Most Rotational Variables Dominated by a Single Bright Feature are $\alpha^{2}$ CVn Stars

The Asteroid Terrestrial-impact Last Alert System (ATLAS; Tonry et al., 2018a) is a NASA-funded planetary defense survey that scans the sky for near-Earth asteroids while simultaneously producing well-calibrated data useful for many other astrophysical investigations. Each ATLAS image is photometrically calibrated using a customized, highly-precise catalog (Tonry et al., 2018b) created by mutually calibrating several state-of-the-art photometric catalogs.

In its first two years on the sky, ATLAS operated only one telescope (it now has four). This single ATLAS unit surveyed one fourth of the accessible sky every night, obtaining four 30-second exposures of each target field over a period of about one hour. Hence, during good weather in its observing season, a given star would be observed an average of once per night – but these observations occur in clumps of four in one hour, with a four-day gap before the next clump. Not all images yield flux measurements of every object in the field: for example, faint stars would not be detected in bad seeing. Nevertheless, in two years ATLAS obtained 100 or more photometric measurements for each of 142 million distinct stars, of which 4.7 million were identified as candidate variables. Photometric time series for these candidate variables, as well as classifications we obtained for them using machine learning, constitute ATLAS variable star Data Release One (DR1) and are publicly available through STScI (Heinze et al., 2018).

While preparing ATLAS DR1, we manually examined thousands of light curves of objects that had periods, amplitudes, or other characteristics not typical of the classes the machine had assigned them. We identified a rare but well-defined class of light curves, mostly identified as pulsators by the machine, that did not seem to match any known type of variable star. These objects had coherent, periodic light curves with a distinctive shape defined by narrow, symmetrical maxima and broad, flat minima (Figure 1). They looked like the light curves of contact eclipsing binaries turned upside down. Since we’d defined a light curve category called CBH (Contact eclipsing Binaries folded at Half the true period), we called this new set of stars the upside-down CBH variables, or UCBH stars. They have typical periods of 1–10 days and peak-to-trough amplitudes of 0.05–0.20 magnitudes. The amplitudes are usually similar between the ATLAS $c$ and $o$ bands¹¹1These broad, customized bandpasses are described in Tonry et al. (2018a); briefly, $c$ corresponds approximately to Sloan $g+r$ and $o$ to $r+i$..

Herein, we present a catalog of 98 UCBH stars identified in ATLAS DR1 photometry. This catalog constitutes the entire set of ATLAS variables we have confidently assigned to the UCBH class. We carry the analysis of UCBH stars beyond pure photometry for the first time, presenting low-resolution spectra for 14 of them (chosen based on brightness and observability during our scheduled telescope time), intensive multi-band photometry for one, and HR diagrams based on Gaia parallaxes for all.

Our spectra (Section 3) indicate that a majority of UCBH stars are $\alpha^{2}$ CVn variables. An $\alpha^{2}$ CVn variable is an Ap or Bp star that exhibits rotationally modulated variability (Peterson, 1970; Catalano & Leone, 1993). Ap and Bp stars are A-type or B-type stars with enormously enhanced photospheric abundances of specific heavy elements (silicon, chromium, strontium, europium, and others). The enhancement is believed to be produced by radiative levitation (Michaud, 1970). This levitation occurs because the elements in question interact more strongly with the radiation field than most other atoms — i.e., they have many strong spectral lines at wavelengths near the peak of the star’s spectral energy distribution (Hümmerich et al., 2018). Radiation pressure therefore exerts a stronger upward force (relative to their mass) on the atoms of these elements than on the majority constituents of the stellar atmosphere. This upward force is believed to concentrate the elements in the upper layers of the stars. The stellar atmospheres must be remarkably free from convection for the extremely weak force of radiative levitation to produce the observed concentrations of heavy elements. Michaud (1970) calculated that convective velocities must be slower than $10^{-5}$ m/sec, and theorized that strong magnetic fields might be able to stabilize the ionized atmospheres of these stars against convective stirring.

That some Ap/Bp stars should exhibit rotational variability is not surprising: longitudinal inhomogeneity in the concentration of heavy elements would naturally cause rotational variation (Peterson, 1970). The shape, amplitude, and detectability of this variation depend on the details of the inhomogeneity (Shulyak et al., 2010), which in turn might arise from spatial variations in the magnetic field (Michaud et al., 1981).

