Fitting trends in quasar emission and absorption line redshifts

The spectrum of a quasar consists of a few emission lines whose wavelengths are shifted by similar redshifts and numerous absorption lines whose wavelengths are shifted by different redshifts. Hence each quasar is characterised by an emission line redshift and the absorption lines redshifts are all less than the emission line redshift. The distribution of observed absorption line redshifts (zabs) with respect to emission line redshift (zem) for a large sample of quasars shows a systematic trend as pointed out by Kantharia (2016). They noticed that increase in zem is accompanied by a monotonic increase in the lowest detected value of zabs and inferred that the emission and absorption lines were all formed in the quasar.

This study focuses on modeling the systematic trend in the observed zem → zabs distribution. We considered the redshift data of absorption lines of singly ionized magnesium (denoted by MgII) and triply ionized carbon (denoted by CIV) for a large sample of quasars. We find that the envelope of data points defining the lowest value of the MgII absorption line redshift (which we denote by zM gIImodel) for a given zem satisfies zM gIImodel = (0.418±0.008)zem −(0.482±0.02) with an R2 value of 0.99. The model can be used to predict the lowest expected MgII absorption line redshift for any zem. We find a similar model for the lowest expected redshift of triply ionized carbon lines for any zem which is zCIV model = 0.845(±0.0002)zem − 0.153(±0.0006).

The main results of the paper can be summarised to be:

• When the redshifts by which absorption lines detected in a quasar spectrum are displaced zabs from their rest wavelengths are plotted against the quasar emission line redshift zem, then a systematic trend is noticed such that increase in zem is accompanied by an increase in the lowest detected zabs.

• We find the best fit model for the systematic trend seen in the zem → zM gII distribution is zM gIImodel = 0.418(±0.008)zem − 0.48(±0.02) with R2 = 0.99. Here zM gII refers to observed redshifts of singly ionized magnesium lines in absorption while zM gIImodel refers to the lowest zM gII for a zem. The observed MgII redshifts obey zM gIImodel < zM gII < zem.

• The best fit model for the systematic trend in the zem → zCIV distribution is zCIV model = 0.845(±0.0002)zem − 0.153(±0.0006) with R2 = 0.99. Here zCIV refers to the observed redshifts of triply ionized carbon in absorption while zCIV model refers to the lowest zCIV for a zem. The observed CIV redshifts obey zCIV model < zCIV < zem.

• Similar trends are shown by the redshifts of other absorption lines.

The main implications of these results are:

• The models enable us to estimate the lowest zM gIImodel and zCIV model for any zem.

• The observed increase in zM gIImodel and zCIV model with increasing zem means that the redshifts of the absorption lines and emission lines are not independent. It also implies that there is an upper bound on the difference redshift ∆z = (1+zem)/(1+zM gIImodel) − 1 for magnesium lines and similarly for carbon lines.

• If it was true that emission lines are formed in the quasar and the absorption lines are formed in the intervening medium between us and the quasar then as zem increased, the largest zabs would increase as is observed. But there should be no influence on the lowest zabs. In fact, the lowest zabs should be the same for all zem. The observed systematic increase in lowest zabs with increasing zem means that in the intervening origin, distant quasars detect only distant intervening media and not local ones. This effectively rules out the intervening medium origin for the absorption lines.

• Our findings imply that all spectral lines are formed in the quasar. This, in turn, means that the lowest detected redshift has to be its cosmological redshift. The redshift distributions of emission and absorption lines should be studied against the lowest redshift which is often zM gII.

• zem which is the largest redshift in quasar spectrum is not its cosmological redshift.

• The absorption and emission lines detected in quasar spectra are displaced to longer wavelengths due to two redshift components - (1) a cosmological redshift which is the same for all lines from a quasar and (2) a variable redshift component.

Improvements to AI Systems:

1. Predictive Envelope Modeling for Spectral Line Distributions

• AI can be trained to fit lower-envelope regression models (e.g., quantile regression or piecewise linear bounds) to quasar redshift data, automatically detecting systematic trends like z abs,min = a times z em + b with uncertainty quantification.

