THE STELLAR POPULATION OF h AND χ PERSEI: CLUSTER PROPERTIES, MEMBERSHIP, AND THE INTRINSIC COLORS AND TEMPERATURES OF STARS

2.1.1. Observations, Image Processing, and Photometry

2.1.2. Saturation and Completeness

The initial photometric catalog has roughly 52,000 candidate sources detected in at least one filter for at least one exposure time. To remove sources with bad photometry, we check each star for blending, check stars for contamination from image artifacts (e.g., diffraction spikes from nearby bright stars), and identify stars with point-spread functions (PSFs) indicative of saturation. By comparing the photometry from different exposure times, we empirically identify a saturation limit of V ∼ 15 and 16.5 for t = 75 s and 300 s exposures and I ∼ 15.5 for t = 75 s. The saturation limit for the shortest V-band exposures (t = 2 s) is V ∼ 11 (see Section 2.1.3). Photometry for saturated stars was then flagged and removed from the catalog, while blends and contaminated stars were identified. Priority was given to stars lacking contamination or blending flags regardless of rms errors. Otherwise, the photometry for the final catalog was selected from the exposure that yielded the smallest rms errors.

The final catalog lists 47,060 stars with detections in both filters. Of these, we use photometry derived from the longest exposures (300 s for V band, 75 s for I band) for ∼ 90% of the detections in either filter. Other sources are either bright stars saturated in the long exposures or are near bright stars and masked from view in the long exposures. Photometry is chosen from shorter exposures for these sources. Table 1 lists all stars detected at both V and I bands.

Table 1. Optical Photometry Catalog

Running Number	R.A.	Decl.	t$_{\rm{int.}, V}$	V	σ(V)	Photometry Flag (V)	t$_{\rm{int.}, I_{c}}$	Ic	σ(Ic)	Photometry Flag (Ic)
1	35.6018	57.1095	2	7.8257	0.0001	−9	2	6.3208	0.0000	−9
2	35.7515	57.3870	2	7.1912	0.0000	−9	2	6.5893	0.0000	−9
3	34.7691	57.1355	2	7.1731	0.0000	−9	2	6.6876	0.0000	−9
4	35.4814	57.2429	2	7.2686	0.0000	−9	2	6.7332	0.0000	−9
5	35.2484	57.1583	2	7.7409	0.0001	−9	2	6.7185	0.0000	−9

Note. The photometry flags have the following meanings: −1 = unsaturated, uncrowded; −2 = crowded, PSF fitting used; −9 = likely saturated.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Figure 1 shows the distribution of V and I magnitudes versus their photometric uncertainties. There are clearly three (two) distributions of V versus σ(V) (I versus σ(I)), which result from the three (two) separate exposure times used. The 5σ (10σ) limits in the V band are V = 21, 23, and 24 (19.5, 22, 23.25) for 2, 75, and 300 s exposure times. The corresponding limits in the I band are I = 19.5, 23.5 (19, 23) for 2 s and 75 s exposures. The number counts in V-band plateau at V ∼ 22–24 and fall rapidly for fainter magnitudes. The number counts in the I-band peak at I ∼ 21.

Zoom In Zoom Out Reset image size

2.1.3. Comparisons with Previous Photometric Surveys

To provide a context for our photometry, we cross correlate our source list with catalogs from three major photometric surveys: Mayne et al. (2007), Slesnick et al. (2002), and Keller et al. (2001). Mayne et al. (2007) is by far the deepest of the three but has a slightly smaller coverage area than our photometry (∼ 0.45 deg²). Slesnick et al. (2002) is the shallowest but has a larger coverage (∼ 1 deg²), and Keller et al. (2001) is intermediate in depth and has the smallest coverage (∼ 0.37 deg²). The Mayne et al. (2007) and Keller et al. (2001) catalogs include I-band photometry; Slesnick et al. (2002) lacks I-band photometry.

To limiting magnitudes of V = 22 and I = 19.5, our photometry agrees very well with data from Mayne et al. (2007). To make this comparison, we consider a broad range of V = 11–22 where our photometry is unsaturated and where the Mayne et al. (2007) data have errors ≲ 0.1 mag. For this range of V, the V − I colors for most stars range from ∼ 0 to 2.5. Using a 10 matching radius, we find 13,806 common sources brighter than V = 22. Figure 2 (top panels) shows histogram plots of the differences in V and I magnitudes binned in units of 0.02 mag. The differences in magnitudes are consistent with Gaussian distributions that are strongly peaked about zero with full width half-maxima of ≈0.04 and 0.06 mag for V and I.

Zoom In Zoom Out Reset image size

The agreement between our V-band photometry and that from Slesnick et al. (2002) is also excellent. The distribution of V magnitude differences among 1307 common sources has a full width half-maximum of ∼ 0.04 mag (Figure 2, middle panels). For nearly all sources with photometric differences greater than ∼ 0.1 mag, we find fainter magnitudes from our photometry. Slesnick et al. (2002) measure stars' brightnesses using aperture photometry, whereas our method deblends overlapping sources. Therefore, the few cases with slightly discrepant photometry were plausibly blended sources in Slesnick et al. (2002) that were deblended with our photometry.

Our V-band photometry shows good agreement with that from Keller et al. (2001, Figure 2, bottom left panel). The distribution of magnitude differences from 5355 common sources (V ≲ 21) has an FWHM of ∼ 0.06 mag. However, we find substantial disagreement between the Keller et al. (2001) photometry and our I-band photometry (Figure 2, bottom right panel): there is a ∼ 0.2 mag zero-point offset and an additional, possibly color-dependent term which results in a wide dispersion (FWHM ∼ 0.2 mag). We speculate that this difference may arise because Keller et al. (2001) used a nonstandard I-band filter or had larger uncertainties in their color transformations.

To supplement the optical photometry, we acquired low-resolution optical spectroscopy of Two Micron All Sky Survey (2MASS)-detected stars within 1 deg² of the cluster centers. For faint (J ⩾ 14.25; V ⩾ 16) stars, we used the multiobject, fiber-fed spectrograph Hectospec (Fabricant et al. 2005) on the 6.5 m MMT. Brighter stars were observed with the fiber-fed spectrograph Hydra (Barden et al. 1993) on the 3.5 m WIYN telescope at Kitt Peak National Observatory and single-slit FAST spectrograph (Fabricant et al. 1998) on the 1.5 m Tillinghast telescope at the Fred Lawrence Whipple Observatory.

2.2.1. Spectroscopy Reduction, Survey Coverage, and Completeness

We obtained Hectospec spectra of 9373 stars with V ∼ 16–19, J ∼ 14.25–16.25, and J−H ∼ 0–1.5 during the Fall 2006 and Fall 2007 observing trimesters in queue mode. Each source was observed in three 10-minute exposures using the 270 mm⁻¹ grating. This configuration yields spectra at 4000–9000 Å with ∼6 Å resolution. The data were processed using the standard Hectospec reduction pipeline (Fabricant et al. 2005) and typically have signal-to-noise ratio (S/N) ≳ 30–50 at 5000 Å.

We acquired additional spectra of 610 sources with the Hydra multifiber spectrograph on the WIYN 3.5 m telescope at the Kitt Peak National Observatory. Hydra spectra were obtained by A. Bragg and S. Kenyon during two observing runs in 2000 November and 2001 October and include stars with V ∼ 14–17 and J ∼ 12–14.5. Exposure times ranged from 30 minutes to 90 minutes, depending on the source brightness and seeing conditions, and yielded spectra with S/N ≈ 10–30. We used the 400 g mm⁻¹ setting blazed at 42°, with a resolution of 7 Å and a coverage of 3600–6700 Å. The standard IRAF task dohydra was used to reduce the spectra. We also obtained spectra of 257 bright (J ⩽ 14.25) stars surrounding h and χ Per with the FAST spectrograph on the 1.5 m Tillinghast telescope at Whipple Observatory. Finally, we added archived data of 1,025 h and χ Persei sources from Bragg & Kenyon (2005) and Bragg (2004).

The combined Hectospec, FAST, and Hydra observations yield 11,265 spectra of stars on the h and χ Per field. The spatial coverage of the Hectospec, FAST, and Hydra observations are shown in Figure 3. Hectospec and FAST observations cover about 1 deg²; Hydra observations and archival data focus on regions within ≈15' of the cluster centers (black dots).

Zoom In Zoom Out Reset image size

Our survey comprises a significant fraction of all 2MASS-detected sources on the field, especially those within ∼10'–15' of the cluster centers. Within the ≈1 deg² area surrounding h and χ Persei, we obtained spectra for 75% of all the 2MASS detections (11,265/14,951). Because many bright stars with colors suggestive of foreground M stars were not selected for observations with Hydra and FAST, completeness is better at faint survey limits (J ⩾ 15; 95%) than for brighter stars (J < 15; 63%)

Completeness in the cluster-dominated regions (r ⩽ 5'–15') is good for stars of all magnitudes. Within 5' of both h Persei and χ Persei, we have spectra for nearly all stars (≳ 98%). Within 10', we have spectra for >80% of bright stars (J < 14), > 95% of faint (J ⩾ 15) stars, and >90% of all stars. The majority (60%–70%) of bright stars at 10'–15' away from the cluster centers are detected. Thus, our spectroscopic survey comprises the vast majority of stars in the cluster-dominated regions, is unbiased within 10' of the cluster centers, and is not biased for faint stars regardless of radial distance from the cluster centers.

2.2.2. Spectral Classification

The large number of spectra observed and the large number of stars earlier than K/M—which can be difficult to spectral type—makes manual, spectral classification inefficient. To spectral type stars, we employ the semiautomatic quantitative spectral-typing code SPTCLASS,⁸ an IRAF/IDL code based on the method described in Hernandez et al. (2004).

SPTCLASS calculates the spectral types of stars using spectral indices, comparing the line flux of spectral features which are sensitive to stellar effective temperature (Payne 1924, 1925, and later references). Three independent spectral typing modules are included in SPTCLASS: indices that characterize early (OBA, 44 indices), intermediate (FG, 11 indices), and late spectral type (KM, 16 indices) stars. Each index is based on the equivalent width for each spectral feature which is obtained by measuring the decrease in flux due to line absorption from the continuum that is expected when interpolating between two adjacent bands. Indices measured by this procedure are largely insensitive to reddening as long as the wavelength coverage of each band is relatively small. Three spectral type estimates are then calculated by averaging the indices characterizing early, intermediate, and late-type stars. In general, visual inspection of the spectrum and the dispersion of individual results indicate which of these three results is the correct one for the star. The errors in these estimates are computed from the dispersion in spectral types for individual indices weighted by their correlation functions.

