The MESAS Project: ALMA observations of the F-type stars $\gamma$ Lep, $\gamma$ Vir A, and $\gamma$ Vir B

The Band 7 observations were made on 2018 September 22 for 36.1 min (18.5 min on-source) and the Band 6 observations on 2018 September 28 for 65.3 min (42.0 min on-source). Both of the Execution Blocks (EB) used a 43 antenna configuration with baselines ranging from $15-1397$ m. The two EBs also used an identical calibration setup. Quasar J0522-3627 was the flux and bandpass calibrator; quasar J0609-1542 was the phase calibrator; quasars J0544-2241, J0609-1542, and J0522-3627 were used to calibrate the WVR. The average precipitable water vapor (PWV) was 0.24 mm for Band 7 and 0.97 mm for Band 6.

Both of the bands were imaged using the CASA CLEAN algorithm using threshold of $\frac{1}{2}~{}\sigma_{rms}$ and natural weighting. The Band 7 data achieve a $\sigma_{rms}$ sensitivity of $30~{}\rm\mu Jy~{}beam^{-1}$ and the Band 6 data achieve a sensitivity of $10~{}\rm\mu Jy~{}beam^{-1}$ in the CLEANed images. The sizes of the resulting synthesized beams are $0\farcs 25\times 0\farcs 20$ at a position angle (PA) of $83.1^{\circ}$ for Band 7 and $0\farcs 36\times 0\farcs 30$ at a PA of $81.4^{\circ}$ for Band 6. These correspond to $\sim 2$ au and $\sim 3$ au at the system distance of 8.9 pc for Bands 7 and 6, respectively.

The Band 7 observations were made on 2018 December 20 for 49.2 min (29.4 min on-source) and 2019 March 20 for 49.7 min (29.4 min on-source). The December EB used a 43 antenna configuration with baselines ranging from $15-500$ m and the March EB used a 43 antenna configuration with baselines ranging $15-313$ m. Quasar J1256-0547 was the flux and bandpass calibrator. Quasar J1229+0203 was the phase calibrator in December and quasar J1218-0119 was used in March. Quasars J1229+0203, J1256-0547, and J1222+0413 were used to calibrate the WVR in December, and J1218-0119, J1220+0203, and J1256-0547 were used in March. The average precipitable water vapor (PWV) was 0.70 mm in December and 0.40 mm in March.

The EBs were imaged using the CASA CLEAN algorithm using threshold of $\frac{1}{2}~{}\sigma_{rms}$ and natural weighting. Together, these Band 7 data achieve a $\sigma_{rms}$ sensitivity of $15~{}\rm\mu Jy~{}beam^{-1}$ in the CLEANed image. The size of the resulting synthesized beam is $0\farcs 79\times 0\farcs 69$ at a position angle of $81.2^{\circ}$, corresponding to $\sim 8.7$ au at the system distance of 11.7 pc.

The Band 6 observations were made on 2019 March 09 for 52.8 min (34.5 min on-source) and 2019 March 18 for 52.9 min (34.4 min on-source). Both of the EBs used a 43 antenna configuration with baselines ranging from $15-312$ m. The two EBs also used an identical calibration setup. Quasar J1256-0547 was the flux and bandpass calibrator; quasar J1232-0224 was the phase calibrator; quasars J1218-0119, J1256-0547, and J1232-02243 were used to calibrate the WVR. The average precipitable water vapor (PWV) was 1.90 mm on March 09 and 1.82 mm on March 18.

The EBs were imaged using the CASA CLEAN algorithm using threshold of $\frac{1}{2}~{}\sigma_{rms}$ and natural weighting. Together, these Band 6 data achieve a $\sigma_{rms}$ sensitivity of $10~{}\rm\mu Jy~{}beam^{-1}$ in the CLEANed image. The size of the resulting synthesized beam is $1\farcs 43\times 1\farcs 25$ at a position angle of $-65.2^{\circ}$, corresponding to $\sim 16$ au at the system distance.

All of the stars observed are effectively point sources given the achieved synthesized beams. Therefore we utilize the same approach used in White et al. (2018a, 2019) and obtain the flux using the CASA task uvmodelfit and a point source model for all targets. This approach converges on a minimum $\chi^{2}$ through an iterative procedure. The results of the visibility model fitting are summarized in Table 1. The flux uncertainties in Table 1 do not include the absolute flux calibration uncertainties, which we adopt as $\sim 10\%$ (this is the commonly adopted uncertainty at these wavelengths per Sec. A.9.2 in the ALMA Proposer’s Guide). As the same flux calibrator was used for both $\gamma$ Lep EBs, and the same for all $\gamma$ Vir EBs, the absolute flux uncertainty between observations of each system should be relatively minimal.

