QUANTITATIVE SPECTROSCOPIC J-BAND STUDY OF RED SUPERGIANTS IN PERSEUS OB-1^*

For the analysis of RSGs in our sample we utilize two grids of synthetic spectra calculated using LTE and NLTE radiative transfer. Both grids of model spectra are calculated using as input an underlying grid of marcs model atmospheres (Gustafsson et al. 2008). These atmospheric models are calculated in one-dimensional (1D) LTE and, while not sharing the complexity of state of the art 3D models, are well suited for this work. Notably, the marcs model atmospheres have been well tested in the literature and converge quickly such that large grids are possible.

The marcs grid used in this work covers a four dimensional parameter space including effective temperature, log gravity, metallicity (normalized to Solar values), and microturbulence (T_eff, log g, Z, ξ). The dimensions of this grid can be found in Table 2.

The grids of synthetic model spectra used in the analysis of this paper are calculated in first in LTEusing turbospectrum (Alvarez & Plez 1998; Plez 2012), and second with NLTEdiagnostic lines (iron, titanium, and silicon) using the codes developed in Bergemann et al. (2012, 2013). See Figure 3 for a visualization of the effects of the NLTE corrections.

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At high resolutions it is straightforward to scale a model to the continuum level of the data. This is accomplished by selecting the flat regions of the spectrum, performing a polynomial fit to the ratio of those points to the matching observed flux as a function of wavelength, and then dividing the full wavelength range of the model by this derived fit. In this way we are comparing the depth and shape of spectral features between the observed spectrum and model.

At lower resolutions the effort to correct the continuum increases in complexity as the dense forest of weak molecular lines blend together to form a "pseudocontinuum" such that the entire observation technically lies below continuum level. We illustrate this effect in Figure 4 for Z = −1.0, 0.0, +0.5, and +1.0 at a spectral resolution of 3000. It is not possible to know a priori how to then properly correct for the continuum as depth below the true continuum is a function of the stellar parameters themselves, especially metallicity, the primary target of our work.

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Our fitting method then becomes a measurement of the ratio of line depth to pseudocontinuum level. We proceed by selecting the points in any given model with normalized flux nearest to unity (see Figure 4, top panel). Assuming this is the continuum we construct an array of the ratio of model to data fluxes at these points. We correct for the continuum by fitting with a low order polynomial and applying that fit to the full model spectrum. In the lower panel of Figure 4 we correct each model to the Z = 0.0 model to demonstrate that the models are not degenerate; they remain unique with respect to metallicity even at resolutions suffering the effects of the pseudocontinuum.

While a spectrograph disperses incident flux at a characteristic resolution based on grating and slit width, the exact spectral resolution can vary significantly from these expected values based on the size of large-scale turbulent motions, terrestrial atmospheric conditions (e.g., seeing, especially in the case where a point spread function is narrower than the slit width of a spectrograph), and instrument setup (e.g., the focus of the telescope). For these reasons a measurement of spectral resolution is an important component in our analysis.

To accomplish this, each model is degraded to a set of resolutions ranging from twice the expected spectral resolution and down until a χ² minimum is passed. We fit a parabola through χ² versus resolution. The minimum of this fit is adopted as the best fit resolution for that model. Upon completion we have a set of local minimum χ² values each paired with a spectral resolution. We adopt the model with the lowest overall χ² as the "best model" and the paired spectral resolution as the proper value for the observed data. At this point we refit the full grid of models locking each at the measured best spectral resolution to calculate a uniform grid of χ² values for parameter determination.

The expected resolution of IRCS in our particular setup is R of ∼20,000. We measure resolutions of 11,000 to 14,000 (see Tables 3 and 4). Assuming the difference is caused by macro turbulence, we calculate expected v_macro ≈ 15−25 [km s⁻¹]. As the resolution of our observations is on order of 15 [km s⁻¹], we note that these values should serve only as estimates. Still, they are in good agreement with literature values. Ramírez et al. (2000) and Cunha et al. (2007) find RSG macroturbulences of between 11–25 [km s⁻¹] using R = 40,000 spectra for a population of galactic RSGs.

