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expanding photosphere method

{{Short description|Method used to measure distances to Type II supernovae}}

The expanding photosphere method (EPM) is a method used to measure distances to Type II supernovae. It was developed by Robert Kirshner and John Kwan in 1974, based on the Baade–Wesselink method (1926).{{cite journal |last1=Kirshner |first1=R. P. |last2=Kwan |first2=J. |title=Distances to extragalactic supernovae |journal=The Astrophysical Journal |date=1974 |volume=193 |page=27 |doi=10.1086/153123 |bibcode=1974ApJ...193...27K}}{{cite journal |last1=Schmidt |first1=B. P. |last2=Kirshner |first2=R. P. |last3=Eastman |first3=R. G. |title=Expanding photospheres of type II supernovae and the extragalactic distance scale |journal=The Astrophysical Journal |date=1992 |volume=395 |pages=366–386 |doi=10.1086/171659 |bibcode=1992ApJ...395..366S|arxiv=astro-ph/9204004 |s2cid=119342854 }} EPM is a geometrical method that compares a supernova's angular size to its physical size determined from spectroscopic measurements.{{cite journal |last1=Mitchell |first1=R. C. |last2=Didier |first2=B. |last3=Ganesh |first3=S. |last4=Acharya |first4=K. |last5=Khadka |first5=R. |last6=Silwal |first6=B. |title=Locating Type II-P Supernovae Using the Expanding Photosphere Method. I. Comparing Distances from Different Line Velocities |journal=The Astrophysical Journal |date=January 2023 |volume=942 |issue=1 |pages=38 |doi=10.3847/1538-4357/aca415|doi-access=free |bibcode=2023ApJ...942...38M }}

The method works by comparing a supernova photosphere's angular radius θ to its linear radius R to calculate its distance d through direct geometric calculation. This calculation requires determining two key parameters: the temperature of the ejecta's photosphere and its expansion velocity. The temperature is typically found by fitting a blackbody curve to the continuum spectrum. The photosphere's expansion velocity is calculated from the Doppler blueshift of specific absorption lines that form at the photosphere. Isolated, easily identified spectral lines should be used for calculations, because blended or misidentified lines can introduce significant uncertainties into the velocity measurement. Because the method relies on intrinsic luminosity of supernova, it is independent from the cosmic distance ladder, and doesn't require external calibration.{{cite journal |last1=Jones |first1=M. I. |last2=Hamuy |first2=Mario |last3=Lira |first3=P. |last4=Maza |first4=J. |last5=Clocchiatti |first5=A. |last6=Phillips |first6=M. |last7=Morrell |first7=N. |last8=Roth |first8=M. |last9=Suntzeff |first9=N. B. |last10=Matheson |first10=T. |last11=Filippenko |first11=A. V. |last12=Foley |first12=R. J. |last13=Leonard |first13=D. C. |title=Distance determination to 12 Type II-P Supernovae using the Expanding Photosphere Method |journal=The Astrophysical Journal |date=10 May 2009 |volume=696 |issue=2 |pages=1176–1194 |doi=10.1088/0004-637X/696/2/1176|arxiv=0810.5538 |bibcode=2009ApJ...696.1176J }} The method is "observationally demanding" and requires a good quality spectra.{{Cite web|url=https://ned.ipac.caltech.edu/level5/March18/Czerny/Czerny3.html|title=Astronomical Distance Determination in the Space Age - B. Czerny et al.|website=ned.ipac.caltech.edu}}

The method requires correcting for atmospheric dilution effects using theoretically calculated dilution factors. These account for electron scattering in the supernova's atmosphere causing it to deviate from a perfect blackbody. Different sets of dilution factors have been published, notably by Eastman et al. (1996) and Dessart & Hillier (2005).

EPM relies on several assumptions regarding supernovae photospheres:{{Cite book|title=AIP Conference Proceedings|first1=J.|last1=Vinko|first2=K.|last2=Takats|chapter=The Expanding Photosphere Method: Progress and Problems |date=April 4, 2007|volume=937 |pages=394–398 |doi=10.1063/1.2803597 |via=arXiv.org|arxiv=0704.0552}}

  1. the expansion of the ejected material is spherically symmetric
  2. the ejecta is expanding homologously
  3. the ejecta is optically thick
  4. the photosphere radiates as a blackbody

Modified EPM was used to measure the Hubble constant.{{Cite journal|url=https://www.aanda.org/articles/aa/abs/2023/10/aa46306-23/aa46306-23.html|title=Measuring the Hubble constant with kilonovae using the expanding photosphere method|first1=Albert|last1=Sneppen|first2=Darach|last2=Watson|first3=Dovi|last3=Poznanski|first4=Oliver|last4=Just|first5=Andreas|last5=Bauswein|first6=Radosław|last6=Wojtak|date=October 1, 2023|journal=Astronomy & Astrophysics|volume=678|pages=A14|via=www.aanda.org|doi=10.1051/0004-6361/202346306|arxiv=2306.12468 |bibcode=2023A&A...678A..14S }}{{Cite journal|url=https://ui.adsabs.harvard.edu/abs/1996ApJ...466..911E/|title=The Atmospheres of Type II Supernovae and the Expanding Photosphere Method|first1=Ronald G.|last1=Eastman|first2=Brian P.|last2=Schmidt|first3=Robert|last3=Kirshner|date=August 1, 1996|journal=The Astrophysical Journal|volume=466|pages=911|via=NASA ADS|doi=10.1086/177563|bibcode=1996ApJ...466..911E }}

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Category:Supernovae