Typically, the most important lines were Ca ii (3933 Å), the G band (4305 Å), and Na i (5890 Å) for mid A to mid G stars and the TiO bands for later stars (Payne & Williams 1929; Gray & Corbally 2009). The spectral types as determined from individual indices for each of the three modules usually showed strong agreement. In cases where scatter was large (e.g., greater than 2–3 subclasses), we manually smoothed the spectra with splot and measured the indices for highly correlated lines listed above as a check on the computed spectral type.

For O, B, and early A stars, the strongest lines are the Balmer lines and the He i lines (e.g., Payne & Williams 1929, and later references). Because accreting pre-main-sequence stars and Be stars can have Balmer line emission, spectral types based on the Balmer lines are produced by SPTCLASS but are not explicitly included in the semiautomated estimates. However, no B to mid A stars show accretion signatures; the Be star population is well known (e.g., Slesnick et al. 2002; Bragg & Kenyon 2002; Currie et al. 2008b). The absence of Balmer lines in the final spectral type determination may then introduce errors, especially for stars earlier than B5, where strengths of the important Mn i and Fe i lines become uncorrelated with spectral type. Therefore, we slightly modified our approach for early-type stars (B1–A2, as identified by SPTCLASS), basing the spectral types solely on the Balmer indices and He i indices. We selected lines that yielded a minimal scatter in the empirical Hertzsprung–Russell (HR) diagram (V versus spectral type), specifically H_β, H_γ, H_δ, He i 4026 Å, and He i 6678 Å. The median average of the spectral types determined from each of these indices was chosen as the star's spectral type; the standard deviation in these spectral types is identified as the uncertainty in spectral type. While this method produced essentially identical results for B5–A2 stars compared to the nominal SPTCLASS calculation, it significantly tightened the HR diagram locus for earlier stars, thus improving precision. Of the 11,265 stars with spectra, 10,934 were assigned spectral types. Stars without spectral types either had extremely low signal to noise or were cases where the Hectospec or Hydra fibers failed to center on the stars, possibly because of small astrometric errors.

We applied a final correction for the spectral types of the earliest stars by cross-correlating our source list with the spectroscopic survey of Slesnick et al. (2002). There are 108 stars in common. Agreement in spectral types determined from Slesnick et al. (2002) and those determined from SPTCLASS is typically good, within 1 subclass. However, as noted by many authors (Slesnick et al. 2002; Bragg & Kenyon 2005; Schild 1965, 1967), h and χ Persei contains a large population of B supergiants, giants, and subgiants. Differences in luminosity classes for the earliest stars imply differences in surface gravities. Surface gravities affect line strengths and thus induce scatter in determining spectral types from these line strengths if the index-spectral type relationship is derived primarily from main-sequence/pre-main-sequence dwarfs. Therefore, we identify all stars listed by Slesnick et al. (2002) as having luminosity class I–IV and replaced our spectral types with those determined by Slesnick et al. (2002). Aside from shifting several stars initially classified as O9.5–O9.9 to slightly later types (B0–B1.5; see also Bragg 2004), this correction yields inconsequential changes in the spectral type distribution and thus has a negligible impact on our later analysis. Figure 4 displays a spectral type sequence from our sample.

Zoom In Zoom Out Reset image size

Finally, we added 44 stars in the Slesnick et al. (2002) spectroscopic catalog that were not targeted with our survey (see Figure 3 for spatial distribution). These stars were predominantly optically and infrared bright B giants and supergiants, infrared bright red supergiants, and likely foreground dwarfs. Spectral type uncertainties for these 44 stars were set to two subclasses, consistent with the maximum dispersion in spectral types for early-type stars implied by comparing the Slesnick et al. (2002) results to SPTCLASS and previous literature measurements.

Because SPTCLASS does not determine luminosity classes, we manually analyzed the spectra of stars to identify giants and supergiants. Our identification criteria follow Gray & Corbally (2009) and Walborn (1971). For early-type stars, we measured the Si iii 4552/He 4387 I line ratio as a primary indicator with the Si 4116 IV/He 4121 I line ratio and the O ii 4415–4417 line strength as secondary indicators, using spectra from Gray & Corbally (2009) as standards. For M stars, we use the strength of the Ca i 4226 line and the shape of the TiO lines to identify giants and supergiants. Our analysis confirms the identification of giants and supergiants from Slesnick et al. (2002) and adds 30 more for a total of 103 giants and supergiants. Our primary spectra selection criteria (J>14) removes many foreground FGK stars (likely giants/supergiants) from our target list. Moreover, our spectroscopic survey is most complete for regions close to the cluster centers, where we expect the ratio of cluster stars to background/foreground stars to be the highest. Thus, the overwhelmingly large number of dwarfs assuredly overestimates the true ratio of dwarfs to giant stars on the field. Figure 5 displays a luminosity class sequence for early B stars.

Zoom In Zoom Out Reset image size

Our final catalog contains 11,309 stars of which 10,983 have spectral types. Figure 6 shows the distribution of spectral types. The sample contains one O6.5 dwarf star, 914 B stars, 1330 A stars, 4362 F stars, 2525 G stars, 1300 K stars, and 551 M stars. Thus, a large fraction of our sample are either F stars or G stars. Because later-type stars at a given age correspond to lower-mass stars, the large number of FG stars compared to OBA stars is likely a consequence of the IMF. Only 2MASS sources were selected for our Hectospec observations. Cluster sources with JHK_s magnitudes near the 2MASS sensitivity limit (J ∼ 15.7) likely have spectral types between G0 and K0 (Currie et al. 2007a, see also Baraffe et al. 1998). Therefore, the 2MASS sensitivity limits are likely responsible for the low number of detected mid G, K, and M stars.

Zoom In Zoom Out Reset image size

The distribution of uncertainties in spectral types is shown in Figure 7. Most stars have σ(ST) ∼ 2–2.5 subclasses, which indicates that the dispersion in spectral types determined from individual indices is small for the vast majority of our sample. Stars with spectral types between O5 and F0 and K0–M5 have the smallest uncertainties (∼ 1 subclass); stars with spectral types between F5 and G5 have the largest uncertainties (∼ 2.5–3 subclasses). Intermediate spectral type stars have higher uncertainties because they have fewer lines whose indices strongly correlate with spectral type. The deep Balmer lines and He i lines make spectral typing early-type stars robust; spectral typing later-type stars is aided by the TiO lines, whose strengths correlate extremely well with spectral type for stars later than K0. Table 2 lists the properties of stars with spectra. Each spectra taken with Hectospec, Hydra, and FAST is downloadable from the Telescope Data Center Web site: http://tdc-www.cfa.harvard.edu/instruments/hectospec/progs/HXP/ for Hectospec, http://tdc-www.cfa.harvard.edu/instruments/hectospec/progs/hxp/hydra.html for Hydra, and http://tdc-www.cfa.harvard.edu/instruments/fast/progs/ (Programs 83 and 170).

Zoom In Zoom Out Reset image size

Table 2. Spectroscopy Catalog

Running	Source	R.A.	Decl.	Numerical	Spectral Type	J	σ(J)	H	σ(H)	Ks	σ(Ks)
Number				Spectral Type	Uncertainty
1	2	35.4850	57.1471	29.00	3.00	13.3940	0.0450	13.2400	0.0380	13.0114	0.1614
2	2	35.6214	57.2132	29.00	3.00	13.8380	0.0420	13.7570	0.0490	13.5912	0.0256
3	2	35.0118	57.0850	38.50	2.00	11.0890	0.0270	10.8950	0.0210	10.7218	0.0433
4	2	34.8023	57.1390	35.00	3.00	13.2410	0.0420	13.1680	0.0390	12.8050	0.0170
5	2	35.3507	57.2118	22.00	1.90	13.3940	0.0410	13.3100	0.0420	13.1569	0.0821

Notes. The numerical spectral type has the following formalism: 10 = B0, 11 = B1... 68 = M8. The spectral type uncertainty is given in subclasses. The "Source" column refers to the source of the spectroscopic data: Hectospec (1), Hydra (2), FAST (3), or Slesnick et al. 2002 (4).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

2.2.3. Optical Color–Magnitude Diagrams, HR Diagrams, and the Combined Photometric and Spectroscopic Catalog

Figure 8 shows the V/V − I color–magnitude diagram for all stars in our optical catalog. To better identify trends in the V/V − I distribution, we use a Hess diagram, which plots the density of stars in color–magnitude diagrams, using bin sizes of 0.03 mag in V − I and 0.06 mag in V. The densest (darkest) region is located within the range of colors and magnitudes consistent with main-sequence field stars with a wide range of distances, spectral types, and reddenings (e.g., Mayne et al. 2007).

Zoom In Zoom Out Reset image size

Exceptional among nearly all young open clusters, the locus of h and χ Persei stars is obviously distinguishable from the background star population by eye. An extremely narrow (δ(V − I) ∼ 0.25) distribution of stars with bluer colors than the background field star population defines the Hess diagram for V < 17. Equally striking is the distribution of stars extending from V ∼ 19, V − I ∼ 1.75 to V ∼ 24, V − I ∼ 3.5, which has a far more narrow dispersion in color for a given magnitude than the field star population: δ(V − I) ∼ 0.5 at V = 19 to δ(V − I) ∼ 0.75 at V = 24. These distributions are consistent with a single narrow locus of young cluster stars.

Using a 1'' matching radius, there are 7465 sources with spectral types, near-IR photometry, and optical photometry from either our VI survey or from Slesnick et al. (2002). Thus, a substantial percentage (∼ 68%) of stars with spectra have optical data.

For our combined photometric and spectroscopic catalog, we adopt our optical photometry in a first iteration. Our V-band photometry show excellent agreement with that of Slesnick et al. (2002) over a wide magnitude range; our V-band data saturates at V < 11–12. Therefore, we adopt the Slesnick et al. (2002) V-band photometry for stars brighter than V = 12.

Sources with both optical photometry and spectroscopy show a clear distribution from early- to late-type stars (Figure 9). Nearly all stars brighter than 16th magnitude and blueward of V − I = 1 have spectral types between B0 and A5. Similarly, stars from V = 16 to 19 become progressively later (A5 to K0). Comparing both panels of Figure 9 clearly reveals foreground and interloping stars, whose spectral types are discrepant compared to other stars located in the same regions in V/V − I space. Table 3 lists the 7465 stars with optical photometry and spectroscopy. Our study focuses on these stars and on the ∼ 47,000 with optical photometry.

