大尺度結構與星系性質之間的關係：大尺度與小尺度環境對於星系的光學性質之研究

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(1)國立臺灣師範大學理學院地球科學系天文組碩士論文 Department of Earth Science College of Science. National Taiwan Normal University Master Thesis. 大尺度結構與星系性質之間的關係：大尺度與小尺度環境對於星系的光學性質之研究 The Relation between Large Scale Structure and Properties of Galaxies : Investigation of Large & Small Scale Environments on Optical Properties of Galaxies. 鄭守倫 Shou-Lun Cheng. 指導教授：橋本康弘 Advisor : Yasuhiro Hashimoto. 中華民國 104 年 8 月 Aug, 2015.

(2) 國立臺灣師範大學地球科學系天文組. 碩士論文. 大尺度結構與星系性質之間的關係：大尺度與小尺度環境對於星系的光學性質之研究. 鄭守倫. 2015 Aug.

(3) 要我們進行了大尺度結構與星系的性質之間關係的調查研究，採用了由 SDSS DR8 Groups and Clusters of Galaxies Value-Added Catalogues，與 MPA/JHU value-added galaxy catalog 兩者合併的 data catalog。在大尺度下星系並非是均勻的隨機分布在宇宙空間，而是分布在大尺度結構，像是 Filaments，Webs，Voids 之中。這種不同位置的變化，在對於每個星系的形成與演化的歷史，其所在的不同環境應該會對於當地環境中的星系造成不同的影響。由於已知星系的性質與其所在的環境是有相關性的，調查或研究星系在各種不同大尺度環境與各種不同小尺度環境上的差異，並了解其關係，能夠提供寶貴的資訊讓我們一定程度的了解星系的形成和演化上的機制。例如環境密度以外的影響因素。我們開發了一個定量的方法，用以客觀的描述星系周圍的宇宙大尺度結構，進而定量地分析其星系性質與大尺度環境之間的關係。我們的目標是要了解不同的大尺度環境與小尺度環境之中星系性質的差異，與大尺度結構的形成與演化歷史之機制，經由調查研究星系的性質，與其所處的大尺度環境或小尺度環境之間的關係性。. 關鍵字：環境 (Environment), 纖維狀結構 (Filament), 星系 (Galaxy), 大尺度結構 (Large-Scale Structure), 史隆數位巡天 (SDSS), 空洞 (Void).. i.

(4) Abstract We are conducting the investigation of the relationship between largescale structure and the kinematic & photometric properties of galaxies, using spectroscopic catalog from Sloan Digital Sky Survey Data Release 8 (SDSS dr8). In large scale, galaxies are not distributed randomly, but lying inside the large-scale structure, such as, sheets, filaments, webs, and voids. This variation of the location should provide various environments for each galaxy to form and evolve. Since the properties of galaxies are known to correlated with their environments, investigations of the relationship between the galaxies properties and the large- & small-scale environments should provide precious additional constraints for understanding the formation and evolution of galaxies, beyond well known environmental effect of smaller scale, such as the effect of local galaxy density.. We have developed quantitative methods to objectively characterize the large-scale structure of the universe surrounding galaxies, to quantitatively investigate the relation between the properties of galaxies and their large-scale environments. Our methods characterized the large-scale environments by various measures such as ’Multi-Axis Density (MAD)’, ’Large-Scale-Filament Factor (LSFF)’, and ’Small-Scale-Filament Factor (SSFF)’.. ii.

(5) Our goal is to understand the difference of galaxies in different environments by investigating the relation between the kinematic & photometric properties of galaxies and their large- & small-scale environments.. Key words: Environment, Filament, Galaxy, Large-Scale Structure, SDSS, Void.. iii.

(6) Contents 要. i. Abstract. ii. Contents. iv. List of Figures. vi. 1 Introduction. 1. 2 DATA. 3. 2.1. Mocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.2. Millennium Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5. 2.3. SDSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6. 3 Method. 10. 3.1. Spherical Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11. 3.2. Large Scale Filament Factor (LSFF) . . . . . . . . . . . . . . . . . . . .. 12. 3.3. Small Scale Filament Factor (SSFF) . . . . . . . . . . . . . . . . . . . .. 17. 4 Result. 19. 4.1. Quantitative Definition of Large Scale Structure . . . . . . . . . . . . . .. 19. 4.1.1. LSS by Spherical Density . . . . . . . . . . . . . . . . . . . . .. 20. 4.1.2. LSS by Large Scale Filament Factor (LSFF) . . . . . . . . . . .. 27. 4.1.3. LSS by Small Scale Filament Factor (SSFF) . . . . . . . . . . . .. 34. iv.

(7) 4.2. Environmental Effect on Properties of Galaxies . . . . . . . . . . . . . .. 42. 4.2.1. LSS by Spherical Density on Properties of Galaxies . . . . . . . .. 43. 4.2.2. LSS by LSFF on Properties of Galaxies . . . . . . . . . . . . . .. 54. 4.2.3. LSS by SSFF on Properties of Galaxies . . . . . . . . . . . . . .. 65. Summary & Discussion. 76. References. 79. v.

(8) List of Figures 2.1. The distribution of dummy sample; we create two different types of dummy structures, such as ”cross (bottom panel)” and ”spherical sheet (top panel)”. Both figures include approximately 600 galaxies. . . . . . . . . . . . . .. 2.2. 4. Three-dimensional distribution of 2454 galaxies in the Millennium Simulation in Cartesian grid X, Y, and Z, in the unit of Mpc/h, Y axis corresponds to a line of sight. . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.3. 5. The distributions of galaxies in Sloan Digital Sky Survey Legacy Survey. Top figure is the Equatorial distribution. Bottom left figure in right ascension (RA) and declination (DEC). And the bottom right figure in η and λ, the coordinate of Sloan Digital Sky Survey. . . . . . . . . . . . . . . . .. 2.4. The three-dimensional distribution of selected region in Cartesian, include 966 galaxies grid X, Y, and Z. . . . . . . . . . . . . . . . . . . . . . . .. 3.1. 7. 9. Schematic diagram for how we got axis density of our main method. The blue dot is the galaxy around which we calculate the ”Axis Density”, while the orange dots are neighbor galaxies around the blue one. We project every neighbor galaxy to one axis, then calculate the axis density around the blue dot, we repeat this procedure for every axes and every galaxy. . .. 3.2. 12. There are the distribution of Mock samples. Top is log(f) of spherical shell structure, and bottom is log(f) of cross lines structure. In mock samples, we select ln(F ) > µln(F ) which is mock structures. . . . . . . . . . . . .. vi. 15.

(9) 3.3. There are the 3-D distribution of Mock samples. Top is 3-D distribution of spherical shell structure, and bottom is 3-D distribution of cross lines structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.4. 16. The figure shows the distribution of Large-Scale-Filament Factor (LSFF) versus Spherical Density(by log) of selected region, we can see LSFF is correlate Spherical Density, so we fitting for that as a Green curve line(f0 ), which we use least square fit by second order, this line is means the average structural trend of galaxies for the local environment, we set that ”LSF F0 (F0 )”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.1. 18. The figure shows the distribution of Spherical Density of Millennium Simulation, we select and define [ln(ρ5th ) > µln(ρ5th ) + 1σln(ρ5th ) ] are Extremely High Density type. [ln(ρ5th ) > µln(ρ5th ) and ln(ρ5th ) < µln(ρ5th ) + 1σln(ρ5th ) ] are High Density type. [ln(ρ5th ) < µln(ρ5th ) and ln(ρ5th ) > µln(ρ5th ) −1σln(ρ5th ) ] are Low Density type. [ln(ρ5th ) < µln(ρ5th ) −1σln(ρ5th ) ] are Extremely Low Density type. With Red, Blue, Gray, and Green color, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.2. 21. Here is the three-dimension distribution of Millennium Simulation in Cartesian grid X, Y, and Z. Define by Spherical Density. Units and location of this region is same as Fig. 2.1. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density. . . . . . . . . . . . . . . . . . . . . . . . .. 4.3. 22. These three figures are two-dimension distribution of Millennium Simulation. Define by Spherical Density. Top figure is projection of X-Y plan, right figure is projection of X-Z plan, left figure is projection of Y-Z plan. Shown Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are with Red, Blue, Gray, and Green color dots, respectively. . . . . . . . . . . . . . . . . . . . . . . .. vii. 23.