Interestingly, Peterson (1970) found that a photospheric spot having an enhanced concentration of silicon will be brighter at optical wavelengths, because the strong silicon absorption lines in the UV will redistribute flux into the optical. We might expect that the heavy elements would be most concentrated at the regions of strongest magnetic field (where convection is most strongly suppressed and radiative levitation can have the greatest effect), and that the flux redistribution would render these regions the brightest at optical wavelengths. This would imply that the (optical) photometric maximum should coincide with points when the region of greatest magnetic field strength is centered on the hemisphere of the star that faces us. Accordingly, Dukes & Adelman (2018) found that the $\alpha^{2}$ CVn star HD 215441 has its photometric maximum at about the same rotational phase as the maximum of the magnetic field measured by Zeeman splitting of the spectral lines. This might not, however, be a general rule: both theory (Michaud et al., 1981) and observation (Kochukhov & Wade, 2010; Kochukhov et al., 2015) indicate that different radiatively levitated elements can be affected differently by the magnetic field and hence have different photospheric distributions. Despite this complexity, there is broad observational evidence (e.g. Pyper, 1969) that optical photometric maxima do tend to occur near the same rotational phase where the greatest abundance of radiatively levitated elements is measured, consistent with the UV flux redistribution predicted by Peterson (1970).

Known $\alpha^{2}$ CVn stars have amplitudes mostly smaller than is typical for the ATLAS UCBH stars, and some have longer periods, but the distributions of both period and amplitude overlap heavily. Sikora et al. (2019) have shown that the rotation periods of most of the magnetic, chemically peculiar A and B stars whose variability enables their periods to be measured fall within the same 1–10 day range that characterizes UCBH stars, with the few exceptions mostly having longer periods.

The light curves of known $\alpha^{2}$ CVn stars have a variety of shapes, including some that exactly match our UCBH stars and many that do not. Hensberge et al. (1977) present $uvby$ photometry of six $\alpha^{2}$ CVn stars with periods from 1.48 to 4.75 days, of which only one (HD 207188) shows a UCBH-type lightcurve. Ryabchikova et al. (1990) find the $\alpha^{2}$ CVn star HD 192913 to have a period of 16.5 days and an amplitude of 0.04 magnitudes, with a saw-tooth rather than UCBH-type light curve. Catalano & Leone (1993) present multi-band ($uvby$) light curves of eight bright $\alpha^{2}$ CVn stars with periods ranging from 1.3 to 6.8 days and amplitudes from 0.03–0.10 mag. Two of them (HD 54118 and HD 73340) exhibit UCBH-type light curves in at least one of the four photometric bands, while the others have various different shapes. Poretti et al. (1997) also probe $\alpha^{2}$ CVn stars with $uvby$ photometry: HR 2746 (period 0.92 days; amplitude 0.004–0.024 mag depending on photometric band) and HR 2761 (period 2.06 days; amplitudes 0.015–0.057 mag). They find a UCBH-type lightcurve for HR 2746 and sinusoidal variations for HR 2761. Drury et al. (2017) present Kepler and ground-based photometry of the $\alpha^{2}$ CVn star KIC 2569073, finding a period of 14.67 days, approximately sinusoidal variations, and peak-to-trough amplitudes varying from 0.03 to 0.34 magnitudes, with a phase reversal seen in the $B$-band relative to the $V$, $R_{\mathrm{C}}$, and $I_{\mathrm{C}}$ bands. Dukes & Adelman (2018) acquired precise $uvby$ lightcurves of eight $\alpha^{2}$ CVn stars. One of these, HD 26792, shows a perfect UCBH-type light curve in all filters, while HD 5797 shows a noisy but UCBH-like light curve in the $y$ filter only. Among the other six stars, none shows a UCBH-type light curve shape in any filter. Most recently, Bernhard et al. (2020) analyzed and published light curves for 294 magnetic chemically peculiar stars (i.e., Ap/Bp stars) using data from three recent surveys that used very small apertures and hence maintained photometric precision for very bright stars. We find that 33 of the Bernhard et al. (2020) light curves are of the UCBH type (more on this in Section 4). Finally, after this work was accepted for publication, we learned of another paper (Bernhard et al., 2021) demonstrating that many of the ATLAS UCBH stars are $\alpha^{2}$ CVn variables. While this same result is also an important conclusion of the current work, our very different emphasis makes our work and that of Bernhard et al. (2021) substantially complementary.

