are not saturated. They find that σ Ori C is 263 ± 0.01 mag fainter than σ Ori D, and 274 ± 0.01 mag fainter than σ Ori E in the V band. Using the V magnitudes from Table 1 for σ Ori D and σ Ori E yields V = 944 and V = 940, respectively, for σ Ori C. These measurements were done using small apertures which are not significantly contaminated by scattered light. We will adopt V = 942 ± 0.02 for the magnitude of σ Ori C (uncorrected for reddening).

The three papers that report UBV photometry for σ Ori D quote significantly different V magnitudes, and, to a lesser extent, colors. Greenstein & Wallerstein (1958) report a V magnitude of 662. Eighteen years later, Vogt (1976) reported a V magnitude of 673. Guetter (1979) reported a V magnitude of 684. These discrepant V magnitudes may indicate variability, or that stray light from σ Ori AB affected the measurements of σ Ori D. Mermilliod & Mermilliod (1994) list a weighted averaged of the UBV photometry for σ Ori D which we have used in Table 1.

The B2Vp star σ Ori E has unusually strong He lines (Greenstein & Wallerstein 1958) which make it spectroscopically peculiar. It has variable line widths and photometric variations (Δmag ∼ 003–015) with a period of 1.19 days (Hesser et al. 1976; Townsend et al. 2005). There are conflicting opinions as to whether σ Ori E is physically associated with σ Ori AB. Much of the uncertainty surrounding the membership of σ Ori E with σ Ori AB follows from uncertainty on the mass and evolutionary status of σ Ori E. Greenstein & Wallerstein (1958) estimated the absolute magnitude of σ Ori E using three different methods, thereby placing the star on or near the main sequence (which would put σ Ori D, and σ Ori E at the same distance). They found that the equivalent widths of two components of the interstellar K line are similar for both σ Ori AB and σ Ori E, as are the radial velocities. Attempts to model the UV flux from the V-band flux and spectroscopic features lead to models of σ Ori E that have masses that are far too small (∼3 M_☉) for an early B main-sequence star (M ∼ 9 M_☉). The main reason for the low masses in these models is that the profiles of the Balmer and helium lines indicate a low gravity (Hunger et al. 1989). More recent models postulate emission from plasma clouds magnetically confined above the photosphere (Townsend et al. 2005) which may explain the discrepancy between the gravity estimated from line profiles and data that indicate that σ Ori E is a main-sequence star. Given the significant uncertainties on the models, we take the observations indicating that σ Ori E is a main-sequence star with a normal mass and radius for its spectral type at face value.

A B2V star has (B − V)₀ of −024 (Kenyon & Hartmann 1995). The measured B − V for σ Ori E is −018 (Guetter 1979), which makes E(B − V) 006. This is consistent with the observed N(H) column density of 4.5 × 10²⁰ cm⁻² (Fruscione et al. 1994; Shull & Van Steenberg 1985). The uncertainty on the column density is 20%.

BD −02 1323C was not found by our initial SIMBAD search for early-type stars within 30' of σ Ori. This star came to our attention because SIMBAD notes that HD 294272 is a member of a triple system, ADS 4240 (Aitken 1932). ADS 4240A is HD 294271. ADS 4240B is HD 294272 which is separated from HD 294271 by ∼68''. ADS 4240C (BD −02 1323C) is separated from HD 294272 by 8.5''. SIMBAD listed a V magnitude of 103 for BD −02 1323C, and no other photometric measurements. This value is not correct.

Guetter (1979) reported photometry for BD −02 1323A and BD −02 1323B. Guetter (1981) used the same names when he reported the spectral types. SIMBAD, which does not recognize the names BD −02 1323A and BD −02 1323B, assigned the Guetter (1979) photometry for BD −02 1323B (ADS 4240C) to BD −02 1323 which is ADS 4240B or HD 294272. Consequently, HD 294272 (ADS 4240B) was listed in SIMBAD as having the photometry and spectral type of BD −02 1323C (ADS 4240C). The measurements for the two stars from Guetter (1979, 1981) and Mermilliod & Mermilliod (1994) have been correctly assigned in Table 1.