Table 4. Perseus OB-1 Red Supergiants LTE

Target	Teff	log g	Z	ξ	$\frac{\lambda }{\delta \lambda }$
	(K)		(dex)	(km s−1)
BD+59 372	3930 ± 90	+0.1 ± 0.3	−0.10 ± 0.06	3.4 ± 0.2	13400
BD+56 595	3970 ± 25	+0.2 ± 0.3	−0.08 ± 0.12	4.1 ± 0.2	12400
HD 14404	3950 ± 40	+0.2 ± 0.1	+0.06 ± 0.09	4.1 ± 0.2	11500
HD 14826	3870 ± 25	+0.3 ± 0.2	+0.04 ± 0.10	3.6 ± 0.2	12600
HD 236979	4040 ± 30	−0.5 ± 0.1	+0.01 ± 0.06	3.1 ± 0.2	12300
HD 13136	4030 ± 40	+0.4 ± 0.2	−0.11 ± 0.09	4.3 ± 0.2	12200
HD 14270	3890 ± 25	+0.2 ± 0.3	+0.06 ± 0.12	3.8 ± 0.2	11200
BD+56 724	3740 ± 25	−0.5 ± 0.1	+0.10 ± 0.06	3.2 ± 0.2	11200
HD 14469	3730 ± 25	−0.1 ± 0.3	+0.11 ± 0.13	4.1 ± 0.2	10800
BD+56 512	3940 ± 40	+0.4 ± 0.4	+0.13 ± 0.11	4.1 ± 0.2	11000
HD 14488	3720 ± 70	+0.2 ± 0.1	+0.17 ± 0.08	3.2 ± 0.2	11700

Note. Parameter fits to observed RSGs using the turbospectrum grid of synthetic spectra calculated in LTE (Plez 2012; Alvarez & Plez 1998).

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After calculating a full four dimensional grid of χ² values we extract the best fit parameters. The methodology is as follows. We begin by selecting the "best" model−the model with the lowest χ² value. We use the parameters of this model to inform the selection of six two dimensional χ² planes (see Figure 5). Functionally, two parameters are locked at the "best values" for each plane and the remaining two parameters are varied against each other. We interpolate the χ² grid of each plane onto a parameter grid four times as dense and take the minimum of the dense grid as the best fit values for the two free parameters. After completing this procedure for each of the six planes, we have three measured best values for each parameter. We average these values to arrive at a final fit for each parameter.

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We assess the significance of our parameter fits with a Monte Carlo simulation. We begin by constructing a spectrum at the exact extracted parameters by linearly interpolating between points in the model grid. For each of 1000 trials we add random Gaussian noise of strength characteristic of the signal to noise of the measured spectrum. We fit each noisy interpolated model as described in this section. For each trial we determine the fit parameters and, after completing the computations, analyze the distributions of fitted values for each parameter. In each parameter the zone of ±1σ is contained between the 15.9 and 84.1 percentile levels. This technique accounts for the noise level in our data as well as any effects based on the spacing in our model grid. We adopt a minimum 1σ value of 20% of the grid spacing for each parameter as we consider a fit more precise than that to be unrealistic given the possibility of nonlinear behavior between grid points. In general our measured significance in metallicity lies above this minimum σ value such that we may confidently trust that our grid is fine enough in metallicity space for this work. In this work we find that lines of Mg i are never well fit. While the cause is under investigation, for this analysis we mask out lines of Mg i before calculating χ².

Initial fits of the spectral database observed for this work measure a slightly sub-solar population metallicity for the Perseus OB-1 RSGs. We measure Z = +0.04 ± 0.10 (LTE) and Z = −0.04 ± 0.08 (NLTE), where the ±σ values denote the standard deviation of the sample. Estimates of the global metallicity of the cluster are more precise, as the error in the mean scales the reported σ's by N^−0.5 = 0.3 for our population of eleven stars.

The LTE model grid measures higher metallicities for cluster stars than the NLTE grid. This is to be expected; the cores of our strongest diagnostic lines (Fe i, Ti i, and Si i) are deeper in the NLTE case (see Figure 3). For any given observed spectrum, a NLTE fit will provide a lower measurement of metallicity. We find that using a fully LTE grid of marcs models induces, on average, a shift in Z of +0.07 dex for RSGs near solar metallicity.

We find good agreement between microturbulence values calculated in this work (2.9–4.3 [km s⁻¹] when compared to high resolution spectroscopy (R ∼ 10⁵) of α Ori. Lundqvist & Wahlgren (2005) calculate a value of 4.5 km s⁻¹ using 1D ATLAS9 LTE models. In Wahlgren et al. (2008), the authors refine that value of 3.1 km s⁻¹ after fitting the same data with the newer 1D ATLAS12 LTE models.