(10) 4.4. The figure shows the distribution of Spherical Density of SDSS selected region, we select and define [ln(ρ5th ) > µln(ρ5th ) + 1σln(ρ5th ) ] are Extremely High Density type. [ln(ρ5th ) > µln(ρ5th ) and ln(ρ5th ) < µln(ρ5th ) + 1σln(ρ5th ) ] are High Density type. [ln(ρ5th ) < µln(ρ5th ) and ln(ρ5th ) > µln(ρ5th ) −1σln(ρ5th ) ] are Low Density type. [ln(ρ5th ) < µln(ρ5th ) −1σln(ρ5th ) ] are Extremely Low Density type. With Red, Blue, Gray, and Green color, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.5. 24. Here is the three-dimension distribution of SDSS selected region in Cartesian grid X, Y, and Z. Define by Spherical Density. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density. . . . . . . . . . . . . . . . . . . . . . . . .. 4.6. 25. These four figures are two-dimension distribution of SDSS selected region. Define by Spherical Density. Top left figure is projection of X-Y plan, top right figure is projection of X-Z plan, bottom left figure is projection of Y-Z plan, and bottom right figure is projection of RA and DEC. Shown Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are with Red, Blue, Gray, and Green color dots, respectively.. 4.7. . . . . . . . . . . . . . . . . . . . . . . . . . .. 26. The figure shows the distribution of LSFF of Millennium Simulation, we select and define [ln(F ) > µln(F ) + 1σln(F ) ] are Extremely High LSFF. [ln(F ) > µln(F ) and ln(F ) < µln(F ) + 1σln(F ) ] are High LSFF. [ln(F ) < µln(F ) and ln(F ) > µln(F ) − 1σln(F ) ] are Low LSFF. [ln(F ) < µln(F ) − 1σln(F ) ] are Extremely Low LSFF. With Red, Blue, Gray, and Green color, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. viii. 28.

(11) 4.8. Here is the three-dimension distribution of Millennium Simulation in Cartesian grid X, Y, and Z. Define by LSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.9. 29. These three figures are two-dimension distribution of Millennium Simulation. Define by LSFF. Top figure is projection of X-Y plan, right figure is projection of X-Z plan, left figure is projection of Y-Z plan. Shown Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are with Red, Blue, Gray, and Green color dots, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30. 4.10 The figure shows the distribution of LSFF of SDSS selected region, we select and define [ln(F ) > µln(F ) + 1σln(F ) ] are Extremely High LSFF. [ln(F ) > µln(F ) and ln(F ) < µln(F ) + 1σln(F ) ] are High LSFF. [ln(F ) < µln(F ) and ln(F ) > µln(F ) − 1σln(F ) ] are Low LSFF. [ln(F ) < µln(F ) − 1σln(F ) ] are Extremely Low LSFF. With Red, Blue, Gray, and Green color, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31. 4.11 Here is the three-dimension distribution of SDSS selected region in Cartesian grid X, Y, and Z. Define by LSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32. 4.12 These four figures are two-dimension distribution of SDSS selected region. Define by Spherical Density. Top left figure is projection of X-Y plan, top right figure is projection of X-Z plan, bottom left figure is projection of Y-Z plan, and bottom right figure is projection of RA and DEC. Shown Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are with Red, Blue, Gray, and Green color dots, respectively.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ix. 33.

(12) 4.13 The figure shows the distribution of SSFF of Millennium Simulation, we select and define [f > µf +σf ] are High SSFF. [f < µf − σf ] are Low SSFF. [µf − σf < f < µf +σf ] are Middle SSFF. With Red, Gray, and Green color, respectively . . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 4.14 Here is the three-dimension distribution of Millennium Simulation in Cartesian grid X, Y, and Z. Define by SSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37. 4.15 These three figures are two-dimension distribution of Millennium Simulation. Define by SSFF. Top figure is projection of X-Y plan, right figure is projection of X-Z plan, left figure is projection of Y-Z plan. Shown High SSFF, Middle SSFF, and Low SSFF type galaxies, are with Red, Gray, and Green color dots, respectively. . . . . . . . . . . . . . . . . . . . . .. 38. 4.16 The figure shows the distribution of SSFF of SDSS selected region, we select and define [f > µf +σf ] are High SSFF. [f < µf − σf ] are Low SSFF. [µf − σf < f < µf +σf ] are Middle SSFF. With Red, Gray, and Green color, respectively . . . . . . . . . . . . . . . . . . . . . . . . . .. 39. 4.17 Here is the three-dimension distribution of SDSS selected region in Cartesian grid X, Y, and Z. Define by SSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40. 4.18 These four figures are two-dimension distribution of SDSS selected region. Define by Spherical Density. Top left figure is projection of X-Y plan, top right figure is projection of X-Z plan, bottom left figure is projection of Y-Z plan, and bottom right figure is projection of RA and DEC. Shown High SSFF, Middle SSFF, and Low SSFF type galaxies, are with Red, Gray, and Green color dots, respectively. . . . . . . . . . . . . . . .. x. 41.

(13) 4.19 The figure shows the cumulative distribution of g − r color of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45. 4.20 The figure shows the cumulative distribution of u − r color of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46. 4.21 The figure shows the cumulative distribution of stellar mass of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47. 4.22 The figure shows the cumulative distribution of Dynamical mass of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xi. 48.

(14) 4.23 The figure shows the cumulative distribution of Dynamical mass/Stellar mass of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . .. 49. 4.24 The figure shows the cumulative distribution of [OII] equivalent width of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50. 4.25 The figure shows the cumulative distribution of Halpha equivalent width of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51. 4.26 The figure shows the cumulative distribution of Hbeta equivalent width of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xii. 52.

(15) 4.27 The figure shows the cumulative distribution of sSFR of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53. 4.28 The figure shows the cumulative distribution of g − r color of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s pvalue, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.001). . . . . . . . . . . . . . . . . . . . . .. 56. 4.29 The figure shows the cumulative distribution of u − r color of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s pvalue, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.0001). . . . . . . . . . . . . . . . . . . . .. 57. 4.30 The figure shows the cumulative distribution of Stelar mass of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s pvalue, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.001). . . . . . . . . . . . . . . . . . . . . .. xiii. 58.

(16) 4.31 The figure shows the cumulative distribution of Dynamical mass of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.01). . . . . . . . . . . . . . . . . .. 59. 4.32 The figure shows the cumulative distribution of Dynamical mass/Stellar mass of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. the KS-test shows them is likely(p > 0.5). . . . . . . . . . . . .. 60. 4.33 The figure shows the cumulative distribution of [OII] equivalent width of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.001). . . . . . . . . . . . . . .. 61. 4.34 The figure shows the cumulative distribution of Halpha equivalent width of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.001). . . . . . . . . . . . . . .. xiv. 62.

