The Masses of the B Stars in the High Galactic Latitude Eclipsing Binary IT Librae¹

Faint blue stars at high Galactic latitude were first detected in a survey conducted by Humason & Zwicky (1947). Soon after, Bidelman (1948) brought attention to a number of high‐velocity stars of early spectral type. The faint apparent magnitudes (sizable distances) and high velocities led to the conclusion that these objects, which appear at low spectroscopic dispersions to be Population I stars, were a part of the Galactic halo. A debate has raged since about the origin and characteristics of these high Galactic latitude B stars. Uncertainty about the masses or true distances of these stars has left the door open to many different scenarios. The discovery that IT Lib is an eclipsing binary (Kazarovets et al. 1999) raises to three the number of known eclipsing binaries at least 1 kpc above the Galactic plane whose components are B‐type stars. The other two are V Tuc (Wood 1958) and DO Peg (Hoffmeister 1935). IT Lib is the brightest of the three and has light‐curve and radial velocity data gathered for it. As a result, IT Lib presents us with an excellent opportunity to directly measure the masses of a pair of high Galactic latitude B stars.

Photometric variability was first noted in IT Lib (HD 138503) by Strohmeier (1967). Hill (1970) noted variability on the order of 0.2 mag. Houk & Smith‐Moore (1988) classified the spectra of IT Lib (HD 138503) as B2/B3 (IV)(n) with a note that the lines appeared "somewhat filled in." Later observations by the Hipparcos satellite confirmed IT Lib's (HIP 76161) photometric variability. The 74th naming list of the Information Bulletin of Variable Stars (IBVS; Kazarovets et al. 1999) assigned the designation IT Lib and classified it as a possible eclipsing binary.

Analysis of the Hipparcos photometry annex data yielded an ephemeris with the parameters P = 2.2674600 days, T₀ = JD 2,448,500.76777 (Turon et al. 1997). Unfortunately, there was a beat pattern between the period of IT Lib and the duty cycle of the Hipparcos satellite, so substantial gaps were left in the phase coverage from phase 0.30 to 0.58 and phase 0.63 to 0.75. The Hipparcos data show a strong primary eclipse, but the secondary eclipse falls in the gap of observations.

High‐resolution spectra were taken of IT Lib with the Sandiford Echelle Spectrograph (McCarthy et al. 1993) on the McDonald Observatory 82 inch Struve reflector in 1999 March, 2001 February, and 2002 May. A summary of the observations is given in Table 1. The spectra were reduced and extracted using IRAF² and analyzed using the ASP software package developed by R. E. Luck.

Hi lines, Hei lines, and the Mgii 4481 line all have profiles with two well‐defined minima over most of the observed period (see Fig. 1 for an example). The broadening due to rotation of the individual components is on the order of 100–150 km s⁻¹, so the lines from each component never completely separate from each other. This blending probably accounts for the line peculiarities noted by Houk & Smith‐Moore (1988). As modeled in § 4, the primary component is 3–4 times as bright as the secondary in the bandpass of these spectroscopic observations, so its spectral lines dominate the composite spectra. An assortment of Nii, Oii, Aliii, Siiii, and Feiii lines could be identified at the radial velocity of the primary component, but no lines other than Hi, Hei, or Mgii 4481 could be positively identified and attributed to the secondary.

Zoom In Zoom Out Reset image size

The minima of the Hei line profiles were used to measure the radial velocity of each component. At some phases, the center of the contribution from the secondary could not be measured because of blending, so only the radial velocity of the primary was measured at those phases. Table 2 summarizes the radial velocity measurements made from the observations, and Figure 2 shows them plotted by phase using the Turon et al. (1997) parameters.

Zoom In Zoom Out Reset image size

For the analysis in § 4, the individual weights of each radial velocity measure are set equal to each other. The measurements of the radial velocity of the secondary are somewhat more uncertain than those of the primary's velocity because the lines of the secondary are significantly weaker and often partially blended with the lines of the primary. The relative weighting of the two velocity curves is accounted for in the curve‐dependent weights assigned to each data set as discussed in § 4.

