# Spectral Properties

The spectral properties of a source observed by ACIS include a set of hardness ratios determined from the aperture source photon fluxes in the source region, as well as flux determination by power law, blackbody, and thermal bremsstrahlung model spectral fits to PI event data extracted from the source region.

## Hardness Ratios

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

$P_{H_{xy}}\left( H_{xy} \right) dH_{xy} = \int_{F_{xy}=0}^{\infty} P_{x}\left( \frac{\left( 1 + H_{xy} \right) F_{xy}}{2} \right) P_{y}\left( \frac{\left( 1 - H_{xy} \right) F_{xy}}{2} \right) \frac{F_{xy}}{2} \ dH_{xy} dF_{xy}$

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

$\mathit{hard\_ms} = \frac{F(m) - F(s)}{F(m) + F(s)}$

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

## Spectral Model Fits

The descriptions below apply to fields in both the Master Sources Table and Per-Observation Detections Table, unless noted otherwise. However, the properties of a master source observation represent the "best estimates" of the actual source properties derived from the set of individual source observations contributing to the master source observation. Spectral Fits for Off-Axis Sources

Spectral fit parameters may be unreliable for sources at large off-axis angles, where background levels can be high. A background-fitting approach will be considered for future releases of the catalog.

Master Sources Table:

The master source spectral fit will use the ACIS observations contained in the best block provided the total summed background-subtracted counts for all of the observations is at least 150 counts in the 0.5-7.0 keV energy range. If this is the case then joint fits are made using power law, blackbody, and bremsstrahlung models to the PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

Per-Observation Detections Table:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

### Power Law Model

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

• Power Law Model Photon Index
powlaw_gamma, powlaw_gamma_lolim, powlaw_gamma_hilim

The best-fit power law photon index and the associated two-sided 68% confidence limits, $$\gamma$$, defined as:

$F_{E} \propto E^{-\gamma}$
• Power Law Model Amplitude
powlaw_ampl, powlaw_ampl_lolim, powlaw_ampl_hilim

The best-fit amplitude of the power law model and associated two-sided 68% confidence limits in units of photons/s/cm2/keV defined at 1 keV.

• Power Law Model NH
powlaw_nh, powlaw_nh_lolim, powlaw_nh_hilim

The best-fit equivalent neutral hydrogen absorbing column, $$N_{H}$$, and the associated two-sided 68% confidence limits from an absorbed power law model spectral fit in units of 1020 cm-2.

• Power Law Model Spectral Fit Statistic
powlaw_stat

The power law model spectral fit statistic is defined as the value of the $$\chi^{2}$$ (data variance) statistic per degree of freedom for the best-fitting absorbed power law model.

• Power Law Model Spectral Fit Flux
flux_powlaw, flux_powlaw_lolim, flux_powlaw_hilim

The power law model flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fitting absorbed power law model, in units of erg/s/cm2.

### Blackbody Model

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

• Blackbody Spectral Fit Temperature
bb_kt, bb_kt_lolim, bb_kt_hilim

The best-fit blackbody model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

• Blackbody Spectral Fit Amplitude
bb_ampl, bb_ampl_lolim, bb_ampl_hilim

The best-fit blackbody model amplitude and the associated two-sided 68% confidence limits, proportional to the ratio of the blackbody emitting source radius, $$R$$, and the distance to the source, $$d$$. The amplitude is defined as:

$A = \frac{2\pi}{c^{2} h^{3}} \left(\frac{R}{d}\right)^{2} = 9.884 \times 10^{31} \left(\frac{R}{d}\right)^{2} \left[\mathrm{cm^{-2} keV^{-3} s^{-1}}\right]$
• Blackbody Spectral Fit NH
bb_nh, bb_nh_lolim, bb_nh_hilim

The best-fit total equivalent neutral hydrogen column density, $$N_{H}$$, and the associated two-sided 68% confidence limits from an absorbed blackbody model fit, in units of 1020 cm-2.

• Black Body Model Spectral Fit Statistic
bb_stat

The fit statistic defined as the value of the $$\chi^{2}$$ (data variance) statistic per degree of freedom for the best-fitting blackbody model.

• Blackbody Spectral Fit Flux
flux_bb, flux_bb_lolim, flux_bb_hilim

The blackbody flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed blackbody model, in units of erg/s/cm2.

### Bremsstrahlung Model

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

• Bremsstrahlung Spectral Fit Temperature
brems_kt, brems_kt_lolim, brems_kt_hilim

The best-fit bremsstrahlung model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

• Bremsstrahlung Spectral Fit Normalization
brems_norm, brems_norm_lolim, brems_norm_hilim

The best-fit bremsstrahlung model normalization and the associated two-sided 68% confidence limits. The model normalization is defined by:

$A = \frac{3.02 \times 10^{-15}}{4\pi D^{2}} \int n_{e} n_{i} dV$

where $$n_{e}$$ and $$n_{i}$$ are the electron and ion number densities, respectively, in cm-3 and $$D$$ is the distance to the source in cm.

• Bremsstrahlung Spectral Fit NH
brems_nh, brems_nh_lolim, brems_nh_hilim

The best-fit total equivalent neutral hydrogen column density, $$N_{H}$$, and the associated two-sided 68% confidence limits from an absorbed bremsstrahlung model fit, in units of 1020 cm-2.

• Bremsstrahlung Spectral Fit Statistic
brems_stat

The fit statistic defined as the value of the $$\chi^{2}$$ (data variance) statistic per degree of freedom for the best-fitting bremsstrahlung model.

• Bremsstrahlung Spectral Fit Flux
flux_brems, flux_brems_lolim, flux_brems_hilim

The bremsstrahlung flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed bremsstrahlung model, in units of erg/s/cm2.