The Astronomical Journal, 126:353–369, 2003 July # 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.
KINEMATICS AND LUMINOSITY FUNCTION OF DWARF POPULATIONS IN THREE AREAS ´ N-ESO PROPER-MOTION CATALOG1 OF THE CALA Patricio Rojo2 Department of Astronomy, Cornell University, 610 Space Sciences Building, Ithaca, NY 14853-6801; and Departamento de Astronomı´a, Universidad de Chile, Casilla 36-D, Santiago, Chile;
[email protected]
and Marı´a Teresa Ruiz2 Departamento de Astronomı´a, Universidad de Chile, Casilla 36-D, Santiago, Chile;
[email protected] Received 2003 January 9; accepted 2003 March 13
ABSTRACT We have completed the analysis of a sample of 112 stars in the solar neighborhood taken from the statistically complete Cala´n-ESO catalog. From medium-resolution spectroscopy we classified every star, both by direct comparison with spectroscopic standards and by using spectral indices. The latter also allowed discrimination between main-sequence (MS) dwarfs and subdwarfs. Several useful spectral type versus color relations were obtained from CCD photometry of the sample (observed magnitudes were dereddened). Distances and absolute magnitudes were determined. From measured radial velocities and proper motions, we determined the kinematics [Galactocentric velocity components (U, V, W )], which allowed the classification of each star as belonging to the disk or halo population. Luminosity functions (LFs) were then obtained using the 1/Vmax method for the different populations. The maximum in the LF for MS dwarfs was found to be near MV = 12.5 0.5, in accord with previous determinations. On the other hand, we found an increase in the LF of the subdwarf at its faint end, which is in strong disagreement with determinations by other authors. A mass density of MS dwarfs of 0.047 0.021 M pc3 was derived, while the contribution of subdwarfs was found to be negligible. Key words: stars: kinematics — stars: luminosity function — subdwarfs
The determination of the luminosity function (LF), kinematic properties, and spectrophotometric relations of these late-type dwarfs and subdwarfs allows the determination of time-dependent properties of the Galaxy at the epoch when these old stars were formed, given that differences in kinematics and metallicities can translate into differences in formation ages. It is also important to assess the contribution to dark matter from these subluminous stars that might have escaped detection in magnitude-limited surveys. Here we present the first results from an ongoing analysis of the statistically complete sample of stars in the Cala´nESO catalog (Ruiz et al. 2001, hereafter the CE catalog) of nearby high proper motion stars. In x 2 we describe the selection of the sample, along with observations and data reduction techniques. In x 3 we present the classification scheme used. In x 4 we obtain the spectrophotometric distances and perform a kinematic analysis. In x 5 we discuss the luminosity function of the different populations, and finally, in x 6 we summarize results and conclusions.
1. INTRODUCTION
M-type dwarfs are the most common stars in our Galaxy; they are long-lived low-mass stars. Their lifetime can be even longer than that of the universe and hence it is no surprise that some of them might have been formed during the early epoch of formation of the Galaxy. Low-mass stars, which have populated the Galaxy since the earliest epochs, were formed from material poor in heavy elements (metals), their relative abundances being then much closer to the abundances present just after the atomic era; therefore, they constitute an important record of Galactic history. These stars are called subdwarfs and have different degrees of underabundance of metals. They are less luminous than their main-sequence (MS) dwarf counterparts at the same temperature, differences that can be up to 4 mag (Monet et al. 1992; Baraffe et al. 1995; Gizis 1997, hereafter G97). Subdwarfs have been known for more than 60 years (Kuiper 1939); however, the study of late-type subdwarfs (later than K) has been undertaken only recently, mostly because of their faint intrinsic luminosities, in addition to the fact that there is no simple technique that can allow an accurate metallicity determination and hence an accurate luminosity classification for these stars.
2. OBSERVATIONS
2.1. Sample Selection The CE catalog gives positions (J2000.0), estimated red magnitudes, proper motions, position angles, and finding charts for 542 stars selected by their high proper motions from 14 areas of the ESO R survey (5 5 each). Ruiz et al. (2001) show that this sample is statistically complete
1
Based on observations obtained with the VLT (ESO), project 67.D-0224A. 2 Visiting Astronomer, Cerro Tololo Inter-American Observatory, NOAO, which is operated by AURA, Inc., under cooperative agreement with the National Science Foundation.
353
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ROJO & RUIZ TABLE 1 ESO Areas
Area ESO
(J2000.0)
(J2000.0)
l (J2000.0) (deg)
b (J2000.0) (deg)
496 ........................ 381 ........................ 385 ........................
8 49 19.6 12 50 29.8 14 26 23.8
25 20 44 35 07 04 35 16 14
249.5 302.7 324.0
11.6 27.8 23.7
Epoch
TBa (yr)
Antiapex PAb (deg)
1995.1 1995.2 1994.5
11.0 7.8 7.0
101.9 128.8 115.5
Note.—Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. a Difference between plates used to measure proper motions. b Position angle of the antiapex.