Zoom In Zoom Out Reset image size

Table 3. Combined Catalog for Stars with Optical Photometry and Spectroscopy

ID	R.A.	Decl.	Numerical	Spectral Type	E(B − V)	Luminosity	J	σ(J)	H	σ(H)	Ks	σ(Ks)	V	σ(V)	Ic	σ(Ic)
Number			Spectral Type	Uncertainty		Class
1	35.4684	56.9050	6.50	2.00	0.479	5	8.5170	0.0100	7.6218	0.0001	8.1270	0.0270	8.1320	0.0420	8.1240	0.0260
2	34.7945	57.0249	10.50	1.60	0.532	1	9.8700	0.0100	8.6622	0.0002	9.2100	0.0270	9.1150	0.0290	9.1350	0.0210
3	34.6782	57.0726	10.50	1.50	0.610	3	10.6020	0.0100	9.6145	0.0004	9.8270	0.0250	9.8030	0.0290	9.7900	0.0230
4	34.3963	57.0857	10.50	1.80	0.437	5	9.9250	0.0100	8.6521	0.0002	9.5030	0.0240	9.5510	0.0300	9.5290	0.0220
5	34.7768	57.1261	11.00	1.50	0.594	5	9.8200	0.0100	−99.0000	0.0000	9.0430	0.0320	8.9980	0.0320	8.9740	0.0200

Note. The luminosity class has the following meaning: 1 = Class I supergiant; 3 = Class III giant; 5 = Class V dwarf.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

2.2.4. Determining Effective Temperature Scale and Intrinsic Colors of Dwarfs, Giants, and Supergiants

2.2.5. Measuring Reddening and Extinction

To derive the reddening (E(B − V)) for each source, we compare the observed optical/near-IR colors with intrinsic colors for the star's spectral type. We first convert our 2MASS photometry into the Johnson–Cousins–Glass system as formulated by Bessell (1990) using an updated version⁹ of the color transformations from Carpenter (2001). From our effective temperature scale, we identify T_e for each star based on its spectral type. We calculate the star's intrinsic colors by interpolating between values on the ATLAS9/BDDUST99/BaSeL/Fluks grid for a given T_e.

To constrain reddening for dwarfs and hot giants/supergiants, we use the long-baseline V − J, V − H, and V − K colors. From the equations of Cardelli et al. (1989), the wavelength zero points from Bessell & Brett (1988) and Bessell (1990), and for R_V = A_V/E(B − V) = 3.12, we use

$$\begin{eqnarray} &&E(B-V)_{J} = E(V-J)/2.20, \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} &&E(B-V)_{H} = E(V-H)/2.55, \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} &&E(B-V)_{K} = E(V-K)/2.76. \end{eqnarray} \tag{ 3 }$$

Because our I-band data saturate at much fainter magnitudes than either the Slesnick et al. (2002) V-band photometry or 2MASS, we do not derive E(B − V) from I-band photometry. The difference between the reddening derived from individual colors and the mean reddening has a Gaussian distribution with a full width half-maximum ≲ 0.03 mag centered on 0–0.01. To minimize photometric errors whose propagation leads to errors in reddening, we median combine the three values together to derive a final E(B − V) for each star.¹⁰

For M supergiants, we determine reddening solely from the J − K colors. Most M supergiants in h and χ Persei undergo significant radial pulsations (e.g., Levesque et al. 2005) which change their effective temperatures by tens to 100s of K. Because the Johnson BVI bands fall along the Wien tail of M stars' spectral energy distributions, these temperature changes produce large changes in the stars' V − J, H, and K colors. Furthermore, the long-baseline colors (in particular, V − J) are very sensitive to surface gravity. The J − K colors are only weakly affected by pulsation and photometric errors:

$$\begin{equation} E(B-V) = E(J-K)/0.56. \end{equation} \tag{ 4 }$$

Thus, measuring E(B − V) for all stars on the field, we deredden their photometry in each passband using extinction relations from Cardelli et al. (1989):

$$\begin{eqnarray} &&V_{o} = V_{\rm obs} - 3.12\times E(B-V), \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} &&I_{o} = I_{\rm obs} - 1.87\times E(B-V), \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray} &&J_{o} = J_{\rm obs} - 0.92\times E(B-V), \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} &&H_{o} = H_{\rm obs} - 0.57\times E(B-V), \end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray} &&K_{o} = K_{\rm obs} - 0.36\times E(B-V). \end{eqnarray} \tag{ 9 }$$

These relations agree with those from Bessell & Brett (1988) to within ∼ 3%. To verify that these equations deredden the data well, we compare the dereddened and intrinsic colors for our B–M dwarfs. The systematic offsets in V − I, V − J, V − H, and V − K versus spectral type and T_e are 0.005–0.02 mag in all cases, less than the uncertainties in intrinsic colors and reddening.

Figure 10 shows the distributions of reddening versus spectral type for stars in the core-dominated regions (r_core < 10') and the low-density halo population. Most stars on the field have E(B − V) ≈ 0.45–0.65 (top left panel), but closer analyses reveal systematic differences in the reddening distribution as a function of location (top right panel). Specifically, the h Persei core has a slightly higher median reddening among B3–F9 stars¹¹ than the χ Persei core, though its dispersion in reddening is essentially identical:

$$\begin{eqnarray} &&E(B-V)_{\rm{h} {\rm Per}} \sim 0.55 \pm 0.10, \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} &&E(B-V)_{\chi {\rm Per}} \sim 0.52 \pm 0.10. \end{eqnarray} \tag{ 11 }$$

The low-density halo has approximately the same median reddening for B3–A9 stars, E(B − V) ∼ 0.52 ± 0.1, though the far heavier field star contamination prevents robust conclusions about the median reddening for stars earlier than G0 as with the cluster-dominated regions. These results show exceptional agreement with those from Slesnick et al. (2002) who determined E(B − V) for stars earlier than B3–B5.

Zoom In Zoom Out Reset image size

In contrast to results from Bragg & Kenyon (2005), there is no evidence for a spectral type-dependent reddening in either core region through G0 (bottom panels). The population of G0–K0 stars with high reddening is almost completely drawn from stars whose positions on both observed and dereddened color–magnitude diagrams place them foreground to the clusters. The core region stellar population later than G0 is diluted by a combination of survey incompleteness and mass segregation. A substantially non-solar metallicity would be the most likely cause of any spectral-type-dependent reddening, because the colors for a given T_e would be different, especially for stars later than A spectral type. Thus, our data show no clear evidence that h and χ Persei are significantly metal poor or metal rich.

As shown by Figure 11, dereddening stars makes an already narrow and populous upper main sequence even better defined. Both the dereddened V/V − J color–magnitude diagram and the V versus spectral type HR diagram show a thin, dense locus of probable cluster stars from V_o = 10 to V_o = 14.75 that is clearly separable from a second, low-density distribution that presumably contains mostly field stars. Comparing Figure 11 with Figure 8 indicates that the distribution of spectroscopically examined stars widens at V_o = 15.5–16.75, F5–G5 as the cluster locus runs above the background field star distribution. The distribution thins out for stars later than G0–G5 because many late-type stars were too faint to be selected for spectroscopic observations.

Zoom In Zoom Out Reset image size

We now measure the distance moduli to h and χ Persei by "main-sequence fitting." This approach slightly differs from that by other authors (e.g., Slesnick et al. 2002) who argue that main-sequence fitting must be done with post-main-sequence and pre-main-sequence isochrones. Although certainly true with previous, shallower h and χ Per spectroscopic surveys, the colors and magnitudes of dereddened stars from our larger data set define a tight locus for much later spectral types, where stars are on the main sequence for a wide range of ages.

Simple arguments demonstrate that the mean age of h and χ Persei is most likely between ≈ 10 Myr and ≈30 Myr. The field includes only one O star (HD 14434), which is likely an interloping field star (Slesnick et al. 2002). Otherwise, the earliest stars in the cluster are later than B0. Between B0 and B2.5, stars are predominately giants and supergiants: dwarfs only clearly dominate the stellar population later than B3–B4. Because the main-sequence lifetime of early B stars is at least ∼ 10 Myr (compared to Bertelli et al. 1994; Schaller et al. 1992), the clusters are likely at least 10 Myr old. The main-sequence lifetime of B4–B5 stars is ≲ 30 Myr; thus, the lack of giants among mid-B stars implies an upper age limit of 30 Myr.

Figure 12 illustrates the age independence of the luminosity and temperature of B5–A5 stars for over the 10–30 Myr age range. We plot the predicted V versus V − J loci for 10 and 20 Myr old pre-main-sequence stars from the Siess evolutionary tracks (Siess et al. 2000) and D'Antona and Mazzitelli tracks (D'Antona & Mazzitelli 1994),¹² using our conversions from T_e to colors. The leftmost point for each pre-main-sequence track corresponds to the highest mass, bluest star yet to reach the main sequence. We also overplot the 10–30 Myr Padova post-main-sequence evolution tracks (Marigo et al. 2008) and zero-age main sequence. Over a significant range in M_V and V − J color, there is substantial agreement between all pre-main-sequence and post-main-sequence tracks regardless of age. In particular, stars with M_V = 0.5–2, V − J = −0.3–0.15 (∼ B5–A5 stars) are all on the main sequence. If we consider only the D'Antona & Mazzitelli (1994) pre-main-sequence tracks, agreement expands to M_V = 2.5, V − J = 0.5 (∼ A9 stars).

Zoom In Zoom Out Reset image size

Motivated by these comparisons, we measure the distance modulus primarily by identifying where the zero-age main-sequence lines up with B5–A5 stars (i.e., where the density of stars on the ZAMS is highest). Additionally, because stars contract onto the main sequence from the pre-main sequence (losing luminosity), the zero-age main sequence cannot lie above the locus of later-type stars. We divide stars on the field into three groups: those within 10' of the χ Persei center, those within 10' of the h Persei center, and those in the low-density halo region.