(17) 4.35 The figure shows the cumulative distribution of Hbeta equivalent width of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.001). . . . . . . . . . . . . . .. 63. 4.36 The figure shows the cumulative distribution of sSFR of galaxies for different LSFF regions. Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies. the KS-test shows them is unlikely(p < 0.001). . . . . . . . . . . . . . . . . . . . . . . . .. 64. 4.37 The figure shows the cumulative distribution of g − r color of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. We can see the High SSFF type shift to right, it means the High SSFF type galaxies are redder then the Low SSFF type galaxies, the KS-test shows them is unlikely(p < 0.01). . . . . . . . . . .. 67. 4.38 The figure shows the cumulative distribution of u − r color of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. We can see the High SSFF type shift to right, it means the High SSFF type galaxies are redder then the Low SSFF type galaxies, the KS-test shows them is unlikely (p < 0.01). . . . . . . . . . .. xv. 68.

(18) 4.39 The figure shows the cumulative distribution of Stellar mass of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. We find the stellar mass in the High SSFF type galaxies are bigger than Low SSFF type galaxies, but the KS-test shows their correlation are weak (p < 0.02). . . . . . . . . . . . . . . . .. 69. 4.40 The figure shows the cumulative distribution of Dynamical mass of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. We find the dynamical mass in the High SSFF type galaxies are bigger than Low SSFF type galaxies, the KS-test shows they are from different parent population (p < 0.01). . . . . . . . .. 70. 4.41 The figure shows the cumulative distribution of Dynamical mass/Stellar mass of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. . . . . . . . . . . . . . . . .. 71. 4.42 The figure shows the cumulative distribution of [OII] equivalent width of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type.. . . . . . . . . . . . . . . .. 72. 4.43 The figure shows the cumulative distribution of Halpha equivalent width of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. . . . . . . . . . . . . . . . .. xvi. 73.

(19) 4.44 The figure shows the cumulative distribution of Hbeta equivalent width of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. . . . . . . . . . . . . . . . .. 74. 4.45 The figure shows the cumulative distribution of sSFR of galaxies for each SSFF type. Solid line, dash line, and dot line, are correspond to High SSFF, Middle SSFF, and Low SSFF type galaxies, respectively. We also calculate and present this property’s p-value, which is from K-S test of between each SSFF type. In sSFR, Low SSFF type galaxies have stronger sSFR than High, and Middle SSFF type, that KS-test are smaller than (P < 0.004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xvii. 75.

(20) Chapter 1 Introduction In the large-scale, galaxies are not randomly distributed (de Lapparent et al. 1986; Geller & Huchra 1989; Gott et al. 2005; York et al. 2000; Thompson & Gregory 1978; Davis et al. 1982; Bond & Myers 1996; Sathyaprakash et al. 1998; Colless et al. 2001; Gott et al. 2005). The similar structure also found among cosmological N-body simulations of the dark matter (e.g. Davis et al. 1985; Bond, Kofman & Pogosyan 1996; Sathyaprakash, Sahni & Shandarin 1996; Arag’on-Calvo et al. 2007; Hahn et al. 2007a).. After the Big Bang, galaxies constantly attract to each other and form Large-scale Structure (LSS). These numerous galaxies assemble to different types of structures, such as filaments, sheets, webs, and voids. Typical size of LSS is between 50−70 h−1 M pc (Bharadwaj, Bhavsar & Sheth 2004). Unfortunately it is difficult to quantitatively describe LSS, although it is obvious to our eyes.. According to the previous studies, the properties of galaxies are different between in high- and low-density environments (e.g. Dressler, Thompson & Shectman 1985; Couch & Sharples 1987; Balogh et al. 1997, 1998, 1999, 2002; Hashimoto et al. 1998; Poggianti et al. 1999; Couch et al. 2001; Solanes et al. 2001; Lewis at al. 2002a; Gomez et al. 2002). Grogin & Geller (1999) and Rojas et al. (2004) also proved the galaxies inside void and outside void will be significantly different. That is to say properties of galaxies and their large & small environments are correlated. 1.

(21) In this paper, we have developed quantitative methods to objectively characterize the large-scale structure of the universe surrounding galaxies, to qualitatively investigate the relationship between the properties of galaxies and their large-scale environments.. First, in Chapter 2 will introduce Data catalog that we use, and as a three-dimensional distribution of galaxies to probe the structure is a good choice, we will explain how the actual data conversion for the three-dimensional distribution. Chapter 3, where will explain the definition and calculation for Spherical Density of this paper, the principles and details of MAD, and exclude Spherical Density effect based on the following MAD. In Chapter 4 we present the MAD operation results, including the appearance and trend of the structure, and explain the result of the properties of galaxies, and trend of the structure of the local environment. Finally, Chapter 5 is a summary of this paper, including a discussion of the physical meaning of the results, possibly error of data, and future research directions.. We assume the following cosmology throughout this paper:Hubble constant H0 = 100hkms1 M pc−1 , Matter density Ωm = 0.27, and Dark energy density ΩΛ = 0.73。. 2.

(22) Chapter 2 DATA In this paper, we use the main data combined from SDSS DR8 Groups and Clusters of Galaxies Value-Added Catalogues (Tempel, Tago & Liivamägi 2012a), and MPA/JHU value-added galaxy catalog (Kauffmann et al. 2003; Salim et al. 2007; Brinchmann et al. 2004; Tremonti et al. 2004). That is based on Sloan Digital Sky Survey Data Release 8 (SDSS DR8;. Aihara et al. 2011), and SDSS Data Release 7 (DR7;. Abazajian et al. 2009), respectively. We have also used Mini Millennium Run Semi-Analytic Galaxy Catalogue (Croton et al. 2005), to test our methods introduced in this paper.. 2.1 Mocks We have created several ’mock’ samples of various structures in three-dimensions. That contains linear structures with different angles, cross-shaped structures, and spherical shell-like structures. Figure 2.1 presents the structure and distribution of dots (galaxies) in the two mock samples. The top figure and the bottom figure are the spherical shell-like structure and the cross-like structure, respectively. Both include 600 points.. 3.

(23) 50 0. z. -50 0. 50. 100. z. 0. 50. x. 100 -50. 50 0. -50 0. y. 50 x. Figure 2.1: The distribution of dummy sample; we create two different types of dummy structures, such as ”cross (bottom panel)” and ”spherical sheet (top panel)”. Both figures include approximately 600 galaxies. 4.

(24) 2.2 Millennium Simulation We also used the ”Mini Millennium Run Semi-Analytic Galaxy Catalogue (Croton et al., 2005)” to test our methods. This catalog ”consists of 18960 galaxies” is taken from ”Millennium Run Lambda-Cold Dark Matter N-body Simulation (Springel et al. 2005)”. We chose one 30 ∗ 30 ∗ 30M pc/h area, which contains 2454 galaxies. Figure 2.2 is a three-dimensional distribution of galaxies in this area. The large-scale structure is already apparent.. 40 30. Z. 20 20. 20. 30. 30 40. 40. Y X. Figure 2.2: Three-dimensional distribution of 2454 galaxies in the Millennium Simulation in Cartesian grid X, Y, and Z, in the unit of Mpc/h, Y axis corresponds to a line of sight.. 5.