for stars with apparent magnitudes 7.5 mR 19.5 and proper motions l 0>2 yr1. Here we present the analysis of objects in three of the ESO areas, Area 496 (stars CE 32 to CE 65), Area 381 (stars CE 256 to CE 296), and Area 385 (stars CE 421, CE 423 to CE 444, CE 446, 447, and 449, CE 452 to CE 454, CE 457, 458, 460, and 461, and CE 467 to CE 469). Table 1 summarizes the information regarding these areas. A total of 111 stars are included in these areas, which are a statistically complete sample in a 75 deg2 surface in the sky within the established limits. The star CE 457b was identified as a common proper motion companion to the star CE 457. CE 457b, whose red magnitude lies below the limit of the CE catalog, was discovered during the VLT spectroscopic observation of CE 457. Therefore, the sample analyzed in this work consists of 112 stars. For the present study, we obtained B, V, R, and I photometry and medium-resolution spectra for all stars in the sample. Table 2 summarizes the new data for the sample derived from observations and the analysis. Column (1) lists the CE number; column (2), the ESO area; column (3), the telescope used to obtain the spectra; columns (4)–(7), B, V, R, and I photometry, respectively; column (8), the spectral type; column (9), absolute magnitude; column (10), the distance; column (11), the average radial velocities; and columns (12)–(14), the Galactocentric velocities U, V, and W, respectively, with U positive toward the Galactic center. The CE catalog has all the remaining important quantities (we found that the position angle of CE 277 is in error in the CE catalog, the correct value being 246=6). 2.2. Photometry CCD photometry was obtained at the Cerro Tololo Inter-American Observatory (CTIO) 1.5 m and 0.9 m telescopes. Data reduction was performed using IRAF software, with its specialized packages NOAO.DIGIPHOT .APPHOT and NOAO.DIGIPHOT.PHOTCAL. Photometric standards from Landolt (1983) were used for calibration. The obtained photometry is shown in columns (4), (5), (6), and (7) of Table 2. We estimate a 3% uncertainty in the photometry, except for CE 42, whose precision is very low in all bands, and CE 53 and CE 457b, whose precision in the B band is low and should be considered only an upper limit. 2.3. Spectroscopy We obtained medium spectral resolution spectroscopy ˚ ) for all stars. This resolution is more than enough (1.5 A
for a rough metallicity classification (G97), allowing us also to compute radial velocities. The spectra were obtained using three telescopes: UT2 plus FORS2 (VLT, ESO), Blanco 4 m plus RC spectrograph (CTIO) and the CTIO 1.5 m plus spectrograph. At the VLT UT2 plus FORS2 we used the 600RI (No. 19) grism and a ˚ . At the GG435 (No. 81) filter, obtaining FWHM 1.2 A CTIO 4 m telescope, we used grating KPGLF-1 and a ˚ , and for the 1.5 m GG495 filter, obtaining FWHM 1.4 A telescope, we used grating No. 36 and filter GG495, obtain˚ . The spectral range observed with the ing FWHM 1.5 A VLT plus UT2 and with the CTIO 4 m telescopes were ˚ , while in the 1.5 m the range was 6550–7450 A ˚. 5500–8800 A In column (3) of Table 2 we present the site and instrument used to observe each star. Bad weather prevented us from observing CE 461. The white dwarfs in this sample have already been analyzed and published (Ruiz & Bergeron 2001). Along with the program stars, we observed photometric standards, radial velocity standards (see x 2.4), some known parallax stars (Ruiz & Anguita 1993), and some spectral type standards (Leggett et al. 2000; Kirkpatrick, Henry, & McCarthy 1991) These reference stars are presented in Table 3. With the IRAF routines in the package NOAO .TWODSPEC.APEXTRACT we extracted the onedimensional spectra, which were then dispersion-corrected and flux-calibrated with tasks in the package NOAO .ONEDSPEC. When possible (exposure times long enough), we wavelength-calibrated the spectra using telluric lines obtained from the work of Osterbrock et al. (1996), rather than with the available comparison lamps. Using telluric lines we ˚ ) several times obtained a dispersion precision (rms 0.05 A better than by using the lamp. 2.4. Radial Velocities Low-resolution spectra of all the stars, obtained for spectroscopic classification by using the 3.6 m telescope at La Silla (ESO) and the Blanco 4 and 1.5 m telescopes at CTIO, helped us establish that most of the stars in our sample were M type, a few were K type, and only very few were from earlier types; therefore, we chose the radial velocity standards of spectral types that were mostly M, including a few K type. The different sources from which we selected our radial velocity standards claim to have high precision: the standards from Dawson & de Robertis (1998) have an rms of 4 km s1, Skuljan, Hearnshaw, & Cottrell (2000) estimate a precision of 200 m s1, and Marcy & Benitz (1989) standards have a precision of 230 m s1.
TABLE 2 Data for the Star Sample
CE (1)
ESO Area (2)
Tel.a (3)
B (4)
V (5)
R (6)
I (7)
S.T. (8)
MV (9)
d (pc) (10)
vr (km s1) (11)
U (km s1) (12)
V (km s1) (13)
W (km s1) (14)
32.......... 33.......... 34.......... 35b ........ 36.......... 37.......... 38.......... 39.......... 40.......... 41d ........ 42b ........ 43.......... 44.......... 45.......... 46.......... 47.......... 48.......... 49.......... 50e ......... 51e ......... 52.......... 53.......... 54.......... 55.......... 56.......... 57.......... 58.......... 59.......... 60.......... 61.......... 62.......... 63.......... 64.......... 65b ........ 256 ........ 257 ........ 258 ........ 259 ........ 260 ........ 261 ........ 262 ........ 263 ........ 264 ........ 265b ...... 266 ........ 267 ........ 268 ........ 269b ...... 270 ........ 271 ........ 272 ........ 273 ........ 274 ........ 275 ........ 276 ........ 277 ........ 278 ........ 279 ........ 280 ........ 281 ........ 282 ........ 283 ........ 284 ........
