{"work":{"id":"651e5dd2-01a9-40b5-bc6f-0a87b097d8a1","openalex_id":"https://openalex.org/W2505702019","doi":"10.1093/mnras/stw3020","arxiv_id":"1607.08538","raw_key":null,"title":", archivePrefix = \"arXiv\", eprint =","authors":[{"given":"Michele","family":"Cappellari","sequence":"first","affiliation":[]}],"authors_text":"Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions","year":2017,"venue":"astro-ph.GA","abstract":"I start by providing an updated summary of the penalized pixel-fitting (pPXF) method, which is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies, via full spectrum fitting. I then focus on the problem of extracting the kinematic when the velocity dispersion $\\sigma$ is smaller than the velocity sampling $\\Delta V$, which is generally, by design, close to the instrumental dispersion $\\sigma_{\\rm inst}$. The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when $\\sigma<\\Delta V/2$, due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids the evaluation of the under-sampled kernel, and instead directly computes its well-sampled analytic Fourier transform, for use with the convolution theorem. A simple analytic transform exists when the kernel is described by the popular Gauss-Hermite parametrization (which includes the Gaussian as special case) for the line-of-sight velocity distribution. I describe how this idea was implemented in a significant upgrade to the publicly available pPXF software. The key advantage of the new approach is that it provides accurate velocities regardless of $\\sigma$. This is important e.g. for spectroscopic surveys targeting galaxies with $\\sigma\\ll\\sigma_{\\rm inst}$, for galaxy redshift determinations, or for measuring line-of-sight velocities of individual stars. The proposed method could also be used to fix Gaussian convolution algorithms used in today's popular software packages.","external_url":"https://doi.org/10.1093/mnras/stw3020","cited_by_count":1188,"metadata_source":"doi_reference","metadata_fetched_at":"2026-05-22T09:11:19.929684+00:00","pith_arxiv_id":"1607.08538","created_at":"2026-05-08T16:48:28.119446+00:00","updated_at":"2026-05-22T09:11:19.929684+00:00","title_quality_ok":false,"display_title":"2017, Monthly Notices of the Royal Astronomical Society, 466, 798, doi: 10.1093/mnras/stw3020 —","render_title":"2017, Monthly Notices of the Royal Astronomical Society, 466, 798, doi: 10.1093/mnras/stw3020 —"},"hub":{"state":{"work_id":"651e5dd2-01a9-40b5-bc6f-0a87b097d8a1","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":22,"external_cited_by_count":1188,"distinct_field_count":2,"first_pith_cited_at":"2025-08-14T18:00:06+00:00","last_pith_cited_at":"2026-05-20T18:01:04+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-04T01:46:49.284962+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"method","n":6},{"context_role":"background","n":2}],"polarity_counts":[{"context_polarity":"use_method","n":6},{"context_polarity":"background","n":1},{"context_polarity":"unclear","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}