(25) 2.3 SDSS Our data catalog is combined the SDSS DR8 Groups and Clusters of Galaxies ValueAdded Catalogues(Tempel, Tago & Liivamagi 2012a), which derived from Sloan Digital Sky Survey Data Release 8 (SDSS DR8; Aihara et al. 2011), and the MPA/JHU valueadded galaxy catalog (Kauffmann et al. 2003; Salim et al. 2007; Brinchmann et al. 2004; Tremonti et al. 2004), that based on SDSS Data Release 7 (DR7; Abazajian et al. 2009). Its magnitude limit is mr = 17.77, and to find a clear structure, we have chosen the redshift z in a range between 0.009 to 0.2. This catalog contains 576,493 galaxies and contains ugriz band, co-moving distance, stellar mass, and [OII]，[Hα ]，[Hβ ] spectral lines and other information. Figure 2.3 is galaxies distribution of our data catalog.. In general large-scale structure is between 50−70 h−1 M pc (Bharadwaj, Bhavsar & Sheth 2004). In the millennium-II simulation, Boylan-Kolchin et al.(2009) also classified several two-dimensional scales large than 40 ∗ 40h−1 M pc. In light of Bharadwaj, Bhavsar & Sheth (2004), we chose 60 ∗ 60 ∗ 60M pc/h threedimensional scale to study large-scale environment. But, the aperture of our method is 10M pc/h, so the final scale is effectively 40 ∗ 40 ∗ 40M pc/h after removing objects near the edge. This scale is similar to the large-scale structure by Boylan-Kolchin et al.(2009).. We chose the same sky region as Tempel et al.(2013) to compare our results of quantitative definitions of large-scale structure to their results. Although the three-dimensional distribution to study the large-scale structure is a better way and choice, but it must be considered ”finger of god”, and suppress the redshift distortion effect on the line of sight. So we introduced comoving distance dgal to eliminate the factors, based and from Tempel et al. (2012a):. dgal = dgroup + (d∗gal − dgroup )σr /(σv /H0 ). 6. (2.1).

(26) 0h00 6h. 18. h0. 00. 0. 60. 12h00. 0. 70 60 60 40 50 20 Lambda(deg). DEC. 40. 30. 0. -20. 20. 10. -40. 0. -60 120. 140. 160. 180. 200. 220. 240. 260. -30. RA. -20. -10. 0. 10. 20. 30. 40. Eta(deg). Figure 2.3: The distributions of galaxies in Sloan Digital Sky Survey Legacy Survey. Top figure is the Equatorial distribution. Bottom left figure in right ascension (RA) and declination (DEC). And the bottom right figure in η and λ, the coordinate of Sloan Digital Sky Survey.. 7.

(27) Where d∗gal is the initial distance to the galaxy, dg roup is the distance to the group center, σr is the root mean square sizes of galaxy groups, and σv is their rms radial velocities.. Then we transform SDSS angular coordinate λ and η, to Cartesian grid. Calculated and translated following the relationship of Tempel et al.(2013) between two-dimension and three-dimension: x = −dgal sin λ, y = dgal cos λ cos η,. (2.2). z = dgal cos λ sin η Figure 2.4 presents the distribution of galaxies in three-dimensional in this region. The space location, X axis is -15 to 25 Mpc/h, Y axis is 205 to 245 Mpc/h, Z axis is 15 to 55 Mpc/h, Y-axis direct the line of sight, and contains 966 galaxies. For study properties of galaxies, in this paper, we also determine the Dynamical mass to study the relationship between mass and the small-scale environment, following Beifiori et al. (2012):. Mdyn = βRe σ 2 /G. (2.3). G is gravitational constant, and the dimensionless constant β, set to β = 5.0, is based on Belli et al. (2014), and Cappellari et al. (2006, 2009). Wherein the velocity dispersion σ and effective radius Re contained in our data catalog, taken from the MPA/JHU valueadded galaxy catalog (Kauffmann et al. 2003; Salim et al. 2007; Brinchmann et al. 2004; Tremonti et al. 2004).. 8.

(28) 50 30 40 Z[Mpc=h] 20 ¡10. 210. 10 0 X[Mpc= h]. 240. 230 Y[M 220 pc=h ]. 20. Figure 2.4: The three-dimensional distribution of selected region in Cartesian, include 966 galaxies grid X, Y, and Z.. 9.

(29) Chapter 3 Method We proposed a new quantify detection method of large-scale structure (LSS), which we called ”Multi-Axis Density (MAD)”. MAD would give a quantitative value for each galaxy represents their large-scale environments, that we called Large-Scale-Filament Factor (LSFF). We also calculated traditional environmental Spherical Density around each galaxy. Difference between LSFF and Spherical Density is that Spherical Density can not distinguish orientation of the structure inside their spherical aperture, but MAD was able to differentiate it. Unfortunately previous studies could only achieved in qualitatively.. Finally, we know there are higher density inside the filaments, lower density in the voids. In other words, the LSS and density are positively correlated, but we want to know the small-scale structure’s effect on the properties of galaxies. On the basis of above correlation, we do a fitting for the LSFF and Spherical Density, to exclude factor of density, get a value to quantify the local small-scale structure, then to understand the small-scale environmental effect on properties of galaxies. Then after fitting, we are able to identify small-scale structures, such as filaments in small-scale environment. In the chapter 4, we will compare LSFF and Spherical Density effect, on the properties of the galaxies. And then present the relationship between real structural trends of galaxies in the local small-scale environment and the properties of galaxies. 10.

(30) 3.1 Spherical Density We know that the distribution of the large-scale structure (LSS) and the Spherical Density are related, so here calculated as the Spherical Density around each galaxy’s space. We use that Spherical Density to distinguish between the different density regions. We first calculate the distance of each galaxy and neighboring galaxies in three-dimensional space, then we take from the most closest n-th galaxy as a radius. The Spherical Density ρnth is defined as:. ρnth = n/((4/3)πd3nth ). (3.1). dnth is the distance between the galaxy and n-th neighboring galaxies, this paper we use n=5 to calculate the Spherical Density. According to Spherical Density ρ5th , we separate four different density regions, Extremely High Density, High Density, Low Density, and Extremely Low Density. Because Spherical Density ρnth after taking log will approximate normal distribution, we classify each density region based on the following relations: 1. ln(ρ5th ) > µln(ρ5th ) + 1σln(ρ5th ) are Extremely High Density type. 2. ln(ρ5th ) > µln(ρ5th ) and ln(ρ5th ) < µln(ρ5th ) + 1σln(ρ5th ) are High Density type. 3. ln(ρ5th ) < µln(ρ5th ) and ln(ρ5th ) > µln(ρ5th ) − 1σln(ρ5th ) are Low Density type. 4. ln(ρ5th ) < µln(ρ5th ) − 1σln(ρ5th ) are Extremely Low Density type. Where µln(ρ5th ) is the mean of normal distribution, σln(ρ5th ) is the standard deviation of normal distribution.. 11.

(31) 3.2 Large Scale Filament Factor (LSFF) Here we propose a new method to detect the large-scale structure of the universe (Cosmic Web), that provides us with quantitative measures of large-scale structure (LargeScale-Filament Factor; LSFF) for each galaxy. The higher the value indicates that galaxies are inside the filaments. We use this value to classify environments into Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF, four environment types. First, we introduce the background of the principles of this method (Figure 3.1). Consider the case of a simple plane, assuming a linear structure distributed in space and parallel to the X axis, perpendicular to the Y axis. If all the galaxies in this region are projected to the X and Y axis, we will find the density is uniformly distributed along X axis, in the Y-axis we will see a dense areas due to projection of structure. We called ”Axis Density”.. Figure 3.1: Schematic diagram for how we got axis density of our main method. The blue dot is the galaxy around which we calculate the ”Axis Density”, while the orange dots are neighbor galaxies around the blue one. We project every neighbor galaxy to one axis, then calculate the axis density around the blue dot, we repeat this procedure for every axes and every galaxy. However, if the structure is 45 degrees or -45 degrees to the X and Y axis, only X and Y axis we can not detected the structure, so we increase two axes there, then we will be able to identify structures from different angles on the plane. And extended to threedimensional space we need a total of 13 axes to identify the structure with various angles 12.

