Selection function effects on vertical metallicity gradients

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A brief history : Milky Way from observations

Milky Way and its origin had a place in the mythology of ancient civilizations all over the world. May that be the Hindu mythology – the story of the churning of the ocean of milk, samudra manthan, that appears in ancient Hindu scriptures like Srimad Bhagavatam, the Mahabharata and the Vishnu Purana. The more popular ones from the Greek Mythology include the Milky Way being created by the Greek gods, not to mention the origin of the word Galaxy from the greek word for milk, galaktos. There are numerous other old beliefs and stories showing the interest and subsequent imaginations that the Milky Way has generated in humans.
In the early 17th century, the father of modern observational astronomy, Galileo Galilei, discovered that this nebulous band consists of innumerable stars based on his observations through the telescope. This was followed up with speculative theories about solar systems, orbiting of the Sun around the ’Divine Centre’ of the star system and hierarchical or fractal models of the Universe by René Descartes (The World ; 1636), Thomas Wright (An Origi-nal Theory or New Hypothesis of the Universe; 1750), Immanuel Kant (1755) and Johann Lambert (1761), respectively. All of these theories lacked observational validation.
A detailed observational study of the Milky Way star distribution was carried out by William Herschel towards the end of the 18th century. He assumed that the stars observed in different directions had the same intrinsic luminosities. Based on this, he presented his famous picture of the structure of the Milky Way with a flattened disc of stars and the Sun located close to its center, as shown in the Figure 1.1 His assumption of constant luminosity for all stars was countered by John Mitchell, who advocated the existence of binary systems as well as star clusters which would lead to a dispersion in intrinsic luminosities of stars. Finally, William Herschel had to agree with John Mitchell’s conclusion when he measured the magnitudes of visual binary stars in 1802.
Meanwhile, there have been speculations about the objects that show a diffuse or fuzzy appearance, differing from the stars. Most of them were considered to be ’island universes’ similar to the Milky Way that are too distant to be resolved. Charles Messier started catalogu-ing many of these bright nebulae and the catalogue contains a mixture of brightest Galactic and extra-galactic nebulae, commonly referred to by their Messier numbers. William Her-schel and his sister Caroline also started a similar cataloguing of nebulae, continued by his son John Herschel, which resulted in the publication of the General Catalogue of Nebulae and Clusters of Stars in 1864. John Dreyer followed this up with the New General Catalogue of Nebulae and Clusters of Stars in 1888, the objects of which are commonly referred to by their NGC numbers.
It was in the year 1900 that the Milky Way was given the spiral arms for the first time by Cornelius Easton, though his model galaxy was small and Sun-centered. Harlow Shapley (1918, 1919) presented a much larger sized Galaxy, calculating the distances to globular clusters using the period-luminosity relation discovered by Henrietta Leavitt for Cepheid variable stars. He found the most distant globular cluster to be located at a distance of 67 kpc. In addition, this meant that the spiral nebulae could hardly be comparable galactic systems, rather they should belong to the enormously large Milky Way galaxy. At the same time, Heber Curtis’s Milky Way was only 10 kpc across, with the Sun located at 3 kpc from the center. He was also suggesting the spiral nebulae to be island universes citing the resemblance of the spectrum of the average spiral nebula to that of the integrated spectrum of the Milky Way. The questions about the true nature of the spiral nebulae (island universes or Milky Way subsystems) together with that about the size/structure of the Milky Way, lead to the famous ’The Great Debate’ between Harlow Shapley and Heber Curtis in 1920. The size/structure of the Milky Way was investigated by Jacobus Katpeyn with the de-termination of the luminosity function of stars near the Sun based on star counts in different directions without accounting for absorption by dust. His model of the Milky Way had a flattened structure with the thickness of 1500 pc and extending about 8 times this size in the Galactic plane, with the Sun located slightly off from the center. Though the debate was unable to throw any significant light upon the issues, Edwin Hubble established that the spi-ral nebulae are indeed distant extragalactic systems based on his observations of cepheid variables in the Andromeda nebula. This was followed up with his finding in 1929 that the extragalactic nebulae are moving away from the Milky Way with velocities that are propor-tional to the distance from the Milky Way (Hubble, 1929). This discovery lead to the theory of Big Bang cosmology and eventually the lambda cold dark matter ( -CDM) models which describes our current understanding of the formation of the expanding Universe and the struc-tures in it. I will summarise them in the context of Galaxy formation in the section.

