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Modelling quasar absorption line spectra

The CASt dataset


Astronomical background

Quasars, the most luminous continuously emitting objects in the Universe, arise from the accretion (infall) of gas onto supermassive black holes in the center of galaxies.  Quasars were much more active when the Universe was young so (due to the expansion of the Universe) most appear at high redshifts.  In addition to studies of black hole phenomenology, quasar spectra are uniquely useful for studies of intergalactic matter that happen to lie between a quasar and the observer on Earth.  Quasars show several types of absorption lines reflecting different structures in intergalactic space.  These include the "Lyman-alpha forest" from small clouds that do not appear to lie in galaxies, "damped Lyman-alpha" lines from dense clouds likely present in the disks of intervening galaxies, and "strong and weak Mg II absorption" systems likely arising in the halos of intervening galaxies.

Weak Mg II absorption systems give an opportunity to study the evolution of metals (which astronomers view as all elements heavier than helium and the interstellar media of galaxies over a wide span of ages.  Often, several intervening absorbers are seen at widely separated redshifts, and for each absorber one or several clouds separated by small Doppler shifts can be seen.  Absorption from different line of different elements permit detailed study of the elemental abundances and ionization phases of the absorbing gas. 


We give here two small portions of the spectrum of a bright quasar described in the following study:

    Jane C. Charlton, Jie Ding, Stephanie G. Zonak, Christopher W. Churchill, Nicholas A. Bond, and Jane R. Rigby

We give regions around the 3-times-ionized silicon line Si IV 1394 and the 3-times-ionized carbon line C IV 1551 for the z=0.653411 absorption system, which are two of the right-hand panels shown below.  The datasets have two columns: velocity in kilometers per second with respect to the absorber rest frame; and normalized intensity of the quasar light.  Accompanying each spectrum is a best-fit model constructed with a complex astrophysical model of the underlying quasar spectrum, cloud velocities and ionizations, fitted to all of the lines shown below simultaneously. This fit is made using the CLOUDY code developed by G. Ferland.  The model and data are not provided at exactly the same velocities, so interpolation may be needed. 

Statistically, it can be viewed as a least-squares fit of a normal mixture model to each spectrum, with constraints provided by the other line spectra.  The plotted model has three clouds centered at (0,24,54) km/s with widths of (13,9,14) km/s. 

Quasar absorption line spectra

Statistical exercises

  • Perform a normal mixture model for the two spectra, independently and jointly, and recover the published results.  Establish the confidence that 3 (and not 2 or 4) clouds are present, and confidence intervals for the cloud central velocities, widths, and amplitudes.
  • Measure the noise level in spectral regions away from the absorption system and evaluate its impact on the results above.  Note that the noise may not be Gaussian due to the presence of other, unidentified absorption lines.
Thanks to Anand Narayanan and Jane Charlton (Penn State) for providing this dataset

NSFDepartment of StatisticsEberly College of ScienceDepartment of Astronomy and Astrophysics