We obtained new spectra for HD 294273 & HD 294279 since the only published spectral types that we could find are A2 and A3, respectively, in the HD catalog. The Ca ii K lines are far too strong for early A spectral types. The revised spectral types are early F (F0-F3) for HD 294279 and A7 for HD 294273. We do not assign a luminosity class, but it is likely that they are both class V.

The SIMBAD data base lists this star with a spectral type of A0V. This spectral type appears to be from the SAO catalog (SAO catalog 1966). Guetter (1981) reports a spectral type of A8V; however, the measured value of B − V is slightly bluer than (B − V)₀ for an A8V star (Kenyon & Hartmann 1995). If the color is correct, then HD 37564 should have a spectral type of A7 or earlier if it is reddened. In our spectrum the Balmer lines match spectral type A5 standards, while the depth of the Ca ii K line suggests a slightly later type of about A7.

HD 37564 is the reddest of the three bright outliers in Figure 3. At spectral type A7V, it lies roughly 1.4 magnitude above the 2.5 Myr isochrone. HD 37564 could be a foreground field star at a distance of ∼150 pc. If the spectral type is later than A7V, then the mismatch between the measured V magnitude and the expected V magnitude for a distance of 440 pc is even larger. This is consistent with previous studies that concluded that HD 37564 is probably not a member of Orion OB1 (Brown et al. 1994).

HD 37333, the other obvious outlier, is 0.75 mag brighter than expected for a dereddened A0V star at a distance of 440 pc. Since 0.75 mag is the exact magnitude difference which an equal mass binary would have, it is quite plausible that HD 37333 is a cluster member that is an equal mass binary.

If HD 37333 is not an equal mass (or nearly equal mass) binary, then it is too bright to be a member of the cluster. If it is a main-sequence field star, its likely distance modulus would be ∼310 pc. A distance of 310 pc would be consistent with membership in the Orion OB1a group, but an A0V ZAMS star would be more than 0.5 mag. fainter than an A0V main-sequence field star.

HD 294272 is a member of a multiple system, ADS 4240. It is not clear if ADS 4240A (HD 294271), ADS 4240B (HD 294272), and ADS 4240C (BD −02 1323C) are a bound system or a chance alignment. The small separation between HD 294272 and BD −02 1323C (8.5'') suggests that at least these two stars are a physical system. However, HD 294272 has been classified as a B9.5III star (Guetter 1981) and is 029 brighter than BD −02 1323C which is a B8V star. HD 294272 lies ∼08 above the 2.5 Myr isochrone (Palla & Stahler 1999). The location of BD −02 1323C on the CMD is consistent with the best-fit distance to the cluster. If HD 294272 and BD −02 1323C are in fact a bound pair, then HD 294272 is too bright to be a main-sequence star. One possibility is that HD 294272 is a binary with a pre-main-sequence (PMS) companion. This would make the unresolved binary brighter and redder. Since the PMS companion would be brighter than a main-sequence star of the same color, the unresolved system could be consistent with cluster membership. An alternative is that HD 294272 is not a cluster member, although this makes the small apparent separation unlikely.

As stated above, we find that HD 294279 has a spectral type of F0-F3. This is consistent with the observed B − V color of 0.39 and modest reddening. An A_V of ∼0 places the star ∼1 mag above the main sequence and 1 mag below the 2.5 Myr isochrone at the best-fit distance to the cluster. This strongly suggests that HD 294279 is a foreground field star.

Caballero (2006) report a spectral type of F3 to F5 and the detection of Li in the spectrum. If the spectral type were as late as F5, then HD 294279 would lie near the isochrone, but its observed B − V is 0.39 which is much too blue for an F5 star with the cluster's measured E(B − V). Such a star should have B − V = 0.50. The detection of Li in the spectrum suggests that HD 294279 may be a member of Orion OB1a. HD 294279 lies closer to an 11 Myr old isochrone at 330 pc than it does to the σ Ori isochrone.