The photometric data for IT Lib from the Hipparcos Catalog Epoch Photometry Annex has substantial gaps in phase space. An effort was made to obtain more photometric observations of IT Lib at the unobserved phases in order to verify that the system does have a secondary eclipse and to provide more points for light‐curve fitting in order to determine the properties of the system. Two sets of additional data were obtained. J. Feldmeier & J. C. Mihos (2002, private communication) obtained observations with the 2048 × 2048 Tektronix CCD (T2KA) with a Johnson B filter on the Kitt Peak 2.1 m. Those observations were reduced using sky flats and the nonlinearity correction of Mochejska et al. (2001). The bulk of the CCD observations were obtained using the 1024 × 1024 FLICam (SIA‐003 AB SITe back‐illuminated CCD) using Cousins R and I filters on the Warner and Swasey Observatory, Nassau Station 36 inch reflector. Table 3 gives a summary of the observations.

The data were reduced in IRAF and aperture photometry was done with the IRAF procedure QPHOT. The apertures for QPHOT were set to approximately 3 σ, the FWHM of the stellar profiles. Table 4 identifies the reference stars. All the reference stars are between 3 and 5 mag fainter than the target. There are no brighter reference stars in the fields of view (104 × 104 for the 2.1 m data and 5^' × 5^' for the 36 inch data). As a result, uncertainty in the background turned out to be the largest contributing factor to the photometry errors.

The simple average of the scaled relative magnitudes with respect to each reference star is taken to be the measured relative magnitude of IT Lib for each individual image. The σ is taken as the random error of each individual measurement. The errors are higher for the measurements in Cousins R because the night sky is significantly brighter in that bandpass. Larger errors also occurred on nights where moonlight and/or clouds and humidity made significant contributions to the sky brightness. Only data with errors smaller than 50 mmag were used in the analysis (Fig. 3).

Zoom In Zoom Out Reset image size

There was no need for absolute calibration of the photometry gathered. The Wilson (2001) code used to perform the analysis is capable of performing a simultaneous solution to multiple light curves in multiple filters/bandpasses. The relative magnitudes in each filter were converted to relative intensity normalized to phase 0.25 and inputted as four separated data sets (Johnson B, Cousins R, Cousins I, and Hipparcos V) along with the appropriate effective wavelength data for each filter. Individual data points were weighted by the inverse square of their error.

The parameters of the IT Lib system were derived from the radial velocity and photometric data using the program of Wilson (2001). Wilson (2001) uses the model of Wilson & Devinney (1971) with some modifications. The following assumptions are used: synchronous rotation of the components, the components radiate as blackbodies, an orbital period of 2.267460 days and a zero epoch of JD 2,448,500.76777 (Turon et al. 1997), and the luminosity of the secondary component is computed as a function of temperature and surface area of that component. The logarithmic limb‐darkening law was used. Limb‐darkening coefficients used in the models are taken from the tables of Van Hamme (1993) for stars of the appropriate mass and temperature. The gravity brightening and reflective albedo coefficients used are the ones suggested by Wilson (2001) for hot stars with radiative envelopes. While the temperature of the secondary component is allowed to float, the temperature of the primary component is held constant at 22,000 K, which is consistent with the observed colors of the system and the mass of the primary component.

Curve‐dependent weights were applied in order to compensate for the differences in precision between the light and velocity data sets. The Wilson (2001) code allows the weighting of curves by the standard deviation of the curve (σ_c). The method of Kallrath & Milone (1999) using the differences between pairs of consecutive points in phase space was used for calculating the value of σ_c for each light curve. In the case of the radial velocity curves, the values were not spaced close enough to evaluate differences between consecutive points in phase space, so the truncated FFT method (Kallrath & Milone 1999) was used instead by simulating the velocity curve to first order with a sine function. The curve‐dependent weights calculated from this method are listed in Table 5.

The σ_c for each velocity curve, when normalized to the curve amplitude, is roughly 20 times larger than the σ_c of each of the light curves, which translates to a relative weight in the total solution on the order of 400 times smaller than the light‐curve weights. Some parameters have no dependence on the light curves (such as the semimajor axis and Γ velocity). Full simultaneous solutions of both light and velocity data together calculated errors for these parameters on the order of 50%–60% of the parameter values. Solutions performed using only the velocity data produced parameters with almost the same values but with errors that were 2–4 times smaller than those obtained in the full simultaneous solution. This led to the conclusion that the weights of the velocity curves were probably understated relative to the light curves. It seems reasonable that the velocity data sets should have lower curve weights since they have significantly fewer data points. However, the velocity data are more evenly distributed in phase space than any of the light curves.

