LOW-RESOLUTION NEAR-INFRARED STELLAR SPECTRA OBSERVED BY THE COSMIC INFRARED BACKGROUND EXPERIMENT (CIBER)

We measure the relative pixel response (flat field) in the laboratory before each flight (Arai et al. 2015). The second- and third-flight data are normally corrected with these laboratory flats. However, for the fourth flight the laboratory calibrations do not extend to the longest wavelengths ($\lambda \geqslant 1.4\,\mu {\rm{m}}$) because the slit mask shifted its position with respect to the detector during the flight. We therefore use the second-flight flat field to correct the relative response for the fourth-flight data, as this measurement covers $\lambda \gt 1.6\,\mu {\rm{m}}$. To apply this flat field, we need to assume that the intrinsic relative pixel response does not vary significantly over the flights. To check the validity of this assumption, we subtract the second flat image to the fourth flat image for overlapped pixels and calculate the pixel response difference. We find that only 0.3% of pixels with response measured in both are different by 2σ, where σ is the standard deviation of the pixel response. Finally, we mask 0.06% of the array detectors to remove those pixels with known responsivity pathologies and those prone to transient electronic events (Lee et al. 2010).

For each flight, the absolute brightness and wavelength irradiance calibrations have been measured in the laboratory in collaboration with the National Institute of Standards and Technology. The details of these calibrations can be found in Tsumura et al. (2013). The total photometric uncertainty of the LRS brightness calibration is estimated to be ±3% (Tsumura et al. 2013; Arai et al. 2015).

The raw image contains not only spectrally dispersed images of stars but also the combined emission from zodiacal light $\lambda {I}_{\lambda }^{\mathrm{ZL}}$, diffuse galactic light $\lambda {I}_{\lambda }^{\mathrm{DGL}}$, the extragalactic background $\lambda {I}_{\lambda }^{\mathrm{EBL}}$, and instrumental effects $\lambda {I}_{\lambda }^{\mathrm{inst}}$ (Leinert et al. 1998). The measured signal $\lambda {I}_{\lambda }^{\mathrm{meas}}$ can be expressed as

$$\begin{eqnarray}&&\lambda {I}_{\lambda }^{\mathrm{meas}}=\lambda {I}_{\lambda }^{* }+\lambda {I}_{\lambda }^{\mathrm{ZL}}+\lambda {I}_{\lambda }^{\mathrm{ISL}}+\lambda {I}_{\lambda }^{\mathrm{DGL}}+\lambda {I}_{\lambda }^{\mathrm{EBL}}+\lambda {I}_{\lambda }^{\mathrm{inst}},\end{eqnarray} \tag{ 1 }$$

where we have decomposed the intensity from stars into a resolved component $\lambda {I}_{\lambda }^{* }$ and an unresolved component arising from the integrated light of stars below the sensitivity of the LRS $\lambda {I}_{\lambda }^{\mathrm{ISL}}$. It is important to subtract the sum of all components except $\lambda {I}_{\lambda }^{* }$ from the measured brightness to isolate the emission from detected stars. At this point in the processing, we have corrected for multiplicative terms affecting $\lambda {I}_{\lambda }^{\mathrm{meas}}$. Dark current, which is the detector photocurrent measured in the absence of incident flux, is an additional contribution to $\lambda {I}_{\lambda }^{\mathrm{inst}}$. The stability of the dark current in the LRS has been shown to be 0.7 nW m⁻² sr⁻¹ over each flight, which is a negligible variation from the typical dark current (i.e., 20 nW m⁻² sr⁻¹; Arai et al. 2015). As a result, we subtract the dark current as part of the background estimate formed below.

The relative brightnesses of the remaining background components are wavelength-dependent, so an estimate for their mean must be computed along constant-wavelength regions, corresponding to the vertical columns in Figure 1. Furthermore, because of the LRS's large spatial PSF, star images can extend over several pixels in the imaging direction and even overlap one another. This complicates background estimation in pixels containing star images and reduces the number of pixels available to estimate the emission from the background components.

To estimate the background in those pixels containing star images, we compute the average value of pixels with no star images along each column, as summarized in Figure 2. We remove bright pixels that may contain star images, as described in Arai et al. (2015). The spectral smile effect shown in Figure 1 introduces spectral curvature along a column. We estimate it causes an error of magnitude $\delta \lambda /\lambda \lt {10}^{-2}$, which is small compared to the spectral width of a pixel. Approximately half of the rows remain after this clipping process; the fraction ranges from 45% to 62% depending on the stellar density in each field. This procedure removes all stars with $J\gt 13$ and has a decreasing completeness above this magnitude (Arai et al. 2015).

