Hubble Space Telescope Snapshot Survey for Resolved Companions of Galactic Cepheids: Final Results^{* †}

For these close companions lying within the PSF wings of the bright Cepheid primaries, we proceeded as follows. The data processing started with the geometrically distorted, flat-fielded individual frames (FLT images) from the HST archive. We then applied a custom data-reduction procedure to deal with saturation and charge bleed.

4.1.1. Masking the Charge Bleed

4.1.2. Combining Exposures

4.1.3. Cutting Out Subimages

Sources more than 2'' from the Cepheid are discussed in Paper II and Section 3 above. In this section, we study the region within 2'', where the image is dominated by the PSF of the Cepheid.

4.2.1. Locally Optimized Combination of Images (LOCI)

In order to detect and perform photometry on potential companions, we need to subtract the PSF of the Cepheid itself. This is challenging because the HST PSF changes with time. Several observational and computational approaches to detect faint sources close to a much brighter primary have been developed in the past years, especially with an application to exoplanets. One of the most common observational techniques is angular differential imaging, where the same source is observed more than once with a different orientation of the instrument, such that instrumental features rotate on the sky, but true companions are fixed in sky coordinates. The scheduling of a snapshot program did not allow for this approach, so we are limited to computational methods to reduce the impact of the Cepheid PSF. Lafrenière et al. (2007) introduced a method called LOCI; see their paper for a mathematical description of the algorithm. In short, this algorithm describes an image as a linear combination of companion-free reference images. The coefficients that lead to the smallest residual between target image and the combination of reference images can be found essentially by a matrix inversion, which is computationally more efficient than numerical function minimizers. Fitting the whole image at once would introduce two major problems. First, the temporal change in the PSF might depend on the position, e.g., some parts of the PSF change more than others due to a temperature change of the telescope. Describing the full image at once thus requires a large number of reference images. Second, if a companion exists and is included in the fit, the fit will try to subtract it as much as possible, compromising the photometry. Thus, for LOCI the image is divided into several smaller regions. To find the best linear combination of templates for a specific region, we perform the optimization on an area that is outside the region of interest (see Figure 1).

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4.2.2. Modification of Standard LOCI Procedures

Several enhancements of the LOCI method developed by Lafrenière et al. have been suggested in the literature, including template LOCI (Marois et al. 2014), which considers spectral information, or matched LOCI (Wahhaj et al. 2015), which inserts artificial point sources with known properties to inform the fitting process. Another approach is to decompose the set of PSF templates into eigenimages, thus using information from all images to isolate the true PSF components and separate them from observational noise that varies from image to image (Soummer et al. 2012). After reviewing these ideas in the literature, we modified the basic LOCI algorithm for the specific characteristics of our data set.

For any one Cepheid observation, we use the set of the other 69 observations taken in the same filter in our program as template images. This is justified because they are all taken within a few months of each other, use an identical instrumental setup (except for the exposure time), and all expose the central source well into saturation, bringing out faint PSF features visible beyond 2'', which are generally hidden in the noise for other archival data taken in the same filter. The drawback of this method is that some of the template images might themselves contain companions, which would leave negative imprints on the reduced images. We thus perform an initial source detection (see next subsection) and mask regions potentially affected by a companion. For fits involving this region, only the remaining 68 images are used as templates. Similarly, the region affected by bleed differs from image to image. To perform a fit close to the central source, we used only those images that have valid data in this region as fitting templates. Following this prescription, a typical image in our data set is separated into more than 500 regions, each potentially with a different set of template images (Figure 2).

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4.2.3. Initial Source Detection

4.2.4. Application of LOCI and PSF Fitting

We perform LOCI fitting to each of our images and subtract the result of the best fit in each region from the original image. Figure 3 shows an example. Most of the PSF features, including the diffraction spikes, are significantly reduced, but within about 1'' from the Cepheid, residuals from the subtraction increase. We find that source-detection algorithms do not perform well in this region. We thus inspect every image by eye and perform PSF photometry on all source candidates from Section 4.2.3. In principle, our procedure requires iteration, where any new sources identified would now be masked and the LOCI fitting repeated. However, no new sources beyond the previous candidates are identified. Table 2 lists the resulting source detections.

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4.2.5. Uncertainty Estimates

The uncertainty of the properties of the companion is dominated by systematics introduced through the LOCI subtraction. Additionally, there is a risk of oversubtraction in the LOCI procedure. We quantify those effects through simulations in which we insert fake sources with known fluxes into the images, run the same LOCI subtraction, and measure the flux of the detected companions. From our images, we select sources that are not visibly impacted by the PSF of the Cepheid. We checked the Gaia Data Release 2 (DR2) catalog (Gaia Collaboration et al. 2016, 2018) for these sources. While this release does not explicitly mark extended or multiple sources, the errors on the coordinates are a good proxy. We reject any sources with Gaia coordinate errors above 0.1 milliarcsec as likely binaries. We fit a beta function as analytical PSF to the remaining sources and reject sources when the fit parameters are significantly different than the sample mean. We finally have a set of 18 PSF template stars. We fix the parameters of the shape and use the resulting analytical PSF for fits to both the real data (Section 4.2.4) and the LOCI-subtracted images with simulated companions inserted.