The power of the methodology presented in DFK10 is the need for only moderate resolution of the "new" spectra. In Figure 6 we demonstrate the effect of this degredation for one of our objects. Our high resolution spectral catalogue allows for the first systematic tests of the resolution limits of the J-band technique. In the following tests we degrade the resolution of our observed spectra and those spectra become the inputs to our fitting procedure. To achieve this degradation we convolve the high resolution observed spectrum with a Gaussian with characteristic width of FWHM = $\sqrt{(\lambda /R)^{2} - (\lambda /R_{\rm {data}})^{2}}$, where R represents the output resolution of the "new" spectra.

We then follow identically the techniques presented in Section 3, treating each degraded spectra as an independent observation using nothing learned from the actual observations. We iterate from R of 10,000 to 2000 in steps of 1000. At each resolution we calculate the average and standard deviation of measured metallicity for the eleven objects. These values have been plotted in Figure 7. We find that the fitted average metallicity remains stable for both LTE and NLTE grids from spectral resolutions of 12,000 through 2000. Furthermore, the standard deviation in the individual metallicity measurements holds stable at ∼0.12 dex down to R = 3000. At this point individual atomic spectral features become too blended and diluted; the parameter fits of individual objects begin to diverge from high resolution fit values.

We conclude from these tests that the J-band technique can be utilized on RSGs down to spectral resolutions of 3000. To study large populations of RSGs at extragalactic distances, then, one needs a multi object spectrograph operating at R ⩾ 3000 on a telescope with enough collecting area so that the limiting magnitude is fainter than the target RSGs. Two such instruments exist: MOSFIRE on Keck operates at R ∼ 3200 and KMOS on the Very Large Telescope (VLT) operates at R ∼ 3400. These ideal instruments for the study of extragalactic populations of RSGs operate near but safely above the resolution limits of our technique.

In our tests for parameter stability as a function of spectral resolution we assume that at each resolution step we have the same signal-to-noise ratio (S/N) as in the original, high resolution spectrum. This value of S/N is ≈100–150 per object. By reducing the spectral resolution we functionally increase the S/N per resolution element. In the following, we devise a test to measure the minimum S/N as a function of resolution for which we obtain the same accuracy with respect to metallicity as for our high resolution case.

We calculate the S/N for our original spectra, S/N_meas as follows:

$$\begin{equation} {{\rm \rm S/N_{meas}}} = \left [{\frac{1}{N}}\sum _{i=1}^N (F_i - M_i)^2 \right ]^{-\frac{1}{2}}. \end{equation} \tag{ 1 }$$

In Equation (1), F is the input spectrum with N points and M is the model in the grid which returns the lowest χ². To measure the required S/N at each resolution we must adjust the effective S/N of the observed spectrum to any S/N_target less than S/N_meas. This is accomplished by noting that the target S/N is just a quadrature sum of S/N_meas and the additional noise spectrum required. The strength of that Gaussian noise, σ_scale is then

$$\begin{equation} \sigma _{\rm {scale}} = \sqrt{\rm {\rm S/N}_{\rm {target}}^{-2} - \rm {\rm S/N}_{\rm {meas}}^{-2}}. \end{equation} \tag{ 2 }$$

Adding random Gaussian noise scaled by σ_scale to our observed spectrum degrades it to S/N_target.

To understand the S/N necessary to reach our target precision of σ_Z ≈ 0.10 we use the above method starting with a modest S/N_target = 5 and iteratively increase that value until the σ_Z we extract are consistent with those measured for the original spectrum, i.e., any additional S/N provides no increase in fit precision given the data and model grid. The results of this test are plotted in Figure 8, and indicate that for instruments operating at resolutions of ∼3000, a S/N of ∼100 per resolution element is an ideal target for observational programs.

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As with our discussion in Section 3.4, we note that the residuals between data and model will not be purely Gaussian in nature. This can be due to any combination of telluric contamination, detector noise, and imperfect model atmospheres. The $\chi ^2_{{\rm data}}$ spectrum will contain larger sporadic deviations due to those effects. As a result, the S/N_meas of Equation (1) will slightly underestimate the actual S/N of the data. When this propagates into Equation (2), we end up adding too little noise and not quite reaching S/N_target. This means that the curve in Figure 8 may be skewed downwards. The amplitude of this effect will vary due to the specifics of each observation. This likely accounts for the scatter present in Figure 8. The overall shift must be small due to the quality of our data and spectral fits. Still, we recommend using the upper limits of the error bars in Figure 8 as a target S/N when planning observations.

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We perform a final experiment to test the effects of metallicity on S/N requirements. We interpolate three models from our NLTE grid to values between grid points (Z = +0.8, 0.0, and −0.8) and reanalyze each model as described earlier in this section. The results are plotted in the lower panel of Figure 8. A trend of increasing S/N requirements with decreasing metallicity is indeed seen. The effect is not overwhelming, with less than a factor of two difference between models at Z = −0.8 and +0.8. The S/N required for this set of spectra are globally lower than the case of the actual data. This is to be expected as the experiment is performed starting with perfect models which show no contamination from non-Gaussian noise sources.