496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 496 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381 381
b b a c b b b a ... b b b b a b b b b a a b a a b c b b a c a c a c c a a b b b b b b b c b b b c ... b b ... b b a c c c a a ... a c
16.44 12.62 19.97 19.44 13.48 17.10 15.72 20.86 20.73 16.65 18.62 16.99 17.71 20.13 15.30 11.70 15.20 19.55 20.06 19.43 9.61 18.10 21.27 15.56 19.38 15.22 17.77 21.44 16.69 19.73 14.94 21.80 9.44 7.70 18.50 20.64 16.16 16.27 16.72 16.94 17.76 17.86 13.68 15.20 17.73 13.35 13.82 8.15 20.55 14.96 18.17 14.72 16.67 16.32 22.31 18.50 13.10 13.24 19.18 21.22 20.84 19.98 13.91
14.88 11.54 18.52 17.81 11.98 15.67 14.31 19.04 19.49 16.00 17.66 15.48 16.02 18.49 13.79 10.81 13.69 17.73 18.03 18.07 8.62 17.11 19.16 13.91 17.72 13.68 15.94 19.64 15.28 18.03 13.41 19.97 8.60 7.21 16.81 18.66 14.53 14.65 15.59 15.40 16.21 16.33 12.56 13.73 16.17 11.87 12.34 7.44 19.66 13.55 16.58 14.63 15.34 14.92 20.36 16.82 12.29 12.01 17.68 19.15 19.54 18.44 12.59
13.73 10.90 17.64 16.61 10.82 14.62 13.38 17.53 18.82 15.61 17.12 14.46 14.84 17.45 12.66 10.28 12.73 16.22 16.30 17.50 8.06 15.96 17.16 12.56 16.41 12.56 14.45 18.61 14.10 16.83 12.36 18.14 8.16 6.86 15.91 17.20 13.32 13.43 14.89 14.32 14.94 15.12 11.36 12.79 14.99 10.81 11.39 7.09 19.21 12.61 15.42 14.50 14.52 13.90 19.10 15.65 11.80 11.27 16.59 17.46 18.92 17.29 11.79
12.29 10.38 16.85 15.04 9.32 13.23 12.35 15.58 18.23 15.22 16.60 13.22 13.39 16.42 11.32 9.79 11.75 14.31 14.16 17.34 7.65 15.01 14.90 10.82 14.76 11.16 12.51 17.46 12.83 15.33 11.06 15.89 7.75 6.56 15.08 15.35 11.79 11.83 14.28 13.01 13.31 13.54 10.52 11.84 13.54 9.57 10.36 6.74 18.68 11.59 13.91 14.41 13.77 12.61 18.06 14.17 11.35 10.64 15.20 15.36 18.30 15.88 11.07
M2.5 g sdK7 M3.0 M2.5 M2.0 M1.0 sdM5.0 WD-C sdg sdk M1.5 M3.0 sdM0.5 M2.0 g M0.5 M4.5 sdM5.0 WD-C g sdM1.0 M6.0 M4.0 M3.0 M2.5 M5.0 sdM1.0 M2.5 sdM3.0 M1.5 M6.0 g g sdM0.0 sdM4.0 M3.0 M3.0 sdk M2.0 M3.5 M3.5 M0.0 M0.0 M3.0 M1.5 M0.0 g WD-C M1.0 M3.0 WD-C sdK7 M2.0 esdM4.0 M3.0 g K5 M2.5 M5.5 WD-C M3.0 K7
12.2 6.2 9.7 12.8 12.5 11.6 9.6 15.9 15.7c 6.0 7.2 10.9 12.4 11.1 11.8 5.6 9.6 15.0 17.4 17.2c 5.5 11.2 17.3 14.0 13.5 12.0 15.0 11.5 11.7 13.3 11.3 16.8 5.0 4.1 9.9 15.4 12.8 13.1 8.2 11.4 13.3 12.9 10.1 9.4 12.3 11.2 9.8 4.4 14.9c 9.7 12.5 12.4c 9.3 11.1 13.4 12.4 5.2 7.1 11.7 16.0 15.7c 12.0 7.8
33.2 112.7 547.4 96.2 7.7 62.8 82.6 40.9 57.9 943.7 1185.4 80.9 52.8 285.8 24.7 105.8 64.2 34.7 13.4 14.7 41.4 142.7 23.2 9.5 68.1 21.5 15.0 408.7 51.3 85.4 25.7 42.2 52.3 40.6 225.4 43.5 21.9 20.3 285.2 60.6 36.8 46.6 31.0 72.6 56.7 13.8 31.5 40.6 88.4 58.4 64.1 27.7 154.9 55.8 237.0 74.3 248.6 91.7 150.5 41.3 58.8 186.1 89.2
11.7 6.3 126.7 21.1 90.3 84.4 98.5 93.1 ... 21.1 94.9 142.5 4.3 87.8 6.5 65.4 64.8 66.7 112.4 ... 49.7 362.3 6.8 55.3 33.4 48.0 30.1 186.6 45.9 90.9 36.9 55.7 17.4 42.4 19.3 194.3 1.8 51.7 45.0 17.5 27.6 2.3 2.1 14.2 2.3 7.1 29.0 39.8 ... 28.7 88.8 ... 17.4 36.5 102.7 57.4 3.3 35.6 127.0 31.9 ... 38.0 0.6
44.7 119.1 454.0 36.4 65.6 87.1 65.9 71.3 ... 719.1 1684.4 33.6 68.5 281.0 18.1 114.8 87.5 60.0 21.1 ... 83.0 201.4 57.3 37.3 39.0 40.4 31.2 246.0 114.1 88.6 9.8 54.6 42.0 49.5 251.8 28.2 21.2 28.6 380.1 42.2 10.8 45.1 17.0 48.3 48.4 11.7 15.7 96.3 ... 62.1 4.1 ... 20.2 60.9 110.4 107.8 54.2 102.7 95.3 13.9 ... 133.8 69.3
31.1 44.7 307.8 25.4 67.0 58.4 102.2 76.2 ... 153.9 939.1 183.9 23.5 207.2 16.5 0.6 25.8 52.7 99.4 ... 26.7 451.8 12.3 48.0 59.0 34.1 23.9 316.7 21.8 83.9 54.3 43.3 8.6 58.2 181.4 159.7 16.0 68.1 170.5 50.2 43.2 10.7 22.2 55.0 16.3 14.7 39.8 46.1 ... 2.1 118.8 ... 114.2 20.5 297.2 34.0 156.0 24.4 167.0 50.0 ... 112.7 13.1
6.0 16.7 110.3 82.5 22.0 5.5 98.3 11.1 ... 654.2 617.6 48.6 6.4 22.7 6.7 97.1 46.2 7.4 62.2 ... 12.1 30.2 0.7 4.4 34.0 10.3 9.4 155.2 41.2 60.2 34.5 3.9 47.9 15.3 10.3 128.0 9.0 27.7 199.2 1.9 0.4 20.8 13.3 8.5 16.9 3.1 13.6 66.3 ... 5.3 2.3 ... 113.8 48.0 127.0 69.5 285.7 10.9 92.1 3.4 ... 44.4 54.0
356
ROJO & RUIZ
Vol. 126
TABLE 2—Continued
CE (1)
ESO Area (2)
Tel.a (3)
B (4)
V (5)
R (6)
I (7)
S.T. (8)
MV (9)
d (pc) (10)
vr (km s1) (11)
U (km s1) (12)
V (km s1) (13)
W (km s1) (14)
285 ........ 286 ........ 287 ........ 288 ........ 289 ........ 290 ........ 291b ...... 292 ........ 293 ........ 294 ........ 295 ........ 296 ........ 421 ........ 423 ........ 424 ........ 425 ........ 426b ...... 427 ........ 428b ...... 429 ........ 430b ...... 431b ...... 432 ........ 433e ....... 434e ....... 435 ........ 436 ........ 437b ...... 438 ........ 439 ........ 440 ........ 441b ...... 442 ........ 443 ........ 444 ........ 446 ........ 447b ...... 449b ...... 452 ........ 453 ........ 454 ........ 457e ....... 457bb,e... 458b ...... 460 ........ 461 ........ 467 ........ 468 ........ 469b ......
