A Chandra Study: Are Dwarf Carbon Stars Spun Up and Rejuvenated by Mass Transfer?

1.1. Dwarf Carbon Stars

1.2. The Planetary Nebula Connection

1.3. Binary Evolution Scenarios

1.4. Stellar Rotation and Activity

The list of six targets for this initial Chandra study of X-rays from dC stars was compiled from our uniformly selected SDSS sample of high-latitude C stars (Green 2013). We selected only those that are definitively main sequence, based on high proper motions measured between USNO-B and SDSS (Munn et al. 2004). (Any giant with such high proper motion would be nearby and much too bright for SDSS.) For the most resource-efficient exploration of dC stars, we restricted the sample to either DA+dC systems or dCs showing Hα emission (dCe stars, henceforth) with i < 17, yielding six objects (two DA+dCs, and four dCes). One was already observed in X-rays; SDSS J125017.90+252427.6 falls serendipitously in both XMM-Newton and Chandra fields (Green 2013), as it is only about 6' away from the galaxy NGC 4725.

The small pilot sample we consider here likely includes dC stars (1) with a relatively short time since accretion (the dC systems including still-hot DA WDs) and/or (2) those still showing clear signs of activity (the dCe stars, for which the presumed DA WD has cooled beyond detectability even in the optical/UV). SDSS spectra are shown in Figure 1 for the objects in our Chandra sample, illustrating the range of dC types herein.

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For context, we make use of the distance information derived from Gaia Data Release 2 (Gaia Collaboration et al. 2018) by Bailer-Jones et al. (2018) to plot the range of color and absolute magnitude for a compilation of non-AGB carbon-enhanced stars in Figure 2. While originally selected based on their large proper motions, the dC systems in our sample are confirmed as definitively main sequence, having M_G > 8.

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Our targeted Chandra observations of dC stars were performed using the S3 (backside illuminated CCD) on ACIS-S between 2014 October and 2016 May (proposals 15200243 and 16200105; PI: P. Green). Exposure times ranged from 16 to 28 ks per star. Some of the observations were split into several exposures (ObsIDs) as part of the requirement to keep various Chandra subsystem temperatures within their acceptable ranges. None of the observations uses a grating. Most are in VFAINT ACIS mode, but several are in FAINT mode; observation details are listed in Table 1.

For SDSS J163718.64+274026.5, we analyzed the merged observations, since they use the same instrument, and are only separated by two days (and just 4° in roll angle). SDSS J125017.90+252427.6 falls within three archival observations, with significantly different dates and instrument configurations, so we chose to analyze the longest observation only (29.6 ks; PI: Garmire).

We reprocessed the Chandra event lists with the CIAO (ver 4.10) chandra_repro script and CALDB (4.7.8), which account for afterglows, bad pixels, charge transfer inefficiency, and time-dependent gain corrections. All our dCs were detected in every Chandra ObsID, at positions within 2'' of those measured in Gaia DR2 (epoch 2015.5). We used the CIAO srcflux tool to estimate source properties in the 0.3–3.0 keV energy range, which includes all detected photons. X-ray source properties are shown in Table 2. To estimate intervening absorption from extinction due to Milky Way dust, we used the dustmaps Python package (Bayestar17) of Green (2018); for every dC direction, these columns were inconsequential.