We also explore the variability of each target, and within each EB, by using the same uvmodelfit procedure applied to each on-source scan. We plot the time series for each star and discuss the results in Sec. 4.2.

There is a third source present in the field of the $\gamma$ Vir system (see NW object in the top panels of Fig. 1). We were unable to identify the object in any catalogues, likely due to its very close proximity to $\gamma$ Vir (current projected separation of $\sim 4\farcs 2$). We detected the object at a signal-to-noise of $\gtrsim 10$ in all EBs, so it is indeed a real source. The location of the peak flux is consistent between the 2018 December 20 EB and the 2018 March 08 EB to $<0\farcs 05$, which implies that the object is likely not located within the foreground of the $\gamma$ Vir system (11.7 pc). The position angle of the object is different from that of the synthesized beam and the two $\gamma$ Vir stars, which implies that the source is at least marginally resolved. Given the galactic latitude of $+61^{\circ}$, it is unlikely that the object is a background circumstellar disk in a star forming region.

To properly characterize the flux of this object, we fit both a point source and Gaussian model to the object with uvmodelfit and find it to be more consistent with a Gaussian. The Band 7 total flux is $430\pm 25~{}\mu\rm Jy$ and the Band 6 total flux is $160\pm 16~{}\mu\rm Jy$. This corresponds to a spectral index $\alpha\approx 2.5$ and a dust emissivity $\beta\approx 0.5$ assuming the object is in the Rayleigh-Jeans regime with $S_{\nu}\propto\nu^{2+\beta}$. These values do not appear to be consistent with the typical $\beta$ values of $1.5$ to $2.0$ (e.g., Casey et al., 2014) for nearby dusty star forming galaxies. The angular size of $\sim 1^{\prime\prime}$ and spectral index, however, can be more common for high redshift galaxies (R. Hill, priv. comm.). González-López et al. (2020) use ALMA Band 6 number counts from the Hubble Ultra Deep Field to estimate the expected number of high redshift galaxies with a flux $>160~{}\mu$Jy to be $\sim 19080~{}\rm deg^{-2}$, meaning the expected number of objects within our ALMA Band 6 field-of-view is about 0.5. Given all the considerations listed above, we conclude that the object is likely a background galaxy with either a high redshift or an anomalous spectral index.

We use this object, along with the assumption that it has a relatively constant flux during each EB, to constrain the potential variability of the two stars in the $\gamma$ Vir system (see Sec. 4.2).

At far-infrared/mm wavelengths, stellar emission in FGK-type stars is dominated by optically thick free-free radiation (Dulk, 1985; Güdel, 2002). The flux is proportional to the plasma temperature (T_R) at a given wavelength and can be used to probe the temperature structure as a function of height above the photosphere. The stellar spectrum can therefore be used to build a model of the thermal structure of the chromosphere. In the Appendix (Figures 4, 5, and 6), we show the semi-empirical models for $\gamma$ Lep, $\gamma$ Vir A, and $\gamma$ Vir B. These models were generated using the KINICH-PAKAL code (Tapia-Vázquez, & De la Luz, 2020). This code iteratively modifies the radial temperature and hydrogen density profiles, the ionization balance, and the opacity of a base model using the Levenberg-Marquardt algorithm to adjust the synthetic spectrum to the ALMA data presented here and the Herschel/PACS data for $\gamma$ Lep (Montesinos et al., 2016). In the atmosphere, the chromosphere has a higher temperature than the photosphere leading to a strong deviation from radiative equilibrium. Therefore, we do not assume that ionization-excitation and radiative transfer are in local thermal equilibrium. For our models, a semi-empirical Solar model (model C7 from Avrett & Loeser, 2008) in hydrostatic equilibrium was adopted as the starting point. This can be taken as an average of the most commonly used Solar models (Vernazza et al., 1981; Fontenla et al., 1993; Loukitcheva et al., 2004). For stars with a higher effective temperature than the Sun, this model serves as an initial condition. In order to constrain the region where the emission is generated in the models obtained from KINICH-PAKAL, we plot the contribution function (CF) (Tapia-Vázquez, & De la Luz, 2020) for each star at each wavelength. For $\gamma$ Lep, the Fig.  4(c) shows that the emission at millimeter wavelengths (1.29 mm and 0.87 mm) is generated at high chromosphere altitudes. At submillimeter wavelengths (0.16 mm and 0.10 mm) the emission is generated in the low chromosphere, close to photosphere. For $\gamma$ Vir A and $\gamma$ Vir B, Figs. 5(c) and 6(c) show that the radiation is generated around 2000 km over the photosphere. The models for these three F-type stars were adjusted to observations made by ALMA and Herschel/PACS, leading the synthethic spectrum to be in agreement with the observed one shown in Fig. 3. The brightness temperature for $\gamma$ Lep follows a Solar-like trend but $\gamma$ Vir A and $\gamma$ Vir B exhibit a large increase, likely due to the lack of constraining observations at longer wavelengths. The temperature structures and stellar spectra are discussed further in Sec. 4.1.