381 381 381 381 381 381 381 381 381 381 381 381 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385 385
c c c a b c c b b c b ... ... c c b a c c a b a c c c c b b a c c c c a c b c c ... c a a a c c ... c c b
16.28 17.18 17.29 20.04 16.87 16.04 10.96 17.63 16.87 11.52 17.99 15.97 18.77 15.93 17.45 14.82 20.68 17.78 10.83 18.57 18.52 21.76 10.63 14.64 16.25 15.50 17.84 16.79 20.00 17.42 17.73 14.92 16.88 20.74 10.51 20.41 10.22 10.59 20.45 16.64 19.77 22.27 23.34 17.73 14.84 17.31 14.37 15.67 7.86
14.62 15.53 15.69 18.41 15.78 14.59 10.36 16.22 15.58 10.78 16.23 15.77 17.86 14.43 15.82 13.42 18.74 16.29 10.18 17.06 16.98 19.75 9.98 13.14 14.65 14.12 16.09 15.28 18.23 15.78 16.11 13.53 15.35 18.96 9.68 18.55 9.53 9.97 19.25 15.15 18.37 20.43 21.91 16.18 13.36 15.73 12.89 14.15 7.34
13.46 14.33 14.59 17.09 15.13 13.65 9.97 15.43 14.77 10.35 14.96 15.61 17.35 13.29 14.61 12.55 16.52 15.30 9.78 15.97 16.04 17.82 9.58 12.03 13.40 13.25 14.66 14.46 16.89 14.51 14.93 12.63 14.29 17.96 9.22 16.94 9.13 9.60 18.63 14.15 17.53 18.64 19.96 15.01 12.33 14.68 11.69 13.02 7.08
11.97 12.76 13.22 15.50 14.52 12.65 9.61 14.61 14.05 9.93 13.34 15.46 16.88 11.81 13.07 11.65 14.03 14.12 9.38 14.51 15.12 15.65 9.22 10.65 11.85 12.41 12.83 13.63 15.21 12.94 13.47 11.81 12.88 16.82 8.81 14.91 8.76 9.25 18.08 13.00 16.76 16.45 17.54 13.59 11.14 13.42 10.12 11.53 6.78
M3.0 M3.0 M2.0 M4.0 sdk M0.5 g sdM0.0 sdK5 g M3.0 WD-C WD-A M3.0 M3.0 M0.5 M7.0 M1.5 g M3.0 sdM0.0 M5.5 g M2.0 M3.0 M0.0 M4.5 sdM0.0 M3.5 M3.0 M3.0 M0.0 M3.0 sdM0.5 g M5.0 g g WD-C M1.5 sdK7 M5.5 M6.5 M2.0 M1.5 M2.0 M3.0 M3.0 g
12.5 12.9 11.7 13.3 8.0 9.5 4.4 9.5 9.1 4.8 13.3 12.8c 15.4c 12.3 12.8 8.8 18.7 10.4 4.7 12.0 10.4 16.8 4.5 11.9 13.0 8.5 14.5 9.7 13.7 13.1 12.4 8.6 11.7 11.3 4.9 15.6 4.6 4.3 15.5c 10.4 9.4 16.5 17.5 12.2 10.8 11.1 12.9 12.4 3.8
26.6 33.2 59.7 101.4 340.5 98.4 146.1 207.3 185.9 146.6 37.8 39.9 31.7 25.7 39.2 79.8 10.0 140.2 120.6 100.2 197.4 37.3 119.9 17.6 21.0 125.4 20.3 125.7 78.3 33.2 54.2 92.8 51.2 320.7 85.0 38.0 94.8 129.1 55.7 84.9 581.3 59.0 72.1 61.1 32.0 82.1 9.8 22.4 50.6
24.6 6.5 21.4 24.9 32.8 37.3 33.6 176.7 52.7 49.2 91.5 ... ... 17.8 0.7 1.0 14.6 9.0 27.5 12.5 186.2 19.1 53.6 9.7 14.3 11.6 40.8 64.2 25.9 24.4 91.0 42.3 87.8 5.6 8.1 52.6 74.4 103.7 ... 47.2 51.1 24.3 32.2 42.9 3.2 ... 8.1 66.2 44.2
44.4 30.6 54.7 88.7 256.5 10.1 133.7 307.1 339.5 128.9 64.2 ... ... 2.6 24.3 52.9 9.0 25.0 138.1 56.5 10.5 3.7 36.0 7.9 11.5 108.3 43.7 75.5 1.8 16.9 131.7 92.2 43.2 209.2 55.3 18.1 64.3 170.0 ... 37.0 280.0 33.5 39.0 72.5 11.5 ... 0.2 54.1 65.8
11.1 39.1 31.1 125.4 244.0 19.1 49.3 234.4 254.4 37.7 95.5 ... ... 42.6 32.8 68.6 37.5 107.1 153.0 52.3 292.8 58.8 125.2 22.9 28.7 71.1 7.3 177.6 73.4 68.4 55.9 119.5 91.5 364.6 58.2 63.0 31.5 36.0 ... 121.7 565.9 83.6 103.4 25.2 23.8 ... 13.4 52.8 44.6
23.8 16.4 33.5 46.8 43.0 102.5 1.7 278.4 96.2 87.9 16.1 ... ... 4.6 3.2 8.5 1.4 106.5 24.4 64.7 59.3 22.8 97.2 20.3 23.0 73.7 10.5 212.9 28.1 2.7 48.6 83.4 17.8 67.1 10.9 13.9 92.1 18.3 ... 40.2 74.8 21.9 27.8 0.5 40.8 ... 3.4 6.8 39.0
a
Telescope used for obtaining the spectra: (a) VLT Unit Telescope 2; (b) CTIO 4 m; (c) CTIO 1.5 m. Uncertainty in radial velocity greater than 10 km s1. c Absolute magnitude taken from Ruiz & Bergeron 2001. d Using only kinematic (as opposed to metallicity) criteria would suggest that this star is a subdwarf (sdg). e Common proper motion binary. b
Tasks in the package NOAO.RV of IRAF allow the crosscorrelation between the program and standard stars. To avoid any instrumental systematic errors, we correlated only stars from the same night. After having filtered the spectra in the Fourier space the task FXCOR cross-correlates in the real domain to get rid of the high-frequency noise and the
low-frequency structure. The same task corrects the relative velocity to a barycentric radial velocity. For stars with spectral types K or earlier, there are fewer spectral features to correlate in the wavelength range we have. Therefore, in this case we also compare the spectra with rest absorption lines, obtained from the atlas of Davis
No. 1, 2003
DWARF POPULATIONS
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TABLE 3 Parallax, Spectral Type, and Radial Velocity Standards Used
LHS 1827 ... 2272 347 ... 386 ... ... 57 ... ... ... 2045 3181 3548 375 407 473
Other Name
MVa
Vr (km s1)
S.T.b
Ref.