In order to rectify the difference between the errors in the full solution and the solution using only the velocity data, the calculated σ_c values for the velocity curves were divided by a factor of 10. This change gave the velocity curves roughly the same but still less weight than each of the light curves. When these curve weights were applied to the full simultaneous solution, none of the derived parameter values were significantly different from those obtained using the unaltered curve weights. However, using the altered curve weights did reduce the errors of the velocity‐dependent parameters to essentially the same error values given by the solution to the velocity data alone. These corrected σ_c values were used in the analysis to obtain the best‐fit parameters.

The Wilson (2001) code uses a least‐squares fit that is iterated to simultaneously solve the parameters of the system. The program was run in a mode reserved for detached binary systems. Table 6 lists the best fits to the parameters defining the IT Lib system. Figure 2 shows the fit to the radial velocity data, and Figure 3 shows the fit to the light curve. The eclipses in the system are partial, and the system is best modeled by stars of 9.8 ± 0.7 and 4.6 ± 0.3 M_⊙ separated by 17.6 ± 1.1 solar radii.

The calculated masses of the components are consistent with main‐sequence stars of spectral class B2 and B7. The primary component is about 3–4 times as bright as the secondary, so its spectra dominates the observed composite spectra.

The photometric distance to the system can be found knowing the relative brightness of the components and the absolute magnitude of the primary component. It is possible to find the distance from the absolute magnitude of the combined system, but this introduces additional uncertainties in the form of assumptions that would have to be made about the absolute properties of both the primary and secondary component. Since the light from the system is dominated by the primary, its absolute properties are better constrained. The relative brightness of the components is also well defined by the fit to the light curves. The absolute bolometric magnitude of the primary as calculated by the Wilson (2001) code is −5.20. The bolometric correction for a B2 V star is −2.35 (Cox 2000), which yields an absolute V magnitude of −2.85 for the A component.

The apparent V magnitude of the primary (V₁) can be obtained from the apparent magnitude of the combined system (V_c) and the fraction of light from the primary relative to the combined system (F):

The calculation is carried out at maximum light in Johnson V (phase 0.271). The observed maximum apparent V magnitude of the combined system taken from Turon et al. (1997) is 9.09. The apparent magnitude comes from the maximum apparent magnitude of the system in the Tycho V filter, corrected to Johnson V by the method prescribed by Turon et al. (1997). The fraction of light from the primary relative to the combined system (F) is 0.7767 as calculated by the Wilson (2001) code. This yields an apparent V magnitude of 9.71 for the primary alone. The extinction factor (A_V) from Schlegel, Finkbeiner, & Davis (1998) is 0.702 [assuming A_V/E(B−V) = 3.1]. From the above quantities, a distance of 2.4 kpc is obtained, which places IT Lib 1.0 kpc above the Galactic plane.

There are many sources of error to consider, including the uncertainty in the physical parameters of the primary component, uncertainty in the extinction factor, and uncertainty in the relative brightness of the components. An error of a few tenths of a magnitude would translate into a 20%–30% error in distance. The true errors in this case are unknown, so a standard photometric distance error of 30% is assumed in the following analysis.

Knowing the distance, the systemic radial velocity, and the proper motions allows one to compute the true space velocity of the system. Proper motions for this system are present in Hipparcos (Turon et al. 1997), the ACT2000 (Urban, Corbin, & Wycoff 1997), the Tycho‐2 catalog (Høg et al. 2000), and the UCAC1 (Zacharias et al. 2000). These independent measures were averaged together by the method of Martin & Morrison (1998) to obtain a more accurate average proper motion of μ_α = 1.82 ± 0.67 mas yr⁻¹ and μ_δ = -1.26 ± 0.76 mas yr⁻¹. The systemic radial velocity (-50.9 ± 7.0 km s⁻¹) was taken from the analysis of the radial velocity curves.

The UVW space velocities were computed by the method of Eggen (1961). The UVW velocities were converted to V_π, V_θ, V_z assuming the solar motion of (V_π, V_θ, V_z) = (−9, 232, 7 km s⁻¹) for an object in close proximity to the Sun with (U, V, W) = (0, 0, 0) (Mihalas & Binney 1981). IT Lib's true space velocity was computed to be (V_π, V_θ, V_z) = (-1.6 ± 4.1, 207.0 ± 13.3, -35.9 ± 7.7 km s⁻¹). Errors are difficult to estimate for these velocities because the true error in the distance in unknown. For this analysis, the distance error is assumed to be 30% (±0.7 kpc), which is reasonable for a photometric distance. V_π are V_θ are consistent with a star within the rotating Galactic disk; V_z and the height above the plane lead to the conclusion that while components of IT Lib's velocity are disklike, it has been somehow ejected out of the disk into the Galactic halo. Of particular interest is that IT Lib is moving back toward the plane of the Galaxy, presumably traveling on the downhill side of a ballistic trajectory.