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To generate an interpolated background map, each candidate star pixel is replaced by the average of nearby pixels calculated along the imaging direction from the ±10 pixels on either side of the star image. We again do not explicitly account for the spectral smile. This interpolated background image is subtracted from the measured image, resulting in an image containing only bright stellar emission. The emission from faint stars and bright stars that inefficiently illuminate a grating slit that contributes to ${I}_{\lambda }^{\mathrm{ISL}}$ is naturally removed in this process.

The bright lines dispersed in the spectral direction in the background-subtracted images are candidate star spectra. To calculate the spectrum of candidate sources, we simply isolate individual lines of emission and map the pixel values onto the wavelength using the ground calibration. However, this procedure is complicated both by the extended spatial PSF of the LRS and by source confusion.

To account for the size of the LRS spatial PSF (FWHM ∼1.2 pixels) as well as optical distortion from the prism that spreads the star images slightly into the imaging direction, we sum five rows of pixels in the imaging direction for each candidate star. Since the background emission has already been accounted for, this sum converges to the total flux as the number of summed rows is increased. By summing five rows, we capture $\gt 99.9$% of a candidate star's flux. The wavelengths of the spectral bins are calculated from the corresponding wavelength calibration map in the same way.

From these spectra, we can compute synthetic magnitudes in the J- and H-bands, which facilitate comparison to Two-Micron All-Sky Survey (2MASS) measurements. We first convert surface brightness in nW m⁻² sr⁻¹ to flux in nW m⁻² Hz⁻¹ and then integrate the monochromatic intensity over the 2MASS band, applying the filter transmissivity of the J- and H-bands (Cohen et al. 2003). To determine the appropriate zero magnitude, we integrate the J- and H-band intensity of Vega's spectrum (Bohlin & Gilliland 2004) with the same filter response. The J- and H-band magnitudes of each source are then calculated, allowing both flux and color comparisons between our data and the 2MASS catalog.

Candidate star spectra may be comprised of the blended emission from two or more stars, and these must be rejected from the catalog. Such blends fall into one of two categories: (i) stars that are visually separate but are close enough to share flux in a 5 pixel-wide photometric aperture or (ii) stars that are close enough that their images overlap so as to be indistinguishable. We isolate instances of case (i) by comparing the fluxes calculated by summing both three and five rows along the imaging direction for each source. If the magnitude or J − H color difference between the two apertures is larger than the statistical uncertainty (described in Section 3.6), we remove those spectra from the catalog. To find instances of case (ii), we use the 2MASS star catalog registered to our images using the procedure described in Section 3.5. Candidate sources that do not meet the criteria presented below are rejected.

To ensure the catalog spectra are for isolated stars rather than for indistinguishable blends, we impose the following requirements on candidate star spectra: (i) each candidate must have $J\lt 11;$ (ii) the J-band magnitude difference between the LRS candidate and the matched 2MASS counterpart must be $\lt 1.5;$ (iii) the J − H color difference between the LRS candidate star and the matched 2MASS counterpart must be $\lt 0.3;$ and (iv) among the candidate 2MASS counterparts within the 500'' ($=6$ pixel) radius of a given LRS star, the second-brightest 2MASS star must be fainter than the brightest one by more than 2 mag at the J band. Criterion (i) excludes faint stars that may be strongly affected by residual backgrounds, slit mask apodization, or source confusion. The second and third criteria mitigate mismatching by placing requirements on the magnitude and color of each star. In particular, the J − H color of a source does not depend on the slit apodization or the position in image space (see Figure 3), so any significant change in J − H color as the photometric aperture is varied suggests that more than a single star could be contributing to the measured brightness. Finally, it is possible that two stars with similar J − H colors lie close to each other, so the last criterion is applied to remove stars for which equal-brightness blending is an issue. Approximately one in three candidate stars fails criterion (iv). The number of candidate stars rejected at each criterion is described in Table 2.

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In addition, three LRS candidate stars are identified as variables in the SIMBAD database.¹² We also identify two stars as binary and multiple-star systems as well as four high proper motion stars. Through these stringent selection requirements, we conservatively include only the spectra of bright, isolated stars in our catalog. Finally, 105 star spectra survive all the cuts, and the corresponding stars are selected as catalog members.