For each template star, we extract squares 25 pixels wide centered on these sources from background-subtracted images. For each simulation, we select one of these sources, scale its F621M and F845M flux as required, and add it to one of the original Cepheid images. We then perform LOCI subtraction on the image with the artificially inserted companion and measure the source flux through PSF photometry. For each source in Table 2 we run 200 simulations. Depending on the position of the companion in Table 2, we select positions that are similarly effected by the Cepheid PSF. For instance, for R Cru, where the companion is found almost 2'' from the Cepheid but only a few pixels from the bleed column, we inject the artificial companions into the image at the opposite side of the Cepheid with a similar distance to the bleed column (Figure 4) and vary the insert location slightly to probe any background fluctuations statistically. Typically, some of the companion flux is subtracted in the LOCI procedure, and thus the measured magnitudes (pink histograms in Figure 4) are fainter than the input magnitudes (red line). We thus conclude that the true flux of the companion in the real image must also be higher than the measured flux, and we apply the offset determined from the simulations to correct the measured companion magnitude (black line). We take the standard deviation of the simulated magnitudes as the error estimate for the companion flux because the distribution of magnitudes is typically peaked, but the distribution has a significant tail toward fainter magnitudes for S Nor, which means that the true magnitudes could be up to 0.5 mag brighter than the number given in Table 2.

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4.2.6. Saturated Companions

4.3.1. Completeness

To quantify our detection limits, we employ a procedure similar to our uncertainty estimate for detected companions. We insert companions into Cepheid images at a certain radius from the Cepheid, apply our source-detection algorithm, and measure the fraction of companions recovered in both bands. The inserted companions have a color m₆₂₁ − m₈₄₅ = 1, similar to the values observed in the detected companions (Table 2). We verified that the detection fraction changes little for reasonable choices of this color. Figure 5 shows the limits. We note that these limits describe the detectability in our whole sample. The flux level at a given distance from the Cepheid differs by three orders of magnitude between the brightest and faintest image due to different exposure times and Cepheid magnitudes. A companion that could be detected in one image can therefore be hidden in the background in another. We note further (in the image segments we discuss outside of 05) that between 1'' and 05, the bleed column obliterates a significant part of the image.

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At 04, only a small fraction of companions is detected, even for the brightest sources. For bright sources, this number rises quickly with increasing distance, and beyond 1'', most companions with m < 12 that do not overlap the diffraction spikes or the bleed columns are detected. Fainter companions require larger distances. Only for distances beyond 1are more than half of the m₆₂₁ = 16 companions detected.

4.3.2. Detected Companions

As discussed in Paper II, the goal of the survey was to detect companions down to dwarf K spectral types, which limits contamination by field stars.

As discussed below (Table 5), in a number cases an absolute magnitude from other sources, such as IUE spectra, is more accurate than the HST photometry for very close companions.

Because of differences in the data-analysis procedures dictated by the angular separations, in the preceding work we divided the resolved companions found in our HST WFC3 imaging survey into three groups (separations >5'', 2''–5'', and <2''). In the following discussion, we combine the first two groups, designating them the "resolved wide" companions. The latter group is called the "resolved close" companions. In terms of physical projected separations, the resolved wide companions lie more than ∼2000 au from the Cepheid, and the resolved close ones are closer to the primary star. We now examine whether the properties of the stars in the two groups differ.

Table 4 presents the results for the combined sample of 16 candidate companions. These data are assembled from Table 2 in Paper II for the top group, with separations greater than 5''. For the middle group, with separations of 2''–5'', the entries are from Table 1. The data for the close companions below 2'' are more complicated, and these companions are discussed individually below. Our measures of separation and magnitude are listed in Tables 2 and 3. However, for very close companions and systems with multiple companions, the most reliable companion parameters come from several sources, which are discussed and assembled in Table 5. Table 4 lists the projected separations in both arcseconds and astronomical units, the V and V − I magnitudes and colors, the dereddened (V − I)₀ color, the E(B − V) reddening, and the distance. The distances and reddenings are from Paper II. As in Paper II, the V − I color excess is found from the relation E(V − I) = 1.15 E(B − V).

Among the possible companions separated by more than 5'' from the primaries, only five systems remained after we eliminated those candidates undetected in X-rays, implying that they are not young enough to be Cepheid companions. The remaining five are R Cru, FF Aql, AP Sgr, RV Sco, and TT Aql. The discussion in Paper II concluded that a Cepheid with a crowded line of sight (a field with more than two possible companions) is more likely to have chance alignments. On this basis, we remove TT Aql. The candidate companion of AP Sgr has the second-largest physical separation in the remaining sample, and it is a K dwarf, which is the most common type of field-star chance alignment. Thus AP Sgr is the most suspect of the remaining retained candidates in the list. As discussed in Appendix C, we retain the candidate wide companion for R Cru.