3.1.1. The Distance to χ Persei

The results of our main-sequence fitting are listed in Table 4 and illustrated in Figures 13 and 14. Figure 13 reveals that main-sequence fitting of χ Persei stars can determine the cluster's distance modulus with high precision. In particular, the V versus spectral type distribution (top panel) defines a sharp locus for nearly all stars earlier than G0, including main-sequence B5–A5 stars. While slightly more dispersed, the positions of stars in V/V − J (bottom panel) as well as V versus log(T_e), V/V − H, and V/V − K (not shown) also define very narrow distributions. Distance moduli measured from spectral types, T_e, and the three infrared colors are essentially identical.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 4. Distance Moduli for h and χ Persei from this Work and from Previous Work

Cluster Properties Used	h Persei Distance	χ Persei Distance	Halo Distance
This Work
Vo vs. Spectral Type	11.80	11.85	11.85
Vo vs. log(Te)	11.80	11.85	11.85
Vo vs. Vo–Io	11.82	11.87	11.87
Vo vs. Vo–Jo	11.80	11.85	11.85
Vo vs. Vo–Ho	11.79	11.84	11.84
Vo vs. Vo–Ko	11.82	11.86	11.87
Average value	11.80	11.85	11.85
Literature Estimates
Mayne & Naylor (2008)	11.78	11.82	⋅⋅⋅
Slesnick et al. (2002)	11.85	11.85	11.08–12.42
Uribe et al. (2002)	11.84	11.84	⋅⋅⋅
Capilla & Fabregat (2002)	11.70	11.70	⋅⋅⋅
Keller et al. (2001)	11.75	11.75	⋅⋅⋅
Marco & Benabeau (2001)	11.66	11.56	⋅⋅⋅

Download table as:  ASCIITypeset image

From main-sequence fitting, we derive a median distance modulus to χ Persei (thick line) dM_χPer = 11.85, which we calculate by taking the median value for the four individual estimates. The main-sequence locus for dM = 11.85 clearly runs through the middle of the main distribution of B5–A5 χ Per stars. By comparison, loci for dM = 11.77 and 11.93 (thin dashed lines) lie above and below the main distribution of B5–A5 stars in most cases. We cannot clearly identify disagreement between the observed distribution and main-sequence loci for distance moduli between these extrema (e.g., 11.82, 11.88). Therefore, we consider our mean distance modulus determination to be accurate within 0.08 mag. Thus,

$$\begin{equation} \mbox{dM}_{\chi {\rm Per}} = 11.85 \pm 0.08 \;\big(d = 2344^{+88}_{-85}\;\mbox{pc}\big). \end{equation} \tag{ 12 }$$

3.1.2. The Distance to h Persei

Though the locus of h Persei stars shows a wider dispersion as a function of spectral type and color, main-sequence fitting yields a precise estimate for its median distance modulus,

$$\begin{equation} \mbox{dM}_{\rm{h} {\rm Per}} = 11.80 \pm 0.08 \; \big(d = 2290^{+87}_{-82}\;\mbox{pc}\big). \end{equation} \tag{ 13 }$$

Thus, the cluster is slightly foreground to χ Persei. While the uncertainty in distance modulus is sufficiently large that formally h and χ Persei are at the same distance (within errors), h Persei is systematically foreground by the same amount as inferred from each of the four estimates by identical amounts (see Table 4 and Figure 14). Moreover, because the distance modulus is derived from analyzing main-sequence stars, not post-main-sequence stars, h Persei's offset cannot be due to subtle differences in its evolved star population.

The difference in distance modulus is plausibly real because the difference is systematic and also because it is consistent with some previous independent analysis performed using completely separate methods. Using the Q method,¹³ Mayne & Naylor (2008) also found a small but systematic difference in distance modulus nearly identical to ours. The distance moduli derived by Mayne & Naylor (2008)—11.78 for h Persei and 11.82 for χ Persei—are within 0.02–0.03 mag of our estimates. Our dM estimates also agree with those from Slesnick et al. (2002, dM = 11.85 for both clusters). Because their spectroscopic survey was limited to early-to-mid B stars, they were unable to measure a clear difference in dM for the two clusters. The main sequence steeply rises in M_V for a given spectral type for B stars; the main sequence is more horizontal for late B stars/early A stars, which makes differences in distance modulus stand out more.

3.1.3. Distance to the Halo Population of h and χ Persei

Our most unique contribution regarding the distance to h and χ Persei stars is a first precise estimate for stars in the halo population. Figure 15 plots our fits. The huge density change between the population of stars earlier and later than B5 is solely a reflection of our survey bias: the earlier stars were too bright to be selected for Hectospec observations and were derived solely from FAST observations which were fewer in number, while Hectospec data covers later stars. To more clearly present the empirical locus of main-sequence stars, we shrink the symbol sizes by 30%. The upper main sequence of halo stars (B5–A5) is separable from the field star population despite the higher level of contamination.

Zoom In Zoom Out Reset image size

Interestingly, we find that stars in the halo population have a well-defined locus implying a distance modulus essentially identical to that of the core region stars, especially χ Persei's:

$$\begin{equation} \mbox{dM}_{\rm halo} = 11.85 \pm 0.08 \big(d = 2344 \rm{ pc}^{+88 \rm{ pc}}_{-85 \rm{ pc}}\big). \end{equation} \tag{ 14 }$$

The halo stars with spectra are drawn throughout the ∼ 1 deg² region surrounding both clusters. At the distance of h and χ Persei, the projected size of the halo is ≈41 pc, which is comparable to the difference in distance modulus between the cluster cores. If the halo region has a roughly spherical shape, it may surround both cluster cores. Previous estimates for the halo population's distance modulus place it within 30% of the core regions (Slesnick et al. 2002). Our analysis indicates that stars in the low-density regions surrounding both cores that are most plausibly associated with the cores are at distances within ∼ 5% of the cores' distances.

3.1.4. Uncertainties in Distance Modulus

We now estimate the post-main-sequence ages of h and χ Persei stars via two methods. Identifying the location of the main-sequence turnoff, where stars of increasing luminosity become cooler as they evolve to become giants, provides a robust age estimate for massive clusters. We measure the location of the main-sequence turnoff by comparing the spectral types and colors of stars of a given V magnitude to predictions from the Padova stellar evolution models (Girardi et al. 2002; Marigo et al. 2008). Isochrones whose spectral types/colors bisect the stellar population at a given V magnitude at the turnoff best reflect the clusters' main-sequence turnoff age. Figures 13 and 14 imply that the turnoff occurs at V ≈ 8 for both clusters. The main-sequence turnoff age is the source of nearly all previous age estimates for h and χ Persei (e.g., Keller et al. 2001; Slesnick et al. 2002; Bragg 2004). With our large spectroscopic survey, we can strengthen previous constraints on the Double Cluster's main-sequence turnoff age(s).

The luminosities and colors of M supergiants also constrain the ages of h and χ Persei. Between 10 and 20 Myr, stars with masses ≈10–15 M_☉ reach the M supergiant phase and rapidly evolve in luminosity; M supergiants dim by nearly an order of magnitude over this age range (e.g., Bertelli et al. 1994; Schaller et al. 1992). Because the temperature of the reddest supergiants also varies with age and metallicity (Bertelli et al. 1994; Marigo et al. 2008), combining V-band luminosities and long-baseline colors (e.g., V − J, V − H, and V − K) provides a sensitive probe of the stars' ages and may constrain the clusters' metallicities (see Appendix B). Because isochrones did not extend to very cool temperatures thought to characterize M supergiants (e.g., Slesnick et al. 2002), most previous investigations did not infer cluster ages from these stars. However, the recent recalibration of the M supergiant T_e scale to systematically higher temperatures by Levesque et al. (2005) makes age estimates possible. Table 5 summarizes our results, which are described in more detail below.

3.2.1. Ages from the Main-sequence Turnoff

Figures 16 and 17 plot V versus spectral type and V versus log(T_e) for stars within 10' of the cluster cores against the Padova post-main-sequence isochrones for 10 Myr and 20 Myr and one intermediate age, which varies from panel to panel. In each figure, we assume the distance moduli derived in previous sections. If the cluster's age and distance spread is minimal, nearly all stars should deredden to a single, well-defined locus. However, Be stars, which are abundant in h and χ Persei (e.g., Bragg & Kenyon 2002; Currie et al. 2008b), can have intrinsically red near-IR colors (Dougherty et al. 1991, 1994) due to circumstellar gas/dust shells. Therefore, we do not consider these stars in locating the main-sequence turnoff.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Adopting a solar metallicity and the Padova stellar evolution models, the main-sequence turnoff age of χ Persei is about 14 Myr. In Figure 16, the agreement between the 14 Myr isochrone (solid line, top panels) and the observed turnoff is unambiguous. The curve in the isochrone at V_o ∼ 7.5–9.5 clearly rules out a 10 Myr age because almost all sources lie to the right in both spectral type and log(T_e) space. Similarly, a 20 Myr age is ruled out because the vast majority of stars in both panels lie to the left of its isochrone. The 14 Myr isochrone bisects the stars' positions in both top panels, especially in V_o versus spectral type space.

The HR diagram in V_o–log(T_e) space allows a firmer constraint on the age of χ Persei. The 12 Myr isochrone (lower left panel of Figure 16) clearly overestimates the temperatures of the earliest B stars at the turnoff by ∼ 0.05 dex and overpredicts the temperatures at a given M_V for all bright cluster stars except for the Be stars. Conversely, the 16 Myr isochrone plotted in the lower right panel generally predicts too cool temperatures, including at the turnoff (∼ 0.05 dex too cool). Though we consider the 14 Myr isochrone to provide the best visual fit, isochrones for 13 Myr and 15 Myr also correctly predict the temperature at the MS turnoff. Therefore, χ Persei has a formal MS turnoff age of

$$\begin{equation} t_{\chi {\rm Per, MS\,turnoff}} = 14 \pm 1\,{\rm Myr}. \end{equation} \tag{ 15 }$$

Figure 17 reveals that the main-sequence turnoff for h Persei is nearly indistinguishable. For h Persei, both the 13 Myr (shown) and 14 Myr (not shown) isochrones correctly predict the turnoff temperature and follow the distribution of cluster stars from V_o = 6.5 to 10. Given the larger photometric and spectroscopic scatter for h Persei, it is impossible to choose confidently between the two isochrones. Thus, we average them for our best-fit value. Compared to χ Persei, h Persei's range of possible turnoff ages may be very slightly shifted toward younger ones. Comparing the bottom panels of Figures 16 and 17, the 12 Myr isochrone does not overpredict the turnoff temperature as badly for h Persei as it does for χ Persei. However, because the intrinsic dispersion of V_o versus log(T_e) is much larger for h Persei, we interpret this observation to mean that the age uncertainty is larger. Our adopted MS turnoff age for h Persei is

$$\begin{equation} t_{\rm{h} {\rm Per, MS\,turnoff}} = 13.5 \pm 1.5\,{\rm Myr}. \end{equation} \tag{ 16 }$$

Because our spectroscopic sample is very incomplete for B stars in the low-density halo regions surrounding the cluster cores, our turnoff age estimate for the halo population is formally more uncertain. However, as Figure 18 suggests, the likely turnoff age for h and χ Persei halo stars is about the same as the core dominated regions. The shape of the observed turnoff clearly rules out both the 10 Myr and 16 Myr isochrones; isochrones with intermediate ages are plausibly consistent. Therefore, our derived turnoff age for the halo population is

$$\begin{equation} t_{\rm halo, MS\,turnoff} = 13 \pm 2\, {\rm Myr.} \end{equation} \tag{ 17 }$$

Zoom In Zoom Out Reset image size

Thus, within our measurement uncertainties, the turnoff ages for all regions of h and χ Persei are ∼14 Myr determined from V_o versus spectral type and log(T_e). While differences in cluster loci for different ages are more pronounced for V_o versus log(T_e), the loci are also more prone to random errors. Specifically, in Figures 16 through 18 the distribution of V_o versus log(T_e) for h and χ Per stars exhibits a larger dispersion about the 14 Myr locus than they do in V_o versus spectral type space. Taken at face value, the V-band magnitudes and temperatures for some bright, hot stars are more consistent with the 20 Myr isochrone. We cannot definitively rule out the existence of a small population of 20 Myr old stars. However, the tight clustering in V_o versus spectral type indicates that uncertainties in log(T_e) provide a more simple explanation for this larger dispersion than a true age spread.

