Determining the velocity of celestial objects like pulsars and quasars is a crucial aspect of astrophysical research. This comprehensive guide will delve into the techniques and formulas used by astronomers to measure the velocity of these fascinating cosmic phenomena.
Understanding Redshift
The key to finding the velocity of pulsars and quasars lies in the concept of redshift. Redshift is the shift in the wavelength of light due to the expansion of the universe. This shift can be quantified using the formula:
z = (λobs - λrest) / λrest
where z is the redshift, λobs is the observed wavelength, and λrest is the rest wavelength of a particular spectral line.
Once the redshift is known, the velocity v of the object can be calculated using the formula:
v = cz
where c is the speed of light.
Measuring Velocity in Quasars
Quasars, which are extremely luminous active galactic nuclei, can have their velocity determined by analyzing their emission line spectra. Here’s a step-by-step process:
- Identify Emission Lines: In a lab exercise, students are asked to identify five emission lines (such as Balmer or O III) in the quasar’s spectrum and record their rest and observed wavelengths.
- Calculate Redshift: For each emission line, the redshift is calculated using the formula
z = (λobs - λrest) / λrest. - Find Average Redshift: The average redshift value is then determined from the individual redshift calculations.
- Calculate Velocity: The velocity of the quasar is then calculated using the formula
v = cz, wherezis the average redshift value.
For example, if a quasar has an observed wavelength of 600 nm for the Hβ emission line, and the rest wavelength of Hβ is 486 nm, the redshift and velocity can be calculated as follows:
z = (600 nm - 486 nm) / 486 nm = 0.2344
v = c × z = 3 × 10^8 m/s × 0.2344 = 70,320 km/s
Measuring Velocity in Pulsars
Pulsars, which are rapidly rotating neutron stars, do not typically have emission lines like quasars. Instead, astronomers use the pulsar’s timing data to measure its velocity and other properties.
- Measure Pulse Arrival Times: Pulsars emit regular pulses of radiation, and by measuring the arrival times of these pulses, astronomers can determine the pulsar’s velocity and other properties.
- Analyze Orbital Decay: In the case of binary pulsars, such as the famous 1913+16 system, astronomers have measured the orbital decay caused by gravitational radiation from the system. By comparing the observed orbital decay with the predictions of general relativity, they have been able to measure the masses of the two objects and their orbital parameters with high precision.
This has allowed astronomers to test the predictions of general relativity and gain valuable insights into the properties of neutron stars.
Additional Considerations
- Figures and Data Points: The figure at right in the “Imaging the Universe: Part 2: Measuring Redshifted Wavelengths” resource illustrates the deceleration of the universe, while the lab exercise provides data points for the observed wavelengths of various emission lines in a quasar’s spectrum.
- Values and Measurements: The velocity of quasars and pulsars can be expressed in km/s, and the redshift can be expressed as a decimal value. The wavelengths of the emission lines can be measured in nanometers (nm) or angstroms (Å).
Conclusion
Determining the velocity of pulsars and quasars is a crucial aspect of astrophysical research, and it relies on the concept of redshift. By measuring the shift in the wavelength of light due to the expansion of the universe, astronomers can calculate the velocity of these celestial objects using well-established formulas and techniques. This guide has provided a comprehensive overview of the methods used to find the velocity in pulsars and quasars, including specific examples and numerical problems to help you better understand the process.
References
- Imaging the Universe: Part 2: Measuring Redshifted Wavelengths
- The Steady State Theory – Explaining Science
- BASIC PHYSICS AND COSMOLOGY FROM PULSAR TIMING DATA
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