Three Hypervelocity White Dwarfs in Gaia DR2: Evidence for Dynamically Driven Double-degenerate Double-detonation Type Ia Supernovae

Mass transfer between two WDs can be dynamically stable or unstable, depending on the donor's response to mass loss, whether or not the mass transfer is conservative, and the degree to which the angular momentum of the transferred mass can be converted back into orbital angular momentum (Marsh et al. 2004). For large enough mass ratios ≳0.2, the accretion stream directly impacts the more massive WD, and no accretion disk is formed, which implies inefficient angular momentum transfer to the orbit. Furthermore, the mass transfer can be super-Eddington and thus non-conservative. Both of these effects destabilize the binary, and thus most double WD binaries are expected to undergo dynamically unstable mass transfer.

Double WD binaries with extreme mass ratios ≲0.2 can have sub-Eddington accretion rates and form accretion disks, both of which help to stabilize mass transfer. However, Shen (2015) pointed out that even these systems can be driven to unstable mass transfer. The accumulation of the donor's hydrogen- and helium-rich layers on the accretor lead to classical-nova-like events in which the accreted shell expands relatively slowly due to thermonuclear burning. Dynamical friction between the donor and the expanding envelope causes the binary separation to decrease, which increases the mass transfer rate into the super-Eddington regime and destabilizes even these extreme mass ratio binaries. This theoretical possibility is borne out by the relatively low birth rate of AM CVn systems (Brown et al. 2016), providing evidence that all double WD systems eventually undergo runaway mass transfer.

In the original double-degenerate scenario (Iben & Tutukov 1984; Webbink 1984), such double WD systems undergoing dynamically unstable mass transfer coalesce to form a single merger remnant that explodes as a Type Ia supernova after ∼10⁴ yr. However, recent studies have suggested that the SN Ia can be triggered during the coalescence itself due to the presence of helium in the surface layers of the companion WD, which initiates the SN Ia explosion via the double-detonation mechanism (Guillochon et al. 2010; Dan et al. 2011; Raskin et al. 2012; Pakmor et al. 2013; Dan et al. 2015). We name this combination of explosion mechanism, companion star, and mode of mass transfer the "dynamically driven double-degenerate double-detonation" (D⁶) scenario. In fact, when all appropriate nuclear reactions are accounted for (Shen & Moore 2014), helium shell detonations, and subsequent carbon core detonations, may even occur during the relatively quiescent initial phases of dynamical mass transfer, before the complete tidal disruption of the companion WD (Pakmor et al. 2013; Shen & Schwab 2017). Thus, there is the exciting possibility that the D⁶ scenario yields a smoking gun in the form of a surviving companion WD.

While theoretical confirmation of the existence of a surviving companion WD awaits future detailed simulations, several observables suggest it is a necessary outcome if double WD binaries make up the bulk of SN Ia progenitors. If fully disrupted, the companion WD would form a thick torus surrounding the primary WD (Guerrero et al. 2004; Dan et al. 2014), which would impart significant asymmetry to the ejecta when the explosion occurred (Raskin et al. 2014). However, such asymmetry is at odds with the low levels of polarization measured in SNe Ia (Wang & Wheeler 2008; Bulla et al. 2016). Furthermore, much of the disrupted WD material would remain at low velocities throughout the evolution of the SN (Pakmor et al. 2012). In the late-time nebular phase, when the SN ejecta become optically thin, oxygen in the disrupted WD material may become visible as strong, narrow emission features, but these are almost never detected (although see Kromer et al. 2013 and Taubenberger et al. 2013 for the case of SN 2010lp). Given these observational constraints and theoretical motivation, we proceed under the presumption that most, if not all, SNe Ia leave an intact companion WD.

An estimate of the number of runaway WDs that Gaia will detect requires knowledge of their brightness following the SN Ia explosion. As a lower limit, we can assume that the evolution up to the explosion and its aftermath have no effect on the companion, so its luminosity is the same as that of a WD that has cooled in isolation since its birth. Using publicly available DB WD cooling tables²⁵ (Holberg & Bergeron 2006; Kowalski & Saumon 2006; Tremblay et al. 2011; Bergeron et al. 2011), we find that a 0.6 (1.0) M_⊙ WD that has cooled for 1 Gyr since its birth has an absolute visual magnitude of 12.9(12.8). However, this declines to 14.3 (14.0) by 3 Gyr. Given Gaia's magnitude limit of 21, this lower limit to the luminosity implies a 3 Gyr-old 0.6 M_⊙ WD can only be seen out to 200 pc, while a 1 Gyr-old 1.0 M_⊙ WD will be detected out to 400 pc.