3.2.2. Ages Determined from M Supergiants

The red supergiants provide additional evidence for an age of ≈ 13–14 Myr. In each panel of Figure 19, we plot the predictions for 10 Myr and 16 Myr isochrones as dashed lines; the solid line represents the intermediate-age isochrone, which is varied between 12 Myr and 14 Myr. Because there are no M supergiants within 10' of h Persei, we can only estimate ages for χ Persei and the halo population.

Zoom In Zoom Out Reset image size

Inspection of the panels clearly rules out 10 Myr and 16 Myr as the ages for χ Per and the halo region. From the positions of M supergiants relative to the isochrones, 13 Myr and 14 Myr are equally plausible ages for both the χ Per core and halo regions. The 12 Myr isochrone slightly overpredicts the maximum luminosity of M supergiants and underpredicts the maximum V − J color. The 15 Myr isochrone (not shown) slightly underpredicts the typical luminosities and overpredicts the maximum V − J color. Therefore, we consider the best-estimate ages for χ Persei and the halo population as

$$\begin{eqnarray} &&t_{\chi {\rm Per, M\,supergiants}} = 13.5 \pm 1.5\,{\rm Myr}{,} \end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray} &&t_{{\rm halo,M\,supergiants}} = 13.5 \pm 1.5\,{\rm Myr}{.} \end{eqnarray} \tag{ 19 }$$

As shown in Figure 8, our new optical photometry reveals faint, low-mass stars plausibly associated with h and χ Persei whose V-band luminosity at a given color is significantly higher than that of the background field star population. The photometry extends over 14 mag in V: over this range the positions of solar/subsolar-mass stars in V versus V − I color–magnitude diagrams are a sensitive function of stellar age (e.g., Baraffe et al. 1998). We now derive the pre-main-sequence age of h and χ Persei stars by comparing their color–magnitude diagram positions to predictions from the Baraffe et al. (1998) isochrones.

Even though a plausible cluster locus is clearly observable and can be fitted from visual inspection of Figure 8, we follow a slightly more statistical approach to obtain a more robust pre-main-sequence age. Field star contamination is larger for fainter stars. A Hess diagram of all stars on the field will have an increased density in regions occupied by fainter cluster stars (at a given color), which may artificially dim the apparent cluster locus. Thus, to be conservative, we must subtract out the background field star population near the cluster locus.

Our method is as follows. We construct Hess diagrams of stars within the h and χ Persei cores (r < 7')¹⁴ and halo region (10'–20' away from both cluster centers). Next, we construct a Hess diagram of the "background," which we obtain from stars greater than 21' distant from both cluster centers. The cluster and halo Hess diagrams are box-car smoothed by two resolution elements; the background diagram is smoothed by four resolution elements, essentially yielding an "unsharp mask" of the background V/V − I distribution. Finally, we scale the background diagram to the densities of the core/halo diagrams and subtract the background from the core/halo diagrams. We determine the pre-main-sequence age by overplotting solar metallicity Baraffe et al. (1998) isochrones, assuming a mixing length parameter of 1.9 H_p and distance moduli/reddenings equal to those found in previous sections.

Figures 20, 21, and 22 illustrate our results. In each figure, the black line (dash-three dots) identifies the main-sequence/post-main-sequence locus from the Padova isochrones. The solid dark gray line identifies the Baraffe et al. (1998) isochrone position for 0.6 M_☉ (lower right end) to 1.4 M_☉ (upper left end) stars. In Figures 20 and 21, the entire cluster locus is plainly visible. The background has been almost completely subtracted out. The halo population is more poorly defined (Figure 22): the locus of cluster stars is entirely absent in some regions (V − I ∼ 1.5–1.6). This poorer definition probably occurs because even regions > 20' away have some small population of halo stars, so the halo population is partially subtracted out. However, both the upper main sequence and the pre-main sequence redder than V ∼ 1.7–2 are clearly visible and well separated from the background field star population. Comparing both panels of Figure 22 demonstrates that the apparent cluster locus in the subtracted diagram is real.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Assuming that the faintest h and χ Per stars (V ∼ 23.5–24) are as reddened as the bright, spectroscopically observed stars analyzed in the previous section, they typically have intrinsic V − I ∼ 3. According to Table 7 and Baraffe et al. (1998), these stars likely have T_e ≈ 3000 K and masses ∼ 0.1 M_☉. Although these determinations are highly uncertain, it is possible that the faintest cluster stars detected in our survey have masses approaching the hydrogen burning limit. At the very least, cluster stars with V ∼ 23–24 likely probe well into the M dwarf spectral type range.

Comparing the distribution of h and χ Per stars to the Baraffe et al. (1998) isochrones clearly shows that the pre-main-sequence ages for all three components of the Double Cluster are nearly identical to the post-main-sequence ages:

$$\begin{eqnarray} &&t_{\rm{pre-MS}, \chi {\rm Per}} = 14^{+1.9}_{-1.4}\; {\rm Myr}, \end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray} &&t_{\rm{pre-MS}, {\rm h} {\rm Per}} = 14^{+1.9}_{-1.4}\; {\rm Myr}{,} \end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray} &&t_{\rm{pre-MS}, {\rm halo}} = 14^{+1.9}_{-1.4}\; {\rm Myr}. \end{eqnarray} \tag{ 22 }$$

In all cases, the 14 Myr isochrone best bisects the densest regions of the cluster loci: isochrones for 12.6 Myr overpredict the V-band luminosity at a given color, while the 15.9 Myr isochrone underpredicts the luminosity. Moreover, the slope of the 14 Myr Baraffe et al. (1998) isochrone accurately tracks the observed locus. This agreement is remarkable considering that the important processes driving post-main-sequence evolution for high-mass stars—changes in internal structure fundamentally due to nuclear reaction rates and the lack of hydrogen and helium in the stellar core—are not the same as those driving pre-main-sequence evolution for low-mass stars: Kelvin–Helmholtz contraction and the onset of hydrogen burning as a star follows a radiative or convective track onto the main sequence.

The Baraffe et al. (1998) isochrones are only one of many that are often used to determine cluster ages from the observed loci of pre-main-sequence stars. To compare the Baraffe et al. isochrones with others, we overplot 10–20 Myr isochrones from D'Antona & Mazzitelli (1994, 1997) and Siess et al. (2000) on the color–magnitude diagram for χ Persei in Figures 23 and 24. For both sets of isochrones, we transform the computed luminosities and effective temperatures into V-band magnitudes and V − I color using our effective temperatures and intrinsic colors. We display isochronal positions for stars more massive than 0.5 M_☉.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

While neither set of isochrones yields ages less than 10 Myr or greater than 20 Myr, they show a clear disagreement with the 14 Myr Baraffe et al. (1998) locus and a failure to accurately reproduce the shape of the observed pre-main-sequence locus. The slope of both sets of isochrones are systematically steeper than the Baraffe et al. (1998) isochrones. The mismatch between the D'Antona & Mazzitelli (1994, 1997) isochrones and the observed locus is particularly striking. The 10 Myr isochrone overpredicts the luminosities of 1.5–2 M_☉ stars (V − I ∼ 1–1.5) but underpredicts the luminosities of slightly redder stars (V − I ∼ 1.5–2). The 20 Myr isochrone underpredicts the luminosity of cluster stars redder than V − I ∼ 1. The D'Antona & Mazzitelli (1994, 1997) grid lacks published entries at intermediate ages. However, unless only the 1.5–2 M_☉ stars fade in V while at a constant temperature (unlikely), isochrones at intermediate ages would not clearly provide a better match to the observed locus. Thus, we cannot derive a best-fit pre-main-sequence age based off of these isochrones.

Compared to the D'Antona & Mazzitelli (1994, 1997) isochrones, the Siess et al. (2000) isochrones show slightly better agreement with the observed locus, especially for stars redder than V − I ∼ 1.5. In particular, the 14 Myr and 16 Myr isochrones (dashed lines) show reasonably good agreement for V − I ∼ 1.75–2.5. In contrast, the 12 Myr and 18 Myr isochrones systematically overpredict and underpredict the luminosities of cluster stars over this range in V − I. Thus, based on the Siess et al. (2000) isochrones for stars with V − I ∼ 1.75–2.5, χ Persei has an age of ≈14–16 Myr, though this estimate is somewhat uncertain given the poorer fidelity that the isochrones have to the slope of the locus for V − I = 1.5–2.5.

For bluer, earlier stars (V − I ∼ 0.75–1), all Siess et al. (2000) isochrones systematically overpredict luminosities. Based solely on the apparent position of the pre-main-sequence "turn on"—where the observed locus first becomes brighter than the main sequence—the Siess et al. isochrones would yield an age greater than 20 Myr, which is inconsistent with all other age estimates. Moreover, Siess et al. predict that over a narrow color range the V-band luminosities of cluster stars increase with redder color and thus with decreasing mass. We find no clear evidence for such a trend in the data. Likewise, none of the Baraffe et al. (1998) isochrones for 0.6–1.4 M_☉ stars and ages of 1–20 Myr have this trend: it is likely a unique feature of the Siess et al. (2000) models.

In summary, comparing the photometric data with isochrones from D'Antona & Mazzitelli (1994, 1997) and Siess et al. (2000) constrains the age of h and χ Persei to be between 10 Myr and 20 Myr. However, the shape of these isochrones in V versus V − I for any age provides a significantly poorer match to the observed locus. These comparisons justify our choice of the Baraffe et al. (1998) isochrones to determine pre-MS ages, given their far stronger agreement with the observed cluster locus shape for a wide range of color. Adopting the Baraffe et al. tracks as our benchmark, the D'Antona & Mazzitelli tracks are inaccurate for redder pre-MS stars. They are potentially accurate for bluer, higher-mass pre-MS stars, though this is uncertain given their sparse age sampling. The Siess et al. (2000) tracks yield reasonable age estimates for redder pre-MS stars but are inaccurate for bluer, higher-mass pre-MS stars. If these trends are indicative of the isochrones for all ages, we caution against estimating cluster ages from the main-sequence turn-on from the Siess et al. (2000) tracks and against deriving ages from the observed locus of red pre-MS stars from the D'Antona & Mazzitelli (1994, 1997) tracks.