Spitzer GLIMPSE and MIPSGAL

Infrared Array Camera (IRAC; Fazio et al. 2004) and Multiband Imaging Photometer (MIPS; Rieke et al. 2004) are two instruments onboard the Spitzer Space Telescope (Werner et al., 2004), which is a space-borne telescope with 0.85 m aperture. IRAC obtains simultaneous broadband images at 3.6, 4.5, 5.8 and 8 m. All four detector arrays in the camera are 256 × 256 pixels in size, and the FWHM of the point spread function are 1″.6, 1″.6, 1″.8 and 1″.9 at 3.6, 4.5, 5.8 and 8.0 m, respectively. MIPS covers longer wavelengths with imaging bands at 24, 70 and 160 m and very low resolution spectral energy distribution (SED) spectroscopy from 52 to 100 m. MIPS achieves telescope-limited resolutions of 6″, 18″ and 40″ at 24, 70 and 160 m, respectively.
The Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Churchwell et al. 2009a) is one of the legacy programs of the Spitzer Space Telescope that uses IRAC observations to get a deeper understanding of the physics of interstellar dust, star formation, and the large-scale structure of the Milky Way as traced by stars. GLIMPSE consists of three surveys : GLIMPSE I covering an area of 220 deg2 of the Galactic plane from longitudes SlS = 10○ to 65○, GLIMPSE II fully imaging the inner 20○ of the Galactic plane and GLIMPSE 3D extending the GLIMPSE I & II latitude coverage to ±3○ at nine selected latitudes and to ±4○ within 2○ of the Galactic center. MIPSGAL (Carey et al., 2009) is another legacy program of the Spitzer Space Tele-scope that covers 278 deg2 of the inner Galactic plane using the 24 and 70 m bands of the MIPS instrument. MIPSGAL provides far-infrared/submillimeter measurements for both point sources and diffuse emission, complementary to their observations in near infrared regime using 2MASS and GLIMPSE.

The inner Milky Way

The inner Milky Way, in this thesis, refer to the inner 200 pc region across the Galactic major axis (Galactic mid plane or longitude) and 400-500 pc around the Galactic center along the Galactic minor axis (Galactic latitude). This region is characterized by the presence of very high stellar density of stars and star forming molecular clouds that are largely extincted in the optical wavelength regimes by the huge amount of dust. This region hosts the supermas-sive black hole (SMBH), Sgr A∗, the so called nuclear bulge encompassing the nuclear star cluster (NSC), nuclear stellar and molecular discs, as well as the unusually dense molecular cloud complex, also known as the central molecular zone (CMZ) (Launhardt et al., 2002). Figure 1.6 shows the nuclear bulge region of the Milky Way using the RBG color composite image made combining the Herschel 250 m (FIR), Spitzer IRAC 8 m (MIR) and Spitzer IRAC 3.6 m (NIR) maps each of which traces the cold dust emission, warm dust + UV ex-cited polycyclic aromatic hydrocarbon (PAH) emission and the stellar emission respectively. Major molecular clouds and stellar cluster features in the CMZ are also shown in the figure.
The initial identification of the Galactic center was through radio observations that un-covered the Sgr A (Piddington and Minnett, 1951), and later confirmed by the discovery of the unresolved source Sgr A∗ or the SMBH of the Milky Way at (l,b) = (-0.056○ , -0.046○) (Balick and Brown, 1974; Reid and Brunthaler, 2004). The mass of the SMBH was estimated to be 4.2±0.2 × 106 Mb compiled from various studies (Bland-Hawthorn and Gerhard 2016 and references therein). Astrometric and spectroscopic studies using high angular resolution infrared observations aided by adaptive optics have enabled the identification as well as kinematic characterisation of the highly dense population of stars orbiting the SMBH. These stars include a complex population of young hot, early type stars, Wolf-Rayet stars, older and lower mass giants as well as O and B-type main sequence, giants and super giants within the central parsec that belong to the NSC which was discovered by Becklin and Neugebauer (1968). Schödel et al. (2014) found the NSC (earlier assumed spherically symmetric) to be elliptical and flattened with a half light radius of 4.2 ± 0.4 pc, luminosity at 4.5 m of 4.1±0.4 × 107 Lb and mass of 2.5± 0.4 × 107 Mb. Feldmeier et al. (2014) extracted the kinematics of individual stars as well as from integrated light in near infrared spectrum and found the kinematic axis to be misaligned with respect to the photometric axis. Feldmeier-Krause et al. (2015) observed the central >4 pc2 of the Galactic centre and found that early-type stars (>100 of them) are centrally concentrated favouring the in situ formation of early-type stars. Støstad et al. (2015) mapped a smaller area within 0.28-0.92 pc from SgrA∗ and found a break in the distribution of young stars at 0.52 pc. These authors concluded that this break possibly indicated an outer edge to the young stellar cluster in the Galactic centre, which is expected in the case of in situ star formation.
In addition to the NSC, most of the stellar mass of the nuclear bulge is constrained in the nuclear stellar disc (NSD), dominating the stellar mass distribution between ∼30 pc and ∼230 pc with estimated mass of ∼1.4±0.6×109 Mb (Launhardt et al., 2002). From their de-tailed multi wavelength study using the photometric data covering the NIR to radio wave-length range (IRAS, COBE, IRAM), Launhardt et al. (2002) also established the presence of a nuclear molecular disc (NMD) composed of an inner (<120 pc) warm disk and outer cold torus of dust and gas.
Above mentioned molecular gas clouds, stellar clusters and disc structures are all encom-passed within the innermost few hundred pc radius region, i.e., the CMZ. It is a giant molec-ular cloud complex with an asymmetric distribution of molecular clouds (see e.g. Morris and Serabyn 1996; Martin et al. 2004; Oka et al. 2005). It has also been evident from obser-vations that roughly the distribution of molecular gas as well as their kinematics are strongly assymetrical with roughly three quarters of molecular emission coming from positive lon-gitudes. The prominent features detected at 24 m using the MIPS map in the central 2.5○ × 2○ region are shown in the Figure 1.7. This prodigious reservoir of molecular gas is in an active region of star formation, where there is evidence of starburst activity during the last 100,000 years (Yusef-Zadeh et al., 2009). The gas pressure and temperature are higher in the CMZ than in the Galactic disc; these conditions favour a larger Jeans mass for star forma-tion and an initial mass function (IMF) biased towards more massive stars (see Serabyn and Morris 1996; Fatuzzo and Melia 2009). In addition, the tidal force from the SMBH, shocks from the rotating inner spiral arms etc must regulate/feed the star formation in this region. Amidst these unique conditions, the exact star formation rate in the CMZ poses an intriguing question, which will be discussed in detail in the Chapter 4.
While severe extinction and reddening prevents large scale observations in the inner Milky Way especially across the Galactic mid plane, there are similar observational lim-itations upto a certain height above and below the Galactic plane. This has hindered our understanding of the characteristics of the stellar populations in the inner bulge, which is the region that lies within ∼400-500 pc around the Galactic center or within SbS ∼ 3○. Figure 1.8 shows the AKs extinction map estimated using extinction coefficients from Nishiyama et al. (2009) calculated with the methods described in Gonzalez et al. (2012). The bulge outline from the COBE/DIRBE estimate (Weiland et al., 1994) is also shown. In section 1.1.3, I