Obsc
... HD 81797 ... ... HD 120452 ... HD 146051 HD 148786 Barnard’s HD 183275 HD 204867 HD 214952 ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... 14.29 12.12 13.64 14.02 ...
4.59 4.452 8.36 226.1 39.598 30.63 19.635 33.988 110.85 31.404 6.324 0.505 ... ... ... ... ... ...
m0.5 K3 III m1.5 sdk K0 III M1.0 V M1 III G8/K0 III M4.0 V K1/K2 III G0 Ib M5 III esdM4.0 sdm2.0 esdm5.0 esdM4.0 esdm2.0 M3.0 V
1 2 1 3 2 1 2 2 1 2 2 2 4 5 6 5, 7 5 8
abc abc abc abc abc abc abc abc abc abc abc abc a a c a a a
a
Absolute magnitude obtained from parallax. Spectral type standards are written with uppercase. STs assigned after the present work are written with lowercase. c Notation as in Table 2, col. (3). References.—(1) Marcy & Benitz 1989; (2) Skuljan et al. 2000; (3) Dawson & de Robertis 1998; (4) Leggett et al. 2000; (5) Ruiz & Anguita 1993; (6) Monet et al. 1992; (7) G97; (8) Kirkpatrick et al. 1991. b
(1947), selecting those lines of considerable intensity that we can identify in our spectra (see Table 4). The average radial velocities obtained from the crosscorrelation with several standards and the comparison with rest frame lines are given in column (11) in Table 2. The dispersion is the average of these different measures, allowing us to estimate an error in radial velocity of 10 km s1 for all stars, except otherwise marked with a footnote in Table 2. 3. SPECTROPHOTOMETRIC CLASSIFICATION
In this section we present the resulting spectral classification, along with an estimate of the metallicity ([Fe/H]) and some photometric relations. 3.1. Spectral Classification The spectral classification is done in two different ways: through comparison of the spectra as a whole and also through the quantitative use of spectral indices. We used semiautomatic (interactive) techniques to classify the large number of spectra we had. Following the method of Kirkpatrick et al. (1991), to compare the spectra as a whole we developed a program that compares each spectrum with all other spectra on a list that has already been ordered, through a least-squares minimization of the differences among the spectra (fluxnormalized and binned). To avoid noise effects near the normalizing wavelength, the normalized spectra are multiplied by a number near 1 until the minimal square difference is achieved. The program also allows graphic user interaction to check the classification. The final output therefore is a list in which spectra with similar characteristics are together.
To avoid strong telluric absorption bands around 7600 ˚ , only certain spectral ranges were compared. For the UT2 A (VLT) and Blanco 4 m (CTIO) telescopes the spectral ˚ . For the ranges selected were 5600–7500 and 7700–8200 A 1.5 m spectra the procedure was repeated but with a smaller spectral range. The chosen normalizing wavelength is 7500 ˚ , except for the 1.5 m spectra, which we normalized at A ˚ , because of the small amount of absorption around 6530 A ˚ to these wavelengths. The chosen bin intervals were 10 A avoid the effect of Doppler shifts in the analysis. To correctly assign spectral types to each star, we also included in the input list some standard stars, either observed or electronically available. In addition, we also compared the spectra by eye with published standards (Kirkpatrick et al. 1991; G97) before defining the final spectral type. This method does not allow an automatic classification by metallicity, but it certainly helps recognize some characteristic spectral features. The second method we used consists in the quantitative analysis of some selected spectral features. For M- and late K-type stars the TiO and CaH bands change their strengths in proportion to the temperature; therefore it is useful to define a spectral index, Ind ¼
Avg ; Avgcont
ð1Þ
where Avg is the average of the intensity of the feature in a given wavelength range and Avgcont is the average of the appropriate continuum range(s). We use spectral indices defined in Kirkpatrick et al. (1991) and G97; they are shown in Table 5. The indices from G97 also allowed a rough determination of the metallicities
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TABLE 4 Rest Wavelength of Reference Spectral Lines ˚) (A
Ident.
5535.39 ..................... 5588.76 ..................... 5597.77 ..................... 5598.48 ..................... 5857.45 ..................... 5889.87 ..................... 5895.86 ..................... 6102.72 ..................... 6122.21 ..................... 6162.18 ..................... 6242.96 ..................... 6280.65 ..................... 6400.30 ..................... 6439.05 ..................... 6462.63 ..................... 6494.96 ..................... 6531.42 ..................... 6546.27 ..................... 6556.06 ..................... 6562.81 ..................... 6572.77 ..................... 6593.92 ..................... 6599.13 ..................... 6624.95 ..................... 6643.64 ..................... 6717.71 ..................... 6978.93 ..................... 7326.17 ..................... 7344.74 ..................... 7355.89 ..................... 7357.75 ..................... 7364.10 ..................... 7366.57 ..................... 7400.18 ..................... 7568.92 ..................... 7664.83 ..................... 7698.94 ..................... 7978.77 ..................... 7998.97 ..................... 7987.40 ..................... 8070.11 ..................... 8093.51 ..................... 8116.82 ..................... 8183.26 .....................
