The Metallicities and Kinematics of Rr Lyrae Variables from Asas

THE METALLICITIES AND KINEMATICS OF RR LYRAE VARIABLES FROM ASAS

Xiao Chen

A Thesis

Submitted to the Graduate College of Bowling Green State University in partial fulﬁllment of the requirements for the degree of

MASTER OF SCIENCE

August 2015

Committee:

Andrew C. Layden, Advisor

John B. Laird

Dale W. Smith ii

ABSTRACT

Andrew C. Layden, Advisor

Studying RR Lyrae stars (RRLs) is a useful way to understand the formation and struc-

ture of our Galaxy. We obtained spectra of 89 RRLs of Bailey type ab. After processing these

spectra, we obtained the radial velocity for each star. We also derived the pseudoequivalent

widths (EWs) of CaIIK, Hδ,Hγ and Hβ from their absorption lines. Then we transformed

our EWs to the same system used in Layden [14], and calculated the metal abundances.

To investigate the kinematics and metallicities of our RRLs, we derived rotation veloci-

ties and velocity dispersions from stars’ radial velocities. After combining our radial velocities

and the literature proper motions, we derived space motions for 85 of our RRLs. We plotted

rotation velocities against metallicities, and found an abrupt change at [F e/H] ≈ −1.0. iii

ACKNOWLEDGMENTS

My sincere gratitude goes to my advisor, Dr. Andrew C. Layden, for his great patience and helpful guidance. This research project would not be accomplished without him.

I would also like to thank my committe members, Dr. John B. Laird and Dr. Dale W.

Smith. Their assistance and instructions have been of great help to this thesis.

Finally, I would like to thank my parents. Their support and love have encouraged me to get this far. iv

TABLE OF CONTENTS

Page

CHAPTER 1. INTRODUCTION ...... 1

CHAPTER 2. SPECTROSCOPIC DATA ...... 6

2.1 Observing ...... 6

2.2 Image Processing ...... 7

2.3 Spectral Processing ...... 8

CHAPTER 3. DATA FROM THE LITERATURE ...... 15

3.1 Photometry ...... 15

3.2 Galactic Dust Reddening and Extinction ...... 23

CHAPTER 4. RADIAL VELOCITIES ...... 25

4.1 Radial Velocity Method ...... 25

4.2 Radial Velocity Checks ...... 28

4.3 Radial Velocities ...... 31

CHAPTER 5. METALLICITIES ...... 35

5.1 Equivalent Widths ...... 35

5.1.1 Measurements ...... 35

5.1.2 Calibrating EWs ...... 39

5.2 Metallicities ...... 41

5.2.1 Rough [Fe/H] ...... 45

5.2.2 Interstellar CaK ...... 46

5.2.3 Hβ ...... 46

5.2.4 Final [Fe/H] ...... 47

5.2.5 Rising Branch ...... 48

CHAPTER 6. KINEMATICS ...... 50

6.1 Rotation Velocities ...... 50 v

6.1.1 Net Rotations ...... 50

6.1.2 Plots and Analysis ...... 52

6.1.3 Combining ...... 56

6.2 Woolley Solutions ...... 56

6.3 Space Motions ...... 59

6.4 Discussion ...... 62

CHAPTER 7. CONCLUSION ...... 65

REFERENCES ...... 67 vi

LIST OF FIGURES

Figure Page

1.1 Galactic Components ...... 1

1.2 Two Galactic Formation Models ...... 4

2.1 Trim the Spectra ...... 8

2.2 Fix Bad Pixels ...... 9

2.3 2D to 1D ...... 9

2.4 Intensity vs. x-pixel ...... 10

2.5 Typical Final Spectrum ...... 12

2.6 High S/N Final Spectrum ...... 13

2.7 Low S/N Final Spectrum ...... 14

3.1 Good Phase Sample ...... 20

3.2 Bad Phase Sample ...... 21

3.3 Hammer Projection ...... 22

3.4 Galactic Dust ...... 23

4.1 Typical Peak and Object/Template Pair ...... 26

4.2 Poor Peak ...... 26

4.3 Narrow & Wide Peak ...... 27

4.4 HD 693 ...... 29

4.5 Templates ...... 30

4.6 RV vs. Phase for ASAS 004025 ...... 33

4.7 RV vs. Phase for ASAS 232246 ...... 34

5.1 Absorption Lines ...... 36

5.2 Hβ Line ...... 37

5.3 CaIIK Line for A Cool Star ...... 38

5.4 CaIIK Line for A Hot Star ...... 39 vii

5.5 Hδ For Calibrating EWs ...... 40

5.6 H2 vs. Phase ...... 43

5.7 The Relation of Phase and EWs ...... 44

5.8 WK vs. H2 ...... 45

5.9 FeH vs. Phase ...... 49

6.1 Angle Relations ...... 51

6.2 Rotational Velocities ...... 53

6.3 Vs vs. cos Ψ ...... 54 6.4 Combined Rotational Velocities ...... 57

6.5 Combined Vs vs. cos Ψ ...... 58 6.6 Space Motions ...... 61 viii

LIST OF TABLES

Table Page

2.1 Comparison Format Sample ...... 7

3.1 ASAS Data Sample ...... 16

3.2 Photometry Data Sample from ASAS ...... 18

3.3 Final Data from PDM ...... 19

4.1 FXCOR Data ...... 28

4.2 Data of Template Stars ...... 31

4.3 Fitted RVs ...... 33

5.1 EW Regions ...... 38

5.2 Coeﬃcients of the Fitted Lines ...... 40

5.3 Calibrated EWs ...... 42

5.4 Final Metallicities ...... 48

5.5 Calibrating Rising Branch ...... 49

6.1 Values of Rotational Velocities ...... 55

6.2 Values of Combined Rotational Velocities ...... 56

6.3 Woolley Solutions ...... 59

6.4 Woolley Solutions from Combined Data ...... 59

6.5 Space Motions ...... 60

6.6 MWTD ...... 60

6.7 Kinematics of the Halo and Disk Stars ...... 62

6.8 Test1 ...... 63

6.9 Test2 ...... 64 1

CHAPTER 1. INTRODUCTION

The major components of the Milky Way are the disk, the halo and the nucleus or central bulge. Figure 1.1 shows the structure of our Galaxy. The left picture is the top view of the Galaxy, while the right picture is the side view of it.

In order to understand these components, the metallicity must be mentioned ﬁrst. When a massive star is in its last stage, it starts to fuse iron. Then the iron is ejected to space by a supernova detonation. In this case, new stars have higher metal abundances than the old stars. They are metal-rich stars. Thus, the ratio of iron-to-hydrogen, called metallicity, can indicate the age of a star. Its expression is

NF e − NF e [F e/H] = log10( ) log10( )⊙ (1.1) NH NH where NF e and NH are the iron and hydrogen atom numbers per unit of volume respectively. ⊙ means the Sun. Obviously, our Sun has a metallicity of 0.0. Metal-rich stars have large values, around 0.0; and metal-poor stars have small values, some old stars have metallicity as low as −4.5 [7].

The disk contains most of the dust, gas and stars of our galaxy. The dust and gas

Figure 1.1: Components of the Milky Way. This picture is from JCCC [11]. 2

between stars are called the interstellar medium, which has an inﬂuence on the stars’ distance

measurements. Our Sun is a disk star. Instead of residing near the center of the disk, the

Sun lies about one-third away from the center. Its distance from the center of the Galaxy

is 8.0 0.5 kpc. Thin disk and thick disk are the main components of the disk. Thin disk

is about 50 pc in height, while the thick disk has a height of about 1.4 kpc. However, the

stellar number density of the thick disk is about 2% of the density of the thin disk. [7]

The stars in the thin disk are younger than the stars in the thick disk. The metallicities

of thin disk stars have a range of −0.5 < [F e/H] < 0.3, while most thick disk stars have

−0.6 < [F e/H] < −0.4, though some thick disk stars may have very low metallicities, as low

as −1.6 [10]. The disk stars rotate around the center of our galaxy with uniform velocities.

The halo contains plenty of globular clusters and ﬁeld stars (stars that are not in globular

clusters). They are very old stars. Astronomers estimate that there are 230 globular clusters

in the halo, and more than half of the clusters have been detected. Clusters are located in

all directions of the spherical halo. Some younger globular clusters ([F e/H] > −0.8) are

even associated with the thick disk [35]. The halo stars have long ellipsoidal inclined orbits

and a wide range of velocities compared to our Sun. They move in orbits crossing the disk

or the bulge around our galactic center.

The bulge has the highest density of stars in our galaxy. Astronomers have diﬃculty in

studying the properties of bulge stars because the gas and dust between us and the bulge

cause a large amount of extinction. However, some lines of sight, which contain the minimal

amount of extinction, allow us to observe the bulge. One well known example is Baade’s

Window, discovered by Walter Baade in 1944. It is 3.9 degrees below the galactic mid-plane.

The bulge has young stars and old stars. The metallicities vary from −1 to 1. Evidence

shows that the mean [Fe/H] is around +0.3.[7] The bulge stars have almost a spheroidal rotation around the center, although stars with diﬀerent [Fe/H] present diﬀerent kinematics

[19]. 3

There are two competing models describing the formation and evolution of our galaxy.