In 2018 we acquired spectra of five ATLAS UCBH stars with the GMOS spectrograph on the 8-meter Gemini North telescope under proposal ID GN-2018B-Q-216. This proposal was designed to take advantage of the worst usable weather by targeting bright objects that could be usefully observed even through moonlit cloud with bad seeing. This observing plan produced a win-win situation in which we provided Gemini queue observers with targets for conditions when almost nothing else could be observed, while the spectra they acquired for us were in fact considerably better than our nominal requirements. This happened because worst-case observing conditions are statistically rare, so the majority of our data were acquired in somewhat better weather than we had planned for (though still too poor for most observing programs).

Our plan of exploiting the worst usable weather at Gemini determined determined both our choice of target objects (the brightest ATLAS UCBH stars observable) and the slit width (2.0 arcsec, to allow for very bad seeing). We used the GMOS B1200 grating, which delivers a nominal resolution of $R=3744$ at 4630Å  with an 0.5 arcsecond slit²²2https://www.gemini.edu/instrumentation/gmos/components#Gratings. Our 2.0 arcsecond slit would therefore be expected to deliver $R=936$, four times worse than nominal – but the actual resolution could be higher if the seeing was smaller than the slit. We observed each target alternately with two different central wavelength settings, 4400Å  and 4680Å, enabling us to fill in gaps between the three GMOS CCDs and obtain continuous spectral coverage from 3650–5500Å.

In addition to our GMOS observations, we acquired spectra of nine additional UCBH stars using the SNIFS instrument (Lantz et al., 2004) on the University of Hawaii 2.2 meter telescope on Maunakea, in February and March 2019. A substantially larger number of spectra was originally expected from this observing program, but it was plagued with bad weather and equipment problems. The SNIFS instrument has a blue module delivering spectral coverage from 3200–5600Å  with resolution $R\sim 1000$ at 4300Å, and a red module covering 5200-10000Å  with $R\sim 1300$ at 7600Å  (Lantz et al., 2004).

Our nominal resolution element at $\sim 4500$Å  should be $4500/936$ = 4.8Å  with GMOS and $4500/1000$ = 4.5Å  with SNIFS. Comparisons of our GMOS and SNIFS spectra demonstrate that GMOS has actually delivered better resolution — an indication that the seeing was smaller than our 2.0 arcsecond slit width during our GMOS observations.

Our Gemini spectra (Figure 4) showed all five science targets to be Ap/Bp stars: that is, A-type or B-type stars with enormously enhanced abundances of a few specific heavy elements (mainly silicon, europium, chromium, and strontium). The peculiar lines that we detect most strongly form two blends, one near 4080Å  (likely a blend of Sr and Cr) and another near 4130Å  (a blend of Si and Eu). The resolution of our spectra is insufficient to determine the relative contributions of each element to the blended lines. Previous work on such stars (see, e.g. Preston, 1974; Dukes & Adelman, 2018) distinguishes fine gradations of spectral classification depending on magnetic field strength and on what elements are enhanced to what extent. Since multiple lines are blended in our spectra, they do not enable us to assign exact types of chemical peculiarity — but they do establish that our targets fall into the broad category of chemically peculiar A-type or B-type stars.

The SNIFS spectra, though not matching the resolution and signal-to-noise ratio of GMOS, are nevertheless sufficient to show that five of our SNIFS targets are Ap/Bp stars, while the rest are not A or B stars at all. Figure 4 shows spectra for all ten of our spectrally confirmed Ap/Bp stars, five from GMOS and five from SNIFS.

We have attempted to determine spectral types for the UCBH stars for which we have spectra. We have done this classification manually using comparison spectra from the Stellar Spectral Flux Library of Pickles (1998), guided in part by the diagnostic spectral lines mentioned in the Atlas of Stellar Spectra³³3https://ned.ipac.caltech.edu/level5/ASS_Atlas/frames.html. The effective resolution of our SNIFS spectra matches fairly well with the 5Å sampling used in the Pickles (1998) library. The higher resolution of our GMOS spectra made narrow spectral lines look too deep relative to the Pickles (1998) library, so we smoothed the GMOS classification spectra using a Gaussian blur of $\sigma=3$Å.