With a revised spectral type of A7, HD 294273 has an A_V which is the same as that of cluster members. It also lies on the ZAMS for a distance of 440 pc. However, for it to be a cluster member it would need to be ∼5 Myr older than the age of the cluster. Since there is no evidence for such a large age spread, we think that it is far more likely that HD 294273 is a field star. It is probably slightly more distant than the σ Ori cluster because stars on the main sequence are brighter than stars of the same spectral type on the ZAMS.

We examined two empirical ZAMS (Turner 1976, 1979; Schmidt-Kaler 1982) in order to select the best representation of the σ Ori cluster's main sequence. Both ZAMS closely follow the cluster's main sequence.

We use both versions of the ZAMS because, although Turner's ZAMS follows the locus of cluster members on the CMD nearly perfectly, it does not include U-band photometry. The ZAMS from Schmidt-Kaler does not trace the locus of our data quite as well, but includes U-band photometry. The U-band ZAMS values are valuable because the slope of the ZAMS is ∼6 on the (U − B)₀ versus V₀ CMD and ∼4.5 on the (U − V)₀ versus V₀ CMD. These slopes are much shallower than the slope of ∼18 on the (B − V)₀ versus V₀ CMD. This makes the best-fit distance less sensitive to small errors in the reddening correction.

We shifted the ZAMS of Turner (1976, 1979) to match the Pleiades cluster which has in turn been matched to the Hyades cluster (An et al. 2007). The Hyades cluster has [Fe/H] = +0.14 ± 0.05 and a distance modulus of 3.33 ± 0.01 (Perryman et al. 1998). The Pleiades has a nearly solar [Fe/H] of ∼+0.04 ± 0.03 (An et al. 2007).

The left panel of Figure 4 shows the ten members of the cluster which have reached the ZAMS. The lines show the ZAMS of Turner shifted to distances ranging from 350 pc to 464 pc.

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We estimated the most probable distance to the cluster by calculating χ²_ν for the ZAMS shifted to 1000 candidate distances between 280 pc and 530 pc. For each candidate distance we calculated χ²_ν from the separation between the empirical ZAMS and the (B − V)₀ colors of the nine main-sequence cluster members for which we have directly measured B − V colors, or spectral types. We used the (B − V)₀ colors as the dependent variable for the χ²_ν calculation because the uncertainties in the colors dominate the uncertainties on the estimated distance. Our best-fit distance is 442 ± 20 pc.

The small value, 0.5, of our best χ²_ν suggests that we have overestimated the uncertainties on the (B − V)₀ colors.

Using the ZAMS of Schmidt-Kaler (1982), also shifted to match the Pleiades, on the (B − V)₀ versus V₀ CMD, we find a best-fit distance of 462⁺¹⁴₋₃₅ pc. This is 1σ larger than the best-fit distance using the Turner (1976) ZAMS.

The right panel of Figure 4 compares the data for the main-sequence cluster members to the ZAMS on the (U − B)₀ versus V₀ CMD. The best-fit distance is 488⁺¹⁸₋₂₀ pc. The right panel of Figure 4 plots (U − B)₀ colors corrected using the expected value of E(U − B) = 0.04. The V data have been corrected for reddening using the A_V derived from the mean E(B − V) in Section 2.2. If the (U − B) colors were corrected by the mean value of E(U − B) = 0.02, then the derived distance would be 458⁺¹⁵₋₁₇ pc.

We also estimated the cluster's distance on the (U − V)₀ versus V₀ CMD. The best-fit distance is 492⁺¹⁸₋₃₁ pc using a normal reddening law and the observed E(B − V) of 006 ± 0.005, or 457⁺²⁸₋₁₆ pc using the measured value of E(U − V) = 008 ± 0.03. The distances estimated using the U-band photometry combined with a standard reddening law are 2σ larger than the distances estimated from colors corrected by the mean measured E(U − B) or E(U − V). They are also 2σ larger than the distance estimated from the (B − V) colors. This may indicate that the cluster has a non-standard reddening law with E(U − B) = 0.36E(B − V).

