This document discusses using Python to explore the mysteries of the universe. It introduces cosmological and astrophysical concepts like the cosmic star formation rate and supermassive black holes. It presents the PyCosmicStar code for modeling the cosmic star formation rate using different dark matter halo mass functions. Wavelet coherence analysis is also demonstrated for studying connections between signals like the sun and Earth.

1. Do Cosmos a Terra: Usando Python para
desvendar os mist´erios do Universo.
Dr. Eduardo S. Pereira1
1Instituto Nacional de Pesquisas Espaciais
Divis˜ao de Astrof´ısica
Dispon´ıvel em: http://pt.slideshare.net/duducosmos
09/Novembro/2015

2. Sum´ario
1 Introduc¸ ˜ao
2 Cosmos, ou A Evoluc¸ ˜ao do Universo.
3 Um pouco mais de Cosmologia e Astrof´ısica
4 PyCosmicStar
5 A Taxa C´osmica de Formac¸ ˜ao Estelar e Os Buracos Negros
Supermassivos
6 Sol e Terra
7 Fim –*.*–
8 Referˆencias Bibliogr´aficas

3. Introduc¸ ˜ao
O Framework de Trabalho.

4. Introduc¸ ˜ao
O Framework de Trabalho.

5. Introduc¸ ˜ao
O Framework de Trabalho.
Rµν −
1
2
Rgµν +Λµν =
8πG
c4
Tµν (1)

6. Introduc¸ ˜ao
O Framework de Trabalho.

7. Cosmos, ou A Evoluc¸ ˜ao do Universo.
O Modelo Cosmol´ogico Padr˜ao

8. Cosmos, ou A Evoluc¸ ˜ao do Universo.
O Modelo Cosmol´ogico Padr˜ao

9. Cosmos, ou A Evoluc¸ ˜ao do Universo.
Regi˜oes de Formac¸ ˜ao Estelar

10. Cosmos, ou A Evoluc¸ ˜ao do Universo.
Redshift

11. Cosmos, ou A Evoluc¸ ˜ao do Universo.
Redshift

12. Um pouco mais de Cosmologia e Astrof´ısica
O Formalismo Tipo Press-Schechter

13. Um pouco mais de Cosmologia e Astrof´ısica
O Modelo de Formac¸ ˜ao Estelar
Halos de mat´eria escura s˜ao poc¸os de potencial gravitacional;
Se o halo tiver massa maior que um certo limiar a formac¸ ˜ao
estelar ir´a ocorrer;
Os primeiros halos capazes de formar estrelas seriam formados
em z ∼ 20 com massa da ordem de 106M
[Salvadori, Schneider e Ferrara 2007]

14. Um pouco mais de Cosmologia e Astrof´ısica
O Modelo de Formac¸ ˜ao Estelar
Halos de mat´eria escura s˜ao poc¸os de potencial gravitacional;
Se o halo tiver massa maior que um certo limiar a formac¸ ˜ao
estelar ir´a ocorrer;
Os primeiros halos capazes de formar estrelas seriam formados
em z ∼ 20 com massa da ordem de 106M
[Salvadori, Schneider e Ferrara 2007]

15. Um pouco mais de Cosmologia e Astrof´ısica
O Modelo de Formac¸ ˜ao Estelar
Halos de mat´eria escura s˜ao poc¸os de potencial gravitacional;
Se o halo tiver massa maior que um certo limiar a formac¸ ˜ao
estelar ir´a ocorrer;
Os primeiros halos capazes de formar estrelas seriam formados
em z ∼ 20 com massa da ordem de 106M
[Salvadori, Schneider e Ferrara 2007]

16. PyCosmicStar
O c´odigo

17. PyCosmicStar
O c´odigo

18. PyCosmicStar
O c´odigo
from pycosmicstar.lcdmcosmology import lcdmcosmology
import matplotlib.pyplot as plt
# I n s t a n c i n g a LCDM Object .
lcdmUniverser = lcdmcosmology(omegam=0.24,omegab=0.04,
omegal=0.73,h=0.7)
z = arange(0, 10.5, 0.1)
# The age of the Universe as a f u n c t i o n of the r e d s h i f t
plt.plot(z, [lcdmUniverser.age(zi) for zi in z])
plt.xlabel(r"$z$ - Redshift")
plt.ylabel(r"$t$ (yr)")
plt.show()

19. PyCosmicStar
O c´odigo

20. PyCosmicStar
O c´odigo
from pycosmicstar.cosmicstarformation import cosmicstarformation
from pycosmicstar.lcdmcosmology import lcdmcosmology
from pycosmicstar.observationalCSFR import ObservationalCSFR
import matplotlib.pyplot as plt
from numpy import arange , array
z = arange(0, 20, 0.1)
#Cosmic Star Formation Rate using
# Tinker e t al . dark haloes mass f u n c t i o n
myCSFR_TK = cosmicstarformation(cosmology=lcdmcosmology ,
massFunctionType="TK",
delta_halo =200)

21. PyCosmicStar
O c´odigo
#Cosmic Star Formation Rate using
# Press and Schechter dark haloes mass f u n c t i o n
myCSFR_PS = cosmicstarformation(cosmology=lcdmcosmology ,
massFunctionType="PS")
#Cosmic Star Formation Rate using
# Seth e t al . dark haloes mass f u n c t i o n
myCSFR_ST = cosmicstarformation(cosmology=lcdmcosmology)

