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\IBVShead{4636}{25 September 1998}

\IBVStitle{THE HERTZSPRUNG SEQUENCE FROM RADIAL VELOCITIES}

\IBVSauth{N.A. GORYNYA}

\IBVSinsto{Institute of Astronomy, Russian Academy of Sciences, 48, Pyatnitskaya Str., Moscow 109017, Russia. E-mail: gorynya@sai.msu.su}

\IBVSabs{Relations between the phase of the secondary minimum on the}
\IBVSabs{radial-velocity curves of classical Cepheids, similar to the}
\IBVSabs{well-known Hertzsprung sequence of their light curves, are studied.}

\IBVStyp{ DCEP }
\IBVSkey{radial velocities, Cepheids}

\begintext

In the 1920ies, photometric data accumulated for a large number of
Cepheid made it possible to study the shape of Cepheid light curves and
to establish an empirical sequence (the so-called Hertzsprung sequence)
showing the dependence of the light curve shape upon the value of the
period (Hertzsprung, 1926).

Somewhat later, Kukarkin and Parenago (1937), from all light curves of 102
Cepheids published by that time, established the relation between the phase of
the secondary maximum (hump) of the light curve upon period: the secondary
maximum appears on the descending branch of the light curve for stars with
periods around 6 days and then shifts itself towards the maximum, coinciding
with the latter at the period of about 10 days. For stars with periods
exceeding 10 days, the hump is already observed on the ascending branch.

The secondary details can be also observed on the radial velocity curve.
It is believed that the hump on the $V_r$ curve is positioned at the same
phase as that on the light curve (Fadeev, 1994). However, this statement
should be carefully verified, especially because the shapes of the light
curve and the velocity curve are not, generally speaking, a mirror
image of each other (Sachkov et al., 1998). The first attempt to
present a sequence similar to the Hertzsprung sequence but for the radial
velocity curves was made by Joy (1937), but he was unable to succeed
because of low accuracy of individual measurements and insufficient
number of observations per Cepheid.

In 1987--1998, we acquired about 6000 individual correlation-spectrometer
measurements of radial velocities for 128 Cepheids, with typical accuracy
about 0.5 km/s (Gorynya et al., 1992, 1996, 1998). For further analysis,
we selected radial velocity curves of 36 classical Cepheids best covered
by observations. We excluded velocity curves of spectroscopic binaries,
double-mode stars, and low-amplitude Cepheids. Thus, our sample contains
only DCEP variables according to the classification system of the GCVS
(1985), which presumably pulsate in the fundamental mode. These data
permitted us, for the first time, to reveal the Hertzsprung sequence quite
confidently.

To study the Hertzsprung sequence for the velocity curves, we used the
so-called standard curves which fix the shape of the curve for each star.
A standard curve is a set of one hundred velocity values for phases from
0 to 0.99 at steps of 0.01, constructed using the method described by
Berdnikov (1992). In this process, the observations were fitted, entirely
or in pieces, by an appropriate function (a Fourier series, a spline, or
a polinomial of the third degree). From the standard curves, the phases
of the details under consideration were determined with errors not
exceeding 0.05.

Figure 1 shows the dependence of the phase of the secondary minimum (the
primary minimum of the radial velocity corresponds to zero phase) upon period;
Fig. 2, the dependence of the phase difference between the same detail and
the velocity maximum upon period. Figure 3 presents the dependence of
the velocity-curve asymmetry upon period. The asymmetry is the duration
of the velocity-curve descending branch expressed as a fraction of the
period. Obviously each of these plots can be derived from two others.

In these relations, similar to the case of the light-curve analysis,
the stars can be readily subdivided into three groups: with periods shorter
than 10 days; with periods from 10 to 20 days; and with periods exceeding
20 days. The first and the third groups show the depression on the ascending
branch of the radial velocity curve, whereas the second group shows it on
the descending branch, the phase of the secondary minimum being essentially
constant, about $-0.2$.

The period grouping of the stars can probably be explained by the different
nature of the secondary minimum for different period values,
similar to the situation with the secondary maximum of the light
curve (Fadeev, 1994).

We are going to extend our sample adding spectroscopic binary Cepheids
(pulsational velocity curves). It is planned to study the behavior of the
depression in more detail for long-period Cepheids, insufficiently
represented in the sample used for this study. Besides that, we are
going to study the phase shift between radial velocity curves and light curves;
this investigation requires simultaneous sets of spectroscopic and photometric
observations (preliminary analysis shows that the phases of the secondary
detail are different for light curves and velocity curves; cf., for
example, Figure 1 in Sachkov et al., 1996).

\IBVSfig{10cm}{4636-f1.ps}{The (period -- phase of the secondary minimum) relation. Phases
  are relative to the minimum of $V_r$ (zero phase) and are expressed
  as fractions of the period. Crosses, Cepheids with P$<$10 days;
  open circles, Cepheids with 10$<P<$20 days; asterisks, Cepheids
  with P$>$20 days}

\IBVSfig{9.4cm}{4636-f2.ps}{The (period -- phase difference between the hump and the radial velocity maximum) relation. Zero phase, maximum $V_r$. Same notation as in Figure 1}

\IBVSfig{9.4cm}{4636-f3.ps}{The (period --- asymmetry) relation from standard curves. See the definition of the asymmetry in the text}



The author wishes to thank M.E. Sachkov for assistance, N.N. Samus,
A.S. Rastorgouev, L.N. Berdnikov, and Yu.A. Fadeev for valuable discussion.
This study was supported, in part, by the Russian Foundation for Basic
Research (grants 96-02-18491, 96-02-18239, 97-02-16739) and by the State
Programme ``Astronomy''. Thanks are due also to the Council of the
Programme of Support for Scientific Schools (grant 96-15-96656).

\vskip 1cm

\references

  Berdnikov, L.N., 1992, {\sl Sov. Astron. Lett.}, {\bf 18}, 207

Fadeev, Yu.A. 1994  in: ``Unstable Processes in the Universe''
                 (ed. A.G. Massevich), Moscow: ``Kosmosinform'', p. 79
                 (in Russian)

  Gorynya, N.A., Irsmambetova, T.R., Rastorgouev, A.S.,
      and Samus, N.N., 1992, {\sl Sov. Astron. Lett.}, {\bf 18}, 316

  Gorynya N.A., Samus, N.N., Rastorgouev, A.S., and Sachkov, M.E., 1996,
    {\sl Astronomy Letters}, {\bf 22}, 175

  Gorynya, N.A., Samus, N.N., Sachkov, M.E. et al., 1998
    {\sl Astronomy Letters}, {\bf 24} (in press)

 Hertzsprung, E., 1926, {\sl Bull Astr. Inst. Netherl.}, {\bf 3}, 115 (No.96)
% Original: Hertzsprung, E., 1926, {\sl Bull Astr. Inst. Netherl.}, {\bf 3}, No.96, 115
% Corrected: Tue Aug 12 15:10:56 MET DST 2003

 Joy, A.H., 1937, {\sl Astrophys. J.} {\bf 86}, No. 4, 363

Kukarkin, B. and Parenago, P. 1937, {\sl Astr. Zhurnal}, {\bf 14}, 181

  Sachkov, M.E., Rastorgouev, A.S.,  Samus, N.N., and Gorynya, N.A., 1998,
       {\sl Astronomy Letters}, {\bf 24}, 377

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