An alternative is to use the reddening-corrected (U − B)₀ and (U − V)₀ colors that correspond to the observed spectral types. Doing that, we find distances of 452 ± 14 pc and 447⁺¹³₋₇ pc, respectively. Since there is much more scatter in the observed U − B colors (which we used to get the U − V colors) than in the observed B − V colors, using the spectroscopic colors to estimate the cluster's distance may be more accurate.

Table 2 collects all of the distances we estimated using different color indices, reddenings, ZAMS, and metallicities.

Table 2. Distance Estimates (pc)

ZAMS/Color	$\frac{Fe}{H}$ = +0.04	$\frac{Fe}{H}$ = 0.0	$\frac{Fe}{H}$ = −0.05	$\frac{Fe}{H}$ = −0.16	$\frac{Fe}{H}$ = −0.27	Color correction
Turner B − V	442 ± 20	436 ± 20	428 ± 19	412 ± 19	397 ± 18	Mean E(B − V)
Schmidt-Kaler B − V	462+14−35	456+14−35	448+14−34	431+13−33	415+13−31	Mean E(B − V)
Schmidt-Kaler U − B	488+18−20	481+18−20	473+17−19	455+17−19	438+16−18	Mean E(B − V)1
Schmidt-Kaler U − B	458+15−17	452+15−17	444+15−16	427+14−16	411+13−15	Mean E(U − B)
Schmidt-Kaler U − B	452 ± 14	445 ± 14	438 ± 14	422 ± 13	406 ± 13	SpT2
Schmidt-Kaler U − V	492+18−31	485+18−31	477+17−30	459+17−29	442+16−28	Mean E(B − V)1
Schmidt-Kaler U − V	457+28−16	451+28−16	443+27−16	426+26−15	411+25−14	Mean E(U − V)
Schmidt-Kaler U − V	447+13−7	441+13−7	433+13−7	417+12−7	402+12−6	SpT2
Combined Estimate3	450 ± 20	444 ± 20	436 ± 20	420 ± 20	404 ± 20

Notes. ¹Assuming a standard reddening law with E(U − B) = 0.72E(B − V). ²We adopted the colors for each star's spectral type given by Kenyon & Hartmann (1995). ³The estimated uncertainties include only the random error from the fit. The systematic uncertainty from the choice of ZAMS is at least 10 pc. Combined with the uncertainty on the metallicity, the total systematic error is ∼25 pc.

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It is not straightforward to combine the best-fit distance estimates into a single best-fit distance. The various results we obtained using the Schmidt-Kaler (1982) and the Turner (1976) ZAMS should not simply be averaged because the differences between them are systematic, not random. Given the difficulties correcting for the reddening on the V, U − B and V, U − V CMDs, we give more weight to the distance estimates we found using the spectroscopic colors. These distance estimates, combined with the distance estimates from the V, B − V CMD, indicate a best-fit distance of 444 ± 20 pc assuming solar metallicity. Correcting for the lower metallicity of the cluster brings the distance estimate down to somewhere between 400 pc and 440 pc. At the most likely metallicity, the best-fit cluster distance is 420 ± 20 (random) ± 25 (systematic) pc or 420 ± 30 pc. As knowledge of the cluster's metallicity is refined, the best estimate of the distance modulus will shift and the systematic component of the uncertainty will be reduced. It is important to note that for the purposes of comparing the cluster to solar metallicity isochrones, the isochrone should be shifted to be ∼012 fainter to compensate for the lower luminosity of a sub-solar metallicity isochrone. For low-mass stars line-blanketing will shift the isochrone by an additional amount that will depend upon the color index used on the CMD.

The final line of Table 2 lists the best "average" distance estimates for five assumed values for the cluster's metallicity. The assumed metallicities range from +0.04 to −0.27. The uncertainties include only the random component of the uncertainty.