(32) and shapes. On the basis of the above background principle, we proposed Multi-Axis Density (MAD) method, where we have established 13-axis around each galaxy. Surrounding galaxies were projected to each axis, then calculated the axis density ρaxis to represent the number of galaxies included in selected aperture around each galaxy, calculated as: ρaxis = 1/(d31 + 1) + 1/(d32 + 1) + ... + 1/(d3n + 1) =. ∑. 1/(d3nth. (3.2). + 1). The aperture of this method, different aperture will effect the result of the measurement, that is like the how smooth and what filament size you want. If the aperture too high that will too smooth, if the aperture too low that will can not find large-scale filaments. In this paper, we select 10M pc/h as the aperture of this method, depend on we assume the smallest large-scale filaments are around 10M pc/h. To classify the type of environment and quantify large-scale structure (LSS) on the basis of Axis-Density, we further established a measure called LSFF (Large-Scale-Filament Factor), calculated as follows: v u 13 u ∑ 3 F =t ρ3axis(i). (3.3). i=1. where F is LSFF, i is the number of axis. On the basis of ’F ’, we classified four different regions: Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF. Because ln(F ) can be regarded as the normal distribution, we classified each region on the basis of the following relations: 1. ln(F ) > µln(F ) + 1σln(F ) are Extremely High LSFF. 2. ln(F ) > µln(F ) and ln(F ) < µln(F ) + 1σln(F ) are High LSFF. 3. ln(F ) < µln(F ) and ln(F ) > µln(F ) − 1σln(F ) are Low LSFF. 4. ln(F ) < µln(F ) − 1σln(F ) are Extremely Low LSFF.. 13.

(33) Where µln(F ) is the mean of normal distribution, σln(F ) is the standard deviation of normal distribution.. Figure 3.2 shows the log(F) of mock samples, where F is LSFF. In mock samples , we select ln(F ) > µln(F ) (red color) to measure our mock structures. In Figure 3.3, red dots indicate that LSFF can differentiate spherical structure (top panel) and cross-shaped structure (bottom panel).. 14.

(34) Spherical shell structure. 90 80 70. Counts. 60 50 40 30 20 10 0. 1.4. 1.6. 1.8. 2.0. 2.2. 2.4. 2.6. log F Cross lines strucutre 50. Counts. 40. 30. 20. 10. 0. 1.2. 1.4. 1.6. 1.8. 2.0. 2.2. 2.4. 2.6. 2.8. log F. Figure 3.2: There are the distribution of Mock samples. Top is log(f) of spherical shell structure, and bottom is log(f) of cross lines structure. In mock samples, we select ln(F ) > µln(F ) which is mock structures. 15.

(35) 50 z. 0. 100 50. -50. 50 0. x. -50 0. z. 0. 50. y. 100 50 -50. 50 0. x. -50 0. y. Figure 3.3: There are the 3-D distribution of Mock samples. Top is 3-D distribution of spherical shell structure, and bottom is 3-D distribution of cross lines structure.. 16.

(36) 3.3 Small Scale Filament Factor (SSFF) We know that large-scale structure and density are positively correlated. Because the positive correlation between both, we will not understand the different properties of galaxies, that difference is due to the galaxies in different environment types (filaments or voids), or simply caused by environmental density (Spherical Density), despite the fact that both can have effect on properties of galaxies.. In small-scale environments, we have small-scale filaments, even inside an aperture of. In other words, we want to understand the small-scale filaments (SSF) in the local small-scale environment. Here we present the Small-Scale-Filament Factor (SSFF) to quantify SSF, then to understand the effect on properties of galaxies. For the relative relation between LSFF and Spherical Density, we exclude the effect of Spherical Density using LSFF, to obtain a quantitative measure of SSFF in the local small-scale environment. This quantitative value we called Small-Scale-Filament Factor (SSFF).. Figure 3.4 presents the relative relation between LSFF and Spherical Density. At higher LSFF that have higher Spherical Density, and lower Spherical Density in the relatively low LSFF regions. Indeed, show a positive correlation between large-scale structure and Spherical Density. For relative relation between the LSFF and Spherical Density, we use second order least squares fitting to do the fitting, and the result of fitting are displayed as a green curve in Figure 3.2, this curve represents the approximately average local small-scale environment, we set that as LSF F0 (F0 ).. Based on this curve, every galaxy is perpendicular project to the curve in this diagram, that projection point we set f0 , and SSFF (f ) can simply calculated by the following rela-. 17.

(37) 3.5 3.0. AAD log<p>. 2.5 2.0 1.5 1.0 0.5. 7. 6. 5. 4 3 2 1 Spherical density log(ρ5th). 0. 1. 2. Figure 3.4: The figure shows the distribution of Large-Scale-Filament Factor (LSFF) versus Spherical Density(by log) of selected region, we can see LSFF is correlate Spherical Density, so we fitting for that as a Green curve line(f0 ), which we use least square fit by second order, this line is means the average structural trend of galaxies for the local environment, we set that ”LSF F0 (F0 )”. tion:. SSF F (f ) = log(F ) − F0. (3.4). Finally, we according SSFF (f ) for each galaxy and for their local small-scale environment to classify three different types. divided into High SSFF, Middle SSFF, and Low SSFF, where classify according to the following relation: 1. f > µf +σf are High SSFF. 2. f < µf − σf are Low SSFF. 3. µf − σf < f < µf +σf are Middle SSFF. Where µf is the mean of normal distribution, σf is the standard deviation of normal distribution.. 18.

(38) Chapter 4 Result 4.1 Quantitative Definition of Large Scale Structure In this chapter, we present the results of our quantitative definition of the large-scale structure. We show the locus using Spherical Density to distinguish different density regions. Through the calculation of MAD, we further classify different types of structures in three-dimensions.. Because of a positive correlation between Large-Scale-Filament Factor (LSFF) and Spherical Density, that classify the different density regions and different structural types, a naive investigation using either of those two measures may produce non-independent result to each other. But the most important thing is the result of our definition of MAD, that has a potential of distinguishing the difference between various structures inside the aperture of Spherical Density.. 19.

(39) 4.1.1 LSS by Spherical Density First, we present the results of using the Spherical Density to separate the different density regions. Figure 4.1, and Figure 4.4, show the Millennium Simulation and SDSS histogram distribution of Spherical Density. Based on this distribution, we according to the Spherical Density, separate four different density regions, Extremely High Density, High Density, Low Density, and Extremely Low Density (see S 3.1). In this section we used the Red, Blue, Gray, Green color, respectively. In Figure 4.2 and Figure 4.5, we have a three-dimensional X, Y, and Z axes to show Millennium Simulation and SDSS distribution of galaxies in three-dimensions, and we can based on each color in the figures, to distinguish the four previously different Spherical Density regions.. Here we can compare Figure 4.2 & Figure 4.5 with Figure 2.2 & Figure 2.4, we found the Spherical Density regions of each color, and that the density of surrounding areas for each galaxy, which are consistent and clear. While Figure 4.3 is based on Figure 4.2, results of Millennium Simulation projected onto different two-dimensional plans. Similar to Figure 4.6, is based on Figure 4.5, the different two-dimensional plans of SDSS galaxies.. 20.

(40) 400 Extremely High Density High Density Low Density Extremely Low Density. Count. 300. 200. 100. 0. 0.01. 0.1. 1. 10. 100. 1000. 1e4. Spherical density. Figure 4.1: The figure shows the distribution of Spherical Density of Millennium Simulation, we select and define [ln(ρ5th ) > µln(ρ5th ) + 1σln(ρ5th ) ] are Extremely High Density type. [ln(ρ5th ) > µln(ρ5th ) and ln(ρ5th ) < µln(ρ5th ) + 1σln(ρ5th ) ] are High Density type. [ln(ρ5th ) < µln(ρ5th ) and ln(ρ5th ) > µln(ρ5th ) − 1σln(ρ5th ) ] are Low Density type. [ln(ρ5th ) < µln(ρ5th ) − 1σln(ρ5th ) ] are Extremely Low Density type. With Red, Blue, Gray, and Green color, respectively.. 21.

