PROPER MOTIONS AND TRAJECTORIES FOR 16 EXTREME RUNAWAY AND HYPERVELOCITY STARS^*

We obtained 6.5 m MMT Blue Channel spectroscopy of the four bound velocity outliers in four different observing runs in 2006 February, 2008 February, 2010 March, and 2014 March. We used the 832 I mm⁻¹ grating in 2nd order with a 1 arcsec slit, providing 1.0 Å spectral resolution over the range 3600–4500 Å. In addition, we observed B485 a second time with a 0.75 arcsec slit to test higher 0.75 Å spectral resolution. We paired every observation with a He–Ne–Ar comparison lamp exposure for wavelength calibration. We chose exposure times to achieve S/N = 50–100 per resolution element in the continuum.

We process and extract the 1D spectra using IRAF.⁵ We measure radial velocities using the cross-correlation package RVSAO (Kurtz & Mink 1998). We then measure effective temperature ${{T}_{{\rm eff}}}$, surface gravity ${\rm log} g$, and projected rotation $v{\rm sin} i$ using stellar atmosphere models as described in Brown et al. (2014). Figure 1 compares the best-fit stellar atmosphere models to the observed spectra. All four bound velocity outliers are late B-type stars, and B733 has significant projected rotational velocity $v{\rm sin} i$ = 240 ± 30 km s⁻¹.

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Our sample contains 15 B-type stars plus the sdO star HVS 2. Figure 2 displays the adopted effective temperature ${{T}_{{\rm eff}}}$ and surface gravity ${\rm log} g$ for the 15 B-type stars in our sample, plotted in comparison to Padova solar metallicity main-sequence tracks (Girardi et al. 2004; Marigo et al. 2008; Bressan et al. 2012). HVS 2 does not appear because it is a ${{T}_{{\rm eff}}}$= 45,560 K sdO star. The clumping of stars in Figure 2 reflects the HVS Survey target selection of stars with the colors of 3 ${{M}_{\odot }}$ main-sequence stars.

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Notably, all four stars with high resolution echelle spectroscopy are fast rotators. Another five B-type stars have statistically significant $v{\rm sin} i$ $\;\geqslant \;150$ km s⁻¹ on the basis of our moderate resolution MMT spectroscopy. Fast rotation is the unambiguous signature of a main-sequence B star. For reference, the mean $v{\rm sin} i$ of late B-type stars is 150 km s⁻¹ (Abt et al. 2002; Huang & Gies 2006). Evolved horizontal branch stars of the same temperature and surface gravity, on the other hand, are slow rotators with $v{\rm sin} i$ $\;\lt \;7$ km s⁻¹ (Behr 2003). Thus these B-type stars are main-sequence stars.

We compare the measured stellar atmosphere parameters to Padova main-sequence stellar evolution tracks to estimate luminosities (Girardi et al. 2004; Marigo et al. 2008; Bressan et al. 2012). Propagating the measurement uncertainties through the stellar evolution tracks implies that our luminosity estimates are precise to 30% in luminosity, or 15% in distance. The precision is relatively poor because surface gravity is our primary constraint on evolutionary status, and the luminosities of B stars increase with age.

The choice of stellar evolution tracks is a source of systematic uncertainty. With the exception of HVS 3 and HVS 7, which have solar iron abundance (Przybilla et al. 2008a, 2008b), the metallicity of the HVSs is unconstrained. If the HVSs are systematically metal-rich or metal-poor, our distance estimates could be systematically wrong by ∼25% (e.g., Bressan et al. 2012). Given that the HVSs are relatively short-lived main-sequence B stars, however, we consider solar metallicity a reasonable assumption.

We calculate heliocentric distance using the de-reddened g-band point-spread function (PSF) apparent magnitudes from Sloan Digital Sky Survey (SDSS) Data Release 10 (DR10; Ahn et al. 2014), except for HVS 3 which has a V-band measurement (Bonanos et al. 2008). The SDSS magnitudes have a typical precision of 2%; however in some cases the DR10 g-band magnitude differs from previous SDSS data release values by as much as 10%. The SDSS photometry is thus an additional source of uncertainty, but a small fraction of the total error budget.