The average metallicity of Z = −0.04 ± 0.08 obtained for the Perseus OB-1 RSGs in this work agrees well with the metallicity of young massive stars in the solar neighborhood. Nieva & Przybilla (2012) studied a large sample early B dwarfs and giants using strongly improved detailed NLTE line diagnostics. They obtained surprisingly narrow (σ ≈ 0.05) abundance distributions for the elements C, N, O, Ne, Mg, Si, Fe with average values very close to the sun (Asplund et al. 2009). This implies that there is little scatter in metallicity of the young massive star population around the sun and also practically no chemical evolution over the last 5 Gyr The fact that we also obtain a metallicity very close to the solar value is, thus, a strong indication that the spectroscopic J-band method leads to reliable results.

Unfortunately, the study by Nieva & Przybilla (2012) does not include objects in Perseus OB-1. However, Firnstein & Przybilla (2012) have recently analyzed A supergiant stars in the solar neighborhood including some objects in Perseus OB-1. While this work does focus on the determination of stellar parameters and does not provide a detailed abundance study, it provides magnesium abundances for three objects with an average value −0.10 dex below the Nieva & Przybilla (2012) average of B stars in the solar neighborhood (the uncertainty for each individual A supergiant is ≈  ±0.07 dex). We take this as a confirmation that the metallicity of Perseus OB-1 is close to solar.

We measure higher T_eff for all stars which overlap the target list of (Levesque et al. 2005; see Table 3). The average difference in temperatures is 270 ± 130 [K]for our NLTE calculations (220 ± 100 when compared with our LTE calculations), a significant discrepancy. There are a number of differences between this work and that of Levesque et al. (2005), including the new NLTE corrections we use when computing synthetic spectra, the fact that we fit for Z, micro turbulence, and spectral resolution, and the near IR spectral window of this work. The latter is the most likely candidate for the large difference in measured T_eff values. While we work in the J-band, Levesque et al. (2005) use optical spectra, concentrating on the strength of molecular bands of TiO to derive temperatures. Davies et al. (2013) have shown that the derivation of RSG temperatures using quantitative spectroscopy in optical bandpasses returns lower values than are measured using methods which are less dependent on model atmospheres (the flux integration method). In addition, Davies et al. (2013) show that optical temperatures over predict the IR flux of RSGs when full spectral energy distributions are available and under predict reddening as compared to nearby stars. Temperatures derived from near IR spectroscopy alone are closer to those values from the flux integration method.

New work with 3D models of RSGs will likely do much to resolve the issue of temperature derivation for RSGs, but only a few of these models are available so far (see, for example, Chiavassa et al. 2011).

To compare our results with stellar evolution models we first construct an observational Hertzsrung–Russel diagram (HRD). We calculate bolometric luminosities for program stars using archival K band 2MASS photometry (Table 1; Skrutskie et al. 2006), the bolometric correction recipes of Davies et al. (2013) and Levesque et al. (2005), and distance modulus of Currie et al. (2010). We applied the Cardelli et al. (1989) extinction law using measurements of the reddening to Perseus OB-1 (Currie et al. 2010). These luminosities are plotted against the effective temperatures from our spectral fit in the HRD of Figure 9. We then over plot evolutionary tracks adopting the Geneva database of stellar evolutionary models including the effects of rotation (Meynet & Maeder 2000). All stars except one align along the evolutionary tracks, having zero age main sequence masses of 15–20 M_☉. This result is in good agreement with the age of Perseus OB-1 of 14 ± 1 Myr (Currie et al. 2010). Only the 15 M_☉ track agrees with this time frame. At the age of Perseus OB-1, 20 M_☉ stars have already evolved from the RSG phase while 12 M_☉ stars are still on the main sequence.

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The object BD+59 372 is a clear outlier with a luminosity corresponding to a mass only slightly higher than 9 M_☉ (see Table 3). At this point we have no explanation for this object.

An independent way to compare our spectroscopic results with stellar evolution is the comparison of gravities log g obtained from the spectroscopy and from evolutionary tracks. For the latter, we obtain a stellar mass from the observed luminosities by interpolating evolutionary track masses and luminosities at the effective temperature observed. This mass is then used in conjunction with the observed luminosity and effective temperature to calculate evolutionary gravities. Figure 10 compares evolutionary gravities obtained in this way with spectroscopic gravities. Besides one outlier (HD 236979) we find general agreement and no indication of a systematic discrepancy. We also note that the outlier in Figure 9, BD+59 372, as the object with the highest gravities agrees within the uncertainties of the error bars.