Table 2.  X-Ray Source Properties in the 0.3–3.0 keV Energy Range

Object	Chandra	Net CR	TX	FX,obs	FX	LX
	ObsID	(cnt ks−1)	(MK)	(10−15 erg cm−2 s−1)		(1028 erg s−1)
J0901	16650	0.16 ± 0.09	2	${3.18}_{-2.25}^{+4.33}$	${3.77}_{-2.67}^{+5.14}$	${15.47}_{-11.02}^{+21.12}$
...	...	...	10	${0.97}_{-0.69}^{+1.33}$	${1.03}_{-0.73}^{+1.41}$	${4.23}_{-3.01}^{+5.79}$
J1015	15702	0.25 ± 0.13	2	${3.64}_{-2.30}^{+4.00}$	${4.82}_{-3.04}^{+5.28}$	${13.02}_{-8.25}^{+14.28}$
...	...	...	10	${1.34}_{-0.85}^{+1.48}$	${1.48}_{-0.93}^{+1.63}$	${4.00}_{-2.53}^{+4.41}$
J1250	409	1.62 ± 0.99	2	${20.40}_{-15.08}^{+29.00}$	${22.90}_{-16.93}^{+32.50}$	${21.91}_{-16.20}^{+31.09}$
...	...	...	10	${8.48}_{-6.27}^{+12.02}$	${8.83}_{-6.53}^{+12.57}$	${8.45}_{-6.25}^{+12.03}$
...	2976	0.64 ± 0.17	2	${12.80}_{-5.00}^{+6.50}$	${14.40}_{-5.64}^{+7.30}$	${13.78}_{-5.40}^{+6.99}$
...	...	...	10	${4.13}_{-1.61}^{+2.11}$	${4.31}_{-1.68}^{+2.19}$	${4.12}_{-1.61}^{+2.10}$
...	17461	0.41 ± 0.12	2	${47.30}_{-19.70}^{+27.00}$	${53.10}_{-22.10}^{+30.30}$	${50.80}_{-21.17}^{+29.01}$
...	...	...	10	${6.03}_{-2.51}^{+3.45}$	${6.28}_{-2.62}^{+3.59}$	${6.01}_{-2.51}^{+3.44}$
J1519	16649	0.54 ± 0.14	2	${12.80}_{-4.77}^{+6.30}$	${14.40}_{-5.39}^{+7.10}$	${33.83}_{-12.72}^{+16.72}$
...	...	...	10	${3.52}_{-1.31}^{+1.75}$	${3.67}_{-1.37}^{+1.81}$	${8.62}_{-3.23}^{+4.26}$
J1548	16651	0.31 ± 0.14	2	${5.35}_{-3.14}^{+5.15}$	${6.00}_{-3.52}^{+5.80}$	${3.84}_{-2.25}^{+3.71}$
...	...	...	10	${0.26}_{-0.26}^{+1.06}$	${0.27}_{-0.27}^{+1.10}$	${0.17}_{-0.17}^{+0.70}$
J1637	16652	0.57 ± 0.18	2	${7.90}_{-3.49}^{+5.00}$	${11.00}_{-4.85}^{+7.00}$	${21.65}_{-9.58}^{+13.80}$
...	...	...	10	${3.03}_{-1.34}^{+1.91}$	${3.40}_{-1.50}^{+2.15}$	${6.69}_{-2.96}^{+4.24}$
...	17534	1.05 ± 0.35	2	${14.20}_{-6.59}^{+9.50}$	${19.80}_{-9.20}^{+13.20}$	${38.97}_{-18.16}^{+26.02}$
...	...	...	10	${5.50}_{-2.55}^{+3.68}$	${6.18}_{-2.86}^{+4.12}$	${12.16}_{-5.65}^{+8.12}$

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For each dC, we derived two X-ray flux estimates, based on either a 2 MK or a 10 MK optically thin plasma (APEC; Smith et al. 2001) with absorption modeled using WABS (Morrison & McCammon 1983). As described in section Appendix, our motivation for these choices comes both from the literature and from attempts to fit the Chandra spectra of the two dCs herein with the most counts. Further discussion of our sample below includes results assuming either 2 or 10 MK plasma temperatures.

Our X-ray analysis is very unlikely to be complicated by emission from the WDs, even in the DA+dC systems, because hot WD photospheric X-ray emission is extremely soft. For WDs in the field, emission of hard X-rays is almost always attributed to coronal emission from a late-type dwarf companion (O'Dwyer et al. 2003). Indeed, among the thousands of WDs that have been observed (mostly serendipitously) by XMM-Newton or ROSAT, only a handful of single WDs have spectra that are hard like the CSPN (Bilíková et al. 2010). The great majority of the CSPNe with hard X-ray emission that do not have an easily detected late-type companion may have, e.g., an accreting WD companion (Miszalski et al. 2019).