• The improved system can predict the minimum expected absorption redshift for any given emission redshift for MgII, CIV, or other ions, enabling rapid classification of anomalous quasars.

2. Causal Inference for Redshift Component Separation

• AI can decompose observed redshifts into two components: a common cosmological redshift (shared by all lines) and a variable intrinsic component, using multi-line data (e.g., MgII, CIV, Lyα).

• This allows the system to estimate the true cosmological redshift of a quasar even when emission lines are not the highest-redshift features, correcting a common bias in cosmological distance calculations.

3. Automated Hypothesis Testing for Spectral Line Origins

• AI can be designed to statistically test whether absorption line redshifts are independent of emission redshifts (intervening medium hypothesis) versus correlated (intrinsic origin hypothesis) by analyzing the slope and scatter of the z abs – z em envelope.

• The system can flag quasars where the lowest absorption redshift deviates from the model, indicating possible line-of-sight anomalies or intervening systems.

4. Generative Models for Synthetic Quasar Spectra

• Using the derived linear relationships, AI can generate realistic synthetic quasar spectra with physically consistent absorption and emission line redshifts, useful for training other models or simulating large surveys without relying on incomplete observational data.

5. Redshift Prior Refinement for Spectroscopic Fitting

• AI-based spectral fitting tools can incorporate the new constraint z abs,min < z abs < z em and the empirical lower-bound models as priors, improving the accuracy and speed of automated redshift estimation in large sky surveys (e.g., DESI, Euclid).

6. Outlier Detection and Anomaly Discovery

• The AI system can use the model residuals to identify quasars with unusually low absorption redshifts (below the envelope), which may indicate exotic physics, gravitational lensing, or measurement errors, triggering follow-up observations.

7. Multi-Ion Consistency Checking

• AI can cross-validate predictions across different ions (MgII, CIV, etc.) to ensure that the derived lower-redshift models are mutually consistent, flagging any ion-specific deviations that might indicate ionization-dependent outflows or infall.

What the Improved AI System Can Do:

• Given a quasar’s emission redshift, it can instantly output the expected minimum absorption redshift for any ion, with error bars.

• It can re-analyze existing quasar catalogs to correct cosmological redshift estimates, potentially revising distance measurements and dark energy constraints.

• It can generate synthetic spectral datasets for training future deep-learning models on quasar physics.

• It can automatically classify quasars as intrinsic absorber or intervening absorber candidates based on the envelope fit, aiding in large-scale statistical studies.

• It can provide a physically motivated prior for Bayesian redshift fitting, reducing catastrophic failures in automated pipelines.

The spectrum of a quasar consists of a few emission lines whose wavelengths are shifted by similar redshifts and numerous absorption lines whose wavelengths are shifted by different redshifts. Hence each quasar is characterised by an emission line redshift and the absorption lines redshifts are all less than the emission line redshift. The distribution of observed absorption line redshifts (z abs) with respect to emission line redshift (z em) for a large sample of quasars shows a systematic trend as pointed out by. They noticed that increase in z em is accompanied by a monotonic increase in the lowest detected value of z abs and inferred that the emission and absorption lines were all formed in the quasar. This study focuses on modeling the systematic trend in the observed z em to z abs distribution. We considered the redshift data of absorption lines of singly ionized magnesium (denoted by MgII) and triply ionized carbon (denoted by CIV) for a large sample of quasars. We find that the envelope of data points defining the lowest value of the MgII absorption line redshift (which we denote by z MgIImodel) for a given z em satisfies z MgIImodel = (0.418 plus or minus 0.008) z em - (0.482 plus or minus 0.02) with an R squared value of 0.99. The model can be used to predict the lowest expected MgII absorption line redshift for any z em. We find a similar model for the lowest expected redshift of triply ionized carbon lines for any z em which is z CIVmodel = 0.845 (plus or minus 0.0002) z em - 0.153 (plus or minus 0.0006).