(41) Extremely High Density High Density Low Density 40. Extremely Low Density. 30. Z. 20 20 30 40. 20. 30. 40. Y X. Figure 4.2: Here is the three-dimension distribution of Millennium Simulation in Cartesian grid X, Y, and Z. Define by Spherical Density. Units and location of this region is same as Fig. 2.1. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density.. 22.

(42) 50. Extremely High Density High Density Low Density Extremely Low Density. Y. 40. 30. 20. 10 10. 20. 30. 40. 50. X. 50. 50. Extremely High Density. Extremely High Density. High Density. High Density. Low Density. Low Density. Extremely Low Density. Extremely Low Density 40. Z. Z. 40. 30. 20. 30. 20. 10. 10 10. 20. 30. 40. 50. 10. Y. 20. 30. 40. 50. X. Figure 4.3: These three figures are two-dimension distribution of Millennium Simulation. Define by Spherical Density. Top figure is projection of X-Y plan, right figure is projection of X-Z plan, left figure is projection of Y-Z plan. Shown Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are with Red, Blue, Gray, and Green color dots, respectively.. 23.

(43) HighDensity ExtremelyHighDensity LowDensity ExtremelyLowDensity. 50. Counts. 40. 30. 20. 10. 0. 0:002. 0:005. 0:01. 0:02. 0:05 0:1 0:2 Sphericaldensity. 0:5. 1. 2. 5. Figure 4.4: The figure shows the distribution of Spherical Density of SDSS selected region, we select and define [ln(ρ5th ) > µln(ρ5th ) + 1σln(ρ5th ) ] are Extremely High Density type. [ln(ρ5th ) > µln(ρ5th ) and ln(ρ5th ) < µln(ρ5th ) + 1σln(ρ5th ) ] are High Density type. [ln(ρ5th ) < µln(ρ5th ) and ln(ρ5th ) > µln(ρ5th ) − 1σln(ρ5th ) ] are Low Density type. [ln(ρ5th ) < µln(ρ5th ) − 1σln(ρ5th ) ] are Extremely Low Density type. With Red, Blue, Gray, and Green color, respectively.. 24.

(44) Extremely High Density High Density Low Density. Z (Mpc/h). 10. 210. -10. 240. 230. 0 X (Mpc/h ). Y (M 220 pc/h ). 20. 20. 30. 40. 50. Extremely Low Density. Figure 4.5: Here is the three-dimension distribution of SDSS selected region in Cartesian grid X, Y, and Z. Define by Spherical Density. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density.. 25.

(45) ExtremelyHighDensity HighDensity LowDensity ExtremelyLowDensity. 240. ExtremelyHighDensity HighDensity LowDensity ExtremelyLowDensity. 50. 40 Z(Mpc=h). Y(Mpc=h). 230. 220. 30. 210. 20. ¡10. 0. 10. 20. ExtremelyHighDensity HighDensity LowDensity ExtremelyLowDensity. 50. 0. ¡10. X(Mpc=h). 10. 20. X(Mpc=h). ExtremelyHighDensity HighDensity LowDensity ExtremelyLowDensity. 46. 44. Z(Mpc=h). 40 DEC. 42. 30. 40. 38 20. 36 210. 220. 230. 240. 176. Y(Mpc=h). 178. 180. 182. 184. 186. 188. 190. RA. Figure 4.6: These four figures are two-dimension distribution of SDSS selected region. Define by Spherical Density. Top left figure is projection of X-Y plan, top right figure is projection of X-Z plan, bottom left figure is projection of Y-Z plan, and bottom right figure is projection of RA and DEC. Shown Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are with Red, Blue, Gray, and Green color dots, respectively.. 26.

(46) 4.1.2 LSS by Large Scale Filament Factor (LSFF) In this section we present the result of through our Multi-Axis Density (MAD), that main method to quantify the large-scale structure, to separate the different types of environments.. Figure 4.7, and Figure 4.10, show the Millennium Simulation and SDSS histogram distribution of Large-Scale-Filament Factor (LSFF). Based on this distribution, we according to the LSFF, separate four different LSFF regions, Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF (see S 3.2). In this section we also used the Red, Blue, Gray, Green color, respectively. In Figure 4.8 and Figure 4.11, we have a three-dimensional X, Y, and Z axes to show Millennium Simulation and SDSS distribution of galaxies in three-dimensions, and we can based on each color in the figures, to distinguish the four previously different LSFF regions.. Here we can compare Figure 4.8 & Figure 4.11 with Figure 2.2 & Figure 2.4, according to the types of environment presented to each color, clearly seen the large-scale structure. And found that each type of environment are consistent with location of galaxies of largescale structure, objectively. Figure 4.9 is based on Figure 4.8, results of Millennium Simulation projected onto different two-dimensional plans. Similar to Figure 4.12, is based on Figure 4.11, the different two-dimensional plans of SDSS galaxies.. But we can found, used LSFF separated and distinguished the types of environment, that presented large-scale structure, and used Spherical Density to distinguish density area shows morphology, both are very similar. This is because we mentioned that in this paper, LSFF and Spherical Density are positively correlated, so we can expected get a similar result. In this section, the results of the actually cases, same as our expectation, that derived similar results. 27.

(47) Extremely High LSFF High LSFF Low LSFF. 100. Extremely Low LSFF. Counts. 80. 60. 40. 20. 0. 2. 3. 4. 5. log Large scale filament factor (LSFF). Figure 4.7: The figure shows the distribution of LSFF of Millennium Simulation, we select and define [ln(F ) > µln(F ) + 1σln(F ) ] are Extremely High LSFF. [ln(F ) > µln(F ) and ln(F ) < µln(F ) + 1σln(F ) ] are High LSFF. [ln(F ) < µln(F ) and ln(F ) > µln(F ) − 1σln(F ) ] are Low LSFF. [ln(F ) < µln(F ) − 1σln(F ) ] are Extremely Low LSFF. With Red, Blue, Gray, and Green color, respectively.. The key difference is using the LSFF separate and classify the types of environment, it can to distinguish the difference between the uniform distribution and non-uniform distribution in the same density regions. If extended to a greater range of detection, which we can not ignore the impact. Therefore, we believe that use this method to quantify the type of environment, and even use the derivative Small-Scale-Filament Factor (SSFF) to quantitative define smallscale structure, it is a preferred choose for study the relation between the large-scale environment and properties of galaxies, or similar research.. 28.

(48) Extremely High LSFF High LSFF Low LSFF Extremely Low LSFF. 40 30. z_1. 20 20 30 40. 20. 30. 40. y_1. x_1. Figure 4.8: Here is the three-dimension distribution of Millennium Simulation in Cartesian grid X, Y, and Z. Define by LSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density.. 29.

(49) Extremely High LSFF High LSFF Low LSFF. Y. 40. Extremely Low LSFF. 30. 20. 15. 20. 25. 30. 35. 40. 45. X. Z. Z. 40. 30. 20. Extremely High LSFF. Ex. High LSFF. Hi. Low LSFF 40 Extremely Low LSFF. Lo. Ex. 30. 20. 15. 20. 25. 30. 35. 40. 45. X. 15. 20. 25. 30. 35. Y. Figure 4.9: These three figures are two-dimension distribution of Millennium Simulation. Define by LSFF. Top figure is projection of X-Y plan, right figure is projection of X-Z plan, left figure is projection of Y-Z plan. Shown Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are with Red, Blue, Gray, and Green color dots, respectively.. 30. 40. 45.

(50) Extremely High LSFF High LSFF Low LSFF. 60. Extremely Low LSFF. 50. Counts. 40. 30. 20. 10. 0. 1.0. 1.5. 2.0. 2.5. 3.0. log Large scale filament factor (LSFF). Figure 4.10: The figure shows the distribution of LSFF of SDSS selected region, we select and define [ln(F ) > µln(F ) + 1σln(F ) ] are Extremely High LSFF. [ln(F ) > µln(F ) and ln(F ) < µln(F ) + 1σln(F ) ] are High LSFF. [ln(F ) < µln(F ) and ln(F ) > µln(F ) − 1σln(F ) ] are Low LSFF. [ln(F ) < µln(F ) − 1σln(F ) ] are Extremely Low LSFF. With Red, Blue, Gray, and Green color, respectively.. 31.