For $\gamma$ Lep, the semi-empirical model is shown in Fig. 4 as the green dashed lines. In the plasma temperature profile, we see a temperature minimum of T_R,min = 4800 K (T_eff/T_R,min = 0.76) at a height of 750 km above the photosphere. At this height, the model shows a hydrogen density of $n_{H}=9\times 10^{14}~{}\rm cm^{-3}$. The high chromosphere has a positive temperature gradient until it reaches 2200 km where the transition zone begins. The purple dashed line in Fig. 5 show the semi-empirical model obtained for $\gamma$ Vir A. The plasma temperature profile presents two temperature drops one around 500 km and another close to 1750 km. In Fig. 5 (c), the CF shows that radiation at 0.87 mm begins to form at 1530 km and 1600 km for 1.29 mm, with its maximum contribution for both around 2080 km. For $\gamma$ Vir B, the semi-empirical model is shown as the blue dashed line in Fig. 6. This model has the same behavior as $\gamma$ Vir A in the plasma temperature profile. In Fig. 6 (c), the CF shows that radiation at 0.87 mm begins to form at 1600 km having its maximum contribution at 1970 km on the photosphere. For 1.29 mm, the greatest contribution is at 2120 km. In both models, the density is higher than the Solar average and the temperature profile shows that before 1500 km the plasma temperature is similar to the effective temperature. For $\gamma$ Vir A and $\gamma$ Vir B, the plasma temperature anomalies below 1000 km and large brightness temperatures at long wavelengths (Fig. 3) are due to the fact that the KINICH-PAKAL framework uses observation data as constraints to model the temperature structure and the lack of data at shorter and longer wavelengths does not allow for restrictions of the plasma temperature profile in the upper and lower layers. Therefore, it is not possible to perform an analysis of the temperature minimum in these two stars. The gray regions in the Fig. 4(a)-(c), Fig. 5(a)-(c), and Fig. 6(a)-(c) show the outer boundaries of the models where the convergence method cannot be applied directly.

The models presented here are a first step towards detailed models of the submm-cm spectra of F-type stars. The location and the depth of the temperature minimum in the chromosphere are influenced by the abundance of CO in the atmosphere (Linsky & Ayres, 1973) and acoustic waves (Schmitz, & Ulmschneider, 1981). A combination of broad spectral coverage and CO spectra (e.g., with ALMA Band 9 and 10) will allow to investigate the formation height of T_R,min and the temperature structure of the chromospheres.

The stellar atmosphere models presented in Sec. 3.3 reproduced the observed flux reasonably well if the observations are combined over the entire time on-source in each EB to increase the signal-to-noise. As is common practice in radio interferometry, the EB observing strategy alternates between the target and a phase calibrator until the total on-source time is achieved. We can therefore further divide up the observations into increments of $6-8$ minutes between individual phase calibrations to assess potential short term variability. For $\gamma$ Lep, we show the time series flux for both Bands 6 and 7 on the left side of Fig. 2. While the curves are indeed not flat, they are roughly consistent with the full integrated flux and there is likely no variability at the level of the flux calibrations over the course of the observations. As these are the first mm wavelength observations of $\gamma$ Lep, we cannot rule out the possibility of variability at time periods longer than the length of the EBs.

For the $\gamma$ Vir system, we have the benefit of observing a binary with two nearly identical stars at multiple dates, as well as a background source (with no presumed variability). The times series is shown on the right side of Fig. 2. For random or uncharacterized observational uncertainties, we would expect both $\gamma$ Vir A and $\gamma$ Vir B to follow a similar trend, as they are both located near the phase center of the observations (i.e., the phase calibration should be better towards the phase center). The background source is included too, as it is unlikely to exhibit any significant variability if it is indeed a high redshift galaxy (we shifted the flux of this source up to match the $\gamma$ Vir stars for ease of presentation). Therefore, we can reasonably assume that the apparent variability in the background source is consistent with observational uncertainty on such short time intervals. We plot the time in minutes but note that it is discontinuous between EBs. Plotting the times series with this approach is the best way to compare all 4 of the EBs which were observed at irregular intervals over a 3 month period. The spacing between data points within a single EB is preserved, allowing for general, short period trends to be identified.