V—Ba Ca i TiO Ca i Ca i Na i Na i Ca i Ca i Ca i Vi Fe i Fe i Ca i Ca i Fe i Vi Ti i Ti i H Ca i Fe i Ti i Vi Ni i Ca i—TiO Fe i Ca i Ti i Cr i Ti i Ti i Ti i Cr i Fe i Ki Ki Ti i Fe i Co i Zr i Vi Vi Na i
Fig. 1.—Comparison of the spectral type classification of this work, with the classification that results by using only the indices defined by G97 and showing the stars classified as dwarfs by G97 and the present work ( filled squares), stars classified as subdwarfs again by G97 and by this work (circles), extreme subdwarfs (open square), and stars classified as subdwarfs in this work but as dwarfs in G97 (open triangles). A spectral type from 0 to 9 indicates the M subtype, 1 indicates a K7 type star, and 2 indicates a K5 type star. The solid line represents the identity.
(dwarfs, subdwarfs, and extreme subdwarfs; see below) by comparing their relative values. The criterion used for the final classification of the stars was to assign them a spectral type after comparing with standards in the least-squares method, while the spectral index method was used to find the metallicity. As Figure 1 shows, both methods agree quite well, except for some stars for which random noise could have affected the indices. We also found a few stars earlier than K. Considering that in the available spectral range they look very similar, we labeled all of them g or g (according to the slope mostly), but they could belong to even earlier spectral types. The final spectral type obtained for each star is presented in column (8) of Table 2 and in Figure 2.
TABLE 5 Spectral Indices
Index Label
Band
D(Cont1) ˚) (A
D(Band) ˚) (A
D(Cont2) ˚) (A
A.............................. B .............................. C.............................. TiO5 ........................ CaH1 ....................... CaH2 ....................... CaH3 .......................
CaH 6975 Ti i 7358 Na i 8183, 8195 TiO CaH CaH CaH
7020–7050 7375–7385 8100–8130 7042–7046 6345–6355 7042–7046 7042–7046
6960–6990 7353–7363 8174–8204 7126–7135 6380–6390 6814–6846 6960–6990
... ... ... ... 6410–6420 ... ...
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˚ , with a constant added. All plots have the same scale to facilitate their comparison. (a–e) Main-sequence dwarf Fig. 2.—Flux-normalized spectra at 7050 A sequence; ( f ) subdwarf sequence along with the extreme subdwarf one. Some spectra show H in emission. Note that CE 41, classified in x 4.2 as a kinematic subdwarf, appears in this figure as an MS dwarf.
3.2. Photometric Relations Figure 3 shows some selected colors versus spectral type diagrams. All dwarf stars follow well-defined trends that can be fitted with S:T: ¼ 35:443 þ 28:546ðBRÞd 7:016ðBRÞ2d þ
0:620ðBRÞ3d
;
S:T: ¼ 17:018 þ 8:548ðBIÞd 1:188ðBIÞ2d þ 0:066ðBIÞ3d ;
S:T: ¼ 9:236 þ 7:067ðV IÞd 1:167ðV IÞ2d þ 0:084ðV IÞ3d ; S:T: ¼ 6:066 þ 8:856ðR IÞd 2:577ðRIÞ2d þ 0:452ðRIÞ3d ;
ð2Þ
where CE 457b has been left out of the first two fits because it does not have a good measurement of the B magnitude and CE 42 has not been included in any fit. The subindex d indicates dereddened colors; see x 4.2. We didn’t try to fit
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Fig. 2.—Continued
the subdwarfs at this point because of the small size of the sample. Figure 4 shows the expected trends for the different populations: the subdwarfs are redder in BV or BR for a given VI (G97; Dahn et al. 1995). 3.3. Metallicities Our sample consists of 85 MS dwarfs, 18 metal-poor subdwarfs (CE 34, 39, 42, 45, 50, 53, 59, 61, 256, 257, 260, 274, 289, 292, 293, 430, 437, and 443), and one with very little metal content, considered an extreme subdwarf (CE 276).
G97 argues that an MS dwarf classification corresponds to a metallicity of [Fe/H] = 0.5 0.5, the subdwarfs class to a metallicity of [Fe/H] = 1.2 0.3, and an extreme subdwarfs classification to a metallicity of [Fe/H] = 2.0 0.5. The analog of Figure 1 in G97 is our Figure 5; it is clear that both metallicity classifications are equivalent. One can also see that both CE 443 and CE 53 lie halfway between the subdwarf and the extreme subdwarf locus. These determinations will be considered later, when estimating the mass. Metallicities can also be estimated from color indices. The solid lines in Figure 4 are models from Baraffe et al. (1997, 1998), with the lower line representing a more
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Fig. 2.—Continued
metal-poor model than the upper line. According to this plot almost all the stars should have metallicities between 0 and 1, a result that is in disagreement with our findings based on the indices of G97. However, given that the metallicity scale by G97 has been successfully tested (Gizis & Reid 1997), we will use it in the present analysis. 4. DISTANCES AND KINEMATICS
4.1. H-R Diagram In this section, we estimate the distance to each star through its photometric parallax, taking into account its
metallicity. Results are compared with available trigonometric parallaxes for the same stars. We will also briefly discuss the kinematical properties of the sample. Modeling low-temperatures stars, such as those in this work, can be very complex, particularly because of the formation of molecules in their atmospheres that produce opacities not fully computed yet (Baraffe et al. 1998). As an example of the well-known discrepancy between models and observations, Figure 6 shows a model from Baraffe et al. (1997, 1998) and some stars with trigonometric parallaxes (see Table 6 for parallaxes of stars in our sample). It is clear that for stars below 0.5 M (MV 10) models are
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Fig. 3.—Spectral type vs. color relations, showing dereddened colors (see x 4.2), dwarfs (triangles), subdwarfs (circles), the extreme subdwarf (encircled cross), and stars not classified (for being earlier than K; squares).