The classification spectra of our $\alpha^{2}$ CVn stars, with appropriate comparison spectra from Pickles (1998), are shown in Figure 5, and the spectral types we assigned are in Table 3. For these A-type (or very late B) stars, classification with uncertainty no greater than one spectral subtype appears to be possible based on the strength of the calcium H line at 3969Å  (which is the only one in our spectra with significant diagnostic power). Based on this, we would expect our spectral types to be quite accurate — with the important caveat that the chemical peculiarity of our stars might have affected the calcium H line or our perception of it (e.g., by changing the nearby continuum). That the spectra are not typical of A stars is obvious even at reduced resolution: besides numerous lines not present in the comparison spectra, the hydrogen Balmer lines seem somewhat weaker in the UCBH stars. However, unless classification biases from the peculiar spectra are extremely severe, there is no doubt that all of our $\alpha^{2}$ CVn stars are early A or very late B-type.

Four of the UCBH stars for which we obtained SNIFS spectra were not $\alpha^{2}$ CVn stars. One of these, ATO J207.7199+36.7006, is in fact the known subdwarf OB star PG 1348+369 (Green et al., 1986; Wesemael et al., 1992). Since our spectra are consistent with the published results, and indicate a star much too hot to be an $\alpha^{2}$ CVn variable, we have not attempted to reclassify this object. Spectra of the remaining three UCBH stars, which have much later spectral types, are shown along with Pickles (1998) comparison spectra in Figure 6. The spectral types we assigned them are provided in Table 3. For these classifications, the diagnostic lines listed in the Atlas of Stellar Spectra were of limited value because our SNIFS spectra of these red objects were very faint in the blue region covered by the Atlas. Hence, we made use of many other lines at much longer wavelengths that appeared to be diagnostic based on their variations with spectral type seen in the Pickles (1998) library. We expect our classifications of these later-type stars to have an accuracy of around two spectral subtypes. Interestingly, all three of our late-type UCBH stars show significant H$\alpha$ emission (Figure 6, right panel).

The single localized bright spot that most simply explains a UCBH-type lightcurve could be produced by phenomona not related to the $\alpha^{2}$ CVn stars. One example is an accretion stream impacting a stellar photosphere. This may be the explanation for some UCBH stars — notably the hot subdwarf PG 1348+369 (Green et al., 1986; Wesemael et al., 1992).

An approximately even longitudinal distribution of dark star spots with a prominent gap could also produce a UCBH-type rotationally modulated lightcurve (Figure 2), with the ‘missing’ dark spots of the gap functioning like a single bright feature. While $\alpha^{2}$ CVn stars are too hot for the ordinary form of dark magnetic starspots, this scenario may apply to the significant minority (22 out of 98 in the ATLAS sample; see Figure 8) of UCBH stars with much later spectral types — a hypothesis which is further bolstered by the detection of strong H$\alpha$ emission in all three of the late-type UCBH stars for which we have spectra. Such emission is characteristic of late type stars that are magnetically active and heavily spotted.

While late-type UCBH stars exist, the variability we observe in A-type or B-type UCBH stars cannot reasonably be attributed to an unresolved late-type companion. Such a companion would have to be several times fainter than the primary to escape detection in our spectra, implying a very large-amplitude photometric variation for the late-type star itself. If late-type stars commonly had high-amplitude UCBH-type lightcurves, they should be much easier to detect in the field than as binary companions to brighter A stars that would dilute their photometric amplitudes. In this case, isolated late-type stars, being far more numerous than A-type or B-type stars, should dominate our UCBH sample — the opposite of what we observe. Additionally, it would be a strange coincidence if late-type UCBH companions were found only around chemically peculiar A-type primaries. Furthermore, the literature contains many examples of UCBH-type variations in $\alpha^{2}$ CVn stars (Section 1.2), and these stars are known to exhibit correlated spectral variations that clearly implicate the Ap/Bp star itself — rather than a hypothetical late-type companion — as the photometric variable.

In short, although a tiny minority of late-type stars do exhibit UCBH-type lightcurves, there is no doubt that the UCBH variations we observe in Ap/Bp stars originate from the bright stars themselves and not from an unresolved late-type companion.

