What happens in Vagus - compassion, positive emotion, vagal tone, and respiratory sinus arrhythmia,

The 10th cranial nerve, the vagus nerve, is distinctive to mammals and supports social engagement and nurturing behaviors as well as feeding, digesting, resting, breeding, etc. Its level of activity (tonus, or tension) is reflected in its inhibitory regulation of heartbeat, slowing it during exhalation and increasing it during inhalation. This change is heart rate is called respiratory sinus arrhythmia (RSA). Thus RSA serves as a measure of vagal tone. Dacher Keltner and collaborators have studied the relationship of vagal activity, reflected by RSA, to compassion and other prosocial emotions. I want to pass on the abstract from a preprint that can be downloaded here on studies correlating respiratory sinus arrhythmia with tonic (but not phasic) positive emotionality

Resting respiratory sinus arrhythmia (RSA_REST) indexes important aspects of individual differences in emotionality. In the present investigation, we address whether RSA_REST is associated with tonic positive or negative emotionality, and whether RSA_REST relates to phasic emotional responding to discrete positive emotion-eliciting stimuli. Across an 8-month, multiassessment study of first-year university students (n = 80), individual differences in RSA_REST were associated with positive but not negative tonic emotionality, assessed at the level of personality traits, long-term moods, the disposition toward optimism, and baseline reports of current emotional states. RSA_REST was not related to increased positive emotion, or stimulusspecific emotion, in response to compassion-, awe-, or pride-inducing stimuli. These findings suggest that resting RSA indexes aspects of a person’s tonic positive emotionality.

Reproducability in these studies may be an issue, because there is an apparent conflict between this abstracts report of no relationship between RSA_REST compassion-, awe-, or pride-inducing stimuli and the "increases in RSA during compassion" mentioned in Study 4 of the first link above. I might as well paste in that abstract also:

Compassion is an affective response to another’s suffering and a catalyst of prosocial behavior. In the present studies, we explore the peripheral physiological changes associated with the experience of compassion. Guided by long-standing theoretical claims, we propose that compassion is associated with activation in the parasympathetic autonomic nervous system through the vagus nerve. Across 4 studies, participants witnessed others suffer while we recorded physiological measures, including heart rate, respiration, skin conductance, and a measure of vagal activity called respiratory sinus arrhythmia (RSA). Participants exhibited greater RSA during the compassion induction compared with a neutral control (Study 1), another positive emotion (Study 2), and a prosocial emotion lacking appraisals of another person’s suffering (Study 3). Greater RSA during the experience of compassion compared with the neutral or control emotion was often accompanied by lower heart rate and respiration but no difference in skin conductance. In Study 4, increases in RSA during compassion positively predicted an established composite of compassion-related words, continuous self-reports of compassion, and nonverbal displays of compassion. Compassion, a core affective component of empathy and prosociality, is associated with heightened parasympathetic activity.

If you simply google "vagus nerve" you will find sites listing means of enhancing vagus activity and tone by self stimulation to improve mood and functioning, as an antidote to anxiety, etc.