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The general agreement between spectroscopic and evolutionary gravities can be used to discuss the influence of convective turbulence pressure on the model atmosphere stratification. The 3D-hydrodynamic convection simulations by Chiavassa et al. (2011) include effects of pressure caused by the convective motion on the atmospheric density stratification. On the other hand, the 1D MARCS models used in our analysis do not account for convective pressure. It is straightforward to show (see, for instance, Chiavassa et al. 2011, Equation (8)) that as the result of convective pressure the stellar gravity is reduced to an effective gravity which can be approximated by

$$\begin{equation} \log g_{\rm {eff}} = \log g - \log \left(1+\beta v_{\rm {turb}}^{2}/v_{\rm {sound}}^{2}\right) \end{equation} \tag{ 3 }$$

where v_turb is the average turbulence speed and v_sound the sound speed. β is a parameter close to unity if the turbulent velocity fields is almost isotropic. Chiavassa et al. (2011) concluded from their calculations and a comparison with MARCS models that gravity corrections of 0.25–0.3 dex are needed to match the density stratifications of the 1D with the 3D models corresponding to turbulence velocities of the order of the sound speed.

Our comparison of spectroscopic and evolutionary gravities does not indicate a systematic effect of this order. On the other hand, our two objects with the lowest spectroscopic gravities may well be influenced by large effects of turbulence pressure. We note, however, that the models used to calculate our synthetic spectra and those models used for the stellar evolution calculations of (Meynet & Maeder 2000) utilize 1D models which may affect stellar evolution and atmosphere predictions in the same way.

The scientific strength of the low resolution J-band technique derives from the radiative power of RSG stars. In this work we carefully demonstrate that the method is stable and precise well below the spectral resolution of current instrumentation on the largest telescopes available, notably MOSFIRE on Keck and KMOS on the VLT. With these multiplexed instruments we are able to efficiently apply this technique to entire populations of RSGs as individual objects over extragalactic distances. DFK10 calculate a limiting distance for the technique of 7–10 MPC using a single RSG.

In Gazak et al. (2013) we presented simulations showing that the near-IR flux of young SSCs is dominated by their RSG members. These simulations show that the J-band spectrum of a SSC older than 7 Myr will appear very similar to that of a single RSGs. This opens the possibility to use the integrated J-band light of SSCs in distant galaxies as a source for spectroscopic determination of galaxy metallicities.

Our collection of Perseus OB-1 spectra allows us to test this possibility. With a total estimated mass of 20,000 M_☉ (Currie et al. 2010) Perseus OB-1 comes close to the observed mass range of extragalactic SSCs. We construct a simulated SSC spectrum by adding our observed RSGs weighted by their J-band luminosities. The spectrum is shown in Figure 11. We then apply the same analysis technique as in Section 3 and obtain a metallicity of Z = −0.03 ± 0.12 (NLTE), very similar to the average metallicity obtained from the analysis of the 11 individual spectra. The effective temperature obtained from the cluster spectrum is T_eff = 3970 ± 30 and the gravity log g = +0.1 ± 0.2. In agreement with the LTE study of the individual Perseus OB-1 supergiants we measured Z = +0.08 ± 0.12, T_eff = 3910 ± 70, and log g= +0.2 ± 0.1 when fitting with the full LTE model grid.

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Gazak et al. (2013) find that the RSG supergiant population will provide ∼95% of the J-band flux in a young SSC. To simulate the effect of the 5% contaminative flux we added a flat spectrum of 5% of the total flux. We then re-fit the spectrum and measured −0.08 ± 0.13 (NLTE) and +0.06 ± 0.14 (LTE). The change in measured metallicity is minimal (with a systematic offset of at most +0.05 dex) and in the proper direction−contaminant flux will weaken the deepest lines more strongly and thus a drop in extracted metallicity is to be expected. However, the two results agree statistically and offer strong evidence that spectroscopy of unresolved young SSCs can become a powerful application of the J-band technique. We find in this case that an unresolved cluster of proper age can be successfully fit with a single RSG template model, a technique which has been used at very high resolution in the H band (Larsen et al. 2006).

We scale the resolution of our synthetic cluster spectrum down to R = 2000. The results of this work echo that of the individual stars, showing stability in fit parameters down to resolutions around 3000. The NLTE and LTE cases of this test are plotted in Figure 12.

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