Applying uncertainties and related checks on the models

Both GALAXIA and TRILEGAL predict the stellar parameters and photometric magnitudes for each star at a given line of sight. Each of the four surveys has intrinsic errors in the measured stellar parameters and observed photometric magnitudes, which should be simulated accordingly in the model in order to make it more realistic. Since we use only the metallicity values from the models to compare the MDFs and vertical gradients, we do this only for the metallicity among the stellar parameters in the model. In order to simulate the metallicity errors, we have fitted a fourth-degree polynomial in the [Fe~H] vs [Fe~H] plane for LAMOST, and GES and a third-degree polynomial for APOGEE. For RAVE, we used the same metallicity error description as described in Kordopatis et al. (2013). We apply a Gaussian filter to the metallicities of the mock catalogues. [Fe~H]APOGEE = 0:023 − 0:015[Fe~H] − 0:001[Fe~H]2 − 0:005[Fe~H]3.

Selection function effects on MDF

With the models described above, we are able to study the effect of the selection function on the MDF for the sample from the common fields of each survey in ALR and AGR. We categorize the sources in the mock fields by the limiting magnitude of the respective surveys and restricted in R-Z range as the parent population. This represents the underlying sample from which the selection function in the form of colour and magnitude cuts are applied to create a subset of mask sources. These mask sources in turn represent the observed sources.
Thus by comparing theMDFof the underlying sample, hereafter called the magnitude limited sample, with that of the mask sample, we can assess the effect of the selection function, if any, on the underlying MDF for each survey. For ALR and AGR, we restrict both the magnitude limited and mask sample in the R-Z range of 7B R B 9 kpc and SZS B 2 kpc and all fields are combined together. The SZS values for sources in the three low latitude fields in AGR do not exceed 1 kpc for the selected R range. As these low latitude fields have different selection cuts and low numbers of stars, we restrict our analysis only towards high latitude fields. We compare the magnitude limited MDFs and the effect of the selection function on the MDF for ALR and AGR in Figures 2.11 and 2.12 respectively. Here again we use the GMM method to fit the multiple number of Gaussians to the MDF. In addition, we use the quartile values to carry out a quantitive comparison of two distributions. Wojno et al. (2017) carried out a similar comparison of distributions using the quartile values for RAVE. As mentioned in Section 2.5.2, we choose 0.1 dex as the threshold for the difference between the respective quartiles of samples below which the distributions are considered to agree thus implying that the selection function has a minimal effect on the MDF. The quartile values for mask and magnitude limited samples are listed in the respective panels in Figure 2.11. We find that all the quartile values estimated for the mask and the magnitude limited sample in GALAXIA are more metal-poor than those in TRILEGAL.