We also checked the Gaia DR2 catalog for parallaxes and proper motions of our candidate companions. Because the candidates are so close to the much brighter Cepheids, parallaxes are not available in most cases, particularly for the closer companions. The candidate companions of V737 Cen, R Mus, and Y Sgr were found to be much more distant than the Cepheids, consistent with the negative results of the X-ray observations reported in Paper IV; they are not included in Table 4. For the possible companions with separations >5'' in Table 4, the DR2 results are as follows. The Gaia DR2 parallax for R Cru itself is negative, but the parallax of the wider of its two candidate companions is consistent with the distance given in Table 4 (and with the Hipparcos parallax of R Cru), and its DR2 proper motion is similar to that of the Cepheid. The parallax of the FF Aql companion agrees within the errors with that of the Cepheid, but as noted by Kervella et al. (2019b), its proper motion is significantly different; this implies a relative velocity too high for it to be bound, unless it is itself a binary. The companion for AP Sgr is listed in DR2, but no parallax is given. Finally, the DR2 parallax for the wider of the two RV Sco companions agrees with that of the Cepheid within the errors, and its proper motion is similar.

The middle group in Table 4 lists the candidate companions with separations between 2'' and 5''. The only companion listed in Gaia DR2 is that of RV Sco, but no parallax or proper motion is given. In the case of V496 Aql, the DR2 parallax is significantly smaller (4.3σ) than that of the Cepheid, and hence is likely to be a chance alignment. It has been omitted from Table 4.

A number of the systems with a companion closer than 2'' to the Cepheid have at least one additional component. This means that disentangling the mass and temperature of the companions often requires information from a number of techniques. Here we discuss what is known about the components of these close systems in the third group in Table 4. This becomes important below in first examining the CMD of the companions and subsequently the distribution of colors as a function of separation, and the multiplicity properties of the sample.

Because massive star systems often have multiple components, in Appendix D we provide considerable detail for each system. The parameters of each component (mass, temperature, and luminosity) can be derived using observations over a wide wavelength range, and also as a function of separation. Many approaches and tools are currently available to do this. Radial-velocity studies extend over many decades. The emphasis in this study is on separations on the 1'' scale, but a number of systems have been observed via interferometry (e.g., Gallenne et al. 2019), accessing closer separations. Both HST and IUE provide information about hot companions in the satellite ultraviolet. Chandra and XMM X-ray observations test the ages of companion candidates. Finally, Gaia and Hipparcos data have contributed in two ways (Kervella et al. 2019a, 2019b). First, the comparison of proper motion from the two satellites in some cases results in proper-motion anomalies, indicative of orbital motion. Second, comoving companions can be identified and classified either as bound or unbound. These data are discussed further in Section 6.9, "Gaia Components."

In the discussion of some of the systems we have estimated masses of the companions. The approach used is discussed in Evans et al. (2018), based on data from detached eclipsing binary systems (Torres et al. 2010). In particular, because the companion to a more massive primary should not have evolved significantly, the lower envelope to the temperature–mass data is used.

Magnitude measurements for sources within 2'' of the Cepheid have substantial uncertainties. This is particularly important in determining the color or temperature using the difference of two filters, resulting in an uncertainty that is a significant fraction of the range of color. In many cases for the companions, there is an alternate measurement that provides a more accurate color or temperature. Specifically, many of the stars have an IUE spectrum, which provides a sensitive determination of the spectral type of the companion; the companion can completely dominate the flux at 1500 Å. Table 5 summarizes the best ("preferred") combination of V₀ and (V − I)₀ available for the companions within 2'' of the Cepheid. V₀ is taken from Table 3 for S Nor, R Cru, U Aql, and U Vul. From this, and the distance in Paper II, M_V is computed (Column 3). Column 4 is the spectral type from the instruments and literature references in Columns 6 and 7. Additional details are given for each star in Appendix D. The closest companions, V659 Cen B and AX Cir B, provide magnitudes that are too uncertain in the WFC3 images, so the value of M_V based on the IUE spectral type has been substituted. For η Aql, the M_V from the VLT/NACO imaging is provided in Appendix D.

This information for complex systems is discussed in Appendix D. We summarize the component parameters in Table 6 for reference. This includes the resolved companions (Table 5), as well as inner spectroscopic binaries and possible wider system members. While there is much detail in the linked inferences, the available observations provide well-constrained properties for most of the stars involved. The top entry for each Cepheid is for the resolved companion identified in this study. The second column is the binary or multiple star notation. V₀, (V − I)₀, and M_V are taken from Table 5. The final right column lists results for very wide companion candidates from Gaia DR2 (Kervella et al. 2019b), where WB signifies bound companions, and WC are comoving companions. Systems in Tables 5 and 6 are ordered by decreasing separation of the resolved companion.

The important characteristic that emerges from the discussion of the complex systems is that all the systems with resolved close companions (companions within 2'') have an interior spectroscopic binary (or at least one is strongly suspected, in the case of S Nor). This is discussed in more detail in Section 6.6.

