The First Radio Spectrum of a Rapidly Rotating A-type Star

A given stellar emission mechanism will have a characteristic spectral index, α, related to the observed flux by F_λ ∝ λ^α . Therefore, a spectral index can be a powerful diagnostic tool for disentangling emission mechanisms and can provide information about the structure of a star's atmosphere. Thermal emission from an optically thick source will have a spectral index of α = −2. Given a lack of observational data at long wavelengths, this values of α is commonly assumed to be the representative for A-type stars in the Rayleigh–Jeans limit and is used to, e.g., estimate the stellar flux contribution in circumstellar disk studies (see Section 3.3). Since Altair's spectrum is clearly not well represented by a blackbody model, then there are likely additional emission/absorption mechanisms contributing to its spectrum.

In Figure 2, we show Altair's spectrum along with spectral indices fit to subsets of the data using a least squares approach with the SciPy function curve_fit (Virtanen et al. 2020). For λ < 1.98 mm, we calculate a spectral index of α_submm = −2.10 ± 0.04. Within the 1σ uncertainties, this is consistent with a deviation from the thermal photospheric emission in the Rayleigh–Jeans regime. A similar cooler spectrum with a slightly steeper spectral index was observed in Sirius A and is well-reproduced by a PHOENIX atmosphere model (black line in Figure 1; White et al. 2018a, 2019). We do not include the 1.3 mm data in the spectral index calculations as the drop in T_B to 1000–2000 K is not reconcilable with any known physical mechanism (see Section 3.2).

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For wavelengths in the range of 1.98 mm < λ < 10 mm, the spectral index has a value of α_mm = −1.59 ± 0.10. In this portion of the spectrum, the spectral index is in broad agreement with solar-like stars (e.g., Villadsen et al. 2014; Liseau et al. 2016), where chromospheric emission begins to contribute significantly to the observed flux. Considering only the VLA data, we find α_cm = −1.21 ± 0.17, continuing the trend toward higher brightness temperatures and a possible contribution from chromospheric emission. Due to the lack of data at wavelengths longer than 1 cm we are unable to determine if the centimeter spectral index is also solar-like.

To model Altair's spectrum, we consider both PHOENIX (Hauschildt & Baron 1999) and KP atmospheres (Tapia-Vázquez & De la Luz 2020). The PHOENIX model includes only the stellar photosphere whereas the KP model includes chromospheric emission from above the photosphere. The MESAS Project previously used PHOENIX to model Sirius A (White et al. 2018a, 2019) and KP to model γ Lep, γ Vir A, and γ Vir B (White et al. 2020).

The PHOENIX approach (version 17.01.02A) includes a gravity-darkened model for Altair's photosphere. We adopted Altair's "β-fixed" parameters (Monnier et al. 2007) and a 019495 parallax (van Leeuwen 2007). We used the modeling code from Aufdenberg et al. (2006), which was previously used to model the photosphere of the rapid-rotator Vega (a similar approach is also used in Lipatov & Brandt 2020). We used 1D PHOENIX model atmospheres to generate 117 LTE radiation fields evaluated at 78 different angles, T_eff values from 6750 to 8750 K in 250 K intervals, and ${\mathrm{log}}_{10}(g)$ values from 3.90 to 4.40 in 0.05 intervals. The temperature–pressure structure of each model atmosphere in radiative equilibrium was computed assuming a hydrostatic atmosphere, including between 1719584 and 1842901 spectral lines in LTE, depending on T_eff and ${\mathrm{log}}_{10}(g)$ values, and 576 bound–bound and bound–free transitions from hydrogen and helium in non-LTE. We then sampled the oblate surface with 100 latitude points and 300 longitude points, integrating the intensities to produce a synthetic photosphere spectrum (see Figure 1).

KP is a nonlinear framework that computes a stellar atmosphere spectrum through a 1D NLTE semiempirical model of the chromosphere at long wavelengths. KP uses PakalMPI (De la Luz et al. 2011) to generate an atmosphere structure in hydrostatic equilibrium and to compute a synthetic spectrum taking into account three opacity functions (Bremsstrahlung, H⁻, and inverse Bremsstrahlung). A Levenberg–Marquardt algorithm is used to iteratively modify the T_R profile, fitting the synthetic spectrum to the observed radio fluxes. KP computed 11848 atmospheres to obtain a new semiempirical model of the Altair. The last radial T_R profile is then smoothed using a Savitzky–Golay filter with a seventh-order polynomial. This model is equilibrated again with PakalMPI to guarantee the hydrostatic equilibrium. The final model structure is shown in Figures 3(a)–(b).

