CHANDRA OBSERVATION OF POLARIS: CENSUS OF LOW-MASS COMPANIONS^*

As with many fairly massive stars, the Polaris system has several components. Polaris Aa is a supergiant, and, in fact, is the nearest classical Cepheid, albeit with a very low pulsation amplitude. The Hipparcos distance is 130 pc, which indicates that it is pulsating in the first overtone mode (Feast & Catchpole 1997; van Leeuwen et al. 2007). Polaris also is a spectroscopic binary with a known orbit (see the summary in Kamper 1996) and inclination (Wielen et al. 2000). Recently, the Cepheid Aa and the spectroscopic companion Ab were resolved with HST at a separation of 017 (Evans et al. 2008). The flux at 2200 Å indicates that the companion is of spectral type of F6 V, and preliminary masses for Aa and Ab were determined (4.5 M_☉ and 1.3 M_☉, respectively). There is an additional star, Polaris B, 18'' away of spectral type F3 V. Its proper motion suggests that it is a bound long-period member of the system (Evans et al. 2008; Kamper 1996). Finally, two fainter and more distant visual companions, C and D, have been proposed as physical members.

Polaris was observed with the Chandra Advanced CCD Imaging Spectrometer (ACIS) for 10 ks on 2006 February 9 (ObsID 6431). Full details of the instrument are available in Weisskopf et al. (2002). The four "I" CCD chips at the best focus provide a 169 × 169 field.

The data were processed with An Archive of Chandra Observations of Regions of Star Formation (ANCHORS) pipeline (B. Spitzbart et al. 2010, in preparation; Currie et al. 2009).⁶ ANCHORS is made up of many Chandra Interactive Analysis of Observations (CIAO) routines, and is especially designed to process Chandra observations containing many point sources. It uses WAVDETECT (Mexican hat wavelet detection) to find sources, with a threshold set an expectation of one false positive in the field.⁷ Recursive blocking is used to match the blurring of the off-axis point-spread function (PSF). For the field center (at Polaris), a 2 pixel (087) wavelet scale was used. Counts are extracted at point-source positions using a PSF appropriate to the off-axis distance and a background determined from an annulus around but well away from each source.

Although the Polaris field does not approach the richness of young clusters for which the package was designed, ANCHORS processing allows us to compare possible young stellar sources in the vicinity of the Cepheid with the numerous ANCHORS samples from galactic clusters of comparable age, on as similar a basis as possible.

Figure 1 shows the central 3' of the field, smoothed to highlight the sources. Positions of the five possible members of the Polaris system (A = Aa + Ab, B, C, and D) are marked. Additional X-ray sources are present. However, as discussed in Section 4, only two have counterparts in the 2MASS catalog (Cutri et al. 2003), and we conclude that the others likely are background active galactic nuclei (AGNs). This point is discussed further in Section 4.3. We focus on the Polaris source first.

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3.1.1. The Main-sequence Star

In this section, we consider main-sequence (or slightly above the main sequence) stars comparable in age to the supergiant to see how they compare with the Polaris X-ray flux and spectrum. The Cepheid is essentially the same age as the supergiant α Per (and the α Per cluster), and distinctly younger than the Pleiades. Meynet et al. (1993) list ages of 50 and 100 Myr for these clusters, respectively.

We use the Chandra Orion Ultradeep Project (COUP; Feigelson et al. 2005), a very deep Chandra exposure of the much younger (≃1 Myr) Orion nebula, as a first comparison. Feigelson et al. created a stacked spectrum of 820 unsaturated cool stars. Figure 3 compares the Polaris energy distribution (from Figure 2) with the stacked Orion spectrum. The latter clearly is much harder. This is in agreement with the general trend of enhanced activity and coronal temperature in stellar youth, and a rapid decrease in both with increasing age.

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A second comparison is the Pleiades, which has been partially observed with both Chandra (Krishnamurthi et al. 2001; Daniel et al. 2002, hereafter DLG) and XMM-Newton (Briggs & Pye 2003).

The stars of interest are the late F (or early G) main-sequence stars with spectral types comparable to Polaris Ab. Binary companions complicate the interpretation of the spectra, and are thought to be the origin of the X-rays in many of the B, A, and early F stars that appear unexpectedly as X-ray sources. Both DLG and Briggs & Pye (2003) discuss several of these sources. In particular, DLG note three of this type, H ii 956, H ii 980, and H ii 1122. They are listed in Table 1 with classifications, X-ray luminosities, and temperatures taken from DLG. (For H ii 980, the temperature is the mean of the values from two pointings.) The count rates for these sources indicate that the spectra would be mildly piled up, but since H ii 980 and H ii 956 are far off-axis, saturation is avoided. H ii 1338 is a similar but fainter system, for which the spectrum was not modeled by DLG. In all three cases, DLG argued that the late F/G star was the dominant source of X-rays. The B6 IV and A7 V primaries in H ii 980 and H ii 956, respectively, are not expected to have coronal emission, making the late-type secondary stars the likely X-ray sources. The spectrum and light variation of H ii 1122 resemble those of H ii 980 and H ii 956 rather than a harder K star, hence the assignment of the X-rays to the F-type primary. The spectra are distinctive in that they are very soft (Table 1), with no indication of a second harder component. Figure 3 illustrates the spectrum of H ii 980 as an example.