(51) Extremely High LSFF High LSFF Low LSFF. Z (Mpc). 20. 30. 40. 50. Extremely Low LSFF. 20. 10. 0. -10. pc) Y (M. 240. 230. 220. 210. X (Mpc). Figure 4.11: Here is the three-dimension distribution of SDSS selected region in Cartesian grid X, Y, and Z. Define by LSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density.. 32.

(52) 240. Extremely High LSFF. Extremely High LSFF. High LSFF 50 Low LSFF. High LSFF. Extremely Low LSFF. Extremely Low LSFF. Low LSFF. 40 Z (Mpc). Y (Mpc). 230. 220. 30. 210. 20. -10. 0. 10. 20. -10. 0. X (Mpc). 10. 20. X (Mpc). 50. Extremely High LSFF. Extremely High LSFF. High LSFF 46 Low LSFF. High LSFF. Extremely Low LSFF. Extremely Low LSFF. Low LSFF. 44. DEC. Z (Mpc). 40. 30. 42. 40. 38 20. 36 210. 220. 230. 240. 176. Y (Mpc). 178. 180. 182. 184. 186. 188. 190. RA. Figure 4.12: These four figures are two-dimension distribution of SDSS selected region. Define by Spherical Density. Top left figure is projection of X-Y plan, top right figure is projection of X-Z plan, bottom left figure is projection of Y-Z plan, and bottom right figure is projection of RA and DEC. Shown Extremely High LSFF, High LSFF, Low LSFF, and Extremely Low LSFF type galaxies, are with Red, Blue, Gray, and Green color dots, respectively.. 33.

(53) 4.1.3 LSS by Small Scale Filament Factor (SSFF) Our Large-Scale-Filament Factor (LSFF) can more accurately describe large-scale structure. But we know in small-scale also have small-scale filaments, even in lowSpherical Density regions. If only used LSFF, because the significant differences of different Spherical Density regions, we can not easily detect the small-filaments among the low-Spherical Density regions. That is, we can not easily detect the small-scale structure (SSS) of the local small-scale environment. Therefore, we eliminate the influence of Spherical Density, then proposed SmallScale-Filament Factor (SSFF) to given a value for each galaxy to quantify the smallfilaments.. Figure 4.13, and Figure 4.16, show the Millennium Simulation and SDSS histogram distribution of SSFF (f ). Based on this distribution, we according to the (f ), separate to three different SSFF regions, High SSFF, Middle SSFF, and Low SSFF(see § 3.3). In this section we used the Red, Gray, Green color, respectively. In Figure 4.14 and Figure 4.17, we have a three-dimensional X, Y, and Z axes to show Millennium Simulation and SDSS distribution of galaxies in three-dimensions, and we can based on each color in the figures, to distinguish the three previously different SSFF regions.. Here we can compare Figure 4.15 & Figure 4.18 with Figure 2.2 & Figure 2.4. SSFF is showing the small-filaments of the small-scale environment, although when we according the small-filaments of the small-scale environment presented by each colors, combined every small-scale environment regions, can still see the large-scale structure. But found not as obvious as LSFF, this is due to LSFF comprise the influence of the Spherical Density. In the small-scale environments, although at the same Spherical Density regions, have small-filaments and have no small-filaments two regions which LSFF ware different, even in low-Spherical Density regions. But Spherical Density factor make and let LSFF only 34.

(54) can see the difference on the large-scale structure.. Finally, we know there are higher density inside the filaments, lower density in the voids. In other words, the LSS and density are positively correlated, but we want to know the small-scale structure’s effect on the properties of galaxies. Small-scale environments also presents uniformly distributed, and non-uniformly distributed. That is, in small-scale will have small-scale filaments, even in low-Spherical Density regions. In other words, we want to understand the small-scale filaments (SSF) in the local small-scale environment, whether is environmental effect on properties of galaxies or not.. Small-Scale-Filament Factor is showing the quantitative value of small-filaments of the small-scale environment. Expressed the case of non-uniform distributed with some small-filaments in the High-Spherical Density regions, or even low-Spherical Density regions. That is, lower SSFF area we can find the distribution of galaxies are uniform in small-scale environment. Conversely, high SSFF regions are found the small-scale environment have small-scale filaments. Figure 4.15 is based on Figure 4.14, results of Millennium Simulation projected onto different two-dimensional plans. Similar to Figure 4.18, is based on Figure 4.17, the different two-dimensional plans of SDSS galaxies.. 35.

(55) High SSFF Middle SSFF Low SSFF 200. Counts. 150. 100. 50. 0. -1.0. -0.5. 0. 0.5. 1.0. Small scale filament factor (SSFF). Figure 4.13: The figure shows the distribution of SSFF of Millennium Simulation, we select and define [f > µf +σf ] are High SSFF. [f < µf − σf ] are Low SSFF. [µf − σf < f < µf +σf ] are Middle SSFF. With Red, Gray, and Green color, respectively. 36.

(56) High SSFF Middle SSFF Low SSFF. 40 30. z_1. 20 20 30 40. 20. 30. 40. y_1. x_1. Figure 4.14: Here is the three-dimension distribution of Millennium Simulation in Cartesian grid X, Y, and Z. Define by SSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density.. 37.

(57) High SSFF Middle SSFF Low SSFF. Y. 40. 30. 20. 20. 30. 40. X. Z. Z. 40. 30. 20. High SSFF. High. Middle SSFF. Midd. Low SSFF 40. Low. 30. 20. 20. 30. 40. 20. X. 30 Y. Figure 4.15: These three figures are two-dimension distribution of Millennium Simulation. Define by SSFF. Top figure is projection of X-Y plan, right figure is projection of X-Z plan, left figure is projection of Y-Z plan. Shown High SSFF, Middle SSFF, and Low SSFF type galaxies, are with Red, Gray, and Green color dots, respectively.. 38. 40.

(58) High SSFF 110. Middle SSFF Low SSFF. 100 90 80. Counts. 70 60 50 40 30 20 10 0. -0.4. -0.2. 0. 0.2. 0.4. 0.6. Small scale filament factor (SSFF). Figure 4.16: The figure shows the distribution of SSFF of SDSS selected region, we select and define [f > µf +σf ] are High SSFF. [f < µf − σf ] are Low SSFF. [µf − σf < f < µf +σf ] are Middle SSFF. With Red, Gray, and Green color, respectively. 39.

(59) High SSFF Middle SSFF. Z (Mpc). 20. 30. 40. 50. Low SSFF. 210 220 230 240. pc). Y (M. Figure 4.17: Here is the three-dimension distribution of SDSS selected region in Cartesian grid X, Y, and Z. Define by SSFF. Units and location of this region is same as Fig. 2.3. Red dots are Extremely High Density, Blue dots are High Density, Gray dots are Low Density, and Green dots are Extremely Low Density.. 40.

(60) High SSFF. High SSFF. Middla SSFF 240. Middla SSFF 50. Low SSFF. Low SSFF. 40 Z (Mpc). Y (Mpc). 230. 220. 30. 210. 20. -10. 0. 10. 20. -10. 0. X (Mpc). 10. 20. X (Mpc). High SSFF. High SSFF. Middla SSFF 50. Middla SSFF. 46. Low SSFF. Low SSFF. 44. DEC. Z (Mpc). 40. 30. 42. 40. 38 20. 36 210. 220. 230. 240. 176. Y (Mpc). 178. 180. 182. 184. 186. 188. 190. RA. Figure 4.18: These four figures are two-dimension distribution of SDSS selected region. Define by Spherical Density. Top left figure is projection of X-Y plan, top right figure is projection of X-Z plan, bottom left figure is projection of Y-Z plan, and bottom right figure is projection of RA and DEC. Shown High SSFF, Middle SSFF, and Low SSFF type galaxies, are with Red, Gray, and Green color dots, respectively.. 41.

