Results of Physical Model

The physical model assumes that the b-parameter of each component can be described by a common turbulent term, \(b_{turb}\), and a thermal term, \(\sqrt{2 k_B T / m}\):

\[b_{eff}^2 = b_{turb}^2 + \frac{2 k_B T}{m} ,\]

where m is the atomic mass of the given ion. The model thus expands the regular set of parameters to include a temperature and turbulent velocity for each component, however, these extra parameters are simultaneously constrained by several transitions of different elements. For the exact implementation of this model, see the script physical_model.py in the scripts folder, or have a look at the predefined input file thermal_model.pars in the test_data folder.

Best fit parameters

Fitting the simulated test data with two components at redshifts z=0.003300 and z=0.003600, we recover the following parameters:

CrII : 2026, 2056, 2062, 2066
    z = 0.003299    b = 4.75 ± 0.01  log(N) = 12.581 ± 0.034
    z = 0.003599    b = 5.44 ± 0.01  log(N) = 12.167 ± 0.084

SiII : 1260, 1304, 1526, 1808
    z = 0.003299    b = 4.84 ± 0.01  log(N) = 14.461 ± 0.006
    z = 0.003599    b = 5.67 ± 0.01  log(N) = 13.955 ± 0.003

FeII : 1260, 1608, 1611, 2249, 2260, 2344, 2374, 2382
    z = 0.003299    b = 4.74 ± 0.01  log(N) = 14.065 ± 0.004
    z = 0.003599    b = 5.42 ± 0.01  log(N) = 13.589 ± 0.003

CII : 1036, 1334
    z = 0.003299    b = 5.11 ± 0.03  log(N) = 15.345 ± 0.016
    z = 0.003599    b = 6.28 ± 0.02  log(N) = 14.763 ± 0.006

OI : 1039, 1302, 1355
    z = 0.003299    b = 4.99 ± 0.02  log(N) = 15.709 ± 0.010
    z = 0.003599    b = 6.02 ± 0.02  log(N) = 15.173 ± 0.005

ZnII : 2026, 2062
    z = 0.003299    b = 4.72 ± 0.01  log(N) = 12.007 ± 0.030
    z = 0.003599    b = 5.38 ± 0.00  log(N) = 11.577 ± 0.082

SII : 1250, 1253, 1259
    z = 0.003299    b = 4.82 ± 0.01  log(N) = 14.176 ± 0.012
    z = 0.003599    b = 5.61 ± 0.01  log(N) = 13.701 ± 0.035

The best-fit is plotted and saved to PDF file: test_2comp.pdf.

Below you see a screenshot of some of the fitted lines:

_images/vfit_thermal_output.png

Total Abundances

The total abundances from the fit are:

logN(CrII) = 12.72 ± 0.03
logN(SiII) = 14.58 ± 0.01
logN(FeII) = 14.19 ± 0.01
logN(CII)  = 15.45 ± 0.01
logN(OI)   = 15.82 ± 0.01
logN(ZnII) = 12.15 ± 0.03
logN(SII)  = 14.30 ± 0.01

Notice that the column densities for the saturated lines OI and CII are overestimated. This is not surprising, as it is almost impossible to accurately constrain the column densities for such strong lines.

Physical Parameters

The input physical parameters and the recovered best-fit parameters are as follows:

Comp. No:

Temperature [K]

Turbulence [km/s]

Best-fit

Input

Best-fit

Input

0

3380 ± 268

4370

4.63 ± 0.02

4.60

1

9280 ± 206

8600

5.16 ± 0.0002

5.20

The Input Column Densities

The table below highlights the input column densities that were used to generate the synthetic data:

Ion

log(N1)

log(N2)

log(Ntot)

CrII

12.58

12.10

12.70

SiII

14.43

13.95

14.55

FeII

14.07

13.59

14.19

CII

15.20

14.72

15.32

OI

15.64

15.16

15.76

ZnII

12.02

11.54

12.14

SII

14.17

13.69

14.29