We match the synthesized LRS J, H, and J − H information with the 2MASS point source catalog (Skrutskie et al. 2006) to compute an astrometric solution for the LRS pointing in each sky image. This is performed in a stepwise fashion by using initial estimates for the LRS's pointing to solve for image registration on a fine scale.

As a rough guess at the LRS pointing, we use information provided by the rocket's attitude control system (ACS), which controls the pointing of the telescopes (Zemcov et al. 2013). This provides an estimated pointing solution that is accurate within 15' of the requested coordinates. However, since the ACS and the LRS are not explicitly aligned to each other, finer astrometric registration is required to capture the pointing of the LRS to single-pixel accuracy.

To build a finer astrometric solution, we simulate images of each field in the 2MASS J-band using the positional information from the ACS, spatially convolved to the LRS PSF size. Next, we apodize these simulated 2MASS images with the LRS slit mask, compute the slit-masked magnitudes of three reference stars, and calculate the ${\chi }^{2}$ statistic using

$$\begin{eqnarray}&&{\chi }_{p,q}^{2}=\displaystyle \sum _{i}{}^{}{\left(\displaystyle \frac{{F}_{\mathrm{LRS},i}-{F}_{2\mathrm{MASS},i}}{{\sigma }_{\mathrm{LRS},i}}\right)}^{2},\end{eqnarray} \tag{ 2 }$$

where index i represents each reference star and subscripts p and q index the horizontal and vertical positions of the slit mask, respectively. ${F}_{\mathrm{LRS},i}$ and ${F}_{2\mathrm{MASS},i}$ are the fluxes in the LRS and 2MASS J-band, and ${\sigma }_{\mathrm{LRS},i}$ is the statistical error of the LRS star (see Section 3.6). The minimum ${\chi }^{2}$ gives the most likely astrometric position of the slit mask. Since, on average, there are around five bright stars with $J\lt 9$ per field, spurious solutions are exceedingly unlikely, and all fields give a unique solution.

Using this astrometric solution, we can assign coordinates to the rest of the detected LRS stars. We estimate that the overall astrometric error is 120'' by computing the mean distance between the LRS and 2MASS coordinates of all matched stars. The error corresponds to 1.5 times the pixel scale. We check the validity of the astrometric solutions by comparing the colors and fluxes between the LRS and matched 2MASS stars. In Figures 3 and 4, we show the comparison of the J − H colors and fluxes of the cross-matched stars in each field. Here, we multiply the LRS fluxes at the J- and H-band by 2.22 and 2.17, respectively, to correct for the slit apodization. The derivation of correction factors is described in Section 5. On the whole, they match well within the error range.

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Even following careful selection, the star spectra are subject to various kinds of uncertainties and errors, including statistical uncertainties, errors in the relative pixel response, absolute calibration errors, wavelength calibration errors, and background subtraction errors.

Statistical uncertainties in the spectra can be estimated directly from the flight data. We calculate the $1\sigma$ slope error from the line fit (see Section 2) as we generate the flight images; this error constitutes the estimate for the statistical photometric uncertainty for each pixel. In this statistical error, we include contributions from statistical error in the background estimate and the relative pixel response. The error in the background signal estimate is formed by computing the standard deviation of the ±10 pixels along the constant-λ direction for each pixel to match the background estimate region. This procedure captures the local structure in the background image, which is a reasonable measure of the variation we might expect over a photometric aperture. Neighboring pixels in the wavelength direction have extremely covariant error estimates in this formulation, which are acceptable since the flux measurements are also covariant in this direction. A statistical error from the relative pixel response correction is applied by multiplying 3% of the relative response by the measured flux in each field (Arai et al. 2015). To compute the total statistical error, each constituent error is summed in quadrature for each pixel.

Several instrumental systematic errors are present in these measurements, including those from wavelength calibration, absolute calibration, and relative response correction. In this work, we do not explicitly account for errors in the wavelength calibration, as the variation is ±1 nm over 10 constant-wavelength pixels, which is $\lt 0.1\,R$. In all flights, <3% absolute calibration error is applied (Arai et al. 2015). For the longest-wavelength regions (λ > 1.6 $\mu {\rm{m}}$) of the fourth-flight data that are not measured even in the second-flight flat, we could not perform flat correction. Instead, we apply a systematic error amounting to 5.3% of the measured sky brightness. The error is estimated from pixels in the short-wavelength regions (λ < 1.4 $\mu {\rm{m}}$) of the fourth-flight flat. We calculate deviations from unity for those pixels and take a mean of 5.3%. The linear sum of systematic errors is then combined with statistical error in quadrature.