However, there are several processes that will increase the luminosity of the companion above this lower limit prior to and just after the SN Ia explosion. The most important of these is likely tidal heating. As the orbit of the two WDs decays due to gravitational wave emission, the binary separation shrinks and the less massive companion begins to feel the tidal field of the primary. If the companion becomes and remains tidally locked to the primary, viscous dissipation yields a luminosity at the onset of mass transfer ranging from 0.15–1000 L_⊙, depending on the component masses (Iben et al. 1998), far higher than that of an old, isolated WD.

These values represent upper limits to the effects of tidal heating, as the companion will not be able to maintain complete synchronicity with the orbit. Recent work has found that tidal effects are dominated by the excitation of gravity waves within the companion, which deposit their energy and angular momentum near the surface of the WD (Fuller & Lai 2011; Burkart et al. 2013). These surface layers can be kept near synchronous rotation all the way to the onset of mass transfer, but since the energy is not deposited deep within the core, the timescale for this excess heat to be radiated away is shorter than the typical >10⁶ yr between the explosion and the present day for nearby runaway WDs (Section 2.5), and thus the WD would cool and approach the luminosity of a dim, isolated WD.

However, as argued by Burkart et al. (2013), the strength of the WD's fossil magnetic field should be more than adequate to maintain solid body rotation between the outer layers, where angular momentum is deposited, and the core, especially if the field is wound up during the evolution toward solid body rotation. As the interior of the WD is spun up, it will also be heated by small-scale turbulence at a comparable level to the dissipation necessary to maintain complete synchronicity with the orbit. In this case, the physical picture approaches that assumed by Iben et al. (1998), and the luminosities at the point of Roche lobe overflow (RLOF) will approach their values. Such luminosities ≥0.1 L_⊙ will be visible to 1 kpc, a distance at which Gaia's faint end parallax errors become the primary limitation (Section 3). Thus, when calculating the expected number of runaway WDs Gaia will find in Section 2.5, we limit our search volume to a sphere around the Sun with a radius of 1 kpc.

In addition to tidal heating, there are several other possible mechanisms that may change the appearance of a surviving companion WD, all of which occur after the explosion of the primary. The first is due to the impact of the SN ejecta on the companion, which will deposit shock energy and may also ablate some material from the surface. While similar processes have been modeled for single-degenerate companions (e.g., Marietta et al. 2000; Pakmor et al. 2008; Liu et al. 2012; Pan et al. 2014), detailed calculations of the post-impact state of a surviving WD have not yet been performed, so quantitative predictions cannot be made (but see Papish et al. 2015 for a preliminary investigation of some of these effects). However, given the >10⁶ yr average delay between the SN and the present day for local runaway WDs (Section 2.5) and the much shorter thermal time at the relatively shallow depths where this shock energy should be deposited, it seems unlikely that these effects will still be observable for all but the youngest WDs within historical SN remnants.

A second mechanism that may heat the surviving WD is due to the rapid expansion of the exploding primary, which causes the tidal field felt by the companion WD to change abruptly. Dissipation during the subsequent relaxation to a new hydrostatic equilibrium will deposit heat throughout the WD. However, as in the first case, most of the tidal deformation occurs near the surface of the WD, so most of the dissipation will also be preferentially located at shallow depths where the thermal timescale is relatively short. As previously discussed, given the large average age of the local surviving WDs, we expect this excess heat to be negligible except for ex-companions to historical SNe.

A final mechanism to increase the surviving companion's post-SN luminosity concerns the capture and accretion of ⁵⁶Ni from the SN ejecta by the surviving companion. As discussed in Shen & Schwab (2017), much of the high-entropy ⁵⁶Ni remains fully ionized as it settles onto the WD's surface and cannot decay via standard bound electron captures until it cools. Thus, the radioactive decay of this accreted ⁵⁶Ni can keep the companion WD relatively bright centuries after the SN has faded.

As mentioned above, detailed calculations of the SN ejecta's interaction with the surviving WD have not yet been performed. This means that stellar evolution calculations, like those in Shen & Schwab (2017), are forced to rely on simple estimates for the amount of radioactive material captured and its initial thermal state. As such, accurate quantitative predictions cannot yet be made. However, similar to shock heating by the SN ejecta and tidal relaxation, it is likely that the delayed radioactive decays only affect the outer layers of the companion WD, limiting the time when they can contribute to the luminosity and alter the colors of the WD to centuries. These effects are important for runaway WDs from historical SNe, such as Tycho, Kepler, SN 185, and SN 1006 (Kerzendorf et al. 2018), but may be negligible for the much older runaway WDs that should form the bulk of our candidates. For most of the hypervelocity WDs Gaia is likely to detect, we expect that the energy deposited much deeper in the WD's interior from tidal heating prior to the SN Ia will likely determine its present-day luminosity.