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We determine that the KP model better reproduces the data and include the final semiempirical model in Figure 3. This model shows that for wavelengths <1 mm the emission comes from the photosphere and for >3 mm the emission originates in the chromosphere. This is due to an optically thick atmosphere at altitudes where T_R is below 10,000 K and is not fully ionized. At 2083 km above the photosphere, we find a T_R minimum of 4207 K (${T}_{R,\min }$/T_eff ≈ 0.55) and a hydrogen density of n_H = 1.5 × 10¹¹ cm⁻³. Overall, T_R gradually decreases until reaching a minimum, typical of photospheric behavior. Starting at a height of 2083 km, we observe a positive temperature gradient that extends for ∼100 km. T_R then plateaus at 10,000 K and extends ∼200 km further. At this point, T_R gradually rises, similar to the chromospheric behavior in models obtained by Gouttebroze et al. (1999) and Ferrero et al. (1995). In Figure 3(c) we plot the contribution function (CF; Tapia-Vázquez & De la Luz 2020) to constrain where the emission is generated.

Previous modeling approaches primarily considered Altair's UV spectrum to compute the structure of the upper photosphere and chromosphere. Anomalies in the C ii line were speculated to be from ISM absorption (Gouttebroze et al. 1999). Our model could not produce the observed 1.3 mm T_B minimum and therefore we did not include these data in the final KP or PHOENIX results. If there is significant foreground absorption, it is not clear if this feature is observable at 1.3 mm. Absorption from interstellar grains would yield a broad feature with a spectral index reflective of the grain's size distribution (e.g., Jones et al. 1996). At 1.3 mm, Altair's emission would be predominately absorbed by ∼millimeter-sized grains, and ISM grains are typically a few micrometers in size (e.g., Weingartner & Draine 2001). If the absorption is from a molecular line, e.g., CO(2–1) with a rest frequency of 230.53 GHz (1.3 mm), then the approximately flat spectral index between the NOEMA sidebands of 1.29 and 1.38 mm implies a line width ≥0.1 mm and a velocity of ∼ 10⁴ km s⁻¹, which is unphysical for the ISM. We determine that the 1.3 mm data are likely not contaminated by foreground material.

The observed 1.3 mm flux density is broadly consistent between the two NOEMA semesters. After consultation with NOEMA support scientists we conclude that significant instrument or calibration uncertainties are unlikely. While there is no known physical mechanism that could reproduce the 1.3 mm flux, we cannot rule out an anomalous absorption or opacity in Altair's atmosphere without more data. Future observations at 0.25–1.3 mm, and follow-up observations at 1.3 mm with another facility such as ALMA, are therefore imperative to accurately determine the cause of the observed drop in flux.

The radio spectra obtained with The MESAS Project are useful outside the context of stellar atmospheric processes. Historically, the presence of debris disks are inferred by excess over the expected stellar emission at a given wavelength when the disks cannot be spatially resolved (Aumann et al. 1984). The first star observed in the campaign was Sirius A, a star with no known circumstellar debris (White et al. 2018a). Radio observations of Sirius A were used to inform a PHOENIX model atmosphere. This spectrum was applied to the millimeter emission of Fomalhaut, an A3V star very similar to Sirius A but with an extended debris disk (e.g., Kalas et al. 2005; Acke et al. 2012; White et al. 2017). In addition to Fomalhaut's well-resolved debris ring, there is an inferred inner asteroid belt that has not been resolved (Acke et al. 2012). Such an asteroid belt would be collisionally evolving to produce millimeter-sized debris that may be detectable at millimeter wavelengths. Instead, Fomalhaut's millimeter emission has a spectrum nearly identical to that of Sirius A (Su et al. 2016; White et al. 2017), which has no known debris. This result casts doubt on the presence of an additional debris component in the Fomalhaut system (White 2018) and highlights the importance of an accurate radio stellar spectrum to determine the presence and characteristic of unresolved circumstellar debris.