still very unsatisfactory. Baraffe et al. acknowledge this problem and suggest that it is most probably because of a missing source of opacity. Given this uncertainty we will use empirical relations previously determined (Gizis & Reid 1999) for the different populations (metallicities) of subdwarfs: MVsdM ¼ 4:24 þ 3:40ðV IÞd ; MVesdM ¼ 4:58 þ 3:92ðV IÞd ; esdG=sdG
MV
¼ 2:99 þ 4:16ðV IÞd ;
ð3Þ
where the first two expressions are valid for VI 1.4 and
the latter for VI 1.4. In the present analysis, instead of choosing the appropriate relation by the color of the star, we will select it by its spectral type (see previous equations). The solid lines in Figure 6 show the fits mentioned, as well as a fit for the population of dwarfs obtained after merging the Baraffe et al. (1998) models and Monet et al. (1992) data. We estimate a precision of 0.5 mag for our fits. Column (9) of Table 2 shows the derived absolute magnitudes. It is interesting to note in Figure 6 that the subdwarf with a measured trigonometric parallax, LHS 3181, is less luminous than the extreme subdwarf, also with a measured parallax, LHS 375, of similar spectral type (both are shown as
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Fig. 4.—Color vs. color relations, showing dereddened colors (see x 4.2) and models from Baraffe et al. (1997, 1998; solid lines). Metallicity decreases from upper to lower curves. Symbols are as in Fig. 3.
squares with VI 2.2 in the figure). This was completely unexpected and constitutes a warning regarding the complexity of the metallicity determinations and subdwarf classification. Maybe differences in element abundances are much more influential in determining absolute magnitudes than previously thought. 4.2. Distance and Velocities Extinction corrections were performed using the model from Ortiz & Lepine (1993). From the absolute magnitude we calculate a first estimate of the distance, and with this we calculate the extinction from the model. A corrected distance is then computed with the obtained extinction and
the absolute magnitude, and we keep iterating until selfconsistent values of distance-extinction were found. Colors and magnitudes corrected by this method have a subindex d in this work. Once the distances are obtained, given that we have the proper motions, we can then compute the transverse and Galactocentric velocities. These are shown in columns (11)–(14) of Table 2. Two stars deserve special consideration: CE 41 and CE 42. Both have extremely high tangential velocities. The inaccurate photometry of CE 42 is clearly the cause of the high velocities. For CE 41, we propose two possible explanations: This star is either a subdwarf (our spectroscopic
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Fig. 6.—H-R diagram, showing models from Baraffe et al. (1997, 1998; dotted lines), fits used in this work for different populations (see text; solid lines), and stars with available parallaxes: stars from Monet et al. (1992; crosses), stars from Ruiz & Anguita (1993; squares), stars from the CE catalog (parallax from SIMBAD; see Table 6; triangles), and white dwarfs from Ruiz & Bergeron model parallaxes (2001; circles).
under this classification. In x 4.3, it will be argued that this classification might still not bring the velocities of this object to reasonable values and that it might be a binary system after all. Figure 7 compares the absolute magnitudes determined photometrically with absolute magnitudes determined from trigonometric parallaxes (for stars with
TABLE 6 Stars in the CE Catalog with Trigonometric Parallax from SIMBAD
Fig. 5.—Relations of the spectral indices of G97 for the sample. Symbols are as in Fig. 3.
method fails to classify it as such given its early K type) or this star is in reality an unresolved binary system. In the remainder of this paper we will consider this star a kinematic subdwarf; values shown in Table 2 are those obtained
CE No.
(arcsec)
(arcsec)
d d (pc)
MV MV (mag)
36............... 47............... 52............... 64............... 65............... 269 ............. 294 ............. 428 ............. 432 ............. 444 ............. 469 .............
111 13.57 32.12 24.23 18.15 37.96 16.5 11.51 6.09 15.6 14.57
12 1.76 1.18 1.18 1.23 1.01 9.37 5.42 2.03 1.96 .86
9þ1 1 74þ11 8 31þ1 1 41þ2 2 55þ4 3 26þ1 1 61þ80 22 87þ77 28 164þ82 41 þ9 647 69þ4 4
þ0:2 12:20:2 þ0:3 6:50:3 þ0:1 6:20:1 þ0:1 5:50:1 þ0:1 3:50:2 þ0:1 5:30:1 þ1:0 6:91:8 þ0:8 5:51:4 þ0:6 3:90:9 þ0:3 5:60:3 þ0:1 3:20:1
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available parallaxes3). The discrepancy is considerably large for early-type stars; however, as stated earlier, in the present analysis no attempt has been made to accurately classify stars with spectral types earlier than K5. Only one of the stars with a measured trigonometric parallax (CE 36) has a spectral type M, and its parallax magnitude agrees with the model-obtained magnitude within the given accuracy of 0.5 mag. 4.3. Kinematics In the distribution of velocities in the UV plane (Fig. 8) CE 42 and CE 41 stand out with abnormally high velocities. It is also apparent that the subdwarfs are moving faster than the MS dwarfs (as expected for an older population). All stars far from the ellipsoid in the rightmost plot in Figure 8 would be classified as belonging to the halo population according to the criterion of Leggett (1992). Our plot shows that this criterion applies to the majority of the stars classified as subdwarfs in this work. Figure 9 shows a Toomre diagram (Axer, Fuhrman, & Gehren 1995), where the dashed line contours correspond Fig. 7.—Comparison of absolute magnitudes derived from available trigonometric parallaxes with those obtained from photometric parallaxes.
3
See http://simbad.u-strasbg.fr/sim-fid.pl.
Fig. 8.—U-V plane of Galactocentric coordinates, showing MS dwarfs of type K or later (triangles), G or earlier type MS dwarfs (stars), M subdwarfs (circles), K subdwarfs (squares), the G subdwarf (kinematically classified; crossed square) and the extreme subdwarf (crossed circle). U is defined positive toward the Galactic center. The plots to the right are a zoom of the enclosed section at the left, and the areas enclosed with a dashed line in the rightmost plot delimit some of the populations defined by Leggett (1992). The Sun’s position is also indicated (circled dot).