As discussed in Shen & Schwab (2017), the surviving WD will capture some of the lowest-velocity SN ejecta, primarily composed of ⁵⁶Ni. The energy released by the slowly decaying ⁵⁶Ni blows a wind from the WD's surface, ejecting much of the accreted SN ejecta, but some of the material should remain bound and might be detectable with follow-up high-resolution spectra. Unfortunately, as before, the lack of relevant hydrodynamic simulations makes accurate predictions of the surface abundances of a surviving WD difficult.

A surviving WD companion should be hydrogen-free, because the hydrogen layer that most WDs are born with will have been transferred to the primary and ejected from the system in the ∼1000 yr prior to the SN (Kaplan et al. 2012; Shen et al. 2013; Shen 2015). Given the long cooling timescales of the expected Gaia WDs within 1 kpc, sedimentation may cause heavy metals to sink (Paquette et al. 1986; Dupuis et al. 1992), leaving only helium or carbon and oxygen in the atmosphere, depending on the initial composition of the companion, but anomalous abundances could potentially still be observable for the young runaway WDs from Tycho, Kepler, SN 185, and SN 1006. However, this statement depends on the existence and depth of a surface convection zone, the thermal profile, and, if the surface layers remain ≳2 × 10⁴ K, the competing effect of radiative levitation (Chayer et al. 1995a, 1995b). We regard the expected surface abundances to be uncertain and thus one of the motivations for follow-up spectroscopy.

Given the uncertainties in the observational characteristics discussed in the previous sections, the clearest and most obvious distinguishing feature of a surviving companion WD is its hypervelocity. The orbital velocity of a companion star during Roche lobe overflow (RLOF), which will be its runaway velocity once the primary WD explodes,²⁶ is a function of its mass, M₂, radius, R₂, and the mass of the exploding WD, M₁:

$$\begin{eqnarray}&&{v}_{\mathrm{runaway}}=\sqrt{\displaystyle \frac{{{GM}}_{1}^{2}}{({M}_{1}+{M}_{2})a}},\end{eqnarray} \tag{ 1 }$$

where the binary separation during RLOF, a, is approximated by Eggleton (1983) as

$$\begin{eqnarray}&&a=\displaystyle \frac{{R}_{2}}{0.49}\left\{0.6+{\left(\displaystyle \frac{{M}_{1}}{{M}_{2}}\right)}^{2/3}\mathrm{ln}\left[1+{\left(\displaystyle \frac{{M}_{2}}{{M}_{1}}\right)}^{1/3}\right]\right\}.\end{eqnarray} \tag{ 2 }$$

We calculate simple mass–radius relationships for isolated helium and C/O WDs, as well as for hydrogen- and helium-burning non-degenerate companions with the stellar evolution code MESA (Paxton et al. 2011, 2013, 2015, 2018). The resulting runaway velocities versus companion masses are shown in Figure 1. We assume the mass of the exploding WD ranges from 0.85 M_⊙ (lower boundary of each region) to 1.1 M_⊙ (upper boundary), as motivated by WD detonation calculations (Sim et al. 2010; Blondin et al. 2017; Shen et al. 2018).

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Both non-degenerate and degenerate SN Ia companions undergo processes that increase their radii compared to isolated stars. As discussed in Section 2.2, tidal effects in the D⁶ scenario lead to dissipation throughout the companion WD, including near its surface where it may cause radial expansion. In single-degenerate scenarios, the long pre-explosion phase of mass transfer pushes the donor out of thermal equilibrium and leads to "thermal bloating" (Knigge et al. 2011). Thus, the actual companion radii when the SN Ia explosion occurs may be slightly larger than the radii of isolated stars we find with MESA. However, since the companion's orbital velocity scales as the square root of its radius, a 10% increase in the radius, e.g., only corresponds to a 5% decrease in the velocities shown in Figure 1.

It is clear that the runaway velocities of surviving companion WDs will be markedly different from those of any other possible companions. A fiducial 0.6 M_⊙ companion to a 1.0 M_⊙ primary WD will have a runaway velocity of 1800 km s⁻¹, while the companion of a near-equal mass ratio 1.0 + 1.0 M_⊙ binary will have a velocity of 2200 km s⁻¹. At a distance of 1 kpc, these velocities translate to proper motions of 04–05 yr⁻¹ if the velocities are in the plane of the sky, easily detectable by Gaia and below the very high proper motions ≥06 yr⁻¹ where completeness becomes an issue (Gaia Collaboration et al. 2016; Brown et al. 2018).

