[Paper Review] The Rate of Supernovae. II. the Selection Effects and the Frequencies Per Unit Blue Luminosity

E. Cappellaro, M. Turatto+4 more|arXiv (Cornell University)|Feb 25, 1993

Gamma-ray bursts and supernovae6 citations

TL;DR

This paper analyzes supernova (SN) detection rates using the control time method on photographic surveys from Asiago and Sternberg Observatories, identifying selection effects such as overexposure in galaxy centers and inclination bias in spirals. It finds SN rates are proportional to blue luminosity across all types, with significant corrections needed for observational biases, especially in distant or inclined galaxies.

ABSTRACT

We present new estimates of the observed rates of SNe determined with the {\em control time} method applied to the files of observations of two long term, photographic SN searches carried out at the Asiago and Sternberg Observatories. Our calculations are applied to a galaxy sample extracted from RC3, in which 65 SNe have been discovered. This relatively large number of SNe has been redistributed in the different morphological classes of host galaxies giving the respective SN rates. The magnitude of two biases, the overexposure of the central part of galaxies and the inclination of the spiral parent galaxies, have been estimated. We show that due to overexposure a increasing fraction of SNe is lost in galaxies of increasing distances. Also, a reduced number of SNe is discovered in inclined galaxies ($i>30\degr$): SNII and Ib are more affected than Ia, as well as SNe in Sbc-Sd galaxies with respect to other spirals. We strengthen previous findings that the SN rates is proportional to the galaxy blue luminosity for all SN and Hubble types. Other sources of errors, besides those due to the statistics of the events, have been investigated. In particular those related to the adopted SN parameters (Cappellaro et al. (\cite{paper1})) and correction factor for overexposure and inclination. Moreover, we show that the frequencies of SNe per unit luminosity vary if different sources for the parameters of the sample galaxies are adopted, thus hampering the comparison of SN rates based on different galaxy samples. The overall rates per unit blue luminosity are similar to the previous

Motivation & Objective

• To quantify selection effects in long-term photographic supernova surveys that bias observed SN rates.
• To correct for overexposure in galaxy centers and inclination effects in spiral galaxies, which reduce detectability of SNe.
• To determine the true supernova rate per unit blue luminosity by accounting for observational biases.
• To assess how different galaxy sample parameters affect the comparability of SN rate measurements across studies.
• To improve the accuracy of SN rate estimates by applying correction factors based on galaxy morphology and distance.

Proposed method

• Applied the control time method to archival photographic data from Asiago and Sternberg Observatories, tracking SN detection efficiency over time.
• Used a galaxy sample from the RC3 catalog with 65 confirmed SNe to compute rates per morphological type.
• Quantified overexposure bias by modeling how central galaxy brightness reduces SN detectability at increasing distances.
• Assessed inclination bias by comparing SN detection rates in spiral galaxies with different inclinations (i > 30° showing reduced detection).
• Calculated correction factors for overexposure and inclination to adjust observed SN rates to intrinsic values.
• Recomputed SN frequencies per unit blue luminosity using corrected rates, comparing results across different galaxy parameter sources.

Experimental results

Research questions

• RQ1 How do overexposure in galaxy centers and inclination affect the observed rates of supernovae in photographic surveys?
• RQ2 To what extent are SN rates per unit blue luminosity biased by observational selection effects in galaxy samples?
• RQ3 How do correction factors for overexposure and inclination impact the derived SN rates across different Hubble types?
• RQ4 Why do SN rate measurements vary when based on different galaxy sample parameters, and how can this be reconciled?
• RQ5 Is the observed proportionality between SN rate and blue luminosity robust after correcting for selection effects?

Key findings

• Overexposure in galaxy centers causes a systematic loss of SNe, with the fraction of missed events increasing at greater distances.
• Inclined spiral galaxies (i > 30°) show reduced SN detection rates, with SN II and Ib events being more affected than SN Ia.
• SNe in Sbc-Sd spiral galaxies are disproportionately underdetected compared to earlier or later types.
• After correction, the SN rate is found to be proportional to blue luminosity across all SN types and Hubble morphologies.
• Frequencies per unit blue luminosity vary significantly depending on the source of galaxy parameters, complicating cross-study comparisons.
• Correction factors for overexposure and inclination are essential for accurate SN rate estimation, especially in large-scale surveys.