When comparing the 3 objects in the $\gamma$ Vir field, we find that $\gamma$ Vir A and $\gamma$ Vir B at times deviate from the trend of the background source and each other. For example, the Band 7 observations from 2019 March 20 show that the background source and $\gamma$ Vir A have a nearly identical trend while $\gamma$ Vir B has a markedly different trend. In contrast to this, during the second half of the 2018 December 20 observations the background source and $\gamma$ Vir B have a similar trend while $\gamma$ Vir A is the star that appears to deviate. Taken at face value, these time series data suggest that there is potentially variability in one or both of the $\gamma$ Vir stars at the minute to 10s of minutes time scales. We caution though that there could still be some unconstrained systematic uncertainty in each flux value that is driving the observed trends. Future observations are necessary in order to confirm or reject the presence of millimeter variability in the $\gamma$ Vir system.

Short period variability that is difficult to model is not completely unheard of for stars. Balona et al. (1994) found $\gamma$ Doradus to be of a new class of short period pulsating F-type stars. There are some rapid pulsators given the designation of hybrid $\gamma$ Dor and $\delta$ Scuti Pulsators (Grigahcène et al., 2010), however these types of stars are also observed to be rapid rotators, which is not the case for the $\gamma$ Vir system. Patsourakos et al. (2019) observed the Sun at 3 mm with ALMA and a $2\,$s cadence. They detected spatially resolved fluctuations in the T_B at the few hundred K level on timescales of several minutes. The fluctuations lagged behind $1600\,\rm\AA$ observations by $\sim 100$ s and may be due to propagating sound waves in the Solar atmosphere. While observations of stars other than the Sun with this level of time resolution would not be possible due to signal-to-noise constraints, this presents a possible explanation for the variability in $\gamma$ Vir, should it indeed be real.

An unconstrained submm-cm stellar spectrum can lead to an inaccurate interpretation of the presence of debris. This is clearly highlighted if we consider the $\gamma$ Vir system. There are three sources present in $\gamma$ Vir (the two stars and a propsoed background galaxy) that would indeed contribute to uncertainty in the flux from a given component for a lower resolution telescope, but to illustrate this example we will only consider the flux from $\gamma$ Vir B in Band 6.

If we take the highest measured Band 6 flux value of 356 $\mu$Jy, and assume that there is an underlying debris belt, we can use other standard estimates of the stellar emission to find out how much “excess” there is. For example, if we assume a Sirius-like emission profile (e.g., White et al., 2019), characterized by $\sim 0.6\,\rm T_{B}$, or a simple full blackbody extrapolation of T_B of from the optical photosphere temperature (i.e., $100\%$ $T_{B}$), we would get an excess of 180 $\mu$Jy and 65 $\mu$Jy, respectively. If we assume this emission comes from an asteroid belt-type structure, then we can get rough estimate of the total amount of debris. This asteroid belt would be unresolved (i.e., located within the synthesized beam) so we can say it is at a radii of $<9$ au. Adopting the methods in White et al. (2017), a lower level total debris mass can be calculated by assuming the excess emission is only coming from $\sim$mm grains located in a single ring at (along with some other basic idealized assumptions such as as the grains being perfect emitters and a density of $2.5\,\rm g\,cm^{-3}$). For simplicity, we assume the asteroid belt is located at 4 au, or half the resolvable radii. For a $\gamma$ Vir-like star with excesses listed above we would expect $2-5\times 10^{-5}\,\rm M_{\oplus}$ of mm debris. If this “excess” were indeed coming from a debris disk, then there should in theory be a full size distribution of grains up to asteroid-sized objects. Again adopting the methods in White et al. (2017), we can assume the disk is spread out between $2-4$ au, is populated by grains ranging from $10\,\mu$m to 25 km with a size distribution of $q\sim 3.5$, and the emission/absorption efficiency of the grains is dependent on the grain’s size. This would lead us to infer $0.02-0.07\,\rm M_{\oplus}$ of total debris in the disk, making it $\sim 100\times$ larger than the asteroid belt in our Solar system.

While the above calculations do indeed make some generous and far reaching assumptions given the lack of information, none of them are out of context for estimating the total mass of a debris disk. If the observed flux at $\sim$mm wavelengths was, for example, $10-100\times$ larger than the expected stellar emission for a given system, then the above approach would likely be used to better characterize the debris. This scenario highlights that it is imperative to have an accurate stellar emission model when studying unresolved circumstellar debris. This is particularly true if currently oversubscribed facilitates, such as ALMA, and future facilities such as the next generation Very Large Array (ngVLA) are to be used to their full potential in studying unresolved debris structures (White et al., 2018b).