As discussed in the previous sections, Gaia will only be able to detect surviving companion WDs that are relatively nearby (≤1 kpc) or that were reheated by historical SNe and have not yet dimmed significantly. The SN remnant most likely to host a surviving WD observable with Gaia is SN 1006, due to its proximity (≃2.2 kpc), low extinction, and lack of crowding (Winkler et al. 2003). Although Kerzendorf et al. (2018) did not detect any young WDs on the WD cooling track within this remnant, it is possible that the accreted iron-group elements have shifted the spectral energy distribution redward so that the surviving WD no longer sits on the WD cooling track. Indeed, some sources ≲1 mag redder than the cooling track do exist within the remnant; we will specifically target these and other sources within SN 1006's remnant in Section 3, as well as performing searches within the remnants of SN 185 (RCW 86) and Tycho's and Kepler's SNe.

In order to estimate the number of runaway WDs unassociated with historical SNe within 1 kpc of the Sun, we require a model for the stellar density as a function of position within the Milky Way. We assume all the stars reside in the thin disk, with an exponential scale length of 2.6 kpc, an exponential scale height of 300 pc, and a normalization that yields a total stellar mass of 5 × 10¹⁰ M_⊙ (Bland-Hawthorn & Gerhard 2016). We take the Sun's Galactocentric distance to be 8.2 kpc, its height from the midplane to be 25 pc, and the Milky Way's specific SN Ia rate to be ${10}^{-13}\,\mathrm{SNe}\,{\mathrm{yr}}^{-1}\,{M}_{\odot }^{-1}$ (Li et al. 2011b).

With these values and additional assumptions that the Galactic potential is negligible and that the runaway WDs all have the same velocity of 1800 (2200) km s⁻¹, we find the expected number of nearby runaway WDs to have a Poissonian distribution centered at 28 (23), with a 95% confidence interval of 17–39 (14–33). Of these, 22 (18) will be more than 10° off the plane of the Milky Way and thus will not be subject to significant extinction or crowding. These numbers are significantly higher than the ≲1 expected hypervelocity stars ejected from the Galactic center currently passing within 1 kpc (Hills 1988; Brown 2015), so we do not expect contamination to be a concern. Even if the rate of hypervelocity ejections from the Galactic center is much higher than previously thought, luminosities, colors, spectra, and whether or not their orbits intersect the Galactic center should allow us to easily differentiate between runaway WDs and hypervelocity stars.

The cumulative distribution function (CDF) of delay times, t_delay, between the SN explosion and the present for these local runaway WDs is shown in Figure 2. The average elapsed time for runaway WDs moving at 1800 (2200) km s⁻¹ is 2.3 × 10⁶ (1.5 × 10⁶) yr. As discussed in Section 2.2, this value is longer than the thermal timescale at the depth where gravity waves dissipate tidal energy, but it is shorter than the thermal timescale from the center of the WD to the surface. Thus, as long as significant tidal heating is deposited deep within the companion, these runaways should be visible to at least 1 kpc for Gaia's limiting magnitude of 21.

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A similar CDF of proper motion velocities, v_proper, is shown in Figure 3. Geometric effects imply that the velocity of the WDs in the plane of the sky will be smaller than their total velocities, but over 80% of the nearby runaway WDs will still have v_proper > 1000 km s⁻¹. At a distance of 1 kpc, 1000 km s⁻¹ translates to a proper motion of 02 yr⁻¹, which is much larger than the expected proper motion errors at Gaia's magnitude limit. Furthermore, while ∼20% of stars with proper motions ≥06 yr⁻¹ may be missing from DR2 (Gaia Collaboration et al. 2016), only the ∼1 runaway WD expected to be closer than 300 pc will be affected.

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The relatively small number (∼30) of expected local hypervelocity runaway WDs within 1 kpc is equivalent to the number of 6σ outliers in a normally distributed set of samples as large as Gaia's data set. We must therefore exercise caution in our search strategy in order to avoid being overwhelmed by false positives.

We begin by restricting the 1.3 × 10⁹ sources to those with proper motions above a conservative limit equivalent to 1000 km s⁻¹ at 1 kpc. For such proper motions μ ≥211 mas yr⁻¹, the fractional errors are <0.01, so we neglect them for simplicity. A ϖ > 3σ_ϖ cut is also applied, although two sources with ϖ < 3σ_ϖ (O1 and O3 in Table 1) were followed up prior to the implementation of this cut. The sources are then rank-ordered by ${v}_{3\sigma }\equiv \mu /(\varpi +3{\sigma }_{\varpi })$, where σ_ϖ is the parallax error. By including the 3σ_ϖ term, we are effectively calculating the proper motion velocity using the 3σ_ϖ upper bound for the parallax.

