How Does Relativistic Motion Affect Star Brightness?

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SUMMARY

The apparent brightness of a receding star compared to a stationary star is influenced by relativistic effects, specifically time dilation and Doppler shift. Time dilation reduces the power output of the receding star, making it appear fainter, while the Doppler effect causes the light to be redshifted, further diminishing its brightness. The combined effect can be expressed using the formula B' = B / (1 + v/c)(z + 1), where B' is the transformed brightness, v is the velocity of the star, and z is the redshift. This analysis assumes negligible gravitational effects and focuses solely on special relativity.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and Lorentz transformations.
  • Familiarity with the Doppler effect and its application to light.
  • Knowledge of electromagnetic wave properties and intensity calculations.
  • Ability to manipulate equations involving gamma factors and redshift calculations.
NEXT STEPS
  • Research the derivation of the relativistic Doppler effect and its implications for light from moving sources.
  • Study the relationship between brightness and redshift in cosmological contexts, particularly using Peebles' surface brightness theorem.
  • Explore the mathematical foundations of Lorentz transformations and their applications in astrophysics.
  • Investigate the effects of gravitational lensing on the apparent brightness of distant stars.
USEFUL FOR

Astronomers, astrophysicists, and students of physics interested in the effects of relativistic motion on light and brightness measurements in cosmology.

  • #31
Antenna Guy said:
...

IMO, if we were to construct a spherical surface of radius ct within the ineterial frame of the moving star, the power density integrated over that surface should equal the power radiated by the star at t=0. This integrated power should hold for the same surface transformed into any other inertial reference frame.

Regards,

Bill

The attenuation of power radiated per unit area of the star only occurs at the rear of the star as seen by an observer who sees the star as receding from him. This is compensated by the amplification of the power radiated per unit area at the front of the star, as seen by an observer that sees the star as aproaching him. However, the total power radiated per unit time by the star is attenuated by time dilation and the stars burns for longer according to obserers that see the star moving relative to them. The focusing and concentrating of power at the front is seen in blazars that eject double jets of luminous material at relativistic velocities with one jet coming towards us. The time dilation effect is seen in 1a type supernovae. They typically shine brightly for one week, but at high recession velocities they shine brightly for two weeks or more.

After working out the power radiated per unit time by the star by allowing for time dilation, the radiated energy is simply redistributed and more concentrated at the front and more diluted at the rear by relativistic aberration but the total radiated power per unit time remains the same.
 
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  • #32
Bill,
regarding your last post, I can only say that Peebles is working in the most general background, where gravity can cause lensing, in which case \Omega and A are independent. In the purely SR background they can probably be elided into one differential.

Unfortunately I haven't had time to study this thread very closely - just dropping in and out.

M
 
  • #33
Mentz114 said:
Bill,
regarding your last post, I can only say that Peebles is working in the most general background, where gravity can cause lensing, in which case \Omega and A are independent. In the purely SR background they can probably be elided into one differential.

Unfortunately I haven't had time to study this thread very closely - just dropping in and out.

M

If you find the time to think about it: If \Omega and A are separable, what two independent surfaces might they relate to?

Regards,

Bill

P.S. I'll be off-line for ~ a week, so there's no rush... :smile:
 

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