We now return to a discussion of the close but resolved companions (Table 5), which are the first entry for each of the systems in Table 6, as discussed in Appendix D. As a first step in assessing the properties of the resolved close companions (within 2'' of the Cepheid (Table 5)), we consider the CMD (Figure 6), which provides a first examination of the properties of these companions. The companions are fairly evenly distributed in color, M_V, and hence in mass. Unlike the field initial mass function (IMF), they are not concentrated at low-mass stars. For wider companions, comparisons with the ZAMS are the way physical companion candidates are identified. In Figure 6 this is only a test for the two coolest companions, R Cru and U Vul because they are the only ones that are based on WFC3 photometry. While these points sit above the ZAMS, indicating some errors, they are consistent with the companions being low-mass stars.

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Because the systems with a companion closer than 2'' have the distinctive property of an inner spectroscopic binary (Table 6), we examine the multiplicity properties of the systems with a companion wider than 2'' to see if they share this characteristic. Components of these systems are summarized in Table 7. Unless discussed below, the spectral types for the companions are derived from (V − I)₀ in Table 7, using the calibration of Drilling & Landolt (2000), their Table 15.11. The details of the components of these systems are discussed in Appendix F.

The possible companions with separations larger than 2'' are more likely to contain a line-of-sight coincidence with an unrelated field star than the inner group. However, of the six Cepheids for which a possible companion has been identified in this group, five have strong evidence of an inner spectroscopic binary, and only for one (BB Sgr) is an inner binary questionable and it is a cluster member. That is, the resolved wide systems share this characteristic of the resolved close companions. This is an additional property consistent with physical system membership.

Ultimately, we wish to examine the properties of possible companions as a function of the (projected) separation in astronomical units, which is shown in Figure 7. Companion candidate properties are taken from Table 5 when available, or from Table 4.

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Companion candidates closer than 2000 au span the full range of (V − I)₀. The hottest companion candidates, however, do not occur at larger separations. The hottest of the more distant companions, FF Aql and RV Sco (with (V − I)₀ colors corresponding approximately to G0 and A7 dwarfs, respectively) have evidence that they are associated with the Cepheid (Appendix F). The other companion candidates with separations larger than 2000 au are all cooler (approximately K0 or later). Thus there appears to be a trend in the color or temperature and mass of the companion candidates to lower mass stars at wider separations. This raises the question whether wider companions actually are preferentially less massive (or have been dynamically widened), or whether they are chance alignments with field stars or possibly a mixture of both.

One of the goals of this study is to determine how far from the Cepheid physical companions occur. The diminishing number with separations greater then 6000 au is consistent with the results of X-ray studies to identify active stars young enough to be Cepheid companions. X-ray observations of 14 of the 39 Cepheids with companion candidates with separations greater than 2'' in Paper II were discussed in Paper IV. The only two Cepheids with X-ray confirmed companions greater than 6000 au were R Cru (above) and S Nor. However, because S Nor is in a cluster, the X-ray source may be a cluster member rather than a gravitationally bound companion. Possible wide but bound companions revealed by Gaia are discussed in Section 6.9. Seven Cepheids in the WFC3 survey (δ Cep, AX Cir, AW Per, V350 Sgr, V659 Cen, BP Cir, and V950 Sco) have possible companions (Tables 9 and 10), as does the cluster Cepheid U Sgr. This indicates further extended low-density companions.

The group of stars with resolved close companions contains companions that are highly likely to be physically related to the Cepheid. As discussed above, the systems are complex, and it requires a number of approaches in addition to the HST WFC3 observations to assemble a picture of the masses and separations of the components. Table 6 summarizes the information on the members of each system. In addition, as discussed in Section 6.9, Kervella et al. (2019b) used Gaia data to identify wide companions from distances and proper motions and test whether they are likely to be gravitationally bound to the Cepheid. The final right-hand column in Table 6 indicates whether a wide bound (WB) or wide comoving (WC) companion candidate was found.

Figure 8 further summarizes the components schematically. We stress that it was developed from the list of Cepheids with resolved companions at separations of typically a few hundred astronomical units (Table 6). It is striking that in the Cepheid list compiled in this way, all have evidence of an inner binary, often with a known orbit. As noted above, because S Nor is in a cluster, it may have a different history of formation or interaction than the field stars and also possible chance alignments with cluster stars. Precise masses are not available for all the companions; however, limits or estimates can often be made from spectral types (Table 6). Figure 8 shows the masses schematically either as comparable to the Cepheid itself (a B star: large blue squares) or a lower mass A, F or G star (small red squares). While this is a crude division, several things are apparent in Figure 8. There is a variety in the component masses. For instance, R Cru and U Vul have only lower mass companions, whereas other systems have a mixture of masses. For AX Cir and V659 Cen, the most massive companion is not the closest companion (Section 6.2). The more massive companions are typically the closer ones, although AX Cir and V659 Cen are exceptions. This might be due to the formation process or subsequent dynamical evolution.