Table 1. Main-sequence X-ray Luminosities

Star	Spec.	log LX	kT
	Type		(keV)
Polaris	F7 Ib	28.89	0.6
H ii 956	A7 V + F6	29.31	0.57
H ii 980	B6 IV + G	29.60	0.56
H ii 1122	F4 V + K	29.06	0.45

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The Polaris spectrum and that of H ii 980 are very similar: very soft with the flux concentrated below 1 keV. Table 1 shows that the L_X of Polaris is only slightly less than that of the Pleiades F/G stars. Hence, the F6 V companion is a plausible source of the Polaris X-rays.

3.1.2. The Supergiants

3.1.3. Additional Diagnostics

The Chandra ACIS image also provides information concerning the more distant visual companions in the system, namely, the fainter stars C and D (Burnham 1894). Recovering their present-day positions in the glare of the Cepheid and very close to the celestial pole is challenging. Positions are available from the end of the 19th century from Burnham (1894). In order to derive current positions, Polaris was "recessed" to the earlier epochs (by BDM) and used to determine the relative positions of C and D at those epochs. These positions were then precessed to 2000, providing two estimates of the positions today, which are listed together with their means in Table 3. Modern confirmation of these companions was provided by Daley (2006), using a focal plane bar mask. His approximate V measures are listed in Table 3. Photometry of these stars is difficult because of contamination from much brighter Polaris. At the distance of Polaris, C and D would have approximate M_V of 8.2 and 8.7 mag, respectively. Using the zero-age main sequence absolute magnitudes of Schmidt-Kaler (1982), these correspond to roughly K7 and M0. Component D also matches a 2MASS source (Cutri et al. 2003). Since K is the only band with A quality data, we use that value: K = 12.15 mag. At a distance of Polaris, this would be M_K = 6.6 mag. Using the energy distributions of Kraus & Hillenbrand (2007b), this corresponds roughly to an M3 star.

Table 3. Distant Companions

Property	R.A.	Decl.
	J2000	J2000
Star C
1884.74	02h35m2509	+89°15'392
1890.79	02h35m3681	+89°15'428
Mean	02h35m31s	+89°15'41''
V	≃ 13.8 mag
Log LX	⩽ 27.18 erg s−1
0.3–8 keV
Star D
1884.74	02h30m4138	+89°14'292
1890.79	02h31m102	+89°14'285
Mean	02h30m51s	+89°14'29''
V	≃ 14.3 mag
Log LX	⩽ 27.40 erg s−1
0.3–8 keV

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As shown in Figure 1, there are no obvious X-ray sources at the positions of C or D. We have made the following estimate of the flux limit. We use five counts for a conservative detection limit for a point source near the field center. (A 1'' radius detect cell has an encircled energy of 90% for ACIS-I and with a background of much less than a count, five counts correspond to ≃ 5σ.) For source C, the 9829 s of exposure results in a limiting count rate of 0.0005 counts s⁻¹. We used PIMMS (Chandra Cycle 7) and a Raymond–Smith model with abundance of 0.2 solar and log T = 6.8, and N_H column density ≃1.0 × 10²⁰ to estimate a flux of 4.0 × 10⁻¹⁵ erg cm⁻² s⁻¹. At the 130 pc distance of Polaris (van Leeuwen et al. 2007), this corresponds to log L_X = 27.18 erg s⁻¹. Unfortunately, star D fell in a gap between the CCD chips. We applied an exposure map to estimate that the effective exposure in this location was only 60% that of star C, leading to an upper limit of log L_X = 27.40 erg s⁻¹.

By way of comparison, the Chandra Pleiades observations (DLG) indicate log L_X ⩾ 29 for the six active K stars in the field. All but one of the active M stars has log L_X ⩾ 28. Among the low-mass stars classified by DLG as inactive are a K2 V star with log L_X 27.85. There also are four M stars (judging from the optical magnitudes), one with log L_X = 28.17 and the rest are upper limits. All the inactive M stars in the Pleiades field are fainter than 19.0 mag, equivalent to approximately 18.7 at the distance of Polaris. Thus, the only possibility not ruled out by the upper limits on C and D is an M star. A similar conclusion can be reached from the ROSAT PSPC observations of the α Per cluster (Randich et al. 1996). Essentially all the G and K stars and two-thirds of the M stars in the α Per cluster were detected at log L_X ⩾ 28.8. Since C and D would be late-K/early-M stars at the Polaris distance, it is highly likely that the Chandra exposure would have detected them if they were as young as the Cepheid.

