[Paper Review] Nonradial and radial period changes of the Delta Scuti star 4 CVn II. Systematic behavior over 40 years

M. Breger, Μ. H. Montgomery+2 more|arXiv (Cornell University)|Dec 20, 2016

Stellar, planetary, and galactic studies15 references6 citations

TL;DR

This study analyzes 40 years of photometric data from the Delta Scuti star 4 CVn, revealing systematic decade-timescale period changes in its pulsation modes. The key finding is that prograde and retrograde nonradial modes exhibit opposite period change trends, best explained by a time-varying rotation profile driven by internal angular momentum redistribution, challenging standard slow-rotation models for p-mode pulsations in δ Sct stars.

ABSTRACT

Pulsators on and near the main sequence show period and amplitude changes that are too large to be the product of stellar evolution. The multiperiodic Delta Scuti stars are well suited to study these changes. This requires a very large amount of photometric data covering years and decades as well as mode identifications. We have examined over 800 nights of high-precision photometry of the multiperiodic pulsator 4 CVn obtained from 1966 through 2012. Because most of the data were obtained in adjacent observing seasons, it is possible to derive very accurate period values for a number of the excited pulsation modes and to study their systematic changes from 1974 to 2012. Most pulsation modes show systematic significant period and amplitude changes on a timescale of decades. For the well-studied modes, around 1986 a general reversal of the directions of both the positive and negative period changes occurred. Furthermore, the period changes between the different modes are strongly correlated, although they differ in size and sign. For the modes with known values of the spherical degree and azimuthal order, we find a correlation between the direction of the period changes and the identified azimuthal order, m. The associated amplitude changes generally have similar timescales of years or decades, but show little systematic or correlated behavior from mode to mode. A natural explanation for the opposite behavior of the prograde and retrograde modes is that their period changes are driven by a changing rotation profile. The changes in the rotation profile could in turn be driven by processes, perhaps the pulsations themselves, that redistribute angular momentum within the star. In general, different modes have different rotation kernels, so this will produce period shifts of varying magnitude for different modes.

Motivation & Objective

• To investigate long-term period and amplitude changes in pulsation modes of the multiperiodic δ Scuti star 4 CVn over four decades.
• To determine whether observed period changes are due to stellar evolution or internal dynamical processes.
• To explore the physical origin of systematic period changes, particularly the correlation between mode azimuthal order m and the direction of period change.
• To test whether changes in the stellar rotation profile can explain the observed mode-specific period shifts.
• To assess the role of angular momentum redistribution in driving observed pulsation mode period variations.

Proposed method

• Analysis of over 800 nights of high-precision photometry of 4 CVn collected from 1966 to 2012, with data spanning multiple observing seasons.
• Derivation of highly accurate period values for 64 significant pulsation frequencies detected in the star, using consistent time-series analysis techniques.
• Comparison of period change rates (1/P dP/dt) across different pulsation modes, including radial and nonradial modes with known spherical degree ℓ and azimuthal order m.
• Use of the rotational splitting relation Δfₙₗₘ ≈ m Δf_rot to infer changes in the stellar rotation frequency from observed mode frequency shifts.
• Evaluation of alternative explanations such as binary interactions, nonlinear mode coupling, and radius-driven changes, which were found inconsistent with the data.
• Assessment of the validity of the slow-rotation approximation (f_rot/f_pulse ≲ 0.2) in the context of observed mode period changes, revealing its failure in this system.

Experimental results

Research questions

• RQ1 Do the observed period changes in 4 CVn's pulsation modes align with predictions from stellar evolution models?
• RQ2 Is there a systematic correlation between the azimuthal order m of a pulsation mode and the direction (increase or decrease) of its period change?
• RQ3 Do the period changes in prograde and retrograde modes occur in opposite directions, and what does this imply about the stellar rotation profile?
• RQ4 Can changes in the rotation profile—particularly differential rotation—explain the observed mode-specific period shifts?
• RQ5 Why do different pulsation modes exhibit varying magnitudes of period change, despite being excited in the same star?

Key findings

• Most pulsation modes in 4 CVn exhibit significant, systematic period changes on decade timescales, with rates of change (1/P dP/dt) ranging from −16×10⁻⁶ to +13×10⁻⁶ year⁻¹, far exceeding evolutionary expectations.
• Around 1986, a general reversal in the direction of period changes occurred for both increasing and decreasing modes, indicating a global structural or rotational change in the star.
• Period changes are strongly correlated across different modes, but the magnitudes and signs vary, with a clear correlation between the sign of the period change and the azimuthal order m of the mode.
• The observed differences in period change magnitudes across modes cannot be explained by the standard slow-rotation approximation (f_rot/f_pulse ≲ 0.2), indicating strong rotational effects on pulsation frequencies.
• The most plausible explanation is a time-varying rotation profile—likely driven by internal angular momentum redistribution—where different modes sample different effective rotation rates due to varying rotation kernels.
• The data suggest that pulsations themselves may drive changes in the rotation profile, requiring a reevaluation of how rotation affects p-mode pulsations in δ Scuti stars, especially in the moderate-rotation regime.