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It is surprising that all the systems with resolved close companions in Table 6 also have an inner binary system, or at least a suspected one. This is markedly different from the fraction of spectroscopic binaries among Cepheids with periods shorter than 20 yr, which is 29% ± 8% (Evans et al. 2015), less than one-third of a Cepheid sample. In a scenario in which systems with wider separations are formed before more closely separated components (in a process such as core fragmentation and subsequent disk fragmentation) it is hard to explain how wide components "know" that an inner binary will be formed later. A more probable explanation for the requirement that a wide component in Figure 8 has an inner binary is that the wide component of the triple (or higher) system was moved outward through dynamical interactions.

The resolved close companions in Figure 8 all appear to be distant third stars in triple systems. Because they are the closest resolved companions in the survey, they are the most likely to be gravitationally bound to the Cepheids. However, the striking result in Figure 8 of inner spectroscopic binaries encouraged us to check the slightly more distant resolved wide companions (from 2'' to 7''). System parameters are summarized in Table 7 and represented schematically in Figure 9. The system summaries in Figure 9 have been simplified in two ways. For two stars from Table 7 (RV Sco and Y Car), there are two possible companions in this range. Because it is dynamically unlikely that they are both system members because they are at very similar apparent separations, Figure 9 shows only the one considered to be the most probable. Second, wider companions discussed below are not shown. From the discussion of the Cepheids with resolved wide companions above (Table 7), all except for BB Sgr have good evidence of an inner spectroscopic-binary system. In addition, as with S Nor, BB Sgr is a cluster member. This provides an alternative possibility for the resolved wide companion, a chance alignment with a cluster member, rather than a bound system member. It is also notable that the outer companion is significantly less massive than the Cepheid. This again fits the picture that a resolved companion with a projected separation of several thousand astronomical units was moved outward through dynamical interactions within the triple system.

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The inner spectroscopic binaries for the 13 Cepheids in Tables 6 and 7 certainly have long-term dynamical stability with respect to the resolved companions from the WFC3 survey because of the very different orbital periods. However, two stars in Table 7 (RV Sco and Y Car) have two companions that have separations from the Cepheid that correspond to period ratios much lower than 5, found by Tokovinin (2018b) in stable triple systems. Anticipating the Gaia results for likely wide but bound companions, V350 Sgr may also have two similar companions. While future studies may rule out one of these possible companions and hence remove the question of stability, the fact that half the stars in Table 7 are in this situation may reflect something about star formation. One way to have a pair of companions at apparently similar separations but in a stable configuration is that they are not coplanar, but have very different inclinations. In summary, RV Sco, Y Car, and V350 Sgr may provide a clue to additional complexity in the formation processes.

The population of triple systems can have important effects on the evolution of the systems, such as in the Kozai–Lidov mechanism (Naoz 2016), as discussed in Section 6.10.

The following example provides an indication of the completeness of the survey. For a typical distance in the WFC3 survey (700 pc) and a typical reddening [E(B − V) = 0.20;  Paper II], we estimate apparent magnitudes for a range of spectral types in Table 8; the M_V values are from Drilling & Landolt (2000). Using these magnitudes, the detection fraction from Figure 5 shows that nearly all the B9 and A3 companions would be detected outside 1''. Later spectral types (K0) are severely missing inside 16. Thus, for the example of 700 pc, essentially all early-type companions would be detected at separations larger than 700 au. For lower mass companions, as represented by the K0 star, they would be largely detected only outside 1100 au.

The Gaia spacecraft has provided new data to investigate multiple systems, particularly, to identify wide components from the outer regions of a star-forming cloud. This is also relevant to the question of whether there are stars formed at the same time that are neither gravitationally bound system members nor in a recognizable star cluster. In particular, studies have been made of proper motions to study orbits (Kervella et al. 2019a) and to identify wide companions (Kervella et al. 2019b).

Kervella et al. (2019a) have used the difference between proper motions from Gaia and Hipparcos to look for proper-motion anomalies resulting from orbital motion between the two epochs. Of the 70 stars in our WFC3 sample, they list data for 63, or 90%. (Of these 16, or 25%, had less-than-perfect Gaia data, often because the Cepheid is too bright.) The Gaia data showed proper-motion anomalies for 28 stars (44%) at the level of 2σ or greater, many of which are known spectroscopic binaries. We stress that this is only a first exploration of the Gaia results, which are expected to improve in the future. Specifically, other stars have indications of proper-motion anomalies, but at a lower significance level. As an example, S Mus is a well-known binary with an orbit, but does not meet the proper-motion-anomaly criterion.

6.9.1. Proper-motion Anomaly

6.9.2. WB and Comoving Companions

Triple stars can form via two modes. First is an outside-in process, whereby core fragmentation on large scales initially produces the wide companions with a_out > 100 au, followed by disk fragmentation on smaller scales that forms the close inner binaries with a_in < 100 au (Moe & Di Stefano 2017; Tokovinin 2017). Second is an inside-out process, where two companions fragment within the same disk near a_in ≃ a_out ≃ 10 au in an initially unstable configuration, and then subsequent dynamical interactions throw one of the components (typically the least-massive) to larger separations or eject it entirely (Reipurth & Mikkola 2012; Moe & Kratter 2018). The Kozai–Lidov mechanism (Naoz 2016) also results in dynamical evolution of the system.