Using the dereddened V versus spectral type HR diagram, we first establish a spectroscopically determined list of h and χ Persei members. Because each component of h and χ Per has an identical post-main-sequence and pre-main-sequence age, we define the locus of cluster members by joining together the Padova 14 Myr post-main-sequence isochrone and the Baraffe 14 Myr pre-main-sequence isochrone. The width of the cluster locus is determined by (1) the physical extent of the cluster, (2) binarity, and (3) uncertainties in spectral types. Including the halo population, the h and χ Per region extends to at least ≈ 20'–25' away from either cluster center. Assuming a distance modulus of ≈ 11.8–11.85 and spherical distribution of cluster and halo stars, the h and χ Persei region is ≈ 52.5 pc in diameter, which translates into δ(dM)= ± 0.05. The typical dispersion in E(B − V) as determined from the V − J, V − H, and V − K colors is ≲ 0.03. This uncertainty in E(B − V) leads to a formal error in the dereddened V magnitude of ≈ 0.09 (≈ 0.1) for each source, which is larger than the δ(dM) from the clusters' physical sizes and slightly widens the V_o versus spectral type locus. The uncertainty in the distance modulus is ≈ 0.08 (see Section 3). Equal mass binaries in h and χ Per may be up to 0.75 mag more luminous than the cluster locus for single stars. Finally, we compute the median formal spectral type uncertainties as a function of V magnitude and define the width of the locus from left to right by these uncertainties. The uncertainties are ≈ 2 subclasses for most spectral types. Therefore, we identify cluster stars in a locus centered on the 14 Myr Padova–Baraffe isochrone with boundaries of −0.75 and +0.2 in V magnitude above and below the isochrone and typically ±2 subclasses in spectral type. Figure 25 illustrates our selection criteria.

Zoom In Zoom Out Reset image size

Second, we identify probable photometric members from the V versus V − I color–magnitude diagram again using the 14 Myr Padova–Baraffe isochrone reddened by the median average cluster reddenings. The upper bound defining the cluster locus is the same as before; for the lower bound, we choose the larger of 0.05 (the physical size of the clusters in mag) and the V-band uncertainty. We choose the boundaries in color assuming that the dispersion in reddening (≈ 0.1 mag) and photometric errors in V − I color ((σ²_V + σ²_I)^0.5) widen the locus. The dispersion in E(B − V) translates into a dispersion of 0.125 mag in V − I. The median errors in color range from ≲ 0.01 mag at V ⩽ 10–12 to 0.08 mag at V = 23. Therefore, the widening of the left/right boundaries of the locus from these two sources of error bound of the locus increases from ∼ 0.125 mag for bright stars to ∼0.2 mag for faint stars. Figure 26 illustrates the region within with we identify probable members.

Zoom In Zoom Out Reset image size

Spectroscopic Membership. Based on our selection criteria, we identify a total of 4702 stars as spectroscopic members: ∼ 63% of the 7465 spectroscopically observed stars with V-band photometry. The frequency of members is highest for the cluster-dominated regions. Within 10' of the h Persei center, 71% (1138/1606) of stars are members. Within 10' of the χ Persei center, 68% (906/1330) of stars are members. The slightly lower membership frequency of 59% (2676/4529) in the low-density halo regions is consistent with the region's greater level of field star contamination.

Photometric Membership. The number of photometric candidate members is substantial: 14,307 stars, or ∼ 30% of the 47,060 stars on the field. Over half of these stars reside in the low-density regions surrounding the cluster cores (8817, or 62% of the total population). The other candidates are almost evenly split between those within 10' of the h Persei center (2724) and 10' of the χ Persei center (2766). Within both core-dominated regions, about 40% of stars are probable members: 2724/6519 for h Persei and 2766/6674 for χ Persei. As with the spectroscopic sample, field contamination is far heavier in the halo region: ∼ 26% of halo-region stars are consistent with membership (8817/33,867).

Taken at face value, these results seem to contradict Currie et al. (2007a) and Currie (2008) who argue that the core-dominated regions have as many stars as the halo. Furthermore, they conflict with previous studies showing that h Persei is ∼30% more massive/populous than χ Persei (e.g., Slesnick et al. 2002; Bragg 2004; Bragg & Kenyon 2005). The first difference is one of semantics: both papers identify the halo region with stars at distances greater than 15' away from either cluster center and extending to 25' distant, not 10' as in this paper. Adopting the previous definition of the core and halo regions yields much more similar results. For example, the number of photometric members would be 4808 (out of 14,567) for the h Persei core, 4993 (out of 15,026), for the χ Persei core, and 4283 (out of 17,467) for the h and χ Per halo population. We primarily adopt 10' as the core boundary because the density of stars is low (Currie et al. 2007a) and our spectroscopic survey is unbiased within this radius, though we consider either definition to be reasonable.

The conflicting results for cluster richness are probably due to survey incompleteness near the h Persei core. The h Persei core has a higher density of early, bright stars (e.g., Currie et al. 2007a; Bragg & Kenyon 2005; Slesnick et al. 2002). The scattered light from these stars reduces the contrast between faint, low-mass stars and the background, which restrict source detection to a brighter limit than for the χ Persei core. Restricting our analysis to brighter stars recovers previous results. For example, we identify 607 stars brighter than V = 16—likely earlier than A2 (see Figure 9)—within the h Persei core as photometric members but only 469 within the χ Persei core as members. Adopting these criteria implies that h Persei is ∼30% more massive, in complete agreement with previous results. Assuming the standard h Per to χ Per mass ratio, there are 700 more lower-mass h Per stars unaccounted for by our survey, bringing the total number to ∼3424.

Some stars identified as members are likely interlopers. In the HR diagrams and color–magnitude diagrams presented here, the locus of cluster stars intersects the main locus of field stars around G spectral types. Thus, we expect some field star contamination among G stars. The increasing scatter of the colors of field stars with increasing V probably also leads to some contamination along the lower boundary of the pre-main-sequence locus in V/V − I. We cannot subtract a field star population from the cluster population and estimate the number of interlopers, because the halo region fills the entire optical survey.

Comparing the membership results for stars based on photometry and spectroscopy yields an estimate of the field star contamination in the photometric member list. There are 3984 stars identified as candidate photometric members and spectroscopic members; 763 stars identified as candidate members from photometry are rejected as members based on spectroscopy. Therefore, about ∼ 16% of the photometric member list is comprised of interloping field stars, not bona fide cluster members. Even though field contamination is greater for fainter magnitudes, analysis in Section 3.3 demonstrates that the region defining the locus of low-mass h and χ Per stars (V ∼ 18–24, V − I ∼ 1.5–4) is less contaminated than the region (V ∼ 16.5–17.5, V − I ∼ 1–1.5) comprising most of our spectroscopically observed members.

The number of B stars can also be used to estimate contamination. Because early to mid B dwarf stars identified as members above cannot be old field stars, they are highly likely to be young cluster members. Assuming a cluster mass function (e.g., Miller-Scalo), the number of B stars yields an expected number of total cluster stars. By comparing the ratio of the expected number of members to the derived number of members, we estimate the number of field stars misclassified as members/candidate members. We choose the B0–B6 star population in the halo as our reference, assume that the B0–B6 star population extends to V ∼ 13.45 (compared to Figure 9) and assume that the field star density is independent of position. Main-sequence B6 stars should have masses of ≈ 4 M_☉ (or log(M_⋆/M_☉) ≈ 0.6).¹⁵ We assume that our survey reaches stars with masses ≈ 0.2 M_☉ (log(M_⋆/M_☉ ∼−0.7): this lower limit is higher than that determined in Section 3.3 (∼ 0.1–0.15 M_☉) but is chosen to be conservative. We derive the expected number of cluster stars using Table 9 in Miller & Scalo (1979).

The halo population includes 217 candidate members brighter than V = 13.45, so it should contain about 7380 stars total. Compared to the 8817 stars listed as candidate members, the percentage of interloping field stars is also ∼ 16%, which is essentially identical to the estimate derived by comparing membership lists. Because the area of the photometric survey consisting of the halo region is ≈ 0.43 deg²—0.6 deg²–2×π10'²—the density of interloping field stars is ∼ 3381 deg⁻², which yields ∼ 295 interlopers in each core region. Thus, within our 0.6 deg² field there are probably 3129 cluster members for h Persei, 2471 for χ Persei, and 7380 for the low-density halo, yielding a total of 12,980 stars in h and χ Persei. If lower-mass halo stars associated with the halo cover 1 deg² on the sky, consistent with our spectroscopic membership results for higher-mass stars, then h and χ Persei may contain up to ≈20,000 members.

Several other factors indicate that our membership estimate is reasonable and conservative. First, the color–magnitude diagram boundaries identifying photometric members assume that all h and χ Per stars have E(B − V) within 0.1 mag of the derived median values for each core region and the halo. However, our spectroscopic membership list clearly identifies some members with reddening outside this range. It is plausible that other members lacking spectroscopic data lie outside the photometric membership boundaries but would deredden to the cluster locus. Second, analysis in Section 3.3 indicates that our survey may have reached close to the hydrogen burning limit (≈ 0.1 M_☉). If so, then the expected number of cluster stars determined from extrapolating the cluster IMF from the B star population will be slightly greater than derived in this section. Because more cluster stars are expected, the number of interlopers drops. Third, because the regions identifying members are defined purely by analysis uncertainties, we implicitly assume that all 13,000–20,000 stars in h and χ Persei formed simultaneously. Analysis in Section 3 indicates that the median age of h and χ Per stars is 14 Myr with no evidence for a substantial age spread. However, our analysis cannot preclude the existence of smaller, 1–2 Myr age spreads (see also discussion in Slesnick et al. 2002). Even 1–2 Myr age spreads would widen the cluster loci and cause us to underestimate the true number of members.

After removing the 763 candidate photometric members rejected by spectroscopy, we compile a final membership list of 14,160 stars including both types of members. For each entry, we list ID numbers, the position, optical photometry, spectral types, and reddening. Table 6 lists the members of h and χ Persei.

With a list of spectroscopically confirmed members, we estimate the total mass of h and χ Persei and probe the spatial distribution of cluster stars in core-dominated regions. To determine the mass, we add up the derived masses of stars earlier than B6 (4 M_☉), assume a Miller–Scalo IMF, calculate the masses of the core regions, and use the ratio of members in the core and halo to determine the total mass. We use the spatial density of cluster stars to investigate mass segregation.