As is clear from Altair's observed radio spectrum, determining the stellar flux at a given wavelength based solely on the flux at a different wavelength is nontrivial. In order to fully characterize the radio spectrum of Altair, observations between 0.25 and 1.29 mm are imperative. The only facility that can fill in the gap on Altair's missing data is ALMA. Follow-up observations at all wavelengths with multiple cadences will assess the long-term variability or stability of Altair's radio emission.

The MESAS Project is currently pushing state-of-the-art radio observatories to their limits. Proposed future facilities, such as the next generation Very Large Array (ngVLA), will be invaluable for revealing stellar atmosphere structures. For example, the ngVLA will yield a 93 GHz (3.22 mm) continuum σ_rms = 0.40–1.0 μJy beam⁻¹ in 1 hr ¹⁵ In addition, a majority of the proposed ngVLA antennas will have a maximum baseline of 1000 km, giving a resolution of 0.66 mas. The ngVLA will resolve Altair by 5–6 beam widths in only a few minutes of integration time. This level of detail is absolutely imperative to determine how the high rotational velocity, and resulting dynamo, can impact the overall T_B structure of the star. The ngVLA's unprecedented sensitivity means all G-type and brighter stars are detectable within ∼75 pc, allowing for a comprehensive survey of our solar neighborhood (see, e.g., Carilli et al. 2018; White et al. 2018b).

Altair was observed with NOEMA in 2018 April 28, 12, and May 17 (ID W17BF, PI White), and in 2019 February, 7, 8, and 15 (ID W18BQ, PI White). The observations were centered on Altair using J2000 coordinates R.A. = 19^h50^m46996 and $\delta =+08^\circ 52^{\prime} 05\buildrel{\prime\prime}\over{.} 956$ and accounting for proper motion. The observations in 2018 used nine antennas in the C and D configurations with baselines ranging from 24–293 m and 24–176 m, respectively. The observations in 2019 used 10 antennas in the A configuration with baselines ranging from 32 to 760 m.

The observations used the Band 1, Band 2, and Band 3 instruments with the PolyFiX correlator and 4064 × 2 MHz channels in each band. In Band 1, the rest frequency of each baseband was tuned to 214.208, 218.269, 229.693, and 233.754 GHz. In Band 2, they were tuned to 134.215, 138.276, 149.700, and 153.761 GHz. In Band 3, they were tuned to 84.219, 88.280, 99.704, and 103.766 GHz. An identical instrument setup was used in 2018 and 2019. The data calibration pipeline and imaging utilized the GILDAS software packages and was done with the assistance of NOEMA contact scientists at IRAM. In 2018, quasars J2002+150 and 1932+204 were used for phase and amplitude calibration and MWC349 was used to calibrate the absolute flux. The Band 1 and Band 2 observations used 3C 345 for bandpass calibration and 3C 454.3 was used for Band 3. In 2019, all bands used quasars J2002+150 and J1938+048 for phase and amplitude calibrations and MWC349 for absolute flux calibration. Quasars 1633+382, 1749+096, and 3C 345 were used as bandpass calibrators in Band 1, Band 2, and Band 3, respectively.

In each of the three receivers, the two upper sidebands were combined and the two lower sidebands were combined to increase the signal-to-noise. This gives effective wavelengths of 1.29, 1.38, 1.98, 2.20, 2.96, and 3.48 mm for each data point. To derive the flux at each wavelength, we used the GILDAS MAPPING package and the UVFIT task to fit a point-source model directly to the visibilities (see Table 1 for a list of fluxes). We used the UVMAP task to make dirty image maps and then Hogbom cleaning to a threshold of one-half the rms noise. The σ_rms of the images is adopted as the representative uncertainty for each data point. The absolute flux calibration uncertainty for NOEMA is ∼20% at 1 mm and less than 10% at 3 mm. ¹⁶

In 2018, from shortest to longest wavelength, the observations achieve sensitivities and synthesized beams of 107 μJy beam⁻¹ and 268 × 160 at a position angle (PA) of 105; 83.9 μJy beam⁻¹ and 285 × 168 at a PA of 59; 45.0 μJy beam⁻¹ and 344 × 211 at a PA of 69; 32.8 μJy beam⁻¹ and 382 × 227 at a PA of 75; 25.1 μJy beam⁻¹ and 278 × 164 at a PA of 315; and 29.8 μJy beam⁻¹ and 318 × 185 at a PA of 400, respectively.