As discussed in Section 6.6, all companions to Cepheids with separations from 100 to 2000 au, and nearly all companions with separations between 2000 and 7000 au, are outer tertiaries to inner spectroscopic-binary companions with separations from 1 to 20 au. The strong link between outer tertiaries and inner binary companions to Cepheids suggests a causal link, e.g., the dynamical-unfolding scenario. Nearly all of the outer tertiary companions are less massive than the inner spectroscopic-binary companions, consistent with the triple-star dynamical-unfolding scenario. In this dynamical-unfolding scenario, the outer tertiaries are expected to be highly eccentric, which may be tested in the future with Gaia astrometry.

Nonetheless, correlation does not necessarily imply causation. The binary fraction of O-type (Sana et al. 2014) and early-B (Moe & Di Stefano 2017) stars is nearly 100% within a < 100 au, and therefore nearly all wide companions beyond a > 100 au to massive stars are outer tertiaries in hierarchical triples. Similarly, Evans et al. (2005) showed that triples are quite common among Cepheids, and again, Evans et al. (2015) found that 30% of Cepheids have companions for a between 1 and 20 au, probably because Cepheids began life as late-B stars. In addition, B stars in short-period orbits will have merged before the Cepheid stage, removing them from the binary statistics. The preponderance of Cepheids in hierarchical triples with a_in between 1 and 20 au and a_out between 100 and 7000 au could simply be due to the efficient formation of companions to massive stars via both disk fragmentation and core fragmentation on small and large scales, respectively. On the other hand, the estimates in Tables 6 and 7 show that the spectroscopic companions are within 20 au, the regime that was well studied in Evans et al. (2015). The binary fraction from that study is 30%. Thus, in Table 6, of the seven Cepheids with companions, two would be expected to have spectroscopic-binary companions, rather than all seven. Similarly, in Table 7, two of the seven stars would be expected to have companions in this range rather than six. In sum, 13 of these 14 stars have spectroscopic companions within 20 au where four are expected, strongly implying that the system structure (triples) is not produced by the standard outside-in process.

Wide companions that derive from core fragmentation have systematically lower masses than inner binary companions that come from disk fragmentation (Moe & Di Stefano 2017). This is the case for Tables 6 and 7. Our wide tertiaries are systematically less massive than the inner binaries, but are still top-heavy compared to random pairings from the IMF.

Although a significant majority of very wide companions to solar-type stars are tertiaries, Tokovinin (2017) argued that most derive from fragmentation of adjacent cores, not dynamical unfolding, and therefore there is no causal link between inner binaries and outer tertiaries. This is related to the possibility that some Cepheids are the remnants of dispersed clusters (Anderson & Riess 2018). The identification of wide binaries formed from separate but adjacent cores derives from the fact that beyond about 10,000 au, the number of companions increases strongly, beyond those presumably formed by core or disk fragmentation. Insight here comes from the Gaia wide companions. Wider companions from Gaia (Tables 9 and 10) from adjacent cores are expected to show some degree of correlation in component masses compared to independent cores (Tokovinin 2017). The frequency of these very wide companions rises steeply beyond about 10,000 au. Tables 9 and 10 show that 16 Cepheids have either bound or unbound Gaia companions, very similar to the 13 Cepheids with resolved companions in the WFC3 study. The most likely explanation is that the Gaia survey only extended to 50,000 au, where core/disk fragmentation stars are mixed with adjacent core stars. This may be an indication of the density of the formation environment (Deacon & Kraus 2020).

In reality, both an outside-in formation via the relatively independent processes of core fragmentation followed by disk fragmentation and an inside-out mode via dynamical unfolding likely contribute to our Cepheid triple sample. The Cepheid sample discussed here contributes to the sample of massive triples needed to fully compare the companion mass distributions to the two different models and determine which scenario is dominant. As indicated above, astrometric orbital solutions (or at least a sense of relative orbital motion) of the outer tertiaries will also help constrain their formation mechanism.

The HST and XMM images are shown in Figure 25, with the locations of the Cepheid and the possible optical companions circled. Either of the possible companions could be the source of the X-rays in the XMM image (although the closer one is more likely).

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The Chandra image of R Cru is shown in Figure 26, which compares the location of the X-ray source to that of the Cepheid and the possible close companion (including a small shift to align the Cepheid in the HST image with its coordinates from SIMBAD). The shape of the X-ray source based on a relatively weak detection has some uncertainty, but it is closer to the Cepheid than to the possible close companion.

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Are the X-rays from the Cepheid itself? We now have a pattern to X-ray activity in Cepheids (Engle et al. 2017): it is relatively constant at about $\mathrm{log}{L}_{{\rm{X}}}=28.8\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ for most of the pulsation cycle, but has a burst of X-rays just after maximum radius (approximately phase 0.5). The X-ray flux from XMM for R Cru ($\mathrm{log}{L}_{{\rm{X}}}=29.8\,\mathrm{erg}\,{{\rm{s}}}^{-1};$ Paper IV) is higher than the quiescent level. The phase of the Chandra observation is 0.94 (using the period 5.825701^d and the epoch of maximum light of JD 2455172.5100 from Usenko et al. 2014), not the phase of X-ray maximum. Thus the X-ray flux is higher than expected for the Cepheid, particularly at a phase other than maximum radius.

