David's Astronomy Pages (Projects) Pulsating Variable Stars, Short Period  Eruptive Variables   Variable Stars   Home Page    Long Period Pulsating

Pulsating Variables

Stars whose surface layer periodically expand and contract. The pulsations may be radial or non-radial. A radially pulsating star remains spherical in shape. In the case of non-radial pulsations, the star's shape periodically deviates from a sphere and even neighbouring zones of its surface may have opposite pulsation phases.

Grouped roughly into Short Period and Long Period variables for convenience.

(This web page is for Short Period. Long Period pulsating variables are placed on a separate page)

Alpha Cygni stars (Type ACYG)

Alpha Cygni stars. Non radially pulsating supergiants. The light changes, with amplitude of the order of 0.1 mag., often seen irregular, owing to the superposition of many oscillations with close periods. Cycles from several days to several weeks are observed.

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Beta Cephei stars (Type BCEP)

Beta Cephei stars, or Beta Canis Majoris stars. Stars with visual amplitudes of 0.03 - 0.3 mag. Light and radial velocity vary with periods of 0.1 to 0.6 days. The light curves are similar in shape to the average radial velocity curves, but lag in phase by a quarter of the period, so that maximum brightness corresponds to minimum stellar radius. Most of these stars are probably radial pulsators, but some, such as V469 Per, are non radial pulsators. Many have multiple periods.

BCEPS 
A short-period group of Beta Cephei stars. Both their periods (0.02-0.04 days)  and their light amplitudes  (0.015 to 0.025 mag) are smaller by an order of magnitude than in normal BCEP stars

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Cepheid variables (Type CEP)

Cepheid variables. Radially pulsating stars of high luminosity (classes IB - II), with periods in the range 1 to 135 days and visual amplitudes from several hundredths of a magnitude up to 2 mag. (amplitudes are greater in the B band than in V light).  Spectral type at maximum light is F; at minimum, the types are G-K. The longer the period of light variation, the later is the spectral type. The maximum of the surface-layer expansion velocity almost coinciding with maximum light. 

CEP(B) 
Cepheids (TU Cas, V 367 Sct) displaying the presence of two or more simultaneously operating pulsation modes (usually the fundamental tone with the period P0 and the first overtone P1). The periods P0 are in the range from 2 to 7 days, with the ratio P1/P0 approx. 0.71.

DCEP 
These are the classical cepheids, or Delta Cep-type variables. Com- paratively young objects that have left the main sequence and evolved into the instability strip of the Hertzsprung-Russell (H-R) diagram, they obey the well-known Cepheid period-luminosity relation and belong to the young disk population. DCEP stars are present in open clusters. They display a certain relation between the shapes of their light curves and their periods. 

DCEPS 
These are Delta Cep variables having light amplitudes <0.5 mag in V (<0.7 mag in B) and almost symmetrical light curves (M-m approx. 0.4 - 0.5 periods); as a rule, their periods do not exceed 7 days. They are probably first-overtone pulsators and/or are in the first transition across the instability strip after leaving the main sequence (SU Cas). 

Traditionally, both Delta Cep and W Vir stars are quite often called Cepheids because it is often impossible to discriminate between them on the basis of the light curves for periods in the range 3 - 10 days. However, these are distinct groups of entirely different objects in different evolutionary stages. One of the significant spectral differences between W Vir stars and Cepheids is the presence, during a certain phase interval, of hydrogen-line emission in the former and of Ca II H and K emission in the latter.

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Delta Cepheid - Variable Star (Cepheid)

As part of an ongoing project examining the variability in Delta Cepheid, further image sets of the variable star  & the reference star SAO 34542 were recorded at around 19:46h UT and 21:42h UT (2005-10-30).  Image sets comprised  7 sequences of  3 x 0.2s V & 3 x 0.6s B (alternated between Delta Cepheid & reference star).  These were analyzed using the methodology described under 2005-10-05 Notes, and combined with previous estimates

B Band Magnitude estimates for Delta Cepheid  (Reference Star SAO 34542)

Magnitude and colour variation in Delta Cepheid based on observations  on 7 observing sessions between 2005-10-02 and 2005-10-30.