Table 1.  List of Candidate Hypervelocity WDs Followed up in This Work

Gaia DR2 ID	Nickname	R.A.	Decl.	Parallax	${\mu }_{{\alpha }^{* }}$ a	μδb	v3σc	P1000d	P1000–3000e
		(degrees)	(degrees)	(mas)	(mas yr−1)	(mas yr−1)	km s−1
5805243926609660032	D6-1	249.3819752	−74.3434986	0.471 ± 0.102	−80.3 ± 0.1	−195.9 ± 0.2	1293	1.00	0.79
1798008584396457088	D6-2	324.6124885	25.3737115	1.052 ± 0.109	98.4 ± 0.2	240.4 ± 0.2	894	0.98	0.98
2156908318076164224	D6-3	283.0078540	62.0361675	0.427 ± 0.126	9.0 ± 0.2	211.5 ± 0.3	1247	1.00	0.57
2050179518946705152	O1	291.3306894	36.4500600	0.237 ± 0.317	−137.6 ± 0.6	−214.7 ± 0.6	1018	1.00	0.17
4396109004117478656	O2	237.5476987	−7.8881665	2.186 ± 0.225	−359.7 ± 0.5	−228.4 ± 0.3	706	0.37	0.37
5884527618445501056	O3	238.9823874	−55.4937974	0.360 ± 0.571	90.0 ± 0.8	−268.9 ± 0.8	649	1.00	0.20
1820931585123817728	O4	296.3894478	17.2130727	0.574 ± 0.076	−82.4 ± 0.1	−149.5 ± 0.1	1010	1.00	1.00

Notes. This is not a complete list of the most highly ranked hypervelocity WD candidates. It only shows the stars that were followed up in this work.

^aHeliocentric proper motion in right ascension. ^bHeliocentric proper motion in declination. ^cHeliocentric proper motion velocity calculated using the 3σ_ϖ upper bound of the parallax. ^dProbability that the proper motion velocity is larger than 1000 km s⁻¹. ^eProbability that the proper motion velocity is bounded by 1000 and 3000 km s⁻¹.

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Since the fractional parallax errors can be ∼1, we apply a Bayesian framework to the top 500 entries to better quantify the posterior probability that the candidates are actually hypervelocity WDs. We use an exponentially decreasing space density distance prior (Astraatmadja & Bailer-Jones 2016),²⁷ assume the likelihoods of the parallaxes are normally distributed, and calculate posteriors

$$\begin{eqnarray}&&P(r| \varpi ,{\sigma }_{\varpi })=\displaystyle \frac{P(\varpi | r,{\sigma }_{\varpi })P(r)}{\int P(\varpi | r,{\sigma }_{\varpi })P(r)}.\end{eqnarray} \tag{ 3 }$$

Finally, we integrate the posterior with appropriate limits to find the probability, P₁₀₀₀, that the proper motion velocity is larger than 1000 km s⁻¹, and the probability, P_1000–3000, that it is bounded between 1000 and 3000 km s⁻¹.

Note that the calculated probabilities, P₁₀₀₀ and P_1000–3000, should not be taken literally, as they may be strongly influenced by the non-Gaussianity of the parallax distribution's tails above ∼4σ_ϖ (Luri et al. 2018). We merely use these probabilities as a guide for ranking our sources for follow-up.

We slightly alter our strategy to additionally search for surviving WDs within the four Galactic remnants of suspected SNe Ia: the remnant of SN 185 (RCW 86), at a distance of 2.0–3.0 kpc (Helder et al. 2013), the remnant of SN 1006 (2.1–2.3 kpc; Winkler et al. 2003), Tycho's SN remnant (3–5 kpc; Hayato et al. 2010), and Kepler's SN remnant (3–6 kpc; Sankrit et al. 2005; Chiotellis et al. 2012). We apply the same search strategy as above, but we relax our proper motion cuts to the equivalents of 1000 km s⁻¹ at the upper limits for the remnants' distances. We also restrict our search regions to circles around the geometric centers of the remnants with radii corresponding to proper motion velocities of 4000 km s⁻¹ at the lower limits for the distances. This high proper motion velocity accounts for the combination of the surviving companion WD's velocity and the initial velocity of the exploding WD and its remnant.

The Gaia source IDs of seven of the candidates that we were able to follow up with ground-based instruments are shown in Table 1, along with their nicknames, which we will use hereafter, astrometric parameters, values for v_3σ, and probabilities, P₁₀₀₀ and P_1000–3000. The associated photometry from Gaia, PS1 (Chambers et al. 2016), and Skymapper (Wolf et al. 2018) and the telescopes used to follow up the sources are shown in Table 2, along with comments about the individual stars. None of the searches within the Galactic SN Ia remnants revealed any obvious hypervelocity candidates.