In 2019, the observations achieve sensitivities and synthesized beams of 75.1 μJy beam⁻¹ and 076 × 037 at a PA of 284; 66.0 μJy beam⁻¹ and 079 × 039 at a PA of 289; 45.6 μJy beam⁻¹ and 114 × 053 at a PA of 172; 36.7 μJy beam⁻¹ and 118 × 058 at a PA of 187; 30.8 μJy beam⁻¹ and 164 × 075 at a PA of 172; and 27.7 μJy beam⁻¹ and 184 × 086 at a PA of 180, respectively.

The data from the VLA were acquired during three Scheduling Blocks (SBs) on 2019 March 15, 19, and 24 (ID 19A-141, PI White). The observations were centered on Altair using J2000 coordinates R.A. = 19^h50^m46996 and $\delta =+08^\circ 52^{\prime} 05\buildrel{\prime\prime}\over{.} 956$ and accounted for proper motion. The data used 27 antennas in the B configuration with baselines ranging from 0.21 to 11.1 km.

Each SB used an identical instrument configuration and observing strategy. The 33 GHz data utilized the Ka-band tuning setup with 4 × 2.048 GHz basebands and rest frequency centers of 28.976, 31.024, 34.976, and 37.024 GHz, yielding an effective frequency of 33 GHz (9.1 mm). The 45 GHz data utilized the Q-band tuning setup with 4 × 2.048 GHz basebands and rest frequency centers of 41.024, 43.072, 46.968, and 48.976 GHz, yielding an effective frequency of 45 GHz (6.7 mm).

The SBs were reduced using the CASA 5.4.0 pipeline (McMullin et al. 2007), which included bandpass, flux, and phase calibrations. For all SBs, quasar J1950+0807 was used for phase and bandpass calibrations. Quasar 0137+331 = 3C 48 was used as a flux calibration source for all SBs. 3C 48 was originally intended to also be used as a bandpass calibrator, but the ongoing flare and a low signal-to-noise in each SPW made it unreliable. Upon consultation with the VLA HelpDesk, we modified the scan intents of the raw data to identify J1950+0807 as the bandpass calibrator and proceeded with a standard pipeline calibration. The ongoing flare of the calibrator increased absolute flux uncertainty to ∼20% in the Q band and ∼15% in the Ka band. ¹⁷

The three SBs were concatenated using the CASA task concat. To derive the flux at each wavelength, we used the CASA task uvmodelfit to fit a point-source model at each frequency. The concatenated data were imaged with a natural weighting and cleaned using CASA's CLEAN algorithm down to a threshold of one-half the rms noise. The observations achieve a sensitivity of 21.9 μJy beam⁻¹ and 5.9 μJy beam⁻¹ for the 6.7 mm and 9.0 mm data, respectively. The size of the resulting synthesized beam is 022 × 017 at a position angle of − 324 and 025 × 021 at a position angle of − 216, respectively.

In addition to the new data presented here, we also include Herschel and VLA Sky Survey (VLASS) data from the literature in our analysis. Altair was observed with the Herschel PACS instrument at 0.10 mm and 0.16 mm on 2010 May 9. We use the two IR photometry data points of Altair presented in Thureau et al. (2014) as part of the DEBRIS survey (we note that the authors report no excess flux that could be attributed to circumstellar material). The observed flux was 329.02 ± 18.88 mJy and 148.26 ± 9.94 mJy at 0.10 mm and 0.16 mm, respectively. We also use Herschel SPIRE data from the Herschel Point Source Catalog (Schulz et al. 2017). Altair was observed with SPIRE on 2011 November 16. The observed flux was 55.7 ± 8.3 mJy at 0.25 mm.

VLASS is an all-sky survey with uniform sensitivity at 3 GHz (100 mm) covering three separate epochs. At the time of writing, only one epoch had been completed. We downloaded a 1' section of the sky centered on the J2000 coordinates of Altair from The Canadian Initiative for Radio Astronomy Data Analysis (CIRADA) server. ¹⁸ The observations were made on 2017 October 25 and have a synthesized beam size of 268 × 232 and a position angle of 255. Altair was not detected, but we use the σ_rms = 120 μJy beam⁻¹ from the surrounding area as an upper level limit on the 3 GHz flux.