Table 1 summarizes the measured and derived properties for the 16 stars. We adopt parameters from published echelle spectra when available; otherwise we adopt parameters derived from our MMT spectra. The stellar atmosphere parameters for the four bound velocity outliers are new.

We imaged the 16 stars using the HST ACS and WFC3/UVIS instruments starting in 2006 September and ending in 2013 March. We obtained images in a few different ways; Table 2 lists the full set of observations.

We first observed HVS 1–HVS 5 using ACS in 2006 (proposal ID 10824). Each star was allocated one orbit, and was observed with a set of 4–7 dithered exposures. Exposure times were chosen to maximize counts on background galaxies while not saturating the HVSs. We obtained a second epoch of observations with ACS in 2009 (proposal ID 11782). For HVS 1–HVS 4, we then obtained a third epoch of observations using WFC3 (proposal ID 12503). We allocated two orbits of time per star in the third epoch, but dropped HVS 5 because its field contained few useful background galaxies. The time baseline of observations for HVS 1–HVS 4 is thus about 6.2 yr, and for HVS 5 it is 3.0 yr.

We observed the other 12 stars exclusively with WFC3 beginning in 2009–2010 (proposal ID 11589). Each star was allocated one orbit of time and observed with a set of dithered exposures. For the brightest six stars, however, we divided the exposures into a set of short $\simeq$1 minute and deep $\simeq$10 minute exposures. Our goal was to optimally expose the bright HVSs and faint background galaxies in the short and deep exposures, respectively, and to tie their astrometric frames together using the intermediate brightness stars available in both sets of exposures. In practice, the finite number of intermediate brightness stars limits the accuracy of this approach. We obtained a second epoch of observations with WFC3 in 2012–2013 (proposal ID 12662) in the same way. The time baseline of the observations is 3.0 yr for these 12 stars.

We made an effort to use the same telescope orientation across all epochs of imaging in order to minimize the impact of changes in charge-transfer efficiency (CTE) and errors in the distortion solution. The effects of CTE increase with time as on-orbit radiation damage creates more and more charge traps in the CCD silicon lattice. The result is that star and galaxy images are trailed along the CCD read-out direction. If we observe in the same orientation in all epochs, the CTE systematic is in the same direction and we minimize its impact on our differential position measurements. Unfortunately, we were unable to use the same guide stars for HVS 2, HVS 3, and HVS 4 in all epochs due to changes in the HST guide star catalog. This issue forced a change in orientation, which exacerbates the astrometric effects of CTE. Table 2 lists the position angle (PA), defined as increasing east of due north, for each observation.

We begin our data reduction procedure by downloading flat-fielded images from the Mikulski Archive for Space Telescopes. Because the CTE correction for WFC3/UVIS images and ACS subarrays is not integrated into the standard pipeline, we run the Anderson & Bedin (2010) pixel-based correction by hand. The CTE correction is calibrated on hot pixels and their charge trails, and is successful at removing the trails behind stars, cosmic rays, and hot pixels, and restoring the flux to the stellar images.

We start our analysis with the first-epoch images. We use empirical models of the ACS and WFC3/UVIS PSFs to measure positions for stars in the CTE-corrected frames of each first epoch exposure. We then correct the positions for geometric distortion using the model in Anderson & King (2006) for ACS and the model in Bellini et al. (2011) for WFC3/UVIS. Finally, we cross identify the stars and define a linear transformation from the distortion-corrected positions of each star in each exposure into the distortion-corrected frame of the first exposure.

Since all of the first-epoch images were taken in a single orbit, we can safely use the stars to define the transformations. This cannot be done for the later epochs, since the stars are all moving, and we need to know the motion of each target star in an inertial frame. Therefore, we use the background galaxies to define the transformation from each exposure into the reference frame. Although all stars can be fit with the same PSF, each galaxy has its own unique distribution of light and must be measured with its own template. An additional complication is that some images were taken at different orientations or with different instruments, such that the PSF for a given object might be different from epoch to epoch, affecting the observed distribution of light. For this reason, we construct templates for each galaxy with a deconvolved model, such that when we fit the template to the pixels in an image, we first convolve it with the PSF appropriate for that location in that detector. This approach ensures that the stars (which are simply delta functions when deconvolved) and galaxies are measured consistently within an exposure.

