Astronomy | Astrophysics Answers

The GBT has sensitive receivers covering the frequency ranges 18 to 26.5 GHz and 26 to 40 GHz. Show how this frequency coverage is sufficient to detect CO emission from galaxies at any redshift from z = 1.9 to at least z = 10, the estimated redshift at which stars first produced significant amounts of interstellar CO.

What is the minimum gas temperature of a molecular cloud that produces strong CO J = 5 − 4 line
emission?

For a 2ms pulsar where we can measure pulse times-of-arrival (TOAs) to a fractional precision of 10−3 of the pulsar period, estimate the frequency precision we can achieve over a 10-year span of data using pulsar timing.

Pulsar astronomers parameterize pulsar spin-down in a model-independent way with the
relation O = On, where n is known as the braking index. Derive a functional form for n in terms of the three observables. What value is n for magnetic dipole radiation?

The Crab pulsar has a very steep radio spectral index of approximately -3 (i.e. v−3) over a frequency range from 10MHz to 10GHz. If the distance to the Crab pulsar is about 2 kpc, the measured flux density at 400MHz is 650mJy, and the spin-down luminosity (i.e. ˙E ) as derived in class is 4×1038 erg s−1, what fraction of ˙E does the radio emission account for?

Measurements of many extragalactic sources have shown that they typically have brightness temperatures of TB = 1011 K and S = 1 Jy. Approximately what size telescope is needed to resolve these sources? How does that compare with the VLBA?

Derive an expression showing how the of an ultra-relativistic electron emitting synchrotron radiation evolves in time. Assume that 0 is the initial value of and that there is a uniform magnetic field of strength B (and so B _ = B sin a). Your expression should involve only the above variables, time t, and physical constants.

The synchrotron power P radiated by an ultrarelativistic (1) electron is extracted from its kinetic energy E mec2. The synchrotron lifetime of such an electron is:

Estimate the synchrotron lifetime of electrons responsible for the 1 GHz radiation from our Galaxy. You may make the approximation that Galactic synchrotron radiation at frequency v = 1 GHz is produced primarily by electrons whose critical frequency in the B = 5 × 10−6 G magnetic field of our Galaxy is vc = 1 GHz.

For an electron moving at a non-relativistic speed v in a region of uniform magnetic field strength B, derive the formula for the total emitted power due to gyro radiation. If the magnetic field is in the plane of the sky, how would the gyro radiation be polarized as measured here on Earth? What if the magnetic field lines pointed towards or away from the observer?

Since the optical depth for free-free absorption is proportional to v−2.1 while T is independent
of frequency, there must be some frequency above which Thomson scattering in the ISM reduces the observed flux density of an extragalactic point source more than free-free absorption does. Estimate that frequency.