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Second Order systems II01:18

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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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The Progenitor Systems of Classical Novae in M31.

C S Abelson1, Carles Badenes1, Laura Chomiuk2

  • 1Department of Physics and Astronomy and Pittsburgh Particle Physics, Astrophysics and Cosmology Center (PITT PACC), University of Pittsburgh, 3941 O'Hara Street, Pittsburgh, PA 15260, USA.

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We characterized the link between novae and their stellar progenitors in M31 using a delay time distribution. Our findings reveal two distinct progenitor populations, suggesting consistent or earlier nova production efficiency.

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Area of Science:

  • * Astrophysics
  • * Stellar Evolution
  • * Galactic Astronomy

Background:

  • * Novae are stellar explosions resulting from mass transfer in binary systems.
  • * Understanding nova progenitor populations is crucial for galactic chemical evolution models.
  • * Previous studies lacked detailed statistical relationships between nova occurrences and progenitor ages.

Purpose of the Study:

  • * To statistically characterize the relationship between novae in M31 and their progenitor stellar populations.
  • * To construct a delay time distribution for nova progenitors.
  • * To infer the nova production efficiency over cosmic time.

Main Methods:

  • * Utilized deep Hubble Space Telescope photometry from the Panchromatic Hubble Andromeda Treasury (PHAT) survey to derive spatially resolved stellar age distributions in M31.
  • * Employed a large catalog of novae in M31.
  • * Calculated the delay time distribution by comparing nova occurrences with stellar population ages.

Main Results:

  • * Identified two statistically significant nova progenitor populations.
  • * Population 1: Ages between 2 and 3.2 Gyr with a rate of (3.7 +/- 2.1) x 10^-9 events M_sun^-1.
  • * Population 2: Ages between 7.9 Gyr and the age of the Universe with a rate of (4.8 +/- 0.2) x 10^-9 events M_sun^-1.

Conclusions:

  • * The derived delay time distribution is consistent with a constant nova production efficiency over time.
  • * Alternatively, results suggest a higher nova production efficiency at earlier cosmic times.
  • * These findings provide critical constraints for models of stellar evolution and galactic nucleosynthesis.