Hydrogen Balmer line emission from the stellar chromosphere is a known tracer of activity; Hα line luminosity is well correlated with projected rotation velocity v sin i (e.g., Maldonado et al. 2017 for M0–M4 dwarfs) after excluding spectroscopic binaries. While all of the dCs in our sample have Hα emission evident by selection, we are unable to reliably use the Hα equivalent widths in these dCs to predict their X-ray emission. Hα equivalent widths are not a suitable indicator of stellar activity and must be transformed into Hα fluxes, as found by multiple studies (Reiners et al. 2012; Maldonado et al. 2017), before fitting Hα–X-ray relations. However the correlation between Hα flux and X-ray flux appears to be a weak one even in K and M dwarfs and becomes only more problematic with dCs given the lack of published model atmospheres needed to transform Hα equivalent width into Hα flux. We therefore did not attempt to use the observed Hα emission to predict X-ray fluxes.

Bolometric luminosity estimates are important for placing dCs in the context of other active stars, because stellar activity is best characterized in the X-rays across a range of stellar types when the X-ray luminosity is normalized by the bolometric luminosity and ${L}_{\mathrm{bol}}$ can vary by a factor of ∼20 across the range of main-sequence spectral types known to show C₂ and CN molecular bands. To estimate bolometric luminosities ${L}_{\mathrm{bol}}$, we assembled a spectral energy distribution (SED) for each dC star in our sample from public cataloged photometry and calculated ${L}_{\mathrm{bol}}$ using the sedkit Python package (Filippazzo et al. 2015; J. C. Filippazzo et al. 2019, in preparation). The exact procedure is detailed in those works and summarized here.

Optical, near-infrared, and mid-infrared magnitudes were obtained from the SDSS Data Release 12 (Alam et al. 2015), 2MASS Point Source Catalog (Skrutskie et al. 2006), and AllWISE Source Catalog (Cutri 2013), respectively. We converted photometry to the VegaMag system and corrected for (small) interstellar extinction using the dustmaps Python package (Green 2018). Synthetic magnitudes were calculated from the SDSS spectrum, which was then normalized to the observational photometry. In wavelength regions with no spectral coverage, the SED was linearly interpolated between photometric points. For the DA/dCs, we excluded the SDSS u-, g-, and r-band photometry and spectral flux, since they are contaminated by the DA WDs. To approximate a Wien tail, the SED was linearly interpolated from the shortest-wavelength data point down to zero flux at zero wavelength. A blackbody spectrum fit to the WISE photometry was used to approximate a Rayleigh–Jeans tail at long wavelengths. We then calculated the bolometric flux ${f}_{\mathrm{bol}}$ as the integral of the complete SED.

Finally, we calculated ${L}_{\mathrm{bol}}$ = 4π${f}_{\mathrm{bol}}$d² for each source using a parallax measurement from the Gaia DR2 and the resulting distances from Bailer-Jones et al. (2018). The results are shown in Table 3, where we adopt the solar bolometric luminosity value of log L_⊙ = 33.583.

Table 3.  Parallaxes, Distances, and Bolometric Luminosities

Object	ϖ	Distance	log (${L}_{\mathrm{bol}}$/L⊙)
	(mas)	(pc)	(erg s−1)
J0901	1.71 ± 0.14	577.1 ± 46.5	−1.26 ± 0.07
J1015	2.10 ± 0.13	469.9 ± 28.6	−1.32 ± 0.05
J1250	3.54 ± 0.08	280.6 ± 6.3	−1.52 ± 0.02
J1519	2.26 ± 0.08	438.0 ± 15.0	−1.47 ± 0.03
J1548	4.32 ± 0.08	229.9 ± 4.3	−1.87 ± 0.07
J1637	2.47 ± 0.09	401.6 ± 15.1	−1.56 ± 0.03