A final argument that C and D are not physical companions of Polaris comes from their proper motion. Assuming a face-on orbit (i.e., a lower limit on separation), C and D would be at about 5000 and 10,000 AU, respectively, from Polaris. Their motion of 97 and 288, respectively, since Burnham's time is inconsistent with orbital motion and also at variance with the proper motion of Polaris which has moved only 52 in the past century. The conclusion is that they are unrelated stars.

As seen in Figure 1, star B also is not a conspicuous X-ray source. As noted previously, B has a proper motion which is consistent with the orbital motion in a wide orbit (Evans et al. 2008; Kamper 1996), and a radial velocity similar to the γ (systemic) velocity of the Cepheid (Usenko & Klochkova 2008). Discussions of the classification, and the optical and ultraviolet spectra (Turner 1977; Evans et al. 2008; Usenko & Klochkova 2008) suggest F3 V. Since this spectral type is at the division between the cooler bright coronal sources and the hotter noncoronal stars, the lack of X-rays is understandable. The X-ray flux upper limit at B would be the same as for companion C (log L_X = 27.18 erg s⁻¹). Again, the best comparison in terms of age is the α Per cluster. Randich et al. (1996) find upper limits for early F stars in their ROSAT observations of log L_X = 29.0–29.5 erg s⁻¹. The lack of X-rays does mean, however, that B is not itself a binary with a lower mass companion earlier than mid-M, or so.

Finally, we consider whether the ACIS image reveals any other possible companions. To this end, we have evaluated the X-ray sources that match stars in the 2MASS point-source catalog (Cutri et al. 2003). At the distance of Polaris, for example, an M0 V star would have K = 10.78 mag (using the calibration of Kraus & Hillenbrand 2007b), and would easily be within the range of 2MASS (if beyond the glare of Polaris).

There are numerous sources on the image, but only two in addition to Polaris itself have 2MASS counterparts (Table 4): CXOANC J021006.2+891626 (Src 1) and CXOANC J021454.3+890852 (Src 2). (All 2MASS photometry in Table 4 is A quality.) To investigate whether these stars are possible companions to Polaris, we list the absolute magnitude values of the 2MASS photometry at the distance of Polaris, which can be compared with the energy distributions of Kraus & Hillenbrand (their Table 5). These correspond reasonably well to M4 and K5–K7. At the age of Polaris, these stars would still be a little above the main sequence, but since the evolutionary tracks are approximately vertical for these masses spectral-type estimates are minimally affected.

Although the sources are weak (12.7 and 8.3 net counts, respectively, for Srcs 1 and 2), they are clearly soft sources, both with median energies of 0.9 keV. This is consistent with a coronal star rather than an AGN. We estimated the X-ray luminosities with PIMMS as previously described obtaining log L_X = 28.3 and 28.1 (Table 4) at the distance of Polaris.

These estimates are significantly lower than for active Pleiades K stars, which have log L_X > 29. Two of the five active M stars in DLG have log L_X in the range of Src 1. There also is one object, HHJ92, which DLG list as an inactive star with a comparable X-ray flux. On this basis, Src 1 plausibly is related to the Polaris system. Src 2 is less likely, but cannot be absolutely ruled out.

As a final consideration for these candidates, Src 1 and 2 are separated from Polaris by 254'' and 462'', respectively, corresponding to 0.16 and 0.29 pc in projected distance, close to the standard outer limit expected for bound companions.

In summary, these attributes cannot conclusively prove that these two stars are physical companions of Polaris. However, they do not rule out this possibility either.

We must add a small qualification to the first paragraph in this section. In Figure 1, there is an X-ray source about 10'' to the SE of the A circle. An optical counterpart for this source would not appear in 2MASS because it would be within the glare of Polaris itself. However, exposures of the field were obtained with the HST WFPC2 using the F218W filter (2200 Å). A combined image (exposure time 300 s) showed nothing at the position of the SE X-ray source. Based on the brightest noise features, any star at that position would be more than 8 mag fainter than Polaris B (H. E. Bond 2009, private communication) in the ultraviolet. Polaris B is an F3 V star with V = 8.7 mag (Evans et al. 2008), and any possible stellar counterpart would be both much fainter and much cooler. Interpretation is complicated somewhat because the F218W filter has a red leak, which can contribute significantly in the case of a cool star.

