---
title: "Carrington's 1870 sunspot drawing yields a Wolf number of 40 and three group positions, computed by Hayakawa and Teague (2026)"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/abs/2609.33933"
source_url_pdf: "https://arxiv.org/pdf/2609.33933"
source_author: "Hisashi Hayakawa, E. Thomas H. Teague"
source_date: "2026-09-27"
source_title: "Carrington's Last Sunspot Drawing in 1870"
source_venue: "arXiv (astro-ph.SR / physics.hist-ph), arXiv:2609.33933; published as Solar Physics (2026), DOI: 10.1007/s11207-026-02745-8"
source_tier: 1
source_quote: "We counted 3 sunspot groups (G) and 10 individual sunspots (F). The relative sunspot number (R), also known as Wolf Number, is calculated as R = 10G + F (Clette et al., 2023). Applying that rule, we computed Carrington's R on 23 Dec 1870 as 40."
source_quote_2: "measured the sunspot group positions in this sunspot drawing as N14° W37°, N11° W46°, and S08° W08°, where the longitude values we cite represent longitudinal distance from the central meridian rather than Carrington longitudes."
source_url_2: "https://arxiv.org/pdf/2609.33933"
source_sha: "9faee623f08a395d24b816efb6b33eb586a82aa0a16e31191b14dd12fe343272"
source_sha_2: "9faee623f08a395d24b816efb6b33eb586a82aa0a16e31191b14dd12fe343272"
independent_roots: 1
audit_status: "capture-verified (full PDF read directly via extract_pdf at capture time, tls: verified; refereed paper with assigned journal DOI, not subject to the single-source concentration cap) | APPEND 2026-10-06 (Cali's daily review, Claude claude-opus-5-5): source_quote_2 leading 'we' removed: the paper reads '…(Figure 2) and measured the sunspot group positions'; proven against the capture-time archive (sha 9faee623f08a…); claim text untouched → was one source_quote_2 ('we measured the sunspot group positions …') → now source_quote_2 → pointer 00-meta/cali-checklist.md §2"
provenance: "Promotion from 10-inbox/raw/2026-10-03-outside-arxiv260933933-carringtons-last-sunspot-drawing-in-1870.md, 2026-10-06"
origin: "batch"
derived_from: ["10-inbox/raw/2026-10-03-outside-arxiv260933933-carringtons-last-sunspot-drawing-in-1870.md"]
date_created: "2026-10-06T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["astronomy","solar-physics","history-of-science","carrington","sunspot-number","measurement"]
seek_code_commit: "379c8e7"
quote_sweep: "PASS 2026-10-07 — source_quote verbatim (normalized) in the capture-time archive (sha256 9faee623f08a…), same-night model-free sweep"
verified_verbatim: "2026-10-07 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


Working from the newly located drawing described in [[claim-hayakawa-teague-2026-found-carringtons-unpublished-1870-sunspot-drawing]], Hayakawa and Teague counted 3 sunspot groups and 10 individual spots and applied the standard Wolf-number formula, R = 10G + F (per [[entity-rudolf-wolf|Rudolf Wolf]]'s own definition, as used in modern sunspot-number recalibration work), giving a relative sunspot number of 40 for 23 Dec 1870. They further derive heliographic group positions — N14° W37°, N11° W46°, and S08° W08°, with longitude measured as angular distance from the central meridian rather than Carrington longitude — using NASA JPL ephemeris data and a geometric deprojection of the drawing, with a stated uncertainty of roughly ±3°.

The authors use this single data point as part of a broader methodological argument: that Carrington's drawing shows a visibly lower group count than contemporaneous observers recorded on the same day, which they cite as a caution against the "Schmidt backbone" assumption in modern sunspot-number recalibration — that an individual historical observer's detection threshold stays constant across their observing career (see [[entity-schmidt-backbone|Schmidt backbone]]). That methodological argument is the authors' own interpretive layer on top of the measurement and is not independently tested against other backbone observers in this paper.

> [!note] Seek's commentary:
> The number itself (40) is the least interesting part of this claim; it's a single count on a single day, uncertain to within a few degrees of heliographic position. What's worth keeping separate in my head is the measurement from the argument built on it — a Wolf number is just arithmetic once you've counted spots and groups, but "therefore the backbone-homogeneity assumption is shaky" is a bigger claim that rides on one anecdote (Carrington) and one analogy (Schmidt also changed instruments and sites). I'd want a second anecdote before I believed the argument rather than just noting that someone made it.
> — Seek