22. PyCosmicStar
O c´odigo
csfrTK = array([myCSFR_TK.cosmicStarFormationRate(zi) for zi in z])
csfrPS = array([myCSFR_PS.cosmicStarFormationRate(zi) for zi in z])
csfrST = array([myCSFR_ST.cosmicStarFormationRate(zi) for zi in z])

23. PyCosmicStar
O c´odigo
obsCSFR = ObservationalCSFR()
x, y = obsCSFR.csfredshift()
xerr , yerr = obsCSFR.errorData()
plt.errorbar(x, y, yerr=yerr , xerr=xerr , fmt=’.’)
plt.plot(z, csfrTK , label="TK")
plt.plot(z, csfrST , label="ST")
plt.plot(z, csfrPS , label="PS")
plt.legend(loc=4)
plt.yscale(’log’)
plt.ylabel(r’$dot{rho}_{*}$( M$_{odot}$Mpc$ˆ{-3}$yr$ˆ{-1}$)’)
plt.xlabel(r’$z$’)
plt.show()

24. PyCosmicStar
O c´odigo

25. PyCosmicStar
O c´odigo
http://duducosmos.github.io/pycosmicstar/index.html

26. PyCosmicStar
Nas nuvens
www.cosmicstarformation.com

27. A Taxa C´osmica de Formac¸ ˜ao Estelar e Os Buracos Negros Supermassivos
Buracos Negros Supermassivos

28. A Taxa C´osmica de Formac¸ ˜ao Estelar e Os Buracos Negros Supermassivos
Buracos Negros Supermassivos na Nossa Gal´axia

29. A Taxa C´osmica de Formac¸ ˜ao Estelar e Os Buracos Negros Supermassivos
O Modelo ´e Concordante com as Observac¸ ˜oes

30. Sol e Terra
Coerencia Wavelet
http://duducosmos.github.io/PIWavelet/

31. Sol e Terra
Coerencia Wavelet
import numpy as np
from piwavelet import piwavelet
# Generation of the Random Signal 1
y1 = np.random.rand(100)
# Generation of the Random Signal 2
y2 = np.random.rand(100)
# Time s t e p
x = np.arange(0,100,1)
# Normalization of the Signal 1
y1 = (y1-y1.mean())/y1.std()
# Normalization of the Signal 2
y2 = (y2-y2.mean())/y2.std()
# Wavelet Coherence A n a l y s i s
myCoherence = piwavelet.wcoherence(y1,y2)

32. Sol e Terra
Coerencia Wavelet
# Plot of the Coherence Map
myCoherence.plot(t = x, title=’Test’,units=’sec’)
# I f you want to know the i n d i v i d u a l p r o p e r t i e s .
Rsq ,period ,scale ,coi ,sig95=myCoherence()

33. Sol e Terra
Coerencia Wavelet
http://duducosmos.github.io/PIWavelet/

34. Sol e Terra
Coerencia Wavelet

35. Sol e Terra
Coerencia Wavelet

36. Fim –*.*–
Obrigado
Star Formation Dreams- ´Oleo sobre
tela. Em andamento.
http:
//pereirasomozartgallery.
edupereira.webfactional.com/
https://www.facebook.com/
pereirasomozagallery/

37. Referˆencias Bibliogr´aficas
COPI, C. J. A stochastic approach to chemical evolution. Apj,
v. 487, p. 704, out. 1997.
DAIGNE, F. et al. Hierarchical growth and satr formation:
Enrichment, outflows and supernova rates. Apj, v. 647, p. 773–786,
ago. 2006.
HOPKINS, A. M. On the evolution of star-forming galaxies. APJ,
American Physical Society, v. 615, p. 209–221, nov. 2004.
HOPKINS, P. F.; RICHARDS, G. T.; HERNQUIST, L. An
observational determination of the bolometric quasar luminosity
function. Apj, v. 654, p. 731–753, jan. 2007.
JENKINS, A. et al. The mass function of dark matter haloes. Mon.
Not. R. Astron. Soc., v. 321, p. 372–384, 2001.

38. Referˆencias Bibliogr´aficas
PEREIRA, E. dos S.; MIRANDA, O. D. The role of the dark matter
haloes on the cosmic star formation rate. New Ast., v. 41, p. 48–52,
2015.
PEREIRA, E. S.; MIRANDA, O. D. Stochastic background of
gravitational waves generated by pre-galactic black holes. MNRAS,
v. 401, p. 1924–1932, jan. 2010.
PEREIRA, E. S.; MIRANDA, O. D. Supermassive black holes:
connecting the growth to the cosmic star formation rate. MNRAS
Letters, v. 418, p. L30–L34., 2011.
PRESS, W. H.; SCHECHTER, P. Formation of galaxies and
clusters of galaxies by self-similar gravitational condesation. Apj, p.
425–438, fev. 1974.
SALPETER, E. E. The luminousity function and stellar evolution.
Apj, v. 121, p. 161–167, 1955.

39. Referˆencias Bibliogr´aficas
SALVADORI, S.; SCHNEIDER, R.; FERRARA, A. Cosmic stellar
relics in the galactic halo. MNRAS, v. 381, p. 647–662, out. 2007.
SCALO, J. M. The stellar initial mass function. Fundamentals
Cosmic Phys., v. 11, p. 1–278, maio 1986.
SHETH, R. K.; MO, H. J.; TORMEN, G. Ellipsoidal collapse and an
improved model for the number and spatial distribuition of dark
matter haloes. Mon. Not. R. Astron, v. 323, p. 1–12, set. 2001.