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Kinematics of Type II Cepheids of the Galactic Halo

In a step toward understanding the origin of the Galactic Halo, we have reexamined Type II Cepheids (T2C) in the field with new input from the second data release (DR2) of Gaia. For 45 T2C with periods from 1 to 20 days, parallaxes, proper motions, and [Fe/H] values are available for 25 stars. Only 5 show [Fe/H]<-1.5, while the remaining stars show thick disk kinematics and [Fe/H]>-0.90. We have compared the T2C stars of the field with their cousins in the globular clusters of the Halo and found that the globular clusters with T2C stars show metallicities and kinematics of a pure Halo population. The globulars may have formed during the overall collapse of the Galaxy while the individual thick disk T2C stars may have been captured from small systems that self-enriched prior to capture. The relationship of these two populations to the micro-galaxies currently recognized as surrounding the Galaxy is unclear.


INTRODUCTION
The concept of stellar populations was introduced by Baade (1944), who called attention to the differences between stars in the spiral arms of galaxies as compared to galactic halos and bulges. At the Vatican Conference (O'Connell 1958), the concepts of halo, thick disk, thin disk, and spiral arms were specified. The Halo was defined by the globular clusters and stars whose motions carried them to large distances above the Galactic Plane. Metallicity studies by Chamberlain & Aller (1951), Schwarzschild et al. (1957), and Helfer et al. (1959) showed that both individual stars and globular clusters of the halo are deficient in metals by factors as large as 100. Subsequent surveys of individual stars and integrated light of globulars showed a substantial range in metallicity (Deutsch 1955, Kinman 1959. The assignment of a star, or a group of stars, to a specific population involves both the location and kinematics of the star or group. It is preferable to employ metallicity as a property of a population rather than as a defining parameter.
Once the difference between Classical Cepheids and Cepheids in globular clusters had been recognized by Baade (1956), the T2C stars seemed to be tracers of the Halo. At that time, the T2C stars were mostly too faint for high dispersion analysis of their metallicity, but their radial velocities could be measured. Using their velocities and positions, Woolley (1966) concluded that most, but not all, of the T2C stars at substantial galactic latitudes belonged to the thick disk population rather than to the Halo population and its globular cluster T2C stars. T2C stars are also found in the Large and Small Magellanic Clouds (Soszyński et al. 2008(Soszyński et al. , 2010, but their velocities and metallicities have not been evaluated because of their faintness. In this paper, we present kinematic and metallicty data for individual T2C stars in the field, and compare their properties with T2C stars in globular clusters.

OBSERVATIONS
The second data release of Gaia provides a substantial upgrade in the avaiable data for T2C stars in the Galac-tic Halo. Over the 50 years since Woolley's paper, many Cepheids have been found at substantial distances above the Galactic Plane. In the General Catalogue of Variable Stars (Samus et al. 2001), they are listed as CW stars. The Catalogue of H. C. Harris (1985), and new identifications by Schmidt et al. ( ,b, 2004, have provided a substantial database for T2C stars in the field. Metallicities have been provided by Maas et al. (2007), , Harris (1981), Kovtyukh et al. (2018b), and Lemasle et al. (2015). So as to avoid the Galactic Bulge, we have excluded from our list stars with a galactic longitude between 350 and 10 degrees, and with a galactic latitude less than ± 10 degrees. Only the stars whose parallax exceeds the probable error of their parallax by a factor of at least 5 have been included. 1 The distances and proper motions of T2C stars had been largely unknown until Gaia DR2 (Luri et al. 2018). Hence, we have assembled a list of T2C field stars with their periods, distances, absolute magnitudes, and metallicities. Our assembled data for T2C stars in the galactic field are shown in Table 1. We plotted [Fe/H] against period for each T2C star in the field in Figure 1, where we separate the halo and disk cepheids by [Fe/H] = -1.0.
For the globular clusters, data are to be found in the catalogue of C. Clement (updated January 2017), combined with the catalogues of H. Sawyer Hogg (Clement et al. 2001), which includes the metallicities of each cluster with a T2C star. We have omitted the cluster Omega Cen, and the 2 unusual globulars NGC 6388 and NGC 6441, as they are probably the remains of elliptical galaxies (Corwin et al. 2006). 2 For the T2C stars in the 1 There is no simple way to balance the need to include as much data as possible without including data with an undesireable level of uncertainty. For a discussion of parallax errors see Luri et al. (2018), Bailer-Jones et al. (2018), as well as Lutz & Kelker (1973).
2 Omega Cen is a special environment for variable stars because it seems to contain stars with [Fe/H] from 0.0 to -2.5. According to Clement et al. (2001), it has 9 stars classified as Cepheids, and one RV Tau star. According to Gonzalez & Wallerstein (1994) Galactic Bulge, see the paper by Bhardwaj et al. (2017). A few stars with periods over 20 days have been excluded because they are rare and may show RV Tau behavior. 3 To compare the field and globular cluster T2C stars, we plotted [Fe/H] against period for each star that is a cluster member in Figure 2.
Globular clusters show an absence of T2C stars with periods between about 3 and 9 days, with the exception of variable 3 in M10, and variable 2 in M13, which fall in the middle of the gap for variables in globular clusters.