A less precise estimate (H. E. Bond 2009, private communication) comes from the inspection of Kitt Peak 2.1 m CCD images. No star is visible at the X-ray position down to about 14–15 mag in V. The wings of the overexposed Polaris image preclude higher precision. Nevertheless, this visible observation avoids the complications of large extrapolation from the ultraviolet and the presence of red leak.

Additional information comes from double star observations, which did not list a star in that location. Racine & Wesemael (2008) cite the resolution of Sirius A and B which have a magnitude difference of 10 mag and a separation between 3'' and 10''. The Washington Double Star Catalog (Mason, Wycoff, & Hartkopf)⁹ lists 355 confirmed pairs with separations less than 20 arcsec and magnitude differences greater than 7 mag, so such systems were routinely recorded. In the Burnham Double Star Catalog, Burnham specifically states that there is nothing closer than Polaris B seen with his 36'' telescope. Aitken (1945) examined every star brighter than 9.0 mag and records no further companions.

All these approaches indicate that the SE source is most likely a background AGN.

To illustrate the challenge of distant companion identification for bright primaries, we did a search of the 2MASS point-source catalog 8' around Polaris (comparable to the Chandra ACIS-I imag). Approximately 200 sources were found (roughly excluding artifacts around such a bright central source). Thus, the "youth criterion" (requiring X-ray flux for sources likely to be young enough to be Cepheid companions) is a powerful discriminant that sifts plausible low-mass resolved companions down to two. X-ray observations are equally powerful for detecting much less massive close (unresolved) companions in systems where the primary itself is not expected to produce X-rays (such as late B stars).

The point-source flux that would be detected in our Chandra image, of course, depends on the distance off axis and the spectrum. However, for illustration, we will use five counts as a source-detection limit. As described previously, this corresponds to a luminosity of log L_X = 27.18 at the distance of Polaris. Using the results from the Pleiades (DLG) and the even more appropriate the α Per cluster (Randich et al. 1996), all mid-F to K-type stars should be detected at this level, and a large fraction of M stars as well. It is these low-mass stars that are the most difficult to detect by other means (such as radial velocity studies) in massive star systems. The X-ray census by ACIS provides very strong constraints on other possible Polaris companions. For instance, there is only one possible wide companion (Src 1), and an additional less likely candidate (Src 2). In addition, Polaris B, the F3 star, is not itself a binary with a cooler companion. Thus, the full count for the system, at least down to M stars is three with a plausible fourth and possible fifth.

If Src 1 proves to be a physical companion, the indicated mass ratio would be impressive. An M4 V star has a mass of 0.29 M_☉, using the calibration of Harmanec (1988). The mass of Polaris is 4.5 M_☉ (Evans et al. 2008), leading to a mass ratio of 0.06. Similarly, the difference in V is more than 15 mag, based on the M_V for an M4 V star from Schmidt-Kaler (1982).

The smallest mass ratio among confirmed companions is between Ab and Aa, q = 0.28 (Evans et al. 2008). The projected separation between A and B is more than 2000 AU and the separation between Aa and Ab is 17 AU. Tokovinin (2000) has shown that there is an excess of binary systems made up of nearly equal components for periods shorter than 40 days. In contrast, the Polaris Aa + Ab system with a period of 30 years falls into the category of a wider system with a much smaller mass ratio.

In relating the binary/multiple characteristics of the Polaris system to the initial state at the end of the star formation process, two events may alter the configuration. First, the system might have a close encounter with an external object which could catastrophically alter the number of stars or their orbits. A group of well-studied binaries can provide some information about such interactions, but we cannot make further inferences about the Polaris system alone. The second event is that when a close binary primary evolves beyond the main sequence, the two stars can interact, and perhaps coalesce. Since Polaris has already ascended the giant branch, this is a possibility we must consider. We can make a rough estimate of how likely coalescence is. For Cepheids in binaries, there are no known orbits shorter than a year, and in fact the shortest period orbit (Z Lac) is the only one with a circular orbit (Sugars & Evans 1996). This is a good indication that the progenitors interacted and in some cases presumably coalesced at periods shorter than this. Duquennoy & Mayor (1991) determined the distribution of periods in binary systems for solar-type stars. More massive Cepheids might not have this same period distribution, but we will adopt it for the sake of an estimate. If we make the approximation that a system containing a Cepheid would have roughly three times as much mass as a system with two solar-type stars, we can adjust the Duquennoy and Mayor distribution and estimate that only one in five Cepheids would have been in a close enough binary to have coalesced somewhere between the main sequence and the red giant phase. Although this estimate is rough, it indicates that the occurrence of a coalesced system among Cepheids is relatively unlikely. Nevertheless, a system as wide as the 30 year Polaris binary provides plenty of room for an inner close binary to have once been part of a stable hierarchal system.