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Field main-sequence stars with outer convection zones are magnetically active, as traced by coronal X-rays and/or chromospheric Hα emission. The large observed range in log ${L}_{{\rm{x}}}/{L}_{\mathrm{bol}}$ from about 10⁻³ down to 10⁻⁸, is thought to occur because stars' rotation rates slow with age, due to mass loss from stellar winds (e.g., Skumanich 1972). Indeed, rotation rates correlate strongly with activity, especially when normalized by the convective turnover time τ via the Rossby number R₀ = P_rot/τ (Noyes et al. 1984). The magnetic dynamo that drives these signatures of activity is thought to be generated by differential rotation inside the star. At the highest rotation rates, corresponding to ${R}_{0}\lesssim 0.13$, activity saturates, and log ${L}_{{\rm{x}}}/{L}_{\mathrm{bol}}$ remains at ∼−3.3 (Micela et al. 1985; Wright et al. 2011). It was long thought that this correlation must be mediated by an αΩ dynamo (Parker 1955), which requires an interface (the tacholine) between a solidly rotating radiative core and a differentially rotating convective envelope. However, the same rotation–activity relationship appears to hold even for late-type stars thought to be fully convective (Wright et al. 2018).

Unfortunately, we do not have the sensitive multiepoch photometry that would be required to measure the rotation rate for the dC stars in our sample. The greatest promise to achieve this in the near future—at least for the brighter dC examples—is after NASA's Transiting Exoplanet Survey Satellite (Ricker et al. 2015) surveys the northern sky, providing photometric measurements every 30 minutes, which can be combined as needed for greater sensitivity (at the cost of lower time resolution). Nor do we have estimates for the convective turnover times, due to a paucity of stellar structure models for dC stars. However, since we have empirical measurements of both ${L}_{{\rm{x}}}$ and ${L}_{\mathrm{bol}}$, we can estimate the range of likely values of P_rot or R₀ for dC stars, reasonably assuming that their internal dynamics and magnetic dynamo have stabilized since the end of mass transfer.

In Figure 3, we show the activity level of dC stars in our sample as a function of rotation period, in context with activity in normal (C/O < 1) main-sequence stars from several recent sources in the literature. Wright et al. (2018) studied the coronal activity–rotation relationship for late-type stars with rotation periods known from the MEarth project (Nutzman & Charbonneau 2008), including main-sequence stars thought to be fully convective—those later than about M3 (${T}_{\mathrm{Eff}}\,\lesssim 3300$ K), corresponding to masses below about $\sim 0.35{M}_{\odot }$ (Chabrier & Baraffe 1997). Stelzer et al. (2016) compiled X-ray data from ROSAT and XMM-Newton catalogs for K2 Superblink stars with well-measured periods. They assumed a thermal (APEC) single temperature model (APEC) of 3.5 MK and a column density of ${10}^{19}\,\mathrm{atoms}\,{\mathrm{cm}}^{-2}$.

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From Figure 3, limits on the rotation periods for these dC stars appear to be in the "saturated" regime where log ${L}_{{\rm{x}}}/{L}_{\mathrm{bol}}\geqslant -3.3$, at least when assuming plasma temperatures of ∼2 MK. About half remain in the saturated regime even when assuming a high plasma temperature ∼10 MK. If the lower temperature applies, then dCs' strong X-ray activity is consistent with rapid rotation rates of several days or less, as might be expected from accretion spin-up. If the higher temperature applies, then periods are more weakly constrained, to about 20 days or less.

We reiterate the caveats that (a) this pilot sample is not representative of dCs more generally, since, as mentioned, all six dC optical spectra in our sample show weak Hα emission lines (see Figure 1) and (b) X-ray counts are too few to actually constrain T_X.

We have sought to test the hypothesis that dC stars, having inherited significant mass from an extinct AGB companion, could have spun up significantly, and that they may therefore show signs of coronal activity often associated with rapid rotation. As a test for such coronal activity, we selected a small sample of dCs for X-ray observation with Chandra. All six dC systems observed were detected by Chandra, but with too few counts to allow useful spectral constraints. We therefore calculate X-ray fluxes assuming plasma temperatures of 2 and 10 MK, bracketing a range of reasonable values. We have estimated the dCs' bolometric luminosities directly by compiling and integrating multiwavelength photometry and using distances from Gaia DR2 parallaxes published after our Chandra observations were performed. When assuming a reasonable plasma temperature of 2 MK, all six systems appear to have log ${L}_{{\rm{x}}}/{L}_{\mathrm{bol}}\,\gtrsim -3$, putting them in the saturated regime so that they might be expected to have short (≲10 days) rotation periods consistent with strong accretion spin-up. At the upper range of expected temperature, near 10 MK, the X-ray activity of dCs could imply longer (≲20 days) periods similar to less active dwarfs.