There is, however, another possibility. R Cru was observed with the CORAVEL radial-velocity spectrograph for four seasons, approximately 1996 July, and 1997 March, July, and December (Bersier et al. 1994). The results are shown in Figure 27, with different symbols for each season. The velocities for the third season (and to some extent, the fourth) fall below the first two, particularly considering that a typical error for the velocities is 0.33 km s⁻¹. This indicates a systemic velocity change within a year, presumably due to orbital motion. This implies that there is a second companion candidate in a close orbit, which would be unresolved from the Cepheid in the Chandra observation. An orbit with a period of almost a year corresponds to a separation near one astronomical unit.

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There is one further piece of information that gives insight into the R Cru system. It was observed with IUE (Evans 1992a), with the result that any companion must have a later spectral type than A2, corresponding to a mass lower than 2.5 M_⊙.

To summarize companion possibilities for R Cru, there are two reasonably close companions, one at a separation of 1580 au (Table 4), and the spectroscopic-binary companion (Figure 27) at approximately 1 au. Note that these two would be dynamically compatible. The Chandra observation in Figure 26 provides an indication favoring the closer companion, but this is tentative. However, Gaia data (Kervella et al. 2019b) provide additional evidence that the candidate at 1580 au is a physical companion, as discussed in Appendix D. Therefore we continue to include it in Table 4. The IUE observation shows that any companion is only about half as massive as the Cepheid (or less).

The HST and XMM images are shown in Figure 28, with the locations of the Cepheid and the possible companion circled. Figure 29 shows the Chandra image with the same two locations overlaid. It has been mildly smoothed with the CIAO tool smooth.

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The Chandra image rules out the 52 (4540 au) companion as young, and hence it is not a physical companion of the Cepheid S Mus. The Cepheid is a member of a spectroscopic-binary system with a period of 505 days ($a\sin i=2.8\,\mathrm{au};$ Paper I). The companion is the hottest known Cepheid companion: B3 V (Evans et al. 2006). Stars this hot produce X-rays through wind shocks (Harnden et al. 1979), typically with L_x/L_bol = 10⁻⁷. When M_bol is used for a B3 star of −4.0 (Drilling & Landolt 2000), the luminosity is 1.2 × 10³⁷ erg s⁻¹. Thus the X-ray luminosity of $\mathrm{log}{L}_{{\rm{X}}}=30.46$ (Paper IV) is close to the expected ratio for a hot star. The phase of the Chandra observation is 0.06 when the pulsation period and epoch of Petterson et al. (2004) are used. Hence, S Mus is much brighter than the quiescent phases. Thus the flux must be at least heavily dominated by the hot companion.

New insight into the system came with HST Faint Object Camera (FOC) and Space Telescope Imaging Spectrograph (STIS) images (PI: D. Massa). The STIS image was made with the G230L grating and the STIS NUV-MAMA detector. A series of spectra were taken at varying roll angles and times in the orbit. Similar data are fully discussed for AW Per (Massa & Evans 2008) and W Sgr (Evans et al. 2009). One of the images is presented as an example in Figure 30. Unexpected complexity in the system is immediately evident. The spectroscopic binary is the bottom spectrum, with the Cepheid Aa as the brightest star in the long-wavelength region and the companion Ab as the brightest star in the short-wavelength region. At the top is the resolved companion C, found in the HST WFC3 imaging (Table 2). Between them, but very close to the spectroscopic binary, is a previously unsuspected companion B. The components are summarized in Table 6. In addition to the separation of C from Table 2, the projected separation of B has been measured from the STIS image. The separation in the spectroscopic binary Aa and Ab has been taken from the interferometry of Gallenne et al. (2019), 10.06 ± 0.16 mas. Using the distance from Paper II (613 pc), this becomes 6.2 au.

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Companion B may be the interferometric pair resolved three times by Ismailov (1992). However, it was not resolved by speckle at SOAR in 2008 and 2016 (Tokovinin et al. 2010, 2018, respectively).

Spectra were extracted from the STIS image as described in Evans et al. (2009). The U Aql observations were made with the G230L and the unfiltered 25MAMA aperture. For the PSF comparison star we used the data set o6hr01040, an observation of the hot subdwarf GRW+70D5824. This exposure has a relatively high signal-to-noise ratio and was taken in 2002 February, only a few months before the first of the U Aql observations. The image of U Aql that was analyzed was o6f101020, selected because it has the best projected separation between the components. The projected separation between the spectroscopic binary with the Cepheid and the closest companion is 0107 using a plate scale of 00247 px⁻¹, which corresponds to 66 au using the distance from Paper II. The results are shown in Figure 31. The Cepheid dominates in the long-wavelength section, but the companions dominate at the short-wavelength end. Components B and C are resolved, and the Cepheid makes no contribution to the spectrum. For the spectroscopic binary Aa and Ab, however, in the region near 1800 Å there is still a contribution from the Cepheid, although the companion Ab dominates. In this section we estimate the spectral types of all three companions, and we correct for the contribution of the Cepheid to the spectrum of Ab as follows. We use the IUE spectra of standard stars to create a spectrum B9.8 V (midway between B9.5 V and A0 V) as in Evans (1992b). (The B9.8 V spectrum has been reddened to match the U Aql spectrum and then scaled for comparison.) Figure 32 shows that the B9.8 V spectrum represents the U Aql companion Aa well at wavelengths shorter than 1500 Å, but the additional contribution from the Cepheid can be seen at longer wavelengths. Therefore we use the flux from the B9.8 V spectrum to estimate the magnitude difference between the three companions in the U Aql system.