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Fig. 9.—Toomre diagram (Axer et al. 1995), showing constant kinetic energy surface contours (dashed lines). Only trustworthy data points are presented in the main plot, while the inset shows an expanded range with all the stars of the sample. Symbols are the same as in Fig. 8.
to surfaces of equal kinetic energy. This plot suggests again that CE 42 has ill-determined velocities, that classifying CE 41 as a subdwarf is not enough to give it a reasonable velocity, and that this is probably a binary system. Leaving out these two, the star with the largest energy is CE 34, which gives us a lower limit for the escape velocity of the Galaxy of 475 km s1, slightly higher than the value of 450 km s1 found by Axer et al. (1995). It is worth pointing out that the latter work did not considered reddening, and that our value agreed with theirs before we dereddened our sample.
5. LUMINOSITY FUNCTIONS
The V-band luminosity function, (MV), can be derived following the technique devised by Schmidt (1968), X 1 ; ð4Þ ðMV Þ ¼ V max M 2fM ðM=2Þ; M þðM=2Þg V
V
V
where Vmax is the maximum volume where a particular star could be found given the limits of the survey. Assuming homogeneity, Vmax ¼
3 3 dmax dmax : 3
ð5Þ
For this particular sample, there is no limit on the minimum distance at which a star could have been located and the maximum distance would be given either by the limits in
magnitude or in proper motion of the CE catalog: l 1=5ðVmax MV þ5Þ ; 10 ; dmax ¼ min d lmin
ð6Þ
where lmin ¼ 0>2 yr1 ;
Vmax ¼ 19:5 þ ðV RÞ :
ð7Þ
The error is estimated to be sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X 1 ¼ 2 Vmax
ð8Þ
(Felten 1976). The completeness of the sample can be checked by the index V d 3 r¼ ¼ ð9Þ Vmax dmax (Gizis & Reid 1999); for a uniform and complete sample we would expect r = 0.5. In the three ESO areas analyzed here we find the values ri = {0.41, 0.54, 0.46}, a reconfirmation that the sample is close to being uniform and complete. Figure 10 shows the resulting LF for the whole sample and for the MS dwarf and the subdwarf populations. The LF derived for the total sample, within the uncertainties, is similar to that determined by other authors (Wielen, Jahreiss, & Kru¨ger 1983; Reid, Gizis, & Hawley 2002) for stars in the solar vicinity. In Figure 10 (lower right), we show with a solid line the LF for all subdwarfs in our sample. The dotted line indicates
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Fig. 10.—Luminosity functions (LFs). Top, LF of the complete sample including the contributions of MS dwarfs and subdwarfs; lower left, derived LF for MS dwarfs; lower right, LF of all the subdwarfs (solid line) and LF of the subdwarfs that most likely belong to the halo (dotted line with squares). Absence of error bars for any point indicates that there is only one star for that bin.
the LF for the subdwarfs that are most likely to belong to the halo. All subdwarfs whose Galactic component velocity V is less than 100 km s1 were defined as being likely to belong to the halo. Eighteen of the 21 subdwarfs in our sample fall under that condition. This criterion is equivalent but superior to the reduced proper motion (RPM) one, which is presented in Figure 11 and shows the VI versus I-band RPM diagram. A clear trend is apparent, in which the subdwarfs lie below the majority of the dwarf stars. An evident drawback of the RPM criterion is that it can identify only subdwarfs belong-
ing to the halo and can even miss some of them. For example, according to the RPM criterion, CE 257 would have been considered a star belonging to the disk, but by using our kinematic criterion its high W velocity classifies it as a likely member of the halo. Comparison of the LFs of the halo metal-poor stars with previous results (Fig. 12) shows some disagreement. Our LF presents an unexpected rise at its faint end, which had not been seen before; however, this cannot be considered a definitive result given that only two stars are responsible for the two faintest data points. Also, our sample presents a dip
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Fig. 11.—Color-reduced proper motion diagram (VI, H i). Symbols are the same as in Fig. 8, but filled symbols represent halo stars and asterisks represent white dwarfs.
where some of the other LFs show their maxima. Even if we ease our kinematical criterion to include the three metallicity-classified stars that we just left out, we cannot overcome this difference. LF determinations by other authors often include some kinematical corrections that result in a modified increased LF. Given that in our case stars have been selected based upon their metallicities and not only by their kinematics, we believe that if a correction factor needs to be applied it would be much less important than the correction factors for kinematically based samples. 6. DISCUSSION AND CONCLUSIONS
We used Baraffe et al. (1997, 1998) models to find the mass-luminosity functions (MLs) We used [Fe/H] = 0 for the MS dwarfs, [Fe/H] = 1.3 for the subdwarfs, [Fe/H] = 1.5 for CE 443 and CE 53,4 and for the extreme subdwarf we used [Fe/H] = 2.0. As Baraffe et al. concluded, their ML relations seem to agree with observations within the errors. Using a fourth-order polynomial for the ML relations and the derived LF, we find a mass density of (3.0 2.3) 104 M pc3 for the subdwarfs and a mass density of 0.047 0.021 M pc3 for the dwarfs. 4
See x 3.3.
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Fig. 12.—Comparison of halo luminosity functions, showing our result (solid line with filled squares), also the Bahcall & Cassertano (1986) LF (dashed line with filled circles), the Dahn et al. (1995) LF (solid line with open squares), the Schmidt (1975) LF (dashed line with open squares), the Gould, Flynn, & Bahcall (1998) LF (solid line with asterisks), and the Gould (2003) LF (dashed line with open circles).
On the other hand, if we consider only K5 and later type stars for which our spectral classification is accurate, we have 17 subdwarfs and 68 MS dwarfs, with a ratio of subdwarfs to dwarfs of 0.017 by number density and 6.7 103 by mass, clearly indicating that the contribution from subdwarfs to the total density is negligible, implying that they can be discarded as important contributors to the local dark mass. A potentially important result of the present analysis is the unexpected rise observed at the faint end of the halo LF, implying that in the past the luminosity function and therefore the mass function were quite different from the present-day ones. Given the small number of stars involved, it is difficult to assert whether the increase at the faint end of the subdwarf luminosity function is a statistical fluctuation or a real trend. We are presently undertaking a full analysis of the CE catalog, which we expect would allow us to obtain a stronger statistical result. This research received partial support from FONDAP (15010003), Fondecyt (1010404), and a Guggenheim Fellowship. We also thank an anonymous referee for helpful comments.
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