The field stars show a deficiency of variables with [Fe/H]
Omega Cen, despite its very wide range in metallicity, shows only metal-poor variables, and similar stars that lie above, or to the left of, the red giant branch.
3 RV Tau behavior is defined as alternating low and high minimum light. It is usally seen in T2C stars with periods greater than 20 days, however, the term has also been used for T2C stars with periods greater than 20 days, even though their minima have not shown alteration.
< -1.0, with the exception of a small clump with periods between 1 and 3 days, and [Fe/H] between -1.5 and -2.0 recently analysed by  and called UY Eridani stars. Short period T2C stars with significantly larger metallicities are usually called BL Herculis stars.

KINEMATICS OF T2C STARS IN THE FIELD
Stellar populations are closely associated with the galactic orbits of the objects in question. Their stellar motions with respect to the local standard of rest (LSR) may best be parameterized by their U, V, W components of motion, where the component U is positive toward the Galactic Anticenter, V is positive in the direction of Galactic Rotation, and W is positive toward the North Galactic Pole. In Table 2, we show the U, V, W, components for each T2C star with a parallax of at least 5 times its probable error in the Gaia catalogue. The U, V, W components of motion were calculated using the gal uvw script (Koposov 2016) 4 available on GitHub, which follows the outline of Johnson & Soderblom (1987), except that U is positive toward the Galactic Anticenter, rather than the Galactic Center, and the J2000 transformation matrix to galactic coordinates was taken from the Hipparcos and Tycho Catalogues (ESA 1997). Radial velocities were taken from Gaia DR2, Beers et al. (2000), Kordopatis et al. (2013), Kharchenko et al. (2007), and Barbier-Brossat et al. (1994). The radial velocities in Gaia DR2 are preliminary, because they were measured during each visit with the Gaia spectrograph, which covers a wavelength from 8500 -8900Å with a resolution of 11,000, just as the Radial Velocity Experiment (RAVE) did. In Figure 3, we show the dependence of the U, V, and W components on the metallicity of each star. The distribution of the W components is the most important for distinguishing the population of halo stars. T2C stars with [Fe/H] from 0.0 to -1.0, show a distribution from -60 to 100 km s −1 , with single outliers near -100 and 180 km s −1 . For the metal-poor stars with [Fe/H] < -1.5, the W components lie from -100 to 100. It is interesting to note the large negative V components for the metalpoor stars, indicating that their orbits are retrograde and the stars must have been captured. Despite the current century being called the "era of big data", there are so few stars in this category that little is proven from this sample.

KINEMATICS OF T2C IN GLOBULAR CLUSTERS
We can still compare the small sample of T2C stars with globular clusters that contain Cepheids as shown on the right side of Figure 3, where the data for their distances, proper motions, and radial velocities have been obtained from the Gaia Collaboration et al. (2018) and Harris (1996).
In Table 3, we show the kinematics of globular clusters with at least 1 T2C star. The sample of T2C stars in globular clusters must be nearly complete due to the many investigations of variable stars in clusters. They are found in globulars with [Fe/H] ≤ -1.0.
There are other environments with T2C stars including the Large Magellanic Cloud (Soszyński et al. 2008    the Small Magellanic Cloud (Soszyński et al. 2010), the Fornax system (Bersier & Wood 2002), and the Galactic Bulge (Bhardwaj et al. 2017), but none of them have been investigated for their metallicity.
In Table 4, we show the kinematics of globular clusters that lack T2C stars.

DISCUSSION
An examination of Figure 3 permits the following relationships between T2C stars in the field and in globular clusters.
2 -The field T2C stars are rather well clumped in the U, V, and particularly W components.
3 -Globular clusters with T2C stars have widely spead U, V, and W velocities.
4 -Non-bulge globulars without Cepheids show a wide range in U and V components, and a significant range in W, which means a wide range in height above of below the Galactic Plane to which they penetrate. It was on this basis that the globulars have been used to define population II. 5 -As shown by their V components, the 5 halo T2C stars appear to be in retrograde orbits, indicating that they are captured.

CONCLUSIONS
We confirm the suggestion by Woolley (1966) that most of the T2C field stars of the Galactic Halo belong to a different population than the globular clusters of the Halo. This raises a number of questions as to the origin of the Halo.
The origin of the Galactic Halo has been an important aspect of research on galactic structure ever since the Vatican Conference (O'Connell 1958). Two different approaches have been suggested; the model of Eggen et al. (1962), which suggests that the Halo consists of material left behind as the galaxy contracted to a central bulge with spiral arms, and that of Searle & Zinn (1978), who proposed a model in which the Halo consists of small systems that have been captured over time by the galaxy's gravitational field. The latter is supported by the discovery of fragments such as those described by Willman (2010) and many others over the past decade (McConnachie 2012), most recently, Myeong et al. (2018).
Of the various stellar types found in the Halo, the T2C stars have the highest visual luminosity, and are easy to recognize by their periods from 1 to 20 days. However, it is surprising that the 2 elliptical companions to M31, NGC 147 and NGC 185, do not have any T2C stars at all ) despite the presence of many RR Lyrae stars in both galaxies. In addition, a search for variables in 6 small companion galaxies of M31 revealed 870 RR Lyrae stars, and 15 annomalous Cepheids, but not a single recognized T2C star (Martínez-Vázquez et al. 2017). A search for T2C stars in the giant ellipticals in nearby galaxy clusters would require photometry down to V=28, and probably a telecope of 30-m aperture. In the meantime, we await the discovery of additional T2C stars in our galaxy with Gaia, Pan-STARRS, and the Large Synoptic Survey Telescope (LSST). This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).
Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.