The X-ray emission from dC stars to date supports the mass-transfer hypothesis. Where dCs have been part of a central binary system of a PN, which could be common, then the activity we detect here argues for spin-down significantly longer than ($\sim {10}^{4}$ yr) PN timescales, because for most dC stars the former CSPNe are now WDs cooled beyond detectability.

To better understand the characteristics of a more typical sample, sufficiently sensitive X-ray observations of the closest known dC stars with reliable distances from Gaia DR2 are critical. Ideally, at least ∼100 counts per object should be obtained, sufficient to constrain individual plasma temperatures to within about ∼30%. The X-ray luminosity fractions ${L}_{{\rm{x}}}/{L}_{\mathrm{bol}}$ can then serve as a more reliable proxy to measure rotation and total accretion, within the context of models predicting longevity and intensity of the binary interaction during the AGB phase. For instance, accretion of both mass and angular momentum is enhanced if there is a longer RLOF phase before the CE phase. A dC enriched by a prolonged period of RLOF would have relatively stronger X-ray emission, faster rotation, and perhaps also higher C/O. Very close PCEB dC systems that have low X-ray activity may indicate a brief pre-CE phase. A dC that experienced only wind accretion may have low rotation and low L_X. A significant sample of dCs with measured orbital and rotation periods and X-ray luminosities would greatly enhance our understanding of these useful and intriguing systems.

The scientific results reported in this article are based on observations made by the Chandra X-ray Observatory, and data obtained from the Chandra Data Archive. This research has made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO and Sherpa.

Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Numbers GO4-15005X and GO5-16004X issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. B.M. acknowledges support from the National Research Foundation (NRF) of South Africa.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is www.sdss.org.

SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

Facilities: 2MASS - , CXO - , Gaia - , Sloan - , WISE. -

Software: Astropy (Astropy Collaboration et al. 2018), matplotlib (Barrett et al. 2005), Numpy (http://www.tramy.us/).

Our motivation for using 2 and 10 MK plasma temperatures for the X-ray spectral models of dC stars comes both from the literature and from our Chandra observations. The higher-temperature model is consistent with median photon energies of ∼0.5–1.0 keV (6–12 MK) seen in X-ray-selected stellar samples observed with Chandra from, e.g., the COSMOS survey (Wright et al. 2010), and also with the temperature of peak emissivity for Mg xi. However, for some single stars with detailed X-ray spectral fitting, plasma temperatures are close to 2 MK (e.g., see the compilation in Table 9 of Testa et al. 2004), the temperature of peak emissivity for O vii.

Even with very few counts detected in our Chandra images, we can examine the median energy values and their location with respect to the thermal models and foreground extinction. Most of the observed counts suggest T_X > 3 MK and likely near 8–10 MK, but this is uncertain without knowing what the circumstellar environment might contribute to extinction.

We can also analyze the two dCs in our sample with the largest number of counts, which are nonetheless insufficient for strong spectral model constraints. SDSS J151905.90+500702.9 (Figure 4) indicates that either a hot plasma temperature (∼10 MK with low absorbing column, ${N}_{{\rm{H}}}\lt 5\times {10}^{21}\,{\mathrm{cm}}^{-2}$) or a cool plasma temperature ($\lesssim 2$ MK, with high absorbing column, ${N}_{{\rm{H}}}\gt 5\times {10}^{21}\,{\mathrm{cm}}^{-2}$) might be applicable. The best-fit spectral model for SDSS J125017.9+252427.6 (Figure 5) is single-peaked toward a cool value near ∼1 MK.

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These crude spectral fits further justify our adopted spectral models of 2 and 10 MK. Formally they may allow for the possibility of significant circumstellar columns above the expected intervening values, but the constraints are very weak. Cool post-AGB wind material may indeed surround dCs, but such an intriguing possibility must be investigated with much more sensitive X-ray and/or submillimeter observations (e.g., Bujarrabal et al. 2013) before being taken seriously.