Delta Cepheid (Cepheus) [ Delta Cepheid is the brightest star , mag +3.6 SAO 34506 is located nearby (41 arc sec separation)  ]

CCD  Image  10s exposure, C filter 2005-10-02  21:41h UT (#96081)

Delta Cepheid through photometric filter (V)

CCD  Image  1s exposure, V filter 2005-09-30 21:54h UT (#96126)

Nearby Reference Star  SAO 34542, Alpha Lacertae ( Lacerta) Mag +3.8

CCD  Image  10s exposure, C filter 2005-10-02  21:49h UT (#96108)

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RT Aur - Cepheid Variable

As part of an ongoing project examining the variability in the cepheid star RT Aur,  further image sets of the variable were recorded at the commencement  of the session.  Image sets comprised  7 sequences of  images (3 x 2s V & 3 x 5s B) alternated between RT Aur & reference star SAO 78571.  These and previous image sets from previous session from Feb-May 2006 were analyzed.  Results are shown in graphs below.  Data is consistent with a regular variation with a period of 3.728115 days.  Quality control for this variable is less tight than ideal due to the faintness of the available check star (particularly in B).  Data quality, particularly in B Band, suffered from increasing Airmass through May, which hampered ability to confirm B-V trends through the magnitude minima. Nevertheless the light curve for RT Auriga has been reasonably well constrained by the total dataset. 
 [ More Notes on RT Aur Analysis & Results ].

V Band Magnitude estimates for RT Aug  Reference Star SAO 78571 (mag +5.75) Check Star GSC 2422:1019 (mag +10.36)

Light Curve for RT Aug  Magnitude and colour variation in RT Auriga based on observations  on 12 observing sessions between 2006-02-10 and 2006-05-12 [ Reference Star SAO 78571 ]

RT Aur (Auriga)  Previous picture from 2006-02-10

CCD Image (50% size)  60 sec exposure, 1x1 binning, C Filter  2006-02-10 22:11h UT (#114120)

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W Virginis stars (Type CW)

Variables of the W Virginis type. These are pulsating variables of the galactic spherical component (old disk) population with periods of approximately 0.8 to 35 days and amplitudes from 0.3 to 1.2 mag in V. They obey a period-luminosity relation different from that for Delta Cep variables (see DCEP). For an equal period value, the W Vir variables are fainter than the Delta Cep stars by 0.7 - 2 mag. The light curves of W Vir variables for some period intervals differ from those of Delta Cep variables for corresponding periods either by amplitudes or by the presence of humps on their descending branches, sometimes turning into broad flat maxima. W Vir variables are present in globular clusters and at high galactic latitudes. 

They may be separated into the following subtypes: 

CWA 
W Vir variables with periods longer than 8 days (W Vir)

CWB 
W Vir variables with periods shorter than 8 days (BL Her).

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Delta Scuti stars (Type DSCT)

Variables of the Delta Scuti type. These are pulsating variables of spectral types A0-F5 III-V displaying light amplitudes from 0.003 to 0.9 mag in V (usually several hundredths of a magnitude) and periods from 0.01 to 0.2 days. The shapes of the light curves, periods, and amplitudes usually vary greatly. Radial as well as nonradial pulsations are observed. The variability of some members of this type appears sporadically and sometimes completely ceases, this being a consequence of strong amplitude modulation with the lower value of the amplitude not exceeding 0.001 mag in some cases. The maximum of the surface layer expansion does not lag behind the maximum light for more than 0.1 periods. DSCT stars are representatives of the galactic disk (flat component) and are phenomenologically close to the SX Phe variables. 

DSCTC 
Low amplitude group of Delta Sct variables (light amplitude <0.1 mag in V). The majority of this type's representatives are stars of luminosity class V; objects of this subtype generally are representative of the Delta Sct variables in open clusters.

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PV Telescopii stars (Type PVTEL)

Variables of the PV Telescopii type. These are helium supergiant Bp stars with weak hydrogen lines and enhanced lines of He and C. They pulsate with periods of approximately 0.1 to 1 days, or vary in brightness with an amplitude of 0.1 mag in V during a time interval of about a year.

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RR Lyrae stars (Type RR)

Variables of the RR Lyrae type, which are radially-pulsating giant A-F stars having amplitudes from 0.2 to 2 mag in V. Cases of variable light-curve shapes as well as variable periods are known. If these changes are periodic, they are called the "Blazhko effect." Traditionally, RR Lyrae stars are sometimes called short-period Cepheids or cluster-type variables. The majority of these stars belong to the spherical component of the Galaxy; they are present, sometimes in large numbers, in some globular clusters, where they are known as pulsating horizontal-branch stars. Like Cepheids, maximum expansion velocities of surface layers for these stars practically coincide with maximum light. 

A number of subtypes are defined :

RR(B) 
RR Lyrae variables showing two simultaneously operating pulsation modes, the fundamental tone with the period P0 and the first overtone, P1 (AQ Leo). The ratio P1/P0 is approximately 0.745; 

RRAB 
RR Lyrae variables with asymmetric light curves (steep ascending branches), periods from 0.3 to 1.2 days, and amplitudes from 0.5 to 2 mag in V; 

RRC 
RR Lyrae variables with nearly symmetric, sometimes sinusoidal, light curves, periods from 0.2 to 0.5 days, and amplitudes not greater than 0.8 mag in V (SX UMa).