From these assumptions, we derive a mass of 4704 M_☉ for the h Persei core and 3699 M_☉ for the χ Persei core. Assuming the ratio of the core populations to the halo (5600/7380), the halo population has a total mass of 11,074 M_☉. Not including the halo regions beyond our photometric coverage, the total mass of h and χ Persei is ≈ 19,477 M_☉: an order of magnitude larger than the Orion Nebula Cluster and the Pleiades.

Our deep spectroscopic survey supports the conclusion of Slesnick et al. (2002) that the h and χ Persei region is unique in mass and structure among nearby (d < 3 kpc) regions and much more similar to other massive "double clusters" such as NGC 1818 in the Large Magellanic Cloud (Johnson et al. 2001) and massive single clusters such as the Arches cluster near the galactic center (Figer et al. 1999).

Mass segregation also probes cluster structure. Dynamical mass segregation occurs because cluster members gravitationally attract one another, exchanging kinetic energy and momentum, which tends to drive the system into energy equipartition. As the cluster ages, this process leaves more massive cluster stars more concentrated in the cluster core and less massive stars concentrated in lower-density regions. Alternatively, clusters may exhibit primordial mass segregation, which occurs as an outcome of the cluster formation process.

To probe mass segregation, we compute the relative number of B star members to A and F star members as a function of distance from the cluster centers. If the clusters lack mass segregation, then the ratio of B stars to A/F members should be nearly constant with distance. Clusters with mass segregation should have a decreasing ratio with cluster-centered distance.

As shown in Figure 27, both clusters exhibit some evidence for mass segregation. The strongest evidence is for h Persei stars (top) within ≈ 3'–4' of the cluster center. Within this region, the relative number of B stars to A stars drops from ∼ 4.5 within 1' to ∼ 2 for larger distances. The ratio of A stars to F stars is also highest within 2' and reaches a constant level (∼ 0.5–1) by ∼ 3'. The ratio of the number of B stars to F stars, comparing a wider range in masses (⩾ 2.2 M_☉ to 1.35–1.5 M_☉), varies the most, exceeding 22 within 1' and reaching constant levels at distances greater than 4'. In all cases, the high number of B stars to later stars implies that higher-mass stars are preferentially concentrated in the cluster centers, consistent with the cluster being mass segregated.

Zoom In Zoom Out Reset image size

For χ Persei, the extent of mass segregation and the physical scale over which it occurs may be comparatively smaller. The ratio of B stars to F stars is high (∼ 4–14) within 2' of the cluster center and drops to a constant level by 3'. The ratios of B stars to A stars and A stars to F stars is high for stars within 2' of the cluster center after which they reach constant levels. These trends are qualitatively similar to those found for h Persei. However, the smaller B/F star ratio in the cluster center and slightly smaller radius beyond which the ratio is constant (3' versus 4' for h Per) indicates that mass segregation in χ Persei is not as strong as it is in h Persei (see also Slesnick et al. 2002; Bragg & Kenyon 2005).

Comparing the dynamical mass segregation timescales with cluster ages determines whether mass segregation must be primordial or dynamical. Dynamical mass segregation occurs on relaxation timescales (Binney & Tremaine 1987), which for h and χ Persei is

$$\begin{equation} t_{\rm relax} \sim \frac{1.8\times 10^{10}\,{\rm yr}}{\ln \Lambda (r)}\left[\frac{\sigma (r)}{10\,{\rm km\,s}^{-1}}\right]^{3} \left(\frac{1 M_{\odot }}{m}\right)\left[\frac{10^{3}M_{\odot }\,{\rm pc}^{-3}}{\rho (r)}\right], \end{equation} \tag{ 23 }$$

where Λ is the number of stars interior to radius r, σ is the velocity dispersion, m is the typical stellar mass (0.63 M_☉), and ρ(r) is the stellar density. Bragg & Kenyon (2005) compute a relaxation timescale of ∼ 15 Myr for h Persei at a core radius of 28 and ∼ 20 Myr for χ Persei at a core radius of 35. The age of h Persei is almost identical to its relaxation timescale at 28 from the cluster center. While the age of χ Persei is 5 Myr less than its relaxation timescale, the cluster only clearly exhibits mass segregation at distances within 2'–3' from the cluster center. Because the relaxation timescale is inversely proportional to stellar density and the natural log of the number of stars, the relaxation timescale for regions interior to 2'–3' is much less than 20 Myr. Conversely, even though the relaxation timescale rises well above 15–20 Myr for distances greater than 3'–4', there is little evidence for mass segregation at these separations. Thus, it is not clear whether mass segregation in h and χ Persei must be primordial. Similarly, for the Arches cluster it is not clear whether mass segregation is primordial or dynamical.

This paper describes the first extensive photometric and spectroscopic survey of main-sequence and pre-main-sequence stars in h and χ Persei. By analyzing optical photometry for 47,000 stars and spectroscopy of 11,000 stars, we derived the median reddening, distance modulus, and age for each component of h and χ Per. We then constructed the first extensive membership list of h and χ Per stars, ranging from massive B–M supergiants to pre-main-sequence stars whose masses are likely comparable to the hydrogen burning limit. Our study yields the following major results.

• 1.  
  The median reddening values for the h Persei core, χ Persei core, and halo region are comparable: E(B − V) ∼ 0.55, E(B − V) ∼ 0.52, and E(B − V) ∼ 0.52, respectively.
• 2.  
  The distance moduli for h Per, χ Per, and the halo region are also nearly identical: dM$_{\rm{h} {\rm Per}}$ = 11.8, dM_χPer = 11.85, and dM_halo = 11.85.
• 3.  
  Ages for all three components of h and χ Persei are identical: ∼ 14 Myr. Moreover, post-main-sequence ages and pre-main-sequence ages for each component are identical. Thus, the properties of h and χ Persei are consistent with the coeval cores and the low-density halo population emerging from a single, explosive star-forming event.
• 4.  
  Within 10' of the two cluster centers, the Double Cluster contains at least ∼ 5000 stars; h Persei is about 30% more populous than χ Persei. The halo region contains at least ∼ 7000 stars and as many as 15,000 stars, bringing the total number of stars in h and χ Persei to ∼ 20,000. The estimated masses for h Persei, χ Persei, and the halo region are ∼ 4700 M_☉, ∼ 3700 M_☉, and ∼ 11,000 M_☉.
• 5.  
  Both clusters show clear evidence of mass segregation within 3' of the cluster centers, though it is stronger for h Persei. The relaxation timescales for both clusters are comparable to or less than their ages within 3'. Therefore, mass segregation may either be primordial or dynamical.

These results support and extend recent studies of h and χ Per conducted by Currie et al. (2009a), Mayne et al. (2007), Currie et al. (2007a), Bragg & Kenyon (2005), Slesnick et al. (2002), and Keller et al. (2001). Remarkably, four mutually exclusive sets of authors using different techniques converge on essentially the same properties for the clusters' reddening, distance, and age. Combined with previous work, our results clearly refute earlier claims that the Double Cluster and its environs have a substantial age spread (Wildey 1964; Marco & Benabeau 2001), have a substantially different age (Schild 1965, 1967; Marco & Benabeau 2001), or are located at substantially different distances (Schild 1967; Kharchenko et al. 2005). All indications are that the different components of h and χ Persei substantially differ only by spatial distribution and mass.

In addition to advancing our understanding of h and χ Persei properties, this study clearly identifies advances needed to paint a more complete picture of the Double Cluster. We highlight several promising areas of future research below.

• 1.  
  Wide-Field Optical Photometry/Deep Optical Spectroscopy. Simple wide-field optical photometric surveys can easily expand our membership list and amplify the scientific output of our work. The mismatch in survey area between our spectroscopy (∼ 1 deg²) and photometry (∼0.6 deg²) leaves ∼ 3500 stars with spectroscopy but no photometry. Our results demonstrate the need for high-quality photometry to measure reddening and to establish membership. Because nearly all of these stars are bright (V ≲ 19), they are easily accessible by wide-field cameras on 1–2 meter-class telescopes. The upper main sequence of halo stars is undersampled largely because of our selection criteria for Hectospec targets (J ⩾ 14). Added to our existing survey, the entire upper main sequence of h and χ Persei can probably be probed after a few additional Hectospec or Hydra fiber settings. Because these stars are extremely bright, obtaining high signal-to-noise spectra will be trivial. Furthermore, our optical photometry identifies many probable cluster members that are beyond the 2MASS detection limit but clearly within range of Hectospec for integration times of ∼ 1–2 hr (V ≲ 21–22). A survey establishing the spectral types for many of these stars would provide valuable information on the luminosity and temperatures of pre-main-sequence stars at ≈14 Myr. Other multiobject spectrographs coming online in the near future (e.g., MODS on the Large Binocular Telescope, Binospec on the MMT) can probe even further down the cluster mass function.
• 2.  
  Robust Membership Determinations from SIM and GAIA. Proper motion studies are the most definitive method for determining h and χ Per membership. Unfortunately, at ∼2.3 kpc distant, h and χ Per stars exhibit tiny proper motions, the size of which render ground-based campaigns to verify our membership list hopeless. However, space-based interferometric missions—specifically SIM and GAIA—are easily capable of detecting the ∼ μas motions of pre-main-sequence cluster stars. SIM's and GAIA's clear ability to yield definitive catalogs of members for h and χ Persei and other distant, populous clusters would have an enormous impact on studies of these clusters and stellar evolution in general.
• 3.  
  Metallicity. Clearly, the greatest source of systematic error in constraining the clusters' properties is metallicity. While we argue that h and χ Per likely have a near-solar metallicity, it is possible that the sources whose properties support our contention are not indicative of the clusters' stars as a whole. To address metallicity, at least three avenues of research should be explored. First, sophisticated stellar atmosphere modeling of stars in a variety of evolutionary states should constrain the photospheric chemical abundances (e.g., Dufton et al. 1990; Smartt & Rolleston 1997; Venn et al. 2002) and help to define the typical chemical composition. Second, high-resolution echelle spectra of cluster stars (e.g., with Hectochelle), especially G-type pre-main-sequence members, should not only constrain the clusters' velocity dispersions (and thus aid membership identification) but will also be capable of yielding metallicity estimates. Third, building upon work by Southworth et al. (2004a, 2004b), metallicities can be estimated by comparing masses and radii of eclipsing binaries to model predictions. In this regard, results from the MONITOR program (Aigrain et al. 2007) may be crucial for ending the debate on metallicity.
• 4.  
  Effective Temperatures. As described in Appendix A, the T_e scale for early B dwarfs and evolved B stars is more poorly constrained than for O stars and A–M stars. Non-LTE modeling of the many early B stars in h and χ Persei may provide better constraints on the T_e scale. More specifically, determining T_e for individual B stars strengthens our ability to derive accurate post-main-sequence ages. As was argued by Slesnick et al. (2002) and can be seen in Figures 16–18, the binning of B stars into discrete T_e values for their spectral type potentially introduces a spurious spread in T_e at a given V magnitude brightness, which could be misinterpreted as a spread in age. Individual measurements for T_e will tighten the locus of cluster stars at the main-sequence turnoff. Accurate T_e estimates may be especially important for cluster Be stars, which are often difficult to spectral type because of their Balmer line emission. A large campaign to derive atmospheric properties of Be stars in h and χ Persei is underway (A. Marsh et al. 2010, in preparation).
• 5.  
  The Halo Population.While our results confirm previous claims (e.g., Currie et al. 2007a) that h and χ Persei contains a large halo population, it is possible that the halo extends beyond 25'–30' from either cluster center, or even well beyond the square-degree field covered by our spectroscopic survey. A more spatially extended survey of stars would yield a better estimate for the total mass of the halo population. A more complete census of young stars within ≈ 5 degrees of the h and χ Persei cores better reveals the large star formation history within which h and χ Per emerged, including the Double Cluster's relationship to other nearby young clusters such as W3, W4, and W5 located several degrees away. Specifically, it may be possible to address the relationship between h and χ Persei and the Perseus OB1 association, determining if the core and halo populations have properties completely distinct from Per OB1, if h and χ Per represents a unique epoch in star formation that propagated through the present day Per OB1 region, or if its properties are characteristic of the Per OB1 association as a whole (e.g., Slesnick et al. 2002; Lee & Lim 2008).
• 6.  
  The Circumstellar Disk Population: Constraints on Planet Formation. Finally, the large sample of stars now confirmed as h and χ Persei members can be used to investigate planet formation by using Spitzer and (later) the James Webb Space Telescope. New Spitzer observations reveal an order-of-magnitude increase in the number of stars detected at 3.6–8 μm (T. Currie et al. 2010, in preparation). Combined with membership information derived here, Spitzer data will yield constraints on the disk population from a sample size easily dwarfing that of the FEPS and Cores-to-Disks Legacy Programs combined and thus providing far superior statistical reliability. This fundamentally different kind of data set allows robust probes of planet formation that are impossible with other samples, providing estimates of the frequency of long-lived protoplanetary disks; warm, terrestrial planet-forming debris disks; and extremely luminous cold debris disks. Combined with data from 3 to 25 Myr old clusters; e.g., IC 348, NGC 2362, Upper Scorpius, Orion OB1, NGC 1960, and NGC 2232 (Currie & Kenyon 2009; Currie et al. 2009b; Carpenter et al. 2006; Hernandez et al. 2007b; Z. Balog et al. 2010, in preparation; Currie et al. 2008a)—it is possible to reconstruct the time history of terrestrial, gas giant, and icy planet formation to compare with our solar system's chronology and models of planet formation (e.g., Kenyon & Bromley 2009; Currie 2009; Castillo-Rogez et al. 2007).