The classical model is called the ELS Model. It was published by Eggen, Lynden-Bell &

Sandage [8]. It tells that the Milky Way formed from a single, large, proto-galactic cloud that collapsed rapidly. This early cloud is almost a sphere and it is spinning very slowly. As the gravity began to collapse the cloud to the center region, according to conservation of angular momentum, the spin of the cloud increased. If this model is correct, since the proto-galacxy always spinned in the same direction, stars formed in this stage (the halo stars) should rotate in the same general direction. As the proto-galaxy collapsed, the newly formed stars will have larger rotational speed and present only a gradual change. The other model was presented by Searle & Zinn [28]. Smaller proto-galactic clouds collapsed and formed early dwarf galaxies, then they merged together and became spheroids. In this way, the oldest stars formed in their dwarf galaxies independently. When these stars merged together, they would show irregular rotations in different directions, but for the stars (the disk stars) formed after the gas and dust from different dwarf galaxies merged together, they would still rotate in the same direction. In addition, if this model is correct, stars with the same metallicities may even show different kinematics. Figure 1.2 shows two different kinematics of the above two models. Thus, studying kinematics of stars can help us investigate the galactic formation models.

To understand the formation history and structure of our Galaxy, old stars are valuable.

Subdwarfs [26], red giants [18], asymptotic giant branch stars [4], horizontal branch stars

[13] and globular clusters [2] have been investigated. However, each of these types has its own disadvantages. The best approach is to combine all the results derived from all kinds of stars.

RR Lyrae stars (RRLs) are also important in studying the Milky Way [25]. RRL stars are commonly observed in Globular Clusters. They are old stars, typically more than 10 billion years old. For a star with similar mass to our Sun, when the hydrogen in the core of 4

Figure 1.2: Two galactic formation models. The left one is for the ELS Model, the right one is for the Searle & Zinn Model. a star is depleted, the star rises up the red giant branch. Its core begins to shrink and heats up, while the outer layer of the star swells. As the core temperature and density keep rising, the temperature in the core ﬁnally becomes high enough to initiate the triple alpha process, then the helium core ﬂash happens as helium fuses into carbon. During this stage, the star is on the horizontal branch with a hydrogen-burning shell and a helium-burning core. It stops shrinking and the core maintains constant temperature. Then some of the stars evolve through the instability strip and become RR Lyrae Variables, depending on the stars’ mass.

A RRL star has stable pulsation. The energy and radiation produced by the star are trapped in the star’s ionization zone. This is caused by the increasing of the star’s opacity over time. Then pressure increases and ﬁnally overcomes the star’s gravity, so the surface of the star begins to expand. Next, expansion allows trapped radiation to escape, so the star becomes cool and pressure decreases. Gravity then will compress the star back to its original size. That is one cycle (0.2 to 1 day). This pulsation leads to the change of star’s color and luminosity, and makes RRL stars easier to be identiﬁed.

There are three types of RRLs. RRab stars pulsate in the fundamental mode, which 5 means their light curves increase rapidly and decline gradually. They have longer periods, between 0.3 to 1.2 days. They are the easiest to ﬁnd because they have larger amplitudes, and most of RRLs are observed as RRab type. RRc stars pulsate in the ﬁrst overtone mode, which means their light curves are more symmetric, and their pulsation periods are shorter, between 0.2 to 0.5 days. The third type is RRd. They pulsate in both the fundamental and overtone modes. Smith [29] points out that RRd stars are often RRL stars which are in the process of switching from RRab to RRc, or vice versa.

Since most RR Lyraes have stable pulsation, they can be identiﬁed easily. And since they have high luminosity (absolute magnitudes MV ≈ 0.6 mag) and can be seen at large distances, they are used as standard candles for the distance scale [6][24][31]. We also trace them for investigating the structure and history of our Galaxy in this study. Metal abundances of RRLs can roughly tell us their ages, thus, the components they belong to.

After combining their abundances with kinematics, we can understand the motions of the stars of diﬀerent components in our Galaxy, including the old components of the early galactic system. Thus, we can better comprehend the galactic formation history and structure.

In this thesis, we use the data of 89 RRLs to investigate their metalicities and kinematics.

In Chap. 2, we describe how we process our spectrograph data to obtain 1-dimensional normalized spectra. In Chap. 3, we describe how we gather photometry and Galactic dust exinction data from the literature to determine the properties of our 89 RRLs. Chap.

4 describes the utilization of red shifts in stars’ light waves in order to get stars’ radial velocities, while in Chap. 5, we discuss the method of determining pseudoequivalent widths of 4 absorption lines, CaIIK, Hδ,Hγ and Hβ, for each star. In Chap.6, we derive the kinematics of our RRLs using two diﬀerent techniques. We also plot net rotation and line of sight velocity dispersion against [Fe/H]. Chap 7 presents the conclusions of this study. 6

CHAPTER 2. SPECTROSCOPIC DATA

2.1 Observing

All of our spectra of RR Lyrae stars were provided by Robert Zinn and Kathy Vivas at

Yale University. Their goal of observing these stars is to add new solar neighborhood RRLs for comparison with the halo RRLs obtained in the La Silla-QUEST Southern Hemisphere

Variability Survey. The project was started in 2008. They picked stars with declination< 20◦ and large absolute value of cos Ψ (Ψ is the angle between a star’s rotational velocity and its line of sight velocity to the Sun) from the All Sky Automated Survey (ASAS). Then they observed these picked stars from August 2009 to February 2011.

All these spectra were taken with the 1.5m telescope operated by the Small and Mod- erate Aperture Research Telescope System (SMARTS). This telescope is located at Cerro

Tololo in the Coquimbo Region of northern Chile at geodetic latitude: 30◦10′09.42′′(s), geodetic longitude: 70◦48′24.44′′(w). Our spectra were taken with the 1.5 m Cassegrain spectrograph (cs60) using the Loral1K 1 CCD, with grating 26/Ia at a grating tilt of 16.14 degrees. This setup gives resolution of 1.47 A/pix˚ over a range 3650 Ato˚ 5400 A.˚

Our spectra were taken in queue mode in which astronomers give object names, coordinates, instrument settings and time of exposure, then the on-site technicians observe the objects. For each star on each night, we took three observations, in case of cosmic rays or other eﬀects. The exposure time varied, being 30 s, 100 s, 150 s or 200 s, depending on the star’s magnitude. Also, a spectrum of HeNe(Ar) comparison source was observed before and after each star’s observations on each night, so for each star, the observations had the sequence shown in Table 2.1.

After organizing and characterizing the spectra returned from SMARTS, we found they contained 89 RR Lyrae stars and 6 radial velocity (RV) standard stars from Table 4 of Layden

[14]. Since the actual radial velocities of these RV standard stars can be easily obtained from 7

Star1 Comparison1 Star2 Comparison1 ... Star1 Spectrum1 Star2 Spectrum1 ... Star1 Spectrum2 Star2 Spectrum2 ... Star1 Spectrum3 Star2 Spectrum3 ... Star1 Comparison2 Star2 Comparison2 ...

Table 2.1: A sample of the observation sequence. the literature, they are normally used to compare with the RRLs to obtain the RVs of RRLs.

We found the RV of each standard star in SIMBAD [32] (see Table 4.2).

2.2 Image Processing

Raw spectra cannot be used directly. Since our spectra were observed by telescope and recorded by CCD camera, the eﬀects caused by bias, ﬂat and bad pixels should be removed

ﬁrst.

For each spectrum, we trimmed oﬀ the edges of both sides and just kept the section which contained useful information. See Figure 2.1.

Then we removed bias eﬀect. Bias is caused by DC oﬀset, which means when the CCD camera is exposed to no light, the pixels on CCD have a non-zero level of counts. To remove this constant level of charge, 25 bias frames were taken with no exposure before each night.

Then we averaged these frames and subtracted it from each spectrum taken that night.

The process of correcting the flat field was similar. Vignetting and the shadows on optical instruments, and the different sensitivity of each pixel on the CCD cause a uniform illumination to give a non-uniform response across the CCD. 25 spectra of an illuminated white screen were taken each night. For each observation night, we combined all flat field frames by calculating the mean value for each pixel, then we divided all star frames by the averaged flat field frame.

The last step of processing is to ﬁx bad pixels. These bad pixels may due to the bad pixels on CCD camera or to cosmic rays. Every spectrum was checked visually. For those 8

Figure 2.1: Trim oﬀ the edges. The white line in the center of the spectrum contains all useful information. bad pixels found away from absorption lines (CaIIK, Hδ,Hγ,Hβ), we replaced them with the average of the two adjacent normal pixels. Fortunately, for all our 2-Dimensional (2D) spectra, we did not get any bad pixels in the absorption lines.

2.3 Spectral Processing

Since 1-Dimensional (1D) spectra merge all useful pixel information together, they are more useful. So the next process was to extract 1D spectra from 2D spectra. First we located the star spectrum region near the middle, and two sky background regions on either side of the star spectrum, as shown in ﬁgure 2.3.

Then we traced the stellar spectrum region of each spectrum along the x-axis, pixel by pixel. For the ith x-pixel, we calculated the weighted sum of the intensities of the pixels in the stellar spectrum regions along the y direction, Si,j, where j (j=1,2, . . . , M) are the M 9

=⇒

Figure 2.2: Fix bad pixels.