The SALT data for D6-1 were obtained through Director's Discretionary Time (proposal 2017-2-DDT-005, PI: Jha) and made use of the Robert Stobie Spectrograph (RSS), with a 15 wide longslit and the PG0900 grating, resulting in a spectral resolution λ/Δλ ≈ 900 over the wavelength range 392–713 nm. The data were reduced with a custom pipeline that incorporates routines from PyRAF and PySALT (Crawford et al. 2010).

D6-2 and D6-3 were observed using the ALFOSC spectrograph on the Nordic Optical Telescope, located at Roque de Los Muchachos on La Palma. All observations were taken using Gr4, which covers the region from 3400–9000 Å at low resolution, and a 1'' slit oriented at the parallactic angle. Weather conditions were excellent, with seeing below 1''. Spectra were reduced using the dedicated pipeline ALFOSCGUI. Overscan and bias subtraction and flat-fielding were performed before 1D spectra were optimally extracted. The dispersion solution for the spectra was obtained from arc lamps taken with the same configuration as the science spectra at the start of the night. In addition, a linear wavelength shift was applied to each spectrum based on sky emission lines. Telluric absorptions have been corrected for using observations of a spectrophotometric standard. The resolution of the spectra (as measured from narrow sky lines in the spectra) was ∼15 Å, while the S/N ratio for D6-2 and D6-3 was ∼25.

Radial velocities (RVs) were measured via cross-correlation against the MILES library, comprising nearly 1000 stellar templates (Sánchez-Blázquez et al. 2006; Falcón-Barroso et al. 2011). We used the rvsao (Kurtz & Mink 1998) implementation of the Tonry & Davis (1979) algorithm. We find over 100 good matches in the template library for each of D6-1, D6-2, and D6-3, based on the reported r statistic (ranging from r = 4 to 8). We average the resulting RVs and take the scatter across templates to be indicative of the scale of potential systematic uncertainties. We note that cross-correlation among D6-1, D6-2, and D6-3 themselves results in a much higher r ≃ 15, showing that these spectra are much more similar to each other than they are to entries in the template library. The resulting RV shifts are shown in Table 3.

Figure 4 shows the spectra of D6-1, D6-2, and D6-3. An RV shift of 1200 km s⁻¹ is applied to D6-1, while the spectra of D6-2 and D6-3 are unshifted. The spectra contain a multitude of absorption features. No transitions of hydrogen or helium are detected, ruling out canonical atmosphere compositions (Kleinman et al. 2013). Comparison with unusual WDs identified by SDSS (Gänsicke et al. 2010; Gentile Fusillo et al. 2015; Kepler et al. 2016) clearly reveals strong features of carbon, oxygen, magnesium, and calcium in the three candidates. Based on their G_BP − G_RP colors, which are slightly redder than those of GD 492, SDSS 1102+2054, and SDSS 1140+1824 (see Section 4.3), we estimate effective temperatures of ≃8000 K. Determining accurate atmospheric parameters for stars with such unusual compositions will require higher-quality spectroscopy.

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As discussed in Section 2.3, the absence of hydrogen is expected for a surviving D⁶ WD, as it would have been transferred stably to the primary WD and ejected from the system prior to the explosion. The non-detection of helium is unconstraining due to the relatively low surface temperatures. In fact, in their modeling of GD 492, a hypervelocity star spectroscopically similar to our three candidates, Raddi et al. (2018b) found significant helium is required even though it is not directly observable.

Figure 5 shows a zoomed-in portion of the D6-1, D6-2, and D6-3 observed wavelength spectra, highlighting the region near the Ca ii H&K lines. It is clear that D6-1 has a radial velocity shift of 1200 km s⁻¹, as shown by the red lines. However, D6-2 and D6-3 have RVs consistent with being <100 km s⁻¹. These very low RVs cast doubt on the interpretation of these stars as hypervelocity stars: it seems unlikely that these stars would have a combination of very high proper motion velocities but very low RVs. As a check, all the Gaia proper motions were confirmed through examination of the fields of these candidates in epochs 1 and 2 of the Digitized Sky Survey, and also the Sloan Digital Sky Survey (Alam et al. 2015) for D6-2. In all cases the long baseline proper motions are consistent with Gaia's values. If we assume that the measured parallaxes of D6-2 and D6-3 are instead systematically incorrect and that the transverse velocities of D6-2 and D6-3 are a more typical 100 km s⁻¹, then the implied distances are ∼100 pc. This would suggest absolute magnitudes of G = 12–13. Thus, a possible interpretation is that these two objects are faint, nearby white dwarfs and that the parallax measurements have extremely large systematic uncertainties.