For O5–B0 dwarfs, sophisticated non-LTE calculations are crucial to accurately determining T_e. Therefore, we adopt the empirically derived scale from Massey et al. (2005) for these stars. The Massey et al. (2005) scale departs from the Gray & Corbally (2009) scale by less than ≈500 K for nearly all subtypes. Because O5–B0 stars have temperatures ≳ 30,000 K, these differences are inconsequential (≲ 1.7%).

For B0.2–A0 stars, there is generally good agreement between Gray & Corbally (2009), Bessell et al. (1998), Humphreys & McElroy (1984) and De Jager & Nieuwenhuijzen (1987) for most subclasses. However, there are serious disagreements between these authors for B1–B3 stars; these stars are crucial for accurately assessing cluster properties (e.g., the main-sequence turnoff) because they cover a wide range in V-band magnitudes for our sample. In particular, the Bessell et al. (1998) scale is up to 2500 K hotter than the others. The origin of Bessell et al.'s scale is in a IAU conference proceedings paper, Crowther (1997). Figure 1 of Crowther (1997) shows that its temperature scale is systematically higher for B0.5–B2 stars than other references listed as well as older scales from Schmidt-Kaler (1982) and Bohm-Vitense (1981). Moreover, the B0.5–B1.5 scale from Humphreys & McElroy (1984), De Jager & Nieuwenhuijzen (1987), Gray & Corbally (2009), and Gray & Corbally (1994) agree against Crowther (1997) by nearly identical amounts.

Given this information, we adopt the scale from Humphreys & McElroy (1984) sampling in spectral type from B0.2 to B1.5. Similarly for B3 stars, all authors except for Gray & Corbally (2009) agree. In this case, we adopt the values from Humphreys & McElroy (1984) and Kenyon & Hartmann (1995). For the B2 spectral type, there appears to be complete disagreement with two primary references (Bessell et al. 1998 and Kenyon & Hartmann 1995) listing hot temperatures (∼ 21,700 K) and two listing cooler temperatures (∼ 19,500–19,700 K; Gray & Corbally 2009 and Humphreys & McElroy 1984). The average of these values is ≈20,700 K, which is also very close to the value given by De Jager & Nieuwenhuijzen (1987) so we adopt it.

The temperature scale for B4–A0 stars shows strong agreement between various authors. We simply adopt a scale from Gray & Corbally (2009), Bessell et al. (1998), and Kenyon & Hartmann (1995) for these spectral types, taking the Kenyon & Hartmann (1995) value by default unless the other two disagree against Kenyon & Hartmann (1995) by more than several 100 K.

For dwarf stars later than A0, only three of our primary references have published values: Gray & Corbally (2009), Kenyon & Hartmann (1995), and De Jager & Nieuwenhuijzen (1987). With the exception of A5–A7 stars, these references show excellent agreement. We adopt the Gray & Corbally (2009) values by default and add the Kenyon & Hartmann (1995) for spectral types where Gray & Corbally (2009) lacks entries.

As with the dwarf star T_e scale, we adopt results from Massey et al. (2005) for all O5–B0 giants and supergiants. For B1–M0 stars, the primary references listing T_e versus spectral type for evolved stars are De Jager & Nieuwenhuijzen (1987), Humphreys & McElroy (1984), and Gray & Corbally (2009). The references show good agreement for stars later than ∼ B4; small disagreements again show up in the B1–B3 range. For these stars, we adopt the middle value if all three references disagree and the more frequent value if two of the three agree against the third.

The T_e scale for M supergiants is notoriously hard to calibrate: values from different authors often wildly disagree. To complicate matters, most T_e scales yield red supergiants that are far redder than post-main-sequence isochrones would allow, preventing the stars' luminosities and colors from being used to estimate cluster ages. The most recent calibrations from Levesque et al. (2005) substantially revise the temperature scale upward; the post-main-sequence isochrones easily extend to these new temperatures. Even though we do not consider Levesque et al. (2005) to be a primary reference, we adopt their T_e scale for M supergiants almost verbatim for several reasons. First, the data are drawn from high signal-to-noise spectrophotometry of galactic supergiants and compared to the NMARCS stellar atmosphere models, which we consider to be robust. Second, the lead author (R. Humphreys) of the primary reference for the T_e scale that Levesque et al.'s replaces refereed the latter paper, which increases our confidence that Levesque's scale is an improvement. Where Levesque et al. (2005)'s sampling becomes sparser (e.g., earlier than M0), we adopt the values listed in Gray & Corbally (2009), which are drawn from other recent work whose calibration agrees with Levesque et al. (2005)'s where they overlap.

Tables 7, 8, and 9 list the intrinsic UBVI_cJHK Johnson–Cousins–Glass colors of stars as a function of T_e, spectral type, and luminosity class. We consider these tables to be updated and more expansive versions of similar tables presented by other authors (e.g., Kenyon & Hartmann 1995; Bessell 1979, 1990; Bessell & Brett 1988; Bessell et al. 1998; De Jager & Nieuwenhuijzen 1987; Humphreys & McElroy 1984; Gray & Corbally 2009).

Though our T_e scale is not drawn from a uniform sample, we consider it to be robust as it is less susceptible to small measurement errors or biases unique to a given paper. Moreover, we can identify general trends in different authors' T_e calibrations by comparing their results to our table. For example, where we determine Gray & Corbally (2009) to be less accurate, they always predicts cooler temperatures than the ones we adopt; when Bessell et al. (1998) is the outlier they almost always predict hotter temperatures. Interestingly, De Jager & Nieuwenhuijzen (1987) appears to be the most accurate source as the majority of other references almost never disagree against it.

Our adopted scales slightly differ from that from Slesnick et al. (2002). Slesnick et al. (2002) used Kilian et al. (1992) for all stars earlier than B3 and Humphreys & McElroy (1984) for everything else, a scale that yields higher temperatures for early B stars. If we adopt the calibration used by Slesnick et al. (2002), our derived reddening is slightly higher and MS turnoff ages are younger by ≈ 1 Myr. However, adopting this calibration leads to a very slight but perceptible systematic offset in the dereddened V versus V − J, H, K, and V versus spectral type loci of cluster stars. It also may induce a small but systematic shift in reddening for B0–B3 stars compared to later-type stars.

Recent studies determining effective temperatures for individual B stars from stellar atmosphere modeling indicates that our cooler T_e scale is more accurate. In particular, more recent non-LTE stellar atmosphere modeling by Crowther, the source of the hotter T_e scale for evolved stars used in Bessell et al. (1998), revises the T_e for supergiants downwards to almost complete agreement with our adopted scale (Crowther et al. 2006). The only clear systematic difference between our two scales is that Crowther et al.'s temperatures for B0.5–B1I supergiants are ∼ 2000–2500 K hotter than our entries. The temperatures are already very hot (∼ 25000 K). Our sample includes only 7 supergiants with spectral types between B0.4 and B1: B1.5–B3 supergiants are far more frequent. Therefore, if Crowther's scale is more correct the disagreement should have only a minimal impact on our analysis.

Other recent determinations for less evolved stars support our adopted scale. Specifically, Fitzpatrick & Massa (2005) determined fundamental parameters; e.g., T_e, [m/H], R/R_☉, and log(g)—for galactic B and early A dwarfs and giants. Their derived temperatures for early B stars agree with our adopted scale against the determinations adopted by Slesnick et al. (2002). If anything, our scale is still too hot for B3 V stars by ≈1000 K. In summary, we consider our T_e scale to be a slight improvement over Slesnick et al. (2002)'s, though they used the best available scale at the time, which can clearly yield good estimates for h and χ Per properties.