We construct the star and galaxy templates from the exposures in the first-epoch data set. The transformations (based on the stars) enable us to accurately map the pixels of all exposures into the reference frame. For each source, we collect all the pixels that map to within the 11 × 11 region about each source (galaxies and stars). We then use iterative forward modeling to construct a deconvolved template for each source. The template for the stars is simply a delta function. The template for the galaxies is a smooth empirical image that, when convolved with the PSF, best described the distribution of light in the contributing exposures. We allowed the galaxies to have an additional point source at their centers, but most did not need one.

We then use these templates, convolved with the appropriate PSF, to measure consistent positions for every source in every exposure in each epoch. We examine the fitting residuals for each source and reject the measurements that were clearly contaminated by cosmic rays or unidentified warm pixels. Measured positions are in the raw frame and must be corrected for geometric distortion, as mentioned above. Next, we use the positions for the galaxies to define the linear transformation from the distortion-corrected frame of each exposure into that of the first exposure of the first epoch. We examine the transformation residuals for each galaxy and reject those galaxies with unreliable and inconsistent positions. This leaves us with 10–15 high quality galaxies for each field. From the residuals, we infer that the transformations are typically good to ±0.93 mas, which corresponds to a 0.31 mas yr⁻¹ systematic uncertainty in the reference frame for a 3 yr time baseline. The systematic uncertainty is a noise floor to all of our measurements.

Finally, we use these galaxy-based transformations to map the position for each star in each exposure into the reference frame, and then solve for the proper motions. Mathematically, the proper motion calculation boils down to a linear least squares fit to the x and y positions versus time of observation, which we know exactly. We convert the x and y pixel motions into mas yr⁻¹ using the appropriate camera pixel scale, image rotation angle, and time baseline of observations. Proper motion uncertainties are determined from the scatter in x and y positions at each epoch, and added in quadrature to the uncertainty of the galaxy reference frame. Total measurement uncertainties range from ±0.35 mas yr⁻¹ for the case of HVS 1, which has a 6.36 yr time baseline of observations, to ±1.33 mas yr⁻¹ for the case of HVS 7, which has only 8 useable reference galaxies. Our final proper motion measurements are in Table 1.

Our proper motion measurements are a six-fold improvement over previous measurements. One of the most accurate proper motion catalogs available today is the UCAC 4, which covers the entire sky to a depth of R = 16 mag (Zacharias et al. 2013). One of our stars, B733, is bright enough to have a UCAC 4 measurement. The UCAC 4 total proper motion for B733, ${{\mu }_{{\rm UCAC}\,4,{\rm B}733}}=13.9\pm 6.6$ mas yr⁻¹, agrees to within 1.5σ of our measurement ${{\mu }_{{\rm B}733}}=4.1\pm 1.2$ mas yr⁻¹. Another catalog is PPMXL (Roeser et al. 2010), which combines 2MASS and USNO-B astrometry. Only B733 is bright enough to have a 2MASS measurement, and the PPMXL total proper motion ${{\mu }_{{\rm PPMXL},{\rm B}733}}=6.3\pm 6.8$ mas yr⁻¹ is in perfect agreement with our measurement. The SDSS survey probes much deeper and, when combined with USNO-B astrometry (Monet et al. 2003), provides proper motion measurements for all of our sample except HVS 3. The average SDSS-USNO-B proper motion uncertainty for our stars is ±5.3 mas yr⁻¹, and only one star, HVS 5, has a SDSS proper motion that differs from zero at greater than 1.5σ significance. In contrast, our HST measurements have an average proper motion uncertainty of ±0.8 mas yr⁻¹, and thus are 6.6 times more accurate.

At first glance, the stars have small proper motions and thus largely radial trajectories. Twelve of the stars have proper motions statistically consistent with zero. Only HVS 2, B434, B485, and B733 have proper motions that differ from zero at better than 3σ significance.

