**2.1. Type II Supernovae and the Expanding Photosphere
Method**

Massive stars come in a wide variety of luminosities and sizes and would seemingly not be useful objects for making distance measurements under the standard candle assumption. However, from a radiative transfer standpoint these objects are relatively simple and can be modeled with sufficient accuracy to measure distances to approximately 10%. The expanding photosphere method (EPM), was developed by Kirshner and Kwan [44], and implemented on a large number of objects by Schmidt et al. [86] after considerable improvement in the theoretical understanding of type II SN (SNII) atmospheres [15, 16, 99].

EPM assumes that SNII radiate as dilute blackbodies

(1) |

where _{ph} is the
angular size of the photosphere of the SN,
*R*_{ph} is the radius
of the photosphere, *D* is the distance to the SN,
*F*_{} is the observed flux density of the SN, and
*B*_{}(*T*) is the Planck function at a
temperature *T*. Since SNII are not perfect blackbodies, we
include a correction factor,
, which is
calculated from radiate transfer models of SNII. SNe freely expand, and

(2) |

where *v*_{ph} is the observed velocity of material at the
position of the photosphere, and *t* is the time elapsed
since the time of explosion, *t*_{0}. For most stars, the
stellar radius,
*R*_{0}, at the time of explosion is negligible,
and Eqs. (1-2) can be combined to yield

(3) |

By observing a SNII at several epochs, measuring the flux density
and temperature of the SN (via broad band
photometry) and *v*_{ph} from the minima of the weakest
lines in the SN spectrum, we can solve simultaneously for
the time of explosion and distance to the SNII. The key to
successfully measuring distances via EPM is
an accurate calculation of
(*T*).
Requisite calculations were performed by Eastman et al.
[16]
but, unfortunately, no other calculations of
(*T*)
have yet been published for typical SNIIP progenitors.

Hamuy et al.
[34]
and Leonard et al.
[52]
have measured the distances to
SN1999em, and they have investigated other aspects
of EPM. Hamuy et al.
[34]
challenged the
prescription of measuring velocities from the minima of weak lines and
developed a framework of cross correlating
spectra with synthesized spectra to estimate the velocity of material at
the photosphere. This different
prescription does lead to small systematic differences in estimated
velocity using weak lines but,
provided the modeled spectra are good representations of real objects,
this method should be more correct.
At present, a revision of the EPM distance scale using this method of
estimating *v*_{ph} has not been made.

Leonard et al. [51] have obtained spectropolarimetry of SN1999em at many epochs and see polarization intrinsic to the SN which is consistent with the SN have asymmetries of 10 - 20%. Asymmetries at this level are found in most SNII [101], and may ultimately limit the accuracy EPM can achieve on a single object ( ~ 10%). However, the mean of all SNII distances should remain unbiased.

Type II SNe have played an important role in measuring the Hubble
constant independent of the rest of the
extragalactic distance scale. In the next decade it is quite likely that
surveys will begin to turn up significant numbers of these objects at
*z* ~ 0.5 and, therefore, the possibility
exists that SNII will be able to make
a contribution to the measurement of cosmological parameters beyond the
Hubble Constant. Since SNII do not have the
precision of the SNIa (next section) and are significantly harder to
measure, they will not replace
the SNIa but will remain an independent class of objects which have
the potential to confirm the interesting results that
have emerged from the SNIa studies.