Measuring cosmological parameters using Type Ia Supernovae

IDC 452: Seminar Delivery Course

Prajakta Mane

MS19054

  • A supernova is a transient astronomical event that occurs during the last evolutionary stages of a massive star or when a white dwarf is triggered into runaway nuclear fusion.
  • Is classified according to the light curves and the absorption lines of different chemical elements that appear in the spectra.
  • Type Ia supernovae occur in binary systems in which one of the stars is a white dwarf.
  • Have the light curves with a sharp maximum and gradual decline, producing a fairly consistent peak luminosity because of the fixed critical mass at which a white dwarf will explode.

Supernova Type Ia

Why study Type Ia Supernovae?

Cosmological parameters governing the evolution of the universe:

H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3} \rho - \frac{\kappa}{a^2}

∵ First Friedmann Equation

Taylor expanding a(t):

\frac{1}{a(t)} \approx 1 - H_0 (t-t_0) + \left(\frac{1+q_0}{2}\right) H_0^2 (t-t_0)^2

∵ Independent of cosmological

    models

\text{where } q_0 = - \left( \frac{\ddot{a}}{a H^2}\right) = \frac{1}{2} \sum_{i}^{} \Omega_{i, 0} (1+3\omega_i)

∵ The Deceleration parameter

Parameters to be found observationally:

H(t), q_0, \rho_i, \omega_i
P = \omega \rho
\dot{\rho} + 3 \frac{\dot{a}}{a} (\rho + P)

∵ Fluid Equation

  • Standard Candles: Type Ia supernovae are the most useful, precise, and mature tools for determining astronomical distances and can provide constraints on value of the Hubble's constant.
D_L = \left(\frac{L}{4 \pi f}\right)^{\frac{1}{2}} \approx \frac{c}{H_0} z \left(1 + \frac{1-q_0}{2}z\right)

The luminosity distance DL is defined as,

L: Standardized luminosity
f: Flux of the standard candle measured on earth

z: Redshift of the standard candle, found from (1+z) = 1/a(t) relation

Collaborations like High-z supernova Search Team, PI: Perlmutter;

Supernova Cosmology Project, PI: Schmidt and Riess

H0 measurement from low-z supernovae,

q0 measurement from high-z supernovae

  • Dark Energy: Discovery and constraints

Riess et al, 1999

Permutter et al, 1999

  • Independent Method to Constrain the value of the Hubble's Constant: The time-delay measurements of the lensed, multiply imaged supernovae.
\Delta t = \frac{D_d D_s}{cD_{ds}}(1+z)\Delta\tau
\frac{D_d D_s}{D_{ds}} \alpha \frac{1}{H_0}

Collaborations like H0LiCoW, COSMOGRAIL, TDCOSMO

References:

1. Perlmutter, S. and Schmidt B., “Measuring Cosmology with Supernovae.” Lecture Notes in Physics 598 (2003): 195-217.

2. Barbara Ryden, "Introduction to Cosmology" (2003): Chapter 7.

3. Riess, A., et al, "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant" (1998), Astrophys. J.

4. Perlmutter, S., et al., "Measurements of Ω and Λ from 42 High-Redshift Supernovae", (1999), Astrophys. J.

5. Refsdal S., "On the Possibility of Determining Hubble's Parameter and the Masses of Galaxies from the Gravitational Lens Effect" (1964), MNRAS.

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