For distant stars, however, the reflex motion caused by the Sun orbiting the Milky Way can dominate the apparent proper motion. The direction and amplitude of solar reflex motion depends on the location and distance of the star. Thus, a correct interpretation of the proper motion measurements requires that we calculate trajectories.

As a first step, we adopt a fixed distance, radial velocity, right ascension, and declination (those listed in Table 1) for each star, and then calculate each trajectory backward in time for all possible proper motions that cross the Galactic plane. We use the Kenyon et al. (2014) three component bulge-disk-halo potential model for the trajectory calculations. This potential model uniquely fits observed mass measurements from the Galactic center to the outer halo, but was originally constructed for a 220 km s⁻¹ circular velocity (Kenyon et al. 2008). Updating the disk mass ${{M}_{d}}=6\times {{10}^{10}}$ ${{M}_{\odot }}$ and disk radial scale length a_d = 2.75 kpc yields a flat rotation curve of 235 km s⁻¹ consistent with the most recent circular velocity measurements (Reid et al. 2014). We refer to this potential model as the Kenyon et al. (2014) model, and use it in all of our trajectory calculations.

Assuming a fixed distance, radial velocity, right ascension, and declination (those listed in Table 1), Figure 3 compares our measured proper motions to the results of our trajectory calculations. The green and blue ellipses show the locus of proper motions with trajectories that pass within 8 and 20 kpc, respectively, of the Galactic center. Statistically, all of our stars have proper motions consistent with a Milky Way origin. Our strongest constraints are for the three closest stars that have significantly non-zero proper motions: HVS 2, B711, and B733. To evaluate the likelihood of a more exact origin requires that we account for all of the measurement errors, in proper motion, radial velocity, and distance.

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HVS 2 is a helium rich sdO star with a 708 ± 15 km s⁻¹ heliocentric radial velocity (Hirsch et al. 2005). The two proposed explanations for its extreme motion are an ejection by the central MBH (Hirsch et al. 2005; Perets 2009) or a Type Ia supernova explosion (Justham et al. 2009; Wang & Han 2009).

HVS 2 has a significant proper motion of $({{\mu }_{{\rm R}.{\rm A}.}},{{\mu }_{{\rm Decl}.}})$ $=\;(-7.33\;\pm \;0.58,2.28\;\pm 0.55)$ mas yr⁻¹. Our measurement is based on three epochs of imaging and therefore has a very well understood error distribution. Given HVS 2's 18.5 ± 2.6 kpc heliocentric distance (Hirsch et al. 2005), the observed proper motion corresponds to a 673 ± 118 km s⁻¹ tangential motion. HVS 2's tangential motion is quite similar to its radial velocity. Thus its space motion in the rest frame of the Milky Way is almost exactly 1000 km s⁻¹(!).

The direction of HVS 2's proper motion takes its trajectory across the Galactic plane at R = 76.5 kpc. This result implies that HVS 2 originates from the stellar halo, possibly launched by a Type Ia supernova explosion as proposed by Justham et al. (2009) and Wang & Han (2009). If HVS 2's distance and proper motion are 1σ smaller, however, its tangential motion is less extreme and it crosses the Galactic plane around R = 20 kpc (see Figure 4). Thus an ejection from the disk is a viable possibility.

A Galactic center origin for HVS 2, on the other hand, is ruled out at greater than 3σ confidence. HVS 2's closest approach to the Galactic center, given the measurement errors, is R = 4.5 kpc among our 1,000,000 Monte Carlo trajectory calculations. In other words, the extreme velocity of HVS 2 cannot be explained by a dynamical interaction via gravitational interaction with the central MBH. Instead, it is an example of a hyper-runaway star.

Wang & Han (2009) perform ejection calculations for helium star companions to white dwarfs that explode in Type Ia supernovae. In this model, the helium stars receive a kick perpendicular to their orbital velocity for total ejection velocities of 500–650 km s⁻¹. Similarly, Geier et al. (2013) calculate a 600 km s⁻¹ velocity from their Type Ia supernova ejection model. Given these ejection velocities, the Type Ia supernova model cannot explain HVS 2's 1000 km s⁻¹ motion with a disk ejection; HVS 2's trajectory is not even in the direction of Galactic rotation (Figure 4). Tauris (2015)'s aysmmetric core-collapse supernova model can produce 1000 km s⁻¹ velocities for low mass stars. However, there would not be enough time for a low mass star to evolve into an sdO star before its core-collapse companion launches it out of the Galaxy. The remaining possibility is that HVS 2 was launched by a Type Ia supernova from a halo binary traveling at ∼400 km s⁻¹ in its current direction of motion.