The star spectral types are determined by fitting known spectral templates to the measured LRS spectra. We use the Infrared Telescope Facility (IRTF) and Pickles (1998) templates for the SED fitting. The SpeX instrument installed on the IRTF observed stars using a medium-resolution spectrograph (R = 2000). The template library contains spectra for 210 cool stars (F to M type) with wavelength coverage from 0.8 to 2.5 μm (Cushing 2005; Rayner 2009). The Pickles library is a synthetic spectral library that combines spectral data from various observations to achieve wavelength coverage from the UV (0.115 μm) to the near-IR (2.5 μm). It contains 131 spectral templates for all star types (i.e., O to M type) with a uniform sampling interval of 5 Å.

To perform the SED fit, we degrade the template spectra to the LRS spectral resolution using a mean box-car smoothing kernel corresponding to the slit function of the LRS. Both the measured and template spectra are normalized to the J-band flux. We calculate the flux differences between the LRS and template spectra using

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{\lambda }{}^{}{\left(\displaystyle \frac{{F}_{\mathrm{LRS},\lambda }-{F}_{\mathrm{ref},\lambda }}{{\sigma }_{\mathrm{LRS},\lambda }}\right)}^{2},\end{eqnarray} \tag{ 3 }$$

where ${F}_{\mathrm{LRS},\lambda }$ and ${F}_{\mathrm{ref},\lambda }$ are the fluxes of the observed and template spectra at wavelength λ normalized at the Jband and ${\sigma }_{\mathrm{LRS},\lambda }$ is the statistical error of the observed spectrum. The best-fitting spectral type is determined by finding the minimum ${\chi }^{2}$.

No early-type (i.e., O, B, A) stars are found in our sample; all stars have characteristics consistent with those of late-type stars (F and later). Because the IRTF library has about twice the spectral type resolution of the Pickles library, we provide the spectral type determined from the IRTF template in Table 3. Since the IRTF library does not include a continuous set of spectral templates, we observe discrepancies between the LRS and best-fit IRTF templates, even though the J − H colors are consistent between 2MASS and the LRS within the uncertainties. The Pickles and IRTF fits are consistent within the uncertainty in the classification (∼0.42 spectral subtypes).

A color–color diagram for the star sample is shown in Figure 6. Although the color–color diagram does not allow us to clearly discriminate between spectral types, qualitatively earlier-type stars are located in the bluer region, while later-type stars are located in the redder region, consistent with expectations. LRS stars well follow the color–color distributions of typical 2MASS stars in LRS fields, as indicated by the gray dots.

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To estimate the error in our spectral type determination, we compare our identifications with the SIMBAD database (Wenger et al. 2000), where 63 of the 105 stars have prior spectral type determinations. Figure 7 shows the spectral types determined from the IRTF fit versus those from the SIMBAD database. The 1σ error of type difference is estimated to be 0.59 spectral subtypes, which is comparable with those in other published works (Gliese 1971; Jaschek & Jaschek 1973; Jaschek 1978; Roeser & Bastian 1988; Houk & Swift 1999). The error can be explained by two factors: (i) the low spectral resolution of the LRS and (ii) the SED template libraries, which do not represent all star types.

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Five stars are observed twice in different flights (BA2_5 and BB4_6, N2_6 and N3_5, BA2_1 and BA3_4, BB2_1 and BB3_1, and BB2_4 and BB3_4; see Figure 8), enabling us to investigate the interflight stability of the spectra. For BA2_5 and BB4_6, the spectral type is known to be F8, while our procedure yields F7V and F1II from the second- and fourth-flight data, respectively. For N2_6 and N3_5, the known type is K5, while we determine M0.5V for both flights. For BA2_1 and BA3_4, the known type is F5, while we determine F7III and F2III–IV in the second and third flights. For BB2_1 and BB3_1, the fitted types are G8IIIFe5 and K4V for a K1-type star, and the types of BB2_4 and BB3_4 are not known but are fitted to F9V for both flights. The determined spectra are consistent within an acceptable error window, though the longer-wavelength data exhibit large differences, which can be attributed to calibration error. We present the spectra of each star from both flights in Table 3. This duplication results in our reporting of 110 spectra in the catalog, even through only 105 individual stars are observed.

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