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RR Lyr - RR variable / prototype

RR Lyrae (Lyra)
Approximate Colour CCD Image  Red 3 x 10s (av, R Filter),  Green 3x10s (V Filter), Blue 3x20s (B Filter) 2005-10-02  20:55h UT (#96020-28)
RR Lyrae (Lyra) [RR Lyrae (bottom left), reference star SAO 48408 (top right),  control star SAO 48415 ]
CCD  Image (at ~ Minimum) 10s exposure, V filter 2005-10-13  22:48h UT (#99409)	CCD  Image (at ~ Maximum) 10s exposure, V filter 2005-10-14  01:02h UT (#99693)
Magnitude Data (B & V Filters)
Goto RR Lyrae Photometric Analysis Notes |  2005-10-13 Study of RR Lyrae

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RV Ari - RR variable

RV Ari is a RR Lyra class variable with with a GCVS catalog period of 0.093128264 days (2 hr 14m) and magnitude min/max of 11.85 to 12.26.

RV Ari - Variable Star (Aries) RR Lyrae like star   [ PGC 8616, Catalog +15.1 ]

CCD Image 2 x 30 sec, 2x2 binning (average combine), C Filter 2006-09-04 22:18 h UT (#145055-57)

Magnitude Data (V & R Filters)

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RW Ari - RR Variable 

RW Ari is a RR Lyra class variable with a GCVS catalog period of 0.354341 days (8 hr 30m) and magnitude min/max of 12.12 to 12.60.
Baseline images acquired in B, R,V and C Filters, as preparation for a future observing project.

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SX Phoenicis stars (Type SXPHE)

Short period pulsating subdwarfs (old stars). Periods of 0.04 to 0.08d, with up to 0.7 mag variation.    

This type of star resemble DSCT (Delta Sct) variables and are pulsating subdwarfs of the spherical component, or old disk galactic population, with spectral types in the range A2-F5. They may show several simultaneous periods of oscillation, generally in the range 0.04-0.08 days, with variable-amplitude light changes that may reach 0.7 mag in V. These stars are often present in globular clusters. 

CY Aqr  - SXPHE variable

CY Aqr (Aquarius)

Annotated CCD Image 3 x 30 sec exposure (average combine), 2x2 binning, C Filter 2007-10-22 21:53hUT (#224177-83)

CY Aqr - Reference Stars

Annotated CD Image 60 sec exposure, 2x2 binning, V Filter 2007-10-22 21:51hUT (#224178

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ZZ Ceti stars (Type ZZ)

ZZ Ceti variables. These are nonradially pulsating white dwarfs that change their brightnesses with periods from 30 s to 25 min and amplitudes from 0.001 to 0.2 mag in V. They usually show several close period values. Flares of 1 mag are sometimes observed; however, these may be explained by the presence of close UV Ceti companions.  Example:ZZ Cet

These variables are divided into the following subtypes: 

ZZA 
ZZ Cet-type variables of DA spectral type (ZZ Cet) having only hydrogen absorption lines in their spectra; 

ZZB 
ZZ Cet-type variables of DB spectral type having only helium absorption lines in their spectra.

ZZO 
ZZ Cet type variables of the DO spectral type showing HeII and and CIV absorpion lines in their spectra.

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V777 Her (GD 358) - ZZB variable (Pulsating White Dwarf)

V777 Her (GD 358) is a pulsating white dwarf whose luminosity varies due to non-radial gravity wave pulsations. Variations in light output (or around 10-15%), arising from a superposition of several vibrational modes with periods of hundreds to thousands of seconds.  The star has helium dominated atmosphere/spectral type DB and forms a group of stars know as ZZB,  DBV or V777 Her stars.
[ GD 358 Paper 1 ,   GD 358 Paper 2 ]

V777 Her / GD 358 (Hercules)

Annotated CCD Image 3 x 60s (average combine), 2x2 binning, C Filter 2008-07-13 00:50 hUT (#294120-24)

V777 Her - reference stars

Annotated CCD Image 60s, 2x2 binning, C Filter 2008-07-13 00:48 hUT (#294120)

V777 Her - photometric test run  A short test run over 25 minutes indicates possible variation of V777 Her  with two peaks separated by around 6 minutes (variability of V777 Her values greater than noise in control star values)  The magnitude error bars associated with 60s V filter exposures (derived from S/N measurements) are  too wide to give useful results moving forward. Whilst longer exposures would have higher S/N and  thus smaller error bars the data points would be too sparse to capture the expected rapid variations. Initial points with 60s clear filter exposures have higher S/N and consequently lower error bars  and seem more appropriate for future photometric runs on this star

C Filter:  60s, 2x2 binning (#294120-26) V Filter : 60s, 2x2 binning (#294121-40)

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