Alternative origins seem less likely. For example, Abadi et al. (2009) propose that the tidal disruption of a dwarf galaxy can explain unbound stars. This mechanism requires the close peri-center passage of a fairly massive $\gt {{10}^{10}}$ ${{M}_{\odot }}$ dwarf to produce unbound stars (Piffl et al. 2011). The non-Galactic-center trajectory of HVS 2, plus the absence of other unbound stars around it, would appear to rule out the dwarf galaxy tidal debris origin. Additional evidence for a Type Ia supernova explosion, perhaps found in the abundance pattern of HVS 2's stellar atmosphere, would better support the supernova origin picture.

B711 and B733 are both bound B-type stars at modest 9–17 kpc distances, and thus plausible candidates for being runaway B stars ejected from the disk. Alternatively, they could be failed HVSs on bound trajectories from the Galactic center. Their radial velocities in the Galactic frame are 290 and 440 km s⁻¹, respectively. In the absence of a positive $v{\rm sin} i$ measurement for B711, it is also possible that B711 could be an evolved low mass star (i.e., a hot horizontal branch star) orbiting in the stellar halo. The fact that B733 is a rapidly rotating 2.5 ${{M}_{\odot }}$ main-sequence star with a 349 km s⁻¹ heliocentric radial velocity, however, requires that it was ejected from a location in the Galaxy with recent star formation.

We measure proper motions that point to a disk runaway origin for both stars. The stars formally cross the Galactic plane at R = 10 kpc (Figure 4). A Galactic center origin is ruled out at greater than 3σ confidence for both stars.

The trajectories of B711 and B733 cross the Galactic plane at angles nearly perpendicular to Galactic rotation, however, implying disk ejection velocities of 533 and 441 km s⁻¹. The supernova ejection mechanism is able to achieve 500 km s⁻¹ velocities for main-sequence stars only in extreme scenarios (Tauris 2015). The dynamical ejection mechanism can achieve 500 km s⁻¹ velocities for main-sequence stars but requires 3-body interactions with contact binaries containing 100 ${{M}_{\odot }}$ stars (Gvaramadze et al. 2009; Gvaramadze & Gualandris 2011). Stars with 100 ${{M}_{\odot }}$ are rare and short-lived. Simulations suggest that perhaps 0.1% of dynamical ejections reach 500 km s⁻¹ velocities (Perets & Subr 2012). The upshot is that we expect to find more Galactic center ejections than disk runaway ejections at these speeds (Bromley et al. 2009; Perets & Subr 2012; Kenyon et al. 2014). The fact that B711 and B733 are $\simeq 500$ km s⁻¹ disk runaway ejections is thus quite intriguing.

Because extreme runaway ejections require massive stars with relatively short lifetimes, we expect B711 and B733 to have flight times similar to their stellar ages. Our proper motions correspond to trajectories with 20–40 Myr flight times from the disk. Our spectroscopic ${\rm log} g$ measurements favor young ages for both B711 and B733 (see Figure 2), however the uncertainties are large and no statistically meaningful constraint is currently possible. High resolution echelle spectroscopy of B711 and B733 would thus be very interesting. B733 is clearly a main-sequence star on the basis of its rapid rotation, and its trajectory is thus evidence for an extreme stellar dynamical ejection from the disk like that seen for HD 271791 (Heber et al. 2008) and HIP 60350 (Irrgang et al. 2010).

HVS 3 is the unbound 9 ${{M}_{\odot }}$ main-sequence B star near the LMC on the sky (Edelmann et al. 2005). If HVS 3 comes from the LMC, then its speed is evidence for a MBH hidden somewhere in the LMC (Gualandris & Portegies Zwart 2007). If HVS 3 comes from the Milky Way, then its speed and stellar nature are evidence of a former binary HVS ejection (Lu et al. 2007; Perets 2009). Both origins are unlikely in terms of ejection rates.