A large majority (73 out of 98) of the ATLAS UCBH stars appear to be $\alpha^{2}$ CVn variables — that is, Ap/Bp stars with rotationally modulated photometric variability. The Ap/Bp stars are chemically peculiar A-type or B-type stars with greatly enhanced abundances of specific heavy elements in their photospheres. The enhanced abundances are believed to be caused by radiative levitation of the heavy elements in question (Michaud, 1970), which is strongly influenced (and likely enabled) by magnetic fields (Michaud et al., 1981).

The rotationally modulated variability of $\alpha^{2}$ CVn variables results from inhomogeneous distributions of the radiatively levitated elements across the stars’ photospheres (Shulyak et al., 2010). For such a star, the single bright feature implied by a UCBH lightcurve is naturally interpreted as the region where the concentration of radiatively levitated heavy elements is the highest. Such a region is bright at optical wavelengths because the strong UV absorption lines of the levitated elements redistribute the star’s intense UV flux into the optical (Michaud et al., 1981). This single region of greatly enhanced heavy element abundance likely owes its existence to a particular configuration of the magnetic field.

The expected causal connection between the magnetic field and the rotational light curve implies that the $\alpha^{2}$ CVn variables that share UCBH-type light curves may also have similar magnetic field topologies. In this context, it is interesting that the lightcurves of some $\alpha^{2}$ CVn UCBH stars show a small ‘bump’ or secondary maximum in the center of the broad, nearly flat minimum. These include ATO J010.7230+57.8087, ATO J110.9074-12.0800, and others in the ATLAS sample — and also examples from the literature such as HD 207188 (Hensberge et al., 1977) and HD 54118 (Catalano & Leone, 1993). A photometric ‘bump’ of this type would naturally be produced by a secondary bright spot at the antipode of the one responsible for the primary maximum. The greatly reduced photometric signature of this antipodal spot could be an effect of latitude. For example, if the two bright features were at stellar latitudes of $+30^{\circ}$ and $-30^{\circ}$, respectively, and the sub-observer latitude were $+30^{\circ}$, we would observe the primary bright feature to pass directly across the center of the stellar disk, producing a maximal photometric signature, while the antipodal feature would barely come into view and would create a greatly reduced photometric ‘bump’ half a rotation later — exactly what we observe in some objects. However, the fact that many lightcurves do not show a secondary photometric ‘bump’ suggests that latitude is not the only effect: if antipodal spots are always present, they must be much smaller/fainter than the primary spot in many cases.

Particularly since there is sometimes evidence of an antipodal spot, it is tempting to conclude that the UCBH lightcurves imply a simple magnetic topology such as a dipole field. However both theory (Michaud et al., 1981) and Zeeman Dopper observations (Kochukhov & Wade, 2010; Kochukhov et al., 2015) point to a complex relationship between magnetic field configurations and inhomogeneity in the heavy element enhancements. For example, some elements concentrate where the magnetic field lines are vertical and some where they are horizontal (Michaud et al., 1981). Hence, conclusions that the UCBH stars have simple magnetic fields — or even that they all have the same magnetic topology — may be unwarranted.

Nevertheless, the shared UCBH-type light curve shape of many $\alpha^{2}$ CVn stars does suggest some commonality in the magnetic field distribution. This could make them interesting targets for Zeeman Doppler imaging and elemental abundace mapping — especially since the ATLAS UCBH stars have photometric amplitudes larger than average for $\alpha^{2}$ CVn variables, likely indicating large and easy-to-measure spatial variations in the magnetic field and elemental abundances. Since the ATLAS UCBH stars are several magnitudes fainter than typical targets of Zeeman Doppler imaging, we have sought and identified 33 UCBH stars among the much brighter sample of $\alpha^{2}$ CVn variables published by Bernhard et al. (2020). Most of these have substantially smaller photometric amplitudes than the ATLAS UCBH stars, but there are exceptions. The most promising of these — bright, high-amplitude variables with perfect UCBH light curves — are HD 191287, HD 77314, and HD 205938 (see Table 4 and Bernhard et al., 2020). These stars are ideal targets for Zeeman Doppler imaging and other forms of high-resolution spectroscopic investigation to probe the detailed astrophysics behind the UCBH-type light curves of $\alpha^{2}$ CVn variables.