The average main‐sequence lifetime of a 10 M_⊙ star is about 22 million years (Iben 1967). The orbital integrator of Harding et al. (2001) was used to estimate the number of years that have elapsed since IT Lib was last in the Galactic plane (Z = 0). By integrating the orbit backward in time, it is found that it took 33 ± 4 million years for IT Lib to travel from Z = 0 to its present location. The maximum Z distance that IT Lib reaches from the disk on this trajectory is just over 1.1 kpc. We shall return to this apparent discrepancy after a discussion of the abundance analysis of the primary component.

The spectrum used for the abundance analysis of IT Lib was taken at phase 0.829 (1999 March 31; see Table 1). According to the model of the system, at this phase both stars are unobscured, so the observed spectra is a straight blend of the light from both components. At this phase, the lines of the primary and secondary component are near maximum separation, making it easier to measure the contribution to the line from each individual component. Equivalent widths of 12 lines identified with the primary component were measured. Because both stars are unobscured at this phase, the continuum contribution from the secondary could easily be removed from the measured equivalent widths. The continuum contribution of the secondary component was removed from the measured equivalent widths by calculating the ratio between the continuum flux of the primary versus the total combined flux of the system (F) and applying this ratio to the equivalent width in this manner:

The value of F is calculated for the appropriate bandpass and phase using the Wilson (2001) code (F = 0.816 at phase 0.829); W is equivalent width measured from the composite spectra and W ^' is the rescaled equivalent width used in the abundance analysis.

There were no lines (other than the Hi, Hei, and Mgii 4481 lines) that could be positively identified and attributed to the secondary. This is not surprising because of a combination of the signal‐to‐noise ratio of the observation, the rotational broadening of the components, and the fact that the light from the primary component dominates the spectra.

The lines that were measured for the primary component are listed in Table 7 along with the atomic data for those lines. The computer program LINES (Sneden 1973; R. E. Luck 2001, private communication) was used to calculate LTE abundances from the equivalent widths for individual lines. The primary broadening mechanism in these stars is the quadratic stark effect, for which this version of LINES uses the method of Cowley (1971). ATLAS9 (Kurucz 1993) was used to build the stellar atmospheric models.

Because the primary is slightly distorted, the gravity varies by a small amount over the surface. The mean surface gravity for the primary component as calculated by the Wilson (2001) code is log (g) = 3.75. The effective temperature of a 9.8 M_⊙ star is approximately 22,000 K. The temperature/gravity relations of Napiwotzki, Schonberner, & Wenske (1993) obtain the following values for the Strömgren photometry published by Hauck & Mermilliod (1998): T = 22,060 K, log (g) = 3.62. This agrees well with the parameters obtained from the model of the system.

The microturbulence was determined using the lines of the 4550 Å Siiii triplet. The relative gf values of the triplet are well known and the lines cover a range of equivalent widths, making this triplet ideal for determining microturbulence. The microturbulence is calculated from the triplet by finding the value at which each line in the triplet gives the same abundance value so that there is no trend in abundance with respect to equivalent width. The microturbulence found for each model used is listed in Table 8. These are rather typical values for a B star of this temperature under the assumption of LTE.

The results of the analysis over a range of temperatures and gravities are presented in Table 8. The favored model is 22,000 K, log (g) = 3.75. The results for individual lines in the favored model are listed in Table 7. The results using other models over a range of temperatures and gravities are presented to demonstrate how differences in the atmospheric models effect the abundances. For comparison, the solar abundance values (Grevesse & Sauval 1998) and the average abundance values for a sample of Population I B stars (Martin 2003) are given. The sample of Population I B stars are 12 stars situated in the Galactic plane covering the range of atmospheric parameters representative of B stars. The abundances in these stars were analyzed in the same manner as IT Lib. The abundances of the primary component are consistent with those for a normal Population I B star over the entire range of temperatures and gravities explored. Nii and Aliii are a bit depressed; however, when the errors in the analysis are considered, these anomalies are negligible.

8.1. Main‐Sequence Lifetime versus Travel Time

8.2. Ejection from the Disk and Rejuvenation through Mass Transfer

8.3. In Situ Halo Star Formation

8.4. Evidence from Abundances

8.5. Conclusion