In 2010, we published a proper motion for HVS 3 that pointed to a Milky Way origin (Brown et al. 2010). This measurement was based on two epochs of ACS imaging with a 3.46 yr time baseline. The readout direction of the ACS CCD was unfortunately aligned with the Milky Way-LMC direction, however, and added an additional systematic uncertainty. We now have a third epoch of WFC3 imaging, obtained at an orientation angle 90 deg from the previous data sets, that doubles our time baseline. Our expectation is that HVS 3's intrinsic motion now dominates the errors. We re-process and re-analyze the epoch 1 and 2 data in the same way as the epoch 3 data, so that everything is in a common reference frame.

Figure 5 presents the results. We plot in panel (a) the position of HVS 3, relative to its mean position, as measured in each individual image. Different epochs are identified by color, and the scatter in positions reflects the underlying precision of our measurements. We observe that HVS 3 moves 10.6 ± 5.0 mas, or 0.27 WFC3 pixels, in 6.15 yr. This motion is quantified in figure panels (b) and (c), which plot the R.A. and decl. positions of HVS 3 versus time. The solid lines in each panel show the linear least squares fit to the measurements. The proper motion of HVS 3 is $({{\mu }_{{\rm R}.{\rm A}.}},{{\mu }_{{\rm Decl}.}})$ = (0.52 ± 0.58, 1.65 ± 0.57) mas yr⁻¹.

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As fate would have it, our HVS 3 proper motion corresponds to a physical trajectory that passes in-between the Milky Way and LMC. Figure 5 panel (d) is identical to Figure 3 except that we now draw the locus of HVS 3 proper motions with trajectories that pass within 3 kpc of the LMC (red ellipse). A 3 kpc radius encompasses the full extent of the LMC bar and all of the young clusters proposed by Gualandris & Portegies Zwart (2007) for the origin of HVS 3. We determine HVS 3's distance to the LMC in Figure 5 assuming that the LMC has a mass of 2 × 10¹⁰ ${{M}_{\odot }}$ moving on an orbit that reproduces the line-of-sight velocity from van der Marel (2001) and the proper motion from Kallivayalil et al. (2006, 2013) in our Milky Way potential model. If we account for the uncertainties in HVS 3 and LMC distances, then both LMC and Milky Way origins are consistent with the measurements at the 1σ level.

The ambiguity on origin is driven by our epoch 3 measurements, which exhibit a larger shift, and scatter, in position than seen in epochs 1 and 2. This result is visually apparent in Figure 5. Fitting only the epoch 1 and 2 measurements yields $({{\mu }_{{\rm R}.{\rm A}.}},{{\mu }_{{\rm Decl}.}})=(0.10,0.89)$ mas yr⁻¹, in 1σ agreement with our previously published value (Brown et al. 2010). Fitting only epoch 2 and 3 measurements, on the other hand, yields $({{\mu }_{{\rm R}.{\rm A}.}},{{\mu }_{{\rm Decl}.}})=(1.01,2.52)$ mas yr⁻¹. Clearly, the third epoch drives the proper motion to larger values, and thus causes HVS 3's trajectory to move away from the Milky Way in physical space.

We repeat our measurement and analysis for HVS 3 using only the five best galaxies and obtain essentially the same result. Our reference frame thus appears robust. We speculate that the F850LP filter, chosen to maximize S/N on the background galaxies while not saturating the bright blue star, may be partly to blame. The F850LP filter has a less well-calibrated distortion solution than the F814W and F606W filters, which were used for all of our other observations. The other HVSs with three epochs of data all have less scatter between epochs: the proper motions derived from epochs 1 and 2 and derived from epochs 2 and 3 agree at the 1σ level, except for the decl. motion of HVS 2 that differs by 2σ. Residual CTE systematic error is also a possible problem for the HVS 3 observations. Answering the question of HVS 3's origin will ultimately require a proper motion measurement with a longer time baseline of observations, or else a better instrument like Gaia.