(61) 4.2 Environmental Effect on Properties of Galaxies We know the properties of galaxies are corrected by their local environment, such as local Spherical Density. But we want to know what difference of the same Spherical Density but different LSFF regions. In other words, we want to know what difference between large-scale structure (LSS) and small-scale structure (SSS) effect on the properties of galaxies. That is, in the related studies, we must know the small-scale environment have smallfilaments or not, which also an important factor can not ignored, when discussing the properties of the galaxies. In the previous studies showed that galaxy types and their environmental density are correlated, galaxy types are corrected to its color, and have a correlation between its density and color, above all show a strong correlation (e.g. Postman & Geller 1984; Dressler 1980; Strateva et al. 2001; Baldry et al. 2003; Hogg et al. 2002; Blanton et al. 2003)。 In Star formation rate (SFR), because usually the large equivalent widths directly shows the strong Star formation rate (e.g Huchra 1977; Kennicutt 1983; Peterson et al. 1986; Broadhurst, Ellis, & Shanks 1988; Colless et al. 1990; Broadhurst, Ellis, & Glazebrook 1992; Koo & Kron 1992; Y. Hashimoto et al. 1998). So we study the Spherical Density, LSFF, and SSFF effect on the EW[Hα ], EW[Hβ ], EW[OII], sSFR. That is, we know colors, masses, and SFR of galaxies, will correlate to their environments. Based on previous studies, we know that in cluster the galaxies close to red color, and will have a strong SFR, and higher mass.(Benson et al. 2003)。. In this section, we study the Spherical Density, Large-Scale-Filament Factor (LSFF), and Small-Scale-Filament Factor (SSFF) effect on the properties of galaxies, such as Stellar mass, Dynamical mass, Color, Star formation rate, and explain the results significant. On the color we use g − r, and u − r, to avoid the effects of low signal noise ratio. To analyse the mass of dark matter using Stellar mass and Dynamical mass. The star formation wrate e use EW [H alpha ], EW [H beta ], EW [OII], and sSFR, etc., to analyse the correlation. 42.

(62) 4.2.1 LSS by Spherical Density on Properties of Galaxies First, in this section, to study the Spherical Density effect on properties of galaxies, we separate four different Spherical Density regions, Extremely High Density (red), High Density (blue), Low Density (gray), Extremely Low Density (green), that detail see § 3.1.. We expect to find the galaxies of Extremely High Density would be more redder than Extremely Low Density. Expectation of SFR, which the latter will be significantly higher than the former. And we expect to find a high mass in the Extremely High Density. To clearly compare the correlation of different density regions, where K-S test of all diagrams, are compare Extremely High Density and Extremely Low Density. That is, KS test of compare the green and red curve, and taking the p-value of K-S test, which to explain the level of similarity.. Figure 4.19 and 4.20, are the correlation of Spherical Density and color. Red, Blue, Gray, and Green solid lines those are correspond to Extremely High Density (red), High Density (blue), Low Density (gray), Extremely Low Density (green), respectively. We can see the red line shift to right side, green line close to left side. close to right side means trend to red color. We also calculate and present this property’s p-value which is from K-S test of Extremely High Density galaxies versus Extremely Low Density galaxies. It means the High Spherical Density galaxies are redder then the low Spherical Density galaxies, the KS-test shows they are unlikely (p < 0.0001).. In Figure 4.21 and 4.22, shows the correlation of Spherical Density and Stellar mass, & correlation of Spherical Density and dynamical mass. We also calculate and present this property’s p-value which is from K-S test of Extremely High Density galaxies versus Extremely Low Density galaxies. We found the red line trend to right side, green line close to left side. the K-S test of stellar mass (p < 0.01) shows that are from different host population. Its means that have a significantly correlation of Spherical Density and stellar mass, but not dynamical mass 43.

(63) (0.05 < p < 0.07). Figure 4.23 are correlation of Spherical Density and Dark matter, there are no correlation (p > 0.15).. Finally, Figure 4.24, Figure 4.25, and Figure 4.26, Figure 4.27, shows that the Spherical Density effect on EW[Hα ], [Hβ ], EW[OII], and sSFR. We all found strong emission and SFR in Extremely Low Density, that p-value of K-S test all less than 0.001 (p < 0.001).. 44.

(64) 1.2. Cumulative Frequency. 1.0. Quantitative definition of LSS by "Spherical density" Extremely High Density High Density Low Density Extremely Low Density. 0.8 0.6. KS-test(p)= 0.0. 0.4 0.2 0.0 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. g−r (Absolute magnitude). 0.8. 0.9. 1.0. Figure 4.19: The figure shows the cumulative distribution of g − r color of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 45.

(65) 1.2. Cumulative Frequency. 1.0. Quantitative definition of LSS by "Spherical density" Extremely High Density High Density Low Density Extremely Low Density. 0.8 0.6. KS-test(p)= 0.0. 0.4 0.2 0.0 1.0. 1.5. 2.0. 2.5. u−r (Absolute magnitude). 3.0. 3.5. Figure 4.20: The figure shows the cumulative distribution of u − r color of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 46.

(66) 1.2. Cumulative Frequency. 1.0. Quantitative definition of LSS by "Spherical density" Extremely High Density High Density Low Density Extremely Low Density. 0.8 KS-test(p)= 0.6 0.0064 0.4 0.2 0.0 8 10. 109. 1010 Stellar mass [M ∗]. 1011. 1012. Figure 4.21: The figure shows the cumulative distribution of stellar mass of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 47.

(67) 1.2. Cumulative Frequency. 1.0. Quantitative definition of LSS by "Spherical density" Extremely High Density High Density Low Density Extremely Low Density. 0.8 0.6. KS-test(p)= 0.0691. 0.4 0.2 0.0 13 10. 1014. 1015 1016 Dynamical massMdyn,r,P [M ∗]. 1017. 1018. Figure 4.22: The figure shows the cumulative distribution of Dynamical mass of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 48.

(68) 1.2. Cumulative Frequency. 1.0. Quantitative definition of LSS by "Spherical density" Extremely High Density High Density Low Density Extremely Low Density. 0.8 0.6. KS-test(p)= 0.1785. 0.4 0.2 0.0 4 10. 105 Mdyn,r,P/M ∗. 106. Figure 4.23: The figure shows the cumulative distribution of Dynamical mass/Stellar mass of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 49.

(69) 1.2. Cumulative Frequency. 1.0. Quantitative definition of LSS by "Spherical density" Extremely High Density High Density Low Density Extremely Low Density. 0.8 KS-test(p)= 0.0002. 0.6 0.4 0.2 0.00. 101 EW[OII]3729 [ ]. 102. Figure 4.24: The figure shows the cumulative distribution of [OII] equivalent width of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 50.

(70) 1.2. Quantitative definition of LSS by "Spherical density". Cumulative Frequency. 1.0 0.8 KS-test(p)= 0.0007. 0.6 0.4. Extremely High Density High Density Low Density Extremely Low Density. 0.2 0.0. 101. EW[Hα] [ ]. 102. 103. Figure 4.25: The figure shows the cumulative distribution of Halpha equivalent width of galaxies for different Spherical Density regions. Extremely High Density, High Density, Low Density, and Extremely Low Density type galaxies, are Red, Blue, Gray, and Green solid lines, respectively. We also calculate and present this property’s p-value, which is from K-S test of two Extremely type galaxies.. 51.