Supernovae Type Ia: Redshift, Luminosity & Speed

In summary: Mpc.Finally, to estimate the time interval measured by an observer near the star, we can use the time dilation formula:T_e=\frac{T_o}{\sqrt{1-\beta^2}}Where T_e is the time measured by the observer, T_o is the time measured by the star, and \beta is the velocity of the star.Substituting the given information, we get:T_e=\frac{60}{\sqrt{1-0.8333^2}}T_e=137.59 daysIn summary, based on the given information, we can estimate that the star is moving away from us at a velocity of 0.833
  • #1
dingo_d
211
0

Homework Statement


Supernovae type Ia has a red shift z=1.1. Observed luminosity of the star has changed in the interval of 60 days. What time interval would an observer measure in the near vicinity of the star? What is the speed that the star is moving away from us? What is the distance of the star from us ([itex]h\approx 0.7[/itex])

Homework Equations



Red shift:

[itex]z=\sqrt{\frac{1+\beta}{1-\beta}}-1[/itex]

[itex]\nu_o=\sqrt{\frac{1-\beta}{1+\beta}}\nu_e[/itex]

o is for observed, and e is for emitted light.

Hubble law:

[itex]v=H_0 d\approx 100 h d[/itex]

The Attempt at a Solution



Using the provided formulas I got:

[itex]\beta=0.630314[/itex]
[itex]d=2692.34 Mpc[/itex]
[itex]T_e=28.5715 days[/itex]

Is this correct?
 
Physics news on Phys.org
  • #2


I would like to first clarify a few things before providing a solution. The given information in the forum post is not sufficient to accurately determine the time interval, speed, and distance of the star. I will explain why below.

Firstly, the forum post mentions a red shift of z=1.1 for a supernova type Ia. This red shift value corresponds to a very high recession velocity of the star, which is not typical for a type Ia supernova. In general, type Ia supernovae have red shift values ranging from 0.01 to 0.1. Therefore, it is important to verify the accuracy of the given red shift value.

Secondly, the observed luminosity of the star changing in an interval of 60 days does not provide enough information to determine the time interval that an observer would measure near the star. This is because the observer's measurement of time would also be affected by the star's motion and the distance between the star and the observer. Without knowing the distance and velocity of the star, we cannot accurately determine the time interval measured by an observer.

Lastly, the formula provided for Hubble's law is not the correct one. The correct formula is v=H_0d, without the approximation of 100h. This approximation is used for small distances, but for a red shift of z=1.1, the distance is large enough that it cannot be approximated in this way.

With that being said, I will provide a general solution based on the given information, but please keep in mind that it may not be accurate due to the limitations mentioned above.

Assuming the given red shift value of z=1.1 is correct, we can use the first formula provided to calculate the velocity of the star:

z=\sqrt{\frac{1+\beta}{1-\beta}}-1

1.1=\sqrt{\frac{1+\beta}{1-\beta}}-1

Solving for \beta, we get \beta=0.8333. This means that the star is moving away from us at a velocity of 0.8333 times the speed of light.

Now, to calculate the distance of the star, we can use the second formula provided:

v=H_0 d\approx 100 h d

0.8333c=100hd

d=\frac{0.8333c}{100h}

Substituting h=
 

1. What is a supernova Type Ia?

A supernova Type Ia is a type of supernova explosion that occurs in a binary star system where one of the stars is a white dwarf. The white dwarf accretes matter from its companion star until it reaches a critical mass, triggering a runaway nuclear fusion reaction that results in a massive explosion.

2. How are supernova Type Ia used to measure distance?

Supernova Type Ia explosions have a well-understood and consistent peak luminosity, making them useful as "standard candles" for measuring distances in the universe. By comparing the observed brightness of a Type Ia supernova to its known peak luminosity, astronomers can calculate its distance from Earth.

3. What is the significance of the redshift of a supernova Type Ia?

The redshift of a supernova Type Ia is a measure of how much the light from the supernova has been stretched to longer, redder wavelengths due to the expansion of the universe. By measuring the redshift, scientists can determine the distance of the supernova and use it as a standard candle to study the expansion rate of the universe.

4. How do scientists use supernova Type Ia to study the acceleration of the universe?

Supernova Type Ia are important tools for studying the acceleration of the universe, as their peak luminosity can also be used to determine their distance. By observing a large number of supernova Type Ia at different distances and measuring their redshift, scientists can map out the expansion rate of the universe over time and determine whether it is accelerating or decelerating.

5. How fast do supernova Type Ia travel?

Supernova Type Ia have been observed to have speeds ranging from 10,000 to 30,000 kilometers per second, or approximately 6,200 to 18,600 miles per second. This is much faster than the speed of light, but it is important to note that this is due to the expansion of space and not actual movement through space.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Astronomy and Astrophysics
Replies
2
Views
2K
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
938
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Astronomy and Astrophysics
Replies
5
Views
2K
  • Astronomy and Astrophysics
Replies
5
Views
3K
Replies
16
Views
3K
Back
Top