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On the other hand, the Gaia noise values for D6-2 and D6-3 imply clean measurements. Moreover, D6-1's extremely high RV makes its proper motion velocity credible.²⁸ Finally, the fact that all three candidates, selected for their extreme proper motion velocities, are similar to each other and to GD 492, another hypervelocity star (Vennes et al. 2017; Raddi et al. 2018a, 2018b), suggests that the proper motion velocities of D6-1, D6-2, and D6-3 are indeed very high.

To emphasize the extreme nature of D6-1, D6-2, and D6-3, Figure 6 shows the posterior distributions of their total Galactocentric velocities. These posteriors were derived by sampling the distance posteriors (Equation (3)), as well as sampling the RVs and proper motions within their assumed Gaussian uncertainties, and applying a heliocentric to Galactocentric coordinate transformation with astropy (The Astropy Collaboration et al. 2018).

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Further velocity information is listed in Table 3. D6-1, D6-2, and D6-3 have high probabilities of being three of the fastest known stars in the Milky Way, possibly only surpassed by pulsars kicked from core-collapse SNe and the stars in close orbit around the Galactic center.

Samples of the orbital solutions for the candidate hypervelocity stars are shown in Figures 7–9, calculated with galpy (Bovy 2015) and assuming an MWPotential2014 gravitational potential and an exponentially decreasing space density distance prior as before. It is clear that all three candidates are unbound from the Milky Way and that almost none of the orbital solutions passes near the Galactic center. Taken as a group, it is highly unlikely that the hypervelocity nature of these stars is due to Galactic center ejection.

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In Figure 10, we show a color–magnitude diagram using Gaia's G_BP − G_RP color and the absolute Gaia G-band magnitude, assuming the measured values of the parallax. The black points and colored regions show a random sub-sample of 5.7 × 10⁶ stars from Gaia DR2 with accurate parallaxes (ϖ/σ_ϖ > 30), clean astrometry (astrometric_excess_noise <1), and low reddening ($| b| \gt 30^\circ$). Our three hypervelocity candidates, GD 492 (Vennes et al. 2017), US 708 (Hirsch et al. 2005; Justham et al. 2009; Geier et al. 2015), and the three peculiar SDSS WDs from Figure 4 are shown as colored symbols.

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D6-1, D6-2, and D6-3 form a relatively tight grouping in color–magnitude space that includes GD 492. These four stars currently have radii between typical WDs and main sequence stars, similar to subdwarf stars; GD 492's radius is estimated to be 0.2 R_⊙ (Raddi et al. 2018a). However, if they had previously been helium-rich subdwarf companions of exploding WDs in SN Ia systems, Figure 1 shows that their velocities would be well below 1000 km s⁻¹. There have been some suggestions that GD 492 is instead the bound WD remnant of a Type Iax supernova explosion that has received a large kick due to asymmetric mass ejection or due to the disruption of the binary system upon instantaneous mass loss (Vennes et al. 2017; Raddi et al. 2018a, 2018b). However, the predicted kicks in these systems due to asymmetric mass ejection range from only ten to several hundred km s⁻¹ (Fink et al. 2014; Long et al. 2014), far below the observed velocities of the D⁶ stars. The orbital velocity of a Chandrasekhar-mass WD in a tight binary with a helium star can approach GD 492's velocity, but it cannot explain the even higher velocities of D6-1, D6-2, and D6-3.

These three stars, and possibly also GD 492, may instead be the surviving companion WDs of D⁶ SNe Ia. While they are clearly not typical WDs now, mechanisms discussed in Section 2.2 that were active during the phase of dynamical mass transfer prior to the SN Ia and the post-explosion evolution may have deposited enough energy to lift the degeneracy of the outer layers and cause the WDs to temporarily appear as subdwarf stars just after the explosion.

Our expectation was that most of the excess energy would be deposited near the surface of the WD, where it would be radiated away on relatively short timescales, so that the stars would quickly return to being dim, typical-looking WDs. This could indeed be true, making it difficult to observe the majority of the runaway WDs in the solar neighborhood. However, a small fraction of these stars will have experienced SNe Ia much more recently than the average runaway WD, possibly rendering them still bright enough to observe.

A similar calculation to the one described in Section 2.5 yields 300 − 400 runaway WDs within the ∼65 kpc³ volume in which we observed D6-1, D6-2, and D6-3. If we include GD 492, we have observed 1% of the potential nearby runaway WDs, which corresponds to stars ejected more recently than ∼4 × 10⁴ yr (Figure 2). Thus, D6-1, D6-2, D6-3, and possibly GD 492 may just represent the small portion of runaway WDs that have been violently altered by SNe Ia so recently they have yet to evolve back into typical-looking WDs.