Vertical metallicity gradients for the observed sample

To estimate the vertical metallicity gradient and compare them between the different surveys, we have to ensure that the metallicities of the different surveys are on the same scale. We applied a small offset to the RAVE and LAMOST metallicities with respect to our reference  sample APOGEE using the linear and second-degree polynomial functions that we fitted in Section 2.2. While estimating the functional relation of metallicity offsets of RAVE and LAMOST with respect to APOGEE, we make sure that the relation holds true seperately for both high and low S~N samples of RAVE and LAMOST. So we can proceed without any major quality cuts for each survey, ensuring a statistically significant sample for our study. Here again we restrict our study to the high latitude fields. Figure 2.13 shows the vertical metallicity gradients plotted separately for ALR and AGR.We follow the same fitting routinementioned in the previous section to estimate the slopes. Table 2.6 lists the slopes of the gradients calculated for each survey in ALR and AGR, along with the slope of the combined sample. We also list the mean vertical metallicity gradient estimated from combined samples of ALR and AGR in the last row of the table.
We measured the vertical gradients of -0.235 ± 0.025 dex kpc−1 and -0.229 ± 0.026 dexkpc−1 for APOGEE in ALR and AGR, respectively. Hayden et al. (2014) measured a slightly steeper slope of -0.31 ± 0.01 dex kpc−1 for their APOGEE DR10 sample located within the solar neighbourhood, 7<R<9 kpc and SZS < 2 kpc. Their sample in the solar neighbourhood is more complete and homogeneous than the volume limited sample we are dealing with. We used the same criterion in Hayden et al. (2014) to distinguish the -poor and -rich sources in Table 2.6: Vertical metallicity gradients measured for ALR and AGR high latitude fields.

Table of contents :

Introduction 
1.1 An overview of the Milky Way Galaxy
1.1.1 A brief history : Milky Way from observations
1.1.2 Lambda Cold Dark Matter model
1.1.3 Components of the Milky Way
1.2 Galactic archaeology
1.2.1 Photometric surveys
1.2.2 Spectroscopic surveys
1.2.3 Stellar population synthesis models
1.2.3.1 TRILEGAL
1.2.3.2 Galaxia/Besançon
1.2.4 Chemical evolution models
1.3 The inner Milky Way
1.4 Goals of this thesis
1.5 Published works
2 Selection function effects on metallicity trends 
2.1 Selection function
2.2 Comparison of stellar parameters
2.3 ALR and AGR
2.4 Distances
2.5 MOCK fields using SPS models
2.5.1 Applying uncertainties and related checks on the models
2.5.2 Comparison between GALAXIA and TRILEGAL
2.6 Selection function effects on MDF
2.6.1 AGR vs ALR
2.7 Selection function effects on vertical metallicity gradients
2.7.1 Vertical metallicity gradients for the observed sample
2.8 Summary and conclusions
3 Chemical characterization of the inner Galactic bulge 
3.1 (Lack of) Observations in the inner Galactic bulge
3.2 Data
3.2.1 Target selection
3.2.2 Observations
3.3 Analysis
3.3.1 SME
3.3.2 K-band line list
3.3.3 Stellar parameters
3.3.4 Stellar abundances
3.3.5 Uncertainties
3.3.5.1 General uncertainties
3.3.5.2 Uncertainties related to stellar-parameters
3.4 Homogeneous Analysis of the North-South sample
3.5 Results
3.6 Discussion
3.6.1 MDF
3.6.2 [/Fe] vs [Fe/H]
3.6.3 Kinematics
3.6.4 North-South symmetry
3.7 Summary and conclusions
4 SFR in the CMZ 
4.1 Estimating SFR
4.1.1 Using cm or mm continuum emission
4.1.2 Using infrared luminosity
4.1.3 YSO counting
4.2 Identifying YSOs
4.3 SFR in the CMZ
4.4 Data
4.4.1 Sample selection
4.4.2 Observations
4.4.3 Data reduction
4.5 Classification
4.5.1 Spectroscopic classification
4.5.2 Classification using photometric criteria
4.6 Mass estimation
4.6.1 Robitaille SED models
4.6.2 SED fits
4.6.3 Fit parameters and mass
4.7 SFR estimate
5 Conclusions and future works 
5.1 Selection function effects
5.1.1 Future works
5.2 Galactic archaeology in the Inner Milky Way
5.2.1 Inner Galactic Bulge
5.2.1.1 Future works
5.2.2 SFR in the CMZ
5.2.2.1 Future works
Bibliography 

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