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For all three companions in the U Aql system (Figure 33) the mean flux from 1650 to 1950 was created (Table 14), and from these, the magnitude difference between the companions and the U Aql spectrum was created. At the bottom of Table 14 the fluxes from the IUE spectra are given. From the difference between the B9.8 V spectrum and the composite U Aql spectrum (Aa + Ab at 1800 Å), a correction of 0.15 mag was derived to account for the contribution to the U Aql spectrum from the Cepheid. The far right column for the far (C) and close (B) companions from the STIS spectra includes this correction. Note that the IUE spectrum of the U Aql system includes all three companions, although the hottest star in the system (Ab) is only affected in a minor way at the shortest wavelengths.

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The spectral type of companion Aa was derived in Evans (1992b). To estimate the spectral type of the magnitude differences (Table 14), Table 15 shows the magnitude differences for main sequence spectral types from the V—ultraviolet colors (Column 2) from Wesselius et al. (1980) and the absolute magnitude calibration (Column 3) from Drilling & Landolt (2000) for the ZAMS, which is essentially the same as used in Evans (1991, 1992b). The far component C is approximately A5 V, and the close component B is A3-4 V, corresponding to M_V = +2.1 and +1.8, respectively. This magnitude for C is very similar to that from the WFC3 value (Table 5).

Previously, Evans et al. (1998) obtained spectra with the Goddard High Resolution Spectrograph (GHRS) to measure the orbital velocity amplitude of the spectroscopic-binary companion with the medium-resolution grating G200M. The velocity difference between the two is −29.1 km s⁻¹ with an estimated error of 3.8 km s⁻¹. Combining this with the orbital velocity amplitude of the Cepheid (Welch et al. 1987) and the mass of the main sequence companion, they derived a mass for the Cepheid of 5.1 ± 0.7 M_⊙.

More recently, a spectrum was obtained with STIS. The spectrum used the E230H grating, and was taken over two days in 2003: August 1 (exposure time 12109 s), and 14 hr later on August 2 (exposure time 7375 s). When the orbit of Welch et al. (1987) is used, the orbital phase is 0.44. The data used are shown in Figure 34. A portion of the spectrum was selected where the blaze correction is satisfactory and there are spectral features. It was used in two ways. First the spectra for the two days were cross-correlated to look for a velocity difference that could be caused by motion in a short-period binary orbit. In addition, the STIS spectrum was cross-correlated with each of the GHRS spectra to confirm the orbital velocity amplitude in the 5 yr orbit.

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Although the spectrum on each day was weak, the cross correlation of these two spectra provided the opportunity to check for possible orbital motion from a short-period binary. The spectral lines are reasonably broad, which is not surprising for a late-B main sequence star, resulting in a broad velocity peak. However, Figure 35 shows no evidence of a change in velocity, which would be an indication of short-term binary motion.

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This is in agreement with the mass of the secondary in Kervella et al. (2019a) incorporating Gaia and Hipparcos proper motions with the orbit. The mass is appropriate for a B9.8 V star, and would not accommodate an additional star.

To check the result from the two GHRS spectra (Evans et al. 1998), the STIS spectrum was cross-correlated with each of the GHRS spectra. The result (Figure 36) showed a similar shift between the two orbital phases to that found previously. On the other hand, it is possible that the STIS spectrum is as much as 30 km s⁻¹ smaller than both the GHRS spectra. In particular, the STIS spectrum should have a very similar orbital velocity to GHRS Visit 1.

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In summary, the STIS spectra taken a day apart do not show any velocity signal that the companion is a very short-period binary. Comparison of the STIS and GHRS velocities (Figure 36) leaves open the possibility of a longer period binary with lower orbital velocity. However, because of the broad lines, and hence the broad correlation, this is only a possibility.

The STIS image (Figure 30) provides an explanation for a surprisingly large discrepancy between an absolute magnitude for the Cepheid from the IUE spectrum of the companion and the Leavitt law (period-luminosity relation) of Feast & Walker (1987). As discussed in Evans (1992b), typical differences between the IUE absolute magnitudes and those of Feast and Walker are 0.2 mag for well-exposed companion spectra with well-known reddening. For U Aql the difference was more than twice this value, even though both conditions were met. However, the addition of the flux from the two additional companions that were unknown at the time (but would have been in the IUE aperture) accounts for the discrepancy.