US 708, a hypervelocity helium-rich subdwarf, sits blueward of this group. It is possible that, as stars like D6-1, D6-2, D6-3, and GD 492 radiate the deposited energy and contract, the unseen helium that Raddi et al. (2018b) require in their best-fit models of GD 492's spectrum becomes directly observable as the photosphere becomes hotter. Thus, these stars could evolve to appear like US 708 on their way back to the WD cooling track. Future observations and detailed stellar evolution calculations and spectral modeling will help to test all of these intriguing possibilities.

Motivated by the possibility that these four stars may have been ejected from the sites of SNe Ia ∼4 × 10⁴ yr ago, we search for existing SN remnants along their past orbital solutions up to their positions ∼10⁵ yr ago. We use the online catalogs of D.A. Green²⁹ and G. Ferrand,³⁰ as well as the Open Supernova Catalog³¹ (Guillochon et al. 2017). Additionally, we searched data from the ROSAT All-Sky Survey for SN remnant sources that emit soft X-rays.

For stars D6-1, D6-3, and GD 492 we find no SN remnant candidate sources along the past velocity vectors. We note that this does not rule out their association with a supernova, because SN remnants can dissipate into the interstellar medium on timescales ranging from a few thousand years up to a few hundred thousand years, depending on the remnant. Furthermore, the regions around these three stars lack high-quality Hα imaging, so limits on the non-existence of remnants are not constraining.

However, as shown in Figure 11, D6-2's position 9 × 10⁴ yr in the past places it 0.9 deg from the approximate geometric center of the faint, old SN remnant G70.0–21.5. This remnant, first identified by Fesen et al. (2015), consists of a shell of Hα filaments, along with several other spectral lines only associated with slowly moving, radiative shocks from an old SN remnant. Additionally, Fesen et al. (2015) reported faint ROSAT X-ray emission from near the center, another indication of a supernova remnant.

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Of the known remnants, G70.0–21.5 lies furthest from the Galactic plane, suggesting it was produced by a Type Ia supernova. The distance to G70.0–21.5 inferred from its shock velocities is 1–2 kpc, consistent with D6-2's parallax-measured distance of 1.0 ± 0.1 kpc. Fesen et al. (2015) also conclude that the remnant is quite old, perhaps between several 10⁴ and 10⁵ yr. The probability of a chance alignment between D6-2's past position and the projected center of an unassociated SN remnant that is at a consistent distance and has a consistent age is likely very small, especially given the lack of any other obvious SN remnants in the VTSS images of this region. However, this probability should be quantified in future work.

At a distance of 1 kpc, G70.0–21.5's height below the Galactic plane is 400 pc, matching D6-2's height 10⁵ years ago. D6-1 and D6-3 were farther from the plane at that time: 700 and 1200 pc, respectively. Such offsets are reasonable since SNe Ia can occur in old stellar populations and the thick disk's scale height is 900 pc (Bland-Hawthorn & Gerhard 2016). Furthermore, D⁶ survivors that were recently ejected from closer to the Galactic plane would suffer higher extinction and could be unobservable. Thus, these three D⁶ candidates may represent more than just 1% of the 300 − 400 expected survivors within 2.5 kpc, after accounting for those that remain obscured at low Galactic latitudes.

While D6-2 did not pass exactly through G70.0–21.5's center as reported by Fesen et al. (2015), the approximate determination of the center of this aspherical remnant makes such a comparison difficult. Moreover, G70.0–21.5's advanced age means that its appearance is heavily influenced by the structure of the inhomogeneous surrounding interstellar medium, further complicating determination of the site of the explosion. We thus do not regard the 0.9 deg offset between D6-2's past position and Fesen et al. (2015)'s reported center as evidence against the association.

It is not possible to rule out other SN remnants present in this field that are even older, fainter, and more diffuse than G70.0–21.5. At some point, as SN remnants age, they simply dissolve away into the interstellar medium, below any possible threshold of detection. Nonetheless, the close association between D6-2 and a known SN remnant, G70.0–21.5, is quite tantalizing. Though the remnant is at a very advanced evolutionary stage, it may be possible to follow up the X-ray emission with deeper observations to determine the ejecta abundances, and thus, the SN type. We note that while none of the other hypervelocity runaway candidates are associated with known SN remnants, they also all lack high-quality Hα imaging, which is how G70.0–21.5 was discovered. Future observations will ascertain if any of the remaining candidates' remnants are observable but are so faint they have been missed by previous lower-quality searches.