Figure 2.3: Process of 2D to 1D. This plot shows the regions of star spectrum and two sky spectrum. The areas of the sky spectra on both sides are the same as the area of the star spectrum. 10

Figure 2.4: Intensity vs. x-pixel. pixels across the stellar aperture. We did the same calculation for the two sky regions and obtained the weighted means of the two regions, Ui and Di respectively. Then we subtracted the average of Ui and Di from Si. So the actual intensity of the ith pixel in the star spectrum region Ai is the sum of the sky-subtracted intensities at each y-value, as shown in Equation 2.1.

∑M Ui + Di Ai = (Si,j − ) (2.1) j=1 2

Therefore, we had one dimensional stellar spectra, x-pixel vs intensity, shown in Figure

2.4. 11

Next, the HeNe(Ar) comparison sources were used to find a relation between x-pixels and wavelengths, so that we could turn the intensity vs. x-pixel plot into intensity vs. wavelength plot. For each star, the sequence of our observations is shown in Table 2.1. We had already extracted star spectra, so next we performed identical extractions on comparison1 and comparison2. Using the known wavelengths of 47 known emission lines, we fitted a second order spline and got relations between wavelength and x-pixel for comparison1 and comparison2, respectively. The root mean squares (RMS) of the fits were around 0.19 A,˚ which gave an uncertainty of 12.6 km/s in the radial velocity. We then interpolated the relations between comparison1 and comparison2 in time, so that comparison1 had more weight on star spectrum1, while comparison2 had more weight on star spectrum3.

Finally, we normalized the continuum to ﬂatten each spectrum to remove the wavelength- dependent instrumental response. For each spectrum, we ﬁtted a cubic spline function to the continuum and rejected any points in tall emission lines or deep absorption lines, then divided the spectrum by that function, so every point of the continuum was equal to 1.

Figures 2.5 to 2.7 show some examples of our ﬁnal spectra. The resulting 624 spectra of 89

RRLs had the resolution of 1.47 A/pix˚ from 3650 Ato˚ 5400 A.˚ 12

Figure 2.5: A typical case of our ﬁnal spectrum. 13

Figure 2.6: High signal-to-noise ﬁnal spectrum. 14

Figure 2.7: Low signal-to-noise ﬁnal spectrum. 15

CHAPTER 3. DATA FROM THE LITERATURE

3.1 Photometry

Star positions are very important to determine the kinematics of RRL variables. The

position of a star is decided by two components: direction and distance. Directions can be

taken from literature, and the distance modulus formula can tell us the distances, d, which

− − − V MV AV = 5 log10 d 5 (3.1)

where V is the apparent magnitude of a star, MV is its absolute magnitude, and AV means extinction. We can tell from this formula that, in order to obtain the distances, we must obtain magnitudes and extinctions.

However, RR Lyrae stars are pulsating stars, so their magnitudes change periodically.

To obtain their actual magnitudes, as if the stars are in equilibrium, we need to determine their periods and light curves ﬁrst.

First, we had expected to obtain accurate periods and magnitudes from the literature, so we gathered data from the ASAS [23]. ASAS is a project that ﬁnds and catalogs variable stars. It has two observing stations; one is located at Las Campanas Observatory

(LCO), Chile, while the other one is in Haleakala, Maui. ASAS takes V-band variables with

2048∗2048 CCD. They use a 0.2 m, f/2.8 lens and the exposure time is 180 s. ASAS has plenty of photometric data of variable stars of the southern hemisphere (declination< +28 degrees). We recorded right ascension, declination, ASAS ID, period, epoch of maximum brightness, magnitude at maximum brightness, amplitude of variation, type and the other name from ASAS for each star, and made a table. Table 3.1 is a sample.

After we checked these data, we noticed that, for many stars, the light curves showed 16

TITLE RA DEC ASAS name Period T0 Vmax Vamp Type OtherName ASAS 000602 00:06:01.86 -36:54:16.1 000602-3654.3 0.43911 1870.55 13.38 0.63 RRAB WW Dcl ASAS 000621 00:06:21.01 -35:17:05.9 000602-3517.2 0.57767 1869.57 13.03 1.20 RRAB NSV00029 ASAS 001543 00:15:41.19 -58:53:05.9 001543-5853.1 0.62538 1870.95 12.88 1.02 RRAB UZ Tuc ASAS 002418 00:24:19.22 -76:16:39.3 002418-7616.9 0.56874 1870.48 13.17 1.12 RRAB T Hyi ASAS 002443 00:24:44.03 -69:49:50.9 002443-6949.7 0.72792 1870.4 10.98 0.38 RRAB/DCEP-FO -

Table 3.1: A sample of stars’ properties from ASAS. 17 on the ASAS’s website had low signal-to-noise and they were scattered, and we found they could be improved. So, we gathered photometric data (magnitudes vs. time) from ASAS to get the best period and mean magnitude for each star. After removing comment lines, we obtained a table like Table 3.2. The average number of data points is around 650. Each data row contains 13 fields. HJD is Heliocentric Julian Date of that observation. MAG shows the magnitude for each of five apertures with different sizes. The difference of the five MAGs is less than 0.1. MER presents the magnitude uncertainty for each aperture. FRAME is the frame number, and for GRADE, A means the best while D is the worst.

To keep our data consistent, we chose aperture 2 in all cases. We also removed pho-

tometric data marked as grade C and D, and used the IRAF package Phase Dispersion

Minimization (PDM) to ﬁnd the best periods. We compared our periods with ASAS peri-

ods; more than 70% of the periods we got from ASAS resulted in light curves with large

scatter, and for half of the 89 stars, we found better periods using PDM. We also determined

the error in period by checking the nearby periods around the best period we found. When

the scatter of the light curve becomes large, then we can deﬁned the range of the error. Then

we plotted the light curve of each star (Figure 3.1 and 3.2) using the ﬁnal periods and used

a program called STDLC to compare the plotted light curve with 10 template RRL light

curves, to find the best fitted one. The first to sixth of the light curves are RRab types; the

seventh light curve is RRc type, and the eighth is sine curve, while the last two are eclipsing

binary types. Next, the program analyzed the best ﬁtted light curve to obtain the following

properties: mean magnitude, maximum magnitude, minimum magnitude, amplitude of vari-

ation, epoch of maximum brightness(T0), number of observations, template number, root

mean square (RMS), sigal to noise (S/N) and period error. RMS and S/N present the scatter

of observation points. If they both have small values, then our data points match the light

curve very well, and vice versa. Table 3.3 shows part of the ﬁnal properties.

To understand the location of our RRL sample on the sky, we used equatorial coordinates 18

HJD MAG 0 MAG 1 MAG 2 MAG 3 MAG 4 MER 0 MER 1 MER 2 MER 3 MER 4 GRADE FRAME 1869.52275 13.869 13.872 13.992 140.79 14.074 0.052 0.035 0.027 0.029 0.029 A 193 1871.60719 13.706 13.730 13.767 13.771 13.711 0.084 0.041 0.031 0.032 0.031 B 507 1873.57974 13.237 13.270 13.353 13.424 13.422 0.072 0.040 0.031 0.033 0.033 A 818 1875.57412 13.643 13.697 13.766 13.811 13.829 0.073 0.042 0.032 0.034 0.033 A 1138 1881.55620 13.319 13.328 13.343 13.305 13.301 0.058 0.037 0.027 0.030 0.030 A 2078 1885.54641 13.254 13.242 13.356 13.552 13.599 0.052 0.038 0.029 0.031 0.033 A 2385

Table 3.2: A sample of photometry data from ASAS. 19

TITLE Period Vmean Vmax Vmin Vamp T0 #Obs T RMS S/N Perr Comment ASAS 000602 0.784880 13.618 13.220 13.926 0.706 3512.43518 383 6 0.201 3.5 2 ASAS 000621 0.577670 13.541 12.915 14.011 1.096 2985.59114 387 2 0.206 5.3 20 ASAS 001543 0.625311 13.168 12.509 13.558 1.049 4736.14325 724 1 0.155 6.8 5 ASAS 002418 0.568740 13.704 13.142 14.166 1.024 2226.51785 968 6 0.280 3.7 20 ASAS 002443 0.727967 11.109 10.928 11.285 0.357 4367.29273 585 7 0.064 5.6 10

Table 3.3: Part of the ﬁnal properties derived by PDM. 20

Figure 3.1: A good case of period. The data points are concentrated. The light curve can be easily recognized. 21

Figure 3.2: A poor case. The scattered points cause a large uncertainty of the light curve. 22

Figure 3.3: Hammer projection. obtained from ASAS, converted them to a galactic coordinate system. In this system, the

Sun in the origin , galactic longitude, l, has a range of 0◦ to 360◦ and points from the Sun to the galactic center in the galactic plane, while galactic latitude, b, has a range of −90◦ to 90◦ with 0◦ at the galactic plane and measures the angle above the galactic plane. We plotted the galactic coordinates of our 89 RRLs on a Hammer equal-area projection. See

Figure 3.3.

It is obvious that most of our stars are concentrated in the fourth quadrant, which means they are below the galactic plane. 23

Figure 3.4: Galactic dust reddening and extinction(Picture from IRSA) [27].

3.2 Galactic Dust Reddening and Extinction

The interstellar medium between the observed star and the observer can absorb and scatter light waves. The absorption and scattering can affect the star’s apparent brightness, thus, the calculation of distance. This effect is called extinction. The interstellar medium is not uniform in space. The disk of our Galaxy contains more gas and dust, while the halo has less. Figure 3.4 shows the galactic dust distribution plotted in an Aitoff projection [27].

Extinction cannot be obtained directly. However, its eﬀect on the colors of stars, reddening, can be easily obtained from the literature. Reddening occurs because the interstellar medium scatters blue wavelengths more than red wavelengths. This eﬀect makes stars ap- pear redder. With the right ascension and declination obtained for all the stars, we gathered their dust reddening for a line of sight provided by Schlegel [27]. Then we assumed the ratio of visual extinction, AV , to reddening, E(B − V ), is

A V = 3.1 (3.2) E(B − V ) 24

in order to calculate AV [27].

Absolute magnitude, MV , is the last term that needs to be determined. According to

Cacciari [5], MV of RRL and the metallicity, [F e/H], have the following relation:

MV = 0.52 + 0.24([F e/H] + 1.5) (3.3)

To calculate MV ,[F e/H] must be obtained ﬁrst. Details of computing [F e/H] will be discussed in Chapter 5. 25

CHAPTER 4. RADIAL VELOCITIES

4.1 Radial Velocity Method

We used the IRAF package FXCOR to measure the radial velocities. This package

compares the object spectra of RRLs with template spectra of RV standards, whose radial

velocities are known, to get the unknown velocities of the objects.

FXCOR uses the Fourier cross-correlation method to ﬁnd the wavelength shift, ∆λ, between an object and a template spectrum [30]. Cross-correlation is a measure of similarity of two waveforms, in this case, two stellar spectra: one object spectrum of unknown velocity, v0, and one template spectrum of known velocity, vt. Figure 4.1 is an example of the FXCOR output for an object/template pair. The x-axis represents pixel shift, ∆p, that is ∆λ divided by the spectral resolution in A/pixel,˚ while y-axis is the correlation fraction. If the correlation peak is high, it means the object spectrum and the template spectrum match well, and they both have high S/N. Figure 4.1 is a typical case; the values of our correlations are around

0.6 (0.5-0.7). We also have a worse case with correlation fraction around 0.4, as shown in

Figure 4.2.

The widths of the correlation peaks depend on the temperatures of stars. For a hot star, the absorption lines are wide, which makes the correlation peak broad. So a broad peak indicates one or both stars with high temperatures. The right plot of Figure 4.3 shows this case. If both spectra were taken from cool stars, the correlation will have a narrow peak, shown on the left of Figure 4.3.

We fit a Lorentzian function to find the peak of the correlation to determine the best estimate of ∆λ and its uncertainty. If the user is unsatisfied with the fit, they can adjust the background level for the Lorentzian fit, or adjust the number of pixels used in fitting the peak. Then wavelength shift, ∆λ, is the x location of the cross-correlation peak, so the radial velocity of the object (RRL) is 26

Figure 4.1: Typical correlation peak and an object/template pair.

Figure 4.2: A poor case of our correlation peak. 27

Figure 4.3: The left side shows a narrow peak, the right side shows a wide peak.

∆λ v = c + v (4.1) o λ t

where λ is the center wavelength of the x-axis, c is the speed of light and vt is the velocity of the template star.

With each velocity, FXCOR provides an uncertainty determined by the full width at

half maximum (FWHM) and the height of the peak, thus, wider peaks with lower heights

usually result in larger uncertainties. The uncertainties derived from our spectra were around

50 km/s.

Additionally, if we have N object spectra Oi (i = 1, 2,...,N) and M template spectra

Tj (j = 1, 2,...,M), FXCOR will ﬁrst compare object spectrum O1 with the M template spectra, which means we will have M diﬀerent velocities and velocity errors for O1. Then it will go to the next object, O2, and repeat the work until the last object spectrum, ON . Table 4.1 shows an example. Finally, we calculate the weighted mean, standard deviation

and standard error of mean (SEM) of the M template spectra for each object spectrum, Oi. 28

object template Vhelio Verr O1 T1 ...... O1 T2 ...... O1 ...... O1 TM ...... ON TM ......

Table 4.1: An example of how FXCOR compares the spectra.

4.2 Radial Velocity Checks

We did some tests using FXCOR to check the results of RVs derived from our spectra.

The purpose of the ﬁrst test was to investigate how our data vary between 25 observation nights. Since RV standard stars are bright and have high signal-to-noise and HD 693 (RV standard star) is the most widely distributed star in our observation nights (11 nights), one of the HD693 spectra was chosen to be the template spectrum, and compared with HD 693 spectra of the other nights treated as object spectra (we randomly selected one HD 693 spectrum for each night). The RV of HD 693 from the literature is 14.81 km/s [32]. Figure

4.4 shows the results of the correlation. The points are scattered, the standard deviation is 45.2 km/s. However, the weighted mean is 7.8 km/s, which matches the paper RV very well. The scattered points may be caused by the wide width of slit of the focal plane in the telescope (2.0 arcsec). If the slit is too wide, the position of the star located on the CCD camera may be shifted relative to the center of the slit, and thus the centers of the comparison specrum lines. Then, when we transform the x-pixels of the spectrum to wavelengths using the comparison source, the values are inaccurate. This may cause the scattered points.

Since our data are scattered, we want to conﬁrm that these data are still trustworthy.

So the second test was to compare RV standard stars with themselves to obtain the RVs, and calculate their weighted means to see if they are close to the values from the literature or not. We selected one spectrum for each of our 6 RV standard stars, set it as the template 29

Figure 4.4: HD 693 self-correlations. 30

Figure 4.5: Templates compared with themselves. The x-axis shows RVs from the literature, each column presents one star, from left to right are HD 180482, HD 65925, HD 693, HD 22413, HD 74000 and BD-17 484 respectively; y-axis shows the diﬀerences of measured RVs and paper based RVs. spectrum, and used it with all the standard star spectra. After we averaged the values for each spectrum, the result is shown in Figure 4.5.

The points are still scattered, but they are better than the points in Figure 4.4, the overall standard deviation is 37.3 km/s. Table 4.2 shows the weighted mean and standard deviation for each template star. The weighted means are close to literature values (vpaper), which means our data are acceptable. 31

name weighted mean (km/s) std (km/s) type Nvisits vpaper (km/s) HD 180482 -22.30 1.41 A2 2 -22.80 HD 65925 -15.32 39.64 F6 V 11 -8.20 HD 693 8.51 42.25 F6 V 10 14.81 HD 22413 54.17 20.89 A3 10 35.8 HD 74000 188.30 30.33 A9 2 206.01 BD-17 484 246.58 27.73 F0 VI 5 234.7

Table 4.2: The measured and literature data of all template stars. From left to right are the name of stars, the weighted mean of the data points in Figure 4.5, the standard deviation of the points in Figure 4.5, the spectral type, the number of visits and the literature values.

4.3 Radial Velocities

Finally, we ran FXCOR on our RRL stars. We compared RRL stars with the 6 RV standard stars. For the 6 RV standard stars, we have 46 separate spectra on 25 nights. This can reduce the scatter seen in the above tests by correlating against many templates. For example, if the standard deviation of the sample is 50 km/s and we have 46 templates, then the standard error of mean (SEM) is just 7.4 km/s.

After calculating the weighted mean, standard deviation and standard error, we obtained the RVs for all our RRL stars. However, because RRLs are pulsating stars, their expansions and contractions will aﬀect their radial velocities. We need to take their pulsations (typically the pulsation velocity is around 70 km/s) into account, and obtain their center of mass RVs.

For each stellar spectrum, we determined the phase of the star at the time of observation, using the star’s period and epoch of maximum brightness obtained in Chapter 3. We also calculated the uncertainty of the phase using the period uncertainty. We shifted the period with the uncertainty and calculate the corresponding phase, the uncertainty in phase is the diﬀerence of the real phase and the phase derived from the shifted period.

Then for each star, we ﬁt a standard radial velocity template to the star’s RVs derived from our own spectra. Our template is based on the model provided by Liu [16]. However, his template and light curve amplitude relation were derived from the weak metal lines. 32

Since our radial velocities were derived mainly from hydrogen lines, we multiplied his velocity template by a factor of 1.63, which is a correlation caused by the hydrogen-dominated observed velocities [21]. We also used Liu’s Equation 1 to scale the template to ﬁt the light curve for each of our stars.

Finally, for each star, we plotted the phases of all the observations against their corre-

sponding RVs. Typically, each star was observed on two separate nights and has six spectra

in total. Then the standard radial velocity template was applied to ﬁt the data points

(shifted and scaled), and gave us a fitted RV (center of mass RV), Vfit (f in the plots), and its error. An RV-Phase plot for ASAS 004025 is shown in Figure 4.6. The fitting in this plot is poor, because the points do not match the RV template light curve well. Figure 4.7 shows a better fitting.

Table 4.3 shows the ﬁnal values of RVs and errors for the stars shown in Table 3.3. We

used Equation 4.2 to calculate the errors, errVfit,

2 2 0.5 errVfit = (e1 + e2) (4.2)

where e1 is the SEM of the points around the template curve; for e2, we applied a phase shift (the uncertainty in phase discussed above) to all the points and ﬁtted the template

curve to obtain the shifted fitted RV, Vshift, then e2 is the difference of Vfit and Vshift. Our errVfit has a range from 1.5 km/s to 42.9 km/s and its typical value is about 15 km/s. The uncertainties are small since we calculated the SEM in e1, which is affected by the number of points. However, the results are still reliable. First, in most cases, the template fitted the points well. Second, our errors in periods are small, less than 0.00002. These small errors in periods will lead to small uncertainties in phases, thus, errVfit will be small. 33

Figure 4.6: RV vs. phase for star ASAS 004025. This one is a poor ﬁtting, the points are scattered and do not match the RV template well.

Name Vfit errVfit Nvisits Nspectra ASAS 000602 66.6 2.7 4 13 ASAS 000621 -31.3 5.9 2 6 ASAS 001543 103.8 3.3 2 6 ASAS 002418 0.9 21.3 1 3 ASAS 002443 169.6 2.4 2 6

Table 4.3: Star’s name, Fitted RV, error of ﬁtted RV, number of visits and number of spectra for a sample of RRLs. 34

Figure 4.7: RV vs. phase for ASAS 232246. This one is better than Figure4.6, because the points ﬁt the RV template better. But it is still not perfect, the points at phase ≈ 0.7 are scattered. 35

CHAPTER 5. METALLICITIES

5.1 Equivalent Widths

To determine the metallicities of RRLs, we use equivalent widths (EWs) of absorption lines. The EW of an absorption line is the area with respect to the continuum line. Figure

5.1 shows the four absorption lines.

True EWs require high resolution spectra, so we can tell the actual continuum level. In our spectra, the resolution is quite low, so our EWs are pseudoequivalent widths.

In our research, four absorption lines are measured in each spectrum, CaIIK, Hδ,Hγ and Hβ. The hydrogen lines indicate the temperature of the star and these lines vary during a star’s pulsation as surface temperature changes. The CaIIK line depends on both temperature and calcium abundance, so it varies with the star’s pulsation, too. At a given temperature, a metal-poor star has a weak CaK line, while a metal-rich star has a strong

CaK line.

5.1.1 Measurements

We used a program called EWIMH to measure the EWs on each spectrum. This code was built on a core written by Taft Armandroﬀ in the mid-1980s. It was improved by Andrew

Layden around 1990 to operate in the IRAF environment.

The program starts by reading a ﬁle which contains the low and high wavelength limits of an absorption line and the low and high wavelength limits of two continuum bands (see table 5.1). One of the continuum bands is located at lower wavelengths next to the absorption line, and one at higher wavelengths. Then for each star, we input its radial velocity, so the program can know how much this spectrum needs to be shifted to correctly match the low and high wavelength limits. After that, we obtain plots of the spectrum around each line, the continuum bands, and the ﬁtted continuum. 36

Figure 5.1: Absorption Lines. 37

Figure 5.2: Boundaries and continuum bands of Hβ line.

The absorption lines of Hδ,Hγ and Hβ are clear enough, so it is relatively simple to get their EWs. To ignore cosmic rays and bad pixels in the continuum bands, the program uses a sigma-clipping algorithm to calculate the average intensities of both continuum bands.

Then a line is drawn to connect the two average intensities. This line is the top boundary.

Then for each x-pixel between the two feature limits (Table 5.1), the program calculates the intensity diﬀerence between the top boundary and spectrum. Then it sums over all intensity diﬀerences to get the area of the absorption line, and creates a rectangle region, which has the same area as the calculated absorption area above, from zero intensity line to the top boundary. Then the width of this rectangle is computed numerically in Angstroms. Figure

5.2 shows one example. 38

Feature Feature Band Blue Continuum Band Red Continuum Band λfeature λblue λred λblue λred λblue λred CaK-n 3926.670 3940.670 3900.000 15.000 3932.000 12.000 3933.666 CaK-w 3923.670 3943.670 3900.000 15.000 3932.000 12.000 3933.666 H-del 4091.740 4111.740 4008.000 4060.000 4140.000 4215.000 4101.735 H-gam 4330.470 4350.470 4206.000 4269.000 4403.000 4476.000 4340.465 H-bet 4851.330 4871.330 4719.000 4799.000 4925.000 4980.000 4861.327

Table 5.1: Regions that EWIMH reads.

Figure 5.3: CaIIK line of a cool star, narrow limits(left) and wide limits(right).

The measurement of CaIIK is more complicated because the region around CaIIK is crowded, so it is not easy to define the limits of continuum bands. For a hot star, the H8 line, located at the low wavelength side, and the Hϵ-CaIIH lines that blend at the high wavelength side force the continuum bands inward to the CaIIK line. In a cool star, the broad K line forces the continuum bands outward. To overcome this, the continuum bands of a fixed range are free to move within certain wavelength limits to seek the highest continuum level on both sides of the CaIIK line. Also, two different wavelength limits are used. The narrow one is more suitable for weak CaIIK, and the wide one suits strong CaIIK, as shown in Figure 5.3 and 5.4.

Eventually, the program outputs narrow CaIIK, wide CaIIK, Hδ,Hγ,Hβ EWs for each 39

Figure 5.4: CaIIK line of a hot star, narrow limits(left) and wide limits(right).

spectrum.

5.1.2 Calibrating EWs

Since we want to combine our data with the data in Layden [14], the metallicities must be consistent. However, our spectra were taken with a different telescope and spectrograph, and the resolution was different. We also used a different CCD, so the instrumental response varied in a way that could affect our continuum normalization. We need to transform our

EWs to the same system used in Layden [14]. To do this, we will compare EWs measured on our spectra of RV standard stars with their values from Table 6 of Layden [14]. Before calibrating, we ﬁrst decided which CaK we wanted to keep. Following to Layden [14], when the EW of the wide CaIIK region, W(Kw)<4A,˚ we chose the narrow one, when W(Kw)≥4A,˚ we kept the wide one. Then, for spectra taken on the same night of the same star, we averaged each EW respectively. After that, we used the 4 EWs of our standard stars, and plotted them with the same EW of the same standard stars in Layden [14]. Figure 5.5 shows one of the plots.

The IRAF task CURFIT was then used to find the best-fit coefficients. Table 5.2 shows the coefficients. 40

Figure 5.5: Hδ ﬁtting. X-axis is EWs from Layden [14], y-axis is our measured EWs. The upper line is the 1:1 line, the bottom line is the ﬁtted line.

EWs C0 C1 CaIIK 0.049 0.935 Hδ -0.546 1.028 Hγ 0.105 1.007 Hβ -0.567 1.028

Table 5.2: Coeﬃcients of the ﬁtted lines. 41

So the standard EWs, Ws, would be

W − C0 Ws = (5.1) C1

where W is the observed EW, C0 is the y-intercept, C1 is slope. We use these relations to transform our measured EWs of all RRL stars onto the stan-

dard system used by Layden [14]. For most observations, we have 3 spectra. Thus, we

averaged EWs for each observation and computed the SEM of the spectra. Values are pre-

sented in Table 5.3.

However, not all the standard EWs are useful. If a star spectrum is taken during its

rising branch (0.8≤phase≤1.0), its eﬀective gravity will increase, and the shock waves in its

atmosphere will double the Balmer line proﬁles [21], thus leading to low estimates of [Fe/H].

To identify the rising branch, we plotted phase vs H2, where H2 is the mean EW of Hδ and

Hγ, see ﬁgure 5.6. We did not include Hβ here because it was aﬀected by the metal lines.

We discussed how we removed this eﬀect in the next section. In addition, this plot can help

us check the phases. We can see it matches the shape of the light curves in Chapter 3 (hotter

when phase=0; cooling as phase increases), and the scatter is small, which means our periods

and phases obtained in Chapter 3 are reliable, and can be used to detect observations taken

during rising light.

5.2 Metallicities

With the standard EWs, now we can calculate the metallicity, [Fe/H]. However, there

are still several details that can be improved. The ﬁrst improvement is to correct the CaK

absorption line. The calcium in the interstellar medium will aﬀect the EW of CaIIK line,

W(K), and the amount of interstellar calcium absorption, W (Kint), is determined by the direction and distance of a star. The absolute magnitude of an RRL, and hence its estimated distance, depends on the metal abundance [Fe/H] and reddening, E(B-V). Since we had 42

Name W(K) SEM(W(K)) W(Hδ) SEM(W(Hδ)) W(γ) SEM(W(γ)) W(Hβ) SEM(W(Hβ)) Number of spectra ASAS 000602 1.80 0.08 6.33 0.12 5.92 0.13 5.70 0.10 3 ASAS 000602 2.87 0.12 4.37 0.08 3.49 0.13 4.03 0.17 4 ASAS 000602 3.14 0.05 4.14 0.22 3.43 0.09 3.92 0.11 3 ASAS 000602 2.75 0.10 4.43 0.23 3.63 0.04 3.79 0.08 3 ASAS 000621 5.52 0.03 4.10 0.17 3.97 0.11 4.36 0.16 3 ASAS 000621 4.39 0.08 5.62 0.16 4.96 0.15 5.12 0.06 3 ASAS 001543 2.47 0.01 4.42 0.01 4.38 0.01 3.97 0.01 1 ASAS 001543 2.61 0.28 3.95 0.18 3.63 0.13 3.91 0.16 3 ASAS 002418 2.83 0.11 4.76 0.27 3.88 0.03 4.04 0.23 3 ASAS 002443 7.02 0.23 4.27 0.24 3.27 0.25 4.39 0.11 3 ASAS 002443 5.77 0.15 4.11 0.17 3.42 0.09 4.07 0.04 3

Table 5.3: Calibrated EWs. 43

Figure 5.6: H2 vs. phase. 44

Figure 5.7: The relation of phase and EWs. This picture is from Layden [14].

already gathered galactic longitude, galactic latitude and reddening, the metal abundance must be known to calculate W (Kint). Next, the Hβ absorption line is contaminated by unresolved metal lines. To subtract the eﬀect of metal lines, again, we need to estimate the metal abundance ﬁrst.

Finally, as mentioned above, spectra taken during the rising branch will decrease our metal abundance, thus these data should be scrutinized. Figure 5.7 was plotted by Layden

[14]. A star observed between 0≤phase≤0.8 ﬁts a line very well, while a star observed between 0.8≤phase≤1.0 falls below the line. The observations taken during a star’s rising branch may aﬀect the [Fe/H] derived from the observed EWs.

The following sections discuss the procedure of calculating metal abundances and solving these complications. 45

Figure 5.8: W (Ko) vs. H2 from Layden [14].

5.2.1 Rough [Fe/H]

As mentioned above, we need to get the ﬁrst-order estimate of metal abundance before making all the improvements. To determine the metal abundances, Layden [14] observed some RR Lyrae stars of known metal abundances, and plotted W(K) against the EW of hydrogen line, W(H), to deﬁne the isometallicity lines. Then he set a polynomial (Equation

5.2) and ﬁt to his entire data

W (K) = a + bW (H) + c[F e/H] + dW (H)[F e/H] (5.2)

where W(H)=H2, W(K) is the uncorrected W (Ko). The coeﬃcients turned out to be a = 13.542, b = −1.072, c = 3.971 and d = −0.271. Figure 5.8 shows the simultaneous ﬁt to several of the calibration stars.

Since we have already converted our EWs to the standard equivalent width system used 46 by Layden [14], we can use these values directly. After substituting our uncorrected W(K) and H2, we got a ﬁrst-order estimate of the metal abundances.

5.2.2 Interstellar CaK

To improve W(K), we need to get the distance of the star perpendicular to the galactic

plane, Zdist. We assume the absolute magnitudes and the abundances have the following relation [5]

MV = 0.52 + 0.24([F e/H] + 1.5) (5.3)

Then we combined absolute magnitude with reddening and galactic coordinates to get

the height of the star from the galactic plane

− ∗ − − V (3.1 E(B V )) MV +5 10 5 Z = sin l (5.4) dist 1000

where l is galactic latitude, V is magnitude from Table 3.3, E(b-v) is the reddening. Using

Beers’s model [3], the interstellar K is

−| | Zdist 1 − e 1.081 W (K ) = 0.192 (5.5) int | sin l|

Our W (Kint) is from 0.08 to 0.52 Aand˚ the typical value is about 0.20 A.˚ Then the corrected W (K) is calculated with Equation 5.6.

W (K) = W (Ko) − W (Kint) (5.6)

5.2.3 Hβ

Then we used metal abundances and the standard EWs of Hδ and Hγ to determine the amount of contamination in the Hβ line, to get the correct W(Hβ). Layden [14] deter- 47 mined the contamination part, W(Zβ), is proportional to [F e/H]1/2 and also varies with the

temperature, so the equation has the form

W (Zβ) = (k + mH2)100.5[F e/H] (5.7)

He found k=2.58+-0.37 Aand˚ m=-0.253+-0.060.

Using the above relation for our data, we computed metal line contamination and sub-

tracted it from W(Hβ) to determine the corrected width, W(Hβz). Our typical W(Zβ) is around 0.2 A(0.1-0.3˚ A).˚

5.2.4 Final [Fe/H]

Now we have corrected W(Hβ), and since the Hβ line contains useful information and

its signal to noise is always the highest, we should keep it in our W(H). So now W(H) is

the average of the EW of Hδ line, W(Hδ), the EW of Hγ line, W(Hγ) and the EW of the

corrected Hβ line, W(Hβz), called H3z. Then we substituted H3z and corrected W(K) into Equation 5.2 using the W(K) vs. H3z

relation from Layden [14](a=13.858, b=-1.185, c=4.228, d=0.320), letting W(H)=H3z, to

get the calibrated [Fe/H] for each spectrum. Table 5.4 shows several ﬁnal [Fe/H] compared

with rough [Fe/H], the diﬀerences are around 0.01. The error in ﬁnal [Fe/H] has three

components. First is the SEM in W (K) of that night; Second is the SEM of H3z of that

night; The last one is the error in W (Kint), we calculated it using Equation 5.8 provided by Beers [3]. Then we added these three components in quadrature. Our calculated errors are

around 0.1.

| | eW (Kint) = 0.019 log10( zdist ) + 0.06 (5.8) 48

Name rough [Fe/H] ﬁnal [Fe/H] error in ﬁnal [Fe/H] ASAS 000602 -2.24 -2.24 0.06 ASAS 000602 -2.22 -2.20 0.06 ASAS 000602 -2.16 -2.13 0.05 ASAS 000602 -2.25 -2.24 0.06 ASAS 000621 -1.28 -1.28 0.05 ASAS 000621 -1.37 -1.38 0.06 ASAS 001543 -2.29 -2.29 0.03 ASAS 001543 -2.33 -2.31 0.10 ASAS 002418 -2.17 -2.19 0.07 ASAS 002443 -0.84 -0.83 0.09 ASAS 002443 -1.27 -1.26 0.06

Table 5.4: Comparison of rough [Fe/H] and ﬁnal [Fe/H].

5.2.5 Rising Branch

The final step is to consider spectra taken during the rising branch. For each star, we chose the spectrum whose phase was closest to 0.4, and calculated the absolute difference between [Fe/H] of this spectrum and [Fe/H] of other spectra of this star. We then plotted the absolute difference of [Fe/H] against phase (see Figure 5.9).

For points located between 0 ≤phase≤ 0.8, we gave full weight. Points located between 0.8

0.8

Then we applied the above weightings to our stars and combined [Fe/H] of diﬀerent observations for each of our 89 RRLs. We also calculated errors in [Fe/H] using two diﬀerent ways, as shown in Table 5.5. e1 is the weighted error in [Fe/H] and e2 is the SEM around the mean [Fe/H]. Most of them are less the 0.1. 49

Figure 5.9: FeH vs. phase.

Star W (Kint) W (Zβ) [Fe/H] e1 e2 Nspm W(K) W(Hδ) W(Hγ) W(Hβz) ASAS 000602 0.19 0.12 -2.20 0.06 0.06 4.0 2.45 4.82 4.12 4.24 ASAS 000621 0.19 0.30 -1.34 0.05 0.05 1.5 4.58 5.11 4.63 4.63 ASAS 001543 0.21 0.10 -2.29 0.04 0.01 1.5 2.35 4.11 3.88 3.92 ASAS 002418 0.27 0.12 -2.19 0.07 9.99 1.0 2.56 4.76 3.88 3.92 ASAS 002443 0.15 0.45 -1.13 0.05 0.22 2.0 6.25 4.19 3.35 3.78

Table 5.5: Data after gave weight from the rising branch. 50

CHAPTER 6. KINEMATICS

6.1 Rotation Velocities

6.1.1 Net Rotations

To determine the kinematics of our RR Lyrae stars, we chose the method provided by

Frenk & White [9]. This method does not use the proper motions of stars. It just uses radial velocities, distances and galactic coordinates of a set of stars to determine the set’s rotational velocity around the galactic center, Vrot, and the line of sight velocity dispersion,

σlos . In chapter 4, we determined the radial velocities of our 89 RRLs, so the next step in determining rotation velocities is to obtain stars’ radial velocities with respect to the local standard of rest (LSR), Vlsr, by converting from the RVs, Vrad. The following equation shows the relation. [9]

Vlsr = Vrad + Vp⊙(cos b⊙ cos b cos(l − l⊙) + sin b⊙ sin b) (6.1) where b means galactic latitude, l means galactic longitude. Here we used the data presented

◦ ◦ by Mihalas & Binney [17]: the solar peculiar motion Vp⊙ is 16.5 km/s, l⊙ = 53 and b⊙ = 25 are the Sun’s motions with respect to the LSR.

Then as mentioned by Frenk & White [9], for the ith star, we could use the geometric relationships to calculate cos Ψi and cos λi. Angles (Ψ and λ) are shown in Figure 6.1, where

Ψ is the angle between Vrot and the line of sight velocity to the Sun, and λ is the angle between the velocity of the Sun and the line of sight velocity to the Sun. Then we have

cos λi = cos b sin l (6.2) 51

Figure 6.1: Deﬁnition of angles for the ithstar with respect to the Galatic Center (From Frenk & White [9]). 52

R⊙ cos λi cos Ψi = 2 2 1/2 (6.3) ((d cos λi) + (R⊙ − d cos b cos l) )

where d is the distance of the ith star.

In our calculation, we assumed R⊙=8 kpc and V⊙ = 220 km/s, the same as Layden [15].

Thus, the line of sight velocity of the ith star, Vs,i, is the sum of its observed RV, Vlsr, and the velocity component of our Sun in the line of sight direction. (Equation 6.4)

Vs,i = Vlsr + V⊙ cos λi (6.4)

Then, as noted by Zinn [35], the calculation of Vrot is just a least-square solution of the following equation.

Vs,i Vrot,i = (6.5) cos Ψi

We plotted Vs,i vs. cos Ψi and ﬁtted a line constrained to cross the origin of the plot to the points. Then the slope of the line was Vrot.

6.1.2 Plots and Analysis

Since we want to compare our data with Layden [15], we separated our RR Lyrae stars

into the same 9 bins with him; the values are presented in Table 6.1. Then we plotted

Vrot, velocity dispersion, σlos, and the ratio of them, Vrot/σ, which shows how much support the system receives from rotational velocities vs. velocity dispersions, against the weighted

mean [Fe/H] of each group, as shown in Figure 6.2. Figure 6.3 plots Vs against cosΨ for each [Fe/H] bin.

In Figure 6.2, we notice an abrupt change at [F e/H] ≈ −1.0. The net rotation velocity

of the metal-poor stars, (d)-(i), is almost zero, but their velocity dispersion is large, around

120 km/s. This means they are most likely to be halo stars. Vrot/σ are also almost zero 53

Figure 6.2: Rotational velocities as a function of abundance. 54

Figure 6.3: Details of rotational velocities. 55

bin [Fe/H] < F e/H > Vrot eVr σ eσ Vr/σ eVr/σ N a −0.45 < [F e/H] 0.02 117.7 24.3 28.7 15.3 4.105 2.275 2 b −0.80 < [F e/H] ≤-0.45 -0.63 233.9 32.8 50.8 21.6 4.599 1.879 4 c −1.00 < [F e/H] ≤-0.80 -0.93 255.3 49.7 66.1 28.5 3.860 1.777 3 d −1.28 < [F e/H] ≤-1.00 -1.22 -2.2 93.7 147.5 42.8 -0.015 0.634 6 e −1.45 < [F e/H] ≤-1.28 -1.37 -28.2 44.4 113.3 20.9 -0.249 0.393 15 f −1.56 < [F e/H] ≤-1.45 -1.52 -50.9 48.1 105.3 21.6 -0.484 0.467 12 g −1.75 < [F e/H] ≤-1.56 -1.69 24.0 38.0 94.2 18.2 0.255 0.403 14 h −1.95 < [F e/H] ≤-1.75 -1.84 -7.9 67.8 155.6 29.5 -0.051 0.435 14 i [F e/H] ≤-1.95 -2.21 33.6 61.3 149.4 24.3 0.225 0.411 19

Table 6.1: Rotational velocities and dispersions for 9 metallicity bins.

for these metal-poor stars. The metal-rich stars, (a)-(c), have a constant rotation velocity

around 200 km/s and small dispersions, which means the kinematics of the metal-rich stars

are similar to thick disk stars.[17] Vrot/σ are large in these groups. We can get the same results from Figure 6.3. For panels (a)-(c), even though we just have a few data points, we

can still recognize the high slopes and narrow scatters, while (d)-(i) show lower slopes and

wide scatters.

Also, the rotation velocity for (a) is just 117.7 24.3 km/s, lower than (b) (Vrot =

233.9 32.8 km/s) and (c) (Vrot = 255.3 49.7 km/s), but the diﬀerences in Vrot/Sigma are not signiﬁcant. Since we just have a few points included in (a)-(c), this result is not reliable.

It was noticed in previous studies that stars with abundances of −1.4 ≤ [F e/H] ≤ −1.0,

which is our groups (d) and (e), present more disk-like kinematics than the more metal-poor

stars. In Layden’s [15] paper, he found Vrot = 53 30 km/s and Vrot = 57 30 km/s for groups d and e respectively. However, in Figure 6.2 of our study, we cannot see this eﬀect.

The rotation velocities for groups (d) and (e) are −2.2 93.7 km/s and −28.2 44.4 km/s

respectively. Group (d) has large uncertainty, but group (e) does not show any evidence for

disk-like kinematics. More tests will be discussed later. 56

bin [Fe/H] < F e/H > Vrot eVr σ eσ Vr/σ eVr/σ N a −0.45 < [F e/H] -0.21 205.9 22.9 59.9 9.6 3.440 0.659 21 b −0.80 < [F e/H] ≤-0.45 -0.65 194.6 15.3 53.0 8.5 3.673 0.616 25 c −1.00 < [F e/H] ≤-0.80 -0.90 209.8 25.1 71.1 11.4 2.950 0.566 23 d −1.28 < [F e/H] ≤-1.00 -1.17 43.7 29.5 107.0 11.5 0.408 0.276 45 e −1.45 < [F e/H] ≤-1.28 -1.37 30.2 24.0 109.3 10.3 0.276 0.220 58 f −1.56 < [F e/H] ≤-1.45 -1.51 -11.5 26.4 109.3 11.0 -0.105 0.240 51 g −1.75 < [F e/H] ≤-1.56 -1.67 -18.4 24.3 108.3 10.4 -0.169 0.223 57 h −1.95 < [F e/H] ≤-1.75 -1.85 -9.3 30.1 126.8 12.5 -0.074 0.236 53 i [F e/H] ≤-1.95 -2.19 41.7 27.4 119.6 11.3 0.349 0.229 58

Table 6.2: Combined rotational velocities and dispersions for 9 bins.

6.1.3 Combining

To obtain a larger sample of RRLs, we combined our 89 stars with 302 stars from Layden

[15] and plotted Figure 6.4 and Figure 6.5.

After plotting rotation velocity against [Fe/H], we found that even though the combined data matched well with data from Layden [15], there are still some small changes. First, as shown in Table 6.2 and Figure 6.4, the change at [F e/H] ≈ −1.0 becomes more apparent.

Second, the rotation velocities of the disk stars ((a)-(c)) are almost at the same level. They vary from 195 km/s to 210 km/s. The difference is about 15 km/s, while in Layden [15], the values are 182 km/s and 230 km/s, a difference of about 48 km/s. This gives a conclution that when more data are included, the values of disk rotation will become closer, which means the disk stars almost have the same rotational velocities. The halo stars ((d)-(i)) also show the same effect, they are closer to 0 km/s, which means there are about equal numbers of stars on prograde and retrograde orbits. Third, for panels (d) and (e), the values are lower, around 35 km/s.

6.2 Woolley Solutions

Woolley [34] provides a way to determine the velocity ellipsoid of a group of stars using radial velocities alone (without using proper motion). It just requires distances, positions 57

Figure 6.4: Combined rotational velocities as a function of abundance. 58

Figure 6.5: Details of combined rotational velocities. 59

[Fe/H] < [F e/H] > σρ σϕ σz N < −1.3 -1.768 186.032.2 123.524.1 98.427.9 73 ≤-1.0 -1.721 171.632.1 134.420.8 96.027.1 80 > −1.0 -0.590 189.9129.5 227.626.4 0.00.0 9

Table 6.3: Woolley solutions.

[Fe/H] < [F e/H] > σρ σϕ σz N < −1.3 -1.726 161.312.6 116.512.0 83.714.6 274 ≤-1.0 -1.640 143.312.3 124.310.3 86.112.9 324 > −1.0 -0.588 91.434.3 220.29.7 0.00.0 67

Table 6.4: Woolley Solutions from combined data. and RVs, thus, it can be used in our sample. Pier [22] improved this technique by providing a treatment of errors. Then Layden [15] modiﬁed the formulations to obtain the velocity ellipsoid in cylindrical coordinates. We used the modiﬁed formulations to calculate the velocity ellipsoid. The solutions are presented in Table 6.3.

Since our sample (89 RRLs) just contains 9 stars with [F e/H] > −1, the Woolley solution showed no useful result for this group. Even after we used the combined data, there was still no solution for it, as shown in Table 6.4. For other stars ([F e/H] ≤ −1), we obtained σρ = 171.6 32.1 km/s, σϕ = 134.4 20.8 km/s, σz = 96.0 27.1 km/s. The combined data were similar to ours, since the uncertainties of our velocity ellipsoid were large.

6.3 Space Motions

We obtained proper motions of our 85 RRLs from the Yale Southern Proper Motion

Survey [33], the other 4 stars were too far north for the proper motions. Then we used the formulas presented by Johnson & Soderblom [12] to calculate the stars’ space velocities:

UVW components. We transformed the UVW velocities and their errors into the cylindrical coordinate system, ρϕz, where ρ is parallel to the galactic plane increasing outward from the 60

[Fe/H] < Vρ > < Vϕ > < Vz > σρ σϕ σz N < −1.3 2.0 21.1 7.2 12.6 −6.7 11.4 176.6 14.9 105.2 8.9 95.7 8.1 70 ≤-1.0 6.3 19.4 13.8 12.4 −9.1 10.7 170.9 13.7 109.8 8.8 94.9 7.6 78 > −1.0 −29.3 25.3 235.1 21.3 −6.6 15.7 67.0 17.9 56.4 15.1 41.5 11.1 7

Table 6.5: Space motions.

ASAS Id [Fe/H] Vρ Vϕ Vz eρ eϕ ez ASAS 074205 -1.28 42.4 262.1 88.7 8.9 17.6 8.6 ASAS 075127 -1.62 -3.9 205.1 -0.8 9.9 22.8 8.8 ASAS 104738 -2.03 -202.4 206.4 -89.0 135.6 86.2 227.3 ASAS 104924 -2.05 45.7 305.6 105.6 18.0 17.0 16.6

Table 6.6: Velocities and uncertainties of the four stars MWTD stars.

galactic center to the object. The direction of ϕ is the same as the galactic rotation, and z

points toward the north galactic pole. Table 6.5 contains the weighted mean velocities and

velocity dispersions for diﬀerent metallicities. We also plotted Vρ,Vϕ and Vz against [Fe/H] (Figure 6.6).

In Figure 6.6, the abrupt change at [F e/H] ≈ −1.0 still exists. The metal-rich stars have

very small velocity dispersions σϕ=56.4 15.1 km/s and < Vϕ >= 235.1 21.3 km/s, while

the metal-poor stars have large dispersions σϕ=105.2 8.9 km/s with < Vϕ >=7.212.6 km/s. These data show the same result that the metallicities of the stars in the disk have

nearly no aﬀect on their kinematics, while the halo stars have diﬀerent kinematics. We also

noticed four stars seemed to be Metal Week Thick Disk (MWTD) stars and we presented

their space motions in Table 6.6. They are metal poor stars with disk-like space motions.

One of them even has metallicity as low as -2. Also, if we compare the Woolley solutions

with the space motion, we found that were almost the same (for the top two lines in the

table). This means both our space motions and Woolley solutions are trustworthy. 61

Figure 6.6: Space motions of 85 RRLs, the open squares are stars with Vϕ >200 km/s. 62

[Fe/H] < [F e/H] > Vrot σ Vr/σ N ≤ −1 -1.72 -4.122.7 126.810.1 -0.0320.179 80 ≤ −1.3 -1.77 -1.924.1 126.210.6 -0.0150.191 72 > −1 -0.59 212.727.4 66.316.7 3.2070.877 9

Table 6.7: Kinematics of the halo and disk stars.

6.4 Discussion

We combined all the disk stars ([F e/H] > −1.0) and all the halo stars ([F e/H] < −1.0)

respectively. We calculated the mean [Fe/H] and ﬁtted lines for the combined groups to

determine Vrot, σ and Vr/σ for them, as shown in Table 6.7.

For the halo stars ([F e/H] <= −1.3), our rotation velocity Vrot = −1.924.1 km/s. It is

smaller than found in Layden’s study [15], which is Vrot = 1813 km/s, but not signiﬁcantly diﬀerent. For the thick disk stars ([F e/H] > −1), our rotation velocity (Vrot = 212.7 27.4

km/s) is also very similar to his work (Vrot = 198 9 km/s). We also noticed our results are

very close to those of Beers & Sommer-Larsen [3] (halo Vrot = −16 18 km/s, σlos = 117 4

km/s; thick disk Vrot = 1957 km/s, σlos = 645 km/s). They selected non-kinematical stars (apparent main-sequence A-type stars, ﬁeld horizontal-branch stars, variable stars including

RRLs, main-sequence dwarf stars, main-sequence turnoﬀ stars, subgiant stars, giant stars

and asymptotic giant branch stars) from many diﬀerent studies with abundances [Fe/H]≤-0.6

and contained large numbers of stars located more than 1 kpc from the Galactic plane.

For the halo stars with −1.4 ≤ [F e/H] ≤ −1.0 ((d) and (e)), as mentioned above, the

eﬀect of disk-like kinematics from our data is not clear. From our data, the values of (d)

and (e) are -2.2 km/s and -28.2 km/s. When they are combined with Layden’s data [15], the

values are lower than his data (for (d), Vrot = 53 30 km/s, for (e), Vrot = 57 30 km/s). This diﬀerence may be caused by two reasons. First, since we do not have many stars in

group (d) and (e), including more stars may show a better result. Second, we noticed in

Figure 6.3, most of our points are on the left side, which means the galactic longitude of 63

test1 *quadrants are shown in Figure 3.3 group d cosΨ > 0(2.3 quadrant) cosΨ ≤ 0(1,4 quadrant) value uncertainty N value uncertainty N t-test Vrot 94.5 33.4 20 20.5 43.0 25 1.36 sigma 66.9 11.1 129.7 18.6 2.90 Vrot/sigma 1.414 0.539 0.158 0.33 1.99 group e Vrot 103.6 38.3 16 3.4 28.9 42 2.09 sigma 89.7 16.2 112.6 12.5 1.12 Vrot/sigma 1.156 0.47 0.03 0.255 2.11 group de Vrot 99.7 24.9 36 9.8 24.0 67 2.60 sigma 76.6 9.4 118.4 10.4 2.98 Vrot/sigma 1.302 0.355 0.083 0.202 2.98

Table 6.8: Test1. these stars has a range of 180 < l < 360. We also noticed that in Figure 6.5, for (d) and (e), especially for (d), the points on the left side are more scattered than the right side points.

Thus, we may have a hypothesis that the halo of our Galaxy is not uniform. To investigate this effect, we did some tests with the combined 391 stars. Since we noticed the different scatters in Figure 6.5, we seperated our stars into two groups, cosΨ ≤ 0 and cosΨ > 0, as shown in Table 6.8. The rotational velocities were different, but not significant. Since most of our 89 RRLs are in the 4th quadrant, we did test 2 (Table 6.9) .

We noticed that both tests showed that the differences existed, but they were not significant. The values of t-test, which combined the information of velocities and uncertainties, were less than three. There are three possibilities. First, the errors in [Fe/H] may cause some stars shifted into wrong metallicity bins. Second, in both of our tests, the data may be separated by wrong space positions. Third, if we get more stars, the difference may become significant. This requires more observations. This effect may due to star streams existing in our observations. If this is real, it supports the Searle & Zinn model that our Galaxy formed from several clouds, or maybe our Galaxy are still merging with new dwarf galaxies.

No matter what the reason is, further studies are needed. 64

test2 *quadrants are shown in Figure 3.3 group d 4th quadrant other value uncertainty N value uncertainty N t-test Vrot 11.5 55.1 15 75.0 33.3 30 0.99 sigma 140.8 26.1 85.7 11.4 1.93 Vrot/sigma 0.082 0.388 0.875 0.4 1.42 group e Vrot -20.2 33.7 26 86.3 32.1 32 2.29 sigma 111.4 15.7 100.3 12.8 0.55 Vrot/sigma -0.181 -0.302 0.86 0.335 2.31 group de Vrot -8.3 29.1 41 81.7 22.9 62 2.43 sigma 121.7 13.6 92.8 8.5 1.80 Vrot/sigma -0.068 0.238 0.881 0.257 2.71

Table 6.9: Test2. 65

CHAPTER 7. CONCLUSION

Spectra of 89 RR Lyrae stars and six radial velocity standard stars were taken with

the 1.5m telescope operated by SMARTS. We processed these spectra by removing the bias

and ﬂat eﬀects, extracting intensities of useful pixels to obtain 1D spectra, determining

the relation of x-pixels and wavelengths, and normalizing the continuum to remove the

instrumental response.

To determine the distances of our stars, we gathered photometric data and extinctions

from ASAS and Schlegel et al. [27] respectively. We then used the IRAF package PDM to

investigate the best periods and other properties of the RRLs.

We used the IRAF package FXCOR to measure the radial velocities of our RRLs, and

converted the RVs to rotation velocities around the center of the Galaxy, using the method

provided by Frenk & White [9], then summarized by Zinn [35] and Armondroﬀ [1]. We then

used a program called EWIMH to get pseudoequivalent widths of Hd, Hg, Hb and CaK lines,

to calculate [Fe/H].

After combining our 89 RRLs with 302 RRLs from Layden [15] and plotting rotation

velocity against [Fe/H], we ﬁnd the disk stars, which are metal-rich stars, have a uniform

rotation velocity (Vrot = 212.7 27.4 km/s, σlos = 66.3 16.7 km/s). The speeds of stars’ rotations around the center of our Galaxy are about the same with each other. The halo stars, which are metal-poor stars, have a near-zero net rotation velocity with a large dispersion

(Vrot = −1.9 24.1 km/s, σlos = 126.2 10.6 km/s). They orbit the Galaxy in diﬀerent velocities. The abrupt change between metal-rich stars ([F e/H > −1.0]) and metal-poor stars ([F e/H] < −1.0) shows evidence that our Galaxy formed from several independent clouds, not an single large one, which means the Searle & Zinn model is reliable.

The space motions of our sample also supports the same result. The metal-poor stars have < Vϕ >= 7.2 12.6 km/s and a large velocity dispersion of σϕ=105.2 8.9 km/s, while 66

the metal-rich stars have σϕ=56.4 15.1 km/s and < Vϕ >= 235.1 21.3 km/s. For the halo stars with −1.4 ≤ [F e/H] ≤ −1.0, we noticed an eﬀect maybe caused by

star streams that stars with galactic longitude of 180 < l < 360 showed halo-like kinematics

(Vrot = 20.543.0 km/s, σlos = 129.718.6 km/s), while stars in the direction of 0 < l < 180

showed disk-like kinematics (Vrot = 94.5 33.4 km/s, σlos = 66.9 11.1 km/s). Since the diﬀerences derived from our sample is not signiﬁcant, more observations will be necessary